定义：
利用干涉效应的光学器件。

干涉仪是利用干涉效应的一种光学装置。一般来说，最初入射光先经过某种分束器（部分透射反射镜）分成单独的两束光，可能有的光束会经过外界环境的影响（例如，长度变化或者经过折射率变化的透明介质），然后在另一个分束器处光束再次符合。得到的光束功率的空间分布就可以用于测量。 

目录

• 干涉仪的类型 
• 1.1 马赫-曾德尔（Mach-Zehnder）干涉仪
• 1.2 迈克尔逊干涉仪
• 1.3 法布里-珀罗干涉仪
• 1.4 Sagnac干涉仪
• 1.5 共路干涉仪
• 1.6 光纤干涉仪
• 干涉仪的物理原理
• 应用
• 噪声影响

干涉仪的类型 
马赫-曾德尔（Mach-Zehnder）干涉仪 

图1：马赫-曾德尔干涉仪。
马赫-曾德尔是由物理学家Ludwig Mach和Ludwig Zehnder提出的。如图1所示，它采用两个单独的分束器（BS）来分离光束和合束，并且具有两个输出端，将输出光输出至光电探测器。干涉仪的两臂近似相等（如图所示），也可以不同（例如，单独加入一个延迟线）。在两输出端口处的功率分配情况与两臂长差和波长有关。 
如果干涉仪排列整齐，可以调节臂长差（例如，通过细微移动其中一个反射镜），这样在某一光学频率时，总的光功率从一个端口输出。而排列不好的光束（例如，一个反射镜稍稍倾斜），在两个输出端都会有干涉条纹，并且臂长差的变化会影响干涉条纹的形状，然而总功率的分布情况不会有很大的变化。 

迈克尔逊干涉仪 

图2：迈克尔逊干涉仪。
迈克尔逊干涉仪是由Albert Abraham Michelson发明的，采用单个分束器来进行分束或者合束。如果两个反射镜放置的严格垂直（见上面的图），可以只得到一个输出，而另一输出端口返回至光源。如果该光学反馈是不需要的（例如在激光器中，会引起不稳定），或者需要第二个输出端口，那么光束可以在分束器另外的位置进行合束。一种可能方案是采用激光反射镜，如下面的图；其另一个优势在于干涉仪中激光反射镜的轻微不对准没有太大影响。或者，也可以采用非垂直入射的简单的反射镜。 
如果臂长差不为0，如图2中，只有在有限带宽内可以实现干涉相消或者相长。迈克尔逊干涉仪最开始在注明的迈克尔逊-莫雷实验中采用的是宽带光源，这样干涉仪的臂长差需要近似为0。 
迈克尔逊干涉仪有很多不同的变化形式。例如，Twywan-Green干涉仪就是采用单色点光源的迈克尔逊干涉仪。它用来表征光学元件。 

法布里-珀罗干涉仪 

图3：法布里-珀罗干涉仪。
法布里-珀罗干涉仪（图3）包含两个平行的反射镜，光可以在其中往返多次。（该干涉仪的单片形式可以采用两边都有反射涂层的玻璃片。）当反射镜具有很高反射率时，这一器件具有很锐的共振曲线（高精细度），即只有当光频率接近某一值时才有很高的透射率。基于这些特性，对于距离的测量分辨率要高于对波长的测量。类似的，共振频率测量的也非常准确。 
一个改进的形式为Fizeau干涉仪，其中第二个反射镜是全反射的，并且稍微倾斜。反射光被用来表征光学组分。 
另一种特殊的法布里-珀罗干涉仪可用于色散补偿，称为Gires-Tournois干涉仪。 

Sagnac干涉仪 
Sagnac干涉仪（以法国物理学家Georges Sagnac命名）在环路中有两相向传播的两束光，通过多个反射镜（如图4）或者采用光纤来实现。如果整个干涉仪绕着垂直于平面的轴旋转，会在两束相反方向的光中产生相位差（Sagnac效应）。测量旋转的灵敏度与环路面积成正比，再乘以环路的圈数（如果采用光纤，该数值会很大）。可以达到足以探测地球自转的角速度。 
Sagnac干涉仪通常用在惯性导航系统中。 
共路干涉仪 
有些干涉仪采用同一个光路径但是利用两光束不同的偏振态。其优势在于几何光路上的涨落对干涉仪的输出没有影响，干涉仪可以作为敏感的双折射探测器。 
光纤干涉仪 
以上所有的干涉仪类型都可以采用光纤。光纤干涉仪不采用分束器，而是利用光纤耦合器。 
一个问题就是光在光纤中传播偏振态会发生变化。这通常需要加入一个光纤偏振控制器（有时需要重新调整）或者采用保偏光纤。 
同样需要注意的是光纤中的温度变化（以及弯曲）会影响光学相移。如果不同光学属于不同的干涉臂就会存在问题。然而，也有的光纤干涉仪采用统一光纤作为两个干涉臂，例如，利用相同光纤的两个不同的偏振方向。 

