High speed wide angle lens system

A high speed wide angle lens system of the same general kind disclosed in Glatzel, U.S. Pat. No. 3,915,558, but with a slightly larger aperture and with improved image formation. While the lens formation of the U.S. Pat. No. 3,915,558 starts with two negative components, followed by a positive component, a meniscus, two negative components and two positive components in the rear part, the improved performance of the present invention is achieved by such a modification which enforces the positive power of the rear part of the lens. For this purpose the rear part is made to consist of three positive components (VII, VIII, IX) which are designed in such a way that the quotient of the sum of the surface powers of the air lenses between the three rear positive components .SIGMA..phi..sub..delta. divided by the refractive power (.phi..sup.+.sub.EO) of the air lens between the two positive components of the front part of the lens (III, IV) lies between a disclosed upper and lower limit and that in addition to this rule the paraxial surface power sum of the second-last component (VIII) also is within disclosed limits times the paraxial surface power sum of the third-last component (VII). Eight specific examples are given to illustrate the validity of the disclosed conditions and rules.

BACKGROUND OF THE INVENTION 
This invention relates to an objective for lens systems having extremely 
high speed and a wide angle of view, useful for photographic and other 
purposes. It is a lens of the same general type as that disclosed in the 
present applicant's Glatzel U.S. Pat. No. 3,915,558, granted Oct. 28, 
1975, the disclosure of which is incorporated herein by reference. The 
prior patent may be referred to for convenience as the "main patent," and 
the present invention may be regarded as an improvement on the main 
patent. By following certain design principles or rules as set forth 
below, it is found that an improved image can be produced, as compared 
with the image produced by the lens of the main patent. 
Moreover, the present invention provides a lens of somewhat greater power 
or speed as compared with the lens of the main patent, and having at least 
in some examples a somewhat wider field of view than the lens of the main 
patent, without sacrificing the quality of the image.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In describing the lens or objective of the present invention, and 
illustrating the same in the diagrams, it will be assumed, as customary in 
lens patents and in scientific literature, that the light is coming from 
the left of the diagram toward the right thereof. Parts described as being 
at the front or in the forward portion of the lens are those parts near 
the left of the diagram, and parts described as being at the rear or back 
of the lens are those parts near the right of each diagram. Light from a 
distant object proceeds rightwardly to the front element of the lens, 
enters the lens system, passes through it, leaves the lens system at the 
last surface of the last or rearmost element of the system, and forms an 
image at an image plane to the rear of the last element. The word "lens" 
is sometimes used with reference to the entire objective or lens system as 
a whole, and sometimes used with reference to a particular individual lens 
element or perhaps a group of elements, but in any event the context will 
make the meaning clear to those skilled in the art. 
First describing the present lens in general terms, and deferring until 
later a discussion of the design rules or characteristics which 
distinguish this lens from others, the lens may be said in general to have 
nine components, respectively designated both in the drawings and in the 
data tables by the consecutive Roman numerals I to IX, inclusive. The 
individual lens elements are also designated by the letter L with an 
Arabic numerical subscript corresponding to the number of the component 
and with a further subscript of "a" or "b" where a particular component is 
split into two elements. Since most of the components are made of a single 
individual element, the Arabic numerical subscripts for the individual 
lens elements will have the same numerical value as the Roman numeral 
designations of the components. In some examples, however, as well as in 
FIGS. 1 and 2 of the lens diagrams, the component III is composed of two 
individual lens elements designated as L.sub.3a and L.sub.3b. 
Components I through V may be regarded as the front member of the lens, 
designated in the tables and the diagrams by the letters "Vgl," and the 
components VI through IX may be regarded as the rear member of the lens, 
designated by the letters "Hgl." Between the front member and the rear 
member (that is, between component V and component VI) is the central 
space CS. 
Now referring in more detail to the various components, the first two 
components I and II have together a negative power, and preferably both of 
them are individual elements of negative power, although one of them could 
be positive provided the combined power of both is negative. 
Behind the components I and II is a third component III which is positive, 
and which is spaced rearwardly from component II to provide between them 
an air space or air lens .alpha. having a diverging action. This component 
III serves essentially as an ocular for the components I and II, and this 
component may be either an individual element (see example IV, and FIG. 3 
of the diagrams) or a combination of two elements (see FIGS. 1 and 2, and 
all of the examples except example IV). 
This component III is followed in turn by the meniscus component IV having 
its convex surface toward the front, and spaced from component III to 
provide between them an air lens .beta. having collecting power. 
