定义：
激光器噪声特性规范。

例如激光输出的噪声强度通常需要量化--特别是在频率测量、敏感光谱测量或光纤通信等应用场合，其中设备或系统的性能受到噪声的限制。

激光器和光放大器噪声规格举例
强度噪声通常是通过分析激光输出与光电二极管和相关的电子设备，如电子光谱分析仪测量。它可以指定的功率谱密度的相对强度噪声作为噪声频率的函数。为了某些目的，均方根（RMS）值的平方根，本质上是对功率谱密度的积分超过一定的频率范围（1赫兹–1兆赫），是足够的。然而，均方根值没有测量带宽规格是荒谬的。带宽确定如下：

• 较高的频率限制通常由光电探测器（包括检测电子）的速度决定.。显然，一个缓慢的检测器是不能够记录快速波动，因此表示较弱的噪声比一个快速检测器。数字录音，测量带宽为采样频率的一半（→Nyquist定理），而在实践中往往更低，低通滤波已被应用在采样之前为了避免混叠效应。
• 较低的频率限制大约是逆测量时间。当强度波动被记录在一些有限的时间间隔，人们不能知道多少的平均记录的功率偏离平均功率超过较长的时间。因此，噪声的影响的频率低于逆测量时间被抑制。

光学相位噪声可以用功率谱密度（PSD）量化的相位波动。另外，对瞬时频率波动的PSD可以指定。这样的功率谱密度往往发散为零频率，所以集成到零频率是不可能的。简单的随机行走过程，一个连贯的时间或相干长度或一个linewidthvalue规格可适当。注意线宽值通常取决于测量时间。

频率噪声与相位噪声直接相关，它是瞬时频率的噪声，后者与相位的时间导数有关。

一列脉冲的定时抖动可以被量化为时间差的功率谱密度（例如一些无声的参考）或定时相位。这也是常见的指定一定范围内的噪声频率的有效值。

在频率计量中，使用艾伦偏差或艾伦方差作为时间函数是常见的.。这些数量可以计算出的功率谱密度，而相反的计算是不明确的。

电子或光学放大器的噪声系数量化放大器的过量噪声。

在频率测量，通常使用归一化相位波动x（t） = δφ（T） / （2π ν0），即相位波动除以平均角频率。归一化相位波动的时间导数，然后提供归一化的频率波动y（t），即，相对于平均频率的瞬时频率的波动。对不同频率源的相位噪声比较，现在去比较合适的功率谱密度Sx（f）归一化相位波动或Sy（F）的归一化频率的波动，而不是相位或频率漂移本身，因为这些标准的波动是什么决定了精度和时钟如准确。

环境条件
激光噪声通常取决于环境条件。因此，显然是必要知道什么是环境条件，某些规格适用。特别地：

• 它是否适用于恒定的室温，或在允许的操作温度范围内的任意温度变化？
• 它是有效的后立即打开设备，或只有在很长的预热时间？
• 是一个无振动的环境假设？

后者是特别重要的波束指向波动的规格。

这是不容易指定的环境噪声源，如振动的影响下的激光噪声，因为它是难以量化这些影响。此外，它们的影响可能强烈地依赖于噪声频率：一个机械装置可能有一些共振，使设备在某些频率的振动非常敏感。

常见问题
出于各种原因，正确的噪声规格往往没有达到：

• 噪声的数学描述是复杂的，往往没有适当的物理或工程课程处理。作为一个结果，无意义的噪声规格在产品数据表中普遍存在，甚至在科学文献。
• 激光物理，有各种不同类型的噪声，这在概念上和不可见的方式身体相关的（例如：光相位噪声和定时锁模激光器相位噪声）。因此，物理洞察力和数学知识一样重要。
• 噪声测量受许多不平凡的技术问题。例如，电子频谱分析仪的内部工作的详细知识，需要获得正确的测量结果，这样的设备。黑盒处理（使用不知道它们是如何产生的设备读数）容易导致错误的结果，例如通过不适当的设备设置或未能应用某些校正因子（例如，在频谱分析仪对数平均）。

Definition: specifications for the noise properties of lasers, for example

The strength of noise e.g. of the output of a laser often needs to be quantified – particularly in the context of applications such as frequency metrology, sensitive spectroscopic measurements, or optical fiber communications, where the performance of devices or systems is limited by noise.

