A new lens system having a six-element configuration has been developed at a focal length of 75 mm and
relative aperture of f/1.6 for use as a 35-mm cinema projector objective. To evaluate the performance of the
new system, another design based on a six-element double Gauss configuration has been developed in similar
conditions. In comparison, the new configuration is found to give better performance compared with the six-
element double Gauss configuration in current use.
1. Introduction
Five-element lenses based on double Gauss configu-ration have been used up to apertures of f/2 for a 35-mm cinematograph projection. A better lens for simi-lar apertures has been proposed by the author.' Forstill better performance and/or high apertures, six-element systems based on double Gauss configurationhave been used. Macher2 has given designs of theCinelux-ultra f/2.0 75-mm lens with better perfor-mance compared with earlier Super-Kiptar lenses.His designs are also based on six-element double Gaussform but without cementing surfaces. Use of unce-mented elements provides more parameters for aber-ration correction, and the danger of deterioration ofcementing due to the lamp heat is avoided. Recentlylenses having apertures up to f/11.6 have been in themarket. 3 Their basic form again is based on dece-mented six-element double Gauss construction.
In this paper, a new configuration comprising sixelements is reported. The new lens is suitable for highaperture applications. The new configuration likedouble Gauss system is comprised of four positive andtwo negative elements. In the new configuration alsono cemented surfaces are used, but the various ele-ments are arranged differently (Fig. 1) than the doubleGauss form. To evaluate the performance capabilityof the new configuration, a design at 75 mm f/11.6 hasbeen developed for use as a 35-mm cinema projectorobjective. Another design based on double Gaussform was also developed with similar specifications tocompare its performance with the new design. Bothdesigns have been developed using CGCRI glasses with
The authors are with Indian Institute of Technology, InstrumentDesign Development Centre, New Delhi, 11016, India.
the help of a lens optimization program. This pro-gram is based on a damped least-squares method4 andis found to be very effective for giving corrected de-signs. The conditions of optimization for both config-urations were kept identical. The performance of thedesigns has been evaluated by plotting aberrationcurves, energy distribution curves, and geometricalMTF curves. By comparison it has been found thatthe proposed new configuration is capable of givingbetter performance than the double Gauss configura-tion in current use. Later, two more designs based ondouble Gauss form, but using superior glasses, weredeveloped. The new design was found to be superiorto these designs as well.
II. System Configuration and Conditions of Optimization
As mentioned earlier the proposed configuration iscomprised of six uncemented elements. The elementsare so arranged that some features of the basic Cooketriplet construction are obtained twice. It is wellknown that the triplet construction derives its mainadvantages from the fact that the height of the margin-al ray on the middle negative lens is less than onpositive lenses. Considering the usual computing di-rection of the projector lenses from the image to theobject side, the various elements in the new configura-tion are so arranged that the first two elements arepositive and the third is negative. This is followed bytwo positive elements, and the last element is negative.The marginal ray is converged by the first two ele-ments, and its height on the third negative element isconsiderably decreased. The third element divergesthe ray, and the ray height is increased subsequently.The following two positive elements again convergethe ray, and the ray height on the last negative elementis less than these positive elements. Thus the newconfiguration utilizes the basic triplet concept twice.This makes the new configuration capable of giving avery high quality system.
The designs have been optimized at a focal length of
75 mm and relative aperture of f/11.6 to cover a field ofh100. The merit of the function (defined as the sum
of the squares of the weighted aberrations), which isminimized by the program to improve the lens quality,is found by calculating the transverse ray aberrationsand Conrady color for a set of twenty-eight rays chosenfrom different sampling points of field and aperture.The ray data are so chosen that the resultant clearapertures of the various elements allow nearly 71% ofthe rays to pass through the system from the extremeedge of the field. This allows good illumination distri-bution over the image, 100% of the rays for the centralimage. In the computing direction the object is takenat infinity, which is nearly the situation in cinemalenses owing to large magnifications of the actual im-age. The designs are based on Indian glasses manu-factured by OGCRI5 Calcutta. For the positive lensesDBC 610573 glass has been used. For the negativelenses the choice of glasses was made with the help ofthe program, first by treating the refractive index anddispersion as variable parameters and thereby chang-ing these to the nearest catalog value for final optimi-zation. The use of high index rare earth glasses orother high index glasses for the positive lenses wouldgive better designs, but no crown glass is available inthe CGCRI catalog which has a higher index than theglasses chosen. The glasses that are used for thesedesigns are also available in Schott and Chance glasscatalogs. The monochromatic aberrations have beenbalanced for the e line of mercury and the chromaticaberrations for the C-F wavelength range using Conra-dy's (d-D) formula.6
As usual, curvatures and thicknesses are treated ascontinuously variable parameters. However, some di-mensional restrictions have been imposed on mini-mum lens thicknesses and air gaps. The minimumedge thicknesses of the positive lenses has been main-tained at 1.7 mm and the minimum axial thickness ofthe negative lenses at 0.7 mm. The air separationbetween two surfaces either at the axis or at the edgehas not been allowed to be <0.3 mm. No dimensionalrestrictions on total length (front vertex to focal plane)and axial thickness (front vertex to rear vertex) havebeen imposed. The back focal length (rear vertex tofocal plane) is not allowed to have a lower value than 36mm, a requirement of the British Standard.7
111. Design Data and System Performance
Table I gives the design data for the new configura-tion. The design is given by tabulating the followingdata: (1) surface curvature C; (2) clear aperture D; (3)separation between surfaces d; (4) refractive index nd;and (5) Abbe value V = (nd - 1)I(nF - nc). Allcurvatures are given in reciprocal millimeters, and allclear apertures and separations are given in millime-ters. The performance of the system is evaluated byplotting the transverse aberration curves, energy dis-tribution curves, and geometric MTF.
