Study Of Diffraction Calculation For Three-dimensional Object

Diffraction calculation is the most important work in information optics. It is widely used in computer generated holography (CGH), optical information processing,3D display, and so on. Thanks the rapid development of computer technology and FFT application, diffraction calculation has been accomplished very quickly.Starting with the Helmholtz equation, the kirchhoff formula, the Rayleigh-Sommerfeld formula and angular spectrum algorithm used to calculate diffraction distribution are deducted, these formulas or methods are all suitable for diffraction calculation between two parallel planes that both are vertical to optical axis. As for many actual cases, only minority meets this condition. So, it’s very necessary to research the diffraction calculation between two non-parallel planes.Based on the angular spectrum theory of light propagation, a spectrum shift interpolation algorithm is propose, which is used to calculate Fourier transform of small matrix rather than a huge matrix. According the method, calculation load and calculating time are decreased remarkably compared with traditional zero-padding algorithm. From the principle of coordinate conversion, the formula of Fresnel diffraction calculation between two non-parallel planes is derived. Moreover, the calculation methods of coordinate conversion and variable replacement are proposed. The spectrum shift caused by coordinate conversion and variable replacement is analyzed. Simulation on a computer is conduced. The Fourier transforms of rectangular and triangular function are developed in forms of analytical expression. A spatial surface can be divided into many rectangular and triangular sub-plane elements, and the spectrum of each element is worked out via analytical formula. After linear combination of these spectrums, the final spectrum of light wave from spatial surface is obtained in a certain plane. Utilizing angular spectrum algorithm, the quick diffraction calculation about a3D object is achieved. Relevant calculating examples are given.