This application performs forward or reverse Fast Fourier
Transforms (FFTs) of one- or two-dimensional
NDFs . The output in the forward
transformation (from the space domain to the Fourier) can be produced in Hermitian form
in a single NDF, or as two NDFs giving the real and imaginary parts of the complex
transform, or as two NDFs giving the power and phase of the complex transform. Any
combination of these may also be produced. The inverse procedure accepts any of these
NDFs and produces a purely real output NDF.
Any bad pixels in the input NDF may be replaced by a constant value. Input NDFs need
neither be square, nor be a power of 2 in size in either dimension; their shape is
arbitrary.
The Hermitian transform is a single image in which each quadrant consisting of a
linear combination of the real and imaginary parts of the transform. This form
is useful if you just want to multiply the Fourier transform by some known
purely real mask and then invert it to get a filtered image. However, if you
want to multiply the Fourier transform by a complex mask (e.g. the Fourier
transform of another NDF), or do any other operation involving combining complex
values, then the Hermitian NDF must be untangled into separate real and imaginary
parts.
There is an option to swap the quadrants of the input NDF around before performing a
forward FFT. This is useful if you want to perform convolutions with the FFTs, since
the point-spread function (PSF) image can be created with the PSF centre at the array
centre, rather than at pixel (1, 1) as is usually required.
FILLVAL = LITERAL (Read)
A value to replace bad pixels before
performing the transform. The input image is also padded with this value if
necessary to form an image of acceptable size. A value of "Mean"
will cause the
mean value in the array to be used. [0.0]
HERMIN = NDF (Read)
Hermitian
frequency-domain input NDF containing the complex transform. If null is entered
no Hermitian NDF is read and then the application should be supplied either
separate real and imaginary NDFs, or the power and phase NDFs. Prompting will not
occur if one of the other (inverse) input NDFs has been given on the command
line, but not HERMIN as well. This parameter is only relevant for an inverse
transformation.
HERMOUT = NDF (Write)
Hermitian output NDF from a forward
transform. If a null value is given then this NDF is not produced.
HM_TITLE
= LITERAL (Read)
Title for the Hermitian Fourier-transform output NDF. A
null (!
) value means using the title of the input NDF. ["KAPPA - Fourier -
Hermitian"]
IM_TITLE = LITERAL (Read)
Title for the frequency-domain imaginary
output NDF. A null (!
) value means using the title of the input NDF. ["KAPPA
- Fourier - Imaginary"]
IMAGIN = NDF (Read)
Input frequency-domain NDF
containing the imaginary part of the complex transform. If a null is given then an
image of zeros is assumed unless a null is also given for REALIN, in which
case the input is requested in power and phase form. This parameter is only
available if HERMIN is not used. One way to achieve that is to supply IMAGIN,
but not HERMIN, on the command line. This parameter is only relevant for an
inverse transformation.
IMAGOUT = NDF (Write)
Frequency-domain output
NDF containing the imaginary part of the complex Fourier transform. If a null
value is given then this NDF is not produced. [!]
IN = NDF (Read)
Real
(space-domain) input NDF for a forward transformation. There are no restrictions on
the size or shape of the input NDF, although the it may have to be padded or
trimmed before being transformed. This parameter is only used if a forward
transformation was requested.
INVERSE = _LOGICAL (Read)
If TRUE
, then the
inverse transform–-frequency domain to space domain–-is required, otherwise a
transform from the space to the frequency domain is undertaken. [FALSE]
OUT =
NDF (Write)
Real space-domain output NDF. This parameter is only used if
an inverse transformation is requested.
PH_TITLE = LITERAL (Read)
Title
for the frequency-domain phase output NDF. A null (!
) value means using the
title of the input NDF. ["KAPPA - Fourier - Phase"]
PHASEIN = NDF (Read)
Input frequency-domain NDF containing the phase of the complex transform.
If a null is given then an image of zeros is assumed unless a null is also
given for PHASEIN, in which case the application quits. This parameter is only
available if HERMIN, REALIN and IMAGIN are all not used. One way to achieve
that is to supply PHASEIN, but none of the aforementioned parameters, on the
command line. This parameter is only relevant for an inverse transformation.
PHASEOUT = NDF (Write)
Frequency-domain output NDF containing the phase of
the complex Fourier transform. If a null value is given then this NDF is not
produced. [!]
POWERIN = NDF (Read)
Input frequency-domain NDF containing
the modulus of the complex transform. Note, this should be the square root
of the power rather than the power itself. If a null is given then an image
of zeros is assumed unless a null is also given for PHASEIN, in which case
the application quits. This parameter is only available if HERMIN, REALIN and
IMAGIN are all not used. One way to achieve that is to supply POWERIN, but
none of the aforementioned parameters, on the command line. This parameter
is only relevant for an inverse transformation.
POWEROUT = NDF (Write)
Frequency-domain output NDF containing the modulus of the complex Fourier transform.
Note, this is the square root of the power rather than the power itself. If a
null value is given then this NDF is not produced. [!]
PW_TITLE = LITERAL
(Read)
Title for the frequency-domain power output NDF. A null (!
) value means
using the title of the input NDF. ["KAPPA - Fourier - Power"]
REALIN = NDF
(Read)
Input frequency-domain NDF containing the real part of the complex
transform. If a null is given then an image of zeros is assumed unless a null
is also given for IMAGIN, in which case the input is requested in power and
phase form. This parameter is only available if HERMIN is not used. One way to
achieve that is to supply REALIN, but not HERMIN, on the command line. This
parameter is only relevant for an inverse transformation.
REALOUT = NDF
(Write)
Frequency-domain output NDF containing the real part of the complex
Fourier transform. If a null value is given then this NDF is not produced. [!]
RL_TITLE = LITERAL (Read)
Title for the frequency-domain real output NDF. A
null (!
) value means using the title of the input NDF. ["KAPPA - Fourier -
Real"]
SHIFT = _LOGICAL (Read)
If TRUE
, the transform origin is to be
located at the array’s centre. This is implemented by swapping bottom-left and
top-right, and bottom-right and top-left array quadrants, before doing the
transform. This results in the transformation effectively being done about pixel x =
INT(NAXIS1/2)$+$1 and
y = INT(NAXIS2/2)$+$1,
where NAXISn are the padded or trimmed dimensions of the NDF. [FALSE]
TRIM =
_LOGICAL (Read)
If TRUE
, when the input array dimension cannot be processed by the
transform, the output arrays will be trimmed rather than padded with the fill value.
[FALSE]
TITLE = LITERAL (Read)
Title for the real space-domain output NDF. A null
(!
) value means using the title of the input NDF. ["KAPPA - Fourier"]