Differentiable Optics &


Louis Desdoigts
The University of Sydney
Slides availale


Code and examples available


Work in collaboration with:
Benjamin Pope (UQ)
Peter Tuthill (USyd)
Jordan Dennis, student (UQ)
You can watch these slides being presented here!

Inference & Design Problems in Optics

JWST, Toliman, & Beyond!

Phase Retireval

Instrumental Calibration


μ-arcsecond astrometry


Low-order wavefront error resistant coronagraphs

Polarisation invariant coatings

Non-common path error correction in AO

Crowded-field signal decontamination

*Your science goes here!*

Automatic Differentiation & Optics

Unifying Machine Learning and Optics


What does a Neural Network DO?


What does an Optical System DO?

Neural Network and Optical Systems are structurally isomorphic

Optical forwards models constructed within ML frameworks can harness Automatic Differentiation!

Automatic Differentiation

What is Autodiff?

  • It is NOT finite differencing
  • It is NOT symbolic differentiation
  • It IS repeated applications of the chain rule to code in order to calcualte derivates

Automatic Differentiation

Why is autodiff usefull?

  • Computational cost of derivative calcualtions do Not scale with the number of parameters
  • Complex, high-dimensional models can optimised simply
  • Parameter gradients let us access a host of better optimsation and inference algorithms!

∂Lux - An open source, Python based, fully differentiable optical modelling framework using Google Jax & Equinox

Git - Docs


  • Automatic Differentiation!
  • Just-in-time (jit) compilation
  • Accelerated Linear Algebra (XLA) - Optimised for GPUs!
  • Object-Oriented models
  • Integration with ML optimisation libraries (Optax)
  • Integration with PPLs (Numpyro)

Toliman Diffractive Pupil Design


How can you design a binary mask using gradients?

Continuous Latent Image Mask Binarisation




How do you design a mask to best constrain binary-star separation AND the instantaneous state of the telescope?

Engineer a loss function!

\[ \text{Loss}(\psi, p) = - \sum_{(x, y)} \Big(\nabla \psi(x, y) (\alpha + \beta\vec{r})\Big)^p \]

Optical Design


How do we compare performace?

Cramer-Rao lower-bound calcualtion under the Laplace approximation

\[ \text{CRLB}(\vec{X}) \propto \frac{1}{\vec{\Sigma}(\vec{X})} \] where \[ \vec{\Sigma}(\vec{X}) = - \Big[ \nabla \nabla \text{ln} \Big( \mathcal {L}(\vec{X}) \rho(\vec{X}) \Big) \Big]^{-1} \]

Going further...

What if we optimised the entropy of the covariance matrix?

Data Analysis


How to understand relationships between a large number of interrelated parameters from data?

Hamiltonian Monte Carlo (HMC)

Phase Retrieval & Instrumental Calibration


Data Initial Resdiuals

Run gradient descent on:

  • Stellar positions & fluxes (45 parameters)
  • Optical aberrations (11 parameters)
  • Interpixel sensitivites (65'536 parameters)

Astrophysical parameter recovery

Optical aberration recovery

Inter-pixel sensitivity recovery

Future Work

Bulk optic design with ray tracing

Holographic phase mask design

Inverse design of Photonics

Non-common path error correction using physical forwards models

Your optical problems!

Have a play with the code! github.com/LouisDesdoigts/dLux