Behind this meniscus member IV is a first negative component V and behind 
it a second negative component VI, followed in turn by a plurality of 
positive elements (preferably three in number, designated VII, VIII, and 
IX) which are air spaced from each other. The negative component V is 
spaced from the meniscus component IV to provide between them an air lens 
.gamma. of negative or diverging power, and the second negative component 
VI is spaced from the component V to provide between them an air space of 
strongly diverging power. The air space between the components VII and 
VIII is designated as the air lens .delta..sub.1 and the air space between 
the components VIII and IX is designated as the air lens .delta..sub.2, 
both of these air lenses having positive or collecting power. 
The positive component III (regardless of whether it is composed of a 
single element or a combination of two elements has a surface refractive 
power .phi..sub.III which is greater than 1.1765 times the absolute 
numerical value of the refractive power .phi..sub.V of the negative 
component V. At the same time, the paraxial surface power sum or lens 
refractive power .phi..sub.V of this negative component V is less than 
0.90 times the surface power sum .phi..sub.VI of the second negative 
element VI in this portion of the lens system. It may be noted again that 
the component VI is separated from the component V by an air space having 
the shape of a collecting lens. 
In accordance with the customary notation commonly used in this art, and as 
explained in column 1 of the main patent, the symbol .phi. stands for the 
refractive power or sum of the surface powers of a particular element or 
component identified by the subscript used with this symbol. Thus 
.phi..sub..beta. means the refractive power or sum of the surface powers 
of the air lens .beta., and .phi..sub..gamma. means the power of the air 
lens .gamma., and .phi..sub.IV means the power of the lens component IV, 
and so on. 
It is an important feature of the present invention that the three positive 
components VII, VIII, and IX behind the just mentioned negative component 
VI enclose between them two air spaces or air lenses .delta..sub.1 and 
.delta..sub.2 the sum of the surface powers of which (designated 
.SIGMA..phi..sub..delta.) is so established that the quotient of this sum 
divided by the refractive power .phi..sub.EO.sup.+ is within the limits of 
0.88 and 1.60. In this expression, the just mentioned refractive power 
.phi..sub.EO.sup.+ represents the refractive power of the collecting air 
lens between the rear ray exit surface of the Newtonian finder section NS 
of the lens on the one hand and the front ray entrance surface of the main 
lens part O on the other hand; in words, the refractive power of the air 
lens .beta.. This relationship contributes to solving the problem of a 
pertinent reduction of the errors of asymmetry of higher order in the 
extreme wide-open lateral beams. 
Another important feature of the invention is the relationship between the 
paraxial surface powers of the components VII and VIII. It is found that 
best results are obtained when these two components are so designed that 
the paraxial surface power .phi..sub.VIII of the lens VIII is within the 
limits of 0.272 and 0.526 times the surface refractive power .phi..sub.VII 
of the lens VII. By observing this relationship between the components VII 
and VIII, assurance is provided that the positive refractive power of the 
component VIII further removed from the place of the diaphragm can be kept 
in such a range relative to the power of the component VII which is closer 
to the diaphragm, without unfavorably disturbing the desired dioptric 
harmony established as a result of the first important feature above 
mentioned, thus avoiding an undesirable increase in the aberrations of 
higher order in the region of the lateral strongly inclined ray paths. 
By complying with these two features or rules above stated, in designing 
the lens, there is obtained in a simple manner a simultaneous increase in 
power, and a very sharp focusing efficiency, which is just as surprising 
as it is welcome, since now the third collecting lens (component IX) at 
the rear of the system need essentially satisfy only the main task of 
obtaining the desired strong total deflection in order to achieve the 
desired high power of the entire system. 
In view of what has been said above, it will now be apparent to those 
skilled in this art that as a result of the new dimensioning ratio above 
set forth, there is now obtained in a surprising and important manner a 
pertinent increase in power. When the air lenses are designed in the 
manner here taught, the lateral courses of the beams in the air lenses can 
be used, with relatively very large ray inclinations with respect to the 
optical axis, and at the same time also with respect to the central beam 
passing through the objective, for a very substantial improvement in the 
lateral image performance. In this present invention, as compared with the 
main patent, this utilization is effected for the first time on the two 
different sides of the large inner central vertex distance, namely, in the 
object-side entrance part of the main objective part "O" producing the 
real image on the one hand, and on the side of the part of the rear 
element of the rear lens part "O" closely adjacent the shorter conjugate 
on the rear side, on the other hand. By this reciprocal position of 
application of this specific design rule with respect to the place of the 
diaphragm, the way is opened to a particularly important increase in 
performance in the further development of a lens system generally in 
accordance with the main patent. 
