# Automated design of compound lenses with discrete-continuous optimization

arXiv: https://arxiv.org/abs/2509.23572 · HTML: https://mlsanity.com/paper/2509.23572/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Curriculum Learning for ab initio Deep Learned Refractive Optics](https://mlsanity.com/paper/2302.01089/) (2023)
- [Differentiable Rendering of Neural SDFs through Reparameterization](https://mlsanity.com/paper/2206.05344/) (2022)
- [Optimistix: modular optimisation in JAX and Equinox](https://mlsanity.com/paper/2402.09983/) (2024)
- [Dr.Jit: A Just-In-Time Compiler for Differentiable Rendering](https://mlsanity.com/paper/2202.01284/) (2022)
- [The Differentiable Lens: Compound Lens Search over Glass Surfaces and Materials for Object Detection](https://mlsanity.com/paper/2212.04441/) (2022)
- [Physics-Based Inverse Rendering using Combined Implicit and Explicit Geometries](https://mlsanity.com/paper/2205.01242/) (2022)
- [A Simple Approach to Differentiable Rendering of SDFs](https://mlsanity.com/paper/2405.08733/) (2024)
- [A Differentiable Wave Optics Model for End-to-End Computational Imaging System Optimization](https://mlsanity.com/paper/2412.09774/) (2024)
- [Quasi-stationary Monte Carlo and the ScaLE Algorithm](https://mlsanity.com/paper/1609.03436/) (2016)
- [Reversible Jump Metropolis Light Transport using Inverse Mappings](https://mlsanity.com/paper/1704.06835/) (2017)
- [Lens Factory: Automatic Lens Generation Using Off-the-shelf Components](https://mlsanity.com/paper/1506.08956/) (2015)
- [Regeneration-enriched Markov processes with application to Monte Carlo](https://mlsanity.com/paper/1910.05037/) (2019)

## Abstract (arXiv)

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.