Abstract
In calculations of the point spread function, conservation of energy between the pupil plane and image plane should be satisfied. However, the conventional treatment is inadequate especially for quantitative theoretical inference (Shibuya and Ooki, 2005). In this paper, we first derive a formula of diffraction caused by a pinhole aperture, which is defined as a two-dimensional δ-function, based on a more in-depth discussion than previous treatments. By considering the fulfillment of the reciprocity theorem between the two planes which are tilted towards each other, we prove the validity of introducing both outgoing and incoming inclination factors in this formula. Next, by applying this equation to the calculation of the point spread function, we deductively and quantitatively reveal that the conservation of energy between the pupil plane and image plane is fulfilled.
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