NICMOS Spectroscopy

The NICMOS spectroscopy calculations include a simulation of the degradation in spectral purity due to the point spread function. This calculation is affected by the size of the rectangular extraction region over which the SNR is calculated and in fact, the line widening calculations are performed as part of the extraction region fraction calculations.

The first step in this calculation is to compute the radial profile at each observation wavelength. The radial profile is then used to calculate the convolution factors.

The radial profile is computed beginning with the rectangular extraction region values at the given wavelength. A 1x1 box is just the center pixel. A 3x1 box is the faction in the center pixel plus the two pixels immediately above and below the center, thus f(0,1) = f(0,-1) = [ f(3x1) - f(1x1) ] / 2 and by symetry, f(0,1) = f(0,-1) = f(1,0) = f(-1,0).

Because of symetry, the values in the four corner regions are all equal. We will describe the calculation of one. In general f(n,m) = [ f(n-1, m) * f(n, m - 1) ] / f(0,0)

For example, the rectangular extraction region fractions at 0.8 microns are:

Using these values in our formula to calculate one quadrant (relying on quadrilateral symetry) of the radial profile and then summing over two quadrants to calculate the convolution profile, we get: