\(
\def\ket#1{{\left|{#1}\right\rangle}}
\def\bra#1{{\left\langle{#1}\right|}}
\def\braket#1#2{{\left\langle{#1}|{#2}\right\rangle}}
\)

[tutorial] Semidefinite Programming for Intensity Only Estimation of the Transmission Matrix

 

The possibility of measuring the transmission matrix using intensity only measurements is a much sought-after feature as it allows us not to rely on interferometry. Interferometry usually requires a laboratory grade stability difficult to obtain for real-world applications. Typically, we want to be able to retrieve the transmission matrix from a set of pairs composed of input masks and output intensity patterns. However, this problem, that corresponds to a phase retrieval problem, is not convex, hence difficult to solve using standard techniques. The idea proposed in [I. Waldspurger et al., Math. Program (2015)] is to relax some constraint to approximate the problem to a convex one that can be solved using the semidefinite programming approach. I briefly detail the approach and provide an example of the procedure to reconstruct the transmission matrix using Python. A Jupyter notebook can be found on my Github account: semidefiniteTM_example.ipynb.

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Off-axis holography [tutorial]

fig0

Off-axis holography is a popular technique to reconstruct a hologram. It allows retrieving the amplitude and the phase of a field pattern by measuring only one image with a digital camera. It relies on an intereferometric setup with a non-zero angle between the reference beam and the signal beam and requires to numerically filter the spatial frequencies.

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  1. Introduction

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