Diffraction patterns in Fresnel approximation of periodic objects for a colorimeter of two apertures

In this work, we present a study of Fresnel diffraction of periodic structures in an optical system of two apertures. This system of two apertures was used successfully for measuring color in textile samples solving the problems of illumination and directionality that present current commercial equipments. However, the system is sensible to the spatial frequency of the periodic sample's area enclosed in its optical field of view. The study of Fresnel diffraction allows us to establish criteria for geometrical parameters of measurements in order to assure invariance in angular rotations and spatial positions. In this work, we use the theory of partial coherence to calculate the diffraction through two continuous apertures. In the calculation process, we use the concept of point-spread function of the system for partial coherence, in this way we avoid complicated statistical processes commonly used in the partial coherence theory.