RU2697892C1 - Two-beam interferometer - Google Patents

Abstract

FIELD: instrument engineering.

SUBSTANCE: proposed invention relates to optical holography and is intended for generation of periodic interference patterns. Rotationally tunable double-beam interferometer designed to generate periodic interference patterns comprises a source arranged in series along the radiation path, beam-splitting element performing two functions which are necessary and sufficient for a double-beam interferometer: splitting of the initial beam into two partial and subsequent their reduction at a given plane under a variable convergent angle, and a photodetector. Light-splitting element with built-in divider mirror and photodetector are mutually fixed and together form a system, which is mirror-symmetrical relative to plane of this divider mirror. Photoreceiver is placed inside the interference region, which in the process of rotational readjustment of the angle of convergence of the partial beams undergoes a shift, which is small compared to the longitudinal size of the given region. Latter is provided by mutual matching of change of angle of incidence of the initial beam to the divider mirror and its movement along this mirror. Control unit generates control signals for rotary motion drive corresponding to this matching law.

EFFECT: high vibration resistance, high contrast depth of the recorded holographic diffraction gratings and high accuracy of measuring wavelengths when detecting spectra of electromagnetic radiation when the disclosed interferometer is used as a static Fourier spectrometer.

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Description

The claimed invention relates to optical holography and is intended for the formation of periodic interference patterns, which are used, for example, in interference lithography to record holographic diffraction gratings, flat and corrugated, to create periodic structures of various dimensions (one-, two- and three-dimensional), including photonic crystals of various crystalline symmetries, for the implementation of static Fourier spectrometers used in spectral analysis, to create Bragg mirrors , frequency and polarization filters in optical fibers, waveguides and photovoltaic materials, for controlling the frequency of generation of distributed feedback lasers, for the purpose of encoding, decoding and storing information and in other areas.

A known technical solution implemented in the manufacture of a three-dimensional diffraction grating [Patent US 3507564, "Method of making a tree-dimensional diffraction grating", IPC G02B 5/18, published 04/21/1970], consisting in the fact that the collimated beam of monochromatic light is directed to an inclined beam-splitting plate that splits this beam into reflected and transmitted partial light beams, two mirrors are installed in the path of these beams, directing them to a block of photosensitive material in which the partial light beams overlap, forming I'm in the overlap region equidistant fringes. The interval between the bands is varied by changing the angle of convergence of the partial light beams, which is accomplished by rotating two mirrors in mutually opposite directions around axes perpendicular to the plane of incidence. When the angle of convergence changes, the overlapping region of the partial light beams moves, and the position of the block of photosensitive material is adjusted so that this region is located inside it.

The disadvantages of the known technical solutions are the complexity of operation due to the fact that the convergence angle is set with uneven discreteness by mutually independent alignment of two mirrors and additionally align the optical paths of the partial light beams, and the block of photosensitive material is moved in accordance with a change in the convergence angle, large the dimensions of the device at small (less than 30 °) values of the angle of convergence of partial light beams, fourthly, its high sensitivity to Librations due to the presence of adjustable mirrors.

There is also a technical solution presented in a two-beam interferometer [RF Patent for the invention No. 2626062, “Two-beam interferometer”, IPC G02B 5/18, G02B 5/32, published July 21, 2017], consisting in the fact that it is implemented as a two-beam interferometer , which is mounted on the base with the possibility of rotational movement and contains a beam splitting element, two mirrors and a photosensitive element fixed motionless and optically coupled to a collimated light beam source. As a beam splitting element, a beam splitting cube composed of two 90-degree prisms tightly connected by their flat hypotenuse surfaces and a dividing mirror built between them is considered. Due to the mirror symmetry of the beam splitting cube relative to the plane of the dividing mirror, its output surfaces turn out to be mirror-symmetrical with respect to this plane. Two mirrors are also installed symmetrically. As a result, the two-beam interferometer is a rigid mirror-symmetric design, providing its high vibration resistance.

The collimated light beam entering the beam splitting cube is split by a dividing mirror into two identical partial light beams. Two mirrors are installed in the path of these beams emerging from the beam splitter cube and reflect them towards each other so that they mutually overlap at a given angle of convergence, determined by the angle of incidence of the collimated light beam on the input surface of the beam splitter and the angle of inclination of the mirrors to the plane of the splitter mirrors. The mirror symmetry of the two-beam interferometer provides mutual symmetry of the partial light beams, due to which the path difference between their axes is always zero. As a result, the periodic interference pattern formed in the region of mutual overlap of the partial light beams is also symmetrical with respect to the plane of the dividing mirror, and the 0th order of interference corresponds to the intersection point of the axes of these beams. The photosensitive element is placed inside said overlap area.

The rotational motion of the base is accompanied by a change in the angle of incidence of the collimated light beam on the input surface of the beam splitter cube and a corresponding change in the angle of convergence of the partial light beams, which makes it possible to continuously control the spatial period of the interference pattern. The axis of rotation is oriented perpendicular to the plane of incidence of the collimated light beam on the dividing mirror and is positioned so that when the base and the angular and linear displacements of the collimated light beam are rotated along this mirror, the position of the interference pattern relative to the photosensitive element is stabilized inside a segment that is small compared to its length along the plane of the dividing mirror. Rotational motion is carried out by the drive, which is controlled by signals generated by the control unit. The performance of a two-beam interferometer in the form of a rigid optomechanical unit gives it high vibration resistance.

