Specific detectivity

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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 (reciprical of its sampling rate).

Specific detectivity is given by $D^{*}={\frac {{\sqrt {Af}}}{NEP}}$ , where $A$ is the area of the photosensitive region of the detector and $f$ is the frequency bandwidth. It is commonly expressed in Jones units ( $cm\cdot {\sqrt {Hz}}/W$ )in honor of R. Clark Jones who originally defined it.^[1]^[2]

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

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.

$D^{*}={\frac {q\lambda \eta }{hc}}\left[{\frac {4kT}{R_{0}A}}+2q^{2}\eta \Phi _{b}\right]^{{-1/2}}$

With q as the electronic charge, $\lambda$ is the wavelength of interest, h is Planck's constant, c is the speed of light, k is Boltzmann's constant, T is the temperature of the detector, $R_{0}A$ is the zero-bias dynamic resistance area product (often measured experimentally, but also expressible in noise level assumptions), $\eta$ is the quantum efficiency of the device, and $\Phi _{b}$ is the total flux of the source (often a blackbody) in photons/sec/cm².

References

↑ R. C. Jones, "Quantum efficiency of photoconductors," Proc. IRIS 2, 9 (1957)
↑ 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)

This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

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