干涉仪的物理原理 
干涉仪采用不同的物理原理。例如，迈克尔逊干涉仪被用在不同的地方，采用不同的光源和光电探测器： 

• 当采用很小光学带宽的光源时（甚至单频激光器），当臂长差变化时，探测器的信号就会发生周期性的变化。这一信号可以测量灵敏度远小于波长的情况，但是有一些模糊。例如，单纯的增加或者减小臂长差会使探测信号产生相同的变化。这一问题可以通过采用波动反射镜来调节臂长差，并且在探测器上控制产生的调制。采用双波长测量也是消除模糊的一种方法。 
• 如果探测器是一种摄像机（例如，CCD芯片），并且表面很平滑，可以通过记录具有不同相移（相移干涉仪）的几个图像来重建其相位特性曲线。解相算法可以得到清晰的表面图。但是，这种方法对于粗糙的表面或者表面具有陡变。 
• 白光干涉仪采用的是宽带光源（例如，超辐射发光二极管），因此只能在零臂长差处很窄范围内观察到干涉条纹。这样就可以消除上面提到的条纹模糊。 
• 波长调谐激光器可用来产生多个波长进行探测。通过观察到的信号，臂长差可以非常准确的得到。这也可以采用二维的探测器（例如，CCD摄像机）。 
• 如果有意使其中的一个反射镜倾斜，可以观察到干涉条纹。任意改变臂长差都会使条纹发生移动。这种方法不仅能够很灵敏的测量相位变化，还可以测量相位随位置的变化。 

另一种干涉方法为空间干涉仪。这里利用的是光谱的干涉。光谱调制周期主要由时间延迟决定。 

应用 
干涉仪有很多方面的应用，不仅仅可以用于长度测量。例如： 

• 测量距离（或者位置的改变，即位移）的精度可以大于一个光学波长（极限情况下，例如探测重力波，灵敏度小于波长几个量级） 
• 测量激光光束的波长（波长计），或者分析光束的波长组分 
• 控制光波长或频率的微小变化（通常利用法布里-珀罗干涉仪的透射曲线） 
• 测量旋转（采用Sagnac干涉仪） 
• 测量光学表面的平滑度 
• 测量激光器的线宽（自差线宽测量，鉴频器） 
• 测量微小折射率变化 
• 调制激光光束的功率或者相位，例如，在光纤通信系统中加入马赫-曾德尔调制器 
• 测量光学元件的色散 
• 作为光学滤波器 
• 通过光谱干涉仪得到超短脉冲的特性 根据应用的不同，干涉仪对光源的要求也不同。很多情况下，需要光谱很纯的光源，例如，单频激光器。有时，激光器需要是波长调谐的。还有的情况下（例如采用白光干涉仪测量色散），需要很大带宽和平滑光谱的光源。 

噪声影响 
干涉测量中存在激光器噪声，还受到量子噪声的影响。一般来说，分束器入射端口的真空噪声决定了灵敏度的标准量子极限（散粒噪声极限）。低于该极限的噪声水平可以通过注入压缩态光进入干涉仪来实现。

Definition: optical devices utilizing the phenomenon of interference

More specific terms: common-path interferometers, Fabry–Perot interferometers, Fizeau interferometers, Gires–Tournois interferometers, Mach–Zehnder interferometers, Michelson interferometers, Twyman–Green interferometers, white light interferometers

An interferometer is an optical device which utilizes the effect of interference. That can be done with different kinds of radiation, but this article specifically deals with optical interferometers, i.e., interferometer for light. Typically, such a device is based on the following operation principle: it starts with some input beam, splits it into two separate beams with some kind of beam splitter (a partially transmissive mirror), possibly exposes some of these beams to some external influences (e.g. some length changes or refractive index changes in a transparent medium), and recombines the beams on another beam splitter. The power or the spatial shape of the resulting beam can then be used e.g. for a measurement.

Interferometers frequently need to be made from high quality optical elements. For example, one often uses mirrors and optical flats with a high degree of surface flatness.

Types of Interferometers

Mach–Zehnder Interferometer

Figure 1: Mach–Zehnder interferometer.