The disadvantages of the known technical solution include the complexity of the design: the presence of two mirrors leads to an increase in the mass-dimensional characteristics of the interferometer, especially at a convergence angle, the values of which lie in the most popular range of 0 ° -30 °.

A technical solution is known that is implemented in a system with an interference filter designed to recognize radio signals [Patent US 4597630 "Self-derived reference beam holography using a dove prism", IPC G03H 1/06, G03H 1/12, G02B 27/10, G02B 27 / 46, published on July 1, 1986]. The technical solution in that part, which relates to the device for splitting the beam, is in the form of a two-beam interferometer. It reduces the partial light beams generated in the splitting device on a predefined plane, for example, on a photodetector, by refracting these beams on the output surfaces of this device. As a result, mirrors that are usually used to perform the mixing function are excluded from the design of the interferometer, and the interferometer in its entirety is a single optical unit that is not subject to mechanical vibrations and combines two functions: splitting the initial collimated light beam into two partial and the subsequent their information on the photodetector.

In a preferred embodiment, the splitting device is composed of two identical 90-degree prisms, the first and second, made of a transparent material, tightly interconnected by the hypotenous (or basic, as they are called in analogue) surfaces so as to form an optical unit symmetrical with respect to them. As an alternative, a similar block of two Dove prisms, representing the corresponding 90-degree prisms, truncated from the right angle, is considered. A film of dielectric material is placed between the base surfaces with a refractive index lower than that of the prism material to exclude total internal reflection on the base surface and to provide partial transmission and partial reflection of the radiation incident on the film. Therefore, the interface between the first and second prisms serves as a splitting mirror in the splitting device.

The initial collimated light beam is directed to the input surface of the first prism at an angle of incidence θ so that after refraction on it this beam falls on the base surface of this prism, usually near the midpoint of its longitudinal length. The dividing mirror splits the initial beam into two partial light beams, called for convenience signal and reference. The signal beam is reflected from this mirror towards the output surface of the first prism, and the reference beam passes through it to the output surface of the second prism. After refraction at the output surfaces, both beams are directed to each other at an angle of convergence of 2α and mutually overlap on the photodetector plane, forming an interference pattern on it with a period

where λ is the radiation wavelength in the initial beam, α = θ-45 °. From the last equality it follows that such an overlap becomes possible if θ> 45 °.

In the system for recording and recognizing signal information provided by this technical solution, the interferometer is designed, firstly, to record the interferogram of the initial beam, subjected to modulation by a test radio signal by means of an acousto-optical modulator, which is subsequently used as a test interference filter, and secondly, to recognize an external radio signal which modulated the original beam by comparing it with a test radio signal.

This comparison is performed using a pre-recorded test interference filter placed at the position where it was recorded on the signal beam path when the reference beam is blocked. The presence or absence of optical radiation diffracted on this filter indicates whether the received radio signal matches the test signal or not. The need to form a diffracted beam in the process of recognizing a received radio signal requires that the relative position of the interferometer and the source beam during this operation exactly coincide with that during recording of the test interference filter. The latter means that the interferometer and the source beam must be mutually immobile.

The disadvantage of this technical solution is the inability to control the period of the interference pattern formed in the area of mutual overlap of the signal and reference beams, due to a fixed value of the angle of incidence θ and, accordingly, a fixed value of the convergence angle 2α of these beams, as follows from the above relation α = θ-45 ° .

этих пучков, подвергшихся преломлению на выходных поверхностях светоделительного элемента, на фотоприемнике под изменяемым углом схождения. В качестве светоделительного элемента в данном случае используется светоделительный кубик. Он состоит из двух идентичных 90-градусных призм, изготовленных из прозрачного материала и называемых первой и второй, причем на гипотенузной поверхности одной из них наносится делительное зеркало. Первая и вторая призмы жестко соединяются между собой по их гипотенузным поверхностям таким образом, чтобы две другие их плоские поверхности, обращенные к фотоприемнику и называемые выходными, располагались зеркально-симметрично относительно плоскости делительного зеркала, для чего ребра их 45-градусных углов, обращенные к светочувствительному элементу, точно совмещаются.Also known is a technical solution presented in a tunable two-beam interferometer [Mikerin S.L., Ugozhaev V.D. A simple two-beam interferometer based on a beam splitting cube, OPTICS AND SPECTROSCOPY, vol. 111, no. 6, p. 1019-1025 (2011)], selected as a prototype. The technical solution is carried out by splitting a collimating light beam into a partial beam of light into two partial light beams and the subsequent

of these beams, subjected to refraction at the output surfaces of the beam splitting element, on the photodetector at a variable angle of convergence. In this case, a beam splitting cube is used as a beam splitting element. It consists of two identical 90-degree prisms made of a transparent material and called the first and second, and a dividing mirror is applied to the hypotenuse surface of one of them. The first and second prisms are rigidly connected to each other along their hypotenous surfaces in such a way that their other two flat surfaces, facing the photodetector and called the output, are mirror-symmetric relative to the plane of the dividing mirror, for which the edges of their 45-degree angles are turned to the photosensitive element, precisely aligned.

