Abramowitz I A
Appl Opt. 1969 Feb 1;8(2):403-10. doi: 10.1364/AO.8.000403.
This paper applies the methods of ray tracing to the evaluation of aberrations produced by Fresnel holograms that are recorded on two dimensional media. Attention is given both to holographic systems that employ lenses to modify the object wave and to lensless systems. Two lensless systems are discussed. The first, a system operating at optical wavelengths, is of numerical aperture 0.025, magnification 25, and unity wavelength ratio, lambda recording/lambda reconstructing. The field size of this device is better than 300 times the resolution; the system is diffraction-limited for points within a depth of 2.5 cm about the nominal object point. The second system, designed to record at x-ray wavelengths and to reconstruct at optical wavelengths, is of numerical aperture 0.0125, magnification 1000, and wavelength ratio 0.001. The field size is better than 3000 times the resolution; the system is diffraction-limited for points within a depth of 0.035 cm about the nominal object point. The performance of a lensless system is compared to that of a holographic system which employs an analytic aplanatic lens of high numerical aperture to form an enlarged real image of the object which is then recorded by a holographic system of unity magnification. The distortions of such a system are those of the lens alone. A method is established to design and ray trace an aplanatic lens. The system with such a lens is found to be in every way superior, at optical wavelengths, to the comparable lensless system.
本文将光线追迹方法应用于对记录在二维介质上的菲涅耳全息图所产生像差的评估。研究对象既包括采用透镜来改变物波的全息系统，也包括无透镜系统。文中讨论了两种无透镜系统。第一种是工作在光学波长的系统，其数值孔径为0.025，放大倍数为25，记录波长与再现波长之比为1。该装置的视场大小优于分辨率的300倍；对于标称物点周围深度为2.5厘米范围内的点，该系统受衍射限制。第二种系统设计用于在X射线波长下记录并在光学波长下再现，其数值孔径为0.0125，放大倍数为1000，波长比为0.001。视场大小优于分辨率的3000倍；对于标称物点周围深度为0.035厘米范围内的点，该系统受衍射限制。将一种无透镜系统的性能与一种全息系统进行了比较，该全息系统采用高数值孔径的解析消球差透镜来形成物体的放大实像，然后由放大倍数为1的全息系统进行记录。这种系统的畸变仅来自透镜。建立了一种设计和对消球差透镜进行光线追迹的方法。发现在光学波长下，带有这种透镜的系统在各方面都优于可比的无透镜系统。
