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Optical reflection from planetary surfaces as an operator-eigenvalue problem

Earth, Moon and Planets

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DOI: 10.1007/BF00057602

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Abstract

The understanding of quantum mechanical phenomena has come to rely heavily on theory framed in terms of operators and their eigenvalue equations. This paper investigates the utility of that technique as related to the reciprocity principle in diffuse reflection. The reciprocity operator is shown to be unitary and Hermitian; hence, its eigenvectors form a complete orthonormal basis. The relevant eigenvalue is found to be infinitely degenerate. A superposition of the eigenfunctions found from solution by separation of variables is inadequate to form a general solution that can be fitted to a one-dimensional boundary condition, because the difficulty of resolving the reciprocity operator into a superposition of independent one-dimensional operators has yet to be overcome. A particular lunar application in the form of a failed prediction of limb-darkening of the full Moon from brightness versus phase illustrates this problem. A general solution is derived which fully exploits the determinative powers of the reciprocity operator as an unresolved two-dimensional operator. However, a solution based on a sum of one-dimensional operators, if possible, would be much more powerful. A close association is found between the reciprocity operator and the particle-exchange operator of quantum mechanics, which may indicate the direction for further successful exploitation of the approach based on the operational calculus. ?? 1986 D. Reidel Publishing Company.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Optical reflection from planetary surfaces as an operator-eigenvalue problem
Series title:
Earth, Moon and Planets
DOI:
10.1007/BF00057602
Volume
36
Issue:
2
Year Published:
1986
Language:
English
Publisher location:
Kluwer Academic Publishers
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Earth, Moon and Planets
First page:
103
Last page:
116
Number of Pages:
14