Specific detectivity

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 $D^{*} = \frac{\sqrt{A}}{N E P}$ , where $A$ is the area of the photosensitive region of the detector, and NEP the noise equivalent power (in units of $W / \sqrt{H z}$ ). It is commonly expressed in Jones units ( $c m \cdot \sqrt{H z} / W$ ) in honor of Robert Clark Jones who originally defined it.

Given that noise-equivalent power can be expressed as a function of the responsivity $ℜ$ (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 $N E P = \frac{S_{n}}{ℜ}$ , it is common to see the specific detectivity expressed as $D^{*} = \frac{ℜ \cdot \sqrt{A}}{S_{n}}$ .

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 λ η}{h c} {[\frac{4 k T}{R_{0} A} + 2 q^{2} η Φ_{b}]}^{- 1 / 2}

With $q$ as the electronic charge, $λ$ 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), $η$ is the quantum efficiency of the device, and $Φ_{b}$ is the total flux of the source (often a blackbody) in photons/s/cm².

Detectivity measurement

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 $Δ f$ directly from the integration time constant $t_{c}$ .

Δ f = \frac{1}{2 t_{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.

{Signal}_{avg} = \frac{1}{N} (\sum_{i}^{N} {Signal}_{i})

{Noise}_{rms} = \sqrt{\frac{1}{N} \sum_{i}^{N} ({Signal}_{i} - {Signal}_{avg})^{2}}

with the $N E P = \frac{{Noise}_{r m s}}{\sqrt{Δ f}}$ . 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{{Signal}_{avg}}{H G} = \frac{{Signal}_{avg}}{\int d H d A_{d} d Ω_{B B}},

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,
$Ω_{B B}$ 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.

NEP = \frac{{Noise}_{rms}}{R \sqrt{Δ f}} = \frac{{Noise}_{rms}}{{Signal}_{avg}} \frac{H G}{\sqrt{Δ 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^{*} = \frac{\sqrt{A_{d}}}{NEP} = \frac{\sqrt{Δ f A_{d}}}{H G} \frac{{Signal}_{avg}}{{Noise}_{rms}}

References

↑ Rogalski, A. (2012-01-01). "History of infrared detectors". Opto-Electronics Review. 20 (3). doi:10.2478/s11772-012-0037-7. ISSN 1896-3757.
↑ 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 Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.

[1] Rogalski, A. (2012-01-01). "History of infrared detectors". Opto-Electronics Review. 20 (3). doi:10.2478/s11772-012-0037-7. ISSN 1896-3757.

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

[3] 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)

Specific detectivity

Detectivity measurement

See also

References