# Diffractive optical system design by cascaded propagation

arXiv: https://arxiv.org/abs/2202.11535 · HTML: https://mlsanity.com/paper/2202.11535/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 62 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018)
- [Single-shot Hyperspectral-Depth Imaging with Learned Diffractive Optics](https://mlsanity.com/paper/2009.00463/) (2020)
- [Miniscope3D: optimized single-shot miniature 3D fluorescence microscopy](https://mlsanity.com/paper/2010.05382/) (2020)
- [Experimental robustness of Fourier Ptychography phase retrieval algorithms](https://mlsanity.com/paper/1511.02986/) (2015)
- [CodedStereo: Learned Phase Masks for Large Depth-of-field Stereo](https://mlsanity.com/paper/2104.04641/) (2021)
- [Spatially-Variant CNN-based Point Spread Function Estimation for Blind Deconvolution and Depth Estimation in Optical Microscopy](https://mlsanity.com/paper/2010.04011/) (2020)
- [Motion Deblurring using Spatiotemporal Phase Aperture Coding](https://mlsanity.com/paper/2002.07483/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learned Off-aperture Encoding for Wide Field-of-view RGBD Imaging](https://mlsanity.com/paper/2507.22523/) (2025)

## Abstract (arXiv)

Modern design of complex optical systems relies heavily on computational tools. These typically utilize geometrical optics as well as Fourier optics, which enables the use of diffractive elements to manipulate light with features on the scale of a wavelength. Fourier optics is typically used for designing thin elements, placed in the system's aperture, generating a shift-invariant Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in many cases of interest, e.g. when dealing with multiple, or out-of-aperture elements, comes from numerical complexity. In this work, we propose and implement an efficient and differentiable propagation model based on the Collins integral, which enables the optimization of diffraction optical systems with unprecedented design freedom using backpropagation. We demonstrate the applicability of our method, numerically and experimentally, by engineering shift-variant PSFs via thin plate elements placed in arbitrary planes inside complex imaging systems, performing cascaded optimization of multiple planes, and designing optimal machine-vision systems by deep learning.