RU1841097C - Deformable mirror - Google Patents

Abstract

FIELD: physics, optics.

SUBSTANCE: invention relates to adaptive optics. A deformable mirror includes an elastic reflecting plate, the profile of which on the back side has a variable thickness, as well as deformation means in the form of a piezoceramic column. The elastic plate is square-shaped with sides measuring $$2a\times 2a,$$

where $$a$$

is the radius of the corrected beam, and is linked to a chassis on two parallel sides. The thickness of the elastic plate in sections parallel to said sides is constant, and in the perpendicular direction satisfies the law: $$\frac{dz}{dx}=-\frac{8x{\text{ e}}^{{\text{x}}^{\text{2}}}-(8x^3-12x){(\alpha +\beta \sin z)}^3}{2(1-2x^2)\beta \cos z},$$

where $$z=\frac{h(x)}{h_{\max }}$$

$$x=\frac{r}{a};$$

h(x) is the variable thickness of the plate; h_max is the structurally determined maximum thickness of the plate; r is the current coordinate along the surface of the elastic plate; $$\alpha =\mathrm{0,5}\frac{h_{\max }+h_{\min }}{h_{\max }};$$

$$\beta =\mathrm{0,5}\frac{h_{\max }-h_{\min }}{h_{\max }};$$

h_min is the minimum allowable thickness. At the centre of the elastic plate, in parallel to the fixed sides, there is a rib with a height L≥h_max, rigidly linked to the plate, one end of which is pivotally linked to a chassis and lies at a distance of $$1,484a$$

from the centre of the elastic plate. A piezoceramic column is pivotally linked to the rib at a point which coincides with the centre of the elastic plate, and additionally includes a rotary drive and a fixed base. The axis of the rotary coincides with the centre of the elastic plate.

EFFECT: high accuracy of phase compensation of thermal distortion of a laser beam in the atmosphere, smaller dimensions.

2 dwg

Description

The present invention relates to optical instrumentation and, in particular, to elements of adaptive optics - deformable mirrors, and is intended for software compensation of nonlinear phase distortion - thermal spreading of the laser beam.

At present, the possibility of a priori (software) correction of thermal nonlinear distortions is known / V.P. Lukin "Atmospheric adaptive optics." "Science", Sib. Dep., 1986, pp. 207 ÷ 209 /. It consists in introducing into the initial phase distribution on the radiating aperture the opposite signs, calculated in the approximation of geometric optics / TIIER, t.65, p.59, D.K. Smith "The Propagation of Powerful Laser Measurement" /:

$$\Delta \varphi (x,y)=-\frac{\varphi }{2}{e}^{-\frac{y^2}{a^2}}\left[\mathrm{one}+erf\left(\frac{x}{a}\right)\right]\text{(one)}$$

where Δφ (x, y) is the necessary predistortion of the phase of the laser beam in the x, y plane;

φ — phase change in the laser beam cross section integrated over the entire propagation path;

erf (...) is the error integral.

Known deformable mirror / "Adaptive Optics", ed. E.A. Vitrichenko, pp. 106 ÷ 115 / used for software compensation of thermal non-linear phase distortion with one control drive. The specified deformable mirror-analogue contains a bearing body, a copper reflecting deformable element - a plate attached to the bearing case on the periphery, and a drive deforming it, for example, a piezole connected to one of its ends with the back of the reflecting plate in its center and the other to the bearing case. Structurally deformable analog mirror provides a symmetrical profile of the deformable surface / "Adaptive Optics" under. ed. E.A. Vitrichenko, p. 109 /. Dependence (1) - Δφ (x, y) is a pronounced asymmetric profile (see Fig. 1). Compensation of this profile by an analog mirror was carried out by displacing the deformable mirror relative to the axis of the beam in its plane of incidence up to 0.9 x / a . The direction of the bias is directed against the resulting component of the wind drift in the atmosphere perpendicular to the optical axis of the laser beam. Because Since the direction of the wind constantly fluctuates during the operation of the optical system, the direction of displacement of the deformable mirror also constantly changes. With this method of compensation, the maximum intensity in the target plane increased by 1.3 times.

