The University of Sydney

louisdesdoigts.github.io/diff_optics/

Code and examples available

Benjamin Pope (UQ)

Peter Tuthill (USyd)

Jordan Dennis, student (UQ)

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!*

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!

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

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

How can you design a binary mask using gradients?

Continuous Latent Image Mask Binarisation

(CLIMB)

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

Engineer a loss function!

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

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

Hamiltonian Monte Carlo (HMC)

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

Bulk optic design with ray tracing

Holographic phase mask design

Non-common path error correction using physical forwards models

Your optical problems!