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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, λ recording/λ 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.
© 1969 Optical Society of America
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