photon_statistics — PHOTON `counting` op

• データ種: image2d → table

• 呼び出し: import photoncount; photoncount.photon_statistics(counts) (または opsphoton.get("photon_statistics"))

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).

• サンプルデータカタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

• photon_timeresolved — py -3.11 examples/photon_timeresolved.py

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*Provenance: photoncount.py — PHOTON operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

photon_statistics — PHOTON counting op