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# Relative Intensity Noise

Acronym: RIN

Definition: noise of the optical intensity (or actually power), normalized to its average value

More general term: intensity noise

German: relatives Intensitätsrauschen

Author:

In the context of intensity noise (optical power fluctuations) of a laser, it is common to specify the relative intensity noise (RIN), which is the power noise normalized to the average power level. The optical power of the laser can be considered to be

$$P(t) = \bar P + \delta P(t)$$

with an average value and a fluctuating quantity <$\delta P$> with zero mean value. The relative intensity is then <$\delta P$> divided by the average power; in the following, that quantity is called <$I$>. The relative intensity noise can be specified in different ways; a common way is to statistically describe it with a one-sided power spectral density (PSD):

$${S_I}(f) = \frac{2}{{{{\bar P}^2}}}\int\limits_{ - \infty }^{ + \infty } {\left\langle {\delta P(t)\;\delta P(t + \tau )} \right\rangle \;\exp \left( {i2\pi f\tau } \right)\;} {\rm{d}}\tau$$

which depends on the noise frequency <$f$>. It is essentially the Fourier transform of the autocorrelation function of the normalized power fluctuations, and can be measured e.g. with a photodiode and an electronic spectrum analyzer.

The factor of 2 in the formula above applies to a one-sided PSD as usually used in the engineering disciplines, and would be missing in variants using two-sided PSDs. The units of the RIN PSD are Hz−1, but it is common to specify 10 times the logarithm (to base 10) of that quantity in dBc/Hz (see also: decibel).

The PSD may also be integrated over an interval <$[f_1, f_2]$>] of noise frequencies to obtain a root mean square (r.m.s.) value of relative intensity noise

$${\left. {\frac{{\delta P}}{{\bar P}}} \right|_{{\rm{rms}}}} = \sqrt {\int\limits_{{f_1}}^{{f_2}} {{S_I}} (f)\;{\rm{d}}f}$$

which is then often specified in percent.

Note that it is not sensible to specify relative intensity noise in percent (e.g. as ±0.5%) without clarifying whether this means an r.m.s. value or something else. See the article on noise specifications for more such details. Figure 1: Simulated relative intensity noise spectrum of a 1064-nm Nd:YAG laser with 100 mW average output power. The shot noise level of −174 dBc/Hz is reached above 5 MHz. There is also a pronounced peak from relaxation oscillations, and excess noise at low frequencies introduced by the pump source.

## RIN from Shot Noise

It might be expected that the amount of RIN of a laser beam will remain constant when the beam is subject to linear attenuation. This is not true, however, when the RIN is limited by shot noise. In that case, the RIN is given by

$${S_{I,{\rm{sn}}}}(f) = \frac{{2h\nu }}{{\bar P}}$$

As an example, a 1-mW laser beam at 1064 nm with intensity noise at the shot noise limit has a RIN of 3.73 × 10−16 Hz−1 or −154 dBc/Hz.

That PSD is independent of noise frequency (white noise). It increases with decreasing average power (e.g., when the beam is attenuated by some absorbing medium). This can be understood as the introduction of additional quantum noise in the attenuation process.

Quantum-limited RIN measurements should be done by detecting the entire laser power e.g. with a photodiode, while minimizing the influence of excess noise (e.g. thermal noise) from the electronics. For high power levels, it can be challenging to find a sufficiently fast photodetector with high power handling capability, while electronic noise issues are more critical at low power levels.

## Questions and Comments from Users

2021-03-08

What is the difference between frequency noise and relative intensity noise?

Frequency noise is noise of the instantaneous frequency, which in optics means noise of the optical frequency. That is related to phase noise.

2021-06-04

How to normalize the intensity fluctuations of a HeNe laser, measured with a photodiode?

This simply means that you divide the fluctuating power by the average power, obtaining a dimensionless quantity fluctuating around 1. You can then further process that, for example estimate the power spectral density.

2021-07-21

How to convert RIN data with 1/sqrt(Hz) unit into a result with % units?

