Use of specklegrams background terms for speckle photography combined with phase-shifting electronic speckle pattern interferometry

Electronic speckle pattern interferometry (ESPI) is combined with digital speckle photography (DSP) to measure out-of-plane deformation in the presence of large in-plane translation or rotation. ESPI is used to measure out-of-plane displacements smaller than the speckle diameter. In-plane displacements larger than the speckle size are obtained by DSP using artifacts images computed from the phase-stepped specklegrams. Previous works use the specklegram modulation for that purpose, but we show that this can lead to errors in the case of low modulation. In order to avoid this, a simple averaging of phase-stepped specklegrams allows obtaining the average irradiance, which contains information on the speckled object image. The latter can be used more efficiently than the modulation in DSP and is simpler to compute. We also perform a numerical simulation of specklegrams, which show that the use of background terms is much more stable against some error sources as compared to modulation. We show experimental evidence of this in various experiments combining out-of-plane ESPI measurements with in-plane translations or rotations obtained by our DSP method. The latter has been used efficiently to restore phase loss in out-of-plane ESPI measurements due to large in-plane displacements.