The collimated light beam is directed to the input surface of the first prism so that after refraction on it this light beam falls on a fission mirror and splits it into two partial light beams, the first and second. The first partial light beam is reflected from the dividing mirror and directed to the output surface of the first prism, and the second partial light beam passes through the dividing mirror into the second prism and is directed to its output surface. The angle of incidence θ of the collimated light beam is selected according to the condition θ> 45 °, due to which the first and second partial light beams, being refracted on the output surfaces of the first and second prisms, respectively, are directed to each other at a convergence angle of 2α, forming an interference pattern in the region of their mutual overlap with period Λ. Due to the symmetry of the beam splitting cube, the pair of partial light beams and the interference pattern are also symmetrical with respect to the plane of the dividing mirror at any angle of convergence, and the difference in the path of these beams along their axes is always zero.

The value of the convergence angle varies by changing the angle of incidence according to the relation α = θ-45 ° by joint rotation of the beam splitter cube and the photodetector around an axis perpendicular to the plane of incidence of the collimated light beam on the input surface of the first prism, relative to the source of this beam. The axis of rotation itself is located near the entrance surface so as to maximize the width of the entrance pupil in the plane of incidence. The photodetector is combined with the plane of the largest width of the interference pattern passing through the point of intersection of the axes of the partial light beams, with the possibility of moving it along the plane of the dividing mirror in accordance with the movement of the interference pattern caused by the rotation of the interferometer.

The interferometer, presented in this technical solution as a single element - a beam splitting cube, has a very high vibration resistance, and also has small dimensions in the region of the most popular values of the convergence angle, lying in the range 0 ° -30 °. However, the presence of a movable photodetector increases the sensitivity to vibration of the device as a whole.

The disadvantages of the known technical solution is its increased sensitivity to vibrations and operational complexity due to the mobility of the photodetector.

The authors were tasked with increasing the vibration resistance of the interferometer.

The problem is solved in that a two-beam interferometer, which includes a collimated light beam source, a base with an axis of rotation and with a beam splitting element mounted on it with a dividing mirror integrated into it, splitting the collimated light beam into a first partial light beam and a second partial light beam, a photodetector and optically coupled to a collimated light beam source so that the first and second partial light beams leaving the beam splitter the th element through its first output surface and the second output surface, were directed towards each other, interfering with each other on the photodetector, the drive providing rotational movement of the base with the axis of rotation around this axis, the control unit, the angular displacement sensor, is additionally equipped with a frame with the possibility of fixing the photodetector motionless, the axis of rotation of the base is made located between the beam splitting element and the photodetector in a position that ensures stabilization of the position of the interference region and the photodetector, and the control unit generates control signals for the actuator to ensure matching the angular and linear displacements of the collimated light beam divider mirror beam-splitting element according to the formula:

- угол падения коллимированного светового пучка на делительное зеркало, n - показатель преломления материала светоделительного элемента, при этом первая выходная поверхность и вторая выходная поверхность светоделительного элемента выполнены взаимно симметричными относительно плоскости делительного зеркала, далее делительное зеркало выполнено с коэффициентом отражения, равным коэффициенту пропускания во всей области изменения угла падения коллимированного светового пучка на делительное зеркало.where W is the distance from the point of intersection of the axis of the collimated light beam with the dividing mirror to the edge of this dividing mirror close to the source, M is the length of the dividing mirror along the collimated light beam, L _ph is the distance from the photodetector to the edge of the dividing mirror nearest to it,

is the angle of incidence of the collimated light beam on the dividing mirror, n is the refractive index of the material of the dividing element, while the first output surface and the second output surface of the dividing element are mutually symmetrical relative to the plane of the dividing mirror, then the dividing mirror is made with a reflection coefficient equal to the transmittance in the whole the area of variation of the angle of incidence of the collimated light beam on the dividing mirror.

The technical effect of the claimed device is to increase the vibration resistance, which allows, firstly, to increase the contrast depth of the recorded holographic diffraction gratings and, consequently, to increase their diffraction efficiency, and secondly, to increase the sensitivity, spectral resolution and accuracy of measuring wavelengths when recording spectra electromagnetic radiation in the case of using the inventive interferometer as a static Fourier spectrometer, in improving operating conditions, simplifying control I am in the period of the interference pattern, reducing the mass and dimensions of the device, as well as expanding the arsenal of means for this purpose.

In FIG. 1 shows a diagram of a two-beam interferometer, where 1 is the source, 2 is the collimated light beam, 3 is the first partial light beam, 4 is the second partial light beam, 5 is the beam splitting element, 6 is the first prism, 7 is the second prism, 8 is the dividing mirror , 9 - photodetector, 10 - frame, 11 - base, 12 - axis of rotation, 13 - direction of rotational movement, 14 - drive, 15 - control unit, 16 - angular displacement sensor.

In FIG. 2 is a diagram of the dependences of the relative distance L / A between the edge of the dividing mirror 8 closest to the photodetector 9 and the intersection point O of the axes of the first 3 and second 4 partial light beams versus the angle of incidence θ, which changes due to the rotational movement of the base 11 around the axis of rotation 12 relative to the base the position of the collimated light beam 2, characterized by the angle of incidence θ ₀ = 50 ° and its position Q ₀ = 0.25A on the input surface of the beam splitter element 5, for five values of the distance T between the axis of rotation 12 and the edge of the dividing mirror 8, closest to the photodetector 9, where A is the length of the input surface along the plane of incidence of the collimated light beam 2, 17 is the dependence L (θ) / A at T = 0.1A, 18 is the dependence L (θ) / A at T = 0.4A, 19 - the optimal dependence of L (θ) / A at T = 0.551A, 20 - the dependence of L (θ) / A at T = 0.7A, 21 - the dependence L (θ) / A at T = A, 22 is the mark of the base angle of incidence θ ₀ = 50 °.

