Accurate and Noise-Robust Wavefront Reconstruction with an Optical Vortex Wavefront Sensor

TL;DR

This work introduces the Optical Vortex Wavefront Sensor (OVWS), which embeds a phase singularity with topological charge $l$ into each Shack-Hartmann subaperture to transform wavefront tracking from bright-spot localization to singularity localization. The authors provide a holographic design that combines a base grating with a spiral phase, yielding a per-aperture phase $\\phi_i = l\theta + 2\pi\left(\frac{n_x + s \lvert\mathbf{V}_i\rvert \cos(\alpha_i)}{p_x} x + \frac{n_y + s \lvert\mathbf{V}_i\rvert \sin(\alpha_i)}{p_y} y\right)$ and frequency mappings $f_{ix}, f_{iy}$ across subapertures, using a hexagonal grid and a mode-limit $Z_{opt} = \left\lfloor 2.04 M^{1.36} \right\rfloor$. Numerical simulations show that localizing Laguerre-Gaussian vortex features yields lower RMS localization errors and reduced residual phase variance $\langle\sigma^2\rangle$ across SNRs from $2$ to $22$, compared to conventional SH. Experimental validation with an SLM-based OVWS demonstrates superior performance over SH across camera gains (10–40 dB) and multiple aberrations, confirming improved noise resilience and dynamic range. The work suggests practical integration with SLMs or DMDs and points to future refractive or microlens implementations, with patent activity noted.

Abstract

The term wavefront sensor refers to the entire class of devices capable of measuring the optical wavefront of the incoming beam. Although numerous solutions have been proposed so far, recent advances in structured light have opened new development possibilities through controlled modification of optical field amplitude and phase. We present an alternative approach to angle-based sensing, introducing optical vortices stable phase singularities within each subaperture of the Shack-Hartmann (S-H) architecture. Rather than changing the fundamental angle-based operating principle, it transforms the tracked quantity and its detection method. The presence of a singularity enables a dedicated tracking algorithm that outperforms conventional methods without increasing computational complexity. We evaluated its performance against the conventional S-H across a broad SNR range (from 2 to 22), corresponding to shot noise limited to high saturation regimes, demonstrating lower mean residual phase variance across all conditions. This work demonstrates that structured beam shaping can extend the capabilities of traditional S-H architectures without requiring fundamental redesign.

Figures (7)

• Figure 1: a) Concept of the hologram design (spatial frequency of diffraction gratings is not in scale). The base grating is inserted in the central subaperture. Starting from there, vector $\mathbf{V}_i$ sets spatial frequencies $f_{ix}$, $f_{iy}$ in subsequent subapertures following equation \ref{['eq:fxy_modified']} together with the spiral phase as shown in equation \ref{['eq:phifinal']} b) Simulated intensity distribution at the Fourier plane with scaling parameter $s=1$
• Figure 2: Concept of the measurement principle with the OVWS.
• Figure 3: a) Localization precision under the manually introduced noise for both the weighted centroid applied to a Gaussian beam (orange) and the Laguerre-Gaussian transform applied to an optical vortex (blue). Arrows indicate the level of the noise shown in subsequent subfigures b) Single iteration of the read noise distribution (13 SNR) for the Gaussian beam c) Scattered localization positions for each iteration of noise presented in b, d) Single iteration of the read noise distribution (13 SNR) for the optical vortex e) Scattered localization positions for each iteration of noise presented in d
• Figure 4:
• Figure 5: a) Experimental setup configuration. b) Exemplary holograms for conventional S-H and OVWS with corresponding intensity distributions.