A square-well model for occultation profiles produced by the Uranian rings is described. The model includes diffraction effects and treats the occulting ring segment as a uniformly transmitting gray screen with abrupt edges. Up to ten parameters of the model can be fit by least squares to a ring profile; those describing the profiles of the ring are: (1) the midtime of the profile, which specifies the position of the occulting ring segment; (2) the duration of the ring occultation, which is proportional to the radial width of the ring; and (3) the fractional transmission of the ring, which is simply related to its optical depth. The diameter of the occulted star can also be fit as a free parameter. For their data with the highest signal-to-noise ratio, the authors can achieve a precision of tens of meters in the placement of a ring segment, a precision of one-hundred meters in the width of a segment, and a precision of a few hundredths in its fractional transmission. This model has been used to fit occultation profiles obtained simultaneously at more than one wavelength in order to constrain the distribution of particle sizes within the rings.
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Elliot et al. (1984) studied this question.