In FIG. 3 is a diagram of the dependences of the half convergence angle α of the first 3 and second 4 partial light beams on the base value θ _{0 of the} angle of incidence of the collimated light beam 2 on the input surface of the beam splitter element 5, made of a material with a refractive index n = 1.5183, for four values of diameter D of this beam, where 23 - lower limit value α ₁ half-angle of convergence at D = 0,065A, 24 - upper limit value α ₂ half-angle of convergence at D = 0,065A, 25 - width of the tuning range Δα = α ₂ -α ₁ polovinnog toe angle at D = 0,065A, 26 - lower limit value of the half angle of convergence at D = 0,1A, 27 - upper limit value α ₂ half-angle of convergence at D = 0,1A, 28 - width of the tuning range Δα = α ₂ - α ₁ half angle of convergence at D = 0.1A, 29 - lower α ₁ boundary value of half angle of convergence at D = 0.15A, 30 - upper α ₂ boundary value of half angle of convergence at D = 0.15A, 31 - range width adjustment Δα = α ₂ -α ₁ half-angle of convergence at D = 0,15A, 32 - lower limit value α ₁ half-angle of convergence at D = 0,2A, 33 - upper boundary α ₂ value at half-angle of convergence D = 0,2A, 34 - width of the tuning range Δα = α ₂ -α ₁ half-angle of convergence at D = 0,2A, 35 - the half-angle of convergence α _m, corresponding to the basic angle of incidence θ ₀ of the collimated light beam 2 of the largest possible diameter D _m for a given θ ₀ , when the condition α ₁ = α ₂ = α _m is satisfied.

по ходу световых пучков. Благодаря зеркальной симметрии оптического блока относительно этой поверхности первая выходная поверхность С₂С₃ и вторая выходная поверхность С₃С₄ оказываются зеркально-симметричными относительно плоскости делительного зеркала 8 (далее плоскость симметрии). Фотоприемник 9 жестко заключен в оправу 10 с возможностью ее неподвижного закрепления на основании 11, поэтому он неподвижен относительно светоделительного элемента 5, который также жестко закреплен на этом основании.The inventive two-beam interferometer operates as follows. A double-beam interferometer whose optical design is shown in FIG. 1 includes a collimated light beam source 1, a base 11 with an axis of rotation 12, on which a beam splitter 5 and a photodetector 9 are located, optically coupled to a source 1. As a beam splitter 5, a beam splitter with an edge length A is used as an example, which is an optical unit of two identical 90-degree prisms: the first prism 6 and the second prism 7, which are tightly connected by their hypotenuse surfaces. On the hypotenous surface of one of the prisms, the first or second, a dividing mirror 8 is previously applied, which as a result is built into the beam splitter element 5 on its interface C ₁ C ₃ length

along the light beams. Due to the mirror symmetry of the optical unit relative to this surface, the first output surface C ₂ C ₃ and the second output surface C ₃ C ₄ turn out to be mirror-symmetric with respect to the plane of the dividing mirror 8 (hereinafter, the plane of symmetry). The photodetector 9 is rigidly enclosed in a frame 10 with the possibility of its fixed mounting on the base 11, so it is stationary relative to the beam splitting element 5, which is also rigidly fixed on this base.

на расстоянии W от его края C₁ и расщепляется им на первый парциальный световой пучок 3 и второй парциальный световой пучок 4, оси которых на всем их пути к фотоприемнику 9 лежат в рабочей плоскости. Первый парциальный световой пучок 3 отражается от делительного зеркала 8 обратно в первую призму 6 и падает на первую выходную поверхность С₂С₃ на расстоянии В от ребра С₃, а второй парциальный световой пучок 4 проходит через делительное зеркало 8 во вторую призму 7 и падает на вторую выходную поверхность С₃С₄ на таком же расстоянии В от ребра С₃. Первый 3 и второй 4 парциальные световые пучки, преломившись на первой и второй выходных поверхностях соответственно, покидают светоделительный элемент 5 и направляются друг к другу под углом схождения 2α с формированием в области их взаимного перекрытия интерференционной картины с периодом Λ согласно (1). Таким образом, обе функции интерферометра: расщепление коллимированного светового пучка 2 на два парциальных световых пучка и последующее их сведение на фотоприемнике 9 исполняются единственным оптическим элементом - светоделительным кубиком, что предельно упрощает конструкцию заявляемого устройства. Благодаря симметричному расположению первой и второй выходных поверхностей относительно плоскости симметрии первый парциальный световой пучок 3 и второй парциальный световой пучок 4 также взаимно симметричны относительно этой плоскости. Поэтому разность их хода по осям равна нулю при любом угле схождения, и точка О их пересечения, удаленная на расстояние L (далее длина схождения) от края С₃ делительного зеркала 8, ближнего к фотоприемнику 9, лежит на плоскости симметрии и характеризуется нулевым порядком интерференции. Такую же симметрию имеет интерференционная картина; в точке О, как в ее центре, пересекаются диагонали сечения этой картины рабочей плоскостью: продольная - длиной S, лежащая на пересечении плоскостей рабочей и симметрии, и поперечная - длиной J, перпендикулярная плоскости симметрии (на фиг. 1 не показаны). Фотоприемник 9 помещается внутри области интерференции на расстоянии L_ph≈L от края С₃ делительного зеркала 8. В общем случае L_ph≠L, и расстояние точки О от фотоприемника 9 определяется смещением ΔL=L-L_ph.In FIG. 1, light beams are shown by their axial rays. Source 1 generates a collimated light beam 2 of diameter D, which is directed to the input surface C ₁ C _{2 of the} first prism 6 of the beam splitting element 5 in a plane perpendicular to its edges C ₁ -C ₄ (hereinafter the working plane), at an angle of incidence θ at a distance Q from the edge C _{1 of the} dividing mirror 8, which is closest to the source 1, to the point of incidence of the axial beam of the collimated light beam 2 on this input surface. Further, this beam enters the first prism 6 at an angle of refraction ψ, falls on a fission mirror 8 at an angle

