Patent Publication Number: US-2017363963-A1

Title: Catadioptric Projection  Objective With Intermediate Images

Description:
This application is a Continuation of co-pending U.S. application Ser. No. 14/672,497, filed on Mar. 30, 2015, which is a Continuation of co-pending U.S. application Ser. No. 14/143,000, filed on Dec. 30, 2013, now U.S. Pat. No. 9,134,618, issued on Sep. 15, 2015, which is a Continuation of co-pending U.S. application Ser. No. 14/079,026, filed on Nov. 13, 2013, now U.S. Pat. No. 8,913,316, issued on Dec. 16, 2014, which is a Continuation of co-pending U.S. application Ser. No. 13/361,707, filed on Jan. 30, 2012, now U.S. Pat. No. 9,019,596, issued on Apr. 28, 2015, which is a Continuation of U.S. application Ser. No. 11/596,868, filed on Oct. 6, 2008, now U.S. Pat. No. 8,107,162, issued on Jan. 31, 2012, which was the National Stage of International Application No. PCT/EP2005/005250, filed on May 13, 2005, which claims the benefit of US Provisional Application No. 60/571,533 filed on May 17, 2004. All of these prior applications are hereby incorporated into the present application in their entireties by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The invention relates to a catadioptric projection objective for imaging of a pattern, which is arranged on the object plane of the projection objective, on the image plane of the projection objective. 
     Description of the Related Art 
     Projection objectives such as these are used in microlithography projection exposure systems for the production of semiconductor components and other finely structured components. They are used to project patterns of photomasks or reticles which are referred to in the following text in a general form as masks or reticles, onto an object which is coated with a light-sensitive layer, with very high resolution and on a reduced scale. 
     In this case, in order to produce ever finer structures, it is necessary on the one hand to enlarge the image-side numerical aperture (NA) of the projection objective, and on the other hand to use ever shorter wavelengths, preferably ultraviolet light at wavelengths of less than about 260 nm, for example 248 nm, 193 nm or 157 nm. 
     In the past, purely refractive projection objectives have been predominantly used for optical lithography. These are distinguished by a mechanically relatively simple, centered design, which has only a single optical axis, that is not folded. Furthermore, it is possible to use object fields which are centered with respect to the optical axis, which minimize the light transmission level to be corrected, and simplify adjustment of the objective. 
     However, the form of the refractive design is primarily characterized by two elementary imaging errors: the chromatic correction and the correction for the Petzval sum (image field curvature). 
     Catadioptric designs, which have at least one catadioptric objective part and a hollow mirror or a concave mirror, are used to simplify the correction for the Petzval condition and to provide a capability for chromatic correction. In this case, the Petzval correction is achieved by the curvature of the concave mirror and negative lenses in its vicinity, while the chromatic correction is achieved by the refractive power of the negative lenses upstream of the concave mirror (for CHL) as well as the diaphragm position with respect to the concave mirror (CHV). 
     One disadvantage of catadioptric designs with beam splitting is, however, that it is necessary to work either with off-axis object fields, that is to say with an increased light conductance value (in systems using geometric beam splitting) or with physical beam splitter elements, which generally cause polarization problems. The term “light conductance value” as used here refers to the Lagrange optical invariant or Etendue, which is defined here as the product of the image field diameter and the image-side numerical aperture. 
     In the case of off-axis catadioptric systems, that is to say in the case of systems with geometric beam splitting, the requirements for the optical design can be formulated as follows: (1) reduce the light transmission level to the maximum extent, (2) design the geometry of the foldings (beam deflections) such that a mounting technology can be developed for this purpose, and (3) provide effective correction, in particular the capability to correct the Petzval sum and the chromatic aberrations jointly in the catadioptric mirror group. 
     In order to keep the geometric light conductance value (Etendue) low, the folding of the design should in principle take place in the region of low NA, that is to say for example close to the object, or in the vicinity of a real intermediate image. 
     However, as the numeric aperture increases, the object-side numerical aperture also increases, and thus the distance between the first folding mirror and the reticle, so that the light transmission level rises. Furthermore, the diameter of the hollow mirror and the size of the folding mirror increase. This can lead to physical installation space problems. 
     These can be overcome by first of all imaging the reticle by means of a first relay system onto an intermediate image, and by carrying out the first folding in the area of the intermediate image. A catadioptric system such as this is disclosed in EP 1 191 378 A1. This has a refractive relay system, followed by a catadioptric objective part with a concave mirror. The light falls from the object plane onto a folding mirror (deflection mirror) which is located in the vicinity of the first intermediate image, from there to the concave mirror and from there onto a refractive object part, with a second real intermediate image being generated in the vicinity of a second deflection mirror, and the refractive object part images the second intermediate image on the image plane (wafer). Concatenated systems having, in that sequence, a refractive (R), a catadioptric (C), and a refractive (R) imaging subsystem will be denoted “R-C-R” type systems in the following. 
     Systems of type R-C-R with a similar folding geometry are disclosed in WO 2004/019128 A, WO 03/036361 A1 and US 2002/019946 A1. Patent application US 2004/0233405 A1 discloses R-C-R type projection objectives with different folding geometries including objectives where the first folding mirror is arranged optically downstream of the concave mirror to deflect radiation coming from the concave mirror towards the image plane. 
     Other catadioptric systems with two real intermediate images are disclosed in JP 2002-372668 and in U.S. Pat. No. 5,636,066. WO 02/082159 A1 and WO 01/04682 disclose other catadioptric systems with more than one intermediate image. 
     SUMMARY OF THE INVENTION 
     It is one object of the invention to provide a catadioptric projection objective which allows very high resolutions to be achieved, with a compact design with optimized dimensions. It is another object to allow correction of the Petzval sum and of the chromatic aberrations with good manufacturing conditions. 
     As a solution to these and other objects this invention, according to one formulation, provides a catadioptric projection objective for imaging of a pattern, which is arranged on the object plane of the projection objective, on the image plane of the projection objective, having: a first objective part for imaging of an object field to form a first real intermediate image; a second objective part for generating a second real intermediate image using the radiation coming from the first objective part; and a third objective part for imaging the second real intermediate image on the image plane; wherein the second objective part is a catadioptric objective part with a concave mirror; a first folding mirror for deflecting the radiation coming from the object plane in the direction of the concave mirror and a second folding mirror for deflecting the radiation coming from the concave mirror in the direction of the image plane are provided; and a field lens with a positive refractive power is arranged between the first intermediate image and the concave mirror, in a region close to the field of the first intermediate image. 
     According to another formulation, a field lens with a positive refractive power is arranged geometrically between the first folding mirror and the concave mirror in a region close to the field of the first intermediate image. This position is optically between the first intermediate image and the concave mirror if the first intermediate image is created optically upstream, i.e. before the field lens in light propagation direction. The first intermediate image may also be positioned optically downstream, i.e. behind the field lens, or may partly extend into the field lens. 
     The enlargement of the numerical aperture which is required in order to achieve very high resolutions frequently leads in conventional systems to a major increase in the diameter of the optical components which are located in the area of preferred diaphragm positions. The invention counteracts this effect. 
     The expression “field lens” describes an individual lens or a lens group with at least two individual lenses. The expression takes account of the fact that the function of a lens can fundamentally also be carried out by two or more lenses (splitting of lenses). The refractive power of this field lens is arranged close to the field, that is to say in the optical vicinity of a field plane. This area close to the field for a field plane is distinguished in particular by the chief ray height of the imaging being large in comparison to the marginal ray height. In this case, the marginal ray height is the ray height of a marginal ray which leads from the innermost point of the object field, which is closest to the optical axis, to an edge of an aperture diaphragm, while the chief ray (principal ray) leads from the outermost field point of the object field parallel to, or at an acute angle to, the optical axis and intersects the optical axis in the area of the system diaphragm, that is to say at a diaphragm location which is suitable for the fitting of an aperture diaphragm. The ratio between the marginal ray height and the chief ray height is thus less than unity in the area close to the field. 
     The expression “intermediate image” describes the area between a paraxial intermediate image and an marginal ray intermediate image. Depending on the correction state of the intermediate image, this area may extend over a certain axial range in which case, by way of example, the paraxial intermediate image may be located in the light path upstream or downstream of the marginal ray intermediate image, depending on the spherical aberration (undercorrection or overcorrection). The paraxial intermediate image and the marginal ray intermediate image may also essentially coincide. For the purposes of this application, an optical element A, for example a field lens, is located “between” an intermediate image and another optical element B when at least a portion of the optical element A is located between the (generally axially extended) intermediate image and the optical element B. The intermediate image may thus also partially extend beyond an optical surface which, for example, may be advantageous for correction purposes. The intermediate image is frequently located completely outside optical elements. Since the radiation energy density in the intermediate image area is particularly high, this may be advantageous, for example, with respect to the radiation load on the optical elements. 
     Positive refractive power in the divergent beam path between an upstream intermediate image and the concave mirror contributes to the capability for the downstream lenses in the beam path and the concave mirror to have small diameters. This applies in particular to the at least one negative lens which is provided in preferred embodiments in the immediate vicinity upstream of the concave mirror and which, in conjunction with the concave mirror, makes a major contribution to the correction of the chromatic longitudinal aberration CHL. If the chromatic longitudinal aberration is corrected in some other way, there is no need for this negative lens. 
     The insertion of positive refractive power between a field plane upstream of the concave mirror and the concave mirror leads in its own right to a contribution to the image field curvature which is proportional to the strength of the positive refractive power. In order to at least partially compensate for this effect, the concave mirror should have greater curvature than in the absence of the positive refractive power. In order, on the other hand, to keep the aberrations which are introduced by the reflection on the concave mirror as small as possible, it is advantageous for the radiation which strikes the concave mirror to strike it essentially at right angles. When positive refractive power is inserted downstream from the intermediate image, this leads to an increase in the negative refractive power directly upstream of the concave mirror, in order to ensure largely perpendicular radiation incidence by virtue of the scattering effect. The increase in the negative refractive power upstream of the concave mirror can at least partially compensate for the reduction in the CHL correction by reducing the size of the lens diameter in this area, so that good CHL correlation is ensured even with a relatively small mirror diameter. 
     In preferred embodiments, the first intermediate image is located in the vicinity of a folding mirror, which makes it possible to keep the Etendue of the system small. The field lens can generally be fitted very close to the intermediate image without being adversely affected by the folding mirror, thus allowing effective correction of imaging errors. In particular, the objective parts can be suitably designed in order to ensure that at least the intermediate image which is close to the field lens is subject to severe aberration. This allows particularly effective correction of imaging errors. The effectiveness of the correction can be assisted by designing at least that lens surface of the field lens which faces the intermediate image as an aspherical surface. 
     In one embodiment, the field lens is arranged geometrically between the concave mirror and at least one folding mirror in a region through which the beam passes twice, in such a manner that a first lens area of the field lens is arranged in the beam path between the object plane and the concave mirror, and a second lens area of the field lens is arranged in the beam path between the concave mirror and the image plane. 
     The field lens can be arranged such that it is arranged not only in the optical vicinity of an intermediate image plane which is located in the beam path upstream of the concave mirror, but also in the optical vicinity of an intermediate image plane which is located in the beam path downstream from the concave mirror. This results in an arrangement close to the field with respect to two successive field planes, so that a powerful correction effect can be achieved at two points in the beam path. 
     At least one multiple area lens can be arranged in a region of the projection objective through which the beam passes twice and has a first lens area, through which the beam passes in a first direction, and a second lens area, through which the beam passes in a second direction, with the first lens area and the second lens area not overlapping one another, at least on one side of the lens. This multiple area lens may be used as a field lens. If the footprints of the beam paths do not overlap on at least one of the two lens faces, a multiple area lens such as this allows two lenses which act independently of one another to be geometrically moved to a common point. It is also possible to physically manufacture two lenses which act independently of one another as one lens, specifically as an integral multiple area lens, from one lens blank. A multiple area lens such as this can be clearly distinguished from a conventional lens through which the beam passes twice since, in the case of a multiple area lens of this type its optical effect on the beams which pass through it independently of one another can be influenced by suitable independent shaping of the refractive surfaces of the lens areas independently of one another. Alternatively, a lens arrangement with one or two half-lenses or lens elements can also be arranged at the location of an integral multiple area lens in order to influence the beams as they pass one another, independently of one another. 
     Projection objectives with geometric beam splitting, an intermediate image and a multiple area lens have been disclosed, for example, in WO 03/052462 A1 from the same applicant. The disclosure in this patent application is included by reference in the content of this description. 
     The projection objective preferably has an image-side numerical aperture of NA&gt;0.85, and an image-side working distance of A≦10 mm. Projection objectives such as these may be used, if required, or immersion lithography with NA&gt;1. The image-side working distance or the working distance in the image area is the (shortest) axial distance between the exit surface of the objective and the image plane. This working distance in the image area, which is filled with a gas during operation in dry systems, is filled with an immersion medium during operation in immersion systems, with the immersion medium having a refractive index which is relatively high in comparison to that of gas. 
     It is generally advantageous for the image-side working distance not to fall below a minimum value. In this case, it should be noted that scratches, dirt and inhomogeneities on or in the last optical element can lead to a disturbance of the image if the working distance is too short. A finite working distance of, for example, 1 mm or more can in contrast lead to relatively large subapertures (footprints of one specific field point) with the high image-side numerical apertures, so that an averaging effect can occur and any image disturbance is reduced or suppressed. 
     Particular criteria must be taken into account for the definition of the working distance in the image area in immersion systems. On the one hand, a long working distance results not only in greater radiation losses owing to the normally lower transmission of immersion liquids (in comparison to gases) but also to a greater amount of aberration of the surfaces which are located in the vicinity of the image plane, specifically for spherical aberration. On the other hand, the image-side working distance should be sufficiently large to allow laminar flow of an immersion fluid. It may also be necessary to provide space for measurement purposes and sensors. In preferred embodiments, the image-side working distance is between about 1 mm and about 8 mm, in particular between about 1.5 mm and about 5 mm. When using an immersion fluid between the exit surface and the image plane, preferred embodiments have an image-side numerical aperture of NA≧0.98, with the image-side numerical aperture preferably being at least NA=1.0, or at least NA=1.1. The projection objective is preferably matched to an immersion medium which has a refractive index of n I &gt;1.3 at an operating wavelength. 
     Very pure water for which n≈1.43 is suitable as an immersion medium for an operating wavelength of 193 nm. The article “Immersion Lithography at 157 nm by M. Switkes and M. Rothschild, J. Vac.Sci. Technol. B 19(6), November/December 2001, pages 1 et seq proposes immersion liquids based on perfluoropolyethers (PFPE) which are sufficiently transparent for an operating wavelength of 157 nm and are compatible with a number of photoresist materials that are currently used in microlithography. One tested immersion liquid has a refractive index of n I =1.37 at 157 nm. 
     The optical design also allows use for non-contacting near-field projection lithography. In this case, sufficient light energy can be injected into the substrate to be exposed via a gap which is filled with gas, provided that a sufficiently short image-side working distance is maintained, averaged over time. This should be less than four times the operating wavelength that is used, in particular less than the operating wavelength. It is particularly advantageous for the working distance to be less than half the operating wavelength, for example less than one third, one quarter or one fifth of the operating wavelength. These short working distances allow imaging in the optical near field in which evanescent fields, which exist in the immediate vicinity of the last optical surface of the imaging system, are used for imaging. 
     The invention thus also covers a non-contacting projection exposure method in which evanescent fields of the exposure light which are located in the immediate vicinity of the exit surface can be used for the lithographic process. In this case, if the working distances are sufficiently short (finite), a light component which can be used for lithography can be emitted from the exit surface of the objective, and can be injected into an entry surface, which is immediately adjacent at a distance, despite geometrical total internal reflection conditions on the last optical surface of the projection objective. 
     Embodiments for non-contacting near-field projection lithography preferably use typical working distances in the region of the operating wavelength or less, for example between about 3 nm and about 200 nm, in particular between about 5 nm and about 100 nm. The working distance should be matched to the other characteristics of the projection system (characteristics of the projection objective close to the exit surface, characteristics of the substrate close to the entry surface) so as to achieve an input efficiency of at least 10%, averaged over time. 
     A method for production of semiconductor components and the like is thus possible within the scope of the invention, in which a finite working distance is set between an exit surface for exposure light which is associated with the projection objective and an entry surface for exposure light which is associated with the substrate, with the working distance within an exposure time interval being set, at least at times, to a value which is less than a maximum extent of an optical near field of the light emerging from the exit surface. 
     Use as a dry objective is also possible, if required, with minor modifications. Dry objectives are designed such that a gap which is filled with gas is produced during operation between the exit surface of the projection objective and the entry surface of an object to be exposed, for example a wafer, with this gap width typically being considerably greater than the operating wavelength. The achievable numerical apertures with systems such as these are restricted to values NA&lt;1, since total internal reflection conditions occur on the exit surface on approaching the value NA=1, preventing any exposure light from being emitted from the exit surface. In preferred embodiments of dry systems, the image-side numerical aperture is NA≧0.85 or NA≧0.9. 
     The third objective part immediately upstream of the image plane is preferably designed to be purely refractive, and can be optimized in order to produce high image-side numerical apertures (NA). It preferably has a first lens group, which follows the second intermediate image, and has a positive refractive power, a second lens group, which immediately follows the first lens group and has a negative refractive power, a third lens group which immediately follows the second lens group and has a positive refractive power, a fourth lens group which immediately follows the third lens group and has a positive refractive power, and a pupil surface which is arranged in a transitional region from the third lens group to the fourth lens group and in whose vicinity a system diaphragm can be arranged. The third lens group preferably has an entry surface which is located in the vicinity of a point of inflection of a marginal ray height between the second lens group and the third lens group, with no negative lens with any substantial refractive power being arranged between this entry surface and the system diaphragm. There are preferably only positive lenses between this entry surface and the image plane. This allows a material-saving design, with moderate lens diameters. 
     The last optical element in the projection objective immediately upstream of the image plane is preferably a plano-convex lens with a high spherical or aspherically curved entry surface and an exit surface which is essentially planar. This may be in the form of a plano-convex lens which is virtually hemispherical or is not hemispherical. The last optical element, in particular the plano-convex lens, may also be composed of calcium fluoride in order to avoid problems resulting from radiation-induced density changes (in particular compaction). 
     The first objective part may be used as a relay system in order to produce a first intermediate image, with a predetermined correction state at a suitable position, from the radiation coming from the object plane. The first objective part is generally purely refractive. In some embodiments, at least one folding mirror is provided in this first objective part, which images the object plane to form a first intermediate image, such that the optical axis is folded at least once, and preferably no more than once, within the objective part which is closest to the object. 
     In some embodiments, the first objective path is a catadioptric objective part with a concave mirror and an associated folding mirror, which may be used as the first folding mirror for the overall projection objective. 
     The provision of at least two catadioptric subsystems has major advantages. In order to identify significant disadvantages of systems with only one catadioptric subsystem, it is necessary to consider how the Petzval sum and the chromatic aberrations are corrected in a catadioptric part. The contribution of a lens to the chromatic longitudinal aberration CHL is proportional to the square of the marginal ray height h, to the refractive power φ of the lens, and to the dispersion v of the material. On the other hand, the contribution of a surface to the Petzval sum depends only on the surface curvature and of the sudden change in the refractive index (which is −2 in the case of a mirror in air). 
     In order to allow the contribution of the catadioptric group to the chromatic correction to become large, large marginal ray heights (that is to say large diameters) are thus required, and large curvatures are required in order to allow the contribution to the Petzval correction to become large (that is to say small radii, which are best achieved with small diameters). These two requirements are contradictory. 
     The contradictory requirements based on Petzval correction (that is to say correction of the image field curvature) and chromatic correction can be solved by introduction of (at least) one further catadioptric part into the system. Since the first catadioptric objective part can be designed such that both the image field curvature and the chromatic longitudinal aberration can be largely or completely corrected, the first intermediate image may have a defined correction state with respect to these aberrations, so that the subsequent objective parts may have an advantageous design. 
     In one embodiment, the first objective part is a catadioptric objective part with a physical beam splitter, which has a polarization-selective beam splitter surface which is used as a folding mirror and at the same time separates that radiation which leads to the concave mirror of the first objective part from that radiation which is reflected by this concave mirror. 
     In some embodiments, a concave mirror is provided which is designed as an active mirror, so that the shape of the concave mirror surface can be varied by a suitable drive. This can be used to compensate for various imaging errors. 
     Some embodiments of projection objectives according to the invention have a crossed beam path at at least one point. For this purpose, they are designed such that a first beam section which runs from the object plane to a concave mirror and a second beam section which runs from the concave mirror to the image plane can be produced, and one folding mirror is arranged with respect to the concave mirror in such a manner that one of the beam sections is folded on the folding mirror, and the other beam section passes through the folding mirror without any vignetting, and the first beam section and the second beam section cross over in a crossing region. 
     The crossed beam path in the region of a catadioptric objective part, allows projection objectives with a compact and mechanically robust arrangement of the optical components. In this case, a beam path without any vignetting can be achieved, so that no folding mirror intersects a beam which is either reflected on the folding mirror or is passed by the folding mirror without reflection. In this way, only the system diaphragm limits the angular distribution of the rays which contribute to imaging, in an axially symmetrical manner. At the same time, even with the largest numerical apertures, which are associated with large maximum beam diameters and, possibly, highly convergent or divergent beams in the region of the field planes, it is possible to achieve a moderate size for the overall field to be corrected. In this case, the expression “overall field” describes the field area which is enclosed by a minimum circle around the generally rectangular field. The size of the overall field to be corrected increases with the field size and the lateral offset of an axially asymmetric field with respect to the optical axis, and should be minimized in order to simplify the correction process. 
     Catadioptric projection objectives with a crossed beam path are disclosed, for example, in the US provisional application with the serial number 60/511,673, which was filed on Oct. 17, 2003, or the US patent application with the Ser. No. 10/734,623, which was filed on Dec. 27, 2003, or the US provisional application with the Ser. No. 60/530,622, which was filed on Dec. 19, 2003, by the same applicant. The disclosure content of these patent applications is included by reference in the content of this description. 
     In preferred embodiments, an off-axis effective object field arranged in the object surface of the projection objective is imaged onto an off-axis effective image field arranged in the image surface of the projection objective. Here, the term “effective object field” relates to the object field which can be effectively imaged by the projection objective without vignetting at a given numerical aperture. The amount of a lateral offset between the effective object field and the first part of the optical axis defined by the first objective part may be characterized by a finite object center height h. Likewise, on the image side of the projection objective, the effective image field is laterally offset with respect to the image side part of the optical axis by a finite image center height h′ related to the object center height h by the magnification ratio  13  of the projection objective according to h′=|β·h|. In some conventional projection objectives having a refractive first objective part, a catadioptric second objective part, and a refractive third objective part (also denoted type R-C-R) efforts have been made to align the parts of the optical axis defined by the object side refractive objective part and the image side refractive objective part such that no lateral axis offset exists between these parts of the optical axis. However, under these conditions, a finite value of an object-image-shift (OIS) defined between an object field center and an image field center results. Where the object surface and the image surface of the projection objective are parallel to each other, the object-image-shift may be defined as a lateral offset between an object field center axis running parallel to the object side optical axis through the center of the effective object field and an image field center axis running parallel to the image side part of the optical axis through the center of the effective image field. It has been found that small values of object-image-shift may be desireable e.g. if the projection objective is to be incorporated into a projection exposure system designed for scanning operations. Also, measuring techniques used for the qualification of the projection objective may be simplyfied with respect to conventional measuring techniques if small amounts of object-image-shift are obtained. Therefore, in preferred embodiments, the following condition holds: 
       0≦OIS&lt;| h ·(1−|β|)|.
 
