Point Spread Functions

 The IRAS90 package contains NDFs holding estimates of the two dimensional point spread function of each active survey detector. These NDFs are called psfxx.sdf (or PSFxx.SDF on VMS) where ``xx'' is the detector number (1 to 62). These PSF images were created at IPAC by Merhdad Moshir, and are described in IPAC Interoffice Memorandum 240-87-80(2), dated 29 June 1987. Each NDF consists of a two dimensional DATA array, oriented so that the first array axis is parallel to the focal plane Z axis and the second array axis is parallel to the focal plane Y axis. The size and position of each pixel in the data array are specified in two ways; firstly, each NDF has two AXIS structures which hold the focal plane coordinates (Z,Y) at the centre of the corresponding pixels (in arc-minutes). Secondly, each NDF has an IRAS extension in which is stored a component called TRANS, consisting of a vector of six real values. These values specify a linear transformation from pixel indices within the PSF array, to focal plane coordinates:

where C1 - C6 are the six elements of the TRANS component; (I,J) are the pixel indices of a pixel in the PSF; DZ is the offset in the direction of the focal plane Z axis, from the detector centre to the centre of the PSF pixel (in radians); DY is similarly the offset in the direction of the focal plane Y axis. The focal plane coordinates of the detector centres are given in II.C.3 of the IRAS Catalogs and Atlases Explanatory Supplement. In fact, C3 and C5 are always zero, and so the area of a PSF pixel (in steradians) is thus given by C2*C6. In addition to the TRANS component, the IRAS extension also contains a component called PSFDET, which is a single integer value giving the detector number to which the PSF refers.

The pixel values are normalised so that they represent ``efficiency'' values, and have a quoted relative error of 0.1. If the PSF pixel with index i has a value of P_i and is illuminated with a mean surface brightness of S_i (in units of Jy/sr), then the incident flux is S_i*A (where A is the solid angle of the PSF pixel, i.e. C2*C6), but the PSF pixel measures a flux of P_i*S_i*A Janskys. Thus the total flux measured by a detector would be $\sum_{i}( P_{i}*S_{i}*A)$. The effective detector solid angles used by IRAS90 are derived from these PSFs, in fact they are just equal to $A*\sum_{i}(P_{i})$, so another way of representing the total flux measured by a detector is $B*\sum_{i}( P_{i}*S_{i} )/\sum_{i}( P_{i} )$, where B is the effective solid angle of the detector.