at a distance W from its edge C ₁ and is split by it into a first partial light beam 3 and a second partial light beam 4, the axes of which lie along the entire path to the photodetector 9 in the working plane. The first partial light beam 3 is reflected from the dividing mirror 8 back into the first prism 6 and falls on the first output surface C ₂ C ₃ at a distance B from the edge C ₃ , and the second partial light beam 4 passes through the dividing mirror 8 into the second prism 7 and falls to the second outlet surface C ₃ C ₄ at the same distance B from the rib C ₃ . The first 3 and second 4 partial light beams, having refracted on the first and second output surfaces, respectively, leave the beam splitter 5 and are directed towards each other at an angle of convergence 2α with the formation of an interference pattern with a period Λ in the region of their mutual overlap according to (1). Thus, both functions of the interferometer: splitting the collimated light beam 2 into two partial light beams and their subsequent reduction at the photodetector 9 are performed by a single optical element - a beam splitting cube, which greatly simplifies the design of the claimed device. Due to the symmetrical arrangement of the first and second output surfaces relative to the plane of symmetry, the first partial light beam 3 and the second partial light beam 4 are also mutually symmetrical with respect to this plane. Therefore, the difference in their axial travel is equal to zero at any convergence angle, and the point O of their intersection, remote at a distance L (hereinafter, the convergence length) from the edge C _{3 of the} dividing mirror 8 closest to the photodetector 9, lies on the plane of symmetry and is characterized by zero interference order . The interference pattern has the same symmetry; at point O, as in its center, the diagonals of the cross section of this picture intersect with the working plane: the longitudinal one is of length S lying at the intersection of the working and symmetry planes, and the transverse one is of length J perpendicular to the symmetry plane (not shown in Fig. 1). The photodetector 9 is placed inside the interference region at a distance L _ph ≈L from the edge C _{3 of the} dividing mirror 8. In the general case, L _ph ≠ L, and the distance of the point O from the photodetector 9 is determined by the offset ΔL = LL _ph .

The base 11 can rotate around the axis of rotation 12 relative to the source 1 in the direction of rotation shown by arrow 13. The axis of rotation 12 lies in the plane of symmetry, is oriented perpendicular to the working plane and is located between the beam splitting element 5 and the photodetector 9 at a distance T from the edge C _{3 of the} dividing mirrors 8. This distance is selected so that when performing the rotational movement of the base 11, mutual coordination of the angular displacement of the collimated light beam 2 is ensured from reflected by a change in the angle of incidence θ, and its linear displacement, displayed by a change in the distance q, along the dividing mirror 8 so that the condition for minimizing the displacement ΔL is satisfied within the entire range of adjustment of the convergence angle realized by the rotational motion. The rotation of the base 11 is carried out by the drive 14, and the control signals for this drive are generated by the control unit 15 according to the law of coordination of these two movements; a formula describing this law is derived below. The position of the base 11 is indicated by the angular displacement sensor 16.

The rotation of the base 11 is accompanied by a change in the angle of incidence θ and a corresponding change in the angle of convergence 2α - in this way, the period Λ of the interference pattern is continuously tuned according to (1). From the course of the light beams shown in FIG. 1, the relation between the angle of incidence θ and the half angle of convergence α follows clearly:

The relationship between the position Q of the collimated light beam 2 at the entrance to the beam splitter element 5 and the positions B of the first 3 and second 4 partial light beams at the exit from it is determined by the formula

Where

and n is the refractive index of the material from which the first prism 6 and the second prism 7 of the beam splitter element 5 are made. In (3) and the following formulas, for reasons of generality, all linear parameters are presented in relative form: q = Q / A, b = B / A , l = L / A, l _ph = L _ph / A, Δl = ΔL / A, t = T / A, r = R / A, s = S / A, j = J / A, w = W / A .

