# Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

arXiv: https://arxiv.org/abs/2310.03384 · HTML: https://mlsanity.com/paper/2310.03384/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2023.

## Built on by (most cited first, 4 of 4)

- [Information hiding cameras: optical concealment of object information into ordinary images](https://mlsanity.com/paper/2401.07856/) (2024)
- [Multiplane Quantitative Phase Imaging Using a Wavelength-Multiplexed Diffractive Optical Processor](https://mlsanity.com/paper/2403.11035/) (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)

## Abstract (arXiv)

As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees-of-freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are non-negative, acting on diffraction-limited optical intensity patterns at the input field-of-view (FOV). Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.