fgauss -- Convolve a FITS image with an elliptical Gaussian function
fgauss infile outfile sigma
FGAUSS convolves the FITS image in \fIinfile\fR with the Gaussian kernel specified by \fIsigma\fR, \fIratio\fR, \fItheta\fR and \fInsigma\fR and places the convolved images in \fIoutfile\fR FITS file. Out of bounds pixels are computed using the algorithm specified by \fIboundary\fR. The FITS image to be smoothed can be in either the primary array or in an image extension. The resulting smoothed image will be placed in either the output files primary array or in an image extension depending on three things; the location of the image in the input file, the value of the copyprime flag and the value of the copyall flag.
If the input image is in the primary array then the resulting image will always be placed in the primary array. In this case, if the copyprime flag is \fIyes\fR then all the keywords from the input primary header will be copied to the output primary header, otherwise only the required keywords will be placed in the output primary header. Setting the copyall flag will cause all the FITS extensions in the input FITS file to be copied over to the output FITS file.
If the input image is in an image extension the the resulting image will be placed in one of three places depending on the values of the copyprime and copyall flags. If the copyprime flag is \fIno\fR the the resulting smoothed image will always appear in the primary array. If the copyall flag is also set then all extension will be copied to the output FITS file and the input primary array will be stored in the image extension that the image was originally stored in the input FITS file. If the copyprime flag is \fIyes\fR then the primary array of the input FITS file will always be copied over to the primary array of the output FITS file. In this case, if the copyall flag is \fIno\fR then the smoothed image will be stored in the first extension of the output FITS file, otherwise the smoothed image will appear in the same extension in both the input and output FITS file and all other extensions will be copied to the output FITS file.
The Gaussian kernel has an elliptical cross-section and Gaussian profile and is defined mathematically as follows.
1. Circularly Symmetric Gaussian Function ratio = 1 theta = 0.0 N = normalization factor G = N * exp (-0.5 * (r / sigma) ** 2) 2. Elliptical Gaussian Function (Theta = 0, 90 or 180) sigmax = sigma sigmay = ratio * sigmax N = normalization factor A = cos (theta) ** 2 / sigmax ** 2 - sin (theta) ** 2 / sigmay ** 2 B = 0.0 C = sin (theta) ** 2 / sigmax ** 2 + cos (theta) ** 2 / sigmay ** 2 z = A * x ** 2 + B * x * y + C * y ** 2 G = N * exp (-0.5 * z) 3. Elliptical Gaussian Function (Arbitrary Theta) sigmax = sigma sigmay = ratio * sigmax N=normalization factor A = cos (theta) ** 2 / sigmax ** 2 - sin (theta) ** 2 / sigmay ** 2 B = -2 * (1 / sigmax ** 2 - 1 / sigmay ** 2) * sin (theta) * cos (theta) C = sin (theta) ** 2 / sigmax ** 2 + cos (theta) ** 2 / sigmay ** 2 z = A * x ** 2 + B * x * y + C * y ** 2 G = N * exp (-0.5 * z)
1. Convolve an image with a circular Gaussian function of sigma 2.0, and size 4.0 sigma using nearest neighbor boundary extension.
cl> fgauss image.fits gimage.fits 2.0
2. Convolve an image with an elliptical Gaussian function whose sigma in the major and minor axis direction is 2.0 and 1.5 respectively, and whose position angle is 45 degrees, using wrap around boundary extension.
cl> fgauss img.fits gimg.fits 2.0 ratio=0.75 theta=45.0 bound=wrap
3. Convolve an image in the 3rd extension with a circular Gaussian function of sigma 2.0, and size 4.0 sigma using nearest neighbor boundary extension and store the resulting image in the primary array.
cl> fgauss imgx.fits[3] gimg.fits 2.0 copyprime=no
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