tb_angular_spectrum_propagate — 2D `typed` op

• Data kinds: cimage → cimage

• Call: fullseye.apply(img, "tb_angular_spectrum_propagate", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

Usage

Exact scalar free-space propagation of a complex field (angular spectrum).

`U(z) = IFFT{ FFT{U(0)} * exp(i*2*pi*z*sqrt(1/lambda^2 - fx^2 - fy^2)) }`

in the `exp(-i*omega*t)` convention, so a positive *distance_um*

propagates forward. Components beyond the propagating cone

(`fx^2 + fy^2 > 1/lambda^2`) are attenuated by

`exp(-2*pi*|z|*sqrt(fx^2 + fy^2 - 1/lambda^2))`, which is the physical

evanescent decay — not zeroed, so `distance_um = 0` is an *exact*

identity and the transfer function is continuous through it.

Unlike Fresnel propagation this makes no paraxial approximation: it is the

exact solution of the Helmholtz equation for a band-limited field, valid

from a fraction of a wavelength outward.

Returns a complex128 array with the same shape as *field*.

Ground truth it reproduces (measured): `distance_um = 0` returns the field

bit-identically (it short-circuits the transform pair); propagating `+z`

then `-z` returns the original to a relative L2 error of 4.3e-16 to

5.3e-16 for a band-limited field (measured on three: 64x64 random at

+/-50 um, a 64x64 Gaussian at +/-250 um, a 128x128 random at +/-500 um);

total power is conserved to between 0 and 3.5e-16 relative on the same

three. A field *with*

evanescent content does not round-trip — those components are gone by

construction, in both directions, because that is what physically happens.

*field* is a field in the space domain, not a spectrum: do not hand it

the fftshifted output of :func:complexops.cx_fft. Real input is promoted

to complex, which loses nothing.

Aliasing: the discrete transfer function is periodic, so a field that

diffracts past the array edge wraps around. The practical guard is the

usual one — pad the field so the propagated support stays inside, and keep

`pixel_pitch_um below lambda/(2*NA)`. No warning can detect this

reliably from the array alone, so none is invented.

Raises `ValueError`: *field* is not 2-D, smaller than 2x2, larger than

:data:MAX_FIELD_ELEMENTS, masked, or non-finite; non-positive or

non-finite *wavelength_um* / *pixel_pitch_um*; non-finite *distance_um*.

Typed bridge of the optics op `angular_spectrum_propagate into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives wavelength_um (default 0.55) and b drives distance_um` (default 100).

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept `cimage` as input)

identity · tb_cx_ifft · tb_cx_magnitude · tb_cx_phase · tb_cx_real · tb_cx_imag · tb_cx_log_magnitude · tb_cx_apply_transfer_function

Same category (`typed`)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

tb_angular_spectrum_propagate — 2D typed op