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A method for analytically determining the complex transmittance of a Fourier-transform hologram whose reconstructed image is a prescribed focal curve contained in a plane parallel to that of the hologram is presented and experimentally verified. The Fourier spectrum of the focal curve is determined by an exact integration over one variable and a nonuniform stationary phase evaluation of the remaining integral. Transmittances obtained in this way permit the reconstruction of a wide class of piecewise twice-differentiable line foci.
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Jaroszewicz et al. (1991) studied this question.
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