Michelson interferometer distance from prism to screen. Types of interferometers. Interference of monochromatic waves that propagate along the axis of the interferometer

30.03.2020

Michelson interferometer

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Description

The Michelson interferometer is one of the most common skeletal interferometer designs designed for various applications in the case when the spatial combination of objects generating interfering waves is impossible or for some reason undesirable.

A schematic representation of the Michelson interferometer design is shown in Fig. 1.

Schematic illustration of the Michelson interferometer design

Rice. 1

A beam of light from an almost point source S, located at the focus of the lens, is converted by this lens into a parallel beam (often in modern applications this beam is simply laser radiation, not collimated by an additional lens). Next, this beam is divided into two by a translucent flat mirror SM, each of which is reflected back by mirrors M 1.2, respectively. These two reflected beams form an interference pattern on the SC screen, the nature of which is determined by the ratio of the shapes of the wave fronts of both beams (see Fig. 2).

Wavefronts of beams forming an interference pattern

Rice. 2

Namely, these two beams at the point where the screen is located can have different radii of curvature of the wave fronts R 1,2, as well as the mutual inclination of the latter a. In particular, it is easy to understand that both indicated radii will be the same, and a =0, if and only if the mirrors M 1,2 are both flat (or generally the same shape), and the position of the mirror M 1 in space coincides with mirror image M 2 in the divisor SM, that is, M 2 "(see Fig. 1).

In this case, the illumination on the screen will be uniform, which means ideal alignment of the interferometer.

In the case of a№ 0, R 1 = R 2 (the distances from the divider to the mirrors are adjusted correctly, but the angles of inclination are not), a picture of equidistant direct interference fringes will appear on the screen, as in the interference of waves reflected from two faces of a thin wedge.

In the case of a =0, R 1 No. R 2 (correct angular adjustment, but incorrect distances of the mirrors to the divider) interference pattern represents concentric rings caused by the intersection of two spherical wave fronts of different curvature.

Finally, in the case of a =0, R 1 =R 2, but the non-ideal flatness of one of the mirrors, the picture will be irregular shape“Newton's rings” around the irregularities of the corresponding mirror surface.

All of these changes in the observed pattern occur with very small (tenths of a wavelength in spatial positioning and height of mirror irregularities, and tens of microradians in angular adjustment) deviations of the adjustment parameters from the ideal. If we take this into account, it becomes clear that the Michelson interferometer is a very precise device for monitoring the positioning of an object in space, its angular adjustment and flatness. Special methods for accurately measuring the intensity distribution in the screen plane make it possible to increase the positioning accuracy to several nanometers.

Timing characteristics

Initiation time (log to -8 to -5);

Lifetime (log tc from -5 to 15);

Degradation time (log td from -8 to -5);

Time of optimal development (log tk from -5 to -4).

Diagram:

Technical implementations of the effect

Technical implementation of the effect

Technical implementation is carried out in full accordance with Fig. 1 content part. The laser beam of a helium-neon laser (for clarity, it is better to expand it with a telescope to a diameter of 10-15 millimeters) is divided into two by a translucent mirror, reflected from two flat mirrors, and a certain interference pattern is obtained on the screen. Then, by carefully adjusting the lengths of the arms and the angular position of the mirrors, the interference pattern in the area of beam overlap on the screen disappears.

Applying an effect

The applications of the Michelson interferometer in technology are very diverse. For example, it can be used for remote monitoring of small deformations (deviations from flatness) of an object (replacing one of the mirrors in Fig. 1). This approach is very convenient when, for one reason or another, close proximity of the object and the reference surface (the second mirror in Fig. 1) is undesirable. For example, the object is very hot, chemically aggressive, and the like.

But the most significant technical application of the Michelson interferometer is the use of this circuit in optical gyroscopes based on the Sagnac effect to control the shift of the interference fringe generated by rotation.

