Optimization of diffractive optical elements with millions of pixels using progressive error reduction algorithm (PERA)

Spatial light modulators (SLMs) comprising millions of micro-pixels have been applied for advanced applications requiring diffractive images of high quality (i.e., low root-mean-squared error, high signal-to-noise ratio, and low signal variation). Diffractive optical elements (DOEs) to be displayed in high-resolution SLMs are calculated using optimization algorithms to produce specific images. Current DOE optimization algorithms are incapable of providing high-quality images or else they consume too much time doing so. This paper presents two algorithms: the large error reduction algorithm (LERA) and the progressive error reduction algorithm (PERA). LERA selects image pixels (px) with the largest error for replacement with a target amplitude to improve image quality beyond what could be achieved using the iterative Fourier transform algorithm (IFTA). LERA tends to be time-consuming; however, it is able to reduce variations in signal intensity to 1.73e-8. PERA accelerates the optimization process by cascading an IFTA and several modified LERAs. Experiments were conducted on six DOEs of 1920×1080 px using a three-stage PERA equipped with three scaling factors.