The specified deformable mirror-analog when compensating for non-linear typical phase distortion has the following disadvantages:

- low quality phase correction of the thermal spreading of the laser beam due to the fundamental impossibility of matching the asymmetric profile of the theoretical phase correction (1) and the symmetric profile of the phase created by the surface of the centrally loaded deformable mirror;

- the inability with a high degree of accuracy to reproduce the same deformation of the surface of the deformable mirror with various design parameters - diameter, thickness, type of fastening and material of its reflecting plate. So, for example, for “hard” reflecting plates a super-Gaussian shape of a deformed surface is characteristic, and for “soft” ones it is Gaussian / OMP No. 11, 1981 /.

Such ambiguity does not allow to obtain reliable, repeatable in various designs results on the compensation of thermal spreading of the laser beam;

- low efficiency of using the corrective aperture due to the need to offset the axis of the deformable mirror relative to the axis of the laser beam. In this case, the required light diameter of the mirror should be equal to 2 a , where a is the diameter of the corrected laser beam.

The closest in technical essence to the claimed deformable mirror is a mirror that can be similarly used to compensate for non-linear thermal distortions, selected as a prototype (French patent No. 2343262, M.cl ⁴ G02B 5/10). A deformable prototype mirror contains a supporting body, an elastic reflecting plate fixed along the contour, and means of its deformation balanced by the supporting body, and the thickness on the back of the reflecting plate changes according to the law:

$$\frac{h}{R}=-12{\left[(\mathrm{one}-\nu )\frac{P}{E}\right]}^{\mathrm{one}/3}{(\mathrm{<figure-callout\; id="2"\; label="i\; \rho "\; filenames="00000046.png"\; state="\{\{state\}\}">i\; </figure-callout>}{\rho }^{}{}^2+\mathrm{<figure-callout\; id="2"\; label="j\; ln\; \rho "\; filenames="00000046.png"\; state="\{\{state\}\}">j\; </figure-callout>}\ln {\rho }^{}{}^2+k)}^{\mathrm{one}/3}\text{(2)}$$

where R is the radius of the reflecting plate;

E and ν are Young's modulus and Poisson's ratio of the material of the reflecting plate;

P is the load per unit area;

- относительный радиус в плоскости заготовки; $$\rho =\frac{r}{R}$$

- relative radius in the plane of the workpiece;

i, j, k are constant coefficients, the value of which is equal to 1.0-1 depending on the load conditions and the support of the reflecting plate.

In the specified device, the choice of the dependence of the change in the thickness of the reflecting plate allows you to reproduce the same surface deformation in the mirror of the prototype for a given material, thickness, diameter and type of fastening.

The known prototype device has the following disadvantages when compensating for non-linear thermal distortions:

- low quality phase correction of the thermal spreading of the laser beam due to the symmetric profile of the deforming mirror, specified by dependence (2);

- low efficiency of using the corrective aperture due to the need to offset the axis of the deformable mirror relative to the axis of the laser beam.

The aim of the invention is to increase the accuracy of phase compensation of the thermal spreading of the laser beam in the atmosphere and reduce the required size of the light diameter of the deformable mirror.

This goal is achieved by the fact that in a deformable mirror containing a reflective elastic plate, the profile of which on the back is made of variable thickness, connected at the periphery with the supporting body, means for deforming this plate, for example, in the form of a piezoceramic column located on the supporting body, the elastic plate is made square with sides 2 a × 2 a , where a is the radius of the beam being corrected, and is connected with the bearing body along two parallel sides, the thickness of the elastic plate in sections parallel to this to the defense, is made constant, and in the perpendicular direction is made according to the law specified by the control:

$$\frac{dz}{dx}=-\frac{8x{\text{e}}^{{\text{x}}^{\text{2}}}-(8x^3-12x){(\alpha +\beta \sin z)}^3}{2(\mathrm{one}-2x^2)\beta \cos z}$$

Where $$x=\frac{r}{a}$$

r is the current coordinate along the surface of the elastic plate;

$$z=\frac{h(r)}{h_{\max }}$$

where h (r) is the variable thickness of the plate;

h _max - structurally set maximum plate thickness;

$$\alpha =\frac{h_{\max }+h_{\min }}{2h_{\max }}$$

h _min - the minimum allowable plate thickness,

$$\beta =\frac{h_{\max }-h_{\min }}{2h_{\max }}$$

wherein in the center of the elastic plate fixed parallel to the sides of the rib is set to the height l≥h _max, is rigidly associated with said plate, one end of which is pivotally connected to the carrier body and the elastic plate is removed from the center by the amount and 1,484, and wherein the piezo ceramic column pivotally connected with an edge at a point coinciding with the center of the elastic plate, and at the same time, a rotary motion drive and a fixed base are additionally introduced into it, and the axis of the rotational motion drive coincides with the center of the elastic plate, and The supporting body is connected with a rotational motion drive and a fixed base with the possibility of rotation of the plate.

