Application About The Method Of The Mulriple Simpson And Comparison With FFT In The Diffractive Computing

Optical diffraction is one symbol of wave-optic. Analysis and computing of diffraction relate to many optical fields, such as, optical system design, optical measure, holography, optical process and so on. Therefore the numerical computing of diffraction is very important. There are many methods of diffractive computing, including, FFT, Fractional Fourier transforms, Monte Carlo and Mulriple Simpson etc. They hold own characteristic and applied region. This paper studies that using Simpson matrix in computing of diffractive formula.This paper analyzes the formula of Mulriple Simpson and deduces the formula of computing two-dimension integral based on the method of Mulriple Simpson compute integral, namely the Simpson-matrix method.Using the Simpson-matrix method to compute the diffractive formula of Rayleigh-Sommerfeld, Kirchhoff and approximation based on the scalar theory of diffraction. Because the expressions of diffractive formula are different, the time of computing are different. When the expression of integral is more complex, it need a longer computational time. It can greatly reduce computational time through predigesting the diffractive formula.Comparing the methods between Mulriple Simpson and FFT in computing the diffractive formula of Fresnel. The results indicate that FFT need less time than the other and Mulriple Simpson is more precise than the other. And analyze the reason that FFT need less time than Mulriple Simpson. The reason is the computational times of plural- exponent multiplication affect the computational speed. The computational times of Mulriple Simpson are much more than FFT, so the computational time is greatly different.