Abstract:
Polarization preserving optical systems for use in deviating plane polarized beams through preselected angles without changing their linear state of polarization. The optical systems have a variety of applications and are particularly suitable for use in the field of distance measuring interferometry (DMI) to enhance measurement accuracy by reducing undesirable polarization effects that can introduce errors associated with an otherwise present undesirable polarization rotation found in classical retroreflectors. Prismatic optical elements are preferably used to construct assemblies which can include polarization beam splitting coating arrangements and/or birefringent materials to enhance the extinction ratio between orthogonally polarized beams propagating through such systems.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is related to commonly owned, copending U.S. patent application No. 09/384,855 (Attorney Docket No. 0202/US) filed on even date herewith in the name of Henry Allen Hill and Peter J. de Groot and entitled INTERFEROMETERS UTILIZING POLARIZATION PRESERVING OPTICAL SYSTEMS. 
     BACKGROUND OF THE INVENTION 
     This invention relates to polarization preserving optical systems and their use in displacement measurement interferometers (DMIs). 
     Non-polarization preserving retroreflectors are well-known and operate to deflect light through 180 degrees such that an incoming beam is exactly reversed in direction traveling as an outgoing beam parallel to the direction of propagation of the incoming direction and spatially offset with respect to it. The classical retroreflector essentially contains the intersection corner of three mutually perpendicular plane surfaces and is known as the cube corner retroreflector or sometimes the tetrahedron. Here, a ray generally undergoes 3 reflections, one from each 120° sector in the process of entering and exiting the retroreflector. Ideally, the direction of the reflected ray is opposite that of the incident ray but displaced due to a reflection through the retroreflector intersection corner. From the standpoint of polarization affects, the primary problem with the classical retroreflector is that the angles the rays make with the mirror surfaces are skew. Detailed calculations using the Jones matrix formalism along with the Fresnel reflection formulas can be used to predict the resultant polarization for different initial polarizations and retroreflector types. From the standpoint of their use in DMI applications where small, linearly polarized beams interact with only small sub-apertures of the retroreflector, the net effect is to rotate the plane of polarization by several degrees (typically 6°). This phenomenon is called Retro Induced Polarization Rotation (RIPR) and misaligns the beam polarization directions with respect to the polarization beam splitter of the interferometer which can cause large periodic errors in the measured interferometric phase. A particularly troublesome periodic or “cyclic” error which occurs in High Stability Plane Mirror Interferometers (HSPMI) produces an error with a frequency at ½ the Doppler shift (as well as other frequencies). It has been shown that this error, which is due to the polarization rotation properties of the retroreflector, can be extremely large and will occur regardless of the beamsplitter quality. 
     Consequently, it is a primary object of the present invention to provide polarization preserving optical systems that provide beam deflection properties for a variety of applications without introducing deleterious polarization effects. 
     It is another object of the present invention to provide polarization preserving optical systems for use in displacement measurement interferometers in place of traditional cube corner retroreflectors. 
     It is yet another object of the present invention to provide polarization preserving optical systems for deflecting plane polarized beams through arbitrary angles without introducing polarization mixing between orthogonally plane polarized beams passing through the system. 
     Yet another object of the present invention is to provide polarization preserving optical systems for use at multiple wavelengths. 
     Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the following detailed description is read in connection with the accompanying drawings. 
     SUMMARY OF THE INVENTION 
     The present invention relates to polarization preserving optical systems for use in deviating plane polarized beams through preselected angles without changing their linear state of polarization. The inventive optical systems have a variety of applications and are particularly suitable for use in the field of distance measuring interferometry (DMI) to enhance measurement accuracy by reducing undesirable polarization effects that can introduce errors associated with an otherwise present undesirable polarization rotation found in classical retroreflectors. 
     The polarization preserving optical systems of the invention comprise a plurality of reflecting surfaces arranged such that a change in the direction of propagation of an input beam, normal to both the input beam and an output beam, causes a change in the direction of propagation of the output beam in a direction opposite to the direction of the change in the input beam, and a change in the direction of propagation of the input beam, normal to the input beam and in a plane orthogonal to a normal to both the input beam and the output beam, causes a rotation in the output beam in the plane that is the same as a corresponding rotation of the input beam caused by the change in the direction of propagation of the input beam and wherein the plane of incidence at each of the reflecting surfaces is either orthogonal or parallel to the plane of polarization of an incident beam thereto. 
     The polarization preserving optical systems are preferably fabricated of a plurality of prismatic optical elements wherein the plurality of reflecting surfaces comprise selected surfaces of the prismatic optical element and preferably operate by total internal reflection. 
     The plurality of prismatic optical elements are preferably arranged as an integral assembly in which at least one surface of each prismatic optical element contacts at least one surface of another prismatic optical element and in which at least one polarizing beam splitter may be included. 
     The prismatic optical elements are selected from the group consisting of Porro, right angle, Dove, penta, and “K” prisms, one embodiment comprises a sequential combination of a right angle prism, a Porro prism, and a pentaprism. 
     At least one of the plurality of reflecting surfaces may have formed thereon a multilayer polarizing beam splitter coating arrangement to enhance the extinction ratio between orthogonally polarized beams entering the polarization preserving optical system and originating upstream of it, and such coatings may be structured to operate at multiple wavelengths. Birefringent materials may also be used to construct the various prismatic optical elements for similar purposes. 
     A variety of input to output beam relationships is demonstrated and depend on the particular design geometry of a system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The structure, operation, and methodology of the invention, together with other objects and advantages thereof, may best be understood by reading the detailed description in connection with the drawings in which each part has an assigned numeral that identifies it wherever it appears in the various drawings and wherein: 
     FIG. 1 a  is a diagrammatic perspective view showing the relationship between beams entering and exiting an optical system having generalized polarization preserving optical system properties; 
     FIG. 1 b  is a diagrammatic perspective view showing the relationship between the input and output beams shown in FIG. 1 a  and a vector normal to both; 
     FIG. 1 c  is a diagrammatic perspective view showing the relationship between the input beam of FIG. 1 a,  the normal vector of FIG. 1 b,  and a vector normal to both; 
     FIG. 1 d  is a diagrammatic perspective view showing the relationship between the output beam of FIG. 1 a,  the normal vector of FIG. 1 b,  and a vector normal to both; 
     FIG. 2 is a diagrammatic perspective view showing the relationship between beams entering and exiting the optical system of FIG. 1 a  after a change in the direction of the input beam compared with its direction in FIG. 1 a,  the change being parallel to the normal of FIG. 1 b;    
     FIG. 3 is a diagrammatic perspective view showing the relationship between beams entering and exiting the optical system of FIG. 1 a  after a change in the direction of the input beam compared with its direction in FIG. 1 a,  the change being in a plane that is perpendicular to the normal of FIG. 1 b  and the input beam of FIG. 1 a;    
     FIG. 4 is a diagrammatic perspective view of a polarization preserving generalized optical system assembly comprising a Porro prism in combination with a right angle prism along with the relationship between input and output beams as they undergo changes in the direction in which the input beam enters the face of the Porro prism, the input and output beams being offset and perpendicular to one another; 
     FIG. 5 is a diagrammatic perspective view of a polarization preserving generalized optical system assembly comprising a Porro prism in combination with a Dove prism along with the relationship between input and output beams as they undergo changes in the direction in which the input beam enters the face of the Porro prism, the input and output beams being offset and at other than a right angle with respect to one another; 
