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544 SHAFER
may be considered "absolute"; however, the densities are only "relative" and will depend to a large extent on the total light output of the source and the sensitivity of the film used. As was mentioned in the text, a Charters-type spark with a 1-mm-diameter source, through which about 5 watt-seconds of electrical energy are discharged, will give high-quality schlieren photographs at exposure times of the order of 10 ~6 second in an //10 schlieren system.
The knife-edge position will depend largely on the phenomena under investigation and can best be determined ultimately by experiment. For large sources, the more the cutoff, the higher will be the image contrast with a subsequent decrease in density. This is, however, a very inefficient way to obtain high contrast; it is much better to use a smaller source.
ACKNOWLEDGMENT
The numerical calculations for this work were carried out by Mrs. Norma Gilbarg, Technical Assistant in the Aeronautical Engineering Department, Princeton University.
REFERENCES
(1) H. Schardin, "Toepler's striation method,' principles for its application and quantitative evaluation," Air Ministry Translation, no. 249; May, 1935 (translated from Ver. Deuts. Ing. For., p. 267; 1934).
(2) F. Zernike, "Diffraction theory of the knife-edge test and its improved form: The phase contrast method," Royal Astron. Soc., Monthly Notices, vol. 94, no. 5, pp. 377-384; March, 1934.
(3) G. H. Linfoot, "A contribution to the theory of the Foucault test," Proc. Royal Soc. A., vol. 186, pp. 72-99; June, 1946.
(4) S. C. G. Gascoigne, "The theory of the Foucault test," Royal Astron. Soc., Monthly Notices, vol. 104, no. 6, pp. 326-334; 1944.
(5) H. J. Shafer, "A physical optic analysis of the schlieren method and phase contrast technique and their application to optical studies of two dimensional compressible flow phenomena in wind tunnels," Masters Thesis, Princeton University, 1948.
(6) H. J. Shafer, "A physical optic analysis of the schlieren method," Phys. Rev., vol. 75, p. 1313(A); April, 1949.
(7) M. Born. "Optik," J. Springer, Berlin, 1933, p. 154.
(8) H. Marganau and G. M. Murphy, "The mathematics of physics and chemistry," D. Van Nostrand, New York, 1943, p. 248.
(9) For definition and tabulation of the Si and Ci functions see Eugene Jahnke and Fritz Emde, "Tables of Functions," Dover, New York, N. Y., 1943, p. 3.
(10) For a more complete discussion of these diffraction patterns see A. I. Mahan, "Focal plane diffraction anomalies in telescopic systems," J. Opt. Soc. Amer., vol. 37, pp. 852-867; October, 1947.