From FIG. 1 it is easy to find that in the general case for arbitrary input parameters θ and q, the convergence length l is expressed by the formula

or subject to (3)

The condition l = const, which is relevant for the task at hand, which means the fixed position of the point O of the intersection of the axes of the first 3 and second 4 partial light beams relative to the beam splitter 5 when θ changes due to the rotational motion of the base 11 allows us to obtain from (5) the required mutual coordination of the input parameters θ and q:

The relationship between these input parameters, on the one hand, and the position of the axis of rotation 12, determined by the distance t, on the other hand, can be established through the radius r of a circle centered on the axis of rotation, touching the imaginary extension of the axis of the collimated light beam 2 until it enters the beam splitter element 5 :

From (7), the dependence q (t) is derived:

Let some position of the collimated light beam 2 incident on the input surface at an angle θ ₀ (hereinafter, the base beam) be taken as the base position. The task is to find the remaining parameters characterizing this position: α ₀ , t ₀ , q ₀ , l ₀ , using the criterion of small displacement Δl compared with the longitudinal length s of the interference pattern discussed below. The need for such a criterion is due to the requirement to maintain a high contrast of the interference bands and, as a consequence, a high diffraction efficiency of the recorded periodic structures. The basic value of the half angle of convergence α ₀ is found by the formula (2). The radius of rotation r _{0 of the} base beam is expressed in terms of the parameters of this beam using (7):

When the interferometer rotates relative to the base beam, its input parameters θ and q will also change. The ratio of their current values is found by substituting the basic parameters included in (8) r = r ₀ from (9) and t = t ₀ :

The expression for the corresponding current value of the length of the convergence is derived from formula (5) taking into account (10):

From (11) it can be seen that for any current value of the angle of incidence θ, the convergence length l will vary with a change in the distance t ₀ ; therefore, each value of t ₀ will have its own dependence l (θ). The only common point for these dependences is the combination of the variables θ ₀ , l ₀ corresponding to the base position of the collimated light beam 2, which is confirmed by the substitution in (11) of the equality θ = θ ₀ :

A similar result is obtained by substituting the basic parameters in (5). In (12), the parameter ψ ₀ is the angle of refraction corresponding to the base angle of incidence θ ₀ , and tgψ ₀ is determined by formula (4) for θ = θ ₀ .

In FIG. 2 shows five dependences l (θ) - curves 17-21, corresponding to five values of the position t _{0 of the} axis of rotation: 0.1; 0.4; 0.551; 0.7 and 1, constructed for the base beam with parameters θ ₀ = 50 ° and q ₀ = 0.25. Of these, curve 19 is distinguished by the fact that the convergence length l varies little with θ and has a minimum l ₀ = 1.222 in the vicinity of θ = θ ₀ . Such properties of this curve indicate a real opportunity to stabilize the position of the interference pattern near the value of l ₀ for almost any base position, which is confirmed by further calculations. To plot the diagram in FIG. 2, the value q ₀ = 0.25 was chosen arbitrarily. An exact calculation under the condition of the adopted criterion of small displacement Δl for θ ₀ = 50 ° gives the value q ₀ = 0.2998.

Binding the base beam to the minimum of the function l (θ) displayed by curve 19 is also advisable because deviating the current value of θ from the base θ ₀ in any direction leads to a one-sided increase in l, which improves the minimization conditions for Δl, making it possible to place the photodetector 9 in the gap between the extreme, on the one hand, and extreme positions, on the other hand, the center of the interference pattern:

where l _{0 is} determined from (12), and l ₁ or l ₂ according to formula (11) with the substitution θ = θ ₁ or θ ₂ :

Such a binding can be done if you find the value of the distance t ₀ corresponding to the specified minimum. For this, the first derivative of the function l (θ), expressed by formula (11), must be equated to zero (dl / dθ = 0) at θ = θ ₀ and expressed from it t ₀ :

Where

In formula (15), only one parameter is known - the base angle of incidence θ ₀ , which is a given angle. The latter is advisable because this parameter, through relation (2), is directly related to the required interval of the convergence angle at which the interferometer is supposed to be operated. This interval, available during rotational adjustment of the convergence angle, is enclosed between its two boundary values. The increase in the angle of incidence θ due to the rotational movement of the base 11 (Fig. 1) from its lower boundary value θ ₁ to the upper boundary value θ _{2 is} accompanied by an increase in half the convergence angle from α ₁ to α ₂ according to (2) and a simultaneous decrease in the distance q from q ₁ up to q ₂ . The boundary conditions are formulated on the basis of the requirement that the refracted collimated light beam 2 does not go beyond its edges C ₁ and C ₃ when it moves along the dividing mirror 8. Therefore, the lower boundary values are due to the contact of this beam with the edges of C ₃ , and the upper ones - the edges of C ₁ . The boundary relations are deduced from here

and

in which the boundary values q ₁ to q ₂ are found from (10):

and the parameter t ₀ is determined by formula (15). Since during rotation the diameter d _{0 of the} base beam does not change, then d ₁ = d ₂ = d ₀ , which gives the first equation of the problem:

containing three unknowns: θ ₁ , θ ₂ and q ₀ .

