== Gaussian 1-D Convolution ==

In an attempt to remove some of the unexpected behavior in stacking and differencing, a new mode was added to the pmSubtraction code.  This mode defines a new kernel type PM_SUBTRACTION_KERNEL_SIMPLE which breaks out from the current Alard-Lupton PSF matching code into work-alike replacement.  

Mathematically, instead of attempting to do the PSF matching with a sum of the product of Gaussians and polynomials, this SIMPLE kernel examines only the measured FWHM values for the two PSFs.  From these values, a Gaussian kernel is constructed with sigma_kern^2^ = (FWHM_large^2^ - FWHM_small^2^)/(2 sqrt(2 log 2))^2^.  The smaller PSF image is then convolved by this kernel and the results returned.

Below are a series of comparison images from tests with real GPC1 data.  The left panel shows the standard pmSubtraction kernels, and the right shows the new SIMPLE kernel.

Convolved stack:
[[Image(1dg_convolved_stack.jpg,800px)]]

Unconvolved stack:

[[Image(1dg_unconvolved_stack.jpg,800px)]]

Warp-warp diff:

[[Image(1dg_diff.jpg,800px)]]

Real object zoom in diff:

[[Image(1dg_diff_object.jpg,800px)]]


After processing the SAS stacks and static sky with the 1-D Gaussian convolution, we can compare the timing for these stages between the two PSF matching codes using the dtime values listed in the database.  For all subsequent plots, the x-axis shows the default time with the pmSubtraction kernels (SAS.20130620), and the y-axis shows the ratio of simple/default (SAS.20130703/SAS.20130620).

[[Image(stack_conv.png)]]

[[Image(stack_stack.png)]]

[[Image(stack_script.png)]]

[[Image(static_sky.png)]]