     FIG. 6 is a diagrammatic perspective view of a polarization preserving generalized optical system assembly comprising a Porro prism in combination with a “K” type prism along with the relationship between input and output beams as they undergo changes in the direction in which the input beam enters the face of the Porro prism, the input and output beams being offset and parallel to one anther; 
     FIG. 7 is a diagrammatic perspective view of a polarization preserving generalized optical system assembly comprising a Porro prism in combination with a right prism and a penta prism along with the relationship between input and output beams and also shows the individual components of the assembly in exploded fashion, the input and output beams being parallel and offset with respect to one another; 
     FIG. 8 is a diagrammatic perspective view of a polarization preserving optical system assembly comprising a polarizing beam splitter with a roof prism, and a Porro prism in combination with two angle right prisms along with the relationship between two input and two output beams of the assembly, the input and output beams being offset, parallel, and all lying in a line; 
     FIG. 9 is a diagrammatic perspective view of a plane mirror interferometer employing two polarization preserving optical system assemblies of the type shown in FIG. 7; 
     FIG. 10 is a diagrammatic perspective view of a high stability plane mirror interferometer employing a single polarization preserving optical system assembly of the type shown in FIG. 7; 
     FIG. 11 is a diagrammatic perspective view of a high stability plane mirror interferometer employing a single polarization preserving optical system assembly of the type shown in FIG. 7 along with a split quarter-wave plate in the intervening space between its polarizing beam splitter and the object mirror, the plates of the split quarter-wave plate being tilted relative to each other to prevent unwanted polarizing mixing; 
     FIG. 12 is a diagrammatic perspective view of a differential plane mirror interferometer employing a single polarization preserving optical system assembly of the type shown in FIG. 7 along with a shear plate with polarizing beam splitter surfaces to spatially separate and combine input and output beams; 
     FIG. 13 is a diagrammatic elevational view of the assembly of FIG. 12 illustrating various paths of travel of beams as they propagate through the assembly; and 
     FIG. 14 is a diagrammatic perspective view of a high stability plane mirror column type interferometer employing a single polarization preserving optical system assembly of the type shown in FIG. 7 along with a split quarter-wave plate in the intervening space between its polarizing beam splitter and the object mirror, the plates of the split quarter-wave plate being tilted relative to each other to prevent unwanted polarizing mixing; 
     FIG. 15 is a diagrammatic plan view of a dual high stability interferometer employing a pair of polarization preserving optical system assemblies for measuring linear and angular displacement; 
     FIG. 16 a  is a diagrammatic perspective of a differential plane mirror interferometer employing polarization preserving optical systems along with a dynamic element for assuring that a measurement beam thereof remains aligned perpendicular to its plane object mirror; 
     FIGS. 16 b  through  16   e  are plane view of various elements of the interferometer of FIG. 16 a;    
     FIG. 17 is a diagrammatic perspective of a polarization preserving optical system assemblies shown in combination with a polarizing beam splitter, one of the prismatic elements of the optical system assemblies having reflecting surfaces with multilayer beam splitter arrangements formed thereon to enhance the extinction ratio of the combination; 
     FIG. 18 is a diagrammatic elevational view of a penta prism formed of a birefringent element illustrating its ability of receiving an incoming beam having two coextensive orthogonally polarized components and separating it into two outgoing orthogonally polarized beams that have different directions of propagation and are spatially separate; 
     FIGS. 19 a - 19   c  relate to lithography and its application to manufacturing integrated circuits wherein FIG. 19 a  is a schematic drawing of a lithography exposure system employing the interferometry system. 
     FIGS. 19 b  and  19   c  are flow charts describing steps in manufacturing integrated circuits; and 
     FIG. 20 is a schematic of a beam writing system employing the interferometry system. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention relates to polarization preserving optical systems and their use as components in displacement measuring interferometers. Accordingly, the structure and properties of the polarization preserving optical systems per se will first be described and then their application in displacement measuring interferometers will be taken up. 
     Various embodiments of the polarization preserving optical systems of the invention will be described, and each polarization preserving optical system comprises two properties. The first property that such optical systems possess is a set of orientations of planes of linear polarization for which the polarization state of an input beam at each reflecting and refracting surface of the optical system and a corresponding output beam are all linear. The set of planes of linear polarization orientations hereinafter will be referred to as eigenmodes. Thus, the optical systems “preserve”, for an input beam to the system having an eigenmode state of linear polarization, the linear states of polarization of the input beam at each reflecting and refracting surface of the optical system and the corresponding output beam. 
     A set of the optical systems that exhibit such eigenmodes comprise reflecting and refracting surfaces such that the plane of polarization of an eigenmode at each of any reflecting or refracting surface in the optical system is either parallel to or orthogonal to the plane of incidence at the surface. 
     The second property that apparatus of the various embodiments described herein further possess is a certain set of transformation properties. The set of transformation properties describe a specific relationship between changes in the direction of propagation of an output beam from an optical system that results from changes in the direction of propagation an input beam where the directions of propagation of the input and output beams may or may not be parallel. This set of transformation properties will hereinafter be referred to as a transformation type T Ret . 
     FIG. 1 a  is a diagrammatic perspective view showing the relationship between vectors {right arrow over (k)} 1  and {right arrow over (k)} 2  representing the directions of propagation of optical beams entering and exiting, respectively, an optical system exhibiting transformation properties of the transformation type T Ret . The magnitudes of input and output vectors, |{right arrow over (k)} 1 | and |{right arrow over (k)} 2 |, respectively, are equal to respective wavenumbers k i =2π/λ i  for i=1 and 2 where λ i  is the wavelength of a respective vector. 
     The transformation properties of the transformation type T Ret  are defined in terms of infinitesimal changes Δ{right arrow over (k)} 1  and corresponding infinitesimal changes Δ{right arrow over (k)} 2  in vectors {right arrow over (k)} 1  and {right arrow over (k)} 2 , respectively, to form vectors {right arrow over (k)}′ 1  and {right arrow over (k)}′ 2 , respectively, wherein infinitesimal changes Δ{right arrow over (k)} 1  and Δ{right arrow over (k)} 2  are orthogonal to vectors {right arrow over (k)} 1  and {right arrow over (k)} 2 , respectively, |{right arrow over (k)}′ 1 |=|{right arrow over (k)} 1 |, and |{right arrow over (k)}′ 2 |=|{right arrow over (k)} 2 |. Thus, the infinitesimal changes Δ{right arrow over (k)} 1  and Δ{right arrow over (k)} 2  produce rotations of {right arrow over (k)} 1  and {right arrow over (k)} 2 , respectively, about axes orthogonal to {right arrow over (k)} 1  and {right arrow over (k)} 2 , respectively. 
     An arbitrary infinitesimal change Δ{right arrow over (k)} 1  can be represented as the sum of two orthogonal infinitesimal vector components Δ{right arrow over (k)} 1∥  and Δ{right arrow over (k)} 1⊥ . Component Δ{right arrow over (k)} 1∥  is defined as a component parallel to a unit vector â. Unit vector â is defined as a vector cross product, {right arrow over (k)} 1 ×{right arrow over (k)} 2 , of {right arrow over (k)} 1  and {right arrow over (k)} 2  normalized by the magnitude, |{right arrow over (k)} 1 ×{right arrow over (k)} 2 |, of {right arrow over (k)} 1 ×{right arrow over (k)} 2 , i.e.                a   ^     =             k   →     1     ×       k   →     2                  k   →     1     ×       k   →     2              .             (   1   )                                
     The relationship of vectors {right arrow over (k)} 1 , {right arrow over (k)} 2 , and â is shown in a diagrammatic perspective view in FIG. 1 b.  Component Δ{right arrow over (k)} 1⊥  is orthogonal to {right arrow over (k)} 1  and orthogonal to unit vector â, i.e. parallel to {circumflex over (k)} 1 ×â where {circumflex over (k)} 1 ={right arrow over (k)} 1 /k 1 . The relationship of vectors {right arrow over (k)} 1 , â, and {circumflex over (k)} 1 ×â is shown in a diagrammatic perspective view in FIG. 1 c.  Δ{right arrow over (k)} 1∥  and Δ{right arrow over (k)} 1⊥  are shown in diagrammatic perspective views in FIGS. 2 and 3, respectively. 
