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Signal-to-noise Ratio

Acronym: SNR

Definition: the ratio of signal power to noise power in a detector

German: Signal-zu-Rausch-Verhältnis

Categories: fluctuations and noise, optical metrology

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The quality of optical and other measurements is often characterized with a signal-to-noise ratio (SNR, S/N ratio). This is generally understood to be the ratio of the detected powers (not amplitudes), and is often expressed in decibels. Usually, the definition refers to electrical powers in the output of some detector. In the context of image processing, the signal-to-noise ratio is often defined in a different way: as the ratio of the mean pixel value and its standard deviation (for constant illumination).

In optical measurements, a common situation is that some light beam impinges a photodetector such as a photodiode, which produces a photocurrent in proportion to the optical power, with some electronic noise added. Depending on the situation, the signal-to-noise ratio may be limited either by optical noise influences (including shot noise) or by noise generated by the detector electronics. Some examples are given below.

The signal-to-noise ratio often limits the accuracy with which some measurement can be done. For digital signals, it can limit the reliability of detecting correctly, which can be quantified with a bit error rate. The latter situation is common in optical fiber communications, where some required bit error rate can only be achieved with a sufficiently high signal-to-noise ratio at the detector.

The Power of Noise

The power of noise is spread over some range of noise frequencies, and can be described with a power spectral density. Assuming white noise for simplicity, where the power spectral density is independent of noise frequency, the noise power is proportional to the detection bandwidth. If some signal is available for a longer time, the noise influence on a measurement can be reduced by averaging over a longer time interval. This can also be described as a reduction of the detection bandwidth (because changes of the signal within that interval could no longer be detected), which implies that the total noise power is reduced and thus the signal-to-noise ratio is increased (see Figure 1). Note also that the minimum possible detection bandwidth roughly equals the inverse measurement time.

signal-to-noise ratio
Figure 1: An optical signal at 1043.4 nm, which is contaminated with some level of white noise (resulting from amplified spontaneous emission in an amplifier), has been recorded with two different values of the resolution bandwidth (RBW). This bandwidth affects the noise level, but not the signal level. Consequently, a better signal-to-noise ratio (≈ 32 dB) is achieved with the smaller resolution bandwidth.
signal-to-noise ratio
Figure 2: Same as in Figure 1, but with averaging over 10 traces, so that the average noise power (the power spectral density) is better approximated. Note that this kind of averaging does not improve the signal-to-noise ratio; it only reduces the uncertainty in the noise level, but not the noise level as such.

Example 1: Optical Measurement Limited by Thermal Noise

When an optical signal with a relatively low optical power such as 1 μW impinges a photodiode, and this photodiode is operated with some reverse bias and a resistor for converting the photocurrent into a voltage signal, the noise of that signal is normally dominated by thermal noise from the resistor or by excess noise from further electronic components.

If the signal is some weak sinusoidal modulation of the optical power, the detected electrical signal power is proportional to the square of the signal amplitude, i.e., to the square of the amplitude of the optical power modulation. Doubling the overall optical power would double that amplitude and quadruple the detected signal power, whereas the noise power remains constant. This means that the signal-to-noise ratio would then be increased by a factor of 4, corresponding to 6 dB.

Example 2: Shot-noise-limited Optical Measurement

When an optical signal with a sufficiently high optical power (for example, 10 mW) impinges a photodiode equipped with high-quality electronics, electronic noise influences are often negligible, even if the optical signal in contaminated only by shot noise.

If we again assume the signal to be a weak sinusoidal modulation of the optical power, doubling the overall optical power would still increase the detected signal power by a factor of 4, but it would also double the noise power resulting from shot noise. In effect, the signal-to-noise ratio would be doubled, corresponding to an increase by 3 dB.

Measures for Improving the Signal-to-Noise Ratio of Optical Measurements

In optical measurements, the signal-to-noise ratio may be increased with various types of measures:

See also: shot noise, laser noise, noise specifications, photodiodes, Spotlight article 2009-07-21, Spotlight article 2009-11-13, Spotlight article 2009-12-13
and other articles in the categories fluctuations and noise, optical metrology

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