It would be nice to compare opd_expand() to a fitting function

[douglase]

I have code for fitting zernike's with scipy optimizers to noisy data. I will put something together to compare that to the simpler decomposing function that already exists in POPPY (

poppy/poppy/zernike.py

Lines 455 to 512 in b6eed44

	def opd_expand(opd, aperture=None, nterms=15, basis=zernike_basis,
	**kwargs):
	"""Given a wavefront OPD map, return the list of coefficients in a
	given basis set (by default, Zernikes) that best fit the OPD map.
	Parameters
	----------
	opd : 2D numpy.ndarray
	The wavefront OPD map to expand in terms of the requested basis.
	Must be square.
	aperture : 2D numpy.ndarray, optional
	ndarray giving the aperture mask to use
	(1.0 where light passes, 0.0 where it is blocked).
	If not explicitly specified, all finite points in the `opd`
	array (i.e. not NaNs) are assumed to define the pupil aperture.
	nterms : int
	Number of terms to use. (Default: 15)
	basis : callable, optional
	Callable (e.g. a function) that generates a sequence
	of basis arrays given arguments `nterms`, `npix`, and `outside`.
	Default is `poppy.zernike.zernike_basis`.
	Additional keyword arguments to this function are passed
	through to the `basis` callable.
	Note: Recovering coefficients used to generate synthetic/test data
	depends greatly on the sampling (as one might expect). Generating
	test data using zernike_basis with npix=256 and passing the result
	through opd_expand reproduces the input coefficients within <0.1%.
	Returns
	-------
	coeffs : list
	List of coefficients (of length `nterms`) from which the
	input OPD map can be constructed in the given basis.
	(No additional unit conversions are performed. If the input
	wavefront is in waves, coeffs will be in waves.)
	"""
	if aperture is None:
	_log.warn("No aperture supplied - "
	"using the finite (non-NaN) part of the OPD map as a guess.")
	aperture = np.isfinite(opd).astype(np.float)
	basis_set = basis(
	nterms=nterms,
	npix=opd.shape[0],
	outside=np.nan,
	**kwargs
	)
	wgood = np.where((aperture != 0.0) & np.isfinite(basis_set[1]))
	ngood = (wgood[0]).size
	coeffs = [(opd * b)[wgood].sum() / ngood
	for b in basis_set]
	return coeffs

)