We propose a novel, to our knowledge, algorithm of iterative simulated quenching with temperature rescaling for designing diffractive optical elements, based on an analogy between simulated annealing and statistical thermodynamics. The temperature is iteratively rescaled at the end of each quenching process according to ensemble statistics to bring the system back from a frozen imperfect state with a local minimum of energy to a dynamic state in a Boltzmann heat bath in thermal equilibrium at the rescaled temperature. The new algorithm achieves much lower cost function and reconstruction error and higher diffraction efficiency than conventional simulated annealing with a fast exponential cooling schedule and is easy to program. The algorithm is used to design binary-phase generators of large irregular spot arrays. The diffractive phase elements have trapezoidal apertures of varying heights, which fit ideal arbitrary-shaped apertures better than do trapezoidal apertures of fixed heights.
© 2000 Optical Society of America
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics
(090.1760) Holography : Computer holography
(090.1970) Holography : Diffractive optics
Jean-Numa Gillet and Yunlong Sheng, "Iterative Simulated Quenching for Designing Irregular-Spot-Array Generators," Appl. Opt. 39, 3456-3465 (2000)