Photon Counting Histogram Analysis for Two‐Dimensional Systems
Bibliographic record
Abstract
Photon counting statistics in 3D photon counting histogram analysis for one-photon excitation is a function of the number of molecules of particular brightness in the excitation-detection volume of a confocal microscope. In mathematical form that volume is approximated by a three-dimensional Gaussian function which is embedded in the PCH theoretical equations. PCH theory assumes that a molecule can be found anywhere inside the excitation-detection volume with equal probability. However, one can easily imagine systems in which this assumption is violated because molecules are constrained by the geometry of the sample. For example, molecules on a surface or in a membrane would be constrained to two dimensions. To enable the analysis of such systems by PCH, the theoretical framework requires modification. Herein, we present an extension of the PCH analysis to systems where molecules exist in thin structures that are effectively two-dimensional. The method, aptly called two-dimensional photon counting histogram (2D PCH), recovers the number of fluorescent particles per unit area and their molecular brightness. Both theoretical background and experimental results are presented. The theory was tested using computer-simulated and experimental 2D PCHs obtained from confocal experiments. We demonstrate that this modification of the theoretical framework provides a tool to extract data that reveal states of aggregation, surface photophysics, and reactivity.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".