Fourier Images IV: The Phase Grating

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Abstract
The nature of the Fourier images obtained from phase objects is investigated theoretically both for the particular case of the sinusoidal grating and also for the general two-dimensional periodic object. The results are verified experimentally with light optics using a two-dimensional phase grating of 50 μ periodicity. A detailed investigation is made of the intensity distribution on planes mid-way between, and in the immediate neighbourhood of Fourier image planes. While there is no contrast on the Fourier image planes themselves, it is shown that a simple relationship (equation (3.4)) exists between the pattern on neighbouring planes and the phase distribution in the general two-dimensional object. It is shown that there will be no moiré effect at full aperture for phase gratings effectively in contact. Analogies with the scattering of electrons by thin crystals are pointed out and it is indicated that under certain conditions a representation of the charge distribution will be obtained with modern electron microscopes. Full consideration of this point is deferred.

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