Another feature of the present invention is that in this case also, in 
agreement with the general object of the main patent, the collecting 
ocular component III of the Newtonian finder part NS can be divided by 
spliting it into two individual components L.sub.3a and L.sub.3b, 
preferably separated from each other by an air space, in order to obtain 
specific additional effects of dioptric corrective action, as described in 
detail in the specification of the main patent and also shown 
diagrammatically in the drawings of said main patent. 
Eight specific examples are given, all of which are designed in accordance 
with the design principles above described. In the data tables, all linear 
measurements such as radii, thicknesses, and spacings are not given as 
absolute dimensions, but rather are stated as proportions of the 
equivalent focal length (F) of the entire objective lens system, which is 
considered as unity. That is, F = 1.00000. The individual lens elements 
are indicated by the letter L with a subscript corresponding to the number 
of the individual lens element as already explained. 
The notations or symbols used in the data tables and also in the lens 
diagrams are in accordance with the notations and symbols often used in 
many lens patents, and will be well understood by those skilled in the 
art. For instance, the radii of curvature of the front surface and the 
rear surface of each element are indicated by R and R', respectively, with 
a subscript indicating the number of that particular element. Positive 
values of R or R' indicates surfaces convex toward the front of the lens, 
and negative values indicates surfaces concave toward the front, in 
accordance with customary usage. The end of the lens toward the distant 
object or longer conjugate is referred to for convenience as the front, 
and the end toward the image (that is, toward the camera, if the lens 
system is used on a photographic camera) is referred to for convenience as 
the rear of the lens. The light is assumed, in accordance with 
conventional lens patent practice, to enter from the front, and to pass 
through the lens from left to right. 
The axial thicknesses of individual lens elements are indicated in the 
tables by the letter "d" with a subscript identifying the particular 
element. Axial spacings between elements are indicated by the letter "s" 
likewise with a subscript, but in the case of these spacings, the 
subscript refers to the identifying number of the lens in front of and the 
lens behind the space in question. Zero spacing indicates elements 
cemented to each other. All spacings greater than zero refer to air 
spacings. 
The index of refraction is indicated by "n" with a subscript identifying 
the lens element, in some of the tables. In other tables, the indices of 
refraction are given in a column headed n.sub.d for the sake of 
compactness when the data also include the Abbe number or dispersive 
index, stated in an adjacent column headed v.sub.d. When an objective is 
designed for use in only a very narrow spectral range, the refractive 
index refers specifically to this narrow range. If the lens system is to 
be used over a wide spectral range, as for example in color photography, 
then instead of monochromatic image error correction, achromatism should 
be brought out over the wider spectral range required. For this purpose, 
in known manner, the glasses used in the elements are to be chosen so that 
the color dispersion of the glasses used serves to eliminate the chromatic 
deviations or errors due to the wavelengths which enter into 
consideration. 
During the course of development of this invention it was found, by way of 
confirmation, that upon the development of the so-called preforms or 
initial forms of the objectives, and then during the course of the 
following technical rough development to produce a rough form in known 
manner with the first correction normally customary in the Seidel range 
(third order), the use of one of the standard refractive indices can take 
place in a routine manner. A convenient index to use for this purpose is 
the index of refraction for the yellow d-line of the helium spectrum, with 
a wavelength of 5876 Angstrom units. Data for this wavelength are 
customarily shown in many commercial catalogues of manufacturers of 
optical glasses. 
In the heading of each data table there is indicated the figure number of 
the particular lens diagram which is intended to illustrate the specific 
example in the table. In this connection it should be borne in mind that 
the lens diagrams are not intended to be drawn strictly to scale, but are 
intended merely to furnish a quick visual indication of the general 
characteristics of the particular specific example. Thus a single lens 
diagram is sufficient to illustrate two or more specific examples which 
are of the same general configuration but which may differ somewhat from 
each other in thicknesses, spacings, curvatures, or other factors. 
The specific example tables also indicate, in each case, the relative 
aperture for which the particular example is intended, expressed as 
conventional "f" number, and the angular field of view, designated as 2 wo 
and expressed in degrees, and the back focus from the axial vertex of the 
last lens element to the focal plane (for an object at infinity) 
designated as S'oo and expressed in proportion to the equivalent focal 
length (F) of the entire objective lens system. It may be noted in this 
connection that in each example, the back focus is greater than the 
equivalent focal length of the entire system, so that there is sufficient 
space for the swinging of a mirror, if it is desired to use the lens on a 
single lens mirror reflex camera. 
