Jitter Sensing and Control for Multi-Plane Phase Retrieval

TL;DR

This paper tackles jitter and tip/tilt issues in multi-plane curvature-based wavefront sensing by showing that tip/tilt information is embedded in nlCWFS measurements and can be extracted in real time using a fast centroiding approach. The authors build a laboratory nlCWFS setup, inject known tip/tilt via a fast steering mirror, and validate that the WA centroiding method yields diffraction-limited tip/tilt estimates in the unaberrated case ($\pm 0.1\,\lambda/D$) and better than $\pm 0.5\,\lambda/D$ under aberrations. They implement a closed-loop tip/tilt control loop at $25$ Hz, achieving convergence within 3–5 iterations and demonstrating improved stability and image quality for subsequent high-order phase reconstructions. The results support integrating tip/tilt correction directly into the nlCWFS reconstruction pipeline, reducing hardware complexity while maintaining or enhancing reconstruction fidelity, with future work focusing on optimizing loop dynamics and extending to joint high-order correction with a deformable mirror.

Abstract

The family of multi-plane phase retrieval sensors, such as the curvature and nonlinear curvature wavefront sensors (WFS), contain tip/tilt information embedded in their signals. We have built a nonlinear curvature WFS to study different wavefront reconstruction methods and test the ability to extract tip/tilt information. Using reliable and fast centroiding algorithms, combined with knowledge of the measured $z$-distance to each measurement plane, we demonstrate that image jitter may be sensed and compensated for using a fast steering mirror and the WFS in closed loop. This approach obviates the need for peripheral components such as quad-cells or access to a separate scientific imaging channel. Our laboratory experiments validate tip/tilt estimation and correction using nlCWFS data, achieving tip/tilt accuracy of +/-0.1, lambda/D for an unaberrated beam and better than ~+/-0.5, lambda/D in the presence of aberrations, consistent with prior numerical simulations. We further demonstrate a closed-loop tip/tilt control implementation and show a qualitative improvement in the stability and overall quality of multi-plane phase retrieval reconstructions.

Figures (10)

• Figure 1: Diagram representing the light path of the experiment. An aberrator plate may be translated through the beam to induce aberrations.
• Figure 2: Images of the FSM (left) and tip/tilt sensing camera (right).
• Figure 3: Tip/tilt calibration images generated at the measurement planes with no aberrations (top) and a known amount of injected tip/tilt (bottom). WA centroid estimation is shown as a red circle in the bottom figure.
• Figure 4: Measured versus injected tip (top left) and tilt (top right) using the WA method and their residuals (bottom). The outer measurement planes (blue) offer more consistent and reliable tip/tilt estimates due to having a larger geometric lever arm. The inner measurement planes (red) require careful calibration and are otherwise less reliable.
• Figure 5: Wrapped phase reconstructions for known tip/tilt cases without (top) and with (bottom) tip/tilt correction. On the left the injected tip/tilt was $-3.84\;\lambda/D$ and $+3.84\;\lambda/D$ while on the right it was $-1.92\;\lambda/D$ and $+1.92\;\lambda/D$. Tip/tilt correction improves wavefront reconstruction by reducing the amplitude of pointing modes, allowing previously hidden features to be more easily observed.