RESOLUTION IN DIFFRACTION-LIMITED IMAGING, A SINGULAR VALUE ANALYSIS .1. THE CASE OF COHERENT ILLUMINATION
RESOLUTION IN DIFFRACTION-LIMITED IMAGING, A SINGULAR VALUE ANALYSIS .1. THE CASE OF COHERENT ILLUMINATION
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DOI：
10.1080/713820912
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发表时间：
1982-01-01
期刊：
影响因子：
--
通讯作者：
PIKE, ER
中科院分区：
文献类型：
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作者：
BERTERO, M;PIKE, ER
利用长球面函数及其特征值谱的成像信息传递理论被扩展到允许物体和图像域不同。适当的理论变成了奇异函数和奇异值的理论，本文从这些方面对相干成像进行了描述。使用物理连续图像，在存在噪声的情况下，可以实现在改进先前标准的意义上的超分辨率，特别是在非常低的香农数下，我们对线性，方形和圆形瞳孔情况下的这种改进进行了定量估计。该理论还证明了相干等平面成像系统的自由度数不受瞳孔相位像差影响的有效证明。概述了这些结果在显微镜中的应用，并在激光散射领域最新发展的数值反演技术的基础上，提出了一种实用的实现方法。
The familiar theory of information transfer in imaging using the prolate spheroidal functions and their eigenvalue spectrum is extended to allow the object and image domains to differ. The appropriate theory becomes one of singular functions and singular values, and in this paper we give a description of coherent imaging in these terms. Super-resolution in the sense of improving on previous criteria in the presence of noise can then be achieved, particularly at very low Shannon numbers, using the physical continued image, and we give quantitative estimates of such improvements for the linear, square and circular pupil cases. The theory is also shown to provide an efficient proof of the theorem that the number of degrees of freedom of a coherent isoplanatic imaging system is unaffected by phase aberrations in the pupil. Applications of these results in microscopy are outlined, and a practical method of implementation is proposed based on a generalization of numerical inversion techniques developed recently in the field of laser scattering.