It has been mentioned above that component III may, if desired, be split 
into two lens elements, and this is the case in all specific examples 
except example 4. When this component is split, the adjacent surfaces may 
be given different signs of curvature, as well as the same sign. The 
possibility of standardization in favor of a single positive lens 
surrounded by air on both sides at this place has been made obvious in 
example 2, in which the splitting is so arranged that the adjacent 
surfaces of the two elements are provided with radii of curvature which 
are of the same sign and of the same length, and having the same glass 
refractive indices. 
Another characteristic of the present invention is that, on account of the 
provision and dimensioning of the two air lenses respectively between 
components VII and VIII and components VIII and IX, and the provision for 
a further increase in speed for the wide open bundle cross section, it is 
no longer necessary to comply with the condition laid down as rule "A" in 
the main patent. Thus it is now possible, as shown by the specific 
examples in the present application, to make the second component II as a 
more strongly refractive negative member than the first component I, 
instead of making it weaker as required by rule "A" in the main patent. 
The collecting air lenses between the components VII, VIII, and IX, on 
account of their different distances from the diaphragm, can provide a 
suitable compensation effect for the errors in asymmetry resulting from 
the negative components I and II at different distances in front of the 
diaphragm, utilizing this in a manner which was both previously unknown 
and unexpected. With such an advance is possible to utilize both a 
power-increasing reduction of the aberrations of higher order of the 
proportions of errors of asymmetry on the one hand as well as a favorable 
smoothing-down of the course of the residual errors of distortion for a 
zonal image field region between about 40.degree. and 55.degree. on the 
other hand, in which correction furthermore there is the possibility of 
displacing this last mentioned zonal region, depending on the purpose of 
use, by a few degrees downward or upward. Three of the following examples 
(examples 3, 6, and 7) are developed in this additional manner, while the 
remaining examples (examples 1, 2, 4, 5, and 8) are developed in such a 
manner that the surface power sum .phi..sub.II of the negative component 
II is larger in absolute value than the surface power sum .phi..sub.I of 
the first negative component I. 
The present lens may be advantageously provided with an aspherically shaped 
surface in order to carry out specific correction processes. Preferably an 
aspherical surface is used for the front surface of the negative component 
V, this surface being adjacent to the diaphragm and hence being on a 
surface of relatively small diameter. The coefficients for the aspherical 
surface (R.sub.5) are shown at the end of the tabular data for each 
specific example. These coefficients are the coefficients for the usual 
well known camber expression, as shown for example in column 15 of the 
main patent. The use of the aspherical shape on the surface R.sub.5 to 
eliminate spherical aberrations for the lateral portions of the wide open 
beam cross sections, facilitates a comparison between the lens of the 
present application and the lens of the main patent. 
The various examples also provide an indication of the width of the 
possible variations which can be utilized by the optical designer, for 
instance with reference to the selection of the type of glass or the like, 
depending on what specific relative apertures or image-field sizes or what 
back focus distances are specifically desired. 
Also, for the sake of facilitating comparison, a number of glasses have 
been used uniformly in these examples. 
The wide possibilities of variation inherent in the present new principles 
of design within the scope of the invention can be appreciated by a quick 
glance at the two data tables, Table I and Table II, which follow the 
specific example tables. The headings of these Tables I and II agree with 
the designations previously used in the foregoing description. The 
refractive power of the entire system is .PHI.. 
In considering the various numerical values given in the various tables and 
elsewhere, it should be borne in mind that customarily a tolerance of plus 
or minus 5% is allowable. 
