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512 S. SABAROFF tf. s. M. P. E.
The required spot field extends to infinity with an intensity that decreases in an oscillatory manner through positive and negative values from a maximum at the origin to zero at infinity.
Such a condition is not exactly obtainable because in this application it does not seem possible to simulate negative spot fields. Also the spot is in reality of finite extent.
It is possible to add another field Pi(S) to equation 63 such that their sum is never negative:
P(S) = /!(5«) + Pi(S) (64)
Equation 63 could be termed a "Bessel distribution" and equation 64 a "partial Bessel distribution."
The frequency characteristic of the partial Bessel distribution may be found by inserting equation 64 in 21, i. e.,
= zu Cajl(S^)JQ(SMl)dS + 2x C Jo Jo
SPi(S)J0(SMl)dS (65)
where a has been taken as the radial extent of the spot.
It is interesting to note that the first integral in equation 65 is a step function16 such that
No tables of equation 66 for a finite upper limit seem to be available. Rough calculations show it to be somewhat similar to the frequency characteristic of the sine distribution discussed in Appendix 1.
REFERENCES
1 WHEELER, H. A., AND LOUGHRAN, A. V. : "The Fine Structure of Television Images," Proc. I. R. E., 26 (May, 1938), pp. 540-575.
2 GOLDMARK, P. C., AND DYER, J. N. : "Quality in Television Pictures," Proc. I. R. E., 28 (Aug., 1940), pp. 343-350.
3 STEPHENS, E.: "The Elementary Theory of Operational Mathematics," McGraw-Hill Book Co., Inc. (1937).
4 DAVIS, H. T. : "The Theory of Linear Operators," Principia Press (1936).
5 MACROBERT, T. A.: "Functions of a Complex Variable," Macmillan Co. (1933), pp. 319-321.
*Ibid., p. 321.
7 COFFIN, J. G. : "Vector Analysis," John Wiley & Sons, Inc. (Second Edition, 1911), p. 131.
8 MERTZ, P., AND GRAY, F.: "A Theory of Scanning and Its Relation to the Characteristics of the Transmission Signal in Telephotography and Television," Bell Telephone System, Mon. B-799.
9 STRYKER, N. R.: "Scanning Losses in Reproduction," /. Soc. Mot. Pict. Eng., XV (Nov., 1930), pp. 610-623.