Rectangular-aperture dimensions from diffraction zeros

A uniformly illuminated rectangle of width $w$ and height $h$ has field proportional to $\mathrm{sinc}(q_{x}w/2)\mathrm{sinc}(q_{y}h/2)$, with angular spatial wavenumbers $q_x,q_y$ measured in inverse length. The first envelope zeros give $w=2\pi /|q_{x,0}|$ and $h=2\pi /|q_{y,0}|$. Two identical rectangles with horizontal centre separation $s$ introduce an additional $\cos (q_{x}s/2)$ factor, so the interference period is $\Delta q_x=2\pi /s$.

The factors $2\pi$ depend on using angular spatial frequency; axes in cycles per length would use the reciprocal widths directly. Fourier light intensity alone cannot determine an overall aperture translation or distinguish a mask from its inverted copy. Extra assumptions about shape and coherent illumination are necessary for a unique geometrical reconstruction.