# Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors

arXiv: https://arxiv.org/abs/2303.13037 · HTML: https://mlsanity.com/paper/2303.13037/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2023.

## Built on by (most cited first, 17 of 17)

- [Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2308.02952/) (2023)
- [All-Optical Phase Conjugation Using Diffractive Wavefront Processing](https://mlsanity.com/paper/2311.04473/) (2023)
- [All-optical image denoising using a diffractive visual processor](https://mlsanity.com/paper/2309.09215/) (2023)
- [Information hiding cameras: optical concealment of object information into ordinary images](https://mlsanity.com/paper/2401.07856/) (2024)
- [Pyramid diffractive optical networks for unidirectional image magnification and demagnification](https://mlsanity.com/paper/2308.15019/) (2023)
- [All-optical complex field imaging using diffractive processors](https://mlsanity.com/paper/2401.16779/) (2024)
- [Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network](https://mlsanity.com/paper/2402.02397/) (2024)
- [Multiplane Quantitative Phase Imaging Using a Wavelength-Multiplexed Diffractive Optical Processor](https://mlsanity.com/paper/2403.11035/) (2024)
- [Integration of Programmable Diffraction with Digital Neural Networks](https://mlsanity.com/paper/2406.10688/) (2024)
- [Unidirectional imaging with partially coherent light](https://mlsanity.com/paper/2408.05449/) (2024)
- [Coherence Awareness in Diffractive Neural Networks](https://mlsanity.com/paper/2408.06681/) (2024)
- [Compute-first optical detection for noise-resilient visual perception](https://mlsanity.com/paper/2403.09612/) (2024)
- [Metasurface-generated large and arbitrary analog convolution kernels for accelerated machine vision](https://mlsanity.com/paper/2409.18614/) (2024)
- [Lying mirror using structured surfaces](https://mlsanity.com/paper/2410.15521/) (2024)
- [Snapshot multi-spectral imaging through defocusing and a Fourier imager network](https://mlsanity.com/paper/2501.14287/) (2025)
- [Snapshot 3D image projection using a diffractive decoder](https://mlsanity.com/paper/2512.20464/) (2025)
- [Illumination Angular Spectrum Encoding for Controlling the Functionality of Diffractive Networks](https://mlsanity.com/paper/2601.04825/) (2026)

## Abstract (arXiv)

Under spatially-coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number (N) of optimizable phase-only diffractive features is greater than or equal to ~2 Ni x No, where Ni and No refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially-incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially-incoherent monochromatic light, the spatially-varying intensity point spread functon(H) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H(m,n;m',n')=|h(m,n;m',n')|^2, where h is the spatially-coherent point-spread function of the same diffractive network, and (m,n) and (m',n') define the coordinates of the output and input FOVs, respectively. Using deep learning, supervised through examples of input-output profiles, we numerically demonstrate that a spatially-incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N is greater than or equal to ~2 Ni x No. These results constitute the first demonstration of universal linear intensity transformations performed on an input FOV under spatially-incoherent illumination and will be useful for designing all-optical visual processors that can work with incoherent, natural light.