任意相干度圆孔成像系统对两物点分辨能力研究

Research on the resolving ability of two object points with arbitrary coherence circular hole imaging system

两点分辨的问题已进行过深入的研究,其中最著名的是Rayleigh和Sparrow判据。然而其通常仅适用于完全相干光或者完全非相干光两种极限状态,对于具有普遍性的部分相干光的情况却研究较少。本文设计了部分相干光照明圆孔成像系统,据此建立了两物点光强在像面分布数学模型,利用MATLAB对两物点像面光强分别在不同间距与任意相干度情况进行了模拟仿真,结果显示当两点间距一定,两物点分辨率随着两点光源间相干度的增加而减小,而当相干度一定时,两物点分辨率随着两点光源间距的增加而增加。本文同时采用像面间距与物面间距的比值以描述系统对两物点分辨能力,分析探讨了两物点恰能分辨,不能分辨,完全能分辨的三种情况,并给出任意相干度的圆孔成像系统一般分辨规律。同时设计了两物点在任意相干度的成像系统实验平台,实验结果表明两物点在此实验条件下间距为1.5 mm时恰能分辨,说明实验结果与理论模拟基本吻合。

The problem of two-point resolution has been discussed by many criteria and methods.The most famous ones are the Rayleigh and Sparrow criteria.However,they are only applicable to the two limited states of completely coherent light or completely incoherent light,while the universal case of partially coherent light is studied less.In this paper,we designed a circular aperture imaging system with partially coherent light illumination to make an analysis of the two-point resolution.Based on the experimental platform,we established the mathematical model of the light intensity distribution of two object points on the image surface.MATLAB is used to simulate the image surface light intensity of the two object points at different distance and arbitrary coherence.The simulation results show that when the distance between the two points is constant,the resolution of the two object points decreases with the increase of the coherence between the two point light sources,and when the coherence is constant,the resolution of the two object points increases with the increase of the distance between the two point light sources.In this paper,the ratio between the distance of image plane and the one of object plane is used to describe the system′s ability to distinguish between two object points.The analysis explores the three situations in which two object points can be distinguished,cannot be distinguished,and can be distinguished completely.At the same time,we got the law of two-point resolution with an arbitrary degree of coherence and the distance between two points.The circular hole imaging system generally is satisfied with the law.We designed an imaging system experimental platform with two object points at any degree of coherence.The experimental results show that the two object points can be resolved at the distance of 1.5 mm under this experimental condition,which indicates that the experimental results are basically in agreement with the theoretical simulations.