How to Correct for Bias in Off-Axis Holography for Transmission Matrix Measurements

Sébastien M Popoff¹ , Antoine Loquet¹

I presented in a previous tutorial how to reconstruct a complex field using a camera and a plane wave reference tilted with respect to the optical axis, known as off-axis holography. This works perfectly with an ideal plane wave as a reference. Of course, real life is not perfect, and the reference usually presents imperfections. While low spatial fluctuations can be compensated for afterward, high spatial frequency noise has the effect of adding a small bias to the estimation of the field. Such bias is typically small, but in transmission matrix measurements—since it is static and added to all measurements—it can affect the singular value distribution and perturb or hide transmission channels that would otherwise be visible.

ZoomFFT for speeding up off-axis computation (and more)

Sébastien M Popoff¹  and Rodrigo Gutiérrez-Cuevas¹

When performing the computation for some tasks such as off-axis holography, we often have to compute the entire FFT of a signal or an image while being only interested in a very small part of the spectrum. The rest of the information is just discarded. While the FFT algorithm and its implementation in standard computing libraries are very efficient, we can still take advantage of a slower approach which only computes what we need. The ZoomFFT algorithm does just that! And it's already available in standard packages such as SciPy for Python or in MATLAB. Using off-axis holography as an example, I will show how to save time – or not – using ZoomFFT.

ERRATUM: Diffraction Effects in DMDs

I made a big mistake in the calculation of the DMD diffraction effects, it affects the following posts:

• A practical guide to Digital Micro-mirror Devices (DMDs) for wavefront shaping, and also the corresponding paper,
• Setting up a DMD: Diffraction effects,
• The online tool.

These will be edited shortly to reflect the corrections, as well as the paper A practical guide to digital micro-mirror devices (DMDs) for wavefront shaping (DOI, Arxiv) that will be retracted and resubmitted.

Long story short, the grating equation was wrong. It should not affect too much the results for low angles, but given the fact that the angles of each micro-mirror is already 12 degrees, it is not negligible at all.

The correct grating equation should be:

\[
  \text{sin}(2\theta_B-\alpha') + \text{sin}(\alpha')
  = 2 \,\text{sin}(\theta_B)  \,\text{cos}(\theta_B-\alpha')
  = p\frac{\sqrt{2}\lambda}{d} \, ,
\]

with the same notations as in the tutorial, so the blazed number then reads:

\[
  \mu =
  \left| 4 \frac{d}{\lambda\sqrt{2}}
  \left[
    \text{sin}(\theta')\text{cos}(\theta'-\alpha')
    \right]
  \mod{2} -1
  \right| \, .
\]

Big thanks to L. Malosse and @NiuYihan1999 for pointing out this error.

Harnessing disorder and symmetries in multimode fibers

Sébastien M. Popoff
IESC Cargèse, France
April 2024

We present how to study light propagation in multimode fibers using transmission matrix measurements and apply it to understand the effect disorder and its impact on the so-called rotational memory effect. This talk is part of the Wave Propagation and Control in Complex Media 2024 workshop (15-19 April 2024, Cargèse, France)