__________________________________________________________________________ 
Example 1.) (FIG. 1) 
F = 1.0000 f/1.27 2.omega..sub.0 = 60.degree. s'.sub..infin. = + 1.02696 
Thicknesses and 
Lens Radii spacings 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.74228 R'.sub.1 = + + 1.03947 
d.sub.1 = 0.130003 s.sub.12 = 0.286084 
##STR1## 
IIL.sub.2 
R.sub.2 = + 6.48164 R'.sub.2 = + 1.17691 
d.sub.2 = 0.087002 s.sub.23 = 0.420510 
##STR2## 
##STR3## 
R.sub.3.sbsb.a = + 1.80649 R'.sub.3.sbsb.a = - 7.56390 R.sub.3.sbs 
b.b = + 15.5044 R'.sub.3.sbsb.b = - 2.47289 
d.sub.3.sbsb.a = 0.270430 s.sub.3.sbsb.a,b = 0.096156 
d.sub.3.sbsb.b .sup..delta. 0.172658 
##STR4## 
s.sub.34 = 0.002039 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.79945 R'.sub.4 = + 0.93950 
d.sub.4 = 0.123465 s.sub.45 = 0.366701 
##STR5## 
VL.sub.5 
R.sub.5 = + 41.9532 R'.sub.5 = + 1.04954 
d.sub.5 = 0.066732 CS = s.sub.56 = 0.210505 
##STR6## 
VIL.sub.6 
R.sub.6 = - 1.31336 R'.sub.6 = + 1.05785 
d.sub.6 = 0.041809 s.sub.67 = 0 
##STR7## 
VIIL.sub.7 
R.sub.7 = + 1.05785 R'.sub.7 = - 1.38749 
d.sub.7 = 0.295507 s.sub.78 = 0.002000 
##STR8## .1) 
VIIIL.sub.8 
R.sub.8 = + 12.9863 R'.sub.8 = - 2.31790 
d.sub.8 = 0.132465 s.sub.89 = 0.002308 
##STR9## .2) 
IXL.sub.9 
R.sub.9 = + 4.07109 R'.sub.9 = - 3.72269 
d.sub.9 = 0.135926 
##STR10## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.964812 .multidot. 10.sup.-1, c.sub.3 = c.sub.4 = c.sub.5 = 0 
__________________________________________________________________________ 
Example 2.) (FIG.2) 
F = 1.0000 f/1.26 2.omega..sub.0 = 60.degree. s'.sub..infin. = + 1.04042 
Thicknesses and 
Lens Radii spacings 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.52595 R'.sub.1 = + 1.09628 
d.sub.1 = 0.128446 s.sub.12 = 0.315556 
##STR11## 
IIL.sub.2 
R.sub.2 = + 6.34487 R'.sub.2 = + 1.41026 
d.sub.2 = 0.119628 s.sub.23 = 0.488096 
##STR12## 
##STR13## 
R.sub.3.sbsb.a = + 1.98000 R'.sub.3.sbsb.a = - 7.46531 R.sub.3.sbs 
b.b = - 7.46531 R'.sub.3.sbsb.b = - 2.08006 
d.sub.3.sbsb.a = 0.236000 s.sub.3.sbsb.a,b = 0.010000 
d.sub.3.sbsb.b = 0.104413 
##STR14## 
s.sub.34 = 0.003068 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.88344 R'.sub.4 = + 1.02017 
d.sub.4 = 0.195929 s.sub.45 = 0.337795 
##STR15## 
VL.sub.5 
R.sub.5 = + 5.69393 R'.sub.5 = + 0.95622 
d.sub.5 = 0.062498 CS = s.sub.56 = 0.233887 
##STR16## 
VIL.sub.6 
R.sub.6 = - 0.90273 R'.sub.6 = + 2.14068 
d.sub.6 = 0.047161 s.sub.67 = 0 
##STR17## 
VIIL.sub.7 
R.sub.7 = + 2.14068 R'.sub.7 = - 1.11219 
d.sub.7 = 0.253442 s.sub.78 = 0.002301 
##STR18## .1) 
VIIIL.sub.8 
R.sub.8 = + 10.49963 R'.sub.8 = - 1.78824 
d.sub.8 = 0.137648 s.sub.89 = 0.002300 
##STR19## .2) 
IXL.sub.9 
R.sub.9 = + 3.34428 R'.sub.9 = - 3.80673 
d.sub.9 = 0.134965 
