Reinterpretation and improvement of Talbot array illuminators

We show that the transmittance of a finite Talbot array illuminator (TAI) can be expressed by the phase distribution of a pixelated lens, modulated by a discrete phase grating (G). Thus the TAI reconstruction field is given by the convolution of the grating's Fourier transform, with the point-spread function of the pixelated lens. On the basis of this approach we propose a method to improve the performance of a finite TAI by modifying the basic cell of the grating factor G.