Studies on the role of spatial coherena in the lau phenomenon

Abstract

The Laue effect is of fundamental importance in the domain of optical interference phenomena. In the Laue experiment, interference fringes are formed in the far field when an extended source illuminates two gratings placed in tandem; these fringes are commonly referred to as the Laue fringes. Recent research has shown that the Laue effect can be usefully employed in several areas such as interferometry, non?coherent processing and theta modulation. The present thesis documents the following: (i) the results of the studies that were carried out to understand the role of spatial coherence in the formation and behaviour of Laue fringes; and (ii) the experiments that were performed to make use of the Laue phenomenon in the study of the relationship between axial and lateral periodicities of propagating wavefields. Under case?1 mentioned above, two kinds of studies are described. First, an experimental investigation that was carried out to study the dependence of the rotation sensitivity of Laue fringes on the spatial coherence of the illumination used is described. In this study, the spatial coherence of the light falling on the first of the two gratings was varied in convenient steps to determine at each step the angle through which the grating has to be rotated with respect to G2G_2G2? for the Laue fringes observed in the focal plane to vanish completely. The rotation sensitivity of Laue fringes is established by the rotation angle thus measured in each case. It was observed that the rotation sensitivity of Laue fringes varied in a well?defined manner with the spatial coherence of the illumination. The experimental results thus obtained have been explained using the theory of partial coherence. In the theoretical analysis it is assumed that the grating G1G_1G1? is uniformly illuminated with partially coherent light whose cross?spectral density function (CSDF) is Gaussian. Grating G1G_1G1? is assumed to be rotated with respect to G2G_2G2? by an angle ?\theta?. The CSDF is then traced through the Laue system right up to the back focal plane of the lens. The intensity of the Laue fringes is obtained from the CSDF at the back focal plane of the lens. The variation of the rotation angle ?r\theta_r?r? required for the Laue fringes to vanish, as a function of the transverse coherence length, is derived. The variation in the contrast of the Laue fringes for fixed coherence length as a function of ?\theta? is also computed. The case of spatially incoherent illumination of G1G_1G1? is also analysed on similar lines. The variation in the contrast of the Laue fringes as a function of ?\theta? was obtained. The theoretical results are concordant with the experimental observations made with a spatially incoherent source. In a second investigation it is shown that as the coherence of the illumination falling on G1G_1G1? is varied from a high degree of coherence to a high degree of incoherence, the optical energy is re?distributed from the Fraunhofer Diffraction Pattern (FDP) into the Laue fringes. In other words, the evolution of the Laue fringes from the FDP has been demonstrated. In the studies under case?2 the Laue experiment performed with specially prepared general objects is described. This experiment provides proof for the theoretical result recently obtained by Indebetouw that a subclass of axially periodic wavefields propagating in free space show lateral periodicity also.