GeezerVison

This article may rely excessively on sources too closely associated with the subject, potentially preventing it from being verifiable and neutral. Please help improve this article by replacing such sources with more appropriate citations to reliable, independent sources. (October 2018) (Learn how and when to remove this message)

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 $D^{\ast }=\frac{\sqrt{A}}{NEP}$, where $A$ is the area of the photosensitive region of the detector, and NEP the noise equivalent power (in units of $W/\sqrt{Hz}$)^[1]. It is commonly expressed in Jones units ($cm\cdot \sqrt{Hz}/W$) in honor of Robert Clark Jones who originally defined it.^[2][3]

Given that noise-equivalent power can be expressed as a function of the responsivity $\Re$ (in units of $A/W$ or $V/W$) and the noise spectral density $S_n$ (in units of $A/H{z}^{1/2}$ or $V/H{z}^{1/2}$) as $NEP=\frac{S_n}{\Re }$, it is common to see the specific detectivity expressed as $D^{\ast }=\frac{\Re \cdot \sqrt{A}}{S_n}$.

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.

$D^{\ast }=\frac{q\lambda \eta }{hc}{[\frac{4kT}{R_{0}A}+2q^2\eta {\Phi }_b]}^{-1/2}$

With $q$ as the electronic charge, $\lambda$ 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, $R_{0}A$ 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/s/cm².

Detectivity can be measured from a suitable optical setup using known parameters. You will need a known light source with known irradiance at a given standoff distance. The incoming light source will be chopped at a certain frequency, and then each wavelength will be integrated over a given time constant over a given number of frames.

In detail, we compute the detection bandwidth $\Delta f$ directly from the integration time constant $t_c$.

$\Delta f=\frac{1}{2t_c}$

Next, an average signal and rms noise needs to be measured from a set of $N$ frames. This is done either directly by the instrument, or done as post-processing.

${\text{Signal}}_{\text{avg}}=\frac{1}{N}\left(\sum _i^N{\text{Signal}}_i\right)$

${\text{Noise}}_{\text{rms}}=\sqrt{\frac{1}{N}\sum _i^N({\text{Signal}}_i-{\text{Signal}}_{\text{avg}}{)}^2}$

with the $NEP=\frac{{\text{Noise}}_{rms}}{\sqrt{\Delta f}}$. Now, the computation of the radiance $H$ in W/sr/cm² must be computed where cm² is the emitting area. Next, emitting area must be converted into a projected area and the solid angle; this product is often called the etendue. This step can be obviated by the use of a calibrated source, where the exact number of photons/s/cm² is known at the detector. If this is unknown, it can be estimated using the black-body radiation equation, detector active area $A_d$ and the etendue. This ultimately converts the outgoing radiance of the black body in W/sr/cm² of emitting area into one of W observed on the detector.

The broad-band responsivity, is then just the signal weighted by this wattage.

$R=\frac{{\text{Signal}}_{\text{avg}}}{HG}=\frac{{\text{Signal}}_{\text{avg}}}{\int dHd{A}_{d}d{\Omega }_{BB}},$

where

• $R$ is the responsivity in units of Signal / W, (or sometimes V/W or A/W),
• $H$ is the outgoing radiance from the black body (or light source) in W/sr/cm² of emitting area,
• $G$ is the total integrated etendue between the emitting source and detector surface,
• $A_d$ is the detector area,
• ${\Omega }_{BB}$ is the solid angle of the source projected along the line connecting it to the detector surface.

From this metric noise-equivalent power can be computed by taking the noise level over the responsivity.

$\text{NEP}=\frac{{\text{Noise}}_{\text{rms}}}{R\sqrt{\Delta f}}=\frac{{\text{Noise}}_{\text{rms}}}{{\text{Signal}}_{\text{avg}}}\frac{HG}{\sqrt{\Delta f}}$

Similarly, noise-equivalent irradiance can be computed using the responsivity in units of photons/s/W instead of in units of the signal. Now, the detectivity is simply the noise-equivalent power normalized to the bandwidth and detector area.

$D^{\ast }=\frac{\sqrt{A_d}}{\text{NEP}}=\frac{\sqrt{\Delta f{A}_d}}{HG}\frac{{\text{Signal}}_{\text{avg}}}{{\text{Noise}}_{\text{rms}}}$

• Sensitivity (electronics)

 This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.