Measuring spatial coherence by using a mask with multiple apertures

A simple method to measure the complex degree of spatial coherence of a partially coherent quasi-monochromatic light field is presented. The Fourier spectrum of the far-field interferogram generated by a mask with multiple apertures (small circular holes) is analyzed in terms of classes of aperture pairs. A class of aperture pairs is defined as the set of aperture pairs with the same separation vector. The height of the peaks in the magnitude spectrum determines the modulus of the complex degree of spatial coherence and the corresponding value in the phase spectrum determines the phase of the complex degree of spatial coherence. The method is illustrated with experimental results.     

Noise reduction in the Fourier spectrum of Hartmann patterns for phase demodulation

A simple method to reduce the noise in the Fourier spectrum of Hartmann patterns for filtering the fundamental sidelobes (first harmonics) is presented. The method consists on replacing the Hartmann pattern by a fringe pattern within a circular pupil. The fringes are cosine square type and the pupil is apodized with a Gaussian function. These fringes follow the centroid spots of the Hartmann pattern along the horizontal and vertical directions. The width of the fringes in each direction is constant and it is determined according to the distortion of the Hartmann pattern. In this way, it is possible to obtain the wavefront’s slopes more accurate in comparison with the traditional method. We present experimental results to show the advantages of our method.     

Hartmann test of small F/# convex mirrors

A modified Hartmann test for testing aspherical convex surfaces of F/# ∼ 1 is analyzed. We present the main differences of this test in comparison to the usual Hartmann test. Theoretical results show that the transverse aberrations yielded by a testing surface have to be measured with respect to its mean sphere. A method to determine the mean sphere is also presented. Experimental results show the feasibility of this method.     

Autocorrelation-based reconstruction of two-dimensional binary objects

A method for reconstructing two-dimensional binary objects from its autocorrelation function is discussed. The objects consist of a finite set of identical elements. The reconstruction algorithm is based on the concept of class of element pairs, defined as the set of element pairs with the same separation vector. This concept allows solving the redundancy introduced by the element pairs of each class. It is also shown that different objects, consisting of equal number of elements and the same classes of pairs, provide Fraunhofer diffraction patterns with identical intensity distributions. However, the method predicts all the possible objects that produce the same Fraunhofer pattern.