Literature

1. Physics. Big encyclopedic dictionary. - M.: Big Russian Encyclopedia, 1999.

2. Sivukhin D.V. General course physics. Optics. - M.: Nauka, 1985.

3. Landsberg G.S. Optics. - M.: Nauka, 1976.

Keywords

interference
monochromatic
ray path difference
refractive index
zero interference band

Sections of natural sciences:

Interfer O meter - a measuring instrument that uses wave interference. Exist interferometers for sound and electromagnetic waves: optical (ultraviolet, visible and infrared regions of the spectrum) and radio waves of various lengths. Apply interferometers very widely. The most widespread are optical interferometers, which will be discussed below. They are used to measure the wavelengths of spectral lines, refractive indices of transparent media, absolute and relative lengths, angular sizes of stars, to control the quality of optical parts and their surfaces, to control the cleanliness of processing metal surfaces, etc.

The principle of operation of all interferometers is the same, and they differ only in the methods of obtaining coherent waves and in what quantity is directly measured. A beam of light using one or another device is spatially divided into two or larger number coherent beams that travel through different optical paths and are then brought together. At the point where the beams converge, an interference pattern is observed, the appearance of which, i.e., shape and mutual arrangement interference maxima and minima, depends on the method of dividing the light beam into coherent beams, on the number of interfering beams, the difference in their optical paths (optical path difference), relative intensity, size of the source, spectral composition of the light.

Methods for producing coherent beams in interferometers are very diverse, so there is big number their various designs. Based on the number of interfering light beams, optical interferometers can be divided into multipath And double beam.

An example of a two-beam interferometer is Michelson interferometer (Figure 3). Parallel beam of light source L, falling on a translucent plate P 1, divided into bundles 1 and 2 . After reflection from mirrors M 1 and M 2 and re-passing through the plate P 1 both beams enter the lens O 2, focal plane D which they interfere. Optical path difference D = 2( A.C. - AB) = 2l, Where l- distance between mirror M 2 and virtual image M 1¢ mirrors M 1 on record P 1 . Thus, the observed interference pattern is equivalent to the interference in an air plate of thickness l. If the mirror M 1 is positioned so that M 1¢ and M 2 are parallel, then bands of equal inclination are formed, localized in the focal plane of the lens O 2 and having the shape of concentric rings. If M 2 and M 1 ¢ form an air wedge, then stripes of equal thickness appear, localized in the plane of the wedge M 2 M 1 ¢ and representing parallel lines.

The Michelson interferometer is widely used in physical measurements and technical devices. With its help it was first measured absolute value wavelength of light, the independence of the speed of light from the movement of the Earth has been proven.

There are two-beam interferometers designed to measure the refractive indices of gases and liquids - interference refractometers. One of them is I. Zhamena ( Figure 4). beam of light S after reflection from the front and back surfaces of the first plate P 1 is divided into two bundles S 1 and S 2. Passing through the ditches K 1 and K 2, beams reflected from the surfaces of the plate P 2, fall into the telescope T, where they interfere, forming bands of equal inclination. If one of the cuvettes is filled with a substance with a refractive index n 1 and the other with n 2, then according to the shift of the interference pattern by the number of fringes m compared to the case when both cuvettes are filled with the same substance, one can find D n = n 1 - n 2 = =m l/ l (l- cuvette length).

IN Rayleigh interferometer (Figure 6 ) interfering beams are separated using two slit diaphragms D. After passing the cuvettes K 1 and K 2, these beams are collected in the focal plane by the lens O 2, where an interference pattern of stripes of equal inclination is formed, which is viewed through the eyepiece O 3. In this case, part of the beams emerging from the diaphragms passes below the cells and forms its own interference pattern located below the first one. If the refractive index n 1 and n 2 substances in the cuvettes, then due to the difference in the path in the cuvettes, the upper picture will shift relative to the lower one. Measuring the amount of displacement by the number of stripes m, we can find D n.

The accuracy of measuring refractive indices using interference refractometers is very high and reaches the 7th and even the 8th decimal place.

Fabry-Perot multibeam interferometer (Figure 7) consists of two glass or quartz plates P 1 and P 2, on whose surfaces facing each other and parallel to each other are applied mirror coatings with a high (85-98%) reflection coefficient. Parallel beam of light incident from the lens O 1, as a result of multiple reflections from the mirrors, forms a large number of parallel, coherent beams with a constant path difference between adjacent beams. As a result of multipath interference in the focal plane L lens O 2, an interference pattern is formed in the form of concentric rings with sharp intense maxima, the position of which depends on the wavelength. Therefore, I. Fabry-Perot decomposes complex radiation into a spectrum.