The Mach–Zehnder interferometer was developed by the physicists Ludwig Mach and Ludwig Zehnder. As shown in Figure 1, it uses two separate beam splitters (BS) to split and recombine the beams, and has two outputs, which can e.g. be sent to photodetectors. The optical path lengths in the two arms may be nearly identical (as in the figure), or may be different (e.g. with an extra delay line). The distribution of optical powers at the two outputs depends on the precise difference in optical arm lengths and on the wavelength (or optical frequency).

If the interferometer is well aligned, the path length difference can be adjusted (e.g. by slightly moving one of the mirrors) so that for a particular optical frequency the total power goes into one of the outputs. For misaligned beams (e.g. with one mirror being slightly tilted), there will be some fringe patterns in both outputs, and variations of the path length difference affect mainly the shapes of these interference patterns, whereas the distribution of total powers on the outputs may not change very much.

Michelson Interferometer

Figure 2: Michelson interferometers.

A Michelson interferometer, as invented by Albert Abraham Michelson, uses a single beam splitter for separating and recombining the beams. If the two mirrors are aligned for exact perpendicular incidence (see the upper figure), only one output is accessible, and the light of the other output goes back to the light source. If that optical feedback is unwanted (as is often the case with a laser, which might be destabilized), and/or access to the second output is required, the recombination of beams can occur at a somewhat different location on the beam splitter. One possibility is to use retroreflectors, as shown in the lower figure; this also has the advantage that the interferometer is fairly insensitive to slight misalignment of the retroreflectors. Alternatively, simple mirrors at slightly non-normal incidence can be used.

If the path length difference is non-zero, as shown in both parts of the figure, constructive or destructive interference e.g. for the downward-directed output can be achieved only within a finite optical bandwidth. Michelson originally used a broadband light source in the famous Michelson–Morley experiment, so that he had to build an interferometer with close to zero arm length difference.

There are many variations of the Michelson interferometer. For example, a Twyman–Green interferometer is essentially a Michelson interferometer with expanded beams in its arms. It is used for characterizing optical elements.

For more details, see the articles on Michelson interferometers and Twyman–Green interferometers.

Fabry–Pérot Interferometer

Figure 3: Fabry–Pérot interferometer.

A Fabry–Pérot interferometer (Figure 3) consists of two parallel mirrors, allowing for multiple round trips of light. (A monolithic version of this can be a glass plate with reflective coatings on both sides.) For high mirror reflectance, such a device can have very sharp resonances (a high finesse), i.e. exhibit a high transmittance only for optical frequencies which closely match certain values. Based on these sharp features, distances (or changes of distances) can be measured with a resolution far better than the wavelength. Similarly, resonance frequencies can be defined very precisely.

A modified version is the Fizeau interferometer, which is used for characterizing optical surfaces.

Another special kind of Fabry–Pérot interferometer, used for dispersion compensation, is the Gires–Tournois interferometer.

For more details, see the articles on Fabry–Pérot interferometers.

Sagnac Interferometer

Figure 4: Sagnac interferometer.

A Sagnac interferometer (named after the French physicist Georges Sagnac) uses counterpropagating beams in a ring path, realized e.g. with multiple mirrors (as in Figure 4) or with an optical fiber. If the whole interferometer is rotated e.g. around an axis which is perpendicular to the drawing plane, this introduces a relative phase shift of the counterpropagating beams (Sagnac effect). The sensitivity for rotations depends on the area covered by the ring, multiplied by the number of round trips (which can be large e.g. when using many turns in an optical fiber). It is possible e.g. to obtain a sensitivity which is sufficient for measuring the rotation of the Earth around its axis.

Sagnac interferometers are used e.g. in inertial guidance systems.

Common-path Interferometers

Common-path interferometers use a common beam path but e.g. different polarization states for the two beams. This has the advantage that fluctuations of the geometric path length do not affect the interferometer output, whereas the interferometer can be a sensitive detector for birefringence. The Sagnac interferometer (see above) is another example; here, the interfering beams have opposite propagation directions.

Fiber Interferometers

All the interferometer types discussed above can also be implemented with optical fibers. Instead of beam splitters, one then uses fiber couplers.

A potential difficulty is that the polarization state of light may change during propagation in the fiber. This often requires one to include a fiber polarization controller (which may occasionally have to be readjusted) or to use polarization-maintaining fibers.

Also note that temperature changes in the fibers (as well as bending) can affect the optical phase shifts. This can be a problem if different fibers belong to different interferometer arms. However, there are also fiber interferometers where one fiber serves for both arms, e.g. using two different polarization directions in the same fiber.