     In embodiments obeying this condition, the object-image-shift OIS is smaller than the object-image-shift of designs where the object side part of the optical axis and the image side part of the optical axis are coaxial. In preferred embodiments, no object-image-shift is present such that the condition OIS=0 is fulfilled. 
     These conditions may be useful in embodiments of the invention having a field lens with positive refractive power arranged between the first intermediate image and the concave mirror in the optical vicinity of the first intermediate image. However, small values for OIS may also be useful for conventional designs having no field lens of this type, such as shown e.g. in WO 2004/019128 A. 
     Another aspect of the invention enables designing projection objectives having potential for very high image side numerical apertures NA&gt;1.2 or NA&gt;1.3 while at the same time the overall track length (axial distance between object surface and image surface) can be limited to values allowing incorporation of the projection objective in conventional projection exposure systems and, at the same time, allowing to limit the maximum size (diameter) of lenses in the refractive objective parts upstream and/or downstream of a folding mirror. To this end, in preferred embodiments, a refractive power and a position of the field lens is set such that for a first chief ray direction cosine CRA 1  at the first intermediate image the following condition holds: 
       |CRA1|&lt;|β 1 *( Y   OB )/( L   HOA )|
 
     where β 1  denotes the magnification of the first objective part , Y OB  is the object height of the outermost field point for which the chief ray is considered and L HOA  is the geometrical distance from the first intermediate image to the concave mirror (length of the horizontal axis). With other words, it may be desireable that the chief ray is telecentric or almost telecentric at a an intermediate image. A chief ray obeying the condition given above will be denoted as an “essentially telecentric chief ray” in the following. Providing an essentially telecentric chief ray at a folding mirror close to such interrmediate image allows to limit the size of lenses immediately upstream and/or downstream of the folding mirror. In addition, it has been found that installation space within the third objective part responsible for providing high image side numerical apertures is obtained. 
     Further, in some embodiments it has been found beneficial for obtaining very high image side numerical apertures if a first axial length AL 1  of the first objective part is smaller than a third axial length AL 3  of the third objective part, wherein the axial length AL 1  is measured between the object plane and an intersection of the optical axis with the first folding mirror and the axial length AL 3  is measured between the intersection of the optical axis with the second folding mirror and the image plane. In preferred embodiments, the condition AL 1 /AL 3 &lt;0.9, more preferably AL 1 /AL 3 &lt;0.8 holds 
     Systems according to the invention can preferably be used in the deep UV band, for example at 248 nm, 193 nm or 157 nm, or less. 
     These features and further features are evident not only from the claims but also from the description and the drawings, in which case the individual features can be implemented in their own right or together in the form of subcombinations of embodiments of the invention, and in other fields, and can represent advantageous embodiments, as well as embodiments which are worthy of protection in their own right. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a schematic illustration of a projection exposure system for immersion lithography with one embodiment of a catadioptric projection objective according to the invention; 
         FIG. 2  shows a schematic illustration of the design of preferred embodiments of projection objectives according to the invention, with a refractive first objective part, a catadioptric second objective part, and a refractive third objective part; 
         FIG. 3  shows a lens section through a first embodiment of a projection objective according to the invention; 
         FIG. 4  shows a lens section through a second embodiment of a projection objective according to the invention; 
         FIG. 5  shows a schematic illustration of the design of one embodiment of a projection objective according to the invention, with a different folding geometry and a crossed beam path; 
         FIG. 6  shows a schematic illustration of one embodiment of a projection objective according to the invention, with a catadioptric first objective part, a catadioptric second objective part and a refractive third objective part; 
         FIG. 7  shows a lens section for one embodiment of a catadioptric first objective part with a physical beam splitter, which can be used for the design shown in  FIG. 6 ; 
         FIGS. 8 a -8 e    show various mirror arrangements for folding mirrors for projection objectives according to the invention; 
         FIG. 9  shows a lens section for an embodiment having coaxial first and third objective parts; 
         FIG. 10  shows a lens section for another embodiment having coaxial first and third objective parts; 
         FIGS. 11 a   - 11   b:    FIG. 11 a    shows a lens section through an embodiment having laterally offset first and third objective parts such that there is no object-image-shift (OIS), whereas  FIG. 11 b    illustrates the conditions therefore; 
         FIG. 12  shows a lens section through a reference system having no field lens; 
         FIG. 13  shows a lens section through an embodiment having an essentially telecentric chief ray at the folding mirrors; 
         FIGS. 14 a   - 14   b:    FIG. 14 a    shows a schematic drawing illustrating the trajectories of the chief ray in a conventional system;  FIG. 14 b    shows a schematic drawing illustrating the trajectories of the chief ray according to embodiments having an essentially telecentric chief ray at the folding mirrors; 
         FIG. 15  shows a lens section through another emobidment having essentially telecentric chief rays at the folding mirrors and a field lens geometrically close to the folding mirrors, where the field lens is optically situated both in the first objective part and in the third objective part; 
         FIG. 16  shows a lens section of an embodiment having a field lens further apart from the folding mirrors optically within the catadioptric, second objective part and having NA=1.30; and 
         FIG. 17  shows a variant of the projection objective of  FIG. 16  having NA=1.35. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description of preferred embodiments, the expression “optical axis” means a straight line or a sequence of straight line sections through the centers of curvature of the optical components. The optical axis is folded on folding mirrors (deflection mirrors) or on other reflective surfaces. Directions and distances are described as being on the “image side” when they are directed in the direction of the image plane or of the substrate which is located there and is to be exposed, and as on the “object side” when they are directed toward the object plane or toward a reticle located there, with respect to the optical axis. The object in the examples is a mask (reticle) with the pattern of an integrated circuit, although it may also be a different pattern, for example a grating. The image in the examples is projected onto a wafer which is provided with a photoresist layer and is used as a substrate. Other substrates, for example elements for liquid crystal displays or substrates for optical gratings, are also possible. 
       FIG. 1  shows, schematically, a microlithographic projection exposure system in the form of a wafer stepper  1 , which is intended for production of large-scale integrated semiconductor components by means of immersion lithography. The projection exposure system  1  has an excimer laser  2  as the light source, with an operating wavelength of 193 nm, although other operating wavelengths, for example 157 nm or 248 nm, are also possible. A downstream illumination system  3  produces a large, sharply constricted, highly homogeneously illuminated illumination field, which is matched to the telecentric requirements of the downstream projection objective  5  on its exit plane  4 . The illumination system  3  has devices for selection of the illumination mode and, in the example, can be switched between conventional illumination with a variable coherence degree, annular field illumination and dipole or quadrupole illumination. 
     A device  40  (reticle stage) for holding and manipulating a mask  6  is arranged behind the illumination system in such a way that it is located on the object plane  4  of the projection objective  5 , and can be moved in a departure direction  7  (y direction) on this plane, for scanning purposes. 
     The plane  4 , which is also referred to as the mask plane, is followed by the catadioptric reduction objective  5 , which images an image of the mask on a reduced scale of 4:1 on a wafer  10  which is covered with a photoresist layer. Other reduction scales, for example 5:1, 10:1 or 100:1 or more, are likewise possible. The wafer  10  which is used as a light-sensitive substrate, is arranged such that the planar substrate surface  11  together with the photoresist layer essentially coincides with the image plane  12  of the projection objective  5 . The wafer is held by a device  50  (wafer stage) which comprises a scanner drive in order to move the wafer synchronously with the mask  6  and parallel to it. The device  50  also has manipulators, in order to move the wafer both in the z direction parallel to the optical axis  13  of the projection objective and in the x and y directions at right angles to this axis. A tilting device is integrated, and has at least one tilting axis which runs at right angles to the optical axis  13 . 
     The device  50 , which is provided for holding the wafer  10 , is designed for use for immersion lithography. It has a holding device  15 , which can be moved by a scanner drive and whose base has a flat depression or recess for holding the wafer  10 . A flat liquid-tight holder, which is open at the top, for a liquid immersion medium  20  is formed by a circumferential rim  16 , and the immersion medium  20  can be introduced into the holder, and can be carried away from it, by devices that are not shown. The height of the rim is designed such that the filled immersion medium completely covers the surface  11  of the wafer  10 , and the exit-side end area of the projection objective  5  can be immersed in the immersion liquid between the objective exit and the wafer surface while the working distance is set correctly. The entire system is controlled by a central computer unit  60 . 
       FIG. 2  schematically illustrates one preferred embodiment of projection objectives according to the invention. The projection objective  200  is used to image a pattern (which is arranged on its object plane  201 ) of a mask on a reduced scale on its image plane  202 , which is aligned parallel to the object plane, on a reduced scale. It has a first, refractive objective part  210 , which images the object field to form a first, real intermediate image  211 , a second, catadioptric objective part  220 , which images the first intermediate image to form a second real intermediate image  221 , and a third, refractive objective part  230 , which images the second intermediate image on a reduced scale on the image plane  202 . The catadioptric objective part  220  has a concave mirror  225 . A first folding mirror  213  is arranged in the vicinity of the first intermediate image, at an angle of 45° to the optical axis  204 , such that it reflects the radiation coming from the object plane in the direction of the concave mirror  225 . A second folding mirror  223 , whose planar mirror surface is aligned at right angles to the planar mirror surface of the first folding mirror, reflects the radiation coming from the concave mirror  225  in the direction of the image plane  202 . 
     The folding mirrors  213 ,  223  are each located in the optical vicinity of the intermediate images, so that the light conductance value can be kept low. The intermediate images, that is the entire region between the paraxial intermediate image and the marginal ray intermediate image, are preferably not located on the mirror surfaces, thus resulting in a finite minimum distance between the intermediate image and the mirror surface, so that any faults in the mirror surface, for example scratches or impurities, are not imaged sharply on the image plane. The minimum distance should be set such that sub-apertures of the radiation, that is to say footprints of beams which originate from a specific field point or converge on it do not have a diameter of less than 5 mm, or 10 mm, on the mirror surface. Embodiments exist in which both the first intermediate image  211 , that is to say the second intermediate image  221  as well, are located in the geometric space between the folding mirrors and the concave mirror  225  (solid arrows). This side arm is also referred to as the horizontal arm (HOA). In other embodiments, the first intermediate image  211 ′ may be located in the beam path upstream of the first folding mirror  213 , and the second intermediate image  221 ′ may be located in the beam path downstream from the second folding mirror (arrows represented by dashed lines). 
     The folding angles in this exemplary embodiment are exactly 90°. This is advantageous for the performance of the mirror layers of the folding mirrors. Deflections by more or less than 90° are also possible, thus resulting in an obliquely positioned horizontal arm. 
     All of the objective parts  210 ,  220 ,  230  have a positive refractive power. In the schematic illustration, lenses or lens groups with a positive refractive power are represented by double-headed arrows with points pointing outwards, while lenses or lens groups with a negative refractive power are, in contrast, represented by double-headed arrows with heads pointing inwards. 
     The first objective part  210  comprises two lens groups  215 ,  216  with a positive refractive power, between which a possible diaphragm position exists where the chief ray  203 , which is shown by a solid line, intersects the optical axis  204 , which is shown by a dashed-dotted line. The optical axis is folded through 90° at the first folding mirror  213 . The first intermediate image  211  is produced in the light path immediately downstream from the first folding mirror  213 . 
     The first intermediate image  211  acts as an object for the subsequent catadioptric objective part  220 . This has a positive lens group  226  close to the field, a negative lens group  227  close to the diaphragm, and the concave mirror  225  which is arranged immediately downstream from this and images the first intermediate image to form the second intermediate image  221 . The lens group  226 , which has a positive effect overall, is used as a “field lens” and is formed by a single positive lens, whose effect can also be produced, however, by two or more individual lenses with a positive refractive power overall. The negative lens group  227  comprises one or more lenses with a negative effect. 
     The second intermediate image  221 , which is located optically immediately in front of the second folding mirror  223 , is imaged by the third refractive objective part  230  on the image plane  202 . The refractive objective part  230  has a first positive lens group  235 , a second negative lens group  236 , a third positive lens group  237  and a fourth positive lens group  238 . There is a possible diaphragm position between the positive lens groups  237 ,  238 , where the chief ray intercepts the optical axis. 
       FIG. 3  shows a lens section through a projection objective  300  which is essentially formed using the principles explained with reference to  FIG. 2 . Identical or corresponding elements or element groups are annotated with the same reference symbols as in  FIG. 2 , increased by 100. 
     One special feature of the system is that a biconvex positive lens  326 , through which the beam passes in two opposite directions, is provided geometrically between the folding mirrors  313 ,  323  and the concave mirror  325  in a region of the projection objective through which the beam passes twice, with the beam passing through it both in the light path between the first intermediate image  311  and the concave mirror  325  and in the light path between the concave mirror and the second intermediate image  321 , or the image plane  302 , in mutually offset lens areas. The positive lens  326  is arranged closer to the folding mirrors  313 ,  323  than to the concave mirror  325 , in particular in the first third of the axial distance between the folding mirrors and the concave mirror. In the region of the positive lens  326 , the marginal ray height is small in comparison to the chief ray height, with the ratio of the marginal ray height to the chief ray height being approximately 0.3. The positive lens  326  is thus arranged close to the field both with respect to the first intermediate image  311  and with respect to the second intermediate image  321 , and thus acts as a field lens for both intermediate images. The positive refractive power in the light path between the first intermediate image  311  and the concave mirror  325  ensures, inter alia, that the diameters of the subsequent lenses  327  and of the concave mirror  325  can be kept small. The positive refractive power in the light path from the concave mirror to the second intermediate image  321  and to the image plane results in a reduction in the incidence angle bandwidth of the radiation which also arrives at the second folding mirror  323  and can thus be coated with advantageous reflection layers, as well as for limiting the lens diameters in the refractive objective part  330  which is closest to the image field and is essentially responsible for production of the high image-side numerical aperture (NA=1.20) of the immersion projection objective. 
     The positive lens can be moved very close to the two intermediate images when required, without being impeded by the folding mirrors, so that a strong correction effect is possible. The positive refractive power which is arranged close to the field allows the horizontal arm to be longer. Because of the large aperture in the first intermediate image  311 , the length of the horizontal arm would normally be shortened, so that the diameter of the concave mirror  325  and of the negative meniscus lenses in the negative group  327  which are arranged immediately upstream of it is linked to the color correction and should therefore not be indefinitely large. The inclusion of a positive lens group  326  close to the field also increases the refractive power of the negative lenses  327 , owing to the compensation for the Petzval curvature (in comparison to the concave mirror), and thus increases the correction of the color longitudinal error for relatively small diameters in the area of the concave mirror. The catadioptric objective part can thus be designed to be compact and with relatively small lens dimensions, with adequate color correction. 
     The field lens  326  which is arranged in the immediate vicinity of two intermediate images  311 ,  321  also has major advantages with respect to optical correction, as will be explained in more detail in the following text. In principle, it is advantageous for the correction of imaging errors to have optical surfaces in the vicinity of intermediate images which are subject to major aberrations. The reason for this is as follows: at a long distance from the intermediate image, for example in the vicinity of the system diaphragm or its conjugate planes, all of the opening rays in a light beam have a finite and monotonally rising height with the pupil coordinate, that is to say an optical surface acts on all the opening rays. Opening beams which are located further outwards at the pupil edge also have an increasingly greater height on this surface (or more correctly: an increasing distance from the chief ray). 
     However, this is no longer the case in the vicinity of an intermediate image which is subject to severe aberrations. If one is, in fact, located within the caustic of the intermediate image, then it is possible for the surface to be located approximately in or close to the marginal ray image, that is to say effectively it does not act on the marginal rays, but has a considerable optical effect on the zone rays. It is thus possible, for example, to correct a zone error in the optical aberrations. This principle may be used, for example, in order to deliberately influence the spherical zone error. 
     The convex lens surface of the positive lens  326  which faces the intermediate images  311 ,  321  and is arranged in their immediate proximity is aspherically curved. In conjunction with the arrangement close to the field, this allows a very major corrective effect to be achieved. 
     At least the two to three lenses closest to the image can be manufactured from calcium fluoride, in order to avoid compaction problems. In order to compensate for intrinsic birefringence, the crystallographic major axes of the lenses can be rotated with respect to one another. The concave mirror  325  may also be in the form of an active mirror, in which the shape of the mirror surface can be varied by means of suitable manipulators. This can be used to compensate for various imaging errors. The beam path in the vicinity of at least one of the intermediate images is virtually telecentric. 
     Table 1 shows the specification of the design in tabular form. In this case, column 1 shows the number of the surface which is refractive, reflective or is distinguished in some other way, column 2 shows the radius r of the surface (in mm), column 3 shows the distance d between the surface and the subsequent surface (in mm), column 4 shows the material of a component, and column 5 shows the optically useable free diameters of the optical components (in mm). Reflective surfaces are annotated by “R” in column 1. Table 2 shows the corresponding aspherical data, with the arrow heights of the aspherical surfaces being calculated using the following rule: 
         p ( h )=[((1 /r ) h   2 /(1+SQRT(1-(1 +K )(1 /r ) 2   h   2 ))] +C 1 *h   4   +C 2 *h   6 + 
     In this case, the reciprocal (1/r) of the radius indicates the surface curvature at the surface apex, and h indicates the distance between the surface point and the optical axis. The arrow height is thus p(h), that is to say the distance between the surface point and the surface apex in the z direction, that is to say in the direction of the optical axis. The constants K, C 1 , C 2 , etc. are shown in Table 2. 
     The immersion objective  300  is designed for an operating wavelength of about 157 nm, at which the calcium fluoride which is used for all of the lenses has a refractive index of n=1.5593. This is matched to a perfluoropolyether (Fomblin®) which is used in vacuum technology, as an immersion medium for which n=1.37 at 157 nm, and has an image-side working distance of about 1.5 mm. The image-side numerical aperture NA is 1.2, and the imaging scale reduction factor is 4:1. The system is designed for an image field whose size is 26×5.0 mm 2 , and it is double telecentric. 
       FIG. 4  shows a lens section through a projection objective  400  which represents a variant of the embodiment shown in  FIG. 3  and is likewise formed using the principles explained with reference to  FIG. 2 . Identical or corresponding elements or element groups are annotated with the same reference symbols as in  FIG. 3 , increased by 100. The specifications for this exemplary embodiment are shown in Tables 3 and 4. 
     In this embodiment as well, a biconvex positive lens  426  which is used as a field lens is arranged in the horizontal arm in the immediate optical vicinity of the intermediate images  411 ,  421  which are arranged between the folding mirrors  413 ,  423  and the concave mirror  425 , thus resulting in the horizontal arm having small dimensions and on the other hand in a major corrective effect to the intermediate images. 
     A further special feature of this embodiment is the design of the third, refractive objective part  430 , which has a particularly compact configuration, with small dimensions and a small maximum diameter. The basic design with an initial positive group  435 , followed by the negative group  436  and two subsequent positive groups  437 ,  438  with an aperture diaphragm (aperture stop) A in between corresponds to the design shown in  FIG. 3 . The entry surface E of the third lens group  437  is located behind the biconcave negative lens  436 , which is the only lens in the second lens group  436 , in the area of maximum divergence of the beam diameter and in the area of a point of inflection of the marginal ray height. There are no negative lenses with a scattering effect that is significant for the optical design between this entry surface and the aperture diaphragm A, or between the aperture diaphragm and the image plane. In particular, only positive lenses are provided between the entry surface E and the image plane. 
     If there are no negative lenses with a significant refractive power in the region in which the beam diameter is relatively large then this allows the maximum diameters of the lenses to be limited to practicable sizes in this region. “Relatively large beam diameter” for the purposes of this application occur in particular when the marginal ray height on a lens is at least as large as half the marginal ray height at a potential diaphragm position, for example at the system diaphragm. This measure takes account of the fact that the scattering effect of a negative lens may admittedly be desirable for correction reasons, but that any scattering effect downstream from the negative lens has a tendency to lead to larger lens diameters than will be necessary in the absence of a negative lens. Furthermore, the rays of the beam are joined together in the direction of the downstream image plane, and positive refractive power is required for this purpose. The positive lenses which are required for this purpose may overall be designed relatively moderately provided that there is also no need to compensate for the scattering effect of negative lenses in the combination of the beams. Furthermore, the number of lenses may be limited. The invention thus allows compact projection objectives with minimal lens dimensions. 
       FIG. 5  shows one embodiment of a projection objective  500  which, from the optical point of view, is designed on the basis of the principles explained with reference to  FIG. 2 . Identical or corresponding elements or element groups are annotated with the same reference symbols as in  FIG. 2 , increased by 300. 
     A comparison between the beam profiles in the systems shown in  FIG. 2  and  FIG. 5  shows that different beam paths are possible within the scope of the invention. An uncrossed beam path is shown in the system in  FIG. 2 , since a first beam section which runs from the object plane to the concave mirror  225  and a second beam section which runs from this concave mirror to the image plane do not intersect anywhere. The embodiment shown in  FIG. 5 , in contrast, has a crossed-over beam path. The first folding mirror  513  is arranged on the side of the optical axis  504  facing away from the second folding mirror  523 , with the second folding mirror being geometrically located closer to the object plane. In consequence, a first beam section which runs from the object plane  501  to the concave mirror  525  and a second beam section which runs from the concave mirror  525  via the second folding mirror  523  to the image plane cross over in the region immediately upstream of the mirror surface of the second folding mirror  523 , in the vicinity of the intermediate images  511 ,  521 . In this case, the second intermediate image  521  is located optically immediately before the second folding mirror  523 , and geometrically in the vicinity of an inner mirror edge  528 , which faces the optical axis  504 , of the first folding mirror. This crossed beam path, in which the radiation is “forced by” the first folding mirror without any vignetting in the direction of the second folding mirror, in the region of the inner mirror edge  528 , allows optimization of the light conductance value of the system. It also provides more physical space for the two folding mirrors. 
     In this embodiment as well, the positive field lens group  526  is located in the optical vicinity of both intermediate images, geometrically between the folding mirrors and the concave mirror, although the second folding mirror and the second intermediate image are somewhat further away from the positive lens  526 . 
     One embodiment of a projection objective  600  will be explained with reference to  FIG. 6 , in which a pattern which is arranged on its object plane  601  is imaged on an image plane  602  aligned parallel to the object plane, generating two real intermediate images  611 ,  621 . The projection objective has a first, catadioptric objective part  610  which produces a first real intermediate image  611  of the object field, a subsequent, catadioptric second objective part  620 , which images the first intermediate image to form a second real intermediate image  621 , and a subsequent third, refractive objective part, which images the second intermediate image  621  directly, that is to say without any further intermediate image, on the image plane  602 . 
     One major difference from the embodiments described so far is that the first objective part  610  is a compact catadioptric subsystem. The catadioptric objective part  610  has a concave mirror  615  whose optical axis is at right angles to the object plane, and a polarization-selective beam splitter  660  (Beamsplitter Cube, BSC) which is arranged between the object plane and the concave mirror and has a planar beam splitter surface  613  which is inclined at 45° to the optical axis  604  and is used as a first folding mirror for the projection objective  610 . A λ/4 plate  661 , a first positive group  662 , a second positive group  663 , the beam splitter  660 , a further λ/4 plate  664  and a negative group  665  arranged immediately in front of the concave mirror are arranged in this sequence between the object plane and the concave mirror. This is followed by a further λ/4 plate  666  and a positive group  667  in the beam path downstream from the folding mirror  613 . The basic configuration of the second, catadioptric objective part  620  with a positive group  626  close to the field corresponds essentially to the basic design shown in  FIG. 2 . The third, refractive objective part has only positive groups between which a diaphragm position is located. 
     In this exemplary embodiment, folding thus takes place within the first, catadioptric objective part, with positive refractive power in the form of at least one positive lens  667  being arranged between the folding mirror  613 , which is responsible for this, and the first intermediate image  611 , which is produced by the first subsystem. The overall system is operated with circularly polarized input light, which is converted by the first X/ 4  plate to linear-polarized radiation, which is p-polarized with respect to the obliquely positioned beam splitter layer  613  and thus essentially completely passes through it to the concave mirror  650 . The λ/4 plate which is arranged between the beam splitter layer and the concave mirror is passed through twice by the linear-polarized radiation and in the process rotates the polarization preferred direction through 90° such that the radiation arriving from the concave mirror at the polarization splitter layer  613  is s-polarized with respect to this, and is reflected in the direction of the subsequent objective parts. The third λ/4 plate  666  converts the radiation to circularly polarized radiation, which then passes through the subsequent subsystems. 
     Since the first, catadioptric objective part  610  can be designed such that, in conjunction with the mirror curvature and the negative refractive power upstream of the mirror, it can largely or completely correct both the image field curvature and the chromatic longitudinal aberration, the subsequent partial objectives are not loaded, or are only slightly loaded, by these imaging errors. Furthermore, this arrangement allows the physical space between the object plane and the horizontally aligned, catadioptric objective part  620  to be enlarged, which can be used in order to reduce the light connductance value. 
     The aperture diaphragm A is preferably arranged in the third objective part  630 , which is closest to the image, where the chief ray intersects the optical axis. Two further possible diaphragm positions are shown in the first and second objective part, in each case close to the concave mirrors  615 ,  625 . 
     The first objective part may be physically compact.  FIG. 7  shows an embodiment of a catadioptric subsystem which can be used as the first objective part  610  for the system shown in  FIG. 6 , and whose specification is shown in Table 5. Identical or corresponding elements or element groups are annotated with the same reference symbols as in  FIG. 6 , increased by 100. All the lenses are spherical, and all the transparent components including the beam splitter block  760  are composed of synthetic quartz glass. 
       FIGS. 8 a -8 e    show various implementation options, schematically, for the folding mirrors which are provided for folding the beam path. The folding mirrors may, for example, be in the form of free-standing planar mirrors, in particular as front surface mirrors ( FIGS. 8 a  and 8 b   ). In this case, in the embodiments shown in  FIG. 2 , separate mirrors as shown in  FIG. 8 b    can be held jointly, as well. The folding mirrors may also be in the form of free-standing prisms, as shown in  FIGS. 8 c  and 8 d   . The reflective prism surfaces may, if required, act as total internal reflection surfaces depending on the incidence angles that occur on them, or may have a reflection coating. In particular for the embodiments shown in  FIGS. 2 to 4 , the mirrors may also be in the form of reflective outer surfaces of a mirror prism as shown in  FIG. 8   e.    
     In  FIG. 9  a further embodiment of a projection objective  900  having R-C-R-type as explained in connection with  FIG. 2  is shown. Reference is made to that description for the basic construction. A first, refractive objective part  910  is designed to image an off-axis effective object field OF arranged in the object surface  901  onto a first intermediate image  911 . A first planar folding mirror  913  is arranged within the first objective part immediately upstream of the first intermediate image. A second, catadioptric objective part  920  including a concave mirror  925  is designed for imaging the first intermediate image into a second intermediat image  921  positioned immediately upstream of a second folding mirror  923  at a distance therefrom. A third, refractive objective part  930  including a freely accessible aperture stop AS is designed to image the second intermediate image onto the image surface  902 , where an effective image field IF arranged outside the optical axis is created. The first objective part  910  serves as a relay system to place the first intermediate image close to the first folding mirror  913 . The catadioptric second objective part  920  includes a single positive lens (field lens  926 ) geometrically close to the folding mirrors and optically close to both intermediate images, thereby allowing efficient correction of field related imaging errors. The third objective part serves as a focussing lens group providing the major part of the reduction ratio of the projection objective to obtain the image side numerical aperture, which is NA = 1 . 20  in this embodiment at a field size of 26 mm·5.5 mm of the effective object field OF. The overall track length (axial distance between object surface  901  and image surface  902 ) is 1400 mm. The wavefront aberration is about 4 mλ rms. The specification is given in tables 9, 9A. The chief ray CR of the imaging is drawn bold to facilitate following trajectory of the chief ray. 
     The lenses of the first objective part  910  define a first part OA 1  of the optical axis, which is the axis of rotational symmetry of the lenses and is perpendicular to the object surface  901 . The axis of rotational symmetry of the concave mirror  925  and the lenses of the second objective part define a second part  0 A 2  of the optical axis which, in this embodiment, is aligned perpendicular to the object side first part OA 1  of the optical axis. With other words, the optical axis is folded by the first folding mirror  913  at 90°. The lenses of the third objective part  930  define a third part  0 A 3  of the optical axis, which is parallel to the first part OA 1  of the optical axis and perpendicular to the image surface  902 . In this embodiment, the object-side first part OA 1  of the optical axis and the image-side third part  0 A 3  of the optical axis are coaxial such that no lateral axis offset exists between these parts of the optical axis. This construction may be desireable with regard to mounting of the lenses of the refractive objective parts. A similar construction with coaxial first and third parts OA 1 ,  0 A 3  of the optical axis is shown as projection objective  1000  in  FIG. 10 . The specifcation of that design is given in table 10, 10A. In both embodiments a finite value for the object-image-shift OIS exists. 
     In the projection objective  900  the lens surface ASP immediately upstream of the first folding mirror  913  is an aspheric surface, which is optically close to the first intermediate image. Efficient correction of field related imaging errors are obtained. In the projection objective  1000  the field lens  1026  has an aspheric lens surface ASP facing the concave mirror. This aspheric surface is the lens surface closest to both the first and second intermediate image  1011 ,  1021  and therefore very effective for correction at two positions along the beam path. The wave front aberration of this design is about 3 mλ rms. 
     The embodiment of a projection objective  1100  shown in  FIG. 11 a    (specification in tables 11, 11A) is an example to demonstrate that practical advantages can be obtained in preferred embodiments if a lateral axis offset AO between the first part OA 1  of the optical axis on the object side and a third part OA 3  of the optical axis on the image side is adjusted appropriately. In order to facilitate understanding of the terms used in the following,  FIG. 11 b    shows a schematic drawing where important features and parameters are shown. 
     From an optical point of view, an off-axis effective object field OF is imaged by the first objective part  1110  into a first intermediate image  1111  arranged between a first folding mirror  1113  and a positive field lens  1126  of the second objective part  1120 . The second objective part includes the concave mirror  1125  and is designed as an imaging subsystem to create a second intermediate image  1121  positioned between positive lens  1126  and a second folding mirror  1123 . The third objective part  1130  serves as a focussing group to generate the off-axis effective image field IF at a very high image-side numerical aperture NA, wherein here NA=1.30. 
     In contradistinction to the embodiments of  FIGS. 9 and 10  the folding prism forming with perpendicular planar faces the first and second folding mirrors is used asymmetrically, whereby a lateral axis offset AO is obtained between the first part OA 1  of the optical axis on the object side and the third part OA 3  of the optical axis on the image side (see  FIG. 11 b   ). In this particular embodiment the axis offset AO is set in such a way that an object field center axis OFCA running parallel to the first part OA 1  of the optical axis through the object field center and an image field center axis IFCA running through the center of the image field IF and parallel to the third part OA 3  of the optical axis coincide (are co-axial). With other words, there is no object-image-shift (OIS) between the centers of the effective object field OF and image field IF. This property is usually not obtained in catadioptric projection objectives with off-axis object field, but only in projection objectives having an effective object field centered around the optical axis (e.g. purely refractive objectives or catadioptric objectives having a physical beam splitter or objectives with pupil obscuration). As evident from  FIG. 11 b    the amount of lateral axis offset AO is to be set such that the sum of the lateral axis offset AO and an image field center height h′ is equal to the object field center height h if OIS=0 is desired. In that case: 
       |AO|= h *(1+|β|).
 
