Rapid wavefront shaping using an optical gradient acquisition

TL;DR

The paper tackles aberration correction in deep tissue imaging under unknown tissue structure by replacing slow coordinate-descent with gradient-descent optimization. It derives and measures the gradient of a non-invasive confocal-energy score $\mathcal{S}(\bm{\rho})$ with respect to the modulation vector $\bm{\rho}$, enabling simultaneous updates to all SLM parameters. The gradient-based method decouples complexity from the number of modulation parameters and demonstrates rapid convergence and high-resolution corrections in a coherent confocal microscope across multiple targets (chrome masks behind tissue, beads in gel, onion slices), achieving a runtime reduction from about 900 minutes with coordinate descent to around 14 minutes, with potential to reach seconds using faster hardware. The work suggests broad applicability to OCT and fluorescence imaging and connects to fast time-reversal approaches, offering a principled, non-invasive route to robust wavefront corrections in thick scattering media.

Abstract

Wavefront shaping systems aim to image deep into scattering tissue by reshaping incoming and outgoing light to correct aberrations caused by tissue inhomogeneity However, the desired modulation depends on the unknown tissue structure and therefore its estimation is a challenging time-consuming task. Most strategies rely on coordinate descent optimization, which sequentially varies each modulation parameter and assesses its impact on the resulting image. We propose a rapid wavefront shaping scheme that transitions from coordinate descent to gradient descent optimization, using the same measurement to update all modulation parameters simultaneously. To achieve this, we have developed an analytical framework that expresses the gradient of the wavefront shaping score with respect to all modulation parameters. Although this gradient depends on the unknown tissue structure, we demonstrate how it can be inferred from the optical system's measurements. Our new framework enables rapid inference of wavefront shaping modulations. Additionally, since the complexity of our algorithm does not scale with the number of modulation parameters, we can achieve very high-resolution modulations, leading to better corrections in thicker tissue layers. We showcase the effectiveness of our framework in correcting aberrations in a coherent confocal microscope.

Figures (10)

• Figure 1: System Schematic:(a) Schematic diagram of our system consisting of two SLMs. The first SLM modulates the illuminating laser light, while the second SLM modulates the reflected light. A validation camera provides reference images and confirms focusing on the desired target. (b) Our algorithm optimizes SLM phase to focus light on multiple adjacent points, by applying simple tilt-shift to the same modulation.
• Figure 2: Tilt-shift and time reversal effects: (a) We show a simplified schematic of our system with two input wavefronts, green focusing into the center of the imaging plane and yellow focusing to a neighboring point to the left. (b) Simulation results showing the incoming phase on the SLM, the conjugate of the output phase after tissue reflection (when reaching the SLM plane), and the intensity at the target plane. With light modulation, strong correlations are observed between the incoming SLM phase and the output phase, as well as between output phases for different points (white circles indicate areas of strong correlation). Without aberration correction, correlation decreases rapidly.
• Figure 3: Algorithm convergence: We used our algorithm to image a glass mask partially covered with chrome, placed behind a $180\mu m$ thick chicken breast tissue as the scattering material. We show captured images on both the main and validation cameras before the algorithm is applied and at the end of each iteration. The first row demonstrates the algorithm's convergence over iterations on the main camera for one of the scanned points. The second row displays the convergence on the validation camera, demonstrating our ability to also focus light on the target plane. The final row depicts the evolution of the phase mask presented on both SLMs. The last column illustrates the improvement of the cost function across iterations. Scale bar is $4\mu m$.
• Figure 4: Effect of target area size: We evaluate how focusing quality depends on the size of the target area ${\bm{\mathcal{A}}}$ over which the confocal score is computed. The experiment used a chrome-covered glass mask overlaid with $240\mu m$ thick chicken breast tissue. Our results show that for single-spot illumination (second column) the algorithm successfully achieved a sharp focused spot on the main camera without actually focusing light to a spot inside the tissue, as evident by the image from the validation camera. As we expanded the size of the focus area, the algorithm demonstrated progressively improved ability to focus light inside the tissue and the validation camera images are sharper. At the same time increasing the scanned area reduces the intensity of the focused spot on the main camera because a single modulation cannot correct very large areas.
• Figure 5: Confocal imaging: of patterns printed on chrome mask, through a scattering layer. Our algorithm successfully focuses light on the desired plane. Each row shows a different target. Columns 1-2: Main camera images of a single focal spot before and after optimization. Columns 3-4: Corresponding validation camera images. Columns 5-7: Confocal scanning results: Without aberration correction, with aberration correction, and reference scan of the target before applying scattering material, respectively. In the first three targets (top rows) the scattering material is chicken breast of thickness of $130\mu m$, $150\mu m$ and $200\mu m$, respectively. In the fourth target the scattering material is two layers of parafilm. Scale bar on confocal images is $4\mu m$.