##STR20## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.841760 .multidot. 10.sup.-1, c.sub.3 = c.sub.4 = c.sub.5 = 0 
__________________________________________________________________________ 
Example 3.) (FIG. 1) 
F = 1.0000 f/1.26 2.omega..sub.0 = 62.degree. s'.sub..infin. = + 1.03465 
Thicknesses and 
Lens Radii spacings 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.35979 R'.sub.1 = + + 1.02872 
d.sub.1 = 0.076463 s.sub.12 = 0.307508 
##STR21## 
IIL.sub.2 
R.sub.2 = + 4.81446 R'.sub.2 = + 1.55048 
d.sub.2 = 0.112234 s.sub.23 = 0.509075 
##STR22## 
##STR23## 
R.sub.3.sbsb.a = + 1.79124 R'.sub.3.sbsb.a = - 7.52983 R.sub.3.sbs 
b.b = + 10.2924 R'.sub.3.sbsb.b = - 3.28521 
d.sub.3.sbsb.a = 0.257776 s.sub.3.sbsb.a,b = 0.077079 
d.sub.3.sbsb.b .sup..delta. 0.171235 
##STR24## 
s.sub.34 = 0.002039 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.83559 R'.sub.4 = + 0.98843 
d.sub.4 = 0.130965 s.sub.45 = 0.318777 
##STR25## 
VL.sub.5 
R.sub.5 = + 5.71180 R'.sub.5 = + 0.85253 
d.sub.5 = 0.059117 CS = s.sub.56 = 0.251891 
##STR26## 
VIL.sub.6 
R.sub.6 = - 0.83756 R'.sub.6 = + 1.90424 
d.sub.6 = 0.042578 s.sub.67 = 0 
##STR27## 
VIIL.sub.7 
R.sub.7 = + 1.90424 R'.sub.7 = - 1.07201 
d.sub.7 = 0.263199 s.sub.78 = 0.002231 
##STR28## .1) 
VIIIL.sub.8 
R.sub.8 = + 8.41147 R'.sub.8 = - 1.53136 
d.sub.8 = 0.146619 s.sub.89 = 0.002039 
##STR29## .2) 
IXL.sub.9 
R.sub.9 = + 2.90643 R'.sub.9 = - 11.65312 
d.sub.9 = 0.130196 
##STR30## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.995362 .multidot. 10.sup.-1, c.sub.3 = c.sub.4 = c.sub.5 = 0 
__________________________________________________________________________ 
Example 4.) (FIG. 3) 
F = 1.0000 f/1.25 2.omega..sub.o = 60.degree. s'.sub..infin. = + 1.04042 
Thicknesses and 
Lens Radii spacings 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.52595 R'.sub.1 = + 1.09628 
d.sub.1 = 0.128446 s.sub.12 = 0.315556 
##STR31## 
IIL.sub.2 
R.sub.2 = + 6.34487 R'.sub.2 = + 1.41026 
d.sub.2 = 0.119628 s.sub.23 = 0.488096 
##STR32## 
IIIL.sub.3 
R.sub.3 = + 1.98000 R'.sub.3 = - 2.08006 
d.sub.3 = 0.340413 s.sub.34 = 0.003068 
##STR33## 
IVL.sub.4 
R.sub.4 = + 0.88344 R'.sub.4 = + 1.02017 
d.sub.4 = 0.195929 s.sub.45 = 0.337795 
##STR34## 
VL.sub.5 
R.sub.5 = + 5.69393 R'.sub.5 = + 0.95622 
d.sub. 5 = 0.062498 CS = s.sub.56 = 0.233887 
##STR35## 
VIL.sub.6 
R.sub.6 = - 0.90273 R'.sub.6 = + 2.14068 
d.sub.6 = 0.047161 s.sub.67 = 0 
##STR36## 
VIIL.sub.7 
R.sub.7 = + 2.14068 R'.sub.7 = - 1.11219 
d.sub.7 = 0.253442 s.sub.78 = 0.002301 
##STR37## .1) 
VIIIL.sub.8 
R.sub.8 = + 10.4996 R'.sub.8 = - 1.78824 
d.sub.8 = 0.137648 s.sub.89 = 0.002300 
##STR38## .2) 
IXL.sub.9 
R.sub.9 = + 3.34428 R'.sub.9 = - 3.80673 
d.sub.9 = 0.134965 
##STR39## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -2.1655465 .multidot. 10.sup.-5, c.sub.3 = c.sub.4 = c.sub.5 = 
0. 