     Another beneficial aspect of preferred embodiments of the invention relates to an appropriate selection of positive refractive power for the field lens. As will be demonstrated exemplarily in the following, a proper selection of refractive power allows to manufacture projection objectives with very high image side numerical apertures, such as NA=1.3 or NA=1.35, while maintaining a maximum size of lenses upstream and/or downstream of the folding mirrors and the overall track length of the projection objective moderate. For demonstration purposes,  FIG. 12  shows a variant of a prior art projection objective of type R-C-R as shown in WO 2004/019128 having an image side numerical aperture NA=1.25 and 1250 mm track length, which is smaller than the track length of the related prior art objective (1400 mm,  FIG. 19  in WO 2004/019128 A1). There is no field lens geometrically between the folding mirrors and the concave mirror. 
     For comparison,  FIG. 13  shows a projection objective  1300  as an embodiment of the invention, having the same numerical aperture (NA=1.25) and track length (1250 mm), where a positive field lens  1326  is positioned geometrically between the folding mirrors  1313 ,  1323  and the concave mirror  1325 . To facilitate comparison, schematic  FIGS. 14 a -14 b    show a prior art system without field lens in  FIG. 14 a    and an embodiment of the invention including a field lens FL in  FIG. 14 b   . The trajectory of a chief ray CR is drawn and bold in  FIGS. 12 and 13  and also outlined in  FIGS. 14 a -14 b    where, in addition, the trajectory of a marginal ray MR is shown. 
     Next, some characteristic features of prior art systems related to the embodiment of  FIG. 12  are summarized using the reference identifications of  FIG. 14 a   . The first objective part is a refractive relay group L 1  designed to create the first intermediate image IMI 1  close to the first folding mirror FM 1  of the folding prism. An axially compact (short) catadioptric second objective part including the concave mirror CM creates the second intermediate image IMI 2  close to the second folding mirror FM 2 . A purely refractive main focussing group L 2  formed by the third objective part forms the image. 
     The first objective part is subdivided into a first lens group LG 1  and a second lens group LG 2  (each positive refractive power), a pupil surface being positioned between these lens groups where the chief ray CR intersects the optical axis OA. The third objective part includes, in that sequence, a third lens group LG 3  with positive refractive power, a fourth lens group LG 4  with negativ refractive power, and a fifth lens group LG 5  with positive refractive power. An image side pupil surface is positioned in the third objective part where the chief ray crosses the optical axis. An aperture stop AS is usually positioned at this position. A pupil surface optically between the first and second intermediate image is positioned close to or at the concave mirror CM. 
     Alternatively an aperture stop may also be positioned in one of the other pupil surfaces, namely in the refractive relay group L 1  or in the catadioptric group, close to the concave mirror. 
     The chief ray CR is convergent at the first intermediate image IMI 1  and the first folding mirror optically close to that interemediate image. Here, a convergent chief ray is a chief ray where the chief ray height CRH, i.e. the radial distance between the chief ray and the optical axis, is decreasing in light propergation direction. On the other hand, the chief ray is divergent (i.e. chief ray height increasing in light propergation direction) at the second intermediate image IMI 2  and the second folding mirror. 
     Due to the folding geometry having the intermediate images between the folding mirrors and the concave mirror, the lenses of the second lens group LG 2  and the third lens group LG 3  closest to the first intermediate image and the second intermediate image, respectively, are optically relatively far away from the intermediate images since the folding mirror is placed between these lenses and the intermediate images. As a consequence of the convergence/divergence of the chief ray these lenses closest to the folding mirrors have a tendency to become large (large lens diameter). Note that this effect may be weaker if a larger distance is set between the concave mirror and the folding mirrors, thereby forming a longer horizontal arm (HOA) of the objective. 
     Given these conditions, there is a tendency for the horizontal optical axis to become shorter if the image side numerical aperture NA is to be increased. This can be understood as follows. The primary purpose of the concave mirror is to correct the Petzvalsum (image field curvature) of the projection objective. The contribution of the concave mirror for Petzval sum correction is directly proportional to the curvature of the concave mirror. If the numerical aperture of the system is to be increased and, at the same time, the length of the horizontal arm HOA would remain constant, the diameter of the catadioptric group including the concave mirror would be increased. One potential consequence is that the curvature of the concave mirror would become smaller, whereby the effect of the concave mirror on Petzval sum correction would decrease. This is considered less desireable since the Petzval sum correction must then be provided in other parts of the projection objective, thereby making the design more complicated. 
     On the other hand, if it desired to maintain the correcting effect of the catadioptric group on Petzval sum correction, the diameter of the catadioptric group including the concave mirror should be maintained essentially constant. This, however, corresponds to a decreasing length of the horizontal arm which, in turn, leads to relatively large chief ray angles at the intermediate images, as shown schematically in  FIG. 14 a    and in the projection objective  1200  of  FIG. 12 . 
     It is evident from  FIG. 12  that very large lens diameters are required particularly for the two or three positive lenses of the second lens group LG 2  immediately upstream of the first folding mirror. 
     However, if it is desired to increase the numerical aperture, sufficient space for lenses must be provided in the third objective part, mainly in the vincinity of the closest pupil position next to the wafer. If it is further desired to limit the track length of the objective to reasonable values, it appears that it is desireable to design the first objective part (relay group L 1 ) axially shorter and to decrease the diameters of the lenses immediately upstream of the first folding mirror. 
     These objects can be obtained by introducing a field lens having sufficient positive refractive power geometrically between the folding mirrors and the concave mirror optically close to the intermediate images, as shown schematically in  FIG. 14 b    and exemplarily in embodiment  1300  of  FIG. 13 . As evident from  FIG. 13 , the positive refractive power provided by a lens  1326  allows to guide the chief ray CR almost parallel to the optical axis or slightly divergent onto the first folding mirror  1313 , whereby the diameters of the two or three lenses immediately upstream of the first folding mirror can be substantially reduced when compared to the design of  FIG. 12 . Also, the first axial length AL 1  of the first objective part  1310  is substantially reduced when compared to the corresponding length of the first objective part  1210  in  FIG. 12 . As a consequence, more space is available in the third objective part for introducing lenses contributing to an increase in numerical aperture. Also, the horizontal arm including the concave mirror is substantially longer and the concave mirror is substantially smaller when a field lens is introduced. 
     In the embodiment of  FIG. 13 , it is also evident that both the first and second intermediate image are positioned in a space between the field lens  1326  and the mirror group including the concave mirror  1325 . Specifically, an axial distance between the intermediate images and the closest optical surface (lens surface of positive lens  1326  facing the concave mirror) is sufficiently large such that the closest optical surface lies outside an intermediate image space defined axially between the paraxial intermediate image (intermediate image formed by paraxial rays) and the marginal ray intermediate image (formed by marginal rays of the imaging). A minimum distance of at least 10 mm is obtained here. The field lens is effective as a last lens of the first objective part  1310  and as a first lens of the third objective part  1330  (when viewed in light propagation direction at the intended use as reduction projection objective). Therefore, it is worth to note that  FIG. 13  shows a projection objective having two refractive imaging subsystems (formed by the first objective part  1310  and the third objective part  1330 ), where a lens (the field lens  1326 ) is arranged optically within both the first and the third imaging subsystem. Also, each folding mirror is positioned inside a refractive imaging subsystem between lenses of the respective subsystem. 
     The embodiments of the following  FIGS. 15 to 17  (specifications in tables 15, 15A, 16, 16A and 17, 17A, respectively) are based on the embodiment of  FIG. 13  and show exemplarily that a basic design having a field lens with sufficient refractive power allows to obtain even higher image side numercial apertures with moderate lens sizes. The specifications are given in tables 15, 15A, 16, 16A and 17, 17A, respectively. 
     An image side numerical aperture NA=1.30 is obtained for the projection objective  1500  in  FIG. 15 . Here, the chief ray CR is almost parallel to the optical axis at the first and second folding mirror. Specifically, a first chief ray direction cosine |CRA 1 |=0.055 is obtained at the first folding mirror and a second chief ray direction cosine CRA 2 =0.058 is obtained at the second folding mirror. 
     In the projection objectives  1300  and  1500 , the positive field lens  1326 ,  1526  in the horizontal arm is arranged very close to the folding mirrors such that intermediate images follow within a space free of optical material between that field lens and the concave mirror. However, as evident from the intersecting lens symbols, one or more truncated lenses must be used close to the folding mirrors, which makes lens mounting more complicated. 
     Such mounting problem is avoided for the projection objective  1600  in  FIG. 16 , where the positive field lens  1626  is positioned far away from the folding mirrors  1613 ,  1623  mostly outside a cylindrical space defined between the lenses immediately upstream and downstream of the folding mirrors. In this embodiment, circular lenses with a stable mounting technique can be used. From an optical point of view, the chief ray angles at the first and second folding mirrors are almost zero (essentially telecentric chief ray). As both intermediate images  1611  and  1621  are positioned essentially between the folding mirrors and the field lens  1626 , the field lens is now part of the catadioptric second imaging objective part  1620  including the concave mirror  1625 . In this variant, the installation space problem close to the folding mirror is avoided. An image side numerical aperture NA=1.30 is obtained. 
     The design type has potential for even higher numerical apertures, which is evident from projection objective  1700  shown in  FIG. 17  having an image side numerical aperture NA=1.35. Like in the embodiment of  FIG. 16 , the chief ray is almost telecentric at the folding mirrors and the intermediate images  1711 ,  1721  are essentially positioned between the folding mirrors and the field lens  1726 . The increase in numerical aperture with respect to the embodiment of  FIG. 16  shows that in that embodiment sufficient space for further and/or stronger lenses is available in the third objective part responsible for providing the high numerical aperture. 
     As mentioned earlier, the invention allows to built catadioptric projection objectives with high numerical aperture, particularly allowing immersion lithography at numerical apertures NA&gt;1, that can be built with relatively small amounts of optical material. The potential for small material consumption is demonstrated in the following considering parameters describing the fact that particularly compact projection objectives can be manufactured. 
     Generally, the dimensions of projection objectives tend to increase dramatically as the image side numerical aperture NA is increased. Empirically it has been found that the maximum lens diameter D max  tends to increase stronger than linear with increase of NA according to D max ˜NA k , where k&gt;1. A value k=2 is an approximation used for the purpose of this application. Further, it has been found that the maximum lens diameter D max  increases in proportion to the image field size (represented by the image field height Y′, where Y′ is the maximum distance between an image field point and the optical axis). A linear dependency is assumed for the purpose of the application. Based on these considerations a first compactness parameter COMP 1  is defined as: 
       COMP1 =D   max /( Y′−NA   2 ). 
     It is evident that, for given values of image field height and numerical aperture, the first compaction parameter COMP 1  should be as small as possible if a compact design is desired. 
     Considering the overall material consumption necessary for providing a projection objective, the absolute number of lenses, N L  is also relevant. Typically, systems with a smaller number of lenses are preferred to systems with larger numbers of lenses. Therefore, a second compactness parameter COMP 2  is defined as follows: 
       COMP2=COMP1 −N   L . 
     Again, small values for COMP 2  are indicative of compact optical systems. 
     Further, projection objectives according to preferred embodiments of the invention have at least three objective parts for imaging an entry side field surface into an optically conjugate exit side field surface, where the imaging objective parts are concatenated at intermediate images. Typically, the number of lenses and the overall material necessary to build an projection objective will increase the higher the number N OP  of imaging objective parts of the optical system is. It is desirable to keep the average number of lenses per objective part, N L /N OP , as small as possible. Therefore, a third compactness parameter COMP 3  is defined as follows: 
       COMP3=COMP1 −N   L /N OP . 
     Again, projection objectives with low optical material consumption will be characterized by small values of COMP 3 . 
     Table 18 summarizes the values necessary to calculate the compactness parameters COMP 1 , COMP 2 , COMP 3  and the respective values for these parameters for each of the systems presented with a specification table (the table number (corresponding to the same number of a figure) is given in column 1 of table 18). Therefore, in order to obtain a compact catadioptric projection objective having at least one concave mirror and at least two imaging objective parts (i.e. at least one intermediate image) at least one of the following conditions (1) to (3) should be observed: 
       COMP1&lt;11   (1)
 