     Infinitesimal changes Δ{right arrow over (k)} 2∥  and Δ{right arrow over (k)} 2⊥  corresponding to infinitesimal changes Δ{right arrow over (k)} 1∥  and Δ{right arrow over (k)} 2⊥ , respectively, have the following properties for the optical system exhibiting the type T Ret  transformation properties: 
     (1) Δ{right arrow over (k)} 2∥  is parallel to vector â and has a direction opposite to that of Δ{right arrow over (k)} 1∥  and 
     (2) Δ{right arrow over (k)} 2⊥  is orthogonal to both {right arrow over (k)} 2  and unit vector â, i.e. parallel to {circumflex over (k)} 2 ×â, {circumflex over (k)} 2 ={right arrow over (k)} 2 /k 2 , with the additional condition that the direction of Δ{right arrow over (k)} 2⊥ ×{right arrow over (k)} 2  is the same as the direction of Δ{right arrow over (k)} 1⊥ ×{right arrow over (k)} 1 . 
     The relationship of vectors {right arrow over (k)} 2 , â, and {circumflex over (k)} 2 ×â is shown in a diagrammatic perspective view in FIG. 1 d.  The relationship of vectors Δ{right arrow over (k)} 1∥  and Δ{right arrow over (k)} 2∥  is shown in a diagrammatic perspective view in FIG.  2 . The relationship of vectors Δ{right arrow over (k)} 1⊥  and Δ{right arrow over (k)} 2⊥  is shown in a diagrammatic perspective view in FIG.  3 . 
     The first embodiment of an optical system in accordance with the present invention exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties. The first embodiment is shown as a diagrammatic perspective view in FIG. 4 where it is designated generally at  10 . Optical system  10  of the first embodiment comprises a Porro prism  20  and a right angle prism  30 . 
     An input beam  71  enters optical system  10  and exits optical system  10  as output beam  72  (see FIG.  4 ). The path of input beam  71  through optical system  10  is shown in FIG.  4 . Input beam  71  enters Porro prism  20  at a surface at normal incidence after which it is reflected sequentially by a first surface and then a second surface of Porro prism  20 , enters right angle prism  30 , is reflected by a hypotenuse surface of right angle prism  30 , and exits right angle prism  30  as output beam  72  at a surface at normal incidence. The planes of incidence at the first and second surfaces of Porro prism  20  are parallel one with the other and orthogonal to the plane of incidence at the hypotenuse surface of right angle prism  30 . 
     There are two polarization preserving eigenmodes of the first embodiment wherein the input polarization states of the two eigenmodes are parallel and orthogonal to the planes of incidence at the first and second surfaces of Porro prism  20 . The corresponding output polarization states of the two polarization preserving eigenmodes are orthogonal and parallel to the plane of incidence of the hypotenuse surface of right angle prism  30 , respectively. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in optical system  10 . 
     The transformation properties of optical system  10  with respect to changes in direction of propagation of output  72  that result from changes in direction of propagation of input beam  71  are the same as the properties of the type T Ret  transformation properties. This will be evident to those skilled in the art upon mapping the effects of changes in the direction of propagation of input beam  71  through optical system  10 . 
     The second embodiment of an optical system in accordance with the present invention exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties. The second embodiment is shown as a diagrammatic perspective view in FIG. 5 where it is designated generally at  110 . Optical system  110  comprises a Porro prism  120  and a trapezoid prism  130 . 
     An input beam  171  enters optical system  110  and exits optical system  110  as output beam  172  (see FIG.  5 ). The path of input beam  171  through optical system  110  is shown in FIG.  5 . Input beam  171  enters Porro prism  120  at a surface at normal incidence after which it is reflected sequentially by a first surface and then a second surface of Porro prism  120 , enters trapezoidal prism  130 , is reflected by a bottom surface of trapezoid prism  130 , and exits trapezoidal prism  130  at an exit surface as output beam  172 . The lengths of the entrance and exit surfaces of trapezoidal prism  130  may be equal or not equal according to requirements of an end use application. 
     The planes of incidence at the first and second surfaces of Porro prism  120  are parallel and orthogonal to the plane of incidence at the surface of trapezoidal prism  130 . The planes of incidence at the surface and at the exit surface of trapezoidal prism  130  are parallel. The directions of propagation of input beam  171  and output beam  172  are generally neither parallel or orthogonal. 
     There are two polarization preserving eigenmodes of the second embodiment wherein the input polarization states of the two polarization preserving eigenmodes are parallel and orthogonal to the planes of incidence at the first and second surfaces of Porro prism  120 . The corresponding output polarization states of the two polarization preserving eigenmodes are orthogonal and parallel to the plane of incidence at the exit surface of trapezoid prism  130 , respectively. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in optical system  110 . 
     The transformation properties of optical system  110  with respect to changes in direction of propagation of output  172  that result from changes in direction of propagation of input beam  171  are the same as the properties of the type T Ret  transformation. This will be evident to those skilled in the art upon mapping the effects of changes in the direction of propagation of input beam  171  through optical system  110 . 
     The third embodiment of an optical system in accordance with the present invention exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties. The third embodiment is shown as a diagrammatic perspective view in FIG. 6 where it is designated generally at  210 . Optical system  210  of the third embodiment comprises a Porro prism  220  and an inversion prism  230 . 
     An input beam  271  enters optical system  210  and exits optical system  210  as output beam  272  (see FIG.  6 ). The path of input beam  271  through optical system  210  is shown in FIG.  6 . Input beam  271  enters Porro prism  220  at a surface at normal incidence after which it is reflected sequentially by a first surface and then a second surface of Porro prism  220 , exits Porro prism  220  at an exit surface and enters inversion prism  230  at an entrance surface, is reflected by a first, second, and third surface of inversion prism  230 , and exits inversion prism  230  at an exit surface as output beam  272 . The planes of incidence at the first and second surfaces of Porro prism  270  are parallel and orthogonal to the planes of incidence at the first, second, and third surfaces of inversion prism  230 . The planes of incidence at the first, second, and third surfaces, the entrance surface, and at the exit surface of the inversion prism are parallel. The directions of propagation of input beam  271  and output beam  272  may be parallel or not parallel according to requirements of an end use application. 
     There are two polarization preserving eigenmodes of the third embodiment wherein the input polarization states of the two polarization preserving eigenmodes are parallel and orthogonal to the planes of incidence at the first and second surfaces of the Porro prism  220 . The corresponding output polarization states of the two polarization preserving eigenmodes are orthogonal and parallel to the plane of incidence of the first, second, and third surfaces of inversion prism  230 , respectively. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in optical system  210 . 
     The transformation properties of optical system  210  with respect to changes in direction of propagation of output  272  that result from changes in direction of propagation of input beam  271  are the same as the properties of the type T Ret  transformation. This will be evident to those skilled in the art upon mapping the effects of changes in the direction of propagation of input beam  271  through optical system  210 . 
     The fourth embodiment of an optical system in accordance with the present invention exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties. The fourth embodiment is shown as a diagrammatic perspective view in FIG. 7 where it is designated generally at  310 . Optical system  310  comprises a right angle prism  320 , Porro prism  330 , and a penta prism  340 . Note that a subsystem of optical system  310  comprising right angle prism  320  and Porro prism  330  exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties, the subsystem being equivalent to optical system  10  of the first embodiment. 
     An input beam  371  enters optical system  310  and exits optical system  310  as output beam  372  (see FIG.  7 ). The path of input beam  371  through optical system  310  is shown in FIG.  7 . Input beam  371  enters right angle prism  320  at a surface at normal incidence after which it is reflected by a hypotenuse surface of right angle prism  320 , exits right angle prism  320  at an exit surface, enters Porro prism  330  at an entrance surface and is reflected sequentially by a first surface and then a second surface of Porro prism  330 , and exits Porro prism  330  at an exit surface. After exiting Porro prism  320 , beam  371  enters penta prism  340  at an entrance surface after which it is reflected by a first surface and a second surface of penta prism  340  and exits penta prism  340  at an exit surface at normal incidence as output beam  372 . 