Two more equations are compiled for the boundaries based on a comparison of the displacement Δl with the longitudinal length s of the interference pattern

in the form of a ratio of it to half the length s:

The geometric meaning of this coefficient is that the difference 1 - k _s shows the transverse length of the interference pattern on the photodetector 9 with respect to the length of its transverse diagonal j. The aforementioned criterion of small displacement Δl is expressed in terms of the coefficient k _s , the value of which should not exceed the tolerance value 0 <η << 1:

When placing the photodetector 9 in an intermediate position between l ₀ and l ₁ or l ₂ according to (13), the absolute value of the coefficient k _s in the base position and at the borders has the greatest value: | k _s | _i = η, which makes it possible to accurately record the displacements | Δl | _i in these three characteristic positions:

where i = 0, 1, 2. Corresponding toe lengths

and

Eliminating the parameter l _ph from (26) using the substitution l _ph = l ₀ + | Δl ₀ | obtained from (25), we can obtain the second and third equations of the problem:

In these equations, l ₁ and l ₂ are calculated by formulas (14), ad ₁ and d ₂ - by (17) and (18). The base diameter d _{0 is} replaced by d ₁ and d ₂ in order to make equations (27) mutually independent, this simplifies the numerical solution of system (20), (27). The value of d ₀ is found by averaging the boundary values of d ₁ and d ₂ :

and the calculations are carried out before their alignment: d ₁ = d ₂ = d ₀ .

The solution of this system gives the values of three parameters: θ ₁ , θ ₂ and q ₀ characterizing the restructuring of the period of the interference pattern at a given base angle of incidence θ ₀ . The found parameters provide the current offset value Δl≤ηs / 2 of the center О of the interference pattern relative to the photodetector 9 in the entire range of half-convergence angle α of the first 3 and second 4 partial light beams from the lower boundary value α ₁ to the upper α ₂ . The base distance t ₀ from the edge C _{3 of the} dividing mirror 8 to the axis of rotation 12 is calculated by the formula (15).

кривых, отображающих α₁ и α₂ для каждого диаметра d, образуют замкнутые фигуры, по форме подобные лепесткам, причем с ростом диаметра d «лепестки» становятся

и короче. Это означает, что чем больше диаметр d, тем короче диапазон перестройки в области меньших значений угла α и меньше интервал, в котором допустим выбор базового угла падения θ₀. Например, для d=0,065 (при А=20 мм диаметр D=1,3 мм) и базового угла падения θ₀=56° ширина диапазона перестройки Δα=11,9°; половинный угол схождения изменяется в интервале α=6,24°-18,12°, что означает отношение соответствующих периодов интерференционной картины Λ₁/Λ₂=2,86 - полторы октавы. Столь широкий диапазон варьирования периода в случае коллимированного светового пучка 2 малого диаметра говорит о том, насколько мала кривизна кривой 19 на фиг. 2 и насколько эффективной для заявляемой конфигурации двухлучевого интерферометра является концепция вращательной перестройки при неподвижном фотоприемнике 9. Это подтверждается результатами расчета для достаточно большого диаметра этого пучка d=0,2 (D=4 мм): α=3,54°-5,61°, Δα=2,08° и Λ₁/Λ₂=1,56 (фиг. 3).In FIG. Figure 3 shows the dependences of the half convergence angle α ₁ , α ₂ and α _m , as well as the range width Δα = α ₂ -α _{1 of the} change in this angle on the base angle of incidence θ ₀ for η = 0.1 for four values of the diameter d of the collimated light beam 2. It is seen that

curves representing α ₁ and α ₂ for each diameter d, form closed figures, similar in shape to the petals, and with increasing diameter d, the “petals” become

and shorter. This means that the larger the diameter d, the shorter the tuning range in the region of smaller values of the angle α and the smaller the interval in which the choice of the base angle of incidence θ _{0 is} acceptable. For example, for d = 0.065 (with A = 20 mm, diameter D = 1.3 mm) and a base angle of incidence θ ₀ = 56 °, the width of the adjustment range is Δα = 11.9 °; the half-convergence angle varies in the range α = 6.24 ° -18.12 °, which means the ratio of the corresponding periods of the interference pattern Λ ₁ / Λ ₂ = 2.86 - one and a half octaves. Such a wide range of period variation in the case of a collimated light beam 2 of small diameter indicates how small the curvature of curve 19 in FIG. 2 and how effective for the claimed configuration of a two-beam interferometer is the concept of rotational tuning with a stationary photodetector 9. This is confirmed by the calculation results for a sufficiently large diameter of this beam d = 0.2 (D = 4 mm): α = 3.54 ° -5.61 °, Δα = 2.08 ° and Λ ₁ / Λ ₂ = 1.56 (Fig. 3).

The above calculation data were obtained for a beam splitter made of a material with a refractive index of n = 1.5183 (optical glass K8, λ = 546.07 nm). Since the convergence of the first 3 and second 4 partial light beams is due to their refraction, the tuning parameters of the inventive two-beam interferometer should to a certain extent depend on the refractive index. For example, at n = 2.2 for the base position of a collimated light beam 2 with a diameter of d = 0.05 (D = 1 mm) with θ ₀ = 60 °, the width of the tuning range is Δα = 23.75 °; the boundary values of the half convergence angle α ₁ = 6.63 and α ₁ = ° 30.38 °, the corresponding ratio of the periods of the interference pattern Λ ₁ / Λ ₂ = 4.38 - more than two octaves, i.e. there is a twofold excess of the previous version in Δα. A lot of materials are known with n≥2.2, transparent in the visible and near IR regions, for example, STF3 optical glass (n≈2.18), lithium tantalate single crystals LiTaO ₃ (n≈2.2), lithium niobate LiNbO ₃ (n≈2.3), strontium titanate SrTiO ₃ (n≈2.4), rutile TiO ₂ (n≈2.6), lead titanate PbTiO ₃ (n≈2.7). So the implementation of an interferometer with such effective characteristics will not constitute fundamental difficulties.