Figure 7 - Fabry-Perot interferometer

I. Fabry-Perot is used as a high-resolution interference spectral device. Special scanning I. Fabry - Perot with photoelectric registration are used to study spectra in the visible, infrared and centimeter wavelength regions. A variation of I. Fabry-Perot are optical resonators of lasers, the emitting medium of which is located between the I. mirrors.

Multibeam interferometers also include various types of diffraction gratings, which are used as interference spectral instruments.

Conclusion

Interference– one of the brightest manifestations of the wave nature of light. This interesting and beautiful phenomenon is observed when two or more light beams are superimposed.

Interferometers- very sensitive optical instruments that allow you to determine minor changes in the refractive index of transparent bodies (gases, liquids and solids) depending on pressure, temperature, impurities, etc.

The applications of interferometers are very diverse. In addition to the above, they are used to study the quality of manufacturing of optical parts, measure angles, study fast processes occurring in the air flowing around aircrafts, etc. Using an interferometer, Michelson was the first to compare the international standard meter with the length of a standard light wave. Interferometers were also used to study the propagation of light in moving bodies, which led to fundamental changes in ideas about space and time.

Related information.

Optical interferometers are used to change optical wavelengths, spectral lines, the refractive index of polarization media, absolute and relative lengths of objects, angular sizes of stars to control the quality of optical parts and their surfaces.

Operating principle:

A beam of light using various devices is divided into 2 or more coherent beams, which pass through different optical paths, are then brought together and the result of their interference is observed.

The type of interference pattern depends on the method of dividing the light beam into coherent beams, on the number of interfering beams, the optical path difference, the relative intensity, the size of the source, and the spectral composition of the light.

Optical interferometers can be divided according to the number of beam interferometers:

Double-beam and multi-beam.

Multibeam interferometers are used as spectral instruments to study the spectral composition of light.

Dual beams can be used to measure physical technical measurements.

Michelson: A parallel beam of light from the source, passing through O1, hits the translucent plate P1 and is divided into two coherent beams.

Next, beam 1 is reflected from mirror M1, beam 2 is reflected from mirror M2. Beam 2 repeatedly passes through plate P1, 1 does not pass through. Both beams pass in the direction AO through the lens O2 and interfere in the focal plane of the diaphragm D. The observed interference pattern corresponds to the interference in the air layer formed by the mirror M2 and the virtual image of the mirror M1 in the plate P1.

Air layer thickness l (optical path difference = 2l).

If the mirror M1 is positioned so that M2 and the virtual image M1 are parallel, then the interference pattern consists of fringes of equal inclination localized in the focal plane of the lens O2. And the picture consists of concentric rings.

Stripes of equal inclination are formed when a transparent layer of constant thickness is illuminated by a non-parallel beam of monochromatic radiation.

If M2 and the image M1 form an air wedge, then stripes of equal thickness appear and appear as parallel lines.

Jamin Interferometer:

Designed for measuring refractive indices in gases and liquids.

A beam of monochromatic light S, after reflection of the front and back surfaces of a glass plate P1, is divided into 2 beams S1 and S2.

In the path of the beams there are 2 cuvettes K1 and K2, through which the beams are reflected from P2.

P2 is rotated relative to P1. and fall into the telescope T, where they interfere, forming straight stripes of equal inclination.

If one of the cuvettes is filled with a substance with a refractive index n1, and the second with n2, then by shifting the interference pattern by the number of fringes m compared to the case when 2 both cuvettes are filled (or not), it is possible to determine n1 and n2, which relate Δn.

The relative error in measuring the refractive index reaches 10 -8.

Fabry-Perot:

It consists of two parallel plates P1 and P2; mirror coatings with a reflection coefficient from 0.85 to 0.98 are applied to the surfaces of the plates facing each other.

A parallel beam of light S incident from lens O1, as a result of multiple reflection from mirrors, acquires a large number of parallel coherent beams with a constant path difference between adjacent beams.

h- Distance between mirrors

θ - angle of reflection of beams from mirrors

The intensity of these beams will be different. As a result of multi-beam interference in the focal plane l of the O2 lens, an interference pattern is formed, which has the shape of concentric rings.

