Refocus criterion from image-plane speckle correlation in digital holographic interferometry

In digital holography and holographic interferometry, refocusing to the correct image plane can be challenging and may be obtained by various metrics. This paper proposes a digital refocus approach utilizing the linear relationship between in-plane speckle motion and defocus as a response to an induced phase gradient. The theory based on cross-correlations between pairs of intensity images reconstructed at different distances from the recording plane is discussed. Two simple metrics, based on the cross-correlation properties of the reconstructed speckle images, are proposed and evaluated utilizing both simulations and experiments. Experiments exhibit similar trends in which the estimate of the correct reconstruction distance differs by a small amount between the two metrics. The difference is found less than 1% in the estimate of the true reconstruction distance. The results show that either metric is able to yield a sufficient reconstruction distance for the reconstruction of the image plane.