How to Measure a Detector's NEP and D*

Scope

This article describes how to measure the noise equivalent power of a photodetector, the optical power that gives a signal equal to the noise in a 1 Hz bandwidth, and how to convert it to specific detectivity, D*, which normalizes for detector area. It applies to photodiodes, avalanche photodiodes and thermal detectors read out through an amplifier.

In short: block the light and measure the output noise spectrum; convert it to an equivalent input current noise using the amplifier's gain; measure the detector's responsivity at the wavelength of interest; divide the noise by the responsivity to get NEP in W/√Hz at each frequency. Report the wavelength, bias, temperature, frequency and amplifier, since NEP depends on all of them.

The quantities

$$\text{NEP}(f) \;=\; \frac{i_n(f)}{\mathcal{R}(\lambda)}, \qquad D^* \;=\; \frac{\sqrt{A}}{\text{NEP}},$$

where $i_n$ is the input-referred noise current spectral density in A/√Hz, $\mathcal{R}$ the responsivity in A/W, and $A$ the active area in cm². NEP comes out in W/√Hz and D* in cm·√Hz/W (Jones). A lower NEP and a higher D* are better. NEP describes a particular detector with its readout; D* allows detectors of different sizes to be compared, on the assumption that noise scales with the square root of area.

Procedure

1. Set the operating point. Fix the bias voltage, temperature and amplifier gain that the detector will be used at. NEP changes with all three.
2. Block all light. Cover the detector with a light-tight cap, not just a shutter in the beam path; room light and thermal background matter at these levels.
3. Record the output noise spectrum. Use an FFT analyzer, a spectrum analyzer or a digitizer and software FFT, reading the noise as a voltage spectral density in V/√Hz over the frequency range of interest. Check that the instrument's own noise floor is well below the reading.
4. Refer the noise to the input. Divide by the amplifier's transimpedance gain in V/A, measured at each frequency if the gain is not flat, to obtain $i_n(f)$ in A/√Hz.
5. Separate the amplifier noise. Repeat with the detector disconnected, or replaced by a capacitor of equal value, to measure the amplifier's own input noise. Report both; if the amplifier dominates, the measured NEP describes the amplifier rather than the detector.
6. Measure responsivity. Illuminate the detector with a known power at the wavelength of interest, from a source calibrated with a reference power meter, and measure the photocurrent. Keep the spot inside the active area.
7. Compute NEP and D* at each frequency. Quote NEP at a stated frequency, often in the flat region of the noise spectrum, and note any rise at low frequency.

Worked example

An InGaAs photodiode 1 mm in diameter has a dark current of 1 nA at its operating bias and a responsivity of 0.95 A/W at 1550 nm. Its dark-current shot noise is $\sqrt{2qI_d}$ = 1.79 × 10⁻¹⁴ A/√Hz, so the detector alone has an NEP of 1.88 × 10⁻¹⁴ W/√Hz and, with an area of 7.85 × 10⁻³ cm², a D* of 4.7 × 10¹² Jones.

Read out through a transimpedance amplifier with a 1 MΩ feedback resistor, the resistor adds thermal noise of $\sqrt{4kT/R}$ = 1.29 × 10⁻¹³ A/√Hz at 300 K, seven times the detector's shot noise. The total, added in quadrature, is 1.30 × 10⁻¹³ A/√Hz, giving a measured NEP of 1.37 × 10⁻¹³ W/√Hz and an apparent D* of 6.5 × 10¹¹ Jones. The measurement in this case describes the resistor. A larger feedback resistor lowers its current noise (as $1/\sqrt{R}$) at the cost of bandwidth; the photodiode noise tool shows the trade.

From spectral density to a bandwidth

A system with a noise-equivalent bandwidth $B$ has a minimum detectable power of about NEP × $\sqrt{B}$ when the noise is flat. For a single-pole filter with a 3 dB bandwidth $f_c$, $B = (\pi/2) f_c$. With the detector-limited NEP above and a 1 MHz single-pole bandwidth, the minimum detectable power is $1.88 \times 10^{-14} \times \sqrt{1.57 \times 10^6}$ = 2.4 × 10⁻¹¹ W, or 24 pW. When the noise is not flat, as with low-frequency excess noise, integrate the noise power over the band instead.

Common errors

Light leaks. A detector that is "dark" behind a shutter may still see scattered room light or, for infrared detectors, thermal radiation from the room. Check that the noise does not change with the room lights on and off.

Amplifier-limited results reported as detector NEP. Always state the readout, or report the detector's contribution separately.

Responsivity at the wrong wavelength. NEP scales inversely with responsivity, which varies strongly near a detector's cutoff.

Low-frequency noise ignored. Excess (1/f) noise and mains pickup raise the noise below some frequency; an NEP quoted only in the flat region can mislead for slow or DC measurements, where a lock-in amplifier and chopped light are often used.

Peak versus RMS. Spectral densities are RMS values; a peak-to-peak noise reading from an oscilloscope is several times larger.

References: E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996); A. Rogalski, Infrared and Terahertz Detectors (3rd ed., CRC Press, 2019); P. C. D. Hobbs, Building Electro-Optical Systems: Making It All Work (2nd ed., Wiley, 2009).