Automated design of compound lenses with discrete-continuous optimization

Arjun Teh, Delio Vicini, Bernd Bickel, Ioannis Gkioulekas*, Matthew O'Toole*

SIGGRAPH Asia 2025 (conference)

teaser
We develop a method that automatically explores the design space of compound lenses, by using Markov chain Monte Carlo sampling to combine gradient-based optimization with discrete changes to the number and type of lens elements. This combination allows our method to find designs that improve the sharpness and throughput of the initial lens design (in this example, the Nikon Nikkor-S 50mm f/1.4, released in 1962), even after it has been optimized by prior gradient-based methods. Our method achieves image quality comparable to that of an improved lens designed by an expert (in this example, the Canon FD 50mm f/1.2, released in 1980). We report image brightness (top-left number of images) in terms of relative exposure.

Abstract

We introduce a method that automatically and jointly updates both continuous and discrete parameters of a compound lens design, to improve its performance in terms of sharpness, speed, or both. Previous methods for compound lens design use gradient-based optimization to update continuous parameters (e.g., curvature of individual lens elements) of a given lens topology, requiring extensive expert intervention to realize topology changes. By contrast, our method can additionally optimize discrete parameters such as number and type (e.g., singlet or doublet) of lens elements. Our method achieves this capability by combining gradient-based optimization with a tailored Markov chain Monte Carlo sampling algorithm, using transdimensional mutation and paraxial projection operations for efficient global exploration. We show experimentally on a variety of lens design tasks that our method effectively explores an expanded design space of compound lenses, producing better designs than previous methods and pushing the envelope of speed-sharpness tradeoffs achievable by automated lens design.

Expanding the throughput-sharpness Pareto front

pareto
By varying the throughput and spot-error weights in the optimization loss, we can explore designs that achieve different tradeoffs between lens speed and sharpness, tracing a Pareto front. Without mutations, lens designs are limited to the Pareto front determined by the initial design's topology. As our method can add and remove elements from the design, it is able to explore a larger space of designs and expand the Pareto front to achieve better tradeoffs.

Visualization

We visualize comparisons with a brute-force baseline and prior work in the interactive supplemental website.

Brute force Initial Ours

Resources

Paper: Our paper is available here.

Code: Our code is available on Github.

Citation

@inproceedings{Teh2024Automatic,
	author = {Teh, Arjun and Vicini, Delio and Bickel, Bernd and Gkioulekas, Ioannis and O'Toole, Matthew},
	title = {Automated design of compound lenses with discrete-continuous optimization},
	year = {2025},
	booktitle = {ACM SIGGRAPH Asia 2025 Conference Papers},
	series = {SIGGRAPH Asia '25}
}

Acknowledgments

We thank Andi Wang for discussions about Restore, and Ozan Cakmakci for discussions on commercial lens design tools. This work was supported by the National Science Foundation (awards 2047341 and 2238485), the Air Force Office of Scientific Research (FA 95502410244), Alfred P. Sloan Research Fellowship FG202013153 for Ioannis Gkioulekas, and a gift from Google Research.