Voelz David G, Roggemann Michael C
New Mexico State University, Klipsch School of Electrical and Computer Engineering, Las Cruces, New Mexico 88003, USA.
Appl Opt. 2009 Nov 10;48(32):6132-42. doi: 10.1364/AO.48.006132.
Accurate simulation of scalar optical diffraction requires consideration of the sampling requirement for the phase chirp function that appears in the Fresnel diffraction expression. We describe three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled. Ideal sampling, where the chirp and its FFT both have values that match analytic chirp expressions, usually provides the most accurate results but can be difficult to realize in practical simulations. Under- or oversampling leads to a reduction in the available source plane support size, the available source bandwidth, or the available observation support size, depending on the approach and simulation scenario. We discuss three Fresnel propagation approaches: the impulse response/transfer function (angular spectrum) method, the single FFT (direct) method, and the two-step method. With illustrations and simulation examples we show the form of the sampled chirp functions and their discrete transforms, common relationships between the three methods under ideal sampling conditions, and define conditions and consequences to be considered when using nonideal sampling. The analysis is extended to describe the sampling limitations for the more exact Rayleigh-Sommerfeld diffraction solution.
标量光衍射的精确模拟需要考虑菲涅耳衍射表达式中出现的相位啁啾函数的采样要求。我们描述了基于快速傅里叶变换（FFT）的传播方法的三种采样方式：理想采样、过采样和欠采样。理想采样中，啁啾及其FFT的值都与解析啁啾表达式匹配，通常能提供最准确的结果，但在实际模拟中可能难以实现。欠采样或过采样会导致可用源平面支持大小、可用源带宽或可用观测支持大小减小，这取决于方法和模拟场景。我们讨论了三种菲涅耳传播方法：脉冲响应/传递函数（角谱）法、单FFT（直接）法和两步法。通过插图和模拟示例，我们展示了采样啁啾函数的形式及其离散变换、理想采样条件下三种方法之间的常见关系，并定义了使用非理想采样时要考虑的条件和后果。该分析扩展到描述更精确的瑞利 - 索末菲衍射解的采样限制。