     The plane of incidence at the hypotenuse surface of the right angle prism  320  is orthogonal to the parallel planes of incidence at the first and second surfaces of Porro prism  330 . The planes of incidence at the first and second surfaces of Porro prism  330  are orthogonal to the planes of incidence at the first and second surfaces of penta prism  340 . The directions of propagation of input beam  371  and output beam  372  are parallel. 
     There are two polarization preserving eigenmodes of the fourth embodiment wherein the input polarization states of the two polarization preserving eigenmodes are parallel and orthogonal to the plane of incidence at the hypotenuse surface of right angle prism  370 . The corresponding output polarization states of the two polarization preserving eigenmodes are parallel and orthogonal to the planes of incidence of the first and second surfaces of penta prism  340 , respectively. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in optical system  310 . 
     The transformation properties of optical system  310  with respect to changes in direction of propagation of output beam  372  that result from changes in direction of propagation of input beam  371  are the same as the properties of the type T Ret  transformation. This will be evident to those skilled in the art upon mapping the effects of changes in the direction of propagation of input beam  371  through optical system  310 . 
     The fifth embodiment of an optical system in accordance with the present invention exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties. The fifth embodiment is shown as a diagrammatic perspective view in FIG. 8 where it is designated generally at  410 . Optical system  410  comprises two beam splitters and a Porro prism  430 . The first beam splitter comprises a right angle prism  421  and a trapezoidal prism  422  with a beam-splitting interface  423 . The second beam splitter comprises a prism  441  and a right angle prism  442  with a beam-splitting interface  443 . 
     The fifth embodiment comprises a subsystem of optical elements that also exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties. The subsystem of optical elements comprises trapezoidal prism  422  with beam splitter interface  423 , Porro prism  430 , and prism  441  with beam-splitting interface  443 . 
     Input beams  471  and  472  enter optical system  410  and exit optical system  410  as output beams  475  and  476 , respectively (see FIG.  8 ). The paths of input beam  471  and  472  through optical system  410  are shown in FIG.  8 . 
     Input beams  471  and  472  enter the first beam splitter with planes of polarization parallel or orthogonal to the respective planes of incidence at beam-splitting interface  423 . Input beams  471  and  472  are reflected by beam-splitting interface  423 , then exit trapezoidal prism  422  and enter Porro prism  430  at a surface at normal incidence, are reflected sequentially at a first surface and then at second surface of Porro prism  430 , and exit Porro prism  430  at a surface at normal incidence as beams  473  and  474 , respectively. The planes of incidence of beams  471  and  472  at the first and second surfaces of Porro prism  430  are either orthogonal or parallel to the respective planes of incidence at the beam-splitting interface  423 . 
     Note that the subsystem of optical system  410  comprising trapezoidal prism  422  and Porro prism  430  exhibits both polarization preserving eigenmodes and the type T Ret  transformation properties, the subsystem being equivalent to optical system  110  of the second embodiment. Beams  471  and  472  are optical beams that meet the conditions to be classified as being eigenmodes of the subsystem and optical beams of the subsystem for which type T Ret  transformations apply. 
     Beams  473  and  474  next enter prism  441  at a entrance surface at normal incidence, sequentially reflected by a first surface and then by beam-splitting interface  443 , and exit prism  441  at an exit surface at normal incidence as output beams  475  and  476 , respectively. The planes of polarization of beams  473  and  474  are parallel or orthogonal to the respective planes of incidence at the first surface and beam-splitting surfaces of prism  441 . 
     There are two polarization preserving eigenmodes of the fifth embodiment wherein the input polarization states of the two eigenmodes are parallel and orthogonal to the plane of incidence at the beam splitter interface of trapezoidal prism  422 . The corresponding output polarization states of the two polarization preserving eigenmodes are parallel and orthogonal to the planes of incidence of the first and beam-splitting surfaces of prism  441 , respectively. The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in optical system  410 . 
     The transformation properties of optical system  410  with respect to changes in direction of propagation of output beams  475  and  476  that result from changes in direction of propagation of input beams  471  and  472 , respectively, are the same as the properties of the type T Ret  transformation. This will be evident to those skilled in the art upon mapping the effects of changes in the direction of propagation of input beams  471  and  472  through optical system  410 . 
     Having described a number of embodiments of polarization preserving optical systems in accordance with the invention, embodiments in which such optical systems may be incorporated to form interferometers will now be described. 
     A sixth embodiment in accordance with the present invention is a plane mirror interferometer  510  shown in diagrammatic perspective view in FIG.  9 . The plane mirror interferometer  510  comprises a polarizing beam splitter  513 , a quarter-wave phase retardation plate  551 , object mirror  553 , and a first and second polarization preserving optical systems designated generally at  511  and  512 , respectively. The components of the polarizing beam splitter  513  are prisms  521  and  522  with a polarizing interface  523 . The description of each of the first and second polarization preserving optical systems is the same as the description given for the polarization preserving optical system of the fourth embodiment shown in FIG.  7 . 
     The input beams comprise two orthogonally polarized beams  571  and  572 , beam  571  serving as the measurement beam and beam  572  as the reference beam. The polarizing beam splitter  513  reflects the reference beam  572  and transmits the measurement beam  571  at polarizing interface  523 . The reference beam returns to the output as beam  574  after being reflected by the second polarization preserving optical system  512  and again by the polarizing beam splitter  513 . The measurement beam returns to the output as beam  573  after being reflected twice from object mirror  553 , transmission through phase retardation plate  551  twice for each round trip to object mirror  553 , being reflected by the first polarization preserving optical system at  511 , and being transmitted twice and reflected twice by the polarizing beam splitter  513 . 
     Input beams  571  and  572  and output beams  573  and  574  are shown in FIG. 9 as being spatially separated. It will be evident to those skilled in the art that input beams  571  and  572  can alternatively be arranged to be coextensive as well as the output beams  573  and  574  without departing from the scope and the spirit of the invention. 
     The seventh embodiment in accordance with the present invention is a high stability plane mirror interferometer  600  shown in diagrammatic perspective view in FIG.  10 . The high stability plane mirror interferometer  600  comprises a polarizing beam splitter  602 , quarter-wave phase retardation plates  651  and  652 , object mirror  653 , reference mirror  654 , and a polarization preserving optical system designated generally at  611 . The components of the polarizing beam splitter  602  are prisms  621  and  622  with a polarizing interface  623 . The description of the polarization preserving optical system is the same as the description given for the polarization preserving optical system of the fourth embodiment shown in FIG.  7 . 
     An input beam  671  comprises two orthogonally polarized beam components. The polarizing beam splitter  602  reflects one component of input beam  671  as a reference beam and transmits the second component of input beam  671  as a measurement beam at polarizing interface  623 . The reference beam returns as a reference beam component of output beam  673  after being reflected twice by the reference mirror  654 , transmission through phase retardation plate  652  twice for each round trip to reference mirror  654 , being reflected by the polarization preserving optical system at  611 , and being reflected twice and transmitted twice by the polarizing beam splitter  602 . The measurement beam returns as a measurement beam component of output beam  673  after being reflected twice from object mirror  653 , transmission through phase retardation plate  651  twice for each round trip to object mirror  653 , being reflected by the polarization preserving optical system at  611 , and being transmitted twice and reflected twice by the polarizing beam splitter  602 . 
     The reference and measurement beam components of input beam  671  and the reference and measurement beam components of output beam  673  are shown in FIG. 10 as being coextensive, respectively. It will be evident to those skilled in the art that the reference and measurement beam components of input beam  671  can alternatively be arranged to be spatially separated as well as the reference and measurement beam components of output beam  673  without departing from the scope and the spirit of the invention. 