Physical Principles of Interferometers

There are also substantially different principles of using interferometers. For example, Michelson interferometers are used in very different ways, using different types of light sources and photodetectors:

• When a light source with low optical bandwidth is used (perhaps even a single-frequency laser), the detector signal varies periodically when the difference in arm lengths is changed. Such a signal makes it possible to do measurements with a depth resolution well below the wavelength, but there is an ambiguity. For example, a monotonic increase or decrease of the arm length difference leads to the same variation of the detected signal. This problem may be solved by modulating the arm length difference e.g. with a vibrating mirror (or with an optical modulator) and by monitoring the resulting modulation on the detector in addition to the average signal power. Simultaneous operation of an interferometer with two wavelengths is another way of removing the ambiguity.
• If the detector is a kind of camera (e.g. a CCD chip) and the surfaces monitored are fairly smooth, the phase profile (and thus the profile of optical path length) can be reconstructed by recording several images with different overall phase shifts (phase-shifting interferometry). A phase-unwrapping algorithm can be used to retrieve unambiguously surface maps extending over more than a wavelength. However, such methods may not work for rough surfaces or for surfaces with steep steps.
• A white light interferometer uses a broadband light source (e.g., a superluminescent diode), so that interference fringes are observed only in a narrow range around the point of zero arm length difference. In that way, the above-mentioned ambiguity is effectively removed.
• A wavelength-tunable laser can be used to record the detector signal for different optical frequencies. From such signals, the arm length difference can be unambiguously retrieved. This works also with two-dimensional detectors (e.g. CCD cameras).
• If one of the mirrors is intentionally tilted, an interference fringe pattern is obtained. Any change in arm length difference will then move the fringe pattern. This method makes it possible to measure phase changes sensitively and also to measure position-dependent phase changes, e.g. in some optical element.
• Instead of measuring distances, one can use interferometers for characterizing light. For example, the optical spectrum can be obtained by measuring the detector signal vs. arm length difference and applying a Fourier transform (Fourier transform spectroscopy). One can also retrieve wavelength-dependent phase shifts, for example for measuring chromatic dispersion of optical elements.

Another class of interferometric methods is named spectral phase interferometry. Here, interference in the spectral domain is exploited. The spectral modulation period is essentially determined by a time delay.

Applications

Interferometers can be used for many different purposes – by far not only for length measurements. Some examples are:

In 2016 it has been announced that a large interferometer operated at LIGO Hanford has detected gravitational waves resulting from the inspiral of two large black holes. An extraordinarily high detection sensitivity had to be achieved for that.

• for the measurement of a distance (or changes of a distance or a position, i.e., a displacement) with an accuracy of better than an optical wavelength (in extreme cases, e.g. for gravitational wave detection, with a sensitivity many orders of magnitude below the wavelength)
• for measuring the wavelength e.g. of a laser beam (→ wavemeter), or for measuring the full optical spectrum
• for monitoring slight changes in an optical wavelength or frequency (typically using the transmittance curve of a Fabry–Pérot interferometer) (frequency discriminators)
• for measuring rotations (with a Sagnac interferometer)
• for measuring slight deviations of an optical surface from perfect flatness (or from some other shape)
• for measuring the linewidth of a laser (→ self-heterodyne linewidth measurement, frequency discriminator)
• for revealing tiny refractive index variations or induced index changes in a transparent medium
• for modulating the power or phase of a laser beam, e.g. with a Mach–Zehnder modulator in an optical fiber communication system
• for measurements of the chromatic dispersion of optical components
• as an optical filter
• for the full characterization of ultrashort pulses via spectral phase interferometry

The first very prominent interferometer-based scientific experiment was the Michelson–Morley experiment in the context of the search for an ether wind. The most recent large discovery based on measurements with interferometers was the detection of gravitational waves [15]. Interferometers played vital roles also in many other scientific discoveries, e.g. in quantum optics.

Depending on the application, the demands on the light source in an interferometer can be very different. In many cases, a spectrally very pure source, e.g. a single-frequency laser is required. Sometimes, the laser has to be wavelength-tunable. In other cases (e.g. for dispersion measurements with white light interferometers), a light source with a very broad and smooth optical spectrum is required.

Noise Influences

Interferometric measurements can be subject to various types of noise:

• Mechanical noise (vibrations, shocks etc.) can affect measurements; one often needs to employ sophisticated mechanical means for suppressing such influences.
• There can be technical noise from light sources, e.g. laser noise, but also quantum noise influences. Typically, vacuum noise entering the open input port at a beamsplitter defines the standard quantum limit (shot noise limit) for the sensitivity [2, 5]. A noise level below that limit can sometimes be achieved by injecting squeezed states of light into an interferometer [2, 4, 12].

Bibliography