Automated design of compound lenses with discrete-continuous optimization

Arjun Teh1     Delio Vicini2     Bernd Bickel2     Ioannis Gkioulekas1     Matthew O'Toole1    
1Carnegie Mellon University, 2Google
ACM SIGGRAPH Asia Conference Papers, 2025
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.

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Arjun Teh, Delio Vicini, Bernd Bickel, Ioannis Gkioulekas, Matthew O'Toole. Automated design of compound lenses with discrete-continuous optimization. ACM SIGGRAPH Asia Conference Papers, 2025.

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@inproceedings{Teh2025automated,
  title     = {Automated design of compound lenses with discrete-continuous optimization},
  author    = {Teh, Arjun and Vicini, Delio and Bickel, Bernd and Gkioulekas, Ioannis and O'Toole, Matthew},
  year      = 2025,
  publisher = {Association for Computing Machinery},
  address   = {New York, NY, USA},
  series    = {SA Conference Papers '25},
  doi       = {10.1145/3757377.3763850},
  isbn      = 9798400721373,
  articleno = 47,
  numpages  = 11
}