Noise-equivalent Power
Author: the photonics expert Dr. Rüdiger Paschotta
Acronym: NEP
Definition: the input power to a detector which produces the same signal output power as the internal noise of the device
Categories: light detection and characterization, fluctuations and noise
Units: W or W / Hz1/2
DOI: 10.61835/n3z Cite the article: BibTex plain textHTML Link to this page LinkedIn
When a photodetector does not get any input light, it nevertheless produces some noise output with a certain average power, which is proportional to the square of the r.m.s. voltage or current amplitude. The noise-equivalent power (NEP) of the device is the optical input power which produces an additional output power identical to that noise power for a given bandwidth (see below). If the input is interpreted as a signal, the output signal and noise powers are then identical, i.e., the signal-to-noise ratio would be 1.
The inverse of the noise-equivalent power is called the detectivity.
The possible signal-to-noise ratio of a measurement (for a 1-Hz bandwidth) can be estimated simply as the available input power divided by the noise-equivalent power. For that purpose, one does not need to know the detector's responsivity.
Note that the noise-equivalent power depends on the optical wavelength, since that influences the responsivity of the detector. The lowest NEP is achieved for those wavelengths where the responsivity is the highest.
Influence of the Bandwidth
The noise power and thus also the noise-equivalent power depends on the measurement bandwidth. (For white noise, it is proportional to that bandwidth.) At a first glance, one may find it most natural to use the full detection bandwidth of the device. Then, however, the NEP would not allow a fair comparison of detectors with different bandwidth; it would be reduced if additional electronic filtering, reducing the detection bandwidth, would be applied. Therefore, it is common to assume a bandwidth of 1 Hz, which is usually far below the detection bandwidth.
Some authors specify the NEP in units of W / Hz1/2 rather than W (watts), as would be the usual units for a power. Effectively, they base the NEP on the square root of a power spectral density (PSD) rather than on a power. The numerical results are the same as when assuming a bandwidth of 1 Hz.
Measurement of Noise-equivalent Power
For experimentally obtaining the noise-equivalent power, one first needs to measure the noise amplitude of the instrument output in the given noise bandwidth (e.g. 1 Hz) without any optical input. That result has to be divided by the responsivity.
For example, consider a photodetector which in the dark produces a photocurrent (dark current or current generated by its electronics) with a noise amplitude of 1 nA / Hz1/2. If its responsivity is 0.5 A/W, and we consider a bandwidth of 1 Hz, the NEP is 1 nA / 0.5 A/W = 2 nW. For a larger bandwidth of 10 kHz, the noise amplitude would rise to 100 nA – not to 10,000 nA, as this scales with the square root of the bandwidth –, and the NEP would rise to 200 nW.
The square root dependence on the bandwidth may be surprising; it is related to the fact that the noise power scales linearly with the bandwidth, and is proportional to the square of the noise amplitude. In our example case, the noise power in a 1-Hz bandwidth generated by the detector current in a 50-Ω-resistor would be 50 Ω · (1 nA)2, and in a 10-kHz bandwidth it would be 10,000 times larger, i.e., 50 Ω · (100 nA)2.
Optimization
Obviously, a low noise-equivalent power is desirable because that power level is about the minimum input power level which can be detected easily when averaging the signal over a time of the order of one second. Using advanced methods such as lock-in detection, one can actually detect much weaker signals, provided that these have a bandwidth far below the detection bandwidth. In effect, one restricts the detection bandwidth to a value far below 1 Hz, which also reduces the noise power with which the signal has to compete. The required averaging time is correspondingly longer.
If the responsivity of a photodetector (e.g. a photodiode) can be increased without increasing the delivered noise power, the noise-equivalent power can be reduced. However, by using an avalanche photodiode, for example, where the responsivity can be greatly enhanced due to an internal amplification mechanism, one also obtains substantially more noise, so that the noise-equivalent power may even be increased.
More to Learn
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Suppliers
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CSRayzer Optical Technology
CSRayzer CR2000AH-1550-70M includes a 200 μm InGaAs avalanche photodiode and a hybrid preamplifier for the use in high speed, ultra-low light detection, in laser range finding, LIDAR and free space communications.
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Ultrafast photodetectors from ALPHALAS for measurement of optical waveforms with rise times starting from 10 ps and total spectral coverage from 170 to 2600 nm (VUV to IR) have bandwidths from DC up to 30 GHz. Configurations include free-space, fiber receptacle or SM-fiber-pigtailed options and have compact metal housings for noise immunity. The UV-extended versions of the Si photodiodes are the only commercial products that cover the spectral range from 170 to 1100 nm with a rise time < 50 ps. For maximum flexibility, most models are not internally terminated. A 50 Ohm external termination supports the highest speed operation, while a high impedance load generates large amplitude signals. Applications include pulse form and duration measurement, mode beating monitoring and heterodyne measurements. Balanced photodiodes complement the large selection of more than 70 unique models.
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NLIR
Our D2250 2.2–5.0 µm single wavelength detector is super-fast (up to 10 GHz bandwidth) and ultra-sensitive (NEP of a few fW/√Hz).
Our D2250’s are based upon a new measuring paradigm where mid-infrared light is converted into near-visible light and then measured with conventional near-visible detector technology.
Menlo Systems
Menlo Systems offers a series of photodetectors for lowest light level signals. From avalanche to PIN photodiodes, you can find the detector that is best for your specific application.
Gentec Electro-Optics
Gentec Electro-Optics offers a great range of power detectors based on silicon or germanium photodiodes for powers up to 750 mW.
FEMTO Messtechnik
FEMTO offers a wide range of photoreceivers. Amplified Si and InGaAs photoreceivers are available in the bandwidth range from Hz to GHz with a sensitivity down to the fW range. Custom versions tailored to specific requirements are also available.
Questions and Comments from Users
2023-02-10
I want to compute the NEP at a different wavelengths. Is there a way to compute the NEP at another wavelength, if the responsivity of the detector R(lambda) is known? Is it true that NEP(lambda1) R(lambda1) = NEP(lambda2) R(lambda2)?
The author's answer:
Yes, that's a good approach.
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2021-03-03
I would like to understand the relationship between the NEP and the signal-to-noise ratio. If the NEP is large, does the signal-to-noise ratio become small?
The author's answer:
Yes, it will. However, the signal-to-noise ratio also depends on the strength of the transmitted signal, while the NEP does not deal with that.