The Nyquist criterion and its applicability in phase-stepping digital shearography

Phase-stepping shearography is a useful speckle interferometric technique having wide applicability in various fields. Nyquist criterion has long been considered to be the gold standard in signal processing and imaging. This criterion states that the spatial frequency of image sampling should be more than twice the maximum spatial frequency in the image. As applied to speckle imaging in shearography, this implies that, if a two-dimensional charge-coupled device (CCD) is used for imaging, the pixel separation of the CCD device should be half of the minimum feature size in the image, or half of the speckle size. We examined the applicability of the Nyquist criterion in image sampling in phase-stepping shearography. We used a shearographic system employing a 24-megapixel digital still camera and a Michelson interferometer based shearing arrangement. We generated phase maps from a deformed object, which was a center-loaded thin aluminum plate fixed at the periphery. For a given amount of deformation and image shear, detailed phase maps where generated using the 4+4 phase stepping protocol for a different F-numbers, representing different sampling situations, ranging from the sub-Nyquist domain (undersampling) through the Nyquist domain, to the above-Nyquist (oversampling) domain. From the generated phase maps and quantitative measurements, we show that adherence to the Nyquist criterion is not a strict requirement in digital shearography. Operation in the sub-Nyquist domain is acceptable, even desirable, in many cases. Phase maps of good contrast and quality, with or without filtering, can be generated in the sub-Nyquist domain, which can be useful in strain analysis and non-destructive testing applications.