The Michelson interferometer is an optical device that produces interference fringes by recombining light that has traveled along two separate paths. It is historically renowned for the Michelson–Morley experiment conducted by its inventor, Albert Michelson, which verified the constancy of the speed of light. Today, it plays a critical role not only in precise optical measurements and spectroscopy but also as a foundational tool for interference-based techniques in advanced research.

In this interferometer, optical components such as a beam splitter, compensating plate, and mirrors are precisely arranged so that the bright and dark patterns produced by interference can be used to accurately determine parameters like wavelength and refractive index. By strictly controlling experimental conditions, even extremely small changes can be detected, enabling the verification of theoretical predictions and the measurement of physical constants. When conducting interference experiments with white light, a compensating plate is essential, and careful adjustment is key to achieving accurate measurements.

This article provides a comprehensive overview of the Michelson interferometer, covering its basic principles, practical applications, calculation methods, and the importance of calibration. It also addresses the effects of environmental factors such as temperature, air pressure, and vibrations on measurements, offering practical insights. The explanation is structured to be accessible for beginners while also providing deeper insights useful for experimental work and research.

1. Principle of the Michelson Interferometer

To understand the fundamentals of the Michelson interferometer, it is essential first to grasp how interference fringes are generated by splitting and recombining light paths.

The Michelson interferometer works by dividing incoming light into two separate paths using a beam splitter and then recombining them. The phase difference that arises due to the difference in path lengths causes constructive or destructive interference, producing alternating bright and dark fringes on a screen or detector. These fringes visualize the wave nature of light and serve as a precise source of information for measuring parameters such as wavelength and refractive index. The shape of the interference fringes can also vary depending on the type of light source and the arrangement of mirrors, which is a noteworthy characteristic.

1-1. Components of a Michelson Interferometer

The main components of a Michelson interferometer include a beam splitter (partially reflective mirror), two highly polished reflective mirrors, a compensating plate, and a screen or detector for observing the interference fringes. The beam splitter divides the incident light, directing it along two separate paths from the same light source. Each path has a mirror that reflects the light back, setting up the conditions for interference. Precise alignment of these elements allows the creation of optical path differences on the order of microns, enabling stable and well-defined interference fringes.

1-2. Role and Importance of the Compensating Plate

The compensating plate is a transparent element used to correct phase differences caused by unequal optical path lengths. In experiments using white light, different wavelength components experience varying optical path differences, making fringe observation difficult without a compensating plate. By introducing the compensating plate, the optical path lengths of both arms are equalized, allowing stable fringes to be observed even with white light. It is important to note that the thickness and refractive index of the compensating plate affect measurement accuracy, so careful consideration is required during its use.

1-3. Fringe Formation and Bright-Dark Conditions

Interference fringes are formed based on whether the optical path difference is an integer multiple or a half-integer multiple of the light wavelength. Specifically, constructive interference occurs at integer multiples, producing bright fringes, while destructive interference occurs at half-integer multiples, producing dark fringes. By precisely analyzing these fringe patterns, physical quantities such as wavelength and refractive index can be determined with high accuracy. Observing interference fringes requires a highly stable environment, and measures to minimize vibrations and temperature fluctuations are essential for reliable measurements.

2. Applications of the Michelson Interferometer

The Michelson interferometer is utilized across a wide range of measurement fields, playing an important role from fundamental optical research to practical technology development.

Because this interferometer produces clear interference fringes, it is used for a variety of purposes such as precise wavelength measurement and determination of a material’s refractive index. For example, by recording the change in the interference pattern while finely controlling the movement of one mirror, it is possible to determine the wavelength of laser light with high resolution. In addition, research combining the interferometer with nonlinear optical materials has been advancing to build even more sensitive detection systems, significantly contributing to the progress of cutting-edge science.

2-1. Measurement of Light Source Wavelength

In wavelength measurement using a Michelson interferometer, the wavelength of light can be determined by counting the number of fringe shifts observed when one of the mirrors is moved a known distance. For instance, by correlating the mirror displacement with the number of fringe movements, the wavelength can be precisely calculated. This technique is also applied in evaluating the spectral characteristics of lasers and plays an important role in high-precision spectroscopy. To improve experimental reproducibility, careful control of mirror movement and minimization of environmental vibrations are essential factors.

2-2. Measurement of the Refractive Index of Gases

When measuring the refractive index of a gas, a gas cell is inserted into one arm of the interferometer, and changes in the interference fringes with and without the gas are observed. By measuring the phase shift caused by the gas in the optical path, the refractive index of the gas can be quantified. To accurately detect the fringe shift compared with a vacuum, it is essential to maintain stable temperature and pressure inside and around the cell. This technique is increasingly being applied not only in laboratory research but also in industrial fields as part of gas analysis technologies.

2-3. Application to Distance Measurement Technologies

A Michelson interferometer using a laser is also applied to high-precision distance and positioning systems. For example, in precision machinery alignment or distance measurement in space development, laser interference enables resolutions on the order of micrometers. In this method, the change in optical path difference is accurately detected and continuously fed back to control the position of the target object. When effective measures are taken to compensate for temperature variations and vibration noise during measurement, a highly reliable system can be established.

