November 27, 2017
Designing the centennial lens
Every four years, optical designers, scientists, and engineers from around the world gather at the International Optical Design Conference (IODC) to discuss the latest developments in the optical design industry and to participate in an optical design competition. Prior to each conference, two optical design challenges are held: one involves solving a lens design problem; the other involves solving an illumination problem.
At the 2017 IODC, 31 optical designers participated in the lens design competition, which had a centennial theme in honor of the 100th anniversary of the Optical Society of America.
The goal of the 2017 IODC lens design problem was to maximize the used portion of the diameters of two ball lenses while maintaining diffraction-limited performance across the full field of view. As shown in the following image, the system had to include a “100 lens” containing a plate and two ball lenses, which are meant to visually represent the number 100. Because the lens design specifications were nonstandard, participants had to think in unconventional ways to solve the problem.
Specifications for the 100 lens design consisted of:
Two ball lenses, each 40 mm in diameter, separated by 5 mm
One 10 mm thick flat plate 5 mm from the first ball lens
Configuration of the 100 lens
To encourage larger fields of view and prevent on-axis only solutions, submissions were judged using a merit function equal to:
largest on-axis marginal ray height x largest full-field chief ray height
Maximum heights could exist on either ball lens surface and did not have to be located on the same surface. Given that the semi-diameter of each ball lens was 20 mm, the maximum merit function was 400.
Participants also had to get creative when it came to the design process. Typically, the first-order properties of a system can be used—such as focal length, entrance pupil diameter, field of view, and overall length—to begin laying out and designing an optical system. However, to encourage participants to find creative solutions, the design process for the IODC competition did not define the first-order properties.
Michael Lewton’s solution
Michael Lewton developed a solution to the 2017 IODC lens design problem using OpticStudio. According to Michael, here is a breakdown of his successful approach.
Step 1: Increase height of rays
At first glance, the merit function appears to correlate with the optical invariant, which immediately adds complexity to the system. To increase the height of the chief ray, I had to increase the field size. Similarly, to increase the height of the marginal ray, I had to increase the aperture (and resolution).
Step 2: Determine image quality factors
I could then easily identify which parts of the system had the greatest impact on image quality (RMS wavefront error must be less than 0.07 waves) by toggling various factors, such as the number of lenses and the entrance pupil position. For the 100 lens, the Petzval curvature would be an issue with larger fields of view, so it needed to be corrected.
Step 3: Break merit function and optical invariant correlation
Since the merit function of the centennial lens is not the optical invariant, I tried to break this correlation to simplify the system. Although attempting to coincide the chief and marginal rays on one of the surfaces sounds simple, it’s theoretically impossible. I could, however, nearly achieve this condition by setting the aperture far from the surface and defining the maximum field to make the height of the chief ray equivalent to the height of the marginal ray on the first lens surface.
The first lens surface with the on-axis beam (blue), full field beam (green), and the corresponding footprint diagram
Step 4: Optimize the axial beam
Next, I started optimizing the axial beam, remembering that both rays are at 0.5 of the pupil’s radius. After achieving the desired results for the first configuration, I had to ensure that the system had several intermediate images—including one inside the 100 lens and one after it. Then, I ran the Global Optimization feature in OpticStudio over the next several days to automatically evaluate and improve my entire design.
Step 5: Induce coma on relevant surface
At this point, I pushed the rays above the chief ray and closer to the optical axis by grouping three lenses and moving them away from the 100 lens.
First lens group
This induced coma at the second 0 of the 100 lens, which meant that I could keep all rays for the field point below the chief ray. This would maximize the merit function for the competition, and minimize the aberrations induced by the 100 lens. Unfortunately, this also made it more difficult to calculate the wavefront error because the rays were less centrally located to the chief ray than they are in most designs.
Footprint diagram at the first surface of second 0 in the 100 lens
Step 6: Optimize wavefront across the field
To get the most from the optical system, I tried to push the image quality at several intermediate field points and even adjusted for the weight of the individual rays. The process involved incrementally increasing the height of the marginal and chief rays and then optimizing to achieve a flat wavefront versus field function.
After optimization, the distance between the groups in the system increased to several meters. I reoptimized the second lens group and added a few intermediate lenses to improve the merit function.
Second lens group with the 100 lens
My final system had a marginal ray height of 19.866 mm and a chief ray height of 19.848 mm, resulting in a final merit function of 394.30.
Michael Lewton is a self-employed optical design professional based in the Munich area. He can be reached at email@example.com.
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