__________________________________________________________________________ 
Example 5.) (FIG.4) 
F = 1.00000 f/1.24 2.omega..sub.o = 60.degree. s'.sub..infin. = + 1.02698 
Thicknesses and 
Lens Radii spacings n.sub.d /.nu..sub.d 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.28038 R'.sub.1 = + 1.03603 
d.sub.1 = 0.075649 s.sub.12 = 0.309443 
##STR40## 
IIL.sub.2 
R.sub.2 = + 5.64519 R'.sub.2 = + 1.33972 
d.sub.2 = 0.101032 s.sub.23 = 0.445243 
##STR41## 
##STR42## 
R.sub.3.sbsb.a = + 1.75286 R'.sub.3.sbsb.a = - 5.54731 R.sub.3.sbs 
b.b = + 15.1975 R'.sub.3.sbsb.b = - 2.90250 
d.sub.3.sbsb.a = 0.272561 s.sub.3.sbsb.a,b = 0.070650 
d.sub.3.sbsb.b = 0.170567 
##STR43## 
s.sub.34 = 0.002231 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.81191 R'.sub.4 = + 0.99154 
d.sub.4 = 0.131338 s.sub.45 = 0.317020 
##STR44## 
VL.sub.5 
R.sub.5 = + 8.48566 R'.sub.5 = + 0.90007 
d.sub.5 = 0.061919 CS = s.sub.56 = 0.249562 
##STR45## 
VIL.sub.6 
R.sub.6 = - 0.97119 R'.sub.6 = + 1.68540 
d.sub.6 = 0.041959 s.sub.67 = 0 
##STR46## 
VIIL.sub.7 
R.sub.7 = + 1.68540 R'.sub.7 = - 1.16566 
d.sub.7 = 0.264753 s.sub.78 = 0.002000 
##STR47## .1) 
VIIIL.sub.8 
R.sub.8 = - 52.9668 R'.sub.8 = - 1.47025 
d.sub.8 = 0.138453 s.sub.89 = 0.002654 
##STR48## .2) 
IXL.sub.9 
R.sub.9 = + 2.09194 R'.sub.9 = + 109.081 
d.sub.9 = 0.131108 
##STR49## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.7736161 .multidot. 10.sup.-1, c.sub.3 = c.sub.4 = c.sub.5 = 
0. 
__________________________________________________________________________ 
Example 6.) (FIG. 1) 
F = 1.00000 f/1.24 2.omega..sub.o = 60.degree. s'.sub..infin. = + 1.04162 
Thicknesses and 
Lens Radii spacings n.sub.d /.nu..sub.d 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.37259 R'.sub.1 = + 1.05220 
d.sub.1 = 0.082227 s.sub.12 = 0.323144 
##STR50## 
IIL.sub.2 
R.sub.2 = + 5.42735 R'.sub.2 = + 1.49703 
d.sub.2 = 0.115655 s.sub.23 = 0.478375 
##STR51## 
##STR52## 
R.sub.3.sbsb.a = + 1.96776 R'.sub.3.sbsb.a = - 9.79152 R.sub.3.sbs 
b.b = + 7.89031 R'.sub.3.sbsb.b = - 2.90218 
d.sub.3.sbsb.a = 0.266661 s.sub.3.sbsb.a,b = 0.096059 
d.sub.3.sbsb.b = 0.190582 
##STR53## 
s.sub.34 = 0.003074 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.86642 R'.sub.4 = + 1.00774 
d.sub.4 = 0.161764 s.sub.45 = 0.330828 
##STR54## 
VL.sub.5 
R.sub.5 = + 5.70604 R'.sub.5 = + 0.90465 
d.sub.5 = 0.059557 CS = s.sub.56 = 0.249370 
##STR55## 
VIL.sub.6 
R.sub.6 = - 0.82980 R'.sub.6 = + 2.54792 
d.sub.6 = 0.041498 s.sub.67 = 0 
##STR56## 
VIIL.sub.7 
R.sub.7 = + 2.54792 R'.sub.7 = - 1.03717 
d.sub.7 = 0.255134 s.sub.78 = 0.003842 
##STR57## .1) 
VIIIL.sub.8 
R.sub.8 = + 9.51371 R'.sub.8 = - 1.77821 
d.sub.8 = 0.139478 s.sub.89 = 0.003074 
##STR58## .2) 
IXL.sub.9 
R.sub.9 = + 3.05211 R'.sub.9 = - 4.40528 
d.sub.9 = 0.139862 
##STR59## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.4253170 .multidot. 10.sup.-1, c.sub.3 = c.sub.4 = c.sub.5 = 
0. 
