Journal of the Society of Motion Picture Engineers (1930-1949)

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1949 SCHLIEREN PHOTOGRAPHY 527 With the additional phase change k$(x\ the complex amplitude of the light vector at a point y in the F plane is then given by G(y) const (6) -A For future mathematical simplicity the effect of the wind tunnel can be represented by a complex function f(x) whose amplitude gives the light-transmission characteristics of the aperture and whose phase is k<j>(x). Since no light is transmitted outside the aperture |/(a;)| = 0, \x\ >A \f(x}\ = 1, \x\ < A f(x) = |/(z)|e^(*) (6) can be rewritten as G(y} = const f^ f (xW**(x)dx. (7) •u •s,. X Y 2 Fig. 3 — Schematic diagram of the image formation in a schlieren system. It can be shown8 that (7) can be transformed into f(x) = const f_^ G(y}e-ik*(x)dy (8) where f(x) and G(y) are known as Fourier transforms of each other. Equations (7) and (8) indicate that if the object f(x) is known the diffraction pattern G(y) can be calculated, and conversely, if the diffraction pattern G(y) is known, the object f(x) that gave rise to it can be calculated. This result may be interpreted to mean that a given object f(x) will give rise to a diffraction pattern G(y) which will then illuminate some