相对强度噪声(relative intensity noise)

定义：缩写：RIN 定义：光强（实际是功率）的噪声，归一化为其平均值。

在激光器的强度噪声（光功率涨落）中，通常需要指出相对强度噪声（RIN），是指归一化为平均功率的功率噪声。激光的功率可表示为：

包含平均值和功率涨落δP，其平均值为0。相对强度噪声就是δP除以平均功率，后面将这一比值称为I。因此相对频率噪声可以由功率谱密度（PSD）统计描述为：

它依赖于噪声频率f。可以通过归一化功率涨落自相干函数的傅里叶变换进行计算，或者利用光二极管和电子光谱分析仪进行测量。（公式中的因子2来自于工程理论要求的单边PSD）RIN PSD的单位为Hz−1，但是常常取它以10为底的对数再乘以10来表示，单位为 dBc/Hz（参阅分贝）。PSD还可以在噪声频率区间 [f1, f2]上积分来得到相对强度噪声的均方根为：

这在目前很常用。需要注意的是，将相对强度噪声表示为百分比并不合适，因为这样不能给出其均方根值的意义。

图1：平均功率为100 mW的1064nm Nd:YAG激光器的相对强度噪声谱。噪声频率大于5MHz时达到散粒噪声水平−174 dBc/Hz。峰值对应弛豫振荡过程，低频率时的附加信号来自于泵浦光源。

来自散粒噪声的RIN当光束存在线性衰减时，光束的RIN仍然是一个常数。但是如果RIN受限于散粒噪声，以上描述则不准确。在这种情况下，RIN表示为：

举个例子，波长为1064nm功率为1 mW的激光光束的强度噪声等于散粒噪声极限时，RIN为3.73 × 10−16 Hz−1或者−154 dBc/Hz。PSD与噪声频率无关（白噪声），并且随着平均功率的减小会增加。这可以理解为衰减过程引入了附加的量子噪声。RIN测量需要采用光二极管探测整个激光器功率，同时最小化电子学器件带来附加噪声的影响。

Acronym: RIN

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

More general term: intensity noise

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

with an average value and a fluctuating quantity δP with zero mean value. The relative intensity is then δP 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):

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 [f1, f2] of noise frequencies to obtain a root mean square (r.m.s.) value of relative intensity noise

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.

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

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), and it increases with decreasing average power. 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.