Multiply it with the square root of the detection bandwidth, and with 100 to get percent. The fluctuations of power will of course not fully remain within that percent value, but often go somewhat beyond it.

2021-12-04

Is RIN the inverse of a signal to noise ratio (SNR)? In this case, the units of 1/RIN are Hz. What would that physically mean? You can multiply RIN by the bandwidth of the detector to get % fluctuation from the average signal. Is there any use for 1/RIN? Is that the bandwidth that gives 100% fluctuation?

The signal-to-noise ratio (SNR) is a ratio, i.e., a dimensionless quantity, and can therefore not be identified with anything having units of Hz. It is usually used in the context of signals, and a continuous-wave laser beam would normally not be considered as a signal.

Further, note that RIN can be quantitatively specified in different ways, one of them being a power spectral density. That has units of 1/Hz, and you get a dimensionless quantity by multiplying it with a noise bandwidth. If you then consider the constant power as a “signal” (somewhat odd), you may identify that product with the inverse SNR.

2021-12-13

How do I measure the reference DC voltage for the RIN Measurement? I have the following setup for the RIN measurement of a 50-MHz oscillator:

Laser → ND filter → lens → photodetector → 50 Ohm resistor → low pass filter (<10 MHz) → DC block → voltage amplifier → spectrum analyzer.

So for the DC measurement should I measure it after the photodetector directly with a 50 Ohm termination or should I measure it after the voltage amplifier (with DC Block removed from the setup) and divide the final DC voltage with the amplification factor of the voltage amplifier?

It is often not so easy to measure the corresponding DC part because you usually cannot feed that through the high-gain amplifier. Indeed, one possibility would be to measure the DC voltage drop at a resistor.

Another way of getting the RIN calibrated relative to the short noise level is to use a homodyne detection measurement setup, containing a 50:50 beam splitter two photodiodes with high quantum efficiency, and circuits to get the sum and the differences of the photocurrents. The sum current gives you the actual noise (when a correction according to the finite quantum efficiency is applied), while the difference current gives you the shot noise level.

2022-01-25

To calculate the RIN from shot noise: let us assume that we have to reduce the power of the laser beam via a neutral density filter to avoid saturation of the detector. For the light power P, do I need to enter the actual power of the laser source (e.g. 200 mW) or the power after passing through the filter (e.g. 1 mW)? The latter would correspond to the actual power that hits the detector.

The latter is correct – the power which actually hits the detector. Attenuation leads to higher RIN from shot noise.

2023-01-06

Is there a mistake? 2 h nu / P has units of seconds. So in your calculations how did you end up with units of dBc/Hz?

Seconds are the same as inverse Hertz, and the dBc part is not a real dimension – just indicating that you use that logarithmic processing.

2023-03-28

Are there some basic noise models for RIN depending on the type of laser? For example, Figure 1 is for a crystal laser. Are there noise models for ECDL, DBG, etc?

Sure, various people have worked out noise models for different kinds of lasers. You need to search the scientific literature for that.

2023-04-06

“That PSD (due to shot noise) is independent of noise frequency (white noise), and it increases with decreasing average power.” Do you mean only a relative increase, or an increase in absolute terms?

What does “additional quantum noise in (optical?) attenuation”?

Consider the noise in the photocurrent of a photodiode. If the beam power is doubled, the PSD of the photocurrent noise is actually also doubled. However, the average photocurrent is also doubled. If you attenuate the photocurrent by a factor 2 to compensate for that (and having the photocurrent reflecting the relative power), you will get a 4 times lower PSD – or 2 times less than in the original situation (with the original beam power and no photocurrent attenuation).

Attenuation can be viewed as the random removal of some of the photons, and that randomness means adding noise.

2023-05-16

Can one simulate the relative intensity noise spectrum from a laser using RP Fiber Power?

That depends on the situation. For example, it can be done for a mode-locked laser. For some continuous-wave multimode laser, for example, it would be difficult, involving things like mode competition.

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