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
configlsst.ip.diffim.PsfMatchConfigAL

Configuration object for the Alard-Lupton algorithm.

targetFwhmPixfloat, optional

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

referenceFwhmPixfloat, optional

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

basisDegGausslist of int, optional

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

metadatalsst.daf.base.PropertySet, optional

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

Returns
basisListlist 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

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