Analytical model of a double grating system with partial temporal and spatial coherence

Abstract

Grating pseudo images are formed in cascade grating systems and are useful in different fields and in many different applications, such as interferometry, optical encoding of position, etc. There are several processes for creating images of a grating by using only gratings as imaging elements, being the most known the Talbot effect. In other configurations one grating acts as an imaging element for another grating, such as the Lau effect where two identical gratings are illuminated with an extended monochromatic light source, and a pseudoimage of the first one is formed at infinity. In Generalized Grating Imaging, pseudoimages form, without the need for lenses, at finite distances of the gratings. One disadvantage that a grating pseudoimaging system presents for most applications is the fact that the contrast of self- and pseudo-images strongly depends on the distance between gratings. This makes the optical devices less tolerant to positioning and/or manufacturing. It has been shown that, for Talbot effect, the use of polychromatic light can eliminate the dependence of the contrast on the grating position. A similar result has been numerically demonstrated for some pseudoimages in a double grating system with spatial and temporal partially coherent light. In this work we present an analytical model for Ronchi gratings that justifies and explains the numerical results previously obtained.