     Preferably COMP 1 &lt;10,7 should be observed. 
       COMP2&lt;340   (2)
 
     Preferably COMP 2 &lt;320, more preferably COMP 2 &lt;300 should be observed. 
       COMP3&lt;110   (3)
 
     Preferably COMP 3 &lt;100 should be observed. 
     In some embodiments COMP 1 &lt;11 and, at the same time, COMP 2 &lt;340, which allows particularly compact designs. 
     Another aspect concerns the size of the concave mirror, which is particularly small in relation to the largest lenses in some embodiments, thereby facilitating manufacturing and mounting. In some embodiments the concave mirror has a mirror diameter D M , the projection objective has a maximum lens diameter D max , and the condition D M &lt;0.75* D max  holds. Preferably D M &lt;0.70* D max  may be fulfilled. 
     Table 18 shows that preferred embodiments according to the invention generally observe at least one of these conditions indicating that compact designs with moderate material consumption and/or small concave mirror are obtained according to the design rules laid out in this specification. 
     The invention has been described in detail using examples of R-C-R type catadioptric projection objectives having a first folding mirror for deflecting the radiation coming from the object plane in the direction of the concave mirror and a second folding mirror for deflecting the radiation coming from the concave mirror in the direction of the image plane. The invention can also be implemented in designs having different folding geometry, for example those where radiation coming from the object plane is directly directed at the concave mirror prior to a reflection on a first folding mirror arranged for deflecting the radiation coming from the concave mirror in the direction of the image plane. In those embodiments, a second folding mirror is usually provided downstream of the first folding mirror to allow a parallel arrangement of object plane and image plane. 
     It is self-evident that all of the systems described above may be complete systems, that is to say systems for forming a real image (for example on a wafer) of a real object (for example a photolithography mask). The systems may, however, also be used as subsystems for larger systems. For example, the “object” of one of the systems described above may thus be an image which is produced by an imaging system (for example a relay system) positioned upstream of the object plane. An image which is formed by one of the systems described above may likewise be used as an object for a system (for example a relay system) downstream from the image plane. The enumeration of the objective parts with the expressions “first objective part” and “second objective part” etc. relates to the sequence in which the beam passes through them when they are used as a reduction objective. The expressions “first” and “second” etc. should be understood as being relative to one another. The “first” objective part is arranged upstream of the “second” objective part in the direction in which the beam passes through them. This need not necessarily be the first objective part in the overall system, that is to say the objective part which immediately follows the image plane in the system. However, this is the case in the illustrated exemplary embodiments. 
     
       
         
           
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 NA = 1.2 Y = 57.7 mm 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 WL 
                 157.2852 
                 157.2862 
                 157.2842 
               
               
                   
                 CAF2 
                 1.55930394 
                 1.55930133 
                 1.55930655 
               
               
                   
                 IMM 
                 1.37021435 
                 1.37021206 
                 1.37021665 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface 
                 Radius 
                 Distance 
                 Material 
                 ½ Diameter 
               
               
                   
               
               
                  0 
                 0.000000000 
                 48.029632171 
                 AIR 
                 57.700 
               
               
                  1 
                 0.000000000 
                 39.172776328 
                 AIR 
                 72.768 
               
               
                  2 
                 −96.971407438 
                 43.719958386 
                 CAF2 
                 74.418 
               
               
                  3 
                 −158.002766036 
                 5.165244231 
                 AIR 
                 98.534 
               
               
                  4 
                 781.518257267 
                 56.238731708 
                 CAF2 
                 120.188 
               
               
                  5 
                 −253.290501301 
                 4.909571912 
                 AIR 
                 123.211 
               
               
                  6 
                 288.016848173 
                 49.396794919 
                 CAF2 
                 124.172 
               
               
                  7 
                 −435.168087157 
                 26.736905514 
                 AIR 
                 122.368 
               
               
                  8 
                 105.910945049 
                 62.394238960 
                 CAF2 
                 94.783 
               
               
                  9 
                 178.598362309 
                 79.753912118 
                 AIR 
                 79.042 
               
               
                 10 
                 −274.352911686 
                 15.001130830 
                 CAF2 
                 42.116 
               
               
                 11 
                 −481.511902624 
                 46.498544862 
                 AIR 
                 46.787 
               
               
                 12 
                 −70.442117850 
                 52.555341121 
                 CAF2 
                 55.942 
               
               
                 13 
                 −90.455727573 
                 1.806830035 
                 AIR 
                 78.160 
               
               
                 14 
                 3232.255140950 
                 36.176140320 
                 CAF2 
                 91.116 
               
               
                 15 
                 −186.488036306 
                 1.000000000 
                 AIR 
                 92.734 
               
               
                 16 
                 365.731282758 
                 20.809036457 
                 CAF2 
                 90.268 
               
               
                 17 
                 −2611.121142850 
                 101.825417590 
                 AIR 
                 88.935 
               
               
                 18 
                 0.000000000 
                 0.000000000 
                 AIR 
                 84.274 
               
               
                 19 
                 0.000000000 
                 65.181628952 
                 AIR 
                 84.274 
               
               
                 20 
                 258.735107311 
                 37.578859051 
                 CAF2 
                 105.187 
               
               
                 21 
                 −1152.159158690 
                 288.921175238 
                 AIR 
                 104.969 
               
               
                 22 
                 −129.279458408 
                 15.003276235 
                 CAF2 
                 81.991 
               
               
                 23 
                 −2262.350961510 
                 56.312694509 
                 AIR 
                 88.341 
               
               
                 24 
                 −117.450410520 
                 15.001009008 
                 CAF2 
                 91.957 
               
               
                 25 
                 −309.800170740 
                 28.401147541 
                 AIR 
                 113.929 
               
               
                 26 R 
                 −175.988719829 
                 0.000000000 
                 AIR 
                 117.602 
               
               
                 27 R 
                 0.000000000 
                 28.401147541 
                 AIR 
                 168.871 
               
               
                 28 
                 309.800170740 
                 15.001009008 
                 CAF2 
                 112.745 
               
               
                 29 
                 117.450410520 
                 56.312694509 
                 AIR 
                 87.774 
               
               
                 30 
                 2262.350961510 
                 15.003276235 
                 CAF2 
                 78.116 
               
               
                 31 
                 129.279458408 
                 288.921175238 
                 AIR 
                 70.315 
               
               
                 32 
                 1152.159158690 
                 37.578859051 
                 CAF2 
                 91.290 
               
               
                 33 
                 −258.735107311 
                 65.181629067 
                 AIR 
                 91.634 
               
               
                 34 
                 0.000000000 
                 0.000000000 
                 AIR 
                 84.438 
               
               
                 35 
                 0.000000000 
                 95.566202561 
                 AIR 
                 84.438 
               
               
                 36 
                 −385.455042894 
                 15.000000000 
                 CAF2 
                 93.816 
               
               
                 37 
                 −452.475904634 
                 1.000000003 
                 AIR 
                 97.482 
               
               
                 38 
                 254.248242468 
                 32.034900497 
                 CAF2 
                 105.601 
               
               
                 39 
                 5899.473023640 
                 1.000023801 
                 AIR 
                 105.353 
               
               
                 40 
                 190.848967014 
                 30.278271846 
                 CAF2 
                 104.456 
               
               
                 41 
                 621.351654529 
                 138.920391104 
                 AIR 
                 102.039 
               
               
                 42 
                 −123.640610032 
                 33.881654714 
                 CAF2 
                 76.579 
               
               
                 43 
                 158.155949669 
                 49.867792861 
                 AIR 
                 80.512 
               
               
                 44 
                 412.757602921 
                 47.829461944 
                 CAF2 
                 98.825 
               
               
                 45 
                 −208.949912656 
                 17.094373280 
                 AIR 
                 103.896 
               
               
                 46 
                 −158.641772839 
                 15.212844332 
                 CAF2 
                 105.038 
               
               
                 47 
                 −313.678744542 
                 1.052590482 
                 AIR 
                 118.827 
               
               
                 48 
                 −829.528825093 
                 55.527291516 
                 CAF2 
                 125.550 
               
               
                 49 
                 −184.492343437 
                 11.796257723 
                 AIR 
                 129.573 
               
               
                 50 
                 260.696800337 
                 37.374556186 
                 CAF2 
                 132.314 
               
               
                 51 
                 497.808165974 
                 65.844307831 
                 AIR 
                 127.088 
               
               
                 STO 
                 0.000000000 
                 0.000000000 
                 AIR 
                 127.776 
               
               
                 53 
                 0.000000000 
                 −22.615444914 
                 AIR 
                 128.288 
               
               
                 54 
                 358.239917958 
                 44.763751865 
                 CAF2 
                 128.404 
               
               
                 55 
                 −739.494996855 
                 1.004833255 
                 AIR 
                 127.649 
               
               
                 56 
                 242.528908132 
                 44.488018592 
                 CAF2 
                 121.037 
               
               
                 57 
                 3949.584753010 
                 1.000094237 
                 AIR 
                 116.970 
               
               
                 58 
                 201.527861764 
                 58.711711773 
                 CAF2 
                 103.897 
               
               
                 59 
                 −1366.391075450 
                 1.000007100 
                 AIR 
                 89.104 
               
               
                 60 
                 62.439639631 
                 63.828426005 
                 CAF2 
                 55.026 
               
               
                 61 
                 0.000000000 
                 1.550000000 
                 IMM 
                 17.302 
               
               
                 62 
                 0.000000000 
                 0.000000000 
                 AIR 
                 14.425 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Aspherical constant 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 2 
                 Surface No. 7 
                 Surface No. 12 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 1.90827109e−008 
                 C1 
                 4.29834963e−008 
                 C1 
                 7.12539594e−008 
               
               
                 C2 
                 1.04825601e−012 
                 C2 
                 −9.32018657e−013 
                 C2 
                 7.81169353e−012 
               
               
                 C3 
                 −1.78093208e−017 
                 C3 
                 3.88421097e−017 
                 C3 
                 2.24285994e−016 
               
               
                 C4 
                 2.90254732e−020 
                 C4 
                 −1.41048066e−021 
                 C4 
                 2.70399434e−019 
               
               
                 C5 
                 −9.28646308e−025 
                 C5 
                 3.20036532e−026 
                 C5 
                 −5.33658325e−023 
               
               
                 C6 
                 9.92757252e−029 
                 C6 
                 −2.55377630e−031 
                 C6 
                 1.07824675e−026 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 17 
                 Surface No. 20 
                 Surface No. 22 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 3.44530878e−008 
                 C1 
                 5.99206839e−009 
                 C1 
                 6.63814399e−008 
               
               
                 C2 
                 −3.20209778e−013 
                 C2 
                 −2.26778093e−013 
                 C2 
                 1.50151781e−012 
               
               
                 C3 
                 4.32090602e−018 
                 C3 
                 −5.52734742e−019 
                 C3 
                 3.42715896e−017 
               
               
                 C4 
                 3.71891782e−022 
                 C4 
                 3.37919534e−022 
                 C4 
                 1.13418489e−020 
               
               
                 C5 
                 −2.41461999e−026 
                 C5 
                 −2.42416300e−026 
                 C5 
                 −1.20800658e−024 
               
               
                 C6 
                 6.86020285e−031 
                 C6 
                 5.56746821e−031 
                 C6 
                 1.36760067e−028 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 31 
                 Surface No..33 
                 Surface No. 41 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 −6.63814399e−008 
                 C1 
                 −5.99206839e−009 
                 C1 
                 3.02036913e−008 
               
               
                 C2 
                 −1.50151781e−012 
                 C2 
                 2.26778093e−013 
                 C2 
                 −8.49897291e−013 
               
               
                 C3 
                 −3.42715896e−017 
                 C3 
                 5.52734742e−019 
                 C3 
                 −2.62757380e−018 
               
               
                 C4 
                 −1.13418489e−020 
                 C4 
                 −3.37919534e−022 
                 C4 
                 2.42290737e−021 
               
               
                 C5 
                 1.20800658e−024 
                 C5 
                 2.42416300e−026 
                 C5 
                 −1.80384886e−025 
               
               
                 C6 
                 −1.36760067e−028 
                 C6 
                 −5.56746821e−031 
                 C6 
                 4.40130958e−030 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 42 
                 Surface No. 44 
                 Surface No. 51 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 1.57083344e−007 
                 C1 
                 −6.63114425e−008 
                 C1 
                 3.97980700e−008 
               
               
                 C2 
                 −5.70047014e−012 
                 C2 
                 1.06389778e−012 
                 C2 
                 −1.14363396e−015 
               
               
                 C3 
                 9.96269363e−016 
                 C3 
                 −1.73700448e−016 
                 C3 
                 2.12173627e−019 
               
               
                 C4 
                 −9.51074757e−020 
                 C4 
                 7.83565903e−021 
                 C4 
                 −1.81177143e−022 
               
               
                 C5 
                 2.78023503e−024 
                 C5 
                 −3.69851418e−025 
                 C5 
                 −9.65440963e−027 
               
               
                 C6 
                 2.11268686e−028 
                 C6 
                 6.43100123e−031 
                 C6 
                 3.69511989e−031 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface No. 59 
                   
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 K 
                 0.0000 
               
               
                   
                 C1 
                 3.28933356e−008 
               
               
                   
                 C2 
                 −4.67953085e−013 
               
               
                   
                 C3 
                 1.96156711e−017 
               
               
                   
                 C4 
                 1.01627452e−022 
               
               
                   
                 C5 
                 −3.59201172e−026 
               
               
                   
                 C6 
                 2.16163436e−030 
               
               
                   
                 C7 
                 0.00000000e+000 
               
               
                   
                 C8 
                 0.00000000e+000 
               
               
                   
                 C9 
                 0.00000000e+000 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 NA = 1.1 Y = 57.7 mm 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 WL 
                 157.2852 
                 157.2862 
                 157.2842 
               
               
                   
                 CAF2 
                 1.55930394 
                 1.55930133 
                 1.55930655 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface 
                 Radius 
                 Distance 
                 Material 
                 ½ Diameter 
               
               
                   
               
               
                  0 
                 0.000000000 
                 47.596241819 
                 AIR 
                 57.700 
               
               
                  1 
                 0.000000000 
                 21.484078486 
                 AIR 
                 71.361 
               
               
                  2 
                 −130.196528296 
                 81.232017348 
                 CAF2 
                 71.411 
               
               
                  3 
                 −201.970612192 
                 1.090292328 
                 AIR 
                 102.064 
               
               
                  4 
                 0.000000000 
                 43.035190104 
                 CAF2 
                 111.239 
               
               
                  5 
                 −219.688636866 
                 1.000008083 
                 AIR 
                 113.511 
               
               
                  6 
                 196.835177454 
                 48.645753259 
                 CAF2 
                 112.440 
               
               
                  7 
                 −1062.563638620 
                 1.011278327 
                 AIR 
                 109.626 
               
               
                  8 
                 102.486371771 
                 51.257817769 
                 CAF2 
                 88.766 
               
               
                  9 
                 125.152226832 
                 78.537765316 
                 AIR 
                 72.052 
               
               
                 10 
                 −276.036111675 
                 19.246024827 
                 CAF2 
                 35.565 
               
               
                 11 
                 −344.559129459 
                 44.417965355 
                 AIR 
                 42.153 
               
               
                 12 
                 −73.158562407 
                 46.803238343 
                 CAF2 
                 53.934 
               
               
                 13 
                 −81.595671547 
                 1.005611042 
                 AIR 
                 71.774 
               
               
                 14 
                 917.859457951 
                 35.862144308 
                 CAF2 
                 83.802 
               
               
                 15 
                 −184.688054893 
                 1.002179985 
                 AIR 
                 85.191 
               
               
                 16 
                 520.342292054 
                 23.034106261 
                 CAF2 
                 82.478 
               
               
                 17 
                 −768.099839930 
                 99.999802859 
                 AIR 
                 80.816 
               
               
                 18 
                 0.000000000 
                 0.000000000 
                 AIR 
                 72.928 
               
               
                 19 
                 0.000000000 
                 49.999962118 
                 AIR 
                 72.928 
               
               
                 20 
                 241.487091044 
                 30.190977973 
                 CAF2 
                 85.575 
               
               
                 21 
                 −1164.355916310 
                 264.025266484 
                 AIR 
                 85.757 
               
               
                 22 
                 −132.516232462 
                 15.000193519 
                 CAF2 
                 81.831 
               
               
                 23 
                 −1356.484422410 
                 61.385058143 
                 AIR 
                 89.265 
               
               
                 24 
                 −108.588059874 
                 14.999993604 
                 CAF2 
                 92.698 
               
               
                 25 
                 −296.429590341 
                 28.045104017 
                 AIR 
                 119.543 
               
               
                 26 R 
                 −171.604551151 
                 0.000000000 
                 AIR 
                 121.617 
               
               
                 27 R 
                 0.000000000 
                 28.045104017 
                 AIR 
                 187.566 
               
               
                 28 
                 296.429590341 
                 14.999993604 
                 CAF2 
                 118.640 
               
               
                 29 
                 108.588059874 
                 61.385058143 
                 AIR 
                 87.692 
               
               
                 30 
                 1356.484422410 
                 15.000193519 
                 CAF2 
                 75.436 
               
               
                 31 
                 132.516232462 
                 264.025266484 
                 AIR 
                 68.614 
               
               
                 32 
                 1164.355916310 
                 30.190977973 
                 CAF2 
                 79.925 
               
               
                 33 
                 −241.487091044 
                 49.999914356 
                 AIR 
                 79.985 
               
               
                 34 
                 0.000000000 
                 0.000000000 
                 AIR 
                 73.069 
               
               
                 35 
                 0.000000000 
                 107.612168038 
                 AIR 
                 73.069 
               
               
                 36 
                 −693.184976623 
                 16.117644573 
                 CAF2 
                 81.276 
               
               
                 37 
                 −696.986438150 
                 2.228062889 
                 AIR 
                 84.557 
               
               
                 38 
                 272.001870523 
                 26.851322582 
                 CAF2 
                 90.453 
               
               
                 39 
                 −11518.014964700 
                 1.683452367 
                 AIR 
                 90.747 
               
               
                 40 
                 204.924277454 
                 41.781211890 
                 CAF2 
                 91.627 
               
               
                 41 
                 3033.528484830 
                 106.582128113 
                 AIR 
                 88.228 
               
               
                 42 
                 −134.400581416 
                 22.683343530 
                 CAF2 
                 70.595 
               
               
                 43 
                 149.085276952 
                 30.111359058 
                 AIR 
                 72.323 
               
               
                 44 
                 −1571.459281550 
                 66.592767742 
                 CAF2 
                 74.527 
               
               
                 45 
                 −685.256687590 
                 11.096249234 
                 AIR 
                 101.072 
               
               
                 46 
                 −661.646567779 
                 85.751986497 
                 CAF2 
                 106.788 
               
               
                 47 
                 −157.414472118 
                 1.578582665 
                 AIR 
                 121.872 
               
               
                 48 
                 281.442061787 
                 38.097581301 
                 CAF2 
                 126.470 
               
               
                 49 
                 2477.671193110 
                 77.916990124 
                 AIR 
                 123.978 
               
               
                 50 
                 0.000000000 
                 0.000000000 
                 AIR 
                 117.805 
               
               
                 51 
                 0.000000000 
                 −4.224796803 
                 AIR 
                 118.082 
               
               
                 52 
                 629.850672554 
                 48.195853438 
                 CAF2 
                 118.380 
               
               
                 53 
                 −440.009879814 
                 0.999978780 
                 AIR 
                 118.034 
               
               
                 54 
                 243.613408298 
                 52.262412712 
                 CAF2 
                 109.822 
               
               
                 55 
                 11973.088705700 
                 1.027491789 
                 AIR 
                 101.920 
               
               
                 56 
                 115.269169988 
                 60.712228046 
                 CAF2 
                 83.889 
               
               
                 57 
                 372.135519803 
                 1.030688086 
                 AIR 
                 63.468 
               
               
                 58 
                 72.776794128 
                 53.208894511 
                 CAF2 
                 48.890 
               
               
                 59 
                 0.000000000 
                 0.000000000 
                 CAF2 
                 14.425 
               
               
                 60 
                 0.000000000 
                 0.000000000 
                 AIR 
                 14.425 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Aspherical constants 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 2 
                 Surface No. 7 
                 Surface No. 12 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 −4.90420246e−011 
                 C1 
                 2.96559302e−008 
                 C1 
                 6.82301843e−008 
               
               
                 C2 
                 7.22127484e−014 
                 C2 
                 −4.45892297e−013 
                 C2 
                 6.13339976e−012 
               
               
                 C3 
                 1.72996941e−017 
                 C3 
                 1.35851832e−017 
                 C3 
                 −1.47536226e−016 
               
