Remarks on the Restoration of Occultation Observations

Abstract

If the limb of the Moon can be regarded as a straight edge, then the diffraction pattern of a point source which it produces at the distance of the Earth is the well known Fresnel diffraction pattern. Observations of stellar occultations reveal the variation of intensity with time as the diffraction pattern passes across the detector due to the orbital motion of the Moon and the rotation of the Earth. The linear scale of the diffraction pattern in monochromatic light depends on both the wavelength of observation, λ, and on the distance of the Moon, D, so that the scale is proportional to (λD)1/2.

Remarks on the Restoration of Occultation Observations

“…But the function p (£) is of course known theoretically, so that from strictly monochromatic observations of a point source, f p [t, X), it is possible to determine an experimental value of the scale factor v/(XD) 1/2 . Since X and D are known, as well as the expected limb velocity from the ephemeris and position angle of occultation, it is possible to compare observed and predicted velocity and so determine a slope for the lunar limb (Nather and Evans, 1970). In finding a restored brightness distribution, it is necessary to know the value of v, both to substitute into Equation (5) for the restoring function, and to convert from 0 to T according to Equation (3).…”

“…The alternatives are either to accept the ephemeris value of limb velocity and to ignore the slope of the lunar limb, or to make models of the theoretical occultation curves for assumed brightness distributions and try to match the observed occultation curves to them. This latter method, which is probably the best if plausible assumptions about the brightness distribution can be made, has been used successfully by Nather and Evans (1970). However, if we wish to pursue the idea of obtaining brightness distributions by direct restoration, it should be clear that some error is introduced by the unknown lunar limb slope, and that it is to some extent possible to trade lunar limb slope for angular diameter.…”

“…However, if we wish to pursue the idea of obtaining brightness distributions by direct restoration, it should be clear that some error is introduced by the unknown lunar limb slope, and that it is to some extent possible to trade lunar limb slope for angular diameter. A recent discussion of lunar limb irregularities has been given by Evans (1970).…”

“…With a typical limb velocity of y~ 1 km sec -1 = 1 m msec -1 , the factor (XD) l ' 2 jv is about 14 msec. Observations by Nather and Evans (1970) involve integration times of about 1-2 msec, so this does not appear to contribute significantly to the degradation of fringe visibility although clearly it sets a limit to the brightness of stars which can be observed. (hi) Finite observing time.…”