Examples of Noise Specifications of Lasers and Optical Amplifiers

Intensity Noise

Intensity noise is often measured by analyzing the laser output with a photodiode and related electronic equipment such as an electronic spectrum analyzer. It can be specified with a power spectral density of the relative intensity noise as a function of noise frequency. For some purposes, a root-mean-square (r.m.s.) value, essentially the square root of the integral of the power spectral density over some frequency range (e.g. 1 Hz – 1 MHz), is sufficient. However, r.m.s. values without specification of the measurement bandwidth are nonsensical. That bandwidth is determined as follows:

• The higher frequency limit is often set by the speed of the photodetector (including detection electronics). Obviously, a slow detector is not able to record fast fluctuations, and therefore indicates weaker noise than a fast detector. For digital recordings, the measurement bandwidth is at most half the sampling frequency (→ Nyquist theorem), and in practice often even lower, as low-pass filtering has to be applied before the sampling in order to avoid aliasing effects.
• The lower frequency limit is approximately the inverse measurement time. When the intensity fluctuations are recorded in some limited time interval, one cannot know how much the average of the recorded power deviates from the average power over longer times. Therefore, the influence of noise at frequencies below the inverse measurement time is suppressed, and its magnitude is unknown.

Phase and Frequency Noise

Optical phase noise can be quantified by the power spectral density (PSD) of the phase fluctuations. Alternatively, the PSD of the fluctuations of the instantaneous frequency can be specified. Such power spectral densities often diverge for zero frequency, so that integration down to zero frequency (e.g. using a theoretically calculated PSD) is not possible. For simple random-walk processes, the specification of a coherence time or coherence length or of a linewidth value can be appropriate. Note that linewidth values often depend on the measurement time.

Frequency noise is directly related to phase noise; it is the noise of the instantaneous optical frequency, the latter being related to the temporal derivative of the optical phase.

In frequency metrology, it is common to use normalized phase fluctuations x(t) = δφ(t) / (2π ν₀), i.e., phase fluctuations divided by the mean angular frequency. The time derivative of the normalized phase fluctuations then delivers the normalized frequency fluctuations y(t), i.e., the fluctuations of the instantaneous frequency relative to the mean frequency. For a comparison of the phase noise of sources with different mean frequencies, it is appropriate to compare the power spectral densities S_x(f) of normalized phase fluctuations or S_y(f) of normalized frequency fluctuations, rather than of the phase or frequency excursions themselves, because these normalized fluctuations are what determines the precision and accuracy e.g. of a clock.

In frequency metrology, the use of a Allan deviation or Allan variance as a function of time is common. These quantities can be calculated from a power spectral density, whereas the opposite calculation is ambiguous.

Timing Noise

Timing jitter of a pulse train can be quantified as the power spectral density of the timing deviation (e.g. from some noiseless reference) or the timing phase. It is also common to specify an r.m.s. value for a certain range of noise frequencies.

Noise Figure

The noise figure of an electronic or optical amplifier quantifies the amplifier excess noise.

Ambient Conditions

Laser noise often depends on ambient conditions. Therefore, it is obviously essential to know what are the ambient conditions for which certain specifications apply. In particular:

• Does it apply to constant room temperature, or for arbitrary temperature changes within the allowed range of operation temperatures?
• Is it valid immediately after switching on the device, or only after a long warm-up time?
• Is a vibration-free environment assumed?

The latter is particularly important for specifications of beam pointing fluctuations.

It is not easy to specify laser noise under the influence of ambient noise sources such as vibrations, since it is difficult to quantify these influences. Also, their impact may strongly depend e.g. on the noise frequency: a mechanical setup may have some resonances, making the device very sensitive to vibrations at certain frequencies.

Common Problems

For various reasons, correct noise specifications are often not achieved:

• The mathematical description of noise is sophisticated, and often not properly treated in physics or engineering courses. As a result, nonsensical noise specifications are widespread in product data sheets and even in the scientific literature.
• In laser physics, there is a variety of different types of noise, which are conceptually and physically related in non-obvious ways (example: optical phase noise and timing phase noise of mode-locked lasers). Therefore, physical insight is as essential as mathematical knowledge.
• Noise measurements are subject to many non-trivial technical issues. For example, detailed know-how on the inner workings of electronic spectrum analyzers is required for obtaining correct results from measurements with such devices. A black-box treatment (using the device readings without knowing how they are generated) easily leads to wrong results, e.g. via inappropriate device settings or the failure to apply certain correction factors (e.g. for logarithmic averaging in the spectrum analyzer).