photon_statistics — PHOTON counting op

Data kinds: image2dtable

Call: import photoncount; photoncount.photon_statistics(counts) (or opsphoton.get("photon_statistics"))

Usage

Poisson statistics of a photon-count frame: is it really shot-noise limited?

Returns a dict: `mean · variance (population, ddof=0`) ·

`fano_factor = variance / mean` (1 for a Poisson process) ·

`snr_poisson = sqrt(mean)` (the theoretical photon-limited SNR) ·

`snr_measured = mean / std` (what this frame actually achieved) ·

`total_counts · n_samples · zero_fraction` (the fraction of pixels

that saw no photon at all — the honest measure of "photon starved";

`exp(-lambda) for a flat field) · max_counts`.

The Fano factor is evidence of Poisson statistics only on a flat field.

On a structured scene the scene's own spatial variance dominates and the

ratio is large and meaningless — this op computes the number, it cannot tell

you which situation you are in. Measured on the test scenes: a flat

`lambda = 100` field (512x512, seed 0) gives 1.001089; the same detector

looking at a linear ramp from 20 to 180 photons gives 22.4102. Both are

"correct" and only one of them means anything.

Raises `ValueError`: negative, non-finite or non-2-D *counts*, fewer

than 2 pixels (no variance), an all-zero frame (`fano_factor` would be

`0/0` — say "no photons were detected" instead of returning NaN), and a

frame with exactly zero variance (`snr_measured would be inf`; for

`n >= 2` a constant frame is not a Poisson realisation but a synthetic

constant, i.e. an input mistake).

Detailed usage guide

photon_timeresolved family guide

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.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

photon_timeresolvedpy -3.11 examples/photon_timeresolved.py

Ops the type connects to (they accept table as input)

Same category (counting)

photon_sample · photon_uncertainty


*Provenance: photoncount.py — PHOTON 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.