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THE INFLUENCE OF PATH-DIFFERENCE IN A DISPERSIVE MEDIUM ON TWO-BEAM INTERFERENCE

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https://hal.archives-ouvertes.fr/jpa-00213181

Submitted on 1 Jan 1967

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THE INFLUENCE OF PATH-DIFFERENCE IN A

DISPERSIVE MEDIUM ON TWO-BEAM

INTERFERENCE

H. Hopkins

To cite this version:

(2)

BTUDE DE PROFILS D E RAIES AVEC CONNAISSANCES DE LA PHASE C 2 - 17 P. FELLGETT. - I agree with what Larry Mertz has

just said. Also, I prefer to consider the phase as an essential part of the transform, rather than to (( cor- rect )) the zero of path difference by interpolation ; as A. S. Filler said, one's concepts should not be confined to symetrical interferograms.

There is a general method for obtaining wrong theo- retical conclusions about the solution of convolutions. One invents for oneself a method of undoing a convo- lution ; the proposal to extrapolate the interferogram is equivalent to this. One then works this method up in sufficiently complicated analysis to ensure that it is difficult to notice when the convoluting function is of the kind that cannot be undone, e. g. one having a Fourier transform which is either 0 or 1 everywhere.

For some curious historical reason communication engineers often understand these matters better than mathematicians.

I will stick my neck out and say that, in the approxi- mation that the interferogram can be made both band- limited and of finite range in its own argument, no extrapolation of the interferogram is necessary.

On a minor point, the signal-to-noise relations are exactly the same whether one makes 1, 2 or co measu- res per sampling interval (a special case is that conti- nuous and step-by-step methods are equivalent) pro- vided that the total time actually used is the same. This follows from the theorem that each set of sampling values is equivalent to the whole band-limited function and therefore to every other set of sampling values.

JOURNAL DE PHYSIQUE Colloque C 2, suppliment au no 3-4, Tome 28, mars-avril1967,page C 2

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17

THE INFLUENCE OF PATH-DIFFERENCE IN A DI SPER SHVE

MEDIUM ON TWO-BEAM INTERFERENCE

H . H. HOPKINS

Imperial College of Science and Technology University of London, England

The temporal coherence between two light beams is no longer the case. The temporal coherence as a having constant spacial coherence is given by Fourier fonction of the total path-difference for the mean transform of the spectral distribution of energy in the wavelength is found for a gaussian profile ; and this is source when the path-difference arises in air. If there used to derive a tolerance on the equality of glass is also a path-difference in a dispersive medium, this thickness in the two arms of an interferometer.

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