     The eighth embodiment in accordance with the present invention is a high stability plane mirror interferometer  700  shown in diagrammatic perspective view in FIG.  11 . The eighth embodiment exhibits reduced cyclic errors and comprises a plane mirror interferometer with a split quarter-wave phase retardation plate in a measurement leg. Many elements of the eighth embodiment form like functions as elements of the seventh embodiment shown in the FIG. 10, the element number of an eighth-embodiment element being 100 larger than the element number of a corresponding seventh-embodiment element. The function of phase retardation plate  651  of the seventh embodiment is achieved in the eighth embodiment by two phase retardation plates  751 A and  751 B. 
     Phase retardation plates  751 A and  751 B are tilted one with respect to the other so as to eliminate a potential source of cyclic errors. The potential source of cyclic errors is a generation of a spurious beam by two ghost reflections from a phase retardation plate such as phase retardation plate  651  found in the seventh embodiment. The description of the reduction of the cyclic errors in the eighth embodiment is the same as corresponding description given in copending commonly owned U.S. patent application 09/384,609 (Attorney Docket Number 0201/US) entitled “INTERFEROMETER HAVING REDUCED GHOST BEAM EFFECTS” by Peter de Groot the contents of which are incorporated herein by reference. The function of the phase retardation plates may be strategically achieved by other surfaces of an interferometer as, for example, by tilting selected surfaces of a polarizing beam splitter. 
     The remaining description of the eighth embodiment is the same as the corresponding portion of the description given for the seventh embodiment. 
     The ninth embodiment in accordance with the present invention is a differential plane mirror interferometer  800  shown in diagrammatic perspective view in FIG.  12  and in a diagrammatic side view in FIG.  13 . The differential plane mirror interferometer  800  comprises a shear plate  816 , a polarizing beam splitter  802 , quarter-wave phase retardation plate  851 , object mirror  853 , reference mirror  854 , and a polarization preserving optical system designated generally at  811 . The components of the polarizing beam splitter  802  are prisms  821  and  822  with a polarizing interface  823 . The description of the polarization preserving optical system is the same as the description given for the polarization preserving optical system of the fourth embodiment shown in FIG.  7 . 
     An input beam  871  comprises two orthogonally polarized beam components. Shear plate  816  transmits one polarization component of input beam  871  as a measurement beam  872 . The second polarization component of input beam  871  is first transmitted by shear plate  816 , after two internal reflections, and then transmitted by a half-wave phase retardation plate  855  as a reference beam  873 . Half-wave phase retardation plate  855  is orientated so as to rotate the plane of polarization of reference beam  873  to be parallel to the plane of polarization of measurement beam  872  and parallel to the plane of FIG.  13 . Measurement beam  872  and reference beam  873  are spatially separated. 
     Measurement beam  872  returns as a measurement beam  874  after being reflected twice by object mirror  853 , transmission through phase retardation plate  851  twice for each round trip to object mirror  853 , being reflected by the polarization preserving optical system  811 , and being reflected twice and transmitted twice by the polarizing beam splitter  802 . Reference mirror  854  comprises two apertures (see FIG. 12) through which the measurement beam passes in transit to and from object mirror  853 . 
     Reference beam  873  returns as a reference beam  875  after being reflected twice from reference mirror  854 , transmission through phase retardation plate  851  twice for each round trip to reference mirror  854 , being reflected by the polarization preserving optical system  811 , and being reflected twice and transmitted twice by the beam splitter  802 . 
     Next, measurement beam  874  is transmitted by half-wave phase retardation plate  856  and then transmitted by shear plate  816 , after two internal reflections, as a measurement beam component of output beam  876 . Half-wave phase retardation plate  856  is orientated so as to rotate the plane of polarization of the measurement beam component of output beam  876  by 90° with respect to the plane of polarization of measurement beam  874 . Reference beam  875  is transmitted by shear plate  816  as a reference beam component of output beam  876 . The measurement and reference beam components of output beam  876  are orthogonally polarized. 
     The remaining description of the ninth embodiment is the same as corresponding portions of the description given for the seventh embodiment. 
     The tenth embodiment in accordance with the present invention is a high stability plane mirror interferometer  902  shown in diagrammatic perspective view in FIG.  14 . The high stability plane mirror interferometer  900  of the tenth embodiment is configured for use in applications requiring a column reference. 
     Many elements of the tenth embodiment form like functions as elements of the seventh embodiment shown in the FIG. 10, the element number of an tenth-embodiment element being 200 larger than the element number of a corresponding eigthth-embodiment element. Mirror  955  reflects the reference beam in transit between reference mirror  954  and a polarizing beam splitter  902 . Reference mirror  954  is attached to a reference object such as a column containing an imaging system for focusing radiation onto a wafer and the measurement mirror  953  is attached to a wafer stage as a measurement object supporting the wafer wherein the imaging system, radiation, wafer, and wafer stage are components of a lithrography tool used in the manufacture of integrated circuits, such lithography apparatus to be described further hereinafter. 
     The remaining description of the tenth embodiment is the same as corresponding portion of the description given for the eighth embodiment. 
     An eleventh embodiment in accordance with the present invention is a dual linear/angular displacement interferometer system  1000  shown in diagrammatic view in FIG.  15 . Certain subsystems of the dual linear/angular displacement interferometer system  1000  exhibit both polarization preserving eigenmodes and the type T Ret  transformation properties. A dual linear/angular displacement interferometer shown as element  1010  in FIG. 15 comprises two interferometers wherein the outputs of the two interferometers are combined to yield a linear displacement and an angular displacement of an object mirror. Dual linear/angular displacement interferometer  1010  further comprises a high stability plane mirror interferometer for each of the two interferometers and the two interferometers have a common polarizing beam splitter  1002 , a common object mirror  1053 , a common reference mirror  1054 , common quarter-wave phase retardation plates  1051  and  1052 , and a common source  1014 . The polarizing beam splitter  1002  comprises prisms  1021  and  1022  with a polarizing interface  1023 . 
     The high stability plane mirror interferometers are each of the polarization preserving type of the seventh embodiment shown in FIG.  10 . The high stability plane mirror interferometers comprise polarization preserving optical systems generally shown at  1011  and  1012 . The polarization preserving optical systems are the same as the one shown in FIG. 7 of fourth embodiment. 
     Common source  1014  generates beam  1071 . Source  1014  is preferably a source such as a single frequency laser and acousto-optical modulator arranged to generate beam  1071  with two orthogonally polarized components having different optical frequencies. The two orthogonal planes of polarization are orientated at angles of 45° to the plane of FIG.  15 . Beam  1071  is incident on non-polarizing beam splitter  1016 A and a first portion thereof is transmitted as a first input beam for one of the two high stability plane mirror interferometers. A second portion of beam  1071  incident on beam splitter  1016 A is reflected by beam splitter  1016 A and then reflected by mirror  1016 B as a second input beam  1072  for the second of the two high stability plane mirror interferometers. 
     The propagation of the first input beam and the second input beam  1072  through the dual linear/angular displacement interferometer  1010  is shown in FIG.  15  and exit interferometer  1010  as output beams  1073  and  1074 , respectively. Output beams  1073  and  1074  each have orthogonally polarized measurement and reference beam components. Output beam  1073  is transmitted by polarizer  1055  as a mixed beam that is detected by detector  1061  preferably by the photoelectric effect to produce a first electrical interference signal or a first heterodyne signal. Output beam  1074  is transmitted by polarizer  1056  as a mixed beam that is detected by detector  1062  preferably by the photoelectric effect to produce a second electrical interference signal or a second heterodyne signal. The first and second heterodyne signals are transmitted to electronic processor and computer  1065  to generate a corresponding first and second relative linear displacements. The first and second relative linear displacements are averaged to produce a relative linear displacement  1075  of object mirror  1053  and subtracted one from the other wherein the resulting difference is used to produce a relative angular displacement  1076  of object mirror  1053 . 
     The remaining description of the eleventh embodiment is the same as corresponding portions of the description given for the seventh embodiment. 
