# What does the PSF look like?

### (3/2/94)

The functional form below is a good description of the mirror and HRI PSF, and is an energy-averaged response.

PSF = A1 * exp( -0.5 * (R/S1) ** 2 ) + A2 * exp( -0.5 * (R/S2) ** 2 ) + A3 * exp( -R/S3 ), with R = radial distance (arc sec), and A1 = 0.9638 S1 = 2.1858 A2 = 0.1798 S2 = 4.0419 A3 = 0.00090 S3 = 31.69The effect is to scatter about ten percent of the photons beyond the central core of about 10 arcsec. This region extends out to about 5 arcmin and is relatively independent of energy. The PSF was derived by combining data from HZ 43, AR Lac, and LMC X-1. The extra scattering (a ground calibration showed less than thirteen percent of the photons were outside 10") occurs, due to the introduction of a shield above the micro-channel plate to remove a serious background problem. The shield is held at the same voltage as the MCP, so a "field-free" region is created in the gap. However, ground tests have shown that a slight positive voltage on the shield would have been better, as a slightly off-axis photon can scatter off the inter-channel region, falling into a neighboring micro-channel. That electron then is amplified, resulting in a larger apparent PSF. Ninety percent of the photons are within 10 arcsec, while about five percent are scattered beyond 60".

The off-axis parameterization is accomodated by modification of S2 as follows:

S2=3.3 + 0.019*theta - 0.016(theta**2) + 0.0044(theta**3)

where theta is the off-axis angle in arcmin.

NB: this expression has not been forced to reproduce the on-axis value. The fact that the off-axis expression gives S2=3.3 for theta=0, compared to the on-axis equation which gives 4.0, reflects the variation in aspect quality from observation to observation.

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