Sub-diffraction measurement challenge: Dobrucki's misrepresentation table shows that objects below ~250 nm all appear the same size in the image — a single FISH probe (~20 nm) and two overlapping probes (~40 nm total) produce images of the same apparent width. This means dot area cannot reliably distinguish singles from doubles below the diffraction limit. Only intensity provides discriminating information for overlapping sub-resolution objects.
PSF and dot intensity: Each point source is convolved with the microscope's point spread function (PSF), spreading its light over a ~250 nm diameter area. The total integrated intensity under the PSF equals the total photon output of the source. When two point sources overlap, their PSFs add, and the total integrated intensity approximately doubles. This additivity is the physical basis for intensity-based cluster counting — divide total intensity by the expected single-dot intensity to estimate the number of sources.
The photon budget for counting: If a single FISH dot produces 100 photons at the detector, a 2-dot cluster produces ~200. The difference must be reliably distinguishable from Poisson fluctuation. A single dot has √100 = 10 photon noise, or 10% uncertainty. The 2-dot cluster has √200 ≈ 14 photon noise, or 7% uncertainty. The 100-photon gap between them spans ~7 noise standard deviations — very reliable. But a dim probe producing only 25 photons per dot has 20% uncertainty, and the gap between 1 and 2 dots is only ~5 noise widths — still distinguishable but with more errors for 3+ clusters.
Clinical significance of counting accuracy: In HER2 FISH, the critical threshold is a HER2/CEP17 ratio of 2.0. A cell with 6 HER2 dots and 3 CEP17 dots has a ratio of 2.0 — right at the threshold. Missing one dot or counting one false positive shifts the ratio to 1.67 or 2.33, potentially changing the clinical decision. This is why accurate dot detection and measurement are critical for FISH-based companion diagnostics.
Below the diffraction limit (~250 nm), all dots look the same size regardless of whether they're singles or clusters. Only brightness distinguishes them — two overlapping dots are twice as bright as one. The accuracy of this intensity-based counting depends on how many photons each dot produces. With strong signals (100+ photons), singles and doubles are clearly separable. With weak signals, the distinction becomes uncertain.
