# Scale-, shift- and rotation-invariant diffractive optical networks

arXiv: https://arxiv.org/abs/2010.12747 · HTML: https://mlsanity.com/paper/2010.12747/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2020.

## Built on by (most cited first, 15 of 15)

- [All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces](https://mlsanity.com/paper/2108.09833/) (2021)
- [Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network](https://mlsanity.com/paper/2203.13482/) (2022)
- [All-optical image denoising using a diffractive visual processor](https://mlsanity.com/paper/2309.09215/) (2023)
- [Classification and reconstruction of spatially overlapping phase images using diffractive optical networks](https://mlsanity.com/paper/2108.07977/) (2021)
- [Physics-aware Differentiable Discrete Codesign for Diffractive Optical Neural Networks](https://mlsanity.com/paper/2209.14252/) (2022)
- [Rubik's Optical Neural Networks: Multi-task Learning with Physics-aware Rotation Architecture](https://mlsanity.com/paper/2304.12985/) (2023)
- [Rotated Digit Recognition by Variational Autoencoders with Fixed Output Distributions](https://mlsanity.com/paper/2206.13388/) (2022)
- [Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network](https://mlsanity.com/paper/2402.02397/) (2024)
- [Physics-aware Roughness Optimization for Diffractive Optical Neural Networks](https://mlsanity.com/paper/2304.01500/) (2023)
- [Coherence Awareness in Diffractive Neural Networks](https://mlsanity.com/paper/2408.06681/) (2024)
- [Scientific Computing with Diffractive Optical Neural Networks](https://mlsanity.com/paper/2302.10905/) (2023)
- [Super-resolution image projection over an extended depth of field using a diffractive decoder](https://mlsanity.com/paper/2510.03938/) (2025)
- [Snapshot 3D image projection using a diffractive decoder](https://mlsanity.com/paper/2512.20464/) (2025)
- [All-Optical Segmentation via Diffractive Neural Networks for Autonomous Driving](https://mlsanity.com/paper/2602.07717/) (2026)
- [Wavelength-Multiplexed 2D Beam Steering via a Passive Diffractive Network](https://mlsanity.com/paper/2606.16261/) (2026)

## Abstract (arXiv)

Recent research efforts in optical computing have gravitated towards developing optical neural networks that aim to benefit from the processing speed and parallelism of optics/photonics in machine learning applications. Among these endeavors, Diffractive Deep Neural Networks (D2NNs) harness light-matter interaction over a series of trainable surfaces, designed using deep learning, to compute a desired statistical inference task as the light waves propagate from the input plane to the output field-of-view. Although, earlier studies have demonstrated the generalization capability of diffractive optical networks to unseen data, achieving e.g., >98% image classification accuracy for handwritten digits, these previous designs are in general sensitive to the spatial scaling, translation and rotation of the input objects. Here, we demonstrate a new training strategy for diffractive networks that introduces input object translation, rotation and/or scaling during the training phase as uniformly distributed random variables to build resilience in their blind inference performance against such object transformations. This training strategy successfully guides the evolution of the diffractive optical network design towards a solution that is scale-, shift- and rotation-invariant, which is especially important and useful for dynamic machine vision applications in e.g., autonomous cars, in-vivo imaging of biomedical specimen, among others.