               
                 C4 
                 −3.83158229e−021 
                 C4 
                 −9.75107227e−022 
                 C4 
                 −7.56092252e−020 
               
               
                 C5 
                 1.65903133e−024 
                 C5 
                 6.40021152e−026 
                 C5 
                 1.52586945e−023 
               
               
                 C6 
                 −1.68929866e−028 
                 C6 
                 −9.93085086e−031 
                 C6 
                 −1.35801785e−027 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 17 
                 Surface No. 20 
                 Surface No. 22 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 4.47108229e−008 
                 C1 
                 2.82365956e−009 
                 C1 
                 6.25856212e−008 
               
               
                 C2 
                 −4.00171489e−013 
                 C2 
                 −3.11781699e−013 
                 C2 
                 9.37857950e−013 
               
               
                 C3 
                 4.13032418e−018 
                 C3 
                 −1.69631649e−018 
                 C3 
                 3.67635940e−017 
               
               
                 C4 
                 6.29956500e−022 
                 C4 
                 1.14900242e−021 
                 C4 
                 8.35698619e−021 
               
               
                 C5 
                 −3.85978221e−026 
                 C5 
                 −1.52629451e−025 
                 C5 
                 −1.33482892e−024 
               
               
                 C6 
                 2.31708241e−030 
                 C6 
                 8.81503206e−030 
                 C6 
                 1.38831758e−028 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 31 
                 Surface No..33 
                 Surface No. 41 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 −6.25856212e−008 
                 C1 
                 −2.82365956e−009 
                 C1 
                 2.31765306e−008 
               
               
                 C2 
                 −9.37857950e−013 
                 C2 
                 3.11781699e−013 
                 C2 
                 −1.15108202e−012 
               
               
                 C3 
                 −3.67635940e−017 
                 C3 
                 1.69631649e−018 
                 C3 
                 2.55992541e−017 
               
               
                 C4 
                 −8.35698619e−021 
                 C4 
                 −1.14900242e−021 
                 C4 
                 6.87393928e−022 
               
               
                 C5 
                 1.33482892e−024 
                 C5 
                 1.52629451e−025 
                 C5 
                 −3.66676084e−026 
               
               
                 C6 
                 −1.38831758e−028 
                 C6 
                 −8.81503206e−030 
                 C6 
                 −2.77895503e−030 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                 Surface No. 42 
                 Surface No. 44 
                 Surface No. 49 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0.0000 
                 K 
                 0.0000 
                 K 
                 0.0000 
               
               
                 C1 
                 1.23211770e−007 
                 C1 
                 −1.18481725e−007 
                 C1 
                 2.68959500e−008 
               
               
                 C2 
                 −2.94099944e−012 
                 C2 
                 −2.04738790e−012 
                 C2 
                 −9.41267411e−014 
               
               
                 C3 
                 1.13325221e−015 
                 C3 
                 −5.33930585e−016 
                 C3 
                 2.54969437e−018 
               
               
                 C4 
                 −1.09316744e−019 
                 C4 
                 −1.51638014e−020 
                 C4 
                 −1.50502498e−022 
               
               
                 C5 
                 2.28727473e−024 
                 C5 
                 1.67227571e−024 
                 C5 
                 6.35633774e−027 
               
               
                 C6 
                 1.03306617e−027 
                 C6 
                 −4.91365155e−028 
                 C6 
                 −9.71849339e−032 
               
               
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
                 C7 
                 0.00000000e+000 
               
               
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
                 C8 
                 0.00000000e+000 
               
               
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
                 C9 
                 0.00000000e+000 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface No. 57 
                   
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 K 
                 0.0000 
               
               
                   
                 C1 
                 3.32050996e−008 
               
               
                   
                 C2 
                 4.58821096e−012 
               
               
                   
                 C3 
                 −7.80384116e−016 
               
               
                   
                 C4 
                 1.16466986e−019 
               
               
                   
                 C5 
                 −1.04436731e−023 
               
               
                   
                 C6 
                 4.66260861e−028 
               
               
                   
                 C7 
                 0.00000000e+000 
               
               
                   
                 C8 
                 0.00000000e+000 
               
               
                   
                 C9 
                 0.00000000e+000 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 NAO = 0.27 Y = 56.08 mm 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 WL 
                 193.3685 
                 193.368 
                 193.3675 
               
               
                   
                 SiO22 
                 1.56078491 
                 1.5607857 
                 1.56078649 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Surface 
                 Radius 
                 Distance 
                 Material 
                 ½ Diameter 
               
               
                   
               
               
                 0 
                 0.000000000 
                 40.000000000 
                 AIR 
                 56.080 
               
               
                 1 
                 700.000000000 
                 30.000000000 
                 SIO2 
                 70.401 
               
               
                 2 
                 −700.000000000 
                 1.000000000 
                 AIR 
                 74.095 
               
               
                 3 
                 700.000000000 
                 30.000000000 
                 SIO2 
                 75.879 
               
               
                 4 
                 −700.000000000 
                 −1.000000000 
                 AIR 
                 77.689 
               
               
                 5 
                 500.000000000 
                 30.000000000 
                 SIO2 
                 78.339 
               
               
                 6 
                 −1000.000000000 
                 15.000000000 
                 AIR 
                 78.060 
               
               
                 7 
                 700.000000000 
                 30.000000000 
                 SIO2 
                 76.609 
               
               
                 8 
                 −700.000000000 
                 0.000000000 
                 AIR 
                 74.839 
               
               
                 9 
                 0.000000000 
                 75.000000000 
                 SIO2 
                 74.070 
               
               
                 10 
                 0.000000000 
                 75.000000000 
                 SIO2 
                 64.964 
               
               
                 11 
                 0.000000000 
                 13.000000000 
                 AIR 
                 55.857 
               
               
                 12 
                 −300.000000000 
                 10.000000000 
                 SIO2 
                 54.317 
               
               
                 13 
                 −500.000000000 
                 5.000000000 
                 AIR 
                 53.682 
               
               
                 14 
                 0.000000000 
                 10.000000000 
                 AIR 
                 52.538 
               
               
                 15 
                 −290.000000000 
                 0.000000000 
                 AIR 
                 55.162 
               
               
                 16 
                 0.000000000 
                 15.000000000 
                 AIR 
                 54.666 
               
               
                 17 
                 500.000000000 
                 10.000000000 
                 SIO2 
                 56.801 
               
               
                 18 
                 300.000000000 
                 13.000000000 
                 AIR 
                 57.279 
               
               
                 19 
                 0.000000000 
                 75.000000000 
                 SIO2 
                 58.589 
               
               
                 20 
                 0.000000000 
                 75.000000000 
                 SIO2 
                 66.927 
               
               
                 21 
                 0.000000000 
                 30.000000000 
                 AIR 
                 75.266 
               
               
                 22 
                 300.000000000 
                 30.000000000 
                 SIO2 
                 82.546 
               
               
                 23 
                 −400.000000000 
                 40.000100000 
                 AIR 
                 82.595 
               
               
                 24 
                 500.000000000 
                 25.000000000 
                 SIO2 
                 76.453 
               
               
                 25 
                 −400.000000000 
                 41.206360088 
                 AIR 
                 74.915 
               
               
                 26 
                 0.000000000 
                 0.000000000 
                 AIR 
                 63.567 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 SURFACE 
                 RADIUS 
                 THICKNESS 
                 MATERIAL 
                 INDEX 
                 SEMIDIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 59.209510 
                   
                   
                 64.0 
               
               
                 1 
                 6291.598274 
                 23.678332 
                 SILUV 
                 1.560491 
                 85.8 
               
               
                 2 
                 −280.600902 
                 1.025405 
                   
                   
                 87.8 
               
               
                 3 
                 144.511042 
                 32.290800 
                 SILUV 
                 1.560491 
                 93.4 
               
               
                 4 
                 416.821920 
                 57.132926 
                   
                   
                 91.4 
               
               
                 5 
                 163.242835 
                 31.337729 
                 SILUV 
                 1.560491 
                 78.6 
               
               
                 6 
                 −661.478201 
                 9.882827 
                   
                   
                 75.2 
               
               
                 7 
                 85.805375 
                 31.336035 
                 SILUV 
                 1.560491 
                 59.0 
               
               
                 8 
                 97.841124 
                 32.157174 
                   
                   
                 46.3 
               
               
                 9 
                 −110.558780 
                 50.000185 
                 SILUV 
                 1.560491 
                 43.4 
               
               
                 10 
                 −105.568468 
                 7.861299 
                   
                   
                 62.9 
               
               
                 11 
                 −95.869843 
                 33.360087 
                 SILUV 
                 1.560491 
                 64.6 
               
               
                 12 
                 −396.465160 
                 25.208502 
                   
                   
                 89.8 
               
               
                 13 
                 −295.388642 
                 49.666565 
                 SILUV 
                 1.560491 
                 103.3 
               
               
                 14 
                 −127.525234 
                 0.999856 
                   
                   
                 109.4 
               
               
                 15 
                 −279.794894 
                 36.644817 
                 SILUV 
                 1.560491 
                 118.2 
               
               
                 16 
                 −160.830350 
                 0.999370 
                   
                   
                 121.6 
               
               
                 17 
                 321.280433 
                 28.683439 
                 SILUV 
                 1.560491 
                 121.8 
               
               
                 18 
                 1713.098384 
                 0.999141 
                   
                   
                 120.6 
               
               
                 19 
                 249.641678 
                 30.928964 
                 SILUV 
                 1.560491 
                 117.3 
               
               
                 20 
                 1775.118866 
                 84.998661 
                   
                   
                 114.7 
               
               
                 21 
                 0.000000 
                 −14.998086 
                 REFL 
                   
                 183.2 
               
               
                 22 
                 −322.738827 
                 −22.708716 
                 SILUV 
                 1.560491 
                 86.5 
               
               
                 23 
                 1794.276655 
                 −198.953288 
                   
                   
                 84.1 
               
               
                 24 
                 102.167956 
                 −12.500000 
                 SILUV 
                 1.560491 
                 72.4 
               
               
                 25 
                 15297.224085 
                 −58.562725 
                   
                   
                 82.5 
               
               
                 26 
                 106.167570 
                 −12.500000 
                 SILUV 
                 1.560491 
                 89.2 
               
               
                 27 
                 192.760260 
                 −27.399192 
                   
                   
                 107.8 
               
               
                 28 
                 154.038668 
                 27.399192 
                 REFL 
                   
                 115.3 
               
               
                 29 
                 192.760260 
                 12.500000 
                 SILUV 
                 1.560491 
                 107.8 
               
               
                 30 
                 106.167570 
                 58.562725 
                   
                   
                 89.2 
               
               
                 31 
                 15297.224085 
                 12.500000 
                 SILUV 
                 1.560491 
                 82.5 
               
               
                 32 
                 102.167956 
                 198.954271 
                   
                   
                 72.4 
               
               
                 33 
                 1794.276655 
                 22.708716 
                 SILUV 
                 1.560491 
                 84.1 
               
               
                 34 
                 −322.738827 
                 14.999504 
                   
                   
                 86.5 
               
               
                 35 
                 0.000000 
                 −84.999766 
                 REFL 
                   
                 179.0 
               
               
                 36 
                 665.918045 
                 −20.162556 
                 SILUV 
                 1.560491 
                 112.6 
               
               
                 37 
                 332.340267 
                 −0.999827 
                   
                   
                 115.0 
               
               
                 38 
                 −545.416435 
                 −30.156611 
                 SILUV 
                 1.560491 
                 121.7 
               
               
                 39 
                 972.309758 
                 −0.999891 
                   
                   
                 122.2 
               
               
                 40 
                 −239.092507 
                 −40.367741 
                 SILUV 
                 1.560491 
                 122.8 
               
               
                 41 
                 −3867.765964 
                 −1.000866 
                   
                   
                 121.0 
               
               
                 42 
                 −145.814165 
                 −43.782811 
                 SILUV 
                 1.560491 
                 108.8 
               
               
                 43 
                 −475.322286 
                 −20.838629 
                   
                   
                 103.7 
               
               
                 44 
                 994.251725 
                 −9.999791 
                 SILUV 
                 1.560491 
                 100.7 
               
               
                 45 
                 −102.926902 
                 −38.025955 
                   
                   
                 82.3 
               
               
                 46 
                 −666.254624 
                 −9.999917 
                 SILUV 
                 1.560491 
                 82.7 
               
               
                 47 
                 −120.991218 
                 −38.125943 
                   
                   
                 83.4 
               
               
                 48 
                 −444.529439 
                 −19.995612 
                 SILUV 
                 1.560491 
                 93.9 
               
               
                 49 
                 7256.085975 
                 −72.078976 
                   
                   
                 96.0 
               
               
                 50 
                 861.320622 
                 −16.316029 
                 SILUV 
                 1.560491 
                 115.4 
               
               
                 51 
                 367.114240 
                 −21.532267 
                   
                   
                 118.5 
               
               
                 52 
                 −578.781634 
                 −19.544116 
                 SILUV 
                 1.560491 
                 135.3 
               
               
                 53 
                 −1539.844110 
                 −1.000064 
                   
                   
                 136.2 
               
               
                 54 
                 −409.215581 
                 −53.967605 
                 SILUV 
                 1.560491 
                 140.1 
               
               
                 55 
                 388.259251 
                 −21.190519 
                   
                   
                 140.0 
               
               
                 56 
                 0.000000 
                 −14.363454 
                   
                   
                 131.6 
               
               
                 57 
                 −492.744559 
                 −42.747305 
                 SILUV 
                 1.560491 
                 135.3 
               
               
                 58 
                 596.175995 
                 −0.999975 
                   
                   
                 134.4 
               
               
                 59 
                 −188.727208 
                 −44.971247 
                 SILUV 
                 1.560491 
                 119.1 
               
               
                 60 
                 −1267.900423 
                 −0.999664 
                   
                   
                 114.6 
               
               
                 61 
                 −118.853763 
                 −29.974419 
                 SILUV 
                 1.560491 
                 90.5 
               
               
                 62 
                 −172.286110 
                 −2.720285 
                   
                   
                 82.2 
               
               
                 63 
                 −83.065857 
                 −24.574193 
                 SILUV 
                 1.560491 
                 67.0 
               
               
                 64 
                 −111.658319 
                 −1.105096 
                   
                   
                 56.0 
               
               
                 65 
                 −69.828581 
                 −43.055955 
                 SILUV 
                 1.560491 
                 50.3 
               
               
                 66 
                 0.000000 
                 −1.001571 
                 H2OV193 
                 1.436823 
                 20.5 
               
               
                 67 
                 0.000000 
                 0.000000 
                   
                   
                 19.0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 9A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 SRF 
                 6 
                 15 
                 20 
                 24 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 7.168010E−08 
                 −6.564766E−09 
                 1.990247E−08 
                 −1.434139E−07 
               
               
                 C2 
                 7.874235E−13 
                  4.352930E−13 
                 2.214975E−13 
                 −3.992456E−12 
               
               
                 C3 
                 3.026860E−16 
                 −2.400883E−17 
                 −2.046213E−17  
                 −3.265156E−16 
               
               
                 C4 
                 −3.434246E−20  
                  3.866886E−22 
                 9.725329E−22 
                  3.104990E−21 
               
               
                 C5 
                 3.870353E−25 
                  1.162444E−27 
                 −2.756730E−26  
                 −1.874174E−24 
               
               
                 C6 
                 7.234455E−29 
                 −1.259764E−32 
                 4.143527E−31 
                 −4.628892E−28 
               
               
                   
               
               
                 SRF 
                 43 
                 45 
                 47 
                 50 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 −1.007015E−08 
                 −4.489903E−08 
                 5.184442E−08 
                  3.174451E−08 
               
               
                 C2 
                 −3.821558E−13 
                  1.198606E−12 
                 5.582183E−12 
                  5.537615E−14 
               
               
                 C3 
                  8.872440E−17 
                 −1.562441E−16 
                 2.393671E−16 
                  3.190712E−18 
               
               
                 C4 
                 −6.956619E−21 
                  1.250805E−20 
                 7.608169E−21 
                 −6.524213E−22 
               
               
                 C5 
                  3.866469E−25 
                  2.467619E−24 
                 −1.988373E−24  
                 −7.379838E−27 
               
               
                 C6 
                 −7.623750E−30 
                 −1.675469E−28 
                 2.670495E−28 
                 −9.847764E−31 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 SRF 
                 62 
                 64 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 C1 
                  6.908374E−08 
                 −2.282295E−07 
               
               
                   
                 C2 
                 −7.414546E−12 
                 −2.062783E−11 
               
               
                   
                 C3 
                  1.971662E−16 
                  1.258799E−15 
               
               
                   
                 C4 
                 −5.334580E−20 
                 −2.146440E−19 
               
               
                   
                 C5 
                  5.884223E−24 
                  4.332875E−23 
               
               
                   
                 C6 
                 −3.743875E−28 
                 −1.189088E−27 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 SUR- 
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 FACE 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 51.000259 
                   
                   
                 64.0 
               
               
                 1 
                 1084.670740 
                 20.061470 
                 SILUV 
                 1.560491 
                 84.0 
               
               
                 2 
                 −489.591572 
                 8.024505 
                   
                   
                 85.7 
               
               
                 3 
                 147.977412 
                 33.265720 
                 SILUV 
                 1.560491 
                 93.2 
               
               
                 4 
                 533.607588 
                 60.035648 
                   
                   
                 91.5 
               
               
                 5 
                 162.257926 
                 31.487872 
                 SILUV 
                 1.560491 
                 79.2 
               
               
                 6 
                 −641.542087 
                 12.321334 
                   
                   
                 75.9 
               
               
                 7 
                 88.691635 
                 37.381348 
                 SILUV 
                 1.560491 
                 60.1 
               
               
                 8 
                 113.767960 
                 26.723349 
                   
                   
                 45.6 
               
               
                 9 
                 −117.888976 
                 42.501530 
                 SILUV 
                 1.560491 
                 42.0 
               
               
                 10 
                 −162.865349 
                 13.700402 
                   
                   
                 59.6 
               
               
                 11 
                 −116.482373 
                 32.902705 
                 SILUV 
                 1.560491 
                 63.1 
               
               
                 12 
                 −306.816392 
                 26.438566 
                   
                   
                 83.9 
               
               
                 13 
                 −323.530175 
                 41.085951 
                 SILUV 
                 1.560491 
                 99.9 
               
               
                 14 
                 −137.244758 
                 5.556612 
                   
                   
                 105.5 
               
               
                 15 
                 −451.636628 
                 44.589731 
                 SILUV 
                 1.560491 
                 115.9 
               
               
                 16 
                 −154.769207 
                 0.999820 
                   
                   
                 119.2 
               
               
                 17 
                 392.370175 
                 25.008628 
                 SILUV 
                 1.560491 
                 118.0 
               
               
                 18 
                 3014.562689 
                 0.999723 
                   
                   
                 117.0 
               
               
                 19 
                 289.177591 
                 25.844242 
                 SILUV 
                 1.560491 
                 114.3 
               
               
                 20 
                 925.962044 
                 84.999670 
                   
                   
                 112.1 
               
               
                 21 
                 0.000000 
                 −14.999476 
                 REFL 
                   
                 175.2 
               
               
                 22 
                 −331.395343 
                 −22.607980 
                 SILUV 
                 1.560491 
                 89.7 
               
               
                 23 
                 3332.007318 
                 −230.559976 
                   
                   
                 87.1 
               
               
                 24 
                 98.691313 
                 −12.500000 
                 SILUV 
                 1.560491 
                 73.1 
               
               
                 25 
                 28881.747267 
                 −55.643371 
                   
                   
                 84.0 
               
               
                 26 
                 105.777999 
                 −12.500000 
                 SILUV 
                 1.560491 
                 89.4 
               
               
                 27 
                 190.916612 
                 −27.579443 
                   
                   
                 109.5 
               
               
                 28 
                 155.323230 
                 27.579443 
                 REFL 
                   
                 118.2 
               
               
                 29 
                 190.916612 
                 12.500000 
                 SILUV 
                 1.560491 
                 109.5 
               
               
                 30 
                 105.777999 
                 55.643371 
                   
                   
                 89.4 
               
               
                 31 
                 28881.747267 
                 12.500000 
                 SILUV 
                 1.560491 
                 84.0 
               
               
                 32 
                 98.691313 
                 230.560091 
                   
                   
                 73.1 
               
               
                 33 
                 3332.007318 
                 22.607980 
                 SILUV 
                 1.560491 
                 87.1 
               
               
                 34 
                 −331.395343 
                 14.999815 
                   
                   
                 89.7 
               
               
                 35 
                 0.000000 
                 −85.031452 
                 REFL 
                   
                 185.4 
               
               
                 36 
                 632.234731 
                 −21.937556 
                 SILUV 
                 1.560491 
                 116.1 
               
               
                 37 
                 312.776852 
                 −1.989523 
                   
                   
                 118.6 
               
               
                 38 
                 −419.317799 
                 −39.548184 
                 SILUV 
                 1.560491 
                 126.0 
               
               
                 39 
                 679.933212 
                 −11.879717 
                   
                   
                 126.0 
               
               
                 40 
                 −359.055554 
                 −33.826228 
                 SILUV 
                 1.560491 
                 122.0 
               
               
                 41 
                 1713.588185 
                 −6.930143 
                   
                   
                 120.4 
               
               
                 42 
                 −130.793879 
                 −40.665153 
                 SILUV 
                 1.560491 
                 103.0 
               
               
                 43 
                 −297.152405 
                 −24.525611 
                   
                   
                 97.5 
               
               
                 44 
                 888.942670 
                 −10.000074 
                 SILUV 
                 1.560491 
                 94.8 
               
               
                 45 
                 −95.853886 
                 −38.822971 
                   
                   
                 77.7 
               
               
                 46 
                 −1286.530610 
                 −10.502279 
                 SILUV 
                 1.560491 
                 78.3 
               