     A variant of the eleventh embodiment in accordance with the present invention comprises a dual linear/angular displacement interferometer system. The variant of eleventh embodiment exhibits reduced sources of certain cyclic errors and certain subsystems of the dual linear/angular displacement interferometer system exhibit both polarization preserving eigenmodes and the type T Ret  transformation properties. The variant of the eleventh embodiment comprises two high stability plane mirror wherein each of the high stability plane mirror interferometers is of the high stability plane mirror interferometer type shown in FIG. 11 of the eighth embodiment. 
     The remaining description of the variant of the eleventh embodiment is the same as corresponding portions of the descriptions given for the eighth and eleventh embodiments. 
     The eleventh embodiment in accordance with the present invention is a dual linear/angular displacement interferometer system  1000  shown as a diagrammatic view in FIG.  15 . Certain subsystems of the dual linear/angular displacement interferometer system exhibit  1000  both polarization preserving eigenmodes and the type T Ret  transformation properties. A dual linear/angular displacement interferometer shown as element  1010  in FIG. 15 comprises two interferometers wherein the outputs of the two interferometers are combined to yield a linear displacement and an angular displacement of an object mirror. Dual linear/angular displacement interferometer  1010  further comprises a high stability plane mirror interferometer for each of the two interferometers and the two interferometers have a common polarizing beam splitter  1002 , a common object mirror  1053 , a common reference mirror  1054 , common quarter-wave phase retardation plates  1051  and  1052 , and a common source  1014 . The polarizing beam splitter  1002  comprises prisms  1021  and  1022  with a polarizing interface  1023 . 
     The high stability plane mirror interferometers are each of the polarization preserving type of the seventh embodiment shown in FIG.  10 . The high stability plane mirror interferometers comprise polarization preserving optical systems generally shown at  1011  and  1012 . The polarization preserving optical systems are the same as the one shown in FIG. 7 of fourth embodiment. 
     Common source  1014  generates beam  1071 . Source  1014  is preferably a source such as a single frequency laser and acousto-optical modulator arranged to generate beam  1071  with two orthogonally polarized components having different optical frequencies. The two orthogonal planes of polarization are orientated at angles of 45° to the plane of FIG.  15 . Beam  1071  is incident on non-polarizing beam splitter  1016 A and a first portion thereof is transmitted as a first input beam for one of the two high stability plane mirror interferometers. A second portion of beam  1071  incident on beam splitter  1016 A is reflected by beam splitter  1016 A and then reflected by mirror  1016 B as a second input beam  1072  for the second of the two high stability plane mirror interferometers. 
     The propagation of the first input beam and the second input beam  1072  through the dual linear/angular displacement interferometer  1010  is shown in FIG.  15  and exit interferometer  1010  as output beams  1073  and  1074 , respectively. Output beams  1073  and  1074  each have orthogonally polarized measurement and reference beam components. Output beam  1073  is transmitted by polarizer  1055  as a mixed beam that is detected by detector  1061  preferably by the photoelectric effect to produce a first electrical interference signal or a first heterodyne signal. Output beam  1074  is transmitted by polarizer  1056  as a mixed beam that is detected by detector  1062  preferably by the photoelectric effect to produce a second electrical interference signal or a second heterodyne signal. The first and second heterodyne signals are transmitted to electronic processor and computer  1065  to generate a corresponding first and second relative linear displacements. The first and second relative linear displacements are averaged to produce a relative linear displacement  1075  of object mirror  1053  and subtracted one from the other wherein the resulting difference is used to produce a relative angular displacement  1076  of object mirror  1053 . 
     The remaining description of the eleventh embodiment is the same as corresponding portions of the description given for the seventh embodiment. 
     A variant of the eleventh embodiment in accordance with the present invention comprises a dual linear/angular displacement interferometer system. The variant of eleventh embodiment exhibits reduced sources of certain cyclic errors and certain subsystems of the dual linear/angular displacement interferometer system exhibit both polarization preserving eigenmodes and the type T Ret  transformation properties. The variant of the eleventh embodiment comprises two high stability plane mirror interferometers wherein each of the high stability plane mirror interferometers is of the high stability plane mirror interferometer type shown in FIG. 11 of the eighth embodiment. 
     The remaining description of the variant of the eleventh embodiment is the same as corresponding portions of the descriptions given for the eighth and eleventh embodiments. 
     Other examples of optical systems exhibiting polarization preserving eigenmodes and the type T Ret  transformation properties are optical systems of a twelfth embodiment in accordance with the present invention. The twelfth embodiment comprises a differential plane mirror interferometer  1100  with a dynamic element  1155  as shown in diagrammatic perspective view in FIG. 16 a.  The orientation of dynamic element  1155  is servoed to maintain the measurement beam perpendicular to an object mirror  1153 . 
     Input beam  1171  comprises two orthogonally polarized components having frequencies different one for the other. Input beam  1171  enters a first beam splitter comprising a right angle prism  1141  and a rhomboidal prism  1142  with a polarizing interface  1143 . A first portion of input beam  1171  incident on polarizing interface  1143  is transmitted as a measurement beam  1173 . A second portion of input beam  1171  incident on polarizing interface  1143  is reflected and exits the first beam splitter, after an internal reflection, as a reference beam  1174 . 
     Measurement beam  1173  and reference beam  1174  exit the differential plane mirror  1100  interferometer as output measurement and reference beams  1175  and  1176 , respectively. Propagation of measurement beam  1173  and reference beam  1174  through the differential plane mirror interferometer  1100  is shown in FIG. 16 a.  The orientation of dynamic mirror  1155  is controlled by transducers  1156 A,  1156 B, and  1156 C. Output measurement and reference beams  1175  and  1176  are combined into a mixed output beam by a second beam splitter comprising right angle prism  1144 , rhomboidal prism  1145 , and beam splitting interface  1146 . The output beam is received by detector and signal processor  1160  that operates to provide information, e.g., such as phase detection and phase analysis, about linear and/or angular displacements of object mirror  1153  and information relating to the alignment of beams, e.g., such as detection of changes in direction of propagation of the measurement beam component of the output beam, used for the servo control of dynamic mirror  1155 . Along with other interferometers having dynamic elements, operation of the differential plane mirror interferometer  1100  is further described in copending, commonly owned U.S. patent application 09/384,851, filed Aug. 27, 1999 (Attorney Docket Number 09712/040001) entitled “Interferometry System Having A Dynamic Beam Steering Assembly For Measuring Angle and Distance” by Henry A. Hill, which copending application is incorporated herein by reference. 
     An optical subsystem indicated as  1100  in FIG. 16 a,  quarter-wave phase retardation plate  1151 , and reference mirror  1154  exhibit, as a first optical system, polarization preserving eigenmodes and the type T Ret  transformation properties for input reference beam  1174 . Also optical subsystem  1100 , quarter-wave phase retardation plate  1151 , object mirror  1153 , and dynamic element  1155  for a fixed orientation exhibit, as a second optical system, polarization preserving eigenmodes and the type T Ret  transformation properties for input measurement beam  1174 . 
     Optical subsystem  1100  comprises a modified Porro prism  1121  and prisms  1125 ,  1129 , and  1133  shown schematically in FIGS. 16 b,    16   c,    16   d,  and  16   e,  respectively. An interface comprising surfaces  1128  and  1130  is a polarizing beam splitter interface. 
     There are two polarization preserving eigenmodes of the first optical system wherein the input polarization states of the two eigenmodes are orthogonal and parallel, respectively, to the plane of incidence at surface  1136  of prism  1133 . The corresponding output polarization states of the two polarization preserving eigenmodes are orthogonal and parallel to the plane of incidence at surface  1123  of prism  1121 . The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in the first optical system. 
     There are also two polarization preserving eigenmodes of the second optical system wherein the input polarization states of the two eigenmodes are orthogonal and parallel, respectively, to the plane of incidence at a first surface of dynamic element  1155 . The plane of incidence at the first surface of dynamic element  1155  is parallel to the plane of incidence of beams of the eigenmodes at surface  1123  of Porro prism  1121 . The corresponding output polarization states of the two polarization preserving eigenmodes are parallel and orthogonal, respectively, to the planes of incidence of a surface of dynamic element  1155 . The eigenmodes are polarization preserving since the polarization states of the eigenmodes are either parallel to or orthogonal to the respective planes of incidence for each reflection and refraction in the second optical system. 
