generateAlardLuptonBasisList

lsst.ip.diffim.generateAlardLuptonBasisList(config, targetFwhmPix=None, referenceFwhmPix=None, basisDegGauss=None, metadata=None)

Generate an Alard-Lupton kernel basis list based upon the Config and the input FWHM of the science and template images.

Parameters:

config : lsst.ip.diffim.PsfMatchConfigAL

Configuration object for the Alard-Lupton algorithm.

targetFwhmPix : float, optional

Fwhm width (pixel) of the template exposure characteristic psf. This is the _target_ that will be matched to the science exposure.

referenceFwhmPix : float, optional

Fwhm width (pixel) of the science exposure characteristic psf.

basisDegGauss : list of int, optional

Polynomial degree of each Gaussian (sigma) basis. If None, defaults to config.alardDegGauss.

metadata : lsst.daf.base.PropertySet, optional

If specified, object to collect metadata fields about the kernel basis list.

Returns:

basisList : list of lsst.afw.math.kernel.FixedKernel

List of basis kernels. For each degree value n in config.basisDegGauss (n+2)(n+1)/2 kernels are generated and appended to the list in the order of the polynomial parameter number. See lsst.afw.math.polynomialFunction2D documentation for more details.

Raises:

RuntimeError

• if config.kernelBasisSet is not equal to “alard-lupton”

ValueError

• if config.kernelSize is even
• if the number of Gaussians and the number of given sigma values are not equal or
• if the number of Gaussians and the number of given polynomial degree values are not equal

Notes

The polynomial functions (f) are always evaluated in the -1.0, +1.0 range in both x, y directions, edge to edge, with f(0,0) evaluated at the kernel center pixel, f(-1.0,-1.0) at the kernel (0,0) pixel. They are not scaled by the sigmas of the Gaussians.

Base Gaussian widths (sigmas in pixels) of the kernels are determined as:

• If not all fwhm parameters are provided or config.scaleByFwhm==False then config.alardNGauss and config.alardSigGauss are used.
• If targetFwhmPix<referenceFwhmPix (normal convolution): First sigma Sig_K is determined to satisfy: Sig_reference**2 = Sig_target**2 + Sig_K**2. If it’s larger than config.alardMinSig * config.alardGaussBeta, make it the second kernel. Else make it the smallest kernel, unless only 1 kernel is asked for.
• If referenceFwhmPix < targetFwhmPix (deconvolution): Define the progression of Gaussians using a method to derive a deconvolution sum-of-Gaussians from it’s convolution counterpart. [1] Only use 3 since the algorithm assumes 3 components.

References

[1]	(1, 2) Ulmer, W.: Inverse problem of linear combinations of Gaussian convolution kernels (deconvolution) and some applications to proton/photon dosimetry and image processing. http://iopscience.iop.org/0266-5611/26/8/085002 Equation 40