National Aeronautics and Space Administration

THE LEIT OFF-AXIS POINT SPREAD FUNCTION AND THE LONG TERM DETECTION EFFICIENCY

1. The Off-axis Point Spread Function.

A cumulative point spread function, PSF(i), gives the fraction of source counts in a square box of side i (in units of 4 arcsec pixels) centered on the barycenter of the photon distribution. PSF(i) will approach unity for larger and larger values of i. In Figure 2a-2f, the measured values of PSF (i) for i ranging from 10 to 114, are shown for a range of distances, d, from the detector center (for the case of LE1 the image center is located at X=136,Y=61). The PSF does not change significantly within 180 pixels of the center (see previous article). At larger distances the following function was found to provide a good description of the data:

where d is in units of 4 arcsec pixels and A(i),B(i),C(i) and D(i) are parameters that depend on the chosen box size. The best fitting model to each case is shown as a solid line in Figures 2a-2f. The best fitting values for 14 different box sizes are given in Table 1. The expected value of the PSF(i) at any given off-axis angle greater than 180 pixels can be calculated using eq (1) and the best fitting parameters listed in Table 1, by interpolating between the given values of i. An example of a PSF constructed with this procedure for the case of an off-axis distance of 27 arcminutes (400 pixels) using 10 values of i and interpolating with a weighted parabola method is shown in Figure 3 as a dashed line. For comparison the measured PSF from a bright pointlike source detected at the same off-axis angle is shown as a solid line. The two curves are almost indistinguishable. The PSFs obtained with this method, and using at feast 10 different values of i, accurately reproduce all the PSFs derived from the sources utilized in our analysis.

II.The LE efficiency as a function of time.

plotted as a function of observation date for the five most frequently used filters. is the Crab Nebula count rate corrected for telemetry dead time, sampling dead time and telescope efficiency, during observation i, and n is the total number of observations in a given filter. As is apparent from Figure 4 the deviations from the mean are consistent with a constant source, with no obvious trend. Variations in the CMA efficiency with an accuracy of a few percent would have been detected. Only in September 1983, when the count rates in every filter were 2 or 3mean value, is there any indication for a deviation from the mean. However, the source was not always at the same position in the FOV such that unknown systematic errors in the variation of the efficiency across the detector FOV may be responsible for this effect. Also the background subtraction uncertainties are of the order of 2

We conclude the following:

(i) the LE sensitivity did not change more than ~1% during the mission.

(ii) There are systematic errors, of the order of 2-3%, which must be taken into account when estimating source count rates. These are caused by uncertainties in the relative quantum efficiency across the detector FOV and by the process of rescaling the (nonuniform) background to the position of the source. This is only valid in the central ~15 arcmin radius part of the detector. The analysis of a raster scan of the Crab Nebula indicates that at large off-axis angles the systematic errors increase to 8-10%.

P. Giommi
L. Angelini

Figure 1

Figure 2 a) - f)

Figure 3

Figure 4