Handbook of holographic interferometry: optical and digital by Thomas Kreis

By Thomas Kreis

The booklet offers the rules and techniques of holographic interferometry - a coherent-optical size approach for deformation and tension research, for the selection of refractive-index distributions, or utilized to non-destructive trying out. Emphasis of the publication is at the quantitative computer-aided assessment of the holographic interferograms. established upon wave-optics the assessment equipment, their implementation in computer-algorithms, and their purposes in engineering are defined.

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By Thomas Kreis

The booklet offers the rules and techniques of holographic interferometry - a coherent-optical size approach for deformation and tension research, for the selection of refractive-index distributions, or utilized to non-destructive trying out. Emphasis of the publication is at the quantitative computer-aided assessment of the holographic interferograms. established upon wave-optics the assessment equipment, their implementation in computer-algorithms, and their purposes in engineering are defined.

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Let Er and Ei be the real and imaginary parts of E 1 = Re{E} = √ N Er 1 = Im{E} = √ N Ei N |E0n | cos φn n=1 N |E0n | sin φn . 96) n=1 The average values over an ensemble of macroscopically similar but microscopically different surfaces are n=1 N 1 √ N = Ei N 1 √ N = Er n=1 1 |E0n | cos φn = √ N 1 |E0n | sin φn = √ N N |E0n | cos φn = 0 n=1 N |E0n | sin φn = 0. 97) n=1 Here the independence of the individual amplitudes from the phases, assumption (i), allows one to take the average over the factors separately.

30: Recording of a Fraunhofer hologram. of the interference maxima, then the hologram should be considered as a volume or threedimensional hologram. 173) where d is the distance between adjacent interference planes [180]. If now the coherent object and reference waves impinge onto the hologram from opposite sides we get interference layers nearly parallel to the hologram surface. 30) and Fig. 3. For reconstruction this thick hologram is illuminated with white light which is reflected at the layers.

102). 100) gives I − 2σ 2 1 4πσ 2 e pI,φ (I, φ) = for I > 0 and otherwise. 105) for − π ≤ φ < π otherwise. 106) 0 1 2π 0 Thus the intensity in a speckle pattern obeys a negative exponential probability distribution and the speckle pattern phase is uniformly distributed. Furthermore we see that the intensity and phase are statistically independent pI,φ (I, φ) = pI (I)pφ (φ). (2σ 2 )n = n! 108) 2 especially the mean value is I = 2σ . 109) we get the result that the standard deviation σI of a speckle pattern equals the mean intensity.

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