Exact formulas are derived for the field of view of an optical instrument with rectangular primary and secondary apertures and a rectangular field stop. The formulas derived include the effects of diffraction at the primary and secondary apertures. Numerical results are presented for an instrument with square optics, viewing a uniform monochromatic source. Similar calculations have been done for optical instruments with circular apertures by Goldberg and McCulloch [Appl. Opt. 8, 1451 (1969)]. The calculations for an instrument with square optics without a secondary aperture show that if the angle θƒ subtended by the geometrically determined field of view is 35 times as large as the ratio of wavelength to aperture size, then less than 5% of the energy collected at the detector will be from areas of the source outside the geometrical field of view. Using these formulas, an expression has been derived for the field of view of the same type of instrument viewing an infinite monochromatic source having two uniform brightness levels separated by a straight edge. Numerical results are presented for an instrument with square optics. If θƒ is at least ten times as large as the ratio of wavelength to aperture size, than 90% of the instrument’s response to the step change in brightness occurs while the step is crossing the geometrically determined field of view.
W. C. Braun, "The Effects of Diffraction on the Field of View of an Optical Instrument," Appl. Opt. 9, 1862-1867 (1970)