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Time-average electronic speckle pattern interferometry and digital holography are two representative full-field coherent optical techniques used in mechanical vibration measurement. In both techniques, the quantitative data processing is affected by several difficulties. The most important are the weak contrast of Bessel-type fringes and the speckle noise. The greatest obstacle in achieving complete amplitude field estimation comes from the orthogonal components of time-averaged digital holograms or speckle interferograms, where multiplicative, high-frequency phase noise covers the deterministic, vibration-related phase. Several researchers studied these problems in relation with the double-exposure method. In the present paper, the author presents in a single, unifying approach, these double-exposure methods, common to speckle interferometry and digital holography. An important reduction of multiplicative high-frequency phase noise allows obtaining fringe-averaged patterns whose intensity noise is much lower than in classical time-average holography. The analysis allows choosing the most appropriate method leading not only to a higher fringe pattern quality, lower noise and extended measurement range, but also to a method of vibration-related phase estimation, which may include in some stages subpixel precision. The method, based on the mathematical inversion of the Bessel function on monotonic intervals, is equivalent to phase unwrapping, but it only uses time-averaged fringe patterns.

Speckle Noise Reduction in Vibration Measurement by Time-Average Speckle Interferometry and Digital Holography-a Unifying Approach