benjaminpope.github.io/talks/fizeau/fizeau.html

Work in collaboration with Sydney students

Alison Wong (PhD)

and Louis Desdoigts (Honours),

Yinzi Xin (Caltech),

and faculty Peter Tuthill (Sydney)

and Laurent Pueyo (STScI).

The main limitation on direct imaging is from wavefront aberrations which corrupt phase information.

Given an image, what were the aberrations in the telescope?

Given an objective, how do we engineer an optimal PSF?

Phase Apodized Coronagraph: Por, 2019, arXiv:1908.02585

How do we correct phase errors in postprocessing?

What if we want to linearize an arbitrary optical system?

Optics is mathematically like machine learning: matrix multiplications and simple nonlinear functions

Can use automatic differentiation!

Autodiff is not finite differences, and it is not symbolic differentiation.

Using the chain rule you can decompose almost-arbitrary code!

Autodiff is the enabling technology for deep neural networks - you use the chain rule to take derivatives of nearly-arbitrary numerical functions.

Implementations in TensorFlow, Theano, PyTorch, Julia...

Here we use Google Jax, which resembles NumPy, to rewrite the Fourier/Fresnel optics code poppy to take derivatives

...Morphine!

Jax permits

- Just-in-time 'jit' compilation - so faster than normal poppy.
- Accelerated Linear Algebra (XLA) - including on GPUs
- Automatic differentiation!

Alison Wong - phase retrieval and design by gradient descent

Coronagraph Phase Mask Design - try it yourself!

Detect planets with μ-arcsec astrometry

Astrometric precision proportional to gradient energy

Use diffractive optic to maximize this subject to constraints

Louis Desdoigts - sensitivity of Toliman to Zernike modes

Basis used in CLIMB

Correlate baselines around a *triangle* of receivers

Kernel phase is a generalization of closure phase to arbitrary pupils.

Take the SVD of a phase error transfer matrix - separate into good and bad observables

Linearize response to phase noise - need derivative

Jacobian matrix is gradient of vector function \(\mathbf{y}(\mathbf{\theta})\):

\[ J_{i,j} \equiv \frac{\partial{y_i}}{\partial{\theta_j}} \\ \]

The Martinache 2010 phase transfer matrix \(\mathbf{A}_\phi\) is an analytically determined Jacobian, mapping pupil phases to their *u, v* effects.

Check out this notebook!

What else can we use this for?