Formula (6) expresses the law of mutual coordination of the angular displacement of the collimated light beam 2, displayed in this formula by changing the angle of incidence θ on the input surface C ₁ C _{2 of the} beam splitting element 5, and the linear movement of this beam along the specified input surface, displayed by changing the distance q from the edge C ₁ dividing mirrors 8 closest to the source 1, to the point of incidence of the axial ray of the collimated light beam 2 on this entrance surface caused by the rotational movement of the base 11 (see. FIG. 1) in the pyr rotation axis 12. This law is implemented in the inventive two-beam interferometer through the control signals for the actuator 14 rotational movements which are generated by the control unit 15.

на это зеркало коллимированного светового пучка 2, преломленного входной поверхностью С₁С₂, а линейное перемещение по нему данного пучка отображается изменением расстояния W от края C₁ делительного зеркала 8, ближнего к источнику 1, до точки падения на него осевого луча преломленного коллимированного светового пучка 2. Угол преломления ψ следующим образом выражается через угол

:In relation to the dividing mirror 8 of the considered law of coordination, with the rotational movement of the base 11 around the axis of rotation 12, the angular displacement is displayed by a change in the angle of incidence

this is a mirror of a collimated light beam 2, refracted by the input surface C ₁ C ₂ , and the linear movement of this beam along it is displayed by changing the distance W from the edge C _{1 of the} dividing mirror 8, which is closest to the source 1, to the point where the axial beam of the refracted collimated light beam 2. The angle of refraction ψ is expressed as follows through the angle

:

Using (29), we can write down tgψ and the angle of incidence θ included in formula (6) of the matching law:

and

whence the formula for the function tgθ, also included in the agreement law, follows:

:From a triangle formed by a segment of a dividing mirror 8 of length w, distance q, and the trailing segment of the axis of the refracted collimated light beam 2 (Fig. 1), we can express the distance q as a function of distance w and angle

:

Substituting (30), (32), (33) into the law of coordination (6) and replacing l with l _{ph in it} , we can derive the desired record of this law in the accepted relative units, tied to the dividing mirror 8:

After multiplying both sides of equality (34) by the normalizing size A, we get the final form of the law of matching two movements:

- угол падения коллимированного светового пучка 2 на делительное зеркало 8, n - показатель преломления материала первой 6 и второй 7 призм светоделительного элемента 5.where W is the distance from the point of intersection of the axis of the collimated light beam 2 with the dividing mirror 8 to the edge C _{1 of} this mirror closest to the source 1, M is the length of the dividing mirror 8 along the collimated light beam 2, L _ph is the distance from the photodetector 9 to the near to it the edges C _{3 of the} dividing mirror 8,

- the angle of incidence of the collimated light beam 2 on the dividing mirror 8, n is the refractive index of the material of the first 6 and second 7 prisms of the beam splitting element 5.

и угол схождения α связаны следующим образом:Angle

and the convergence angle α are related as follows:

The technical effect of the claimed device, which consists in increasing the vibration resistance of the device and improving operating conditions, as well as in expanding the arsenal of means for this purpose, is achieved due to the fact that the axis of rotation of the base is made located between the beam splitting element and the photodetector in a position that ensures stabilization of the position of the interference region on the photodetector by matching the angular and linear movements of the collimated light beam along the dividing mirror element caused by the rotational movement of the base, according to the formula (35) under the action of control signals generated by the control unit to drive the rotational movement. In addition, simplifying the management of the period of the interference pattern is achieved by equipping the inventive device with a fixed frame for the photodetector.

Claims (5)

1. A two-beam interferometer, including a collimated light beam source, a base with an axis of rotation and a beam splitting element fixed to it with a dividing mirror integrated into it, splitting the collimated light beam into a first partial light beam and a second partial light beam, a photodetector and optically coupled with a collimated light beam source so that the first and second partial light beams leaving the beam splitting element through its first output the surface and the second output surface were directed towards each other, interfering with each other on the photodetector, a drive providing rotational movement of the base with an axis of rotation around this axis, a control unit, an angular displacement sensor, characterized in that it is additionally equipped with a frame with the possibility of fixing the photodetector motionless , the axis of rotation of the base is made located between the beam splitting element and the photodetector in a position that ensures stabilization of the position of the interference region on the photodetector nike, and the control unit is configured to generate control signals for the drive, ensuring coordination of the angular and linear movements of the collimated light beam along the dividing mirror of the beam splitting element according to the formula:

where W is the distance from the point of intersection of the axis of the collimated light beam with the dividing mirror to the edge of this dividing mirror close to the source, M is the length of the dividing mirror along the collimated light beam, L _ph is the distance from the photodetector to the edge of the dividing mirror nearest to it, X is the angle of incidence of the collimated light beam on the dividing mirror, n is the refractive index of the material of the beam splitting element. 2. A two-beam interferometer according to claim 1, characterized in that the first output surface and the second output surface of the beam splitting element are mutually symmetrical with respect to the plane of the dividing mirror. 3. A two-beam interferometer according to claim 1, characterized in that the dividing mirror is made with a reflection coefficient equal to the transmittance in the entire range of the angle of incidence of the collimated light beam on the dividing mirror.

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