The Symposium Lens Continued

R. E. Hopkins and V. K. Viswanathan Institute of Optics, College of Engineering & Applied Science, The University of Rochester, Rochester, New York. Received 9 April 1964. This work was sponsored by U.S. Air Force Grant AF-AFOSR-50-63.

In the December 1963 issue of Applied Optics, Beryln Brixner1

submitted a Symposium Lens design. His number two design is now being called LASL 2.

The lens LASL 2 does not have it as far as looks are concerned. Most lens designers would object to the way the first element is bent away from the stop. Since the design was not evaluated in the same way as the SYM and ORD lenses, we thought it would be interesting to make this evaluation on LASL 2. The evaluation has been carried out, and in this report it is compared with the ORD 1 design.

In the evaluation, we have computed energy distributions and the geometrical modulation transfer function. The energy dis­tributions described by Hopkins and Feder2 were computed in D light. In the evaluation reported in this paper, we added F and C light. The energy distributions were computed by tracing 40 rays in F and C light and 80 rays in D light. All the spots were lumped together to make up the energy distribution curve.

Fig. 1. Plots showing encircled energy distributions for LASL 2 and ORD 1. Graphs have been plotted on the same scale as

Fig. 2, Ref. 2.

Fig. 2. Geometrical modulation transfer curves at 0° for LASL 2 and ORD 1.

Figure 1 shows energy distribution curves at 0°, 4°, and 6° for lenses ORD 1 and LASL 2. These curves show remarkable simi­larity. One can see how the LASL 2 design has avoided flare in the image; this comes about from using a root-mean-square ray deviation criterion. In order to compare these lenses, it is helpful to plot the geometrical frequency response curves. The 0° modu­lation curves for the two lenses are given in Fig. 2. At 4° off-axis, LASL 2 has a slightly better modulation out to 2000 lines/in. (79 lines/mm) and a poorer modulation beyond. At 6° off-axis, the two lenses are essentially indistinguishable.

In order to choose between these two lenses it is necessary to know more about the requirements for the lens. As originally described, the Symposium Lens was not specified sufficiently to enable designers to arrive at optimum designs. To accomplish this, it would have been necessary to describe completely the in­tended uses for the lens. In point of fact, the absolute focal length was not specified, and no mention was made of how the lens was to be used. A good optimization program should have refused to work on this problem for lack of precise data on what was expected of it. Perhaps the lack of information was inten­tional, for now everyone can be happy and claim his program designed the optimum lens.

The frequency scale on the modulation transfer curve in Fig. 2 is given in inches, which assumes the lens has a focal length of one inch. Out to 1000 lines/in. (39.4 lines/mm), LASL 2 is better than ORD 1. Beyond 1000 lines/ in., ORD 1 is better .

June 1964 / Vol. 3, No. 6 / APPLIED OPTICS 787

In a 1-in. focal length, these lenses would make good projection lenses. If we assume the observer sits at the projector, he would be able to resolve approximately 5000 lines/in. (196 lines/mm). For this application, ORD 1 would be superior on axis.

It is our opinion that the designs ORD 1, SYM 1, and LASL 2 are nearly equivalent lenses as far as imagery is concerned. Anyone attempting to use these designs for a real application would select the lens using other criterion, such as weight, cost of glass, cost of manufacture, etc.

It was a real surprise to us to find that LASL 2, which looks so strange, is actually a good design. We believe that LASL 2 is in a different region of solution, and that any automatic program started near it would find difficulty ending up with ORD 1. There is some evidence to indicate that ORD 2 is in still another region.

As designers gain access to automatic programs, they will find it instructive to check their program against these Symposium lenses. All of us who have worked on this design have learned a great deal. It would help greatly in the future if designers would give all the clear apertures for their lenses; it is very difficult to compare designs without knowing precisely what rays the designer has chosen to let through the lens.

It should be pointed out that there is a slight error in Table III of Ref. 2. The values for ND and the V number are given for each glass; in parentheses, the equivalent glass names are given as SK 16 and SF 8. However, the indices of these glasses do not agree exactly with the given numbers. If the SK 16 and SF 8 in­dices are used, it is necessary to shift the focus slightly in order to match the energy distribution curves given in Fig. 2.

References 1. B. Brixner, Appl. Opt. 2, 1331 (1963). 2. R, E. Hopkins and D. P. Feder, Appl. Opt, 2, 1227 (1963).

788 APPLIED OPTICS / Vol. 3, No. 6 / June 1964