Channel Photomultiplier (CPM)
Single-channel CPM: anode sensitivity, photon-counting and analog SNR, and pulse resolution with the channel's excess noise.
F ≈ 2 for an unsaturated channel, whose pulse heights are near-exponential. Above a gain of about 10⁷ the channel saturates and the single-electron peak narrows to about 50 % FWHM, so F = 1 + (0.5/2.355)² ≈ 1.05 for single photons. A saturated pulse no longer grows with the number of photoelectrons.
Anode Sensitivity
8.27e+3 A/W
QE·eλ/(hc)·G at 410 nm
Photoelectron Rate
2.50e+3 /s
Signal anode current 4.01e-11 A
Dark Anode Current
1.60e-13 A
Dark counts × e × G (photocathode emission)
Photon-Counting SNR
49.90
1 s gate; below a gain of 10⁷ single pulses sit close to the electronic noise
Analog SNR
35.28
Bandwidth 1/(2T); the gain spread costs √F = 1.414
Pulse Resolution
66.6 % FWHM
25.0 photoelectrons, 0.401 pC
Sanode = QE · eλ/(hc) · G
SNRcount = RsT / √((Rs + Rd)T), Rs = Φ · QE
SNRanalog = Rs / √(2B(Rs + Rd)F), B = 1/(2T)
ΔQ/Q (FWHM) = 2.355 · √(F / Npe), valid while Npe · G ≤ linear limit
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
One channel behind a photocathode. Counting takes every photoelectron as counted, with no dead time and a known dark rate; the analog SNR in B = 1/(2T) differs from it by √F. The pulse resolution holds only below the linear limit; saturated output is not modelled.
- PerkinElmer Optoelectronics (2001). Channel Photomultipliers C900, C1300 and C1900 series, data sheet DS-291 Rev A. Gain above 10⁸ at 3000 V, bialkali dark count rate about 10 cps, saturated single-photoelectron peak above a gain of 10⁷.
- Wiza J. L. (1979). Microchannel plate detectors. Nucl. Instrum. Methods 162, 587–601, eq. (1)–(4) and §2.2. Schagen's channel-gain model (eq. 1) with A ≈ 0.2 and V₀ ≈ 1 eV, exponential pulse heights below saturation, saturated gain proportional to the channel diameter (10⁸ for 1 mm). doi:10.1016/0029-554X(79)90734-1
- Hamamatsu Photonics (2017). Photomultiplier Tubes: Basics and Applications, 4th ed., §4.3.7, Eq. 4-25 to 4-32. Noise figure of a dynode chain, F = 1 + 1/δ₁ + 1/(δ₁δ₂) + … → δ/(δ − 1), and the shot-noise SNR. hamamatsu.com