Digital speckle photography of subpixel displacements of speckle structures based on analysis of their spatial spectra

We have investigated the capabilities of the method of digital speckle interferometry for determining subpixel displacements of a speckle structure formed by a displaceable or deformable object with a scattering surface. An analysis of spatial spectra of speckle structures makes it possible to perform measurements with a subpixel accuracy and to extend the lower boundary of the range of measurements of displacements of speckle structures to the range of subpixel values. The method is realized on the basis of digital recording of the images of undisplaced and displaced speckle structures, their spatial frequency analysis using numerically specified constant phase shifts, and correlation analysis of spatial spectra of speckle structures. Transformation into the frequency range makes it possible to obtain quantities to be measured with a subpixel accuracy from the shift of the interference-pattern minimum in the diffraction halo by introducing an additional phase shift into the complex spatial spectrum of the speckle structure or from the slope of the linear plot of the function of accumulated phase difference in the field of the complex spatial spectrum of the displaced speckle structure. The capabilities of the method have been investigated in natural experiment.