 # Source shape model¶

## TODO¶

In addition to the gaussian model, we would like De Vaucouleur and exponential distribution.
The functional form of the analytic profiles the user profiles, and image template are given below.

expdisk: I = exp (-1.6783 * R/radius)
devauc: I = exp (-7.67 * (R/radius)**1/4)

where R, dX, and dY are defined below, radius is the scale parameter.

The radial profiles are mapped into two dimensional objects by an elliptical transformation.
If the output image coordinates are given by (x,y), and the specified object center coordinates are
given by (xc,yc) then the transformation is defined as shown below.

dx = x - xc
dy = y - yc
dX = dx * cos(pa) + dy * sin(pa)
dY = (-dx * sin(pa) + dy * cos(pa)) / ar
R = sqrt (dX * 2 + dY * 2)

where dx and dy are the object coordinates relative to the object center, dX and dY are the object coordinates in the transformed circular coordinates, and R is the circularly symmetric radius.
The transformation parameters are the axial ratio ar defined as the ratio of the minor axis to the major axis, and the position angle pa defined counterclockwise from the x axis.

Implementation in the code... A lot of stuff...

• Inputs
additional input to define the source shape to be used
1 gauss
2 expdisk
3 devauc
=> TIPS modifications: the class SkySources in tipssky.py, the class Simulation in tipsaxesim.py
=> aXeSIM c code modifications: task sex2gol and gol2af
• add function to compute the profile in axesim/src/model_utils.c
• add function to convolve with PSF in axesim/src/model_utils.c
3 cases:
1 gauss PSF
2 2 gauss PSF
3 image PSF
• create a generic function to replace fill_gaussvalues() in disp_utils.c
• remove PSF computation in python code

Other solutions : use image of source profile and just convolve it with the PSF