Extracting more than two orthogonal derivatives from a Shack-Hartmann wavefront sensor

Abstract

The purpose of this paper is to show that the Shack-Hartmann wavefront sensor (SHWFS) gives access to more derivatives than the two orthogonal derivatives classically extracted either by estimating the centroid or by taking into account the first two harmonics of the Fourier transform. The demonstration is based on a simple model of the SHWFS, taking into account the microlens array as a whole and linking the SHWFS to the multi-lateral shearing interferometry family. This allows for estimating the quality of these additional derivatives, paving the way to new reconstruction techniques involving more than two cross derivatives that should improve the signal-to-noise ratio.

Cross-grating phase microscopy (CGM): In-silico experiment (insilex) algorithm, noise and accuracy

“…Unlike most QPMs, which directly measure and map the phase of light φ(x, y) by interferometry, CGM primarily measures the wavefront profile W of a light beam, or rather its gradients over the two directions of space (that are subsequently integrated). The interferogram consists of a dense array of bright spots, and the working principle resembles that of a Shack-Hartmann sensor [10][11][12], although with a much higher spatial resolution. Then, the wavefront profile W can be converted into the phase profile, if need be, using the relation…”

“…Quantitative phase microscopy (QPM) refers to techniques capable of mapping the phase of a light beam [1-3] using optical microscopy means. Many different QPM techniques implemented on optical microscopes have been developed and improved these last two decades, namely digital holographic microscopy (DHM) [4,5], spatial light interference microscopy (SLIM) [6,7], diffraction phase microscopy (DPM) [8][9][10], shack-Hartmann wavefront sensing [11,12] and quadriwave lateral shearing interferometry (QLSI) [13,14]. QLSI is a QPM technique based on the association of a 2-dimensional diffraction grating (aka cross-grating) and a regular camera, separated by a millimetric distance (Figure 1a) [13].…”

High noise-resistant slope and curvature signal extraction algorithm in frequency domain for the Shack-Hartmann wavefront sensor

“…By introducing the Fourier transform of the SHWS irradiance map, the relationship between the wavefront slope and the spectrum can be established, and then the information of the wavefront can be obtained. Based on the conservation of energy, the relationship between spectral information of light intensity and harmonics was established [11]:…”

“…With the enhancement of computer image processing capability, traditional image processing method can be transformed into a more convenient and simpler field. In 2021, Rouze Bastien [11] et al combined centroid extraction of wavefront information with Fourier transform demodulation method to extract multiple directional derivatives of wavefront (wavefront slope) on the basis of traditional Shaker-Hartmann sensor. However, the study only obtained wavefront slope information in the frequency domain, did not obtain wavefront curvature information, and only conducted a qualitative analysis, without quantitative research.…”

Cross-grating phase microscopy (CGM): In silico experiment (insilex) algorithm, noise and accuracy

“…Quantitative phase microscopy (QPM) refers to techniques capable of mapping the phase of a light beam [1][2][3] using optical microscopy means. Many different QPM techniques implemented on optical microscopes have been developed and improved these last two decades, e.g., digital holographic microscopy (DHM) [4,5], spatial light interference microscopy (SLIM) [6,7], diffraction phase microscopy (DPM) [8,9], shack-Hartmann wavefront sensing [10][11][12] and quadriwave lateral shearing interferometry (QLSI) [13,14]. QLSI is a QPM technique based on the association of a 2-dimensional diffraction grating (aka cross-grating) and a regular camera, separated by a millimetric distance [13].…”