异形孔径光阑成像系统像方空间光强分布计算

Calculation of Light Intensity Distribution in Imaging Space of Imaging System with Arbitrary Aperture Diaphragm

基于异形孔径光阑的成像系统像方光强分布计算对显微系统自动对焦、景深扩展等成像技术领域发展有极其重要的理论价值,而传统的菲涅耳衍射光强分布计算公式仅适用于轴对称孔径光阑,且在焦平面处光强分布的问题.利用标量衍射理论,通过结合频谱变换与正交分离,推导出适用于异形孔径形状、任意离焦量的像方空间光场强度分布数理关系式;并利用离散傅里叶变换原理,获得了基于异形孔径光阑的光学成像系统像方空间光强分布的数值计算表达式.在圆形孔径光阑、焦平面处,对获得的表达式与传统计算公式进行了对比计算与分析,两组计算结果完全一致.针对半圆形孔径光阑,在相同的系统参数下,在离焦量分别为0,4,8μm三个像方位置处,数理模型理论计算的结果与实验测试结果基本一致.从而证明所推导数理模型的准确性,其可适用于任意形状的孔径光阑.

The calculation of light intensity distribution for an imaging system based on specialshaped aperture diaphragm has a significant theoretical importance for developing imaging techniques such as the automatic focus and depthoffield expansion of microscopic systems.The traditional Fresnel diffractive light intensity distribution calculation formula applies only to the problems of an axisymmetric aperture diaphragm and light intensity distribution in the focal plane.We derived the mathematical relationship between the optical field intensity distribution of the image space suitable for the arbitrary aperture shape and arbitrary outoffocus amount using scalar diffraction theory along with a combination of spectral transformation and orthogonal separation.Furthermore,by using the principle of discrete Fourier transform,we obtained the numerical calculation expression of optical intensity distribution for the imaging space of an optical imaging system with a particular aperture diaphragm.Additionally,we compared the calculation and analysis of the obtained numerical calculation expression with that of the traditional calculation formula,which prove the accuracy of the derived mathematical model calculation at a circular aperture diaphragm and focal plane.For a semicircular aperture diaphragm,under the same system parameters,at the three image positions of 0,4,and 8μm,respectively,the results calculated using the obtained mathematical model theory agree with the experimental test results,thereby indicating that the derived mathematical model applies to any shape of the aperture diaphragm.