     The transformation properties of the first and second optical systems of the twelfth embodiment with respect to changes in direction of propagation of output beams  1175  and  1176  that result from changes in direction of propagation of input beams  1173  and  1174 , respectively, are the same as the properties of the type T Ret  transformation. This will be evident to those skilled in the art upon mapping the effects of changes in the direction of propagation of input beams  1173  and  1174  through the first and second optical systems. 
     A thirteenth embodiment in accordance with the present invention exhibits enhanced polarizing beam splitter properties, polarization preserving eigenmodes, and the type T Ret  transformation properties. The use of an optical system in an interferometer exhibiting enhanced polarizing beam splitter properties can for example lead to reduced cyclic errors in phase differences measured with the interferometer. 
     The thirteenth embodiment is shown as a diagrammatic perspective view in FIG.  17  and comprises a beam splitter and a polarization preserving optical system shown generally at  1211 . The beam splitter comprises prisms  1221  and  1222  with a polarizing beam splitting interface  1223 . The polarization preserving optical system comprises the polarization preserving optical system shown in FIG. 7 of the fourth embodiment with polarizing properties for certain reflecting surfaces. The certain reflecting surfaces can comprise one or more of those surfaces of the right angle prism, the Porro prism, and the penta prism of the polarization preserving optical system at which beams corresponding to eigenmodes (of the polarization preserving optical system) are internally reflected. For the thirteenth embodiment, the certain reflecting surfaces comprise the internally reflecting surfaces of the Porro prism and the penta prism of the polarization preserving optical system. 
     Optical flats  1231 ,  1232 ,  1233 , and  1234  are either cemented onto the internally reflecting surfaces of the Porro prism and the penta prism (see FIG. 17) with an optical grade cement or by optical contacting. For optical beams entering and exiting the thirteenth embodiment that are in the ultra violet, the preferred attachment method for the optical flats is optical contacting. Before cementing or optical contacting the optical flats, multi-layer thin film coatings are applied to the surfaces of the optical flats and/or corresponding surfaces of the Porro prism and the penta prism so that after the cementing or contacting procedure, the respective interfaces become polarizing surfaces for the eigenmodes of polarization preserving retroreflector. 
     The polarizing properties of corresponding portions of the polarizing surfaces are chosen so that for an eigenmode reflected (transmitted) by a portion of polarizing interface  1223  of the polarizing beam splitter, the corresponding portions of the polarizing surfaces of the polarization preserving optical system preferably reflect (reflect) the eigenmode. As a consequence, the polarizing surfaces serve as “polarization filters” in that the polarizing surfaces transmit spurious beams generated by the reflection (transmission) of unwanted beams by polarizing interface  1223  of the polarizing beam splitter. 
     It will be evident on examination of respective figures that the polarizing beam splitter and the polarizing preserving optical system of the thirteenth embodiment comprise subsystems of the sixth, seventh, eighth, ninth, ten, eleventh, and twelfth embodiments of the present invention. 
     The polarization filtering properties of polarization preserving optical systems may also be augmented and/or achieved by replacing one or more components of the polarization preserving optical systems with corresponding components made from birefringent mediums, e.g. quartz, calcite, or lithium niobate, such that the corresponding components become polarizers. 
     A penta prism polarizer  1340  is shown in FIG. 18 comprising a birefringent medium. The optic-axis  1341  of the birefrigent medium is parallel to the plane of FIG.  18  and orientated at an angle β to a surface of modified penta prism  1340  as shown in FIG.  18 . The orientation of the surfaces of the penta prism and the angle β are selected so that a desired polarization component of an input beam propagates through the penta prism and exits the penta prism as a polarization preserving eigenmode of the penta prism which comprises polarizaton filtering. An example of penta prism polarizer is described in an article by H. Lotem and K. Rabinovitch entitled “Penta prism laser polarizer” in  Appl. Optics  32(12) pp 2017-2020 (1993). 
     An optical system exhibiting polarization preserving eigenmodes and further comprising polarization filtering can be employed to produce interferometers that work simultaneously at two widely separated wavelengths, in particular two harmonically related wavelengths. The measurement and reference paths for the two wavelengths can be coextensive in respective portions of the interferometer, in particular at a polarizing beam splitter interface, with significantly reduced sources of cyclic errors for both wavelengths compared to sources of cyclic errors in prior art interferometers. 
     The interferometry systems described above can be especially useful in lithography applications used for fabricating large scale integrated circuits such as computer chips and the like. Lithography is the key technology driver for the semiconductor manufacturing industry. Overlay improvement is one of the five most difficult challenges down to and below 100 nm line widths (design rules), see for example the  Semiconductor Industry Roadmap,  p82 (1997). Overlay depends directly on the performance, i.e. accuracy and precision, of the distance measuring interferometers used to position the wafer and reticle (or mask) stages. Since a lithography tool may produce $50-100M/year of product, the economic value from improved performance distance measuring interferometers is substantial. Each 1% increase in yield of the lithography tool results in approximately $1M/year economic benefit to the integrated circuit manufacturer and substantial competitive advantage to the lithography tool vendor. 
     The function of a lithography tool is to direct spatially patterned radiation onto a photoresist-coated wafer. The process involves determining which location of the wafer is to receive the radiation (alignment) and applying the radiation to the photoresist at that location (exposure). 
     To properly position the wafer, the wafer includes alignment marks on the wafer that can be measured by dedicated sensors. The measured positions of the alignment marks define the location of the wafer within the tool. This information, along with a specification of the desired patterning of the wafer surface, guides the alignment of the wafer relative to the spatially patterned radiation. Based on such information, a translatable stage supporting the photoresist-coated wafer moves the wafer such that the radiation will expose the correct location of the wafer. 
     During exposure, a radiation source illuminates a patterned reticle, which scatters the radiation to produce the spatially patterned radiation. The reticle is also referred to as a mask, and these terms are used interchangeably below. In the case of reduction lithography, a reduction lens collects the scattered radiation and forms a reduced image of the reticle pattern. Alternatively, in the case of proximity printing, the scattered radiation propagates a small distance (typically on the order of microns) before contacting the wafer to produce a 1:1 image of the reticle pattern. The radiation initiates photo-chemical processes in the photoresist that convert the radiation pattern into a latent image within the photoresist. 
     The interferometry systems described above are important components of the positioning mechanisms that control the position of the wafer and reticle, and register the reticle image on the wafer. 
     In general, the lithography system, also referred to as an exposure system, typically includes an illumination system and a wafer positioning system. The illumination system includes a radiation source for providing radiation such as ultraviolet, visible, x-ray, electron, or ion radiation, and a reticle or mask for imparting the pattern to the radiation, thereby generating the spatially patterned radiation. In addition, for the case of reduction lithography, the illumination system can include a lens assembly for imaging the spatially patterned radiation onto the wafer. The imaged radiation exposes photoresist coated onto the wafer. The illumination system also includes a mask stage for supporting the mask and a positioning system for adjusting the position of the mask stage relative to the radiation directed through the mask. The wafer positioning system includes a wafer stage for supporting the wafer and a positioning system for adjusting the position of the wafer stage relative to the imaged radiation. Fabrication of integrated circuits can include multiple exposing steps. For a general reference on lithography, see, for example, J. R. Sheats and B. W. Smith, in  Microlithography: Science and Technology  (Marcel Dekker, Inc., New York, 1998), the contents of which are incorporated herein by reference. 
     The interferometry systems described above can be used to precisely measure the positions of each of the wafer stage and mask stage relative to other components of the exposure system, such as the lens assembly, radiation source, or support structure. In such cases, the interferometry system can be attached to a stationary structure and the measurement object attached to a movable element such as one of the mask and wafer stages. Alternatively, the situation can be reversed, with the interferometry system attached to a movable object and the measurement object attached to a stationary object. 
