Abstract
When the two-dimensional Fourier transformation is performed with a lens the optical amplitude and phase in the output plane represent the complex transform. It can be shown that the two-dimensional Hartley transform is mathematically equivalent to the Fourier transform, but is real valued; amplitude alone fully represents everything. This is significant because ordinary optical detectors do not respond to phase. Here we describe the construction of an optical system in the form of a modified Michelson interferometer which physically demonstrates that it is possible to produce the Hartley transform of a plane luminous object. It is thus possible to encode in the form of amplitude the half of the information in a diffraction pattern that normally is carried in the form of phase.
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References
1. Hartley, R. V. L. Proc. Inst. Radio Engrs 30, 144-150 (1942). 2. Bracewell, R. N. The Hartley Transform, 3-112 (Oxford University Press, New York, 1986). 3. Bracewell, R. N., Buneman, O., Hao, H. & Villasenor, J. Proc. Inst. Elect. Electron. Engrs. 74, 1283-1284 (1986). 4. Bracewell, R. N., Bartelt, H., Lohmann, A. W. & Streibl, N. Appl. Opt. 24,1401-1402 (1985). 5. Bracewell, R. N. J. opt. Soc. Am. 73, 1832-1835 (1983).
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Villasenor, J., Bracewell, R. Optical phase obtained by analogue Hartley transformation. Nature 330, 735–737 (1987). https://doi.org/10.1038/330735a0
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DOI: https://doi.org/10.1038/330735a0
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