Quantum Efficiency

Quantum efficiency is the probability that a photon arriving at the sensor frees an electron. It is a probability, so it runs 0 to 1, and a modern back-illuminated sensor reaches about 0.95 at its best wavelength.

That last phrase carries the whole problem. QE is strongly wavelength dependent, the quoted figure is the peak, and the peak usually sits in the green around 550 nm. If your emission is at 680 nm the relevant number might be 0.70; at 750 nm it might be 0.55. Comparing two cameras on their peak QE compares them at a wavelength neither of your dyes emits.

The consequence is not subtle, and it reverses rankings. A sensor quoting 95% peak can sit below one quoting 82% by the time you reach the far red, because the second was designed with a flatter response. Far red is exactly where dim targets are placed to escape autofluorescence, so the comparison that matters is the one nobody runs.

QE exists because light arrives in quanta. A photon either has enough energy to promote an electron across the silicon bandgap or it does not, and no amount of dim steady illumination adds up to the threshold. That is the photoelectric effect, explained by Einstein in 1905 and the work his 1921 Nobel Prize actually cited — not relativity.

The wavelength dependence follows directly. Toward the blue, photons carry ample energy but are absorbed within a few tens of nanometres of the surface, where front-side circuitry can intercept them before they reach the photodiode; this is why back illumination, thinning the wafer and lighting it from behind, lifts blue response so much. Toward the red the opposite applies: photons penetrate deep and may pass entirely through a thin sensor without being absorbed, which is why NIR-sensitive designs use thicker silicon. The curve is a compromise between those two failures.

The specimen does not see the sensor. It sees a chain: objective transmission, every mirror and filter, then QE. System detection efficiency is the product, and a weak term anywhere sets the result.

Run two systems. A 95% QE camera behind an objective transmitting 55% in your emission band delivers 0.52. An 82% QE camera behind one transmitting 92% delivers 0.75 — 44% more signal, with the lower QE. Nothing about this is exotic; objective transmission genuinely varies that much across the visible and into the NIR, and it is the term least often looked up.

So the useful discipline is to evaluate the whole chain at the wavelength you will use. QE is worth optimizing once the rest of the path is not throwing away more than the difference between two sensors.

Take a smFISH spot emitting 300 photons at 670 nm. At 90% QE that is 270 photoelectrons and, with 50 electrons of background, an SNR near 15. At 65% QE the same spot gives 195 electrons and an SNR near 12.5 — a 17% loss, from one number on one curve.

To recover it by exposure you would need (270/195)² = 1.9 times the photons, because SNR follows the square root of signal. Nearly double the exposure, or nearly double the dose, to undo a QE difference that appeared on no specification sheet because both cameras quote their green peak. That is the whole argument for reading the curve at your own wavelength rather than the headline.