Comparative analysis with the prototype shows that the inventive device differs in the square shape of the reflecting plate, fixing the plate for two parallel sides, introducing the ribs rigidly connected to the plate, and also another (cylindrical) profile for changing its thickness, which ensures the reconstruction of the theoretical profile of the correcting phase (1) . In addition, a rotary motion drive and a fixed base are introduced, interacting in such a way that they allow the mirror to be oriented by the rotation of the correction aperture in accordance with the direction of wind drift on the atmospheric path. Replacing the displacement of the aperture of the deformable mirror with its rotation allows you to increase the efficiency of using the corrective aperture and the dynamics of processing fluctuations in wind directions.

The given set of features is inextricable, ensures the implementation of the task and meets the criterion of "significant differences".

These signs in the known authors of domestic and foreign scientific, technical and patent equipment were not found, therefore, the claimed device meets the criterion of "novelty."

The invention is illustrated by drawings, where:

in FIG. 1 shows the profile of the necessary predistortion of the phase of the laser beam according to dependence (1);

in FIG. Figure 2 schematically shows the design of a deforming mirror to compensate for the thermal spreading of a laser beam.

The deformable mirror (see Fig. 2) contains a reflective elastic plate 1 of variable thickness, connected by screws 2 to the supporting body 3, in which a piezoceramic column 4 is installed, a rib 5, rigidly connected to the elastic plate 1 in its center, the hinge 6 connects the rib 5 and the bearing body 3, made in the form of attenuating the cross section of the rib 5, the hinge 7 connects the rib 5 and the piezoceramic column 4, made in the form of an axis, a rotational motion drive 8, for example, a torque motor, a fixed base 9, connected with the bearing case 3 with rotation through ball bearings 10, 11.

The proposed deformable mirror operates as follows.

. В другом направлении пластина 1 имеет переменную толщину, конфигурация которой обеспечивает воспроизведение второй составляющей соотношения (1) ортогонально первому направлению - $$e^{-y^2/a^2}$$

.The control voltage from the power supply (not shown) is supplied to the piezoceramic column 4, as a result of which it is extended in proportion to the applied voltage. The elongation of the column 4 leads to the rotation of the rib 5 around the hinge 6, connecting it with the supporting body 3. Since the rib 5 is closely connected with the reflecting plate 1, the reflecting surface along the direction of the parallel-fixed sides (see Fig. 2) is inclined, which ensures reproduction of this component of the theoretical predistortion profile (1), namely $$\left(\mathrm{one}+erf\left(\frac{x}{a}\right)\right)$$

. In the other direction, the plate 1 has a variable thickness, the configuration of which ensures the reproduction of the second component of the ratio (1) orthogonal to the first direction - $$e^{-{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000046.png"\; state="\{\{state\}\}">y</figure-callout>}}^2/a^2}$$

.

The rotational moment drive 8 is controlled by signals from external wind direction sensors (not shown in the drawing), while it deploys the supporting body 3 with the reflecting plate 1 and the piezoceramic column 4 fixed on it so that the edge 5 coincides with the direction of the recorded wind drift. The rotation of the bearing housing 3 is carried out relative to the fixed base 9 through ball bearings 10, 11.

The laser beam, reflected from the surface of the deformed mirror, acquires a phase shift. After passing through the atmosphere layer due to the presence of nonlinear thermal tensions having a profile conjugate to that shown in FIG. 1, the beam in the final section of the path acquires a flat phase front. The magnitude of the control voltage supplied to the piezoceramic column is constantly changing, which is determined by fluctuations of meteorological parameters in the atmosphere and the range to the target.

In the optical system in which such a mirror is used, the control signal of the piezoceramic column is determined based on the algorithm for maximizing the intensity in the target plane / B.P. Lukin, "Atmospheric adaptive optics", "Science", 1986 /.

An analysis of the theoretical phase profile of the predistortions Δφ (x, y) - (1) shows that in (1) there are two independent factors with separated variables. In addition, each of the factors describes the phase in mutually orthogonal sections.

