Editing Specific detectivity (section)

{{Short description|Parameter characterizing photodetector performance}}
{{third-party|date=October 2018}}
'''Specific detectivity''', or '''''D*''''', for a [[photodetector]] is a [[figure of merit]] used to characterize performance, equal to the reciprocal of [[noise-equivalent power]] (NEP), normalized per square root of the sensor's area and frequency bandwidth (reciprocal of twice the integration time).

Specific detectivity is given by <math>D^*=\frac{\sqrt{A \Delta f}}{NEP}</math>, where <math>A</math> is the area of the photosensitive region of the detector, <math>\Delta f</math> is the bandwidth, and NEP the noise equivalent power in units [W]. It is commonly expressed in ''Jones'' units (<math>cm \cdot \sqrt{Hz}/ W</math>) in honor of [[Robert Clark Jones]] who originally defined it.<ref>R. C. Jones, "Quantum efficiency of photoconductors," ''Proc. IRIS'' '''2''', 9 (1957)</ref><ref>R. C. Jones, "Proposal of the detectivity D** for detectors limited by radiation noise," ''J. Opt. Soc. Am.'' '''50''', 1058 (1960), {{doi|10.1364/JOSA.50.001058}})</ref>

Given that noise-equivalent power can be expressed as a function of the [[responsivity]] <math>\mathfrak{R}</math> (in units of <math>A/W</math> or <math>V/W</math>) and the [[noise spectral density]] <math>S_n</math> (in units of <math>A/Hz^{1/2}</math> or <math>V/Hz^{1/2}</math>) as <math>NEP=\frac{S_n}{\mathfrak{R}}</math>, it is common to see the specific detectivity expressed as <math>D^*=\frac{\mathfrak{R}\cdot\sqrt{A}}{S_n}</math>.

It is often useful to express the specific detectivity in terms of relative noise levels present in the device. A common expression is given below.
: <math>D^* = \frac{q\lambda \eta}{hc} \left[\frac{4kT}{R_0 A}+2q^2 \eta \Phi_b\right]^{-1/2}</math>

With ''q'' as the electronic charge, <math>\lambda</math> is the wavelength of interest, ''h'' is the Planck constant, ''c'' is the speed of light, ''k'' is the Boltzmann constant, ''T'' is the temperature of the detector, <math>R_0A</math> is the zero-bias dynamic resistance area product (often measured experimentally, but also expressible in noise level assumptions), <math>\eta</math> is the quantum efficiency of the device, and <math>\Phi_b</math> is the total flux of the source (often a blackbody) in photons/sec/cm<sup>2</sup>.