The position of maximum interference is determined by:

m – integer

The Fabry-Perot interferometer is used as a high-resolution instrument.

Resolution depends on the reflection coefficient of the mirrors, on the distance between the mirrors and increases with their increase.

The minimum resolving wavelength range is 5*10 -5 nm.

Special Abilities Fabry-Perot interferometers are used to study spectra in the IR, visible and centimeter wavelength ranges.

The difference between the FP interferometer is the optical resonator of lasers, the emitting medium of which is located between the mirrors.

If we assume that between the mirrors there is an EM located normally to them plane wave, then as a result of its reflection from the mirrors, standing waves are formed, and resonance occurs.

h is an integer number of half-waves, m is the longitudinal vibration index or longitudinal mode.

The natural frequencies of the optical resonator form arithmetic progression, which is equal to – c/2*h (step)

The frequency difference between two adjacent longitudinal modes in laser radiation depends on the distance between the cavity mirrors:

Moving one of the mirrors by Δf leads to a change in the difference frequency:

Δf=с* Δh/2h 2.

It can be measured using a photodetector.

Goal of the work – study of the interference method for measuring the refractive index. Measuring the refractive index of a plane-parallel glass plate.

Operating principle of the interferometer

The device used to measure the refractive index is called a refractometer. Let's consider a refractometer, the operating principle of which is based on the interference of light - an interference refractometer. In our work we use a Michelson interferometer. The Michelson interferometer played a huge role in the history of science. In particular, with the help of such an interferometer, the famous Michelson–Morley experiment was carried out, the purpose of which was to detect the motion of the Earth relative to the ether.

The Michelson interferometer diagram is shown in Fig. 1. Arrows show the direction of propagation of rays. Light beam from a light source S falls on the LED beam splitter and is divided into two beams - 1 And 2 . The angle of inclination of the beam splitter to the axis of the incident beam is 45. Bun 1 , reflected from the beam splitter, falls on a flat mirror Z 1, is reflected from it ( 1 ), partially passes through the beam splitter ( 1 ) and hits the screen E. The beam 2 , passed through the beam splitter, falls on a flat mirror Z 2, and is reflected from it ( 2 ), then reflected ( 2 ) from the beam splitter and also

hits the screen E. In the area of beam overlap 1  and 2  An interference pattern is observed on the screen.

The light intensity at each point on the screen depends on the phase difference between the added light oscillations at a given point. Interference measurements require a high-contrast interference pattern, i.e. intensity distribution in which the maxima and minima are significantly different from the average background. This picture is obtained if, ideally, the radiation is strictly monochromatic, then the phase difference of the interfering fields at each point does not depend on time. Such fields are called coherent.

Interfering beams travel through different optical paths. Under the optical path understand the path that light would travel in a vacuum in the same time as during the passage of a geometric path in a medium with a refractive index :



In a vacuum And match up. If there are several sections along the path of the ray with different refractive indices, then the optical path along the entire geometric path is equal to the sum of the optical paths in each section.

In the optics course it is shown that if the difference in the initial phases of interfering waves is zero, then the phase difference
, which arises during wave propagation, is proportional to the optical difference in the path of the rays (difference in optical paths)
:

, (1)

Where – radiation wavelength. Maximum light intensity is observed when the phase difference is a multiple of 2. In this case
,

If the radiation is non-monochromatic, i.e. consists of oscillations at different frequencies, then the phase difference at each point is nonstationary in time. If the interference pattern were recorded using a fast photodetector (for example, a camera with a very short exposure time), then contrasting interference patterns would be visible in the sequence of photographs, but the position of the maxima and minima would change chaotically from picture to picture. An inertial photodetector, such as an eye, averages these random oscillations, and instead of an interference pattern, a uniform “gray” background is visually observed on the screen. For this reason, it is impossible to observe a stationary interference pattern of the fields of two different radiation sources. In all interferometers, two light beams are received from one source.

If the radiation is quasi-monochromatic, i.e. vibration spectrum width
, Where is the average wavelength of the spectrum, then a contrasting interference pattern is observed if the random phase error is much less than 2. To do this, the optical path difference of the beams must be much less than the coherence length of the source, i.e. such a difference in the wave paths at which interference disappears. The coherence length of continuous laser radiation is at least several meters, while the optical path difference of the beams in a given laboratory work does not exceed 1–2 cm. Therefore, the necessary condition for observing a contrast interference pattern is met.

