For an input amplitude rectangular grating with opening ratio 1/M (where M is a positive integer), we put forward a set of simple equations to calculate the Fresnel diffraction field distribution at the fractional Talbot distance z=(p/2M)z_(t) (where p=1, 2, ..., 2M). The main feature of our approach is that both the fractional Talbot distance and the structure of the grating are incorporated into our equations. One obvious advantage of our approach is that it is easy for us to calculate the successive Fresnel diffraction field at the fractional Talbot distance z=(p/2M)z_(t), while the previous distance-oriented equations are inconvenient to do so. Another noteworthy result obtained with our equations is that we have analytically proved the pure-phase condition for above grating, that is, when p and M have no common divisor, the field distribution at the fractional Talbot distance (p/2M)z_(t) is a pure-phase one. Furthermore, we also have derived a set of analytic equations to calculate such a pure-phase distribution at the fractional Talbot distance z=(p/2M)z_(t) when p and M have no common divisor.
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