Figure 1 gives the aberration curves of the system.The aberration curves show the transverse aberrationsin the Gaussian image plane plotted horizontally vs the
Table 1. Data for the New Design
Clear Refractive AbbeCurvature aperture Separation index value
Spatial frequency in cycles/mm.Diameter of circle in mm.
Fig. 2. Energy distribution curves of the new design.
aperture plotted vertically. The aberrations are cal-culated by adopting the usual computing direction forprojection objectives; i.e., the rays are traced from theimage side to the object side. These curves are givenfor axial rays and for rays from three other obliquitiesrepresenting the full field, 0.707 field, and half-field.These curves are given in three wavelengths, namely,5461, 4861, 6563-A. The solid lines show the aberra-tions in the tangential plane; the dashed lines showthose in the sagittal plane. The lateral color is givenby the displacement of the origin of the curves for the4861- and 6563-A wavelengths. The variation of dis-tortion with field angle is represented as a percentageof image height. The field curvature is given by plot-ting the usual astigmatic surfaces (x5 and x') againstthe field angle.
The energy distribution curves for the new designare given in Fig. 2. From the ray trace data of a largenumber of rays in three different colors, the diametersof the smallest possible circles in the image blur spoteach containing 10, 20, 30,..., 100% of the rays, re-spectively, are determined. The energy distributioncurves are obtained by plotting the circle diametershorizontally vs the percentage of rays encircled withinthe circles vertically. Like transverse aberrationcurves, the energy distribution curves are also given foraxial rays and rays from three other obliquities. Theresolving power of a lens system can be calculated fromthe energy distribution curves. It has been shown8
that the resolving power of the lenses is generally givenby the diameter of the circle containing 30-40% of therays. For the present study the resolving power has
Fig. 3. Geometric MTF curves of the new design.
o '0
o 5 7.5
0 02mm.
-0 4'/.Distortion
6563 A I
0.02 mm.
48601 A I 4
0-02 mm.
.s no .t
-0F 1Field curvature in mm.
Fig. 4. Aberration curves of the double Gauss design.
Table IV. Resolving Power from 35% Circle Diameter
Field angle Resolving power inSurface (deg) lines/mm
1 0 1612 5 833 7.5 634 10 64
been calculated from a 35% circle diameter. The val-ues of resolving power at different field angles aregiven in Table II.
The geometrical MTF curves for the new design aregiven in Fig. 3. These curves are again obtained bytracing rays in three wavelengths, namely, 5461, 4861,and 6563 A. Like aberration curves, these curves aregiven for axial rays and for three other obliquities inthe Gaussian image plane. The weighting factors forthe above three wavelengths have been taken as 1, 0.5,and 0.5, respectively. The x axis gives the spatialfrequencies in cycles/mm, and the y axis gives thepercentage MTF.
All three criteria adopted for image evaluation indi-cate that the new configuration is capable of giving awell-corrected system at high apertures.
As pointed out earlier, to compare the performanceof this design with the design based on six-elementdouble Gauss form, a design based on double Gaussform (uncemented) was also developed in similar con-ditions of optimization, first, with CGCRI5 glasses.The performance of this design was evaluated by plot-ting aberration curves, energy distribution curves, andgeometrical MTF curves. The performance of the twodesigns was then compared. It has been found thatthe performance of the design based on the new config-uration is much superior to the design based on thedouble Gauss form. To improve further the doubleGauss design, Lanthanam crown glass was used for theouter positive lenses in place of DBC. The design thusobtained, although it showed improvement in perfor-mance, was still inferior to the performance of the newdesign. Later a design was developed using the glassessuggested by Kidger and Wynne9 for their design 4.
0.00 7.50
100-
5.00
80->1
20 60-
a,, 40-
CL
20-
r- 00
I, IO0
A'I00
II
lIlI
II
II
. I
0004 0.08 0.12Diameter of circle in mm.
Fig. 5. Energy distribution curves of the double Gauss design.
100-
W \< \~~~~~~~~~~~~~~~OO
50 I0 o o
60-
-- a~~~~~~-------
0 20 60 60 80Spatial ftrequency in cycles/mm
Fig. 6. Geometric MTF curves of the double Gauss design.
These glasses were predicted by the lens optimizationprogram and have comparatively higher indices. Theperformance of this design was also found to be inferiorto the design based on the new configuration. Thedetails, only of this last design, based on double Gaussform are given for the sake of brevity. Tables III andIV, respectively, give the design data and resolvingpower of the double Gauss design. Figures 4-6 givethe aberration curves, energy distribution curves, andgeometric MTF curves, respectively.
The proposed new configuration is capable of givingvery good performance. Its performance is betterthan the double Gauss configuration (uncemented) atf/11.6. It is recommended that for high aperture appli-cations for 35-mm cinematograph projection work, thenew configuration should be adopted.
References
1. K. D. Sharma, "Better Lens for 35-mm Cinematograph," Appl.
