Numerical computation of in-plane displacements and their detection in the near field by double-exposure objective speckle photography

A model of a rough surface to the scale of the optical wavelength is proposed, with randomly distributed zero-mean Gaussian heights. It is assumed that the aforesaid surface is illuminated by a coherent light beam of homogeneous intensity. An in-plane pure translation of this surface is simulated on a PC by means of the Matlab program. In the near-field optical regions the Fraunhofer approximation and the subsequent FFT are not suitable for application in the generation of a speckle pattern. Hence, with the aim of calculating the translation of the rough surface by means of double-exposure objective speckle photography using the point-wise filtering technique (PWFT), the Fresnel-Kirchhoff integral is first employed to obtain the speckle intensity near the surface on a photographic plate, and then the intensity pattern produced by the diffraction of the plate is determined in the far field (Fraunhofer), which suffices to calculate the modulus of displacement through the Young’s fringes. The results are analyzed according to surface roughness and the sample distance to the recording plane.