IMENGINE Models Reference
The following models are implemented via direct calculation of the discrete Fourier transform and based on radial functions that are transformed to introduce ellipticity. The example images below are 128x128 pixels (the image size sets the scale for some of the model parameters). Note that parameters are specified in unstretched coordinates. Ellipticity is specified as %{e1,e2} for a single shear, or %{e1,e2;g1,g2} for the combined effects of two shear transforms. When going from the circular source (defined by its radial profile function) to the observed image, {e1,e2} is applied first, and then {g1,g2}. An alternative polar parameterization of the shear is available using %<lambda,phi> or %<lambda,phi;egcos,egsin> (see PolarEllipticityTransform.h for details).
Description 
Parameters 
Example 
%{0,0} 
%{0.1,0.2} 
Disk (step function) 
radius > 0 (pixels) 
disk[32] 


Gaussian 
sigma > 0 (pixels) 
gauss[24] 


Moffat 
fwhm > 0 (pixels), beta > 1 
moffat[32,3] 


Exponential 
re > 0 (pixels) 
exp[33] 


Truncated Sersic 
re > 0 (pixels), index > 0, e1, e2, rmax > 0 (pixels) 
sdemo[33,1,e1,e2,48] 


Full Sersic 
re > 0 (pixels), index > 0, e1, e2 
sdemo[350,4,e1,e2] 


Airy 
fwhm > 0 (pixels), e1, e2 
ademo[40,e1,e2] 


Note that the initial Airy and Sersic implementations require that the ellipticity parameters are passed to them directly, rather than via the general %{e1,e2} mechanism. Also, the Sersic profile with index=1 is equal to the exponential profile, and large values of the index generate a long tail that can extend beyond the generated image and cause aliasing artifacts.
Any two models M1, M2 can be added together with proportions specified by the fraction 0 <= f1 <= 1 of M1:
M12 = f1*M1 + (1f1)*M2
An optional offset (dx,dy) can be applied to M2. The general parser syntax for M12 is:
sum[M1,M2;f1] sum[M1,M2;f1,dx,dy]
where the second form includes an offset of M2. Examples are given below:
M1 
M2 
f1 
dx,dy 
M12 
Image 
disk[32]%{+0.3,0} 
disk[32]%{0.3,0} 
0.7 
(0,0) 
sum[disk[32]%{+0.3,0},disk[32]%{0.3,0};0.75] 

disk[32]%{+0.3,0} 
disk[32]%{0.3,0} 
0.7 
(8,16) 
sum[disk[32]%{+0.3,0},disk[32]%{0.3,0};0.75,8,16] 