               
                 47 
                 −122.332491 
                 −53.312951 
                   
                   
                 80.5 
               
               
                 48 
                 −1046.310490 
                 −29.995767 
                 SILUV 
                 1.560491 
                 98.8 
               
               
                 49 
                 −3155.314818 
                 −35.731529 
                   
                   
                 106.3 
               
               
                 50 
                 −2635.516216 
                 −38.906996 
                 SILUV 
                 1.560491 
                 121.6 
               
               
                 51 
                 253.216058 
                 −1.026566 
                   
                   
                 125.0 
               
               
                 52 
                 −477.178385 
                 −27.726167 
                 SILUV 
                 1.560491 
                 136.5 
               
               
                 53 
                 −1111.410551 
                 −1.006437 
                   
                   
                 137.0 
               
               
                 54 
                 −419.465047 
                 −45.153215 
                 SILUV 
                 1.560491 
                 138.9 
               
               
                 55 
                 657.652879 
                 −27.561809 
                   
                   
                 138.4 
               
               
                 56 
                 0.000000 
                 11.279146 
                   
                   
                 129.1 
               
               
                 57 
                 −1714.364190 
                 −34.463306 
                 SILUV 
                 1.560491 
                 133.1 
               
               
                 58 
                 435.051330 
                 −26.422505 
                   
                   
                 131.9 
               
               
                 59 
                 −217.425708 
                 −40.030383 
                 SILUV 
                 1.560491 
                 113.2 
               
               
                 60 
                 191072.918549 
                 −0.999778 
                   
                   
                 109.6 
               
               
                 61 
                 −106.841172 
                 −32.593766 
                 SILUV 
                 1.560491 
                 85.0 
               
               
                 62 
                 −202.323930 
                 −0.999427 
                   
                   
                 77.0 
               
               
                 63 
                 −79.299863 
                 −25.891843 
                 SILUV 
                 1.560491 
                 63.5 
               
               
                 64 
                 −117.061751 
                 −0.998476 
                   
                   
                 52.9 
               
               
                 65 
                 −70.340516 
                 −36.868819 
                 SILUV 
                 1.560491 
                 46.7 
               
               
                 66 
                 0.000000 
                 −1.001571 
                 H2OV193 
                 1.436823 
                 20.5 
               
               
                 67 
                 0.000000 
                 0.000000 
                   
                   
                 19.0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 6 
                 15 
                 23 
                 24 
                 32 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 8.416890E−08 
                 −2.308559E−08 
                 −8.485003E−09 
                 −1.223767E−07 
                 −1.223767E−07 
               
               
                 C2 
                 1.006640E−12 
                  1.109550E−13 
                 −6.734945E−14 
                 −7.438273E−12 
                 −7.438273E−12 
               
               
                 C3 
                 3.617643E−16 
                 −6.344353E−18 
                  5.661979E−19 
                 −4.704304E−16 
                 −4.704304E−16 
               
               
                 C4 
                 −4.192188E−20  
                  1.566682E−22 
                 −2.504587E−22 
                  3.963572E−21 
                  3.963572E−21 
               
               
                 C5 
                 6.704096E−26 
                 −4.902118E−27 
                  2.908669E−26 
                 −6.736661E−24 
                 −6.736661E−24 
               
               
                 C6 
                 1.721955E−28 
                  4.306889E−32 
                 −1.350234E−30 
                 −4.531767E−28 
                 −4.531767E−28 
               
               
                   
               
               
                 SRF 
                 33 
                 43 
                 45 
                 47 
                 50 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 −8.485003E−09 
                 −3.497951E−09 
                 −4.202804E−08  
                 6.218114E−08 
                  3.138180E−08 
               
               
                 C2 
                 −6.734945E−14 
                 −5.106017E−13 
                 1.982600E−12 
                 4.755456E−12 
                 −3.924136E−13 
               
               
                 C3 
                  5.661979E−19 
                  6.844726E−17 
                 −1.463517E−16  
                 4.467358E−16 
                  5.657046E−18 
               
               
                 C4 
                 −2.504587E−22 
                 −3.263478E−21 
                 9.687863E−21 
                 2.313332E−20 
                 −6.552593E−22 
               
               
                 C5 
                  2.908669E−26 
                  9.349870E−26 
                 2.764278E−24 
                 −3.886568E−24  
                  2.087202E−26 
               
               
                 C6 
                 −1.350234E−30 
                  2.248476E−30 
                 7.460803E−29 
                 4.543438E−28 
                 −5.207993E−31 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 SRF 
                 55 
                 62 
                 64 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                 −5.022929E−10 
                 −2.500268E−08 
                 −1.132630E−07 
               
               
                   
                 C2 
                 −3.387071E−14 
                 −7.360583E−12 
                 −3.255025E−11 
               
               
                   
                 C3 
                 −1.887886E−17 
                  1.175353E−15 
                  6.754420E−15 
               
               
                   
                 C4 
                  6.061750E−22 
                 −2.566402E−19 
                 −9.778374E−19 
               
               
                   
                 C5 
                 −8.730441E−27 
                  2.406082E−23 
                  6.403897E−23 
               
               
                   
                 C6 
                  4.736715E−32 
                 −1.314800E−27 
                  1.523975E−27 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 11 
               
               
                   
               
               
                   
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 SURF 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 42.716567 
                   
                   
                 63.0 
               
               
                 1 
                 187.082284 
                 29.074103 
                 SIO2 
                 1.560491 
                 87.7 
               
               
                 2 
                 1122.624300 
                 13.704059 
                   
                   
                 87.8 
               
               
                 3 
                 257.788495 
                 25.970502 
                 SIO2 
                 1.560491 
                 89.3 
               
               
                 4 
                 4087.923719 
                 6.751806 
                   
                   
                 88.2 
               
               
                 5 
                 149.090802 
                 9.999268 
                 SIO2 
                 1.560491 
                 84.3 
               
               
                 6 
                 112.190840 
                 20.619019 
                   
                   
                 79.4 
               
               
                 7 
                 222.671339 
                 39.005001 
                 SIO2 
                 1.560491 
                 79.4 
               
               
                 8 
                 −171.486868 
                 0.999098 
                   
                   
                 77.9 
               
               
                 9 
                 72.242638 
                 58.534093 
                 SIO2 
                 1.560491 
                 61.0 
               
               
                 10 
                 103.263585 
                 23.657309 
                   
                   
                 38.2 
               
               
                 11 
                 −120.537552 
                 36.218695 
                 SIO2 
                 1.560491 
                 39.7 
               
               
                 12 
                 −79.009690 
                 13.559024 
                   
                   
                 52.6 
               
               
                 13 
                 −70.743286 
                 10.000301 
                 SIO2 
                 1.560491 
                 55.6 
               
               
                 14 
                 −406.875493 
                 15.578104 
                   
                   
                 72.7 
               
               
                 15 
                 −167.014571 
                 41.099022 
                 SIO2 
                 1.560491 
                 76.7 
               
               
                 16 
                 −97.881974 
                 0.999302 
                   
                   
                 86.2 
               
               
                 17 
                 −289.132352 
                 49.908319 
                 SIO2 
                 1.560491 
                 102.4 
               
               
                 18 
                 −127.491717 
                 0.999640 
                   
                   
                 108.2 
               
               
                 19 
                 −915.187280 
                 29.128849 
                 SIO2 
                 1.560491 
                 114.2 
               
               
                 20 
                 −267.279137 
                 70.000315 
                   
                   
                 116.1 
               
               
                 21 
                 0.000000 
                 −99.530888 
                 REFL 
                   
                 163.4 
               
               
                 22 
                 −211.224346 
                 −59.634155 
                 SIO2 
                 1.560491 
                 129.3 
               
               
                 23 
                 847.318306 
                 −285.786240 
                   
                   
                 127.5 
               
               
                 24 
                 108.606993 
                 −12.500000 
                 SIO2 
                 1.560491 
                 68.7 
               
               
                 25 
                 −2037.814268 
                 −40.801930 
                   
                   
                 77.3 
               
               
                 26 
                 98.650256 
                 −12.500000 
                 SIO2 
                 1.560491 
                 79.4 
               
               
                 27 
                 173.699507 
                 −12.863441 
                   
                   
                 95.4 
               
               
                 28 
                 147.630649 
                 12.863441 
                 REFL 
                   
                 98.7 
               
               
                 29 
                 173.699507 
                 12.500000 
                 SIO2 
                 1.560491 
                 95.4 
               
               
                 30 
                 98.650256 
                 40.801930 
                   
                   
                 79.4 
               
               
                 31 
                 −2037.814268 
                 12.500000 
                 SIO2 
                 1.560491 
                 77.3 
               
               
                 32 
                 108.606993 
                 285.786240 
                   
                   
                 68.7 
               
               
                 33 
                 847.318306 
                 59.634155 
                 SIO2 
                 1.560491 
                 127.5 
               
               
                 34 
                 −211.224346 
                 81.116047 
                   
                   
                 129.3 
               
               
                 35 
                 0.000000 
                 −73.612596 
                 REFL 
                   
                 160.7 
               
               
                 36 
                 −389.330139 
                 −33.487696 
                 SIO2 
                 1.560491 
                 114.9 
               
               
                 37 
                 1028.934202 
                 −0.999947 
                   
                   
                 113.5 
               
               
                 38 
                 −174.265376 
                 −32.363134 
                 SIO2 
                 1.560491 
                 104.3 
               
               
                 39 
                 −396.847027 
                 −1.000532 
                   
                   
                 99.8 
               
               
                 40 
                 −121.243745 
                 −48.918207 
                 SIO2 
                 1.560491 
                 89.3 
               
               
                 41 
                 −131.171270 
                 −29.702617 
                   
                   
                 71.3 
               
               
                 42 
                 335.952888 
                 −10.034790 
                 SIO2 
                 1.560491 
                 69.3 
               
               
                 43 
                 −82.977553 
                 −43.925742 
                   
                   
                 61.4 
               
               
                 44 
                 142.301184 
                 −9.999862 
                 SIO2 
                 1.560491 
                 63.2 
               
               
                 45 
                 −263.305242 
                 −23.458962 
                   
                   
                 74.7 
               
               
                 46 
                 2291.125201 
                 −61.398344 
                 SIO2 
                 1.560491 
                 84.5 
               
               
                 47 
                 165.812687 
                 −1.061241 
                   
                   
                 103.9 
               
               
                 48 
                 486.553030 
                 −37.309271 
                 SIO2 
                 1.560491 
                 113.9 
               
               
                 49 
                 194.984003 
                 −21.455915 
                   
                   
                 120.7 
               
               
                 50 
                 −2153.235102 
                 −50.329924 
                 SIO2 
                 1.560491 
                 142.6 
               
               
                 51 
                 291.296473 
                 −0.999132 
                   
                   
                 144.8 
               
               
                 52 
                 −443.499291 
                 −44.594835 
                 SIO2 
                 1.560491 
                 146.7 
               
               
                 53 
                 1173.500711 
                 −8.577265 
                   
                   
                 145.5 
               
               
                 54 
                 0.000000 
                 7.578035 
                   
                   
                 138.4 
               
               
                 55 
                 −337.532449 
                 −35.808358 
                 SIO2 
                 1.560491 
                 139.1 
               
               
                 56 
                 −1836.960645 
                 −1.165380 
                   
                   
                 136.4 
               
               
                 57 
                 −439.395199 
                 −28.816834 
                 SIO2 
                 1.560491 
                 133.5 
               
               
                 58 
                 2161.178835 
                 −0.998190 
                   
                   
                 130.3 
               
               
                 59 
                 −260.497359 
                 −36.004531 
                 SIO2 
                 1.560491 
                 115.8 
               
               
                 60 
                 5382.003743 
                 −0.997164 
                   
                   
                 110.1 
               
               
                 61 
                 −122.176927 
                 −36.201583 
                 SIO2 
                 1.560491 
                 86.2 
               
               
                 62 
                 −321.548352 
                 −1.000000 
                   
                   
                 76.5 
               
               
                 63 
                 −54.686592 
                 −41.835126 
                 SIO2 
                 1.560491 
                 49.5 
               
               
                 64 
                 0.000000 
                 −3.000000 
                 H2O 
                 1.436823 
                 25.2 
               
               
                 65 
                 0.000000 
                 0.000000 
                   
                   
                 18.8 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 11A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 8 
                 14 
                 19 
                 22 
                 25 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.079370E−07 
                  7.669220E−08 
                 −7.045424E−09 
                 1.010508E−08 
                  3.738770E−08 
               
               
                 C2 
                 1.064327E−12 
                 −1.973038E−11 
                 −3.066122E−14 
                 1.795924E−13 
                 −3.496492E−12 
               
               
                 C3 
                 −4.566909E−16  
                  2.138994E−15 
                 −4.118337E−18 
                 1.934995E−18 
                  3.233016E−16 
               
               
                 C4 
                 1.905320E−19 
                 −1.074179E−19 
                  3.495758E−22 
                 1.389960E−22 
                 −3.498294E−20 
               
               
                 C5 
                 −1.972022E−23  
                 −2.090955E−24 
                 −2.483792E−26 
                 −5.289985E−27  
                  2.704951E−24 
               
               
                 C6 
                 8.751032E−28 
                  4.279927E−28 
                  4.016359E−31 
                 1.320749E−31 
                 −9.856748E−29 
               
               
                   
               
               
                 SRF 
                 31 
                 34 
                 42 
                 46 
                 48 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                  3.738770E−08 
                 1.010508E−08 
                  3.117477E−08 
                  8.249850E−08 
                 4.142725E−08 
               
               
                 C2 
                 −3.496492E−12 
                 1.795924E−13 
                 −1.385143E−11 
                 −1.955317E−13 
                 −2.012061E−12  
               
               
                 C3 
                  3.233016E−16 
                 1.934995E−18 
                  2.707311E−15 
                 −8.022466E−17 
                 1.566310E−17 
               
               
                 C4 
                 −3.498294E−20 
                 1.389960E−22 
                 −3.351896E−19 
                 −1.723197E−20 
                 1.046236E−22 
               
               
                 C5 
                  2.704951E−24 
                 −5.289985E−27  
                  2.318550E−23 
                 −8.777152E−25 
                 3.404661E−25 
               
               
                 C6 
                 −9.856748E−29 
                 1.320749E−31 
                 −7.018917E−28 
                 −2.800720E−28 
                 −8.280605E−30  
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 SRF 
                 51 
                 57 
                 60 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                  3.292883E−10 
                  4.807681E−08 
                  3.409977E−09 
               
               
                   
                 C2 
                 −7.254285E−13 
                 −2.265563E−12 
                 −3.641765E−12 
               
               
                   
                 C3 
                  2.476488E−17 
                  6.703492E−17 
                  2.594792E−16 
               
               
                   
                 C4 
                 −1.056859E−21 
                 −1.704146E−21 
                 −1.764035E−20 
               
               
                   
                 C5 
                  4.966804E−26 
                  4.472968E−26 
                  7.777614E−25 
               
               
                   
                 C6 
                 −8.485797E−31 
                 −6.865707E−31 
                 −1.797945E−29 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 12 
               
               
                   
               
               
                   
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 SURF 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 35.040681 
                   
                   
                 61.5 
               
               
                 1 
                 210.405327 
                 30.736588 
                 SIO2 
                 1.560491 
                 81.0 
               
               
                 2 
                 −829.214191 
                 5.286654 
                   
                   
                 81.6 
               
               
                 3 
                 107.948426 
                 51.211605 
                 SIO2 
                 1.560491 
                 82.3 
               
               
                 4 
                 81.561700 
                 24.185596 
                   
                   
                 66.5 
               
               
                 5 
                 129.355284 
                 38.167801 
                 SIO2 
                 1.560491 
                 67.5 
               
               
                 6 
                 −166.842164 
                 0.997639 
                   
                   
                 65.8 
               
               
                 7 
                 73.621253 
                 52.812760 
                 SIO2 
                 1.560491 
                 55.2 
               
               
                 8 
                 87.502326 
                 23.343983 
                   
                   
                 35.4 
               
               
                 9 
                 −63.355137 
                 18.274984 
                 SIO2 
                 1.560491 
                 38.4 
               
               
                 10 
                 −64.795456 
                 15.650649 
                   
                   
                 46.8 
               
               
                 11 
                 −65.436171 
                 11.477841 
                 SIO2 
                 1.560491 
                 52.6 
               
               
                 12 
                 −192.744558 
                 16.904355 
                   
                   
                 69.7 
               
               
                 13 
                 −246.808133 
                 48.828721 
                 SIO2 
                 1.560491 
                 85.8 
               
               
                 14 
                 −107.969356 
                 0.997713 
                   
                   
                 94.9 
               
               
                 15 
                 −447.790890 
                 56.851474 
                 SIO2 
                 1.560491 
                 111.1 
               
               
                 16 
                 −133.844748 
                 0.997553 
                   
                   
                 116.8 
               
               
                 17 
                 315.857486 
                 38.321196 
                 SIO2 
                 1.560491 
                 120.8 
               
               
                 18 
                 −1923.797869 
                 0.996321 
                   
                   
                 119.7 
               
               
                 19 
                 232.932637 
                 43.497172 
                 SIO2 
                 1.560491 
                 114.0 
               
               
                 20 
                 −887.954229 
                 59.994922 
                   
                   
                 110.5 
               
               
                 21 
                 0.000000 
                 −177.093526 
                 REFL 
                   
                 80.1 
               
               
                 22 
                 102.645236 
                 −12.500000 
                 SIO2 
                 1.560491 
                 67.0 
               
               
                 23 
                 942.361489 
                 −43.357484 
                   
                   
                 77.8 
               
               
                 24 
                 90.416551 
                 −12.500000 
                 SIO2 
                 1.560491 
                 79.9 
               
               
                 25 
                 149.946360 
                 −13.736983 
                   
                   
                 97.4 
               
               
                 26 
                 131.782255 
                 13.736983 
                 REFL 
                   
                 100.5 
               
               
                 27 
                 149.946360 
                 12.500000 
                 SIO2 
                 1.560491 
                 97.4 
               
               
                 28 
                 90.416551 
                 43.357484 
                   
                   
                 79.9 
               
               
                 29 
                 942.361489 
                 12.500000 
                 SIO2 
                 1.560491 
                 77.8 
               
               
                 30 
                 102.645236 
                 177.093526 
                   
                   
                 67.0 
               
               
                 31 
                 0.000000 
                 −60.055220 
                 REFL 
                   
                 75.6 
               
               
                 32 
                 104914.890260 
                 −35.073765 
                 SIO2 
                 1.560491 
                 98.4 
               
               
                 33 
                 219.963934 
                 −0.997320 
                   
                   
                 101.4 
               
               
                 34 
                 −485.974374 
                 −33.321196 
                 SIO2 
                 1.560491 
                 106.4 
               
               
                 35 
                 531.348627 
                 −0.997416 
                   
                   
                 106.7 
               
               
                 36 
                 −179.150861 
                 −35.974078 
                 SIO2 
                 1.560491 
                 104.0 
               
               
                 37 
                 −726.299833 
                 −0.997789 
                   
                   
                 101.1 
               
               
                 38 
                 −143.133378 
                 −31.466370 
                 SIO2 
                 1.560491 
                 92.9 
               
               
                 39 
                 −333.246416 
                 −43.619093 
                   
                   
                 87.4 
               
               
                 40 
                 149.805913 
                 −9.999074 
                 SIO2 
                 1.560491 
                 78.6 
               
               
                 41 
                 −96.090593 
                 −42.639692 
                   
                   
                 69.3 
               
               
                 42 
                 224.529027 
                 −9.998160 
                 SIO2 
                 1.560491 
                 70.5 
               
               
                 43 
                 −264.668390 
                 −13.559760 
                   
                   
                 81.5 
               
               
                 44 
                 −938.629305 
                 −29.640517 
                 SIO2 
                 1.560491 
                 87.3 
               
               
                 45 
                 304.621140 
                 −22.447192 
                   
                   
                 93.1 
               
               
                 46 
                 −943.485170 
                 −40.752283 
                 SIO2 
                 1.560491 
                 115.1 
               
               
                 47 
                 271.215785 
                 −2.888195 
                   
                   
                 119.3 
               
               
                 48 
                 −456.833471 
                 −43.199885 
                 SIO2 
                 1.560491 
                 132.8 
               
               
                 49 
                 693.683615 
                 −0.999609 
                   
                   
                 133.5 
               
               
                 50 
                 −281.164030 
                 −30.395117 
                 SIO2 
                 1.560491 
                 132.9 
               
               
                 51 
                 −613.816799 
                 −6.979889 
                   
                   
                 131.4 
               
               
                 52 
                 0.000000 
                 4.747264 
                   
                   
                 128.8 
               
               
                 53 
                 −323.801518 
                 −45.333595 
                 SIO2 
                 1.560491 
                 131.0 
               
               
                 54 
                 567.522747 
                 −0.997957 
                   
                   
                 129.5 
               
               
                 55 
                 −227.500831 
                 −39.940578 
                 SIO2 
                 1.560491 
                 115.7 
               
               
                 56 
                 2013.736081 
                 −0.994433 
                   
                   
                 111.6 
               
               
                 57 
                 −127.539619 
                 −33.332450 
                 SIO2 
                 1.560491 
                 88.1 
               
               
                 58 
                 −263.904129 
                 −0.995386 
                   
                   
                 79.4 
               
               
                 59 
                 −186.455700 
                 −17.466462 
                 SIO2 
                 1.560491 
                 75.0 
               
               
                 60 
                 −223.493619 
                 −1.000000 
                   
                   
                 65.7 
               
               
                 61 
                 −50.654088 
                 −43.114607 
                 SIO2 
                 1.560491 
                 46.1 
               
               
                 62 
                 0.000000 
                 −1.001571 
                 H2O 
                 1.436823 
                 20.2 
               
               
                 63 
                 0.000000 
                 0.000000 
                   
                   
                 18.4 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 6 
                 15 
                 20 
                 23 
                 29 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.415105E−07 
                 −3.894450E−08 
                  3.025563E−08 
                  1.956249E−08 
                  1.956249E−08 
               
