Simulated LCSLM with Inducible Diffractive Theory to Display Super-Gaussian Arrays Applying the Transport-of-Intensity Equation

Abstract

We simulate a liquid crystal spatial light modulator (LCSLM), previously validated by Fraunhofer diffraction to observe super-Gaussian periodic profiles and analyze the wavefront of optical surfaces applying the transport-of-intensity equation (TIE). The LCSLM represents an alternative to the Ronchi Rulings, allowing to avoid all the related issues regarding diffractive and refractive properties, and noise. To this aim, we developed and numerically simulated a LCSLM resembling a fractal from a generating base. Such a base is constituted by an active square (values equal to one) and surrounded by eight switched-off pixels (zero-valued). We replicate the base in order to form 1 ×N-pixels and the successive rows to build the 1024×1024 LCSLM of active pixels. We visually test the LCSLM with calibration images as a diffractive object that is mathematically inducible, using mathematical induction over the N×N-shape (1×1, 2×2, 3×3, …, n×n pixels for the generalization). Finally, we experimentally generate periodic super-Gaussian profiles to be visualized in the LCSLM (transmission SLM, 1024×768-pixels LC 2012 Translucent SLM), modifying the TIE as an optical test in order to analyze the optical elements by comparing the results with ZYGO/APEX.

Keywords

• super-Gaussian patterns
• inducible patterns
• irradiance transport equation
• Fraunhofer diffraction
• patterns in geometric series
• wavefront sensing