simulate op• Data kinds: none → sweep (an op determined by its arguments alone — it takes no image or data input)
• Call: import interferometry; interferometry.csi_signal_simulate(surface_um=6.0, z_start_um=0.0, z_step_um=0.05, n_planes=241, wavelength_um=0.6, envelope_fwhm_um=2.8, envelope_sigma_um=None, bias=0.5, amplitude=0.4, reflectivity=1.0, noise=0.0, seed=0) (or opsinterferometry.get("csi_signal_simulate"))
Synthesise the z-scan interferogram of one pixel over a known surface height.
The coherence-scanning forward model, and the reason every other operator here
has an exact answer to be checked against::
I(z) = bias + amplitude*reflectivity * exp(-(z-z0)^2 / 2 sigma^2)
• cos(4*pi*(z-z0)/wavelength)
with `z0 = surface_um`. The 4 is the double pass — light goes down to the
surface and back, so one fringe is `wavelength/2` of *height*, not a whole
wavelength. Getting that factor wrong is a clean 2x in every height this
module produces, which is why it is written out here rather than hidden in a
constant.
surface_um: the true surface height `z0`, in the scan's own
coordinate. Need not land on a scan plane — the
sub-step case is the interesting one and the tests use
it deliberately.
z_start_um/z_step_um/n_planes: the scan grid,
`z_k = z_start_um + k*z_step_um`.
wavelength_um: mean wavelength of the source.
envelope_fwhm_um: the FWHM of the envelope along the scan axis. Give
this *or* `envelope_sigma_um`, never both. It is
half the source coherence length, because the
double pass makes OPD = 2z;
:func:csi_design returns both under separate names
for exactly that reason.
bias/amplitude: the intensity pedestal `a and fringe amplitude b`.
reflectivity: per-pixel scale on the fringe amplitude (>= 0). It
scales the envelope and therefore
:func:csi_contrast_map, and — this is the honest part
— it does not move the envelope peak, so it does not
bias :func:csi_peak_position. A *spatially varying*
reflectivity biases nothing either; what does bias the
centroid is where the peak sits in the window, and that
is documented on :func:csi_peak_position.
noise: additive Gaussian sigma (0 = the exact model).
seed: integer seed for that noise (no `None`).
Returns a 1-D float64 array of `n_planes` intensities.
Ground truth: with `noise=0` and the surface centred in the scan, the
`"gaussian" estimator of :func:csi_peak_position` returns *surface_um* to
1.43e-07 um over sub-step offsets, and to 2.9e-14 um when the envelope is
given analytically instead of through the Hilbert transform (both pinned in
the tests).
Raises `ValueError`: a non-real / non-finite / string / bool parameter,
a non-positive `z_step_um / wavelength_um` / envelope width, a negative
`bias / amplitude / reflectivity / noise, n_planes` outside
`[3, MAX_SCAN_POINTS], a z_step_um at or past the wavelength_um/4`
Nyquist ceiling, and a *surface_um* outside the scan range (which is the case
a real instrument reports as "no surface found", not as a height).
• coherence_scanning family guide
• 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.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• coherence_scanning — py -3.11 examples/coherence_scanning.py
sweep as input)csi_envelope · csi_peak_position · chromatic_confocal_height
simulate)csi_stack_simulate · chromatic_confocal_simulate
*Provenance: interferometry.py — INTERFEROMETRY operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.