BAND-UNLIMITED RECONSTRUCTION OF OPTICAL OBJECTS AND SPECTRAL SOURCES

Abstract

This paper derives a method for digitally reconstructing any two-dimensional, partially coherent, polychromatic object from experimental knowledge of the image and point spread function. In the absence of noise, the reconstruction is perfect. The object must lie wholly within a known region of the object plane. The optics may be generally coated and tilted, and may be aberrated to any extent. As an illustration, the reconstruction process is applied to the problem of resolving double stars. The reconstruction scheme is also used to correct the output of a conventional spectrometer for instrument broadening, and to correct the output of a Fourier -transform spectroscope for finite extent of the interferogram. Practical use of the method requires the calculation of prolate spheroidal wavefunctions and eigenvalues. The effect of noise upon the accuracy of reconstruction is analytically computed. It is shown that periodic noise and piecewise-continuous noise both cause zero error at all points in the reconstruction, except at the sampling points, where the error is theoretically infinite. Bandwidth -limited noise is shown to be indistinguishable from the object.