Wavefront Sensor for Laser Beams Based on Reweighted Amplitude Flow Algorithm

We present a reference-free computational wavefront sensor based on binary amplitude modulation and phase retrieval. The method employs Digital Micro-mirror Device as a programmable amplitude modulator and reconstructs the complex optical field from multiple far-field intensity measurements using the Reweighted Amplitude Flow algo-rithm with Optimal Spectral Initialization. Unlike classical pupil-plane wavefront sen-sors, the proposed architecture does not include any wavelength-specific optical elements, enabling straightforward adaptation across a broad spectral range. The achievable spatial resolution of the reconstructed wavefront is scalable with the modulator resolution. We experimentally demonstrate wavefront reconstruction at 650 nm and at 2116 nm, where commercial wavefront sensors are not widely available. The reconstructed wavefront is validated against a commercial lateral shearing interferometer at 650 nm, and the method is further integrated into a closed-loop adaptive optics system using a deformable mirror. The approach is particularly suited for applications requiring high spatial resolution and large dynamic range in slowly varying or quasi-static laser fields, where computational reconstruction speed is not of the primary concern.

💡 Research Summary

The authors present a reference‑free computational wavefront sensor that relies exclusively on binary amplitude modulation using a Digital Micromirror Device (DMD) and on phase‑retrieval via the Reweighted Amplitude Flow algorithm with Optimal Spectral Initialization (RAF‑OSI). The system does not contain any wavelength‑specific optics (e.g., lenses, prisms, or phase plates), which makes it intrinsically broadband and easily adaptable from the visible (650 nm) to the mid‑infrared (2116 nm).

In the forward model, the complex field in the DMD plane is multiplied element‑wise by a binary mask, and the resulting field is propagated to the far‑field (Fraunhofer) plane by a single lens. The intensity recorded on a camera for each mask provides a quadratic measurement of the unknown complex field. Recovering the field from these intensity‑only measurements is a non‑convex quadratic system. The authors solve it by first obtaining a spectral estimate of the field (optimal spectral initialization) and then iteratively minimizing a weighted amplitude‑flow loss, where the weights are updated to suppress the influence of noisy measurements. This approach improves convergence speed and robustness compared to classic Gerchberg‑Saxton, Wirtinger Flow, or simple gradient descent methods.

Experimentally, a DLP LightCrafter 6500 evaluation module (1080 × 1920 micromirrors) is grouped into 120 × 120 super‑pixels (each 9 × 9 mirrors) to define the modulation grid. For the visible test, a 650 nm diode laser is expanded to fill the DMD, modulated by 20 random binary masks, and the far‑field intensity is recorded with a 1,292 × 964 CMOS camera. For the infrared test, a Ho‑doped fiber laser at 2116 nm is used, 30 masks are displayed, and a 128 × 128 mid‑IR camera records the patterns. The authors perform a numerical noise analysis that shows the root‑mean‑square error (RMSE) of the reconstructed phase decreases with the number of masks; the chosen mask counts keep the RMSE below 0.05 λ even for signal‑to‑noise ratios as low as 5 dB.

Validation against a commercial lateral shearing interferometer (SID4, Phasics) at 650 nm shows a wavefront RMS difference of less than 0.07 λ, confirming high fidelity. The sensor is then integrated into a closed‑loop adaptive optics (AO) system: the reconstructed wavefront drives a deformable mirror, and the loop operates at a few hertz, reducing residual wavefront error to below 0.1 λ. Although the reconstruction is not real‑time, the latency (≈30 ms on a GPU) is acceptable for slowly varying or quasi‑static high‑power laser beams where spatial resolution and dynamic range are more critical than speed.

Key advantages of the approach include:

• Broadband operation – the same hardware works from the visible to the mid‑IR without re‑alignment or new optics.
• Scalable spatial resolution – the reconstructed wavefront resolution is limited only by the DMD pixel count; higher‑resolution DMDs can be swapped in directly.
• Large dynamic range – intensity‑only measurements avoid the saturation and aliasing problems of Shack‑Hartmann or pyramid sensors.
• Simplicity and cost – no custom phase masks or interferometric arms are required; the system consists of a DMD, a focusing lens, and a camera.

Limitations are also discussed. The measurement time is dominated by sequential mask display and camera readout (seconds to minutes), which precludes high‑speed applications. Noise sensitivity still demands a modest oversampling of masks (especially in the IR where detector SNR is lower). Calibration of the DMD’s reflectivity and correction of geometric distortions are necessary for quantitative phase values.

Future work suggested includes: employing structured or Hadamard‑type masks to reduce the number of required measurements, applying compressive‑sensing concepts to further accelerate acquisition, and developing FPGA‑based hardware pipelines for true real‑time closed‑loop AO. The authors also propose extending the method to multi‑wavelength simultaneous sensing and to larger DMD arrays for ultra‑high‑resolution wavefront mapping.

In summary, this paper demonstrates a versatile, wavelength‑agnostic wavefront sensor that combines binary amplitude coding with a modern, robust phase‑retrieval algorithm. Experimental results at both 650 nm and 2116 nm validate the technique against a commercial interferometer and show successful integration into an adaptive optics loop, positioning the method as a practical solution for high‑resolution, large‑dynamic‑range laser beam diagnostics where speed is not the primary constraint.