Noise Equivalent Power (NEP) & Detectivity (D*)

Calculate NEP and specific detectivity D* from detector noise sources: shot noise, thermal (Johnson) noise, and dark current.

Model: Textbook approximation

Dark Current (nA)Responsivity (A/W)Bandwidth (Hz)Temperature (K)Load Resistor (Ω)Detector Area (mm²)

NEP

2.28e-11 W

Total for bandwidth B

NEP (spectral)

2.28e-11 W/√Hz

Per root Hz

4.39e+9 Jones

√(A·B)/NEP

Noise current (rms)

1.820e-11 A

shot 5.66e-14 A, Johnson 1.82e-11 A

Formulas

i_shot = √(2qI_dB)

i_thermal = √(4kTB/R_L)

NEP = √(i_shot² + i_thermal²) / ℛ (total power equivalent in B)

D* = √(A · B) / NEP (Jones — cm·√Hz/W)

Dark-current shot noise and load-resistor Johnson noise only: no signal shot noise, no amplifier noise.

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

Dark-current shot noise and load-resistor Johnson noise in quadrature, divided by the responsivity. Signal shot noise, amplifier noise and 1/f noise are left out.

Dereniak E. L., Boreman G. D. (1996). Infrared Detectors and Systems. Wiley. Ch. 5: responsivity, noise-equivalent power and specific detectivity D* = √(A·Δf)/NEP.
Saleh B. E. A., Teich M. C. (1991). Fundamentals of Photonics. Wiley. §17.5 Noise in photodetectors: shot noise 2qīB and circuit noise. doi:10.1002/0471213748
Nyquist H. (1928). Thermal agitation of electric charge in conductors. Phys. Rev. 32, 110. Derivation of 4k_B·T·R per unit bandwidth. doi:10.1103/PhysRev.32.110

Report a problem