solprop.hankel#

Transform an axisymmetric field with the raw order-zero QDHT.

The forward transform is H(k) = integral r*f(r)*J0(k*r) dr; its inverse integrates k*H(k)*J0(k*r). Angular frequencies are in rad/m and no 2*pi is hidden in either transform. The integration weights include the azimuthal integral. See docs/guide/free-space/hankel.md for the scalings and finite-transform error.

Classes

QDHT(radius, n_r)

Construct the raw order-zero quasi-discrete Hankel transform.

class solprop.hankel.QDHT(radius, n_r)[source]#

Bases: object

Construct the raw order-zero quasi-discrete Hankel transform.

The matrix is symmetric and approximately self-inverse. Its finite truncation error is distinct from roundoff; it is never replaced by an orthogonal matrix.

Attributes:

radiusfloat: Outer Dirichlet boundary in m, finite and positive.
n_rint: Number of interior radial samples, at least 2.
rnumpy.ndarray: Interior radial samples in m, shape (n_r,); zero is not a sample.
k_rnumpy.ndarray: Transverse angular frequencies in rad/m, shape (n_r,).
zerosnumpy.ndarray: First n_r + 1 positive zeros of J0, dimensionless.
j1numpy.ndarray: Absolute J1 values at the first n_r zeros, dimensionless.
matrixnumpy.ndarray: Symmetric, dimensionless QDHT matrix, shape (n_r, n_r).
radial_weightsnumpy.ndarray: Weights of the area integral 2*pi*r*dr, in m^2, shape (n_r,).
spectral_weightsnumpy.ndarray: Weights of 2*pi*k_r*dk_r, in m^-2, shape (n_r,).
forward_scalefloat: Common forward scaling radius**2 / zeros[-1], in m^2.
inverse_scalefloat: Common inverse scaling zeros[-1] / radius**2, in m^-2.

Raises:

GridError: If the size, radius or resulting floating-point scales are invalid.

References

M. Guizar-Sicairos and J. C. Gutiérrez-Vega, JOSA A 21, 53-58 (2004), doi:10.1364/JOSAA.21.000053.

Examples

>>> from solprop.hankel import QDHT
>>> transform = QDHT(1e-3, 32)
>>> transform.r.shape, transform.matrix.shape
((32,), (32, 32))

forward(values)[source]#

Transform radial samples to a Hankel spectrum along the last axis.

Parameters:

valuesarray_like: Finite real or complex field samples, shape (..., n_r), in V/m.

Returns:

numpy.ndarray: Spectrum of the same shape, in V m; float64 or complex128.

Raises:

GridError: If the last axis has the wrong length or the values are nonfinite.

forward_scale: float#

inverse(values)[source]#

Reconstruct radial samples from a Hankel spectrum along the last axis.

Parameters:

valuesarray_like: Finite real or complex spectra, shape (..., n_r), in V m.

Returns:

numpy.ndarray: Field of the same shape, in V/m; float64 or complex128.

Raises:

GridError: If the last axis has the wrong length or the values are nonfinite.

inverse_scale: float#

j1: Float[ndarray, 'n_r']#

k_r: Float[ndarray, 'n_r']#

matrix: Float[ndarray, 'n_r n_r']#

n_r: int#

r: Float[ndarray, 'n_r']#

radial_weights: Float[ndarray, 'n_r']#

radius: float#

spectral_weights: Float[ndarray, 'n_r']#

zeros: Float[ndarray, 'n_zeros']#