__________________________________________________________________________ 
Example 7.) (FIG. 4) 
F = 1.00000 f/1.24 2.omega..sub.o = 60.degree. s'.sub..infin. = + 1.02697 
Thicknesses and 
Lens Radii spacings n.sub.d /.nu..sub.d 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.25420 R'.sub.1 = + 1.01132 
d.sub.1 = 0.075309 s.sub.12 = 0.314043 
##STR60## 
IIL.sub.2 
R.sub.2 = + 4.58177 R'.sub.2 = + 1.38713 
d.sub.2 = 0.122848 s.sub.23 = 0.491084 
##STR61## 
##STR62## 
R.sub.3.sbsb.a = + 1.79457 R'.sub.3.sbsb.a = - 6.95357 R.sub.3.sbs 
b.b = + 12.9780 R'.sub.3.sbsb.b = - 2.78172 
d.sub.3.sbsb.a = 0.257427 s.sub.3.sbsb.a,b = 0.087963 
d.sub.3.sbsb.b = 0.173580 
##STR63## 
s.sub.34 = 0.002769 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.81634 R'.sub.4 = + 0.94692 
d.sub.4 = 0.139656 s.sub.45 = 0.317428 
##STR64## 
VL.sub.5 
R.sub.5 = + 5.71174 R'.sub.5 = + 0.90726 
d.sub.5 = 0.059347 CS = s.sub.56 = 0.264389 
##STR65## 
VIL.sub.6 
R.sub.6 = - 0.89844 R'.sub.6 = + 1.92688 
d.sub.6 = 0.042808 s.sub.67 = 0 
##STR66## 
VIIL.sub.7 
R.sub. 7 = + 1.92688 R'.sub.7 = - 1.08960 
d.sub.7 = 0.265119 s.sub.78 = 0.003269 
##STR67## .1) 
VIIIL.sub.8 
R.sub.8 = + 20.6329 R'.sub.8 = - 1.51790 
d.sub.8 = 0.150656 s.sub.89 = 0.005000 
##STR68## .2) 
IXL.sub.9 
R.sub.9 = + 2.13877 R'.sub.9 = - 20.7200 
d.sub.9 = 0.136848 
##STR69## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.8265852 .multidot. 10.sup.-1, c.sub.3 = -5.9537649 .multidot 
10.sup.-2, c.sub.4 = c.sub.5 = 0. 
__________________________________________________________________________ 
Example 8.) (FIG. 1) 
F = 1.00000 f/1.23 2.omega..sub.o = 60.degree. s'.sub..infin. = + 1.02697 
Thicknesses and 
Lens Radii spacings n.sub.d /.nu..sub.d 
__________________________________________________________________________ 
IL.sub.1 
R.sub.1 = + 2.52595 R'.sub.1 = + 1.09628 
d.sub.1 = 0.128446 s.sub.12 = 0.315556 
##STR70## 
IIL.sub.2 
R.sub.2 = + 6.34487 R'.sub.2 = + 1.41026 
d.sub.2 = 0.119628 s.sub.23 = 0.488096 
##STR71## 
##STR72## 
R.sub.3.sbsb.a = + 2.00645 R'.sub.3.sbsb.a = - 10.0560 R.sub.3.sbs 
b.b = + 9.35780 R'.sub.3.sbsb.b = - 2.81386 
d.sub.3.sbsb.a = 0.230053 s.sub.3.sbsb.a,b = 0.084353 
d.sub.3.sbsb.b = 0.173307 
##STR73## 
s.sub.34 = 0.003068 (.beta.) 
IVL.sub.4 
R.sub.4 = + 0.88344 R'.sub.4 = + 1.02017 
d.sub.4 = 0.195929 s.sub.45 = 0.337795 
##STR74## 
VL.sub.5 
R.sub.5 = + 5.69393 R'.sub.5 = + 0.95622 
d.sub.5 = 0.062498 CS = s.sub.56 = 0.233887 
##STR75## 
VIL.sub.6 
R.sub.6 = - 0.90273 R'.sub.6 = + 2.14068 
d.sub.6 = 0.047161 s.sub.67 = 0 
##STR76## 
VIIL.sub.7 
R.sub.7 = + 2.14068 R'.sub.7 = - 1.11219 
d.sub.7 = 0.253442 s.sub.78 = 0.002301 
##STR77## .1) 
VIIIL.sub.8 
R.sub.8 = + 10.4996 R'.sub.8 = - 1.78824 
d.sub.8 = 0.137648 s.sub.89 = 0.002300 
##STR78## .2) 
IXL.sub.9 
R.sub.9 = + 3.34428 R'.sub.9 = - 3.80673 
d.sub.9 = 0.134965 
##STR79## 
__________________________________________________________________________ 
Aspherical surfaces: R.sub.5 with c.sub.1 = (2 .multidot. R.sub.5).sup.-1 
c.sub.2 = -3.8418157 .multidot. 10.sup.-1, c.sub.3 = c.sub.4 = c.sub.5 = 
0.