Light reveals. Contrast distinguishes.

What the numbers mean

The detector shows a synthetic two-ring fluorescent bead phantom over a uniform background, in a 16 µm square field. The 3D view shares the bead positions but exaggerates their size and the instrument geometry. Focus and the spatial intensity profile remain fixed. The experiment models photon collection and readout, not a full wave-optical microscope.

At the brightest target pixel, the expected signal S = 5ptTₛ electrons. The expected background B = (8bpTᵦ + 0.4)t electrons. Here p is excitation intensity as a fraction of full power, t is exposure in ms and b = 0.8 is a fixed fluorescent-background burden. Broad collection uses Tₛ = Tᵦ = 1. Selective collection uses Tₛ = 0.65 and Tᵦ = 0.08. These are illustrative transmission factors for different target/background spectra, not specifications of a real filter. Both options assume adequate rejection of excitation light. A narrower band is not automatically better when spectra overlap.

Relative contrast is defined here as S/(S+B), the signal fraction at the brightest target pixel. It is not Weber or Michelson contrast. Increasing exposure scales S and B equally, leaving this ratio unchanged. Expected single-pixel SNR = S/√(S+B+σᵣ²), with read noise σᵣ = 5 electrons RMS. This assumes the background mean is known exactly; estimating it from a noisy reference adds uncertainty. Values describe the unclipped expectation, not a measurement made from the displayed noisy image.

Independent Gaussian noise approximates shot noise and read noise with variance S(x,y)+B+25. The approximation is weaker at very low counts; negative samples are clamped to zero. Raw values clip at an illustrative 2000-electron capacity. The 64-bin histogram uses raw clipped samples, before display gain. Green pseudo-color is a linear display of counts. Mark clipped pixels shows camera saturation in red and display-only clipping in magenta. Sampling another frame changes the random realization, not the expected metrics.

Excitation exposure pt is expressed in full-power-equivalent milliseconds, not physical energy or a damage threshold. The final ≤180 limit is a teaching budget. Bleaching, phototoxicity, fluorophore saturation, dark current, spectral curves, pixel nonuniformity and camera calibration are not simulated. A real acquisition also needs checks for specimen motion, linearity, illumination uniformity and appropriate controls.

Why this lesson uses fluorescence

Contrast mechanisms depend on the specimen and instrument. This lesson isolates spectral selection and photon statistics. Brightfield, phase contrast, DIC and darkfield use different image-formation mechanisms; this experiment does not simulate them.

Nikon MicroscopyU · Fluorescence principles and filters ↗
Waters · Accuracy and precision in quantitative fluorescence microscopy ↗
Evident · Camera exposure and saturation ↗