Digital Diffractive Optics Based On The MATLAB

Optical experiments need stable environment and delicate instruments, which, to some extent, make experiments difficult. However, with the development of computer technology, we can take advantage of computers to calculate or simulate the process of optic diffraction. This not only makes the calculation simpler, but also improves the efficiency of its practical application. As a matter of the fact, computer analogue has become more and more important in the research of optics.We can use computers to calculate or simulate process of optical diffraction in fields of digital holography, interferometer metering technique and produce of diffractive optical element,it is important to find a algorithms exactly and fleetly in the field of digital diffractive opticsThis paper mainly presents the optical simulative algorithm by using Matlab program, by which some fundamental issues during the process of optical diffraction based on scalar diffraction theory and FFT are analyzed. In this paper, the researches done are as follows.1. First, transfer function formulas that are corresponding to the sampling method of Angular spectrum, the sampling method of Point spread function and the sampling method of weighting function are given.2. Second, it is analyzed that although the three algorithms are based on scalar diffraction theory and FFT, they are suitable in different scope of diffraction distances. In the paper, by analyzing corresponding functions'local spatial frequency, a characteristic distance Zc that can be used to judge algorithms'application scope is given. Also, it is proven that the sampling method of Angular spectrum is applied to the situation that diffraction distance is less than characteristic distance Zc, that the sampling method of Point spread function is applied to the situation that diffraction distance is larger than characteristic distance Zc and that the sampling method of weighting function is just applied to characteristic distance.3. Third, in order to testify if the theories above are corresponding to the facts, we simulate circular hole, monolete and double slit's different imagines that are gotten from three different sampling methods mentioned above and different distances. In addition, we testify the results of theory analysis as follows. When the diffraction distance is equal to characteristic distance Zc, the simulation results of three algorithms are the same. When the diffraction distance is less than characteristic distance Zc, the sampling method of Angular spectrum has the best simulation result, while the deviation between the simulation results of the sampling method of Point spread function and the sampling method of Direct Fourier transformation and experiment results is more and more obvious till totally different intensity distribution imagines. When the diffraction distance is large than characteristic distance Zc, while the simulation result will show a kind of more and more severe grid"noise"if we use transfer function sampling and the simulation images of weighting function will show more and more scale compression. We also compare the differences of time when the three different sampling methods at the characteristic distance Zc, which is that it is the fastest if we use transfer function sampling method, that it is the slowest if we use point spread function and the time used by the method of weighting function is in the middle. In general, the testifying on the theories mentioned above provide us the foundation that what kind of method should used in simulation algorithm at different situations.