Lateral Coherence Length of Partially Coherent Light Generated by Rotating Ground Glass or Liquid Crystal Spatial Light Modulators

Partially coherent light finds extensive applications in optical experiments, including laser processing, imaging, and holography. Rotating ground glass or liquid crystal spatial light modulators (SLMs) are common methods for generating partially coherent light. The core principle involves modulating the phase or amplitude of light waves to reduce spatial coherence, thereby controlling the lateral coherence length. In code implementations, this can be modeled using random phase screens with parameterized correlation functions to simulate the scattering effects.

The lateral coherence length (also known as coherence width) describes the distance over which the beam maintains phase correlation in the transverse direction, serving as a key parameter for characterizing the coherence properties of partially coherent light. Its calculation typically relies on the cross-correlation function of the optical field or intensity distribution. Experimentally, it can be indirectly derived by analyzing the contrast of interference fringes or the far-field intensity distribution. Algorithmically, one might implement a coherence estimation function using Fourier transforms or statistical analysis of intensity patterns, similar to how MATLAB's `xcorr2` function computes 2D cross-correlations.

When using rotating ground glass, its rough surface scatters incident light, creating random phase modulation that leads to partial decoherence. Liquid crystal SLMs, conversely, electronically control phase retardation at the pixel level, enabling flexible coherence modulation. The key difference lies in the implementation mechanism: ground glass relies on mechanical rotation for dynamic scattering, while SLMs offer higher programmability and precision through electronic control. In simulation code, SLM behavior can be modeled with pixel-wise phase matrices where each element's value is dynamically updated via control voltages.

For experimental measurements, Young's double-slit interferometer or shearing interferometry are commonly employed. Coherence length is fitted by analyzing fringe visibility or transverse intensity distributions. Additionally, based on the Van Cittert-Zernike theorem, Fourier transforms of far-field diffraction patterns can estimate lateral coherence characteristics. A practical code implementation might involve calculating visibility from interference pattern data using `(max-min)/(max+min)` formulas, or applying `fft2` operations to intensity arrays for spatial frequency analysis.

Understanding the calculation and control of lateral coherence length is crucial for optimizing optical systems, such as reducing speckle noise or improving imaging resolution. Rotating ground glass and liquid crystal SLMs provide distinct technical pathways suitable for different experimental needs and precision requirements. System designers can implement coherence control algorithms that adjust rotation speeds or SLM voltage patterns based on real-time coherence measurements feedback loops.