2-4. Utilization of Nonlinear Michelson Interferometers

Interferometers that utilize nonlinear optical effects can detect information with much higher sensitivity than conventional Michelson interferometers. For example, when light passes through semiconductor materials or nonlinear crystals, wavelength conversion occurs, allowing the observation of unique interference patterns. Such nonlinear interferometers are being studied in a wide range of fields, including biological tissue imaging, trace substance detection, and ultrashort pulse laser spectroscopy. Although the measurement systems are more complex, they offer extremely high sensitivity and are therefore attracting significant attention in cutting-edge research.

3. Extension of Interferometric Methods and Environmental Compensation

To perform interferometric measurements stably, it is essential to address environmental factors and to compare different types of interferometers.

Environmental conditions such as temperature and air pressure significantly affect the propagation of light in interferometric measurements. Vibrations can cause fluctuations in the interference fringes, leading to reduced measurement accuracy. By considering the characteristics of other types of interferometers and applying environmental compensation methods, it is possible to establish a more stable measurement environment. Preparing conditions from the experimental planning stage—such as selecting the setup location or implementing vacuum systems—is key to improving measurement precision.

3-1. Various Forms of Interferometry

In addition to the Michelson type, interferometers also include forms such as the Mach–Zehnder interferometer and the Fabry–Pérot interferometer. The Mach–Zehnder interferometer propagates light along separated paths, which often results in a larger apparatus, but it can offer excellent stability in certain measurement applications. The Fabry–Pérot interferometer, using two parallel reflective surfaces, is widely used for observing spectra with high resolution. Understanding these techniques allows one to select the interferometer best suited to specific measurement goals.

3-2. The Reason Environmental Compensation Is Necessary

Changes in temperature and air pressure affect both the refractive index of air and the physical dimensions of the apparatus, causing shifts in the positions of interference fringes. Additionally, vibrations or acoustic noise can induce minute movements in mirrors and beam splitters, destabilizing the interference pattern. To achieve stable measurements, comprehensive measures are essential, such as using vibration-isolation tables, installing vacuum chambers, and stabilizing the laser light source. These environmental compensation strategies are crucial for detecting extremely small optical path differences with high precision.

4. Calculation Problems and Calibration of the Michelson Interferometer

Accurate calculations and proper calibration of the apparatus are essential for ensuring the reliability of measurements using an interferometer.

Since the interference phenomenon is based on the relationship between optical path difference and wavelength, expressing this relationship mathematically is directly linked to measurement accuracy. Furthermore, if the small errors inherent in the instrument itself are not corrected, discrepancies can arise between the theoretical values and the actual measurements. Therefore, it is common practice to perform calibration through initial setup and periodic adjustments, using known standards or reference samples to enhance the reliability of the measured values.

4-1. Basic Calculation Example

The basic calculations in a Michelson interferometer involve determining how many times the optical path difference corresponds to the wavelength and then deriving the phase conditions of the interference fringes. For example, if the optical path difference is ΔL and the wavelength of the light is λ, a bright fringe is formed when ΔL/λ is an integer, and a dark fringe is formed when it is a half-integer. In practical measurements, a major goal is to determine λ by using the displacement of the mirrors and the number of fringe shifts. Having a solid grasp of these calculation steps makes it easier to analyze experimental results in conjunction with potential sources of error.

4-2. Calculation Problems for the Refractive Index of Air

The refractive index of air varies slightly even at the laboratory scale, and this effect cannot be ignored in long-term or high-precision measurements. A common method to estimate the refractive index is to use the fringe shifts to capture changes in the optical path difference in air. By applying a gas model that accounts for factors such as temperature, pressure, and humidity, and comparing it with experimental data, the precise value of the refractive index can be determined. These calculations are a crucial process for interpreting measurement results with high accuracy.

4-3. The Importance of Calibration

In calibration, the accuracy of the interferometer is periodically checked using reference light sources or length standards. For example, measurement results are compared against a well-known laser wavelength, and if any systematic deviation is detected, the instrument is finely adjusted. Omitting such procedures can significantly compromise the reliability of measurement data, which is why calibration is treated as an essential task in both research and industrial settings. For interferometers in long-term operation, regular maintenance schedules are often implemented alongside calibration.

Summary

Up to this point, we have provided a comprehensive overview of the Michelson interferometer, covering its basic operation, applications, relevant calculations, calibration procedures, and the importance of environmental corrections.

The Michelson interferometer has long supported numerous research achievements as an instrument capable of measuring fundamental optical quantities, such as wavelength and refractive index, with high precision. Today, the principles of this device are applied in large-scale projects, such as laser interferometer-based gravitational wave detectors, and its technological advancements and range of applications are expected to continue expanding.

Accurate measurements rely not only on optical path adjustments using compensating plates and proper calibration but also on stabilizing external environmental factors, such as temperature and vibrations. By comprehensively understanding the interferometer from its fundamentals to its applications, one can achieve more reliable and advanced measurements and research using the Michelson interferometer.