Level 2 Help for SPARSE

1. input image to be blurred or deconvolved.
2. reference image. This is usually a deconvolved image made from a
   filled aperture (optional).
3. the pupil function which can be complex (optional).

1. output image in same format as input image
2. the real part of the complex pupil (optional). 
3. the optical transfer function (optional).
4. the point spread function (optional).

To create round sub apertures in the empty pupil.
Sets of four numbers representing:
1. line coordinate of circle center,
2. sample coordinate of circle center,
3. radius of the circle in pixels.
4. piston phase error in wavelengths ( w ).
Circles are set to a complex amplitude of 1.
If the radius is positive the dn will be set to exp(0,w*twopi).
If the radius is negative the sign and phase are ignored and the circle 
dn is set to (0,0).
 So, circle=(100,100,50,0,100,100,-40,0) creates an annulus 10
pixels thick centered on 100 100.
Circles can be written onto the second input file if it exists.
See METHOD for centering things.

Note: circle data can also be entered as x,y,radius,phase.
 See the SCALE keyword.

A ring of equally spaced sub apertures can be created at the maximum permitted
diameter each of the same radius.
The first argument is the number of sub apertures.
The second argument is the sub aperture radius in pixels.
Example: ring=(13,4.0)

Creates spokes
1. number of spokes.
2. number of mirrors/spoke.
3. center hole radius.
4. radius of inner circle.
5. radius increase factor.
6. (optional) number of circles in an outer ring.

The Wiener signal to noise of the image.
This causes SPARSE to treat the input image as a blurred image and to
apply the Wiener restoration filter:
otf/(|otf|**2 +1/(sn)**2)
If SN is not specified the program applies the otf directly to the input image
and no deconvolution is performed.
See OPTIMIZE keyword.

You have the option to permit SPARSE to determine the SN value for you and
to then use it to deconvolve the input image. In this mode you MUST provide
a second input file which acts as a reference image. This file should be
a restored image obtained by a filled aperture. Optimize finds that SN
value which minimizes the difference between the restoration and this
reference image.

Specifies that the system behaves coherently.
The default is INCOHERE (incoherent behavior).

Amount of defocus expressed as the maximum deviation of a spherical wave
centered at the pupil location nl/2+1, ns/2+1, in wavelengths.
We assume the wave coincides with the pupil on a circle of radius nl/4, ns/4
from the center.
Example: defocus=0.5 gives a 0.5 wavelength of defocus from the ideal focus.

Find specifies the signal to noise value of a filled aperture.
(you get this by running sparse once for a filled aperture and entering the
printed s/n ratio as FIND value)
SPARSE will compute the exposure relative to a filled aperture
required to produce a convolved image
with this signal to noise assuming that photon statitics are the sole cause of
noise in the output image.
There is no effect upon the image.

Smear the otf by rotating it 180 degrees.
This simulates a rotating sparse aperture or linear array of apertures.
The initial pupil orientation doesen't matter.
The default is to not rotate.
Only implemented in the incoherent case.

Add shot noise such that the signal to noise in the output image is the 
specified value.
Example: noise=2.0
The default is to create a noiseless output image.

Add shot noise to the output image assuming that the mean dn of the input image
is at the full well ccd charge and that the full well ccd charge is
FULLWELL electrons.

Example: fullwell=10000, causes shot noise to be added in the following manner:
md=mean input picture dn value.
gain=(10000)/md
newdn=olddn+[sqrt(gain*olddn)*r]/gain
where r is a random number centered on 0 with a mean deviation of 1.

The default is to create a noiseless output image.

The number of input photons/pixel (not the number detected).
The fullwell in electrons = number of photons * QE 
then the fullwell is used to compute the gain as above.

The default is to create a noiseless output image.

Quantum efficiency of the detector. See PHOTONS keqword.
Defaults to 1.0

Reference wavelength.
REFLAMDA, in conjunction with LAMDA permit the user to scale the pupil and to
scale the phase in order to easily simulate bandwidth effects.
The default is for LAMDA=REFLAMDA=0.55 microns.
If they are unequal then the ratio R=LAMDA/REFLAMDA is used to scale the pupil
and the phase in the pupil as follows:
Parameter specified sub pupil locations (relative to the image center) 
 are multiplied by 1/R.
Parameter specified sub pupil sizes are multiplied by 1/R.
Parameter specified sub pupil phases are multiplied by 1/R.

Warning: To keep the pupil from being expanded and running the risk of exceeding
the nl/2 and ns/2 limits I suggest that REFLAMDA <= LAMDA.

Actual wavelength.
See description for REFLAMDA parameter.

The pupil scaling factor.
Defaults to zero.
If the "CIRCLE" parameter values are input as x,y,r,phase instead of as
line,sample,r,phase then the x,y,r values are scaled up to fill the largest
permitted aperture and are then converted to line,sample coordinates. The
computed scaling value is printed out. This is the default for scale=0.
If scale is not zero then the auto scaling to fill the aperture is not
performed but the SCALE value is used instead to scale the circles to some
other value. This is useful to scale many sets of apertures the same.
X,y values are detected from line,samp values by their negative values.