Publication: Line spread function formulation proposed by W. H. Steel: A revision
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Publication Date
1997-07-01
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Chevalier del Río, Margarita
Lakshminarayanan, Vasudevan
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The Optical Society of America
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Abstract
A revised formulation of the image Light distribution of an incoherent line source proposed by Steel [Rev. Opt. 31, 334-340 (1952)] is presented. Analytical and numerical results based on this new representation are given. We explicitly show that a major error in Steel's final expression generates singularities, thereby preventing convenient numerical computation.
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© Optical Society of America.
The financial support of the Spanish Ministry of Health, the Institute of Health “Carlos III”, and the Health Research Foundation under project 95/1518 is acknowledged. Also a grant (A. Manzanares) from the Complutense University (4829) is acknowledged.
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1. W. H. Steel, “Calcul de la répartition the la lumière dans l’image d’une ligne”, Rev. Opt. 31, 334–340 (1952).
2. C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function, Wiley Series in Pure and Applied Optics (Wiley, New York, 1989), Chap. 2.
3. E. W. Marchand, “Derivation of the point spread function from the line spread function”, J. Opt. Soc. Am. 54, 915–919 (1964).
4. E. W. Marchand, “From line to point spread function: the general case”, J. Opt. Soc. Am. 55, 352–355 (1964).
5. M. L. Calvo, A. Manzanares, M. Chevalier, and V. Lakshminarayanan, “Edge image processing: an analysis of modified Heaviside functions as degraded edge generators”, in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J. S. Chang, J. H. Lee, and C. H. Nam, eds., Proc. SPIE 2778, 63–64 (1996).
6. G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1944), p. 350.
7. B. N. Begunov, N. P. Zakaznov, S. I. Kiryushin, and V. I. Kuzichev, Optical Instrumentation, Theory and Design (Mir, Moscow, 1988, Chap. 6, 6.2. (8) M. Abramowitz and I. A. Segun, Handbook of Mathematical Functions (Dover, New York, 1968), Chap. 9, p. 361; Chap. 15, p. 496. (9) J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978, Chap. 11, p. 503.
8. M. Abramowitz and I. A. Segun, Handbook of Mathematical Functions (Dover, New York, 1968), Chap. 9, p. 361; Chap. 15, p. 496.
9. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), Chap. 11, p. 503.
10. Ref. 8, p. 556.