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.

Compensating for phase drifts in holographic measurements

Digital holography allows measuring the complex amplitude of a given wavefront. We presented in detail the off-axis holography approach. However, it requires a separate reference arm. Due to air flow, vibrations, or other perturbations, the optical path length difference between the two arms can fluctuate in time, even in controlled lab experiments on a good optical table. This means that the phase of the measured wavefront is estimated up to a global phase that can randomly change over time. This is very detrimental for transmission matrix measurements as the relative phase between each column has to be precisely estimated. This is particularly true when the measurement time can take few minutes or more when using a liquid crystal spatial light modulator that has a limited frame rate. In [R. Mouthaan et al., Appl. Opt. (2022)], the authors propose a simple yet robust way to compensate for phase fluctuations, even when the phase changes completely between two frames.

Spatiotemporal control of light

Joel A. Carpenter
October 2021

Gerchberg-Saxton is a phase retrieval algorithm, which attempts to retrieve the phase corresponding to two intensity images taken in the near and far-field respectively. It can also be used for calculating computer-generated holograms (phase masks) that generate a desired.