     More generally, the interferometry systems can be used to measure the position of any one component of the exposure system relative to any other component of the exposure system in which the interferometry system is attached, or supported by one of the components and the measurement object is attached, or is supported by the other of the components. 
     An example of a lithography scanner  1400  using an interferometry system  1426  is shown in FIG. 19 a.  The interferometry system is used to precisely measure the position of a wafer within an exposure system. Here, stage  1422  is used to position the wafer relative to an exposure station. Scanner  1400  comprises a frame  1402 , which carries other support structures and various components carried on those structures. An exposure base  1404  has mounted on top of it a lens housing  1406  atop of which is mounted a reticle or mask stage  1416  used to support a reticle or mask. A positioning system for positioning the mask relative to the exposure station is indicated schematically by element  1417 . Positioning system  1417  can include, e.g., piezoelectric transducer elements and corresponding control electronics. Although, it is not included in this described embodiment, one or more of the interferometry systems described above can also be used to precisely measure the position of the mask stage as well as other moveable elements whose position must be accurately monitored in processes for fabricating lithographic structures (see supra Sheats and Smith  Microlithography: Science and Technology ). 
     Suspended below exposure base  1404  is a support base  1413  that carries wafer stage  1422 . Stage  1422  includes a plane mirror for reflecting a measurement beam  1454  directed to the stage by interferometry system  1426 . A positioning system for positioning stage  1422  relative to interferometry system  1426  is indicated schematically by element  1419 . Positioning system  1419  can include, e.g., piezoelectric transducer elements and corresponding control electronics. The measurement beam reflects back to the interferometry system, which is mounted on exposure base  1404 . The interferometry system can be any of the embodiments described previously. 
     During operation, a radiation beam  1410 , e.g., an ultraviolet (UV) beam from a UV laser (not shown), passes through a beam shaping optics assembly  1412  and travels downward after reflecting from mirror  1414 . Thereafter, the radiation beam passes through a mask (not shown) carried by mask stage  1416 . The mask (not shown) is imaged onto a wafer (not shown) on wafer stage  1422  via a lens assembly  1408  carried in a lens housing  1406 . Base  1404  and the various components supported by it are isolated from environmental vibrations by a damping system depicted by spring  1420 . 
     In other embodiments of the lithographic scanner, one or more of the interferometry systems described previously can be used to measure distance along multiple axes and angles associated for example with, but not limited to, the wafer and reticle (or mask) stages. Also, rather than a UW laser beam, other beams can be used to expose the wafer including, e.g., x-ray beams, electron beams, ion beams, and visible optical beams. 
     In addition, the lithographic scanner can include a column reference in which interferometry system  1426  directs the reference beam to lens housing  1406  or some other structure that directs the radiation beam rather than a reference path internal to the interferometry system. The interference signal produce by interferometry system  1426  when combining measurement beam  1454  reflected from stage  1422  and the reference beam reflected from lens housing  1406  indicates changes in the position of the stage relative to the radiation beam. Furthermore, in other embodiments the interferometry system  1426  can be positioned to measure changes in the position of reticle (or mask) stage  1416  or other movable components of the scanner system. Finally, the interferometry systems can be used in a similar fashion with lithography systems involving steppers, in addition to, or rather than, scanners. 
     As is well known in the art, lithography is a critical part of manufacturing methods for making semiconducting devices. For example, U.S. Pat. No. 5,483,343 outlines steps for such manufacturing methods. These steps are described below with reference to FIGS. 19 b  and  19   c.  FIG. 19 b  is a flow chart of the sequence of manufacturing a semiconductor device such as a semiconductor chip (e.g. IC or LSI), a liquid crystal panel or a CCD. Step  1451  is a design process for designing the circuit of a semiconductor device. Step  1452  is a process for manufacturing a mask on the basis of the circuit pattern design. Step  1453  is a process for manufacturing a wafer by using a material such as silicon. 
     Step  1454  is a wafer process which is called a pre-process wherein, by using the so prepared mask and wafer, circuits are formed on the wafer through lithography. Step  1455  is an assembling step, which is called a post-process wherein the wafer processed by step  1454  is formed into semiconductor chips. This step includes assembling (dicing and bonding) and packaging (chip sealing). Step  1456  is an inspection step wherein operability check, durability check, and so on of the semiconductor devices produced by step  1455  are carried out. With these processes, semiconductor devices are finished and they are shipped (step  1457 ). 
     FIG. 19 c  is a flow chart showing details of the wafer process. Step  1461  is an oxidation process for oxidizing the surface of a wafer. Step  1462  is a CVD process for forming an insulating film on the wafer surface. Step  1463  is an electrode forming process for forming electrodes on the wafer by vapor deposition. Step  1464  is an ion implanting process for implanting ions to the wafer. Step  1465  is a photoresist process for applying a photoresist (photosensitive material) to the wafer. Step  1466  is an exposure process for printing, by exposure, the circuit pattern of the mask on the wafer through the exposure apparatus described above. Step  1467  is a developing process for developing the exposed wafer. Step  1468  is an etching process for removing portions other than the developed photoresist image. Step  1469  is a photoresist separation process for separating the photoresist material remaining on the wafer after being subjected to the etching process. By repeating these processes, circuit patterns are formed and superimposed on the wafer. 
     The interferometry systems described above can also be used in other applications in which the relative position of an object needs to be measured precisely. For example, in applications in which a write beam such as a laser, x-ray, ion, or electron beam, marks a pattern onto a substrate as either the substrate or beam moves, the interferometry systems can be used to measure the relative movement between the substrate and write beam. 
     As an example, a schematic of a beam writing system  1500  is shown in FIG. 20. A source  1510  generates a write beam  1512 , and a beam focusing assembly  1514  directs the radiation beam to a substrate  1516  supported by a movable stage  1518 . To determine the relative position of the stage, an interferometry system  1520  directs a reference beam  1522  to a mirror  1524  mounted on beam focusing assembly  1514  and a measurement beam  1526  to a mirror  1528  mounted on stage  1518 . Interferometry system  1520  can be any of the interferometry systems described previously. Changes in the position measured by the interferometry system correspond to changes in the relative position of write beam  1512  on substrate  1516 . Interferometry system  1520  sends a measurement signal  1532  to controller  1530  that is indicative of the relative position of write beam  1512  on substrate  1516 . Controller  1530  sends an output signal  1534  to a base  1536  that supports and positions stage  1518 . In addition, controller  1530  sends a signal  1538  to source  1510  to vary the intensity of, or block, write beam  1512  so that the write beam contacts the substrate with an intensity sufficient to cause photophysical or photochemical change only at selected positions of the substrate. Furthermore, in some embodiments, controller  1530  can cause beam focusing assembly  1514  to scan the write beam over a region of the substrate, e.g., using signal  1544 . As a result, controller  1530  directs the other components of the system to pattern the substrate. The patterning is typically based on an electronic design pattern stored in the controller. In some applications the write beam patterns a photoresist coated on the susbstrate and in other applications the write beam directly patterns, e.g., etches, the substrate. 
     An important application of such a system is the fabrication of masks and reticles used in the lithography methods described previously. For example, to fabricate a lithography mask an electron beam can be used to pattern a chromium-coated glass substrate. In such cases where the write beam is an electron beam, the beam writing system encloses the electron beam path in a vacuum. Also, in cases where the write beam is, e.g., an electron or ion beam, the beam focusing assembly includes electric field generators such as quadrapole lenses for focusing and directing the charged particles onto the substrate under vacuum. In other cases where the write beam is a radiation beam, e.g., x-ray, UV, or visible radiation, the beam focusing assembly includes corresponding optics for focusing and directing the radiation to the substrate. 
     It is understood that while the invention has been described in conjunction with the detailed description thereof, the foregoing description is intended to illustrate and not limit the scope of the invention, which is defined by the scope of the appended claims.