If you smoothly change the optical path difference, then the maximums and minimums of screen illumination will alternate. When changing the optical path difference by
the light spot will be replaced by a dark one, etc. Smooth change in optical path difference by
will cause the screen illumination to pass through the maximum (or minimum) N once. You can change the optical path difference in a Michelson interferometer by moving one of the mirrors along the direction of the beam, or, with fixed mirrors, by changing the refractive index of the medium along the path of one of the interfering beams. High-precision laser interference displacement meters are designed using this principle.

However, to measure the refractive index, the interferometer is misaligned: one of the mirrors is deflected at a small angle from the normal to the axis of the incident beam (mirror H 1 in Fig. 1, dashed line under the mirror). In reality, the inclination angle is several minutes of arc, i.e. significantly less than shown in the figure. Due to the misalignment of the beams 1  and 2  are not parallel and they partially overlap on the screen. As is known from interference theory, when monochromatic plane waves with different propagation directions are superimposed,

However, an interference pattern is observed in the form periodic table light and dark straight stripes perpendicular to the plane of the wave vectors of interfering waves. This picture will be observed on the screen in the region of beam overlap. When the phase difference between the waves changes, the interference pattern as a whole shifts.

Note. Real wave fronts are spherical surfaces, and the deviation of the sphere from the screen plane within the beam diameter reaches (20–30) . It would seem that Newton's interference rings should be observed on the screen. However, the appearance of the interference pattern is determined by the mutual deflection of the two spherical surfaces. It can be shown that at a small misalignment angle the interference pattern will be the same as with the interference of plane waves - a system of straight stripes.

Operating principle:

A beam of light using various devices is divided into 2 or more coherent beams, which pass through different optical paths, are then brought together and the result of their interference is observed.

Optical interferometers can be divided according to the number of beam interferometers:

Double-beam and multi-beam.

Multibeam interferometers are used as spectral instruments to study the spectral composition of light.

Dual beams can be used to measure physical technical measurements.

Michelson: A parallel beam of light from the source, passing through O1, hits the translucent plate P1 and is divided into two coherent beams.

Air layer thickness l (optical path difference = 2l).

Stripes of equal inclination are formed when a transparent layer of constant thickness is illuminated by a non-parallel beam of monochromatic radiation.

If M2 and the image M1 form an air wedge, then stripes of equal thickness appear and appear as parallel lines.

Jamin Interferometer:

Designed for measuring refractive indices in gases and liquids. A beam of monochromatic light S, after reflection of the front and rear surfaces of a glass plate P1, is divided into 2 beams S1 and S2. In the path of the beams there are 2 cuvettes K1 and K2, through which the beams are reflected from P2. P2 is rotated relative to P1.

And they fall into the telescope T, where they interfere, forming straight stripes of equal inclination.

Δn=(m*λ)/l. The relative error in measuring the refractive index reaches 10 -8.

Fabry-Perot:

It consists of two parallel plates P1 and P2; mirror coatings with a reflection coefficient from 0.85 to 0.98 are applied to the surfaces of the plates facing each other. A parallel beam of light S incident from the lens O1, as a result of multiple reflection from the mirrors, acquires a large number of parallel coherent beams with a constant path difference between adjacent beams.

h- Distance between mirrors, θ- angle of reflection of beams from mirrors

The intensity of these beams will be different. As a result of multi-beam interference in the focal plane l of the O2 lens, an interference pattern is formed, which has the shape of concentric rings. The position of maximum interference is determined:

Δ=mλ, m – integer

The Fabry-Perot interferometer is used as a high-resolution device. The resolution depends on the reflection coefficient of the mirrors, on the distance between the mirrors and increases with their increase.

The minimum resolving wavelength interval is 5 * 10 -5 nm. The special abilities of the Fabry-Perot interferometer are used to study spectra in the IR, visible and centimeter parts of the wavelength range. The difference between the FP interferometer is the optical resonator of lasers, the emitting medium of which is located between the mirrors.

If we assume that an EM plane wave is located between the mirrors and normal to them, then as a result of its reflection from the mirrors, standing waves are formed and a resonance occurs.