SCULIB_GENSYCONFN

Generate a convolution function which will set to zero the spatial frequencies with no signal in Dual Beam maps

Description:

This routine will return the symmetric convolution function required for setting to zero the spatial frequencies that have zero sensitivity in the raw chop-scan data. This function is not described in Emerson et al., 1979. A&A 96, 92, which (I think) describes an early version of the NOD2 algorithm before all the wrinkles had been properly understood.

This convolution function has to set to zero those points in the FT of the raw data at zero frequency and harmonics of 1/chop spacing. In the Fourier domain this means multiplying by a function which is 1 at all points apart from those specified, where it is zero. This is the sum of 2 functions, the first being 1 everywhere, the second being -1 at the points to be zeroed. The convolution function required is the sum of the inverse FTs of these two functions. The inverse FT of the first function is simply a delta function at the origin, that of the second is a series of negative spikes with the first at the origin and the others separated by the chop spacing.

The convolution function must cover the map even when the centre of the function is at the left or right hand end of the map. Hence the convolution function must be twice the length of the raw map.

Since the raw data is not sampled such that the chop spacing is an integer number of samples, the actual convolution function must be rebinned onto the sample mesh by sinc interpolation.

Otherwise the only tricky part of the algorithm is the need to normalise the two component functions such that in the Fourier domain the addition of the 2 functions does result in zeroes at the desired points. This is most easily achieved by concentrating on the zero spatial frequency which is just the sum of all the points in each of the 2 functions. The first function is a delta function set to 1, so the sum of that function is 1. The sum of the second function is that of all the points in the convolution function from its centre to one end, a length that corresponds to the map size. This is the length to be used because, in the Fourier domain, the width of the sample to be set to zero is 1/map_size.

Invocation

CALL SCULIB_GENSYCONFN( BSEP, PIXSEP, NPIX, NCFN, CONF, STATUS )

Arguments

BSEP = REAL (Given)
The beam separation in arcseconds
PIXSEP = REAL (Given)
The pixel separation in arcseconds
NPIX = INTEGER (Given)
The number of pixels in the x direction
UNBAL = REAL (Given)
The relative amplitudes of the right and left hand beams UNBAL=amp(lhb)/abs(amp(rhb))
NCFN = INTEGER (Returned)
The length of the convolution array
CONF( ) = REAL (Returned)
The convolution function
STATUS = INTEGER (Given and returned)
Global status

Copyright

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