The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

The family Opisthoproctidae (barreleyes) constitutes one of the most peculiar looking and unknown deep-sea fish groups in terms of taxonomy and specialized adaptations. All the species in the family are united by the possession of tubular eyes, with one distinct lineage exhibiting also drastic shortening of the body. Two new species of the mesopelagic opisthoproctid mirrorbelly genus Monacoa are described based on pigmentation patterns of the "sole"-a unique vertebrate structure used in the reflection and control of bioluminescence in most short-bodied forms. Different pigmentation patterns of the soles, previously noted as intraspecific variations based on preserved specimens, are here shown species-specific and likely used for communication in addition to counter-illumination of down-welling sunlight. The genus Monacoa is resurrected from Opisthoproctus based on extensive morphological synaphomorphies pertaining to the anal fin and snout. Doubling the species diversity within sole-bearing opisthoproctids, including recognition of two genera, is unambiguously supported by mitogenomic DNA sequence data. Regular fixation with formalin and alcohol preservation is shown problematic concerning the retention of species-specific pigmentation patterns. Examination or photos of fresh material before formalin fixation is shown paramount for correct species recognition of sole-bearing opisthoproctids-a relatively unknown issue concerning species diversity in the deep-sea pelagic realm.

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Preservation Obscures Pelagic Deep-Sea Fish Diversity: Doubling the Number of Sole-Bearing Opisthoproctids and Resurrection of the Genus Monacoa (Opisthoproctidae, Argentiniformes).

Diffraction of partially coherent light by an apodized slit aperture

Bibliographic Review on “Studies on Partial Coherence”

The performance of an optical system employing circular aperture has been investigated in the presence of longitudinal vibrations. It is shown that the system performance in the presence of longitudinal vibrations can be improved by introducing defocusing in the system. Two types of coherence functions, Besinc and Gaussian, have been assumed in studying the partially coherent diffraction patterns formed by the aperture.

Partially Coherent Diffraction by a Circular Aperture in the Presence of Longitudinal Vibrations

http://iopscience.iop.org/article/10.1088/0029-4780/2/1/304/pdf

B N Gupta

Papers

Partially space coherent diffraction of a circular aperture in the presence of spherical aberration