morphine
Phase Retrieval and Design with Automatic Differentiation
Benjamin Pope, UQ
benjaminpope.github.io/talks/dsi/dsi.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).
Phase Problems in Direct Imaging
The main limitation on direct imaging is from wavefront aberrations which corrupt phase information.
Problem 1: Phase Retrieval
Given an image, what were the aberrations in the telescope?
Problem 2: Phase Design
Given an objective, how do we engineer an optimal PSF?
Phase Apodized Coronagraph: Por, 2019, arXiv:1908.02585
Problem 3: Kernel Phase
How do we correct phase errors in postprocessing?
See our paper: arXiv:2011.09780!
Automatic Differentiation
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!
Phase Retrieval
Alison Wong - phase retrieval and design by gradient descent
Phase Design
Coronagraph Phase Mask Design - try it yourself!
Toliman Mission
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
The Future
What else can we use this for?