[Paper Review] Phase-probability shaping for speckle-free holographic lithography

Dong Zhao, Weiwei Fu+3 more|arXiv (Cornell University)|Nov 18, 2022

Digital Holography and Microscopy4 citations

TL;DR

This paper introduces phase-probability shaping to eliminate speckle noise in holographic lithography by narrowing the probability distribution of encoded phases, enabling uniform optical interference. Using a machine-learning-assisted probability-shaping (MAPS) method, the authors achieve ultralow speckle contrast (C = 0.08) and record edge sharpness (~1000 mm⁻¹), enabling high-fidelity, arbitrary-shape patterning of complex structures like vortex gratings and 2D random barcodes.

ABSTRACT

Optical holography has undergone rapid development since its invention in 1948, but the accompanying speckles with randomly distributed intensity are still untamed now due to the fundamental difficulty of eliminating intrinsic fluctuations from irregular complex-field superposition. Despite spatial, temporal and spectral averages for speckle reduction, it is extremely challenging to reconstruct high-homogeneity, edge-sharp and shape-unlimited images via holography. Here we predict that holographic speckles can be removed by narrowing the probability density distribution of encoded phase to homogenize optical superposition. Guided by this physical insight, a machine-learning-assisted probability-shaping (MAPS) method is developed to prohibit the fluctuations of intensity in a computer-generated hologram (CGH), which empowers the experimental reconstruction of irregular images with ultralow speckle contrast (C=0.08) and record-high edge sharpness (~1000 mm-1). It breaks the ultimate barrier of demonstrating high-end CGH lithography, thus enabling us to successfully pattern arbitrary-shape and edge-sharp structures such as vortex gratings and two-dimensional random barcodes.

Motivation & Objective

• To overcome the fundamental challenge of speckle noise in optical holography caused by random intensity fluctuations from complex-field interference.
• To develop a method that enables high-homogeneity, edge-sharp, and shape-unlimited image reconstruction in computer-generated holography (CGH).
• To break the performance barrier in CGH lithography by eliminating speckle while preserving structural fidelity and resolution.
• To demonstrate experimental realization of arbitrary-shape, high-precision nanostructures such as vortex gratings and 2D random barcodes.

Proposed method

• The core method involves shaping the probability density function (PDF) of the encoded phase to reduce fluctuations, thereby homogenizing optical interference and suppressing speckle.
• A machine-learning-assisted probability-shaping (MAPS) framework is developed to optimize phase distributions that minimize intensity variance in the reconstructed image.
• The approach uses a differentiable differentiator to map phase PDFs to reconstructed intensity statistics, enabling end-to-end training for optimal phase distribution.
• The method is applied to design computer-generated holograms (CGHs) that produce high-contrast, edge-sharp patterns with minimal speckle.
• Experimental validation is performed using a spatial light modulator (SLM) to reconstruct complex patterns under controlled illumination.

Experimental results

Research questions

• RQ1 Can narrowing the probability distribution of encoded phases effectively suppress speckle in holographic reconstruction?
• RQ2 To what extent can machine learning optimize phase distributions to minimize intensity fluctuations in CGHs?
• RQ3 Can the proposed method achieve both ultralow speckle contrast and high edge sharpness simultaneously in arbitrary pattern generation?
• RQ4 Is it feasible to fabricate complex, shape-unlimited nanostructures such as vortex gratings and 2D barcodes with minimal speckle using this approach?

Key findings

• The method achieves a speckle contrast of C = 0.08, representing a significant reduction compared to conventional holography.
• Record-high edge sharpness of approximately 1000 mm⁻¹ is experimentally demonstrated, enabling sub-micron resolution in patterned structures.
• The technique successfully enables the fabrication of arbitrary-shape structures, including vortex gratings and two-dimensional random barcodes, with high fidelity.
• The machine-learning-assisted probability-shaping (MAPS) framework effectively suppresses intensity fluctuations by controlling the phase PDF, validating the physical insight.