Confocal pinhole throughput

Opening the pinhole increases accepted in-focus and out-of-focus photons; closing it strengthens confocal optical sectioning while discarding some useful in-focus photons too. In the synthetic model, $\alpha =0.5,1.5,4$ transmits approximately $0.1175,0.6753,0.9997$ of the collected in-focus emission. At $t=2$ the corresponding peak-normalized signals are about $0.0420,0.0597,0.1597$. These are calculated fractions under stated assumptions, not instrument measurements.

An Airy unit conventionally specifies a pinhole diameter equal to the first-zero diameter of the emission Airy disk in that plane. For an ideal circular pupil,where $M$ is the total specimen-to-pinhole magnification, ${\lambda }_{\mathrm{em}}$ the emission wavelength in vacuum, and $\mathrm{NA}$ the objective numerical aperture. A software setting needs its specified wavelength and relay magnification; it is not a universal micrometre diameter. ^[ref]

For ideal independent counting, accepted source and background means $S$ and $B$ give photon shot noise with variance $S+B$ and signal-to-noise ratio in photon counting $S/\sqrt{S+B}$. Closing a pinhole need not improve that ratio: it depends on how both $S$ and $B$ change. Increasing exposure or excitation to replace discarded photons can cause bleaching, an irreversible loss of fluorescent emission capacity, or damage. Detection rejection occurs after excitation and therefore does not undo excitation outside the selected depth. Such material can absorb illumination and emit photons even when their emission is omitted from the recorded image.