               
                 C2 
                 2.826103E−11 
                  2.477873E−13 
                 −9.725078E−13 
                 −1.254267E−12 
                 −1.254267E−12 
               
               
                 C3 
                 −2.796060E−15  
                 −1.083388E−17 
                  5.264859E−17 
                  9.958049E−17 
                  9.958049E−17 
               
               
                 C4 
                 −2.054534E−20  
                 −9.685453E−22 
                 −2.790853E−21 
                 −1.339908E−20 
                 −1.339908E−20 
               
               
                 C5 
                 2.141589E−23 
                  4.488758E−26 
                  1.033038E−25 
                  1.243181E−24 
                  1.243181E−24 
               
               
                 C6 
                 2.934466E−27 
                 −1.114090E−30 
                 −1.853921E−30 
                 −1.590289E−29 
                 −1.590289E−29 
               
               
                   
               
               
                 SRF 
                 39 
                 40 
                 42 
                 46 
                 53 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 −2.460699E−08 
                 −1.818564E−07 
                  9.053886E−08 
                  2.136533E−08 
                 3.430277E−08 
               
               
                 C2 
                  7.712743E−13 
                 −5.379726E−12 
                 −1.959930E−12 
                  6.940713E−13 
                 2.113104E−13 
               
               
                 C3 
                 −8.069808E−17 
                  1.480406E−15 
                 −3.377347E−17 
                 −1.785783E−17 
                 −8.054096E−17  
               
               
                 C4 
                 −5.118403E−22 
                 −1.519056E−19 
                  3.600872E−20 
                 −1.433861E−21 
                 3.084255E−21 
               
               
                 C5 
                 −4.277639E−25 
                  1.009523E−23 
                 −8.476096E−24 
                  1.884530E−25 
                 −3.491487E−26  
               
               
                 C6 
                  1.160028E−29 
                 −4.043479E−28 
                  3.114715E−28 
                 −8.828841E−30 
                 5.775365E−32 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 SRF 
                 55 
                 58 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 C1 
                 2.382259E−08 
                  9.580994E−08 
               
               
                   
                 C2 
                 −8.346810E−13  
                 −3.279417E−11 
               
               
                   
                 C3 
                 1.015704E−16 
                  5.067874E−15 
               
               
                   
                 C4 
                 5.829694E−22 
                 −5.784345E−19 
               
               
                   
                 C5 
                 6.456340E−26 
                  4.554897E−23 
               
               
                   
                 C6 
                 −7.406922E−30  
                 −1.883439E−27 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 13 
               
               
                   
               
               
                   
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 SURF 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 35.000921 
                   
                   
                 64.0 
               
               
                 1 
                 187.873268 
                 27.994570 
                 SIO2 
                 1.560491 
                 84.8 
               
               
                 2 
                 1232.241084 
                 0.999905 
                   
                   
                 84.9 
               
               
                 3 
                 208.335351 
                 22.691065 
                 SIO2 
                 1.560491 
                 85.8 
               
               
                 4 
                 516.062469 
                 36.805573 
                   
                   
                 84.3 
               
               
                 5 
                 144.085611 
                 11.684135 
                 SIO2 
                 1.560491 
                 79.4 
               
               
                 6 
                 104.200976 
                 18.908624 
                   
                   
                 74.4 
               
               
                 7 
                 198.091293 
                 38.252361 
                 SIO2 
                 1.560491 
                 74.7 
               
               
                 8 
                 −192.861116 
                 2.099088 
                   
                   
                 73.3 
               
               
                 9 
                 68.893595 
                 56.883996 
                 SIO2 
                 1.560491 
                 61.6 
               
               
                 10 
                 85.948719 
                 33.744342 
                   
                   
                 40.9 
               
               
                 11 
                 −114.007614 
                 22.821973 
                 SIO2 
                 1.560491 
                 45.3 
               
               
                 12 
                 −76.222967 
                 9.221322 
                   
                   
                 52.2 
               
               
                 13 
                 −67.210067 
                 9.999789 
                 SIO2 
                 1.560491 
                 53.7 
               
               
                 14 
                 −429.663877 
                 10.809503 
                   
                   
                 70.6 
               
               
                 15 
                 −265.085106 
                 43.979820 
                 SIO2 
                 1.560491 
                 76.7 
               
               
                 16 
                 −101.149234 
                 0.999957 
                   
                   
                 85.3 
               
               
                 17 
                 −188.336349 
                 61.381983 
                 SIO2 
                 1.560491 
                 94.4 
               
               
                 18 
                 −125.228059 
                 0.999649 
                   
                   
                 108.4 
               
               
                 19 
                 −831.599269 
                 31.650721 
                 SIO2 
                 1.560491 
                 113.5 
               
               
                 20 
                 −227.778209 
                 70.000634 
                   
                   
                 115.5 
               
               
                 21 
                 0.000000 
                 −10.976723 
                 REFL 
                   
                 113.6 
               
               
                 22 
                 −197.591390 
                 −49.195844 
                 SIO2 
                 1.560491 
                 114.4 
               
               
                 23 
                 1113.814097 
                 −282.271651 
                   
                   
                 112.2 
               
               
                 24 
                 95.811897 
                 −12.500000 
                 SIO2 
                 1.560491 
                 68.9 
               
               
                 25 
                 1585.519591 
                 −38.490833 
                   
                   
                 81.2 
               
               
                 26 
                 106.142717 
                 −12.500000 
                 SIO2 
                 1.560491 
                 83.5 
               
               
                 27 
                 160.434031 
                 −12.092178 
                   
                   
                 98.0 
               
               
                 28 
                 144.603311 
                 12.092178 
                 REFL 
                   
                 101.8 
               
               
                 29 
                 160.434031 
                 12.500000 
                 SIO2 
                 1.560491 
                 98.0 
               
               
                 30 
                 106.142717 
                 38.490833 
                   
                   
                 83.5 
               
               
                 31 
                 1585.519591 
                 12.500000 
                 SIO2 
                 1.560491 
                 81.2 
               
               
                 32 
                 95.811897 
                 282.271651 
                   
                   
                 68.9 
               
               
                 33 
                 1113.814097 
                 49.195844 
                 SIO2 
                 1.560491 
                 112.2 
               
               
                 34 
                 −197.591390 
                 10.976723 
                   
                   
                 114.4 
               
               
                 35 
                 0.000000 
                 −70.000758 
                 REFL 
                   
                 113.0 
               
               
                 36 
                 −227.942708 
                 −45.666153 
                 SIO2 
                 1.560491 
                 113.9 
               
               
                 37 
                 815.467694 
                 −8.857490 
                   
                   
                 111.9 
               
               
                 38 
                 −130.706498 
                 −42.732270 
                 SIO2 
                 1.560491 
                 96.7 
               
               
                 39 
                 −422.473074 
                 −3.774367 
                   
                   
                 91.0 
               
               
                 40 
                 −347.973618 
                 −10.000122 
                 SIO2 
                 1.560491 
                 87.2 
               
               
                 41 
                 −187.015492 
                 −26.831797 
                   
                   
                 79.4 
               
               
                 42 
                 305.312838 
                 −9.999427 
                 SIO2 
                 1.560491 
                 77.7 
               
               
                 43 
                 −96.429310 
                 −63.819408 
                   
                   
                 67.9 
               
               
                 44 
                 128.506823 
                 −9.999684 
                 SIO2 
                 1.560491 
                 71.4 
               
               
                 45 
                 −306.117569 
                 −15.977415 
                   
                   
                 85.1 
               
               
                 46 
                 4806.899558 
                 −32.925545 
                 SIO2 
                 1.560491 
                 89.1 
               
               
                 47 
                 230.072868 
                 −16.329646 
                   
                   
                 96.4 
               
               
                 48 
                 1322.097164 
                 −30.272168 
                 SIO2 
                 1.560491 
                 111.8 
               
               
                 49 
                 252.570224 
                 −1.000013 
                   
                   
                 117.3 
               
               
                 50 
                 −862.460198 
                 −42.042752 
                 SIO2 
                 1.560491 
                 133.4 
               
               
                 51 
                 448.126973 
                 −5.878180 
                   
                   
                 135.8 
               
               
                 52 
                 −378.669699 
                 −51.982596 
                 SIO2 
                 1.560491 
                 142.6 
               
               
                 53 
                 730.087868 
                 −26.644994 
                   
                   
                 141.8 
               
               
                 54 
                 0.000000 
                 0.211836 
                   
                   
                 130.3 
               
               
                 55 
                 −454.237341 
                 −34.638587 
                 SIO2 
                 1.560491 
                 132.4 
               
               
                 56 
                 896.710905 
                 −0.999763 
                   
                   
                 131.1 
               
               
                 57 
                 −281.292658 
                 −31.904925 
                 SIO2 
                 1.560491 
                 122.1 
               
               
                 58 
                 −1508.491985 
                 −0.999650 
                   
                   
                 118.8 
               
               
                 59 
                 −157.343378 
                 −32.737319 
                 SIO2 
                 1.560491 
                 105.3 
               
               
                 60 
                 −431.549831 
                 −0.998214 
                   
                   
                 98.8 
               
               
                 61 
                 −227.748250 
                 −34.282018 
                 SIO2 
                 1.560491 
                 96.4 
               
               
                 62 
                 1679.133063 
                 −1.000000 
                   
                   
                 90.0 
               
               
                 63 
                 −57.914528 
                 −47.987219 
                 SIO2 
                 1.560491 
                 52.2 
               
               
                 64 
                 0.000000 
                 −3.000000 
                 H2O 
                 1.436822 
                 24.4 
               
               
                 65 
                 0.000000 
                 0.000000 
                   
                   
                 19.0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 13A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 8 
                 19 
                 22 
                 25 
                 31 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 8.300393E−08 
                 −1.573837E−08 
                 1.023614E−08 
                  2.221568E−08 
                  2.221568E−08 
               
               
                 C2 
                 1.027628E−11 
                 −1.239737E−13 
                 1.645106E−13 
                 −1.740421E−12 
                 −1.740421E−12 
               
               
                 C3 
                 −1.162954E−15  
                  4.333229E−19 
                 5.476658E−18 
                  8.521877E−17 
                  8.521877E−17 
               
               
                 C4 
                 2.985096E−19 
                  4.074898E−23 
                 5.702605E−23 
                 −2.769929E−21 
                 −2.769929E−21 
               
               
                 C5 
                 −2.802134E−23  
                 −1.053291E−26 
                 9.144213E−28 
                 −2.436823E−25 
                 −2.436823E−25 
               
               
                 C6 
                 1.422951E−27 
                  3.216727E−31 
                 2.477447E−32 
                  1.867891E−29 
                  1.867891E−29 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 34 
                 37 
                 39 
                 42 
                 48 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.023614E−08 
                 −2.156946E−08 
                  2.940607E−08 
                 −4.027138E−08 
                 3.236874E−08 
               
               
                 C2 
                 1.645106E−13 
                  7.245612E−13 
                 −3.554065E−12 
                 −8.699926E−12 
                 −3.262283E−13  
               
               
                 C3 
                 5.476658E−18 
                 −3.214615E−17 
                  2.494890E−16 
                  1.342629E−15 
                 2.281353E−17 
               
               
                 C4 
                 5.702605E−23 
                  1.250838E−21 
                 −1.750741E−20 
                 −1.587155E−19 
                 2.583318E−22 
               
               
                 C5 
                 9.144213E−28 
                 −3.654841E−26 
                  8.304704E−25 
                  1.051342E−23 
                 −8.007782E−27  
               
               
                 C6 
                 2.477447E−32 
                  5.939707E−31 
                 −4.233041E−29 
                 −3.667649E−28 
                 2.555841E−30 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 SRF 
                 55 
                 57 
                 60 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                  2.858710E−08 
                 −6.660513E−09 
                 −8.504243E−08 
               
               
                   
                 C2 
                 −4.529671E−13 
                  1.798520E−13 
                  9.820443E−13 
               
               
                   
                 C3 
                 −2.789924E−17 
                  8.149876E−17 
                 −5.540310E−17 
               
               
                   
                 C4 
                  2.259110E−21 
                 −5.213396E−22 
                  1.576819E−20 
               
               
                   
                 C5 
                 −7.538599E−26 
                 −1.301705E−27 
                 −9.640368E−25 
               
               
                   
                 C6 
                  9.633331E−31 
                 −5.575917E−31 
                  1.171801E−29 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 15 
               
               
                   
               
               
                   
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 SURF 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 35.638328 
                   
                   
                 64.5 
               
               
                 1 
                 180.670546 
                 28.377083 
                 SIO2 
                 1.560491 
                 86.9 
               
               
                 2 
                 823.598018 
                 1.194225 
                   
                   
                 86.9 
               
               
                 3 
                 205.952639 
                 21.462318 
                 SIO2 
                 1.560491 
                 87.9 
               
               
                 4 
                 398.186838 
                 32.742116 
                   
                   
                 86.4 
               
               
                 5 
                 132.286925 
                 9.999671 
                 SIO2 
                 1.560491 
                 82.8 
               
               
                 6 
                 105.118100 
                 22.332626 
                   
                   
                 78.4 
               
               
                 7 
                 169.334381 
                 39.894990 
                 SIO2 
                 1.560491 
                 78.9 
               
               
                 8 
                 −204.634515 
                 0.998375 
                   
                   
                 77.3 
               
               
                 9 
                 71.137197 
                 56.763393 
                 SIO2 
                 1.560491 
                 63.5 
               
               
                 10 
                 89.028585 
                 28.411826 
                   
                   
                 42.3 
               
               
                 11 
                 −109.689407 
                 29.990063 
                 SIO2 
                 1.560491 
                 42.5 
               
               
                 12 
                 −79.244543 
                 11.316478 
                   
                   
                 52.9 
               
               
                 13 
                 −69.719014 
                 9.999481 
                 SIO2 
                 1.560491 
                 55.1 
               
               
                 14 
                 −486.086468 
                 8.908815 
                   
                   
                 72.6 
               
               
                 15 
                 −280.858669 
                 63.675056 
                 SIO2 
                 1.560491 
                 77.0 
               
               
                 16 
                 −111.752476 
                 0.999172 
                   
                   
                 95.1 
               
               
                 17 
                 −263.723959 
                 47.422516 
                 SIO2 
                 1.560491 
                 107.8 
               
               
                 18 
                 −134.607968 
                 0.998507 
                   
                   
                 113.2 
               
               
                 19 
                 −648.995845 
                 28.867753 
                 SIO2 
                 1.560491 
                 116.3 
               
               
                 20 
                 −239.623615 
                 69.998695 
                   
                   
                 118.1 
               
               
                 21 
                 0.000000 
                 −9.999382 
                 REFL 
                   
                 115.6 
               
               
                 22 
                 −176.982011 
                 −52.138664 
                 SIO2 
                 1.560491 
                 117.7 
               
               
                 23 
                 2325.743514 
                 −250.507300 
                   
                   
                 115.3 
               
               
                 24 
                 98.260574 
                 −12.500000 
                 SIO2 
                 1.560491 
                 68.0 
               
               
                 25 
                 8846.828964 
                 −46.770944 
                   
                   
                 78.6 
               
               
                 26 
                 91.149491 
                 −12.500000 
                 SIO2 
                 1.560491 
                 80.6 
               
               
                 27 
                 149.955261 
                 −18.614447 
                   
                   
                 98.7 
               
               
                 28 
                 143.121066 
                 18.614447 
                 REFL 
                   
                 106.4 
               
               
                 29 
                 149.955261 
                 12.500000 
                 SIO2 
                 1.560491 
                 98.7 
               
               
                 30 
                 91.149491 
                 46.770944 
                   
                   
                 80.6 
               
               
                 31 
                 8846.828964 
                 12.500000 
                 SIO2 
                 1.560491 
                 78.6 
               
               
                 32 
                 98.260574 
                 250.507300 
                   
                   
                 68.0 
               
               
                 33 
                 2325.743514 
                 52.138664 
                 SIO2 
                 1.560491 
                 115.3 
               
               
                 34 
                 −176.982011 
                 9.999382 
                   
                   
                 117.7 
               
               
                 35 
                 0.000000 
                 −69.999093 
                 REFL 
                   
                 117.4 
               
               
                 36 
                 −198.540813 
                 −50.399536 
                 SIO2 
                 1.560491 
                 120.7 
               
               
                 37 
                 −96842.830748 
                 −0.998438 
                   
                   
                 118.2 
               
               
                 38 
                 −171.973861 
                 −30.749387 
                 SIO2 
                 1.560491 
                 106.4 
               
               
                 39 
                 −310.515975 
                 −0.999047 
                   
                   
                 100.9 
               
               
                 40 
                 −148.789628 
                 −29.674304 
                 SIO2 
                 1.560491 
                 92.9 
               
               
                 41 
                 −216.223375 
                 −29.457017 
                   
                   
                 83.9 
               
               
                 42 
                 244.105965 
                 −9.998957 
                 SIO2 
                 1.560491 
                 81.6 
               
               
                 43 
                 −94.244903 
                 −51.985700 
                   
                   
                 68.7 
               
               
                 44 
                 177.704589 
                 −9.999140 
                 SIO2 
                 1.560491 
                 70.5 
               
               
                 45 
                 −255.547186 
                 −23.809565 
                   
                   
                 80.1 
               
               
                 46 
                 1016.476754 
                 −31.174795 
                 SIO2 
                 1.560491 
                 85.3 
               
               
                 47 
                 185.094367 
                 −0.999190 
                   
                   
                 93.0 
               
               
                 48 
                 1691.382932 
                 −25.547970 
                 SIO2 
                 1.560491 
                 105.3 
               
               
                 49 
                 356.397350 
                 −45.184652 
                   
                   
                 109.5 
               
               
                 50 
                 −673.758971 
                 −45.536220 
                 SIO2 
                 1.560491 
                 137.5 
               
               
                 51 
                 386.080342 
                 −0.998330 
                   
                   
                 139.3 
               
               
                 52 
                 −725.704793 
                 −34.052538 
                 SIO2 
                 1.560491 
                 143.2 
               
               
                 53 
                 1177.576128 
                 −20.729220 
                   
                   
                 143.2 
               
               
                 54 
                 0.000000 
                 19.731628 
                   
                   
                 138.3 
               
               
                 55 
                 −296.953200 
                 −49.211938 
                 SIO2 
                 1.560491 
                 142.1 
               
               
                 56 
                 755.844934 
                 −0.996608 
                   
                   
                 140.3 
               
               
                 57 
                 −413.530408 
                 −40.022653 
                 SIO2 
                 1.560491 
                 135.6 
               
               
                 58 
                 728.550434 
                 −0.994509 
                   
                   
                 133.1 
               
               
                 59 
                 −253.678570 
                 −33.049432 
                 SIO2 
                 1.560491 
                 114.4 
               
               
                 60 
                 −3840.733691 
                 −0.992017 
                   
                   
                 108.6 
               
               
                 61 
                 −147.857222 
                 −36.663873 
                 SIO2 
                 1.560491 
                 91.0 
               
               
                 62 
                 −727.362791 
                 −1.000000 
                   
                   
                 82.4 
               
               
                 63 
                 −54.588882 
                 −41.518373 
                 SIO2 
                 1.560491 
                 49.4 
               
               
                 64 
                 0.000000 
                 −3.000000 
                 H2O 
                 1.436822 
                 25.6 
               
               
                 65 
                 0.000000 
                 0.000000 
                   
                   
                 19.1 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 15A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 8 
                 19 
                 22 
                 25 
                 31 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.080775E−07 
                 −1.359371E−08 
                 1.195268E−08 
                  1.894952E−08 
                  1.894952E−08 
               
               
                 C2 
                 4.576422E−12 
                 −1.179706E−13 
                 3.137653E−13 
                 −2.377925E−12 
                 −2.377925E−12 
               
               
                 C3 
                 −8.540180E−16  
                 −1.702891E−18 
                 4.990292E−18 
                  2.890682E−16 
                  2.890682E−16 
               
               
                 C4 
                 2.711292E−19 
                  8.483261E−23 
                 5.081387E−22 
                 −5.626586E−20 
                 −5.626586E−20 
               
               
                 C5 
                 −3.150111E−23  
                 −9.645405E−27 
                 −1.599365E−26  
                  6.907483E−24 
                  6.907483E−24 
               
               
                 C6 
                 1.652368E−27 
                  2.669817E−31 
                 6.313609E−31 
                 −3.643846E−28 
                 −3.643846E−28 
               
               
                   
               
               
                 SRF 
                 34 
                 42 
                 46 
                 48 
                 51 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.195268E−08 
                 −5.071114E−08 
                 2.526230E−08 
                  1.948430E−08 
                 −7.924272E−09 
               
               
                 C2 
                 3.137653E−13 
                 −7.730551E−12 
                 5.333528E−12 
                 −3.427570E−12 
                 −2.800312E−13 
               
               
                 C3 
                 4.990292E−18 
                  1.390231E−15 
                 −2.388835E−16  
                  8.808674E−17 
                 −1.107739E−18 
               
               
                 C4 
                 5.081387E−22 
                 −1.451491E−19 
                 1.259420E−20 
                 −8.959654E−22 
                 −6.249802E−22 
               
               
                 C5 
                 −1.599365E−26  
                  9.288570E−24 
                 −1.438626E−24  
                  8.169992E−25 
                  3.539057E−26 
               
               
                 C6 
                 6.313609E−31 
                 −2.767389E−28 
                 4.673358E−29 
                 −4.150555E−29 
                 −3.955788E−31 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 SRF 
                 56 
                 57 
                 60 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                 −5.185154E−08 
                 2.760546E−08 
                  2.284067E−09 
               
               
                   
                 C2 
                  1.533838E−12 
                 −1.425919E−12  
                 −5.023236E−12 
               
               
                   
                 C3 
                 −3.899899E−17 
                 4.438919E−17 
                  4.371011E−16 
               
               
                   
                 C4 
                  2.974803E−21 
                 1.556484E−21 
                 −3.186523E−20 
               
               
                   
                 C5 
                 −1.127749E−25 
                 −7.877661E−26  
                  1.530451E−24 
               
               
                   
                 C6 
                  1.290864E−30 
                 3.875637E−31 
                 −3.713691E−29 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 16 
               
               
                   
               
               
                   
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 SURF 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 35.000018 
                   
                   
                 61.5 
               
               
                 1 
                 176.014829 
                 27.505489 
                 SIO2 
                 1.560491 
                 83.2 
               
               
                 2 
                 841.641338 
                 3.539440 
                   
                   
                 83.3 
               
               
                 3 
                 235.708002 
                 18.995896 
                 SIO2 
                 1.560491 
                 84.2 
               
               
                 4 
                 435.386108 
                 31.751453 
                   
                   
                 83.2 
               
               
                 5 
                 145.827863 
                 9.997737 
                 SIO2 
                 1.560491 
                 81.5 
               
               
                 6 
                 108.756276 
                 21.241416 
                   
                   
                 77.5 
               
               
                 7 
                 172.246858 
                 43.116768 
                 SIO2 
                 1.560491 
                 78.7 
               
               
                 8 
                 −170.835113 
                 1.011739 
                   
                   
                 77.5 
               
               
                 9 
                 69.519772 
                 62.982649 
                 SIO2 
                 1.560491 
                 62.1 
               
               
                 10 
                 79.357512 
                 24.125307 
                   
                   
                 37.1 
               
               
                 11 
                 −105.554185 
                 28.151777 
                 SIO2 
                 1.560491 
                 40.1 
               
               
                 12 
                 −75.432491 
                 8.970185 
                   
                   
                 50.0 
               
               
                 13 
                 −65.960377 
                 9.998436 
                 SIO2 
                 1.560491 
                 51.6 
               
               
                 14 
                 −458.378416 
                 15.879266 
                   
                   
                 68.1 
               
               
                 15 
                 −182.010566 
                 40.279435 
                 SIO2 
                 1.560491 
                 74.6 
               
               
                 16 
                 −98.619683 
                 0.998823 
                   
                   
                 84.4 
               
               
                 17 
                 −298.466841 
                 53.135226 
                 SIO2 
                 1.560491 
                 100.4 
               
               
                 18 
                 −121.383228 
                 0.999120 
                   
                   
                 106.3 
               
               
                 19 
                 −835.480319 
                 32.135277 
                 SIO2 
                 1.560491 
                 109.9 
               
               
                 20 
                 −214.880198 
                 81.470423 
                   
                   
                 111.6 
               
               
                 21 
                 0.000000 
                 −104.650759 
                 REFL 
                   
                 105.0 
               
               
                 22 
                 −181.003736 
                 −50.001353 
                 SIO2 
                 1.560491 
                 108.2 
               
               
                 23 
                 25242.924145 
                 −247.127318 
                   
                   
                 104.9 
               
               
                 24 
                 102.272953 
                 −12.500000 
                 SIO2 
                 1.560491 
                 70.6 
               
               
                 25 
                 2103.060508 
                 −45.023548 
                   
                   
                 79.1 
               
               
                 26 
                 93.409938 
                 −12.500000 
                 SIO2 
                 1.560491 
                 81.3 
               
               
                 27 
                 183.538848 
                 −17.774476 
                   
                   
                 102.5 
               
               
                 28 
                 145.905578 
                 17.774476 
                 REFL 
                   
                 106.5 
               
               
                 29 
                 183.538848 
                 12.500000 
                 SIO2 
                 1.560491 
                 102.5 
               
               
                 30 
                 93.409938 
                 45.023548 
                   
                   
                 81.3 
               
               
                 31 
                 2103.060508 
                 12.500000 
                 SIO2 
                 1.560491 
                 79.1 
               
               
                 32 
                 102.272953 
                 247.127318 
                   
                   
                 70.6 
               
               
                 33 
                 25242.924145 
                 50.001353 
                 SIO2 
                 1.560491 
                 104.9 
               
               
                 34 
                 −181.003736 
                 104.650759 
                   
                   
                 108.2 
               
               
                 35 
                 0.000000 
                 −69.997840 
                 REFL 
                   
                 105.8 
               
               
                 36 
                 −274.353554 
                 −38.229015 
                 SIO2 
                 1.560491 
                 110.1 
               
               
                 37 
                 1131.690506 
                 −0.997876 
                   
                   
                 108.9 
               
               
                 38 
                 −183.833011 
                 −33.580596 
                 SIO2 
                 1.560491 
                 101.6 
               
               
                 39 
                 −632.386130 
                 −3.643030 
                   
                   
                 97.6 
               
               
                 40 
                 −138.532192 
                 −34.568737 
                 SIO2 
                 1.560491 
                 86.8 
               
               
                 41 
                 −189.656554 
                 −26.890307 
                   
                   
                 75.9 
               
               
                 42 
                 255.989593 
                 −9.998587 
                 SIO2 
                 1.560491 
                 73.9 
               
               
                 43 
                 −92.462677 
                 −50.122191 
                   
                   
                 64.9 
               
               
                 44 
                 175.417954 
                 −9.998324 
                 SIO2 
                 1.560491 
                 68.1 
               
               
                 45 
                 −239.557458 
                 −20.895117 
                   
                   
                 78.3 
               
               
                 46 
                 893.327075 
                 −36.743354 
                 SIO2 
                 1.560491 
                 83.5 
               
               
                 47 
                 180.351521 
                 −1.580032 
                   
                   
                 92.3 
               
               
                 48 
                 1793.077203 
                 −23.224027 
                 SIO2 
                 1.560491 
                 102.7 
               
               
                 49 
                 346.025735 
                 −46.740042 
                   
                   
                 107.1 
               
               
                 50 
                 −587.720308 
                 −49.840882 
                 SIO2 
                 1.560491 
                 138.2 
               
               
                 51 
                 362.715565 
                 −0.996413 
                   
                   
                 139.9 
               
               
                 52 
                 −802.776800 
                 −32.541316 
                 SIO2 
                 1.560491 
                 143.2 
               
               
                 53 
                 1200.879163 
                 −20.610535 
                   
                   
                 143.1 
               
               
                 54 
                 0.000000 
                 19.614848 
                   
                   
                 138.0 
               
               
                 55 
                 −277.707719 
                 −52.291236 
                 SIO2 
                 1.560491 
                 141.8 
               
               
                 56 
                 708.666176 
                 −0.995494 
                   
                   
                 139.7 
               
               
                 57 
                 −424.462858 
                 −35.408449 
                 SIO2 
                 1.560491 
                 134.6 
               
               
                 58 
                 920.517618 
                 −0.994818 
                   
                   
                 131.9 
               
               
                 59 
                 −257.650413 
                 −33.302544 
                 SIO2 
                 1.560491 
                 115.0 
               
               
                 60 
                 −3892.659133 
                 −0.993481 
                   
                   
                 109.3 
               
               
                 61 
                 −150.518437 
                 −37.001664 
                 SIO2 
                 1.560491 
                 91.7 
               
               
                 62 
                 −815.328045 
                 −1.000000 
                   
                   
                 83.2 
               
               
                 63 
                 −54.709895 
                 −42.146539 
                 SIO2 
                 1.560491 
                 49.5 
               
               
                 64 
                 0.000000 
                 −3.000000 
                 H2O 
                 1.436822 
                 24.8 
               
               
                 65 
                 0.000000 
                 0.000000 
                   
                   
                 18.4 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 16A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 8 
                 19 
                 22 
                 25 
                 31 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 9.477707E−08 
                 −1.630325E−08 
                 8.446555E−09 
                 3.545371E−09 
                 3.545371E−09 
               
               
                 C2 
                 1.961231E−12 
                 −9.812446E−14 
                 2.275492E−13 
                 −6.774437E−13  
                 −6.774437E−13  
               
               
                 C3 
                 −4.595943E−16  
                 −1.945238E−18 
                 −8.360514E−19  
                 4.237596E−17 
                 4.237596E−17 
               
               
                 C4 
                 2.712352E−19 
                  2.190264E−22 
                 1.164424E−21 
                 −5.726376E−21  
                 −5.726376E−21  
               
               
                 C5 
                 −3.717129E−23  
                 −2.392299E−26 
                 −6.873389E−26  
                 1.719638E−25 
                 1.719638E−25 
               
               
                 C6 
                 2.062145E−27 
                  8.993812E−31 
                 2.030241E−30 
                 1.264086E−29 
                 1.264086E−29 
               
               
                   
               
               
                 SRF 
                 34 
                 42 
                 46 
                 48 
                 51 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 8.446555E−09 
                 −3.731377E−08 
                 −7.541203E−09 
                  3.402805E−08 
                 −7.582220E−09 
               
               
                 C2 
                 2.275492E−13 
                 −5.506103E−12 
                  3.280912E−12 
                 −2.111476E−12 
                 −1.607342E−13 
               
               
                 C3 
                 −8.360514E−19  
                  1.183283E−15 
                 −1.338960E−16 
                  3.392400E−17 
                 −9.929315E−18 
               
               
                 C4 
                 1.164424E−21 
                 −1.705010E−19 
                 −2.204551E−20 
                 −3.518123E−21 
                 −4.709955E−22 
               
               
                 C5 
                 −6.873389E−26  
                  1.532771E−23 
                  5.087511E−26 
                  1.006578E−24 
                  4.064977E−26 
               
               
                 C6 
                 2.030241E−30 
                 −6.241836E−28 
                 −4.751065E−28 
                 −2.276157E−29 
                 −5.868799E−31 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 SRF 
                 56 
                 57 
                 60 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                 −5.466505E−08 
                 3.173474E−08 
                  4.604026E−09 
               
               
                   
                 C2 
                  1.620583E−12 
                 −1.360966E−12  
                 −4.261817E−12 
               
               
                   
                 C3 
                 −3.331287E−17 
                 4.744992E−17 
                  3.289463E−16 
               
               
                   
                 C4 
                  2.561164E−21 
                 9.163771E−22 
                 −2.280425E−20 
               
               
                   
                 C5 
                 −1.070898E−25 
                 −7.066436E−26  
                  9.960289E−25 
               
               
                   
                 C6 
                  1.395421E−30 
                 7.159877E−31 
                 −2.271390E−29 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 17 
               
               
                   
               
               
                   
                   
                 THICK- 
                 MATE- 
                   
                 SEMI- 
               
               
                 SURF 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 DIAM. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 0.000000 
                 35.062171 
                   
                   
                 61.5 
               
               
                 1 
                 160.377892 
                 33.915692 
                 SIO2 
                 1.560491 
                 85.2 
               
               
                 2 
                 4339.545820 
                 35.211752 
                   
                   
                 85.0 
               
               
                 3 
                 134.501543 
                 9.996831 
                 SIO2 
                 1.560491 
                 83.7 
               
               
                 4 
                 111.692176 
                 24.343835 
                   
                   
                 80.0 
               
               
                 5 
                 176.022408 
                 44.412851 
                 SIO2 
                 1.560491 
                 81.0 
               
               
                 6 
                 −158.125766 
                 1.097941 
                   
                   
                 79.5 
               
               
                 7 
                 70.127955 
                 63.281412 
                 SIO2 
                 1.560491 
                 62.6 
               
               
                 8 
                 80.899024 
                 23.149420 
                   
                   
                 37.4 
               
               
                 9 
                 −104.439732 
                 28.493683 
                 SIO2 
                 1.560491 
                 39.7 
               
               
                 10 
                 −76.691544 
                 9.373106 
                   
                   
                 50.2 
               
               
                 11 
                 −66.201313 
                 9.999364 
                 SIO2 
                 1.560491 
                 51.9 
               
               
                 12 
                 −449.321456 
                 12.356383 
                   
                   
                 69.1 
               
               
                 13 
                 −193.830863 
                 41.850652 
                 SIO2 
                 1.560491 
                 73.7 
               
               
                 14 
                 −96.808240 
                 0.997395 
                   
                   
                 83.6 
               
               
                 15 
                 −309.193570 
                 53.879882 
                 SIO2 
                 1.560491 
                 100.4 
               
               
                 16 
                 −121.506051 
                 0.996721 
                   
                   
                 106.4 
               
               
                 17 
                 −1347.934891 
                 32.667851 
                 SIO2 
                 1.560491 
                 110.7 
               
               
                 18 
                 −232.958167 
                 69.997839 
                   
                   
                 112.2 
               
               
                 19 
                 0.000000 
                 −95.009945 
                 REFL 
                   
                 106.8 
               
               
                 20 
                 −169.601782 
                 −49.964697 
                 SIO2 
                 1.560491 
                 108.4 
               
               
                 21 
                 −2559.597028 
                 −244.909101 
                   
                   
                 104.7 
               
               
                 22 
                 94.645450 
                 −12.500000 
                 SIO2 
                 1.560491 
                 70.0 
               
               
                 23 
                 2366.726589 
                 −50.185589 
                   
                   
                 83.9 
               
               
                 24 
                 96.645650 
                 −12.500000 
                 SIO2 
                 1.560491 
                 86.5 
               
               
                 25 
                 158.153978 
                 −11.143815 
                   
                   
                 106.9 
               
               
                 26 
                 150.128583 
                 11.143815 
                 REFL 
                   
                 111.0 
               
               
                 27 
                 158.153978 
                 12.500000 
                 SIO2 
                 1.560491 
                 106.9 
               
               
                 28 
                 96.645650 
                 50.185589 
                   
                   
                 86.5 
               
               
                 29 
                 2366.726589 
                 12.500000 
                 SIO2 
                 1.560491 
                 83.9 
               
               
                 30 
                 94.645450 
                 244.909101 
                   
                   
                 70.0 
               
               
                 31 
                 −2559.597028 
                 49.964697 
                 SIO2 
                 1.560491 
                 104.7 
               
               
                 32 
                 −169.601782 
                 95.009945 
                   
                   
                 108.4 
               
               
                 33 
                 0.000000 
                 −69.996314 
                 REFL 
                   
                 106.9 
               
               
                 34 
                 −281.792007 
                 −41.385881 
                 SIO2 
                 1.560491 
                 110.8 
               
               
                 35 
                 657.889902 
                 −0.997396 
                   
                   
                 109.7 
               
               
                 36 
                 −174.312217 
                 −32.438650 
                 SIO2 
                 1.560491 
                 100.1 
               
               
                 37 
                 −476.477690 
                 −1.935634 
                   
                   
                 95.7 
               
               
                 38 
                 −123.498799 
                 −34.625674 
                 SIO2 
                 1.560491 
                 85.0 
               
               
                 39 
                 −152.214034 
                 −29.454227 
                   
                   
                 73.4 
               
               
                 40 
                 230.398053 
                 −9.988522 
                 SIO2 
                 1.560491 
                 71.5 
               
               
                 41 
                 −84.263230 
                 −42.301978 
                   
                   
                 62.8 
               
               
                 42 
                 148.358426 
                 −9.995751 
                 SIO2 
                 1.560491 
                 64.2 
               
               
                 43 
                 −285.965468 
                 −29.500257 
                   
                   
                 76.2 
               
               
                 44 
                 1365.214672 
                 −52.201213 
                 SIO2 
                 1.560491 
                 91.3 
               
               
                 45 
                 197.964169 
                 −1.405485 
                   
                   
                 110.1 
               
               
                 46 
                 471.452295 
                 −43.072393 
                 SIO2 
                 1.560491 
                 120.4 
               
               
                 47 
                 209.873148 
                 −1.120291 
                   
                   
                 130.5 
               
               
                 48 
                 −1186.156898 
                 −60.630783 
                 SIO2 
                 1.560491 
                 155.2 
               
               
                 49 
                 325.015642 
                 −0.999174 
                   
                   
                 157.9 
               
               
                 50 
                 −2211.880008 
                 −27.251892 
                 SIO2 
                 1.560491 
                 162.5 
               
               
                 51 
                 1353.381133 
                 −0.997683 
                   
                   
                 163.0 
               
               
                 52 
                 −333.578758 
                 −60.245043 
                 SIO2 
                 1.560491 
                 162.7 
               
               
                 53 
                 664.853013 
                 −3.960500 
                   
                   
                 160.4 
               
               
                 54 
                 0.000000 
                 2.974292 
                   
                   
                 153.2 
               
               
                 55 
                 −436.081909 
                 −40.203050 
                 SIO2 
                 1.560491 
                 152.1 
               
               
                 56 
                 1058.418471 
                 −0.974875 
                   
                   
                 149.3 
               
               
                 57 
                 −242.988440 
                 −46.663567 
                 SIO2 
                 1.560491 
                 127.0 
               
               
                 58 
                 1737.489827 
                 −0.944194 
                   
                   
                 120.7 
               
               
                 59 
                 −113.935104 
                 −37.162408 
                 SIO2 
                 1.560491 
                 86.5 
               
               
                 60 
                 −237.094762 
                 −1.000000 
                   
                   
                 75.1 
               
               
                 61 
                 −53.008742 
                 −37.444181 
                 SIO2 
                 1.560491 
                 48.1 
               
               
                 62 
                 0.000000 
                 −3.000000 
                 H2O 
                 1.436823 
                 26.7 
               
               
                 63 
                 0.000000 
                 0.000000 
                   
                   
                 18.4 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 17A 
               
               
                   
               
               
                 ASPHERIC CONSTANTS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 SRF 
                 6 
                 17 
                 20 
                 23 
                 29 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                  1.567356E−07 
                 −1.504554E−08 
                 1.102741E−08 
                 1.329977E−08 
                 1.329977E−08 
               
               
                 C2 
                 −1.454311E−12 
                 −1.033827E−13 
                 3.161475E−13 
                 −6.446967E−13  
                 −6.446967E−13  
               
               
                 C3 
                 −4.821299E−16 
                 −5.875858E−18 
                 −3.234527E−18  
                 2.574587E−17 
                 2.574587E−17 
               
               
                 C4 
                  3.177351E−19 
                  7.367131E−22 
                 1.863348E−21 
                 2.145483E−21 
                 2.145483E−21 
               
               
                 C5 
                 −4.247779E−23 
                 −5.690740E−26 
                 −1.058278E−25  
                 −6.859442E−25  
                 −6.859442E−25  
               
               
                 C6 
                  2.417313E−27 
                  1.690737E−30 
                 3.288177E−30 
                 4.363205E−29 
                 4.363205E−29 
               
               
                   
               
               
                 SRF 
                 32 
                 40 
                 44 
                 46 
                 49 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.102741E−08 
                 −7.623733E−08 
                 5.961950E−08 
                  4.163425E−08 
                  1.556511E−08 
               
               
                 C2 
                 3.161475E−13 
                 −2.696128E−12 
                 2.260719E−12 
                 −2.205874E−12 
                 −9.513867E−13 
               
               
                 C3 
                 −3.234527E−18  
                  1.720996E−15 
                 1.675440E−17 
                 −2.145810E−18 
                  1.334037E−17 
               
               
                 C4 
                 1.863348E−21 
                 −3.583626E−19 
                 9.620913E−21 
                 −9.265446E−21 
                 −6.577842E−22 
               
               
                 C5 
                 −1.058278E−25  
                  3.893269E−23 
                 −4.439958E−24  
                  1.471307E−24 
                  4.785308E−26 
               
               
                 C6 
                 3.288177E−30 
                 −1.781650E−27 
                 −3.165933E−29  
                 −4.599952E−29 
                 −1.010940E−30 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 SRF 
                 53 
                 55 
                 58 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                 −4.190276E−08 
                  3.093715E−08 
                  6.193974E−09 
               
               
                   
                 C2 
                  1.643663E−12 
                 −1.212659E−12 
                 −3.507726E−12 
               
               
                   
                 C3 
                 −4.727323E−17 
                  4.234860E−17 
                  2.841523E−16 
               
               
                   
                 C4 
                  7.314393E−22 
                 −1.652445E−21 
                 −1.871154E−20 
               
               
                   
                 C5 
                  7.386195E−27 
                  5.642952E−26 
                  7.577332E−25 
               
               
                   
                 C6 
                 −2.389707E−31 
                 −7.153949E−31 
                 −1.502450E−29 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 18 
               
               
                   
               
               
                 Tab. 
                 D max   
                 D M   
                 D M /D max   
                 Y′ 
                 NA 
                 N L   
                 N OP   
                 COMP1 
                 COMP2 
                 COMP3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 256.8 
                 235.2 
                 0.92 
                 14.4 
                 1.2 
                 23 
                 3 
                 12.4 
                 284.5 
                 94.8 
               
               
                 3 
                 252.9 
                 243.3 
                 0.96 
                 14.4 
                 1.1 
                 25 
                 3 
                 14.5 
                 362.4 
                 120.8 
               
               
                 9 
                 270.6 
                 230.6 
                 0.85 
                 16.0 
                 1.2 
                 28 
                 3 
                 11.7 
                 328.9 
                 109.6 
               
               
                 10 
                 277.8 
                 236.4 
                 0.85 
                 16.0 
                 1.2 
                 28 
                 3 
                 12.1 
                 337.6 
                 112.5 
               
               
                 11 
                 293.4 
                 197.4 
                 0.67 
                 16.0 
                 1.3 
                 27 
                 3 
                 10.9 
                 293.0 
                 97.7 
               
               
                 12 
                 267.0 
                 201.0 
                 0.75 
                 16.0 
                 1.25 
                 27 
                 3 
                 10.7 
                 288.4 
                 96.1 
               
               
                 13 
                 285.2 
                 203.6 
                 0.71 
                 16.0 
                 1.25 
                 27 
                 3 
                 11.4 
                 308.0 
                 102.7 
               
               
                 15 
                 286.4 
                 212.8 
                 0.74 
                 16.1 
                 1.3 
                 27 
                 3 
                 10.5 
                 283.8 
                 94.6 
               
               
                 16 
                 286.4 
                 213.0 
                 0.74 
                 15.4 
                 1.3 
                 27 
                 3 
                 11.0 
                 297.6 
                 99.2 
               
               
                 17 
                 326.0 
                 222.0 
                 0.68 
                 15.4 
                 1.35 
                 26 
                 3 
                 11.6 
                 302.5 
                 100.8