на отрезке $$0\le \frac{x}{a}\le 1$$

может быть с высокой точностью аппроксимирована функцией $$c+b\left(\frac{x}{a}\right)$$

. Коэффициенты C и B были определены по методу наименьших квадратов:Function $$\mathrm{one}+erf\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$a$}\right.\right)$$

on the segment $$0\le \frac{x}{a}\le \mathrm{one}$$

can be approximated with high accuracy by function $$c+b\left(\frac{x}{a}\right)$$

. The coefficients C and B were determined using the least squares method:

$$\mathrm{one}+erf\left(\frac{x}{a}\right)\approx \mathrm{1,022}+0.6888\left(\frac{x}{a}\right)\text{(3)}$$

The standard error of the approximation (3) does not exceed

Σ ² ≤2.2 · 10 ^-4

With this in mind, the corrective phase can be represented:

$$\Delta \varphi (x,y)=-\frac{\varphi }{2}{e}^{-{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000046.png"\; state="\{\{state\}\}">y</figure-callout>}}^2/a^2}\left[\mathrm{1,0222}+0.6888\left(\frac{x}{a}\right)\right]\text{(four)}$$

The response function of the deformable mirror along the X axis in the form of (3) is implemented using the edge 5. From (3) it is easy to find the distance from the center of the deformable mirror to the point of fastening of the edge 5 using the hinge 6 on the supporting body 3.

$$\begin{array}{l}\mathrm{1,022}+0.6888\left(\frac{x}{a}\right)=0\text{(5)}\\ \text{x}=\text{one}\text{, 484}a\end{array}$$

, что обеспечивается выбором закона изменения толщины пластинки. Уравнение изгиба прямоугольной полосы переменной толщины можно представить в виде:The response function along the Y axis should be provided in the form: $$e^{-{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000046.png"\; state="\{\{state\}\}">y</figure-callout>}}^2/a^2}$$

This is ensured by the choice of the law of variation of the plate thickness. The equation of bending of a rectangular strip of variable thickness can be represented as:

$$\mathrm{<figure-callout\; id="2"\; label="D\; d"\; filenames="00000046.png"\; state="\{\{state\}\}">D\; </figure-callout>}\frac{d^{}}{}\frac{{}^2\varphi }{d{x}^2}+\frac{dD}{dx}\frac{d\varphi }{dx}=-\frac{q{a}^{2}x}{8}\text{(6)}$$

Where

D - cylindrical stiffness

$$D=\frac{E{h}^3(x)}{12(\mathrm{one}-{\nu }^2)}\text{(7)}$$

Where

E is Young's modulus,

ν is the Poisson's ratio,

h (x) is a variable thickness,

φ is the angle of rotation of the plane of the plate associated with a transverse bending ratio: $$\varphi =-\frac{dw}{dx}\text{(8)}$$

Where

w is the transverse deflection.

Since when searching for the thickness h (x) in a real deformable mirror, there are always restrictions h _min ≤h (x) ≤h _max , we introduce an auxiliary function that allows us to automatically take into account the indicated condition:

$$\frac{h(x)}{h_{\min }}=\alpha +\beta \sin z\text{(9)}$$

Where

$$\alpha =0.5\frac{h_{\max }+h_{\min }}{h_{\max }}$$

$$\beta =0.5\frac{h_{\max }-h_{\min }}{h_{\max }}$$

, получаем уравнение:We substitute 9, 8, 7 into 6, and also considering that the necessary transverse bending $$w=e^{-x^2/a^2}$$

we get the equation:

$$\frac{dz}{dx}=-\frac{8x{e}^{x^2}-(8x^3-12x){(\alpha +\beta \sin z)}^3}{2(\mathrm{one}-2x^2)\beta \cos z}\text{(10)}$$

Relation (10) is the main one for determining the thickness. The easiest way to determine h (y) from (10) is numerically, for example, using the Runge-Kutta method, MK-61 Table Microcalculator using ready-made programs / A.N. Tsvetkov, V.A. Yepanechnikov, "Application program for microcomputers", Moscow, 1984, p. 61 / allows one to calculate the profile of a deformable mirror in 3-10 minutes depending on the required number of points.

вдоль оси Y и функции $$\mathrm{1,022}+\left(\frac{x}{a}\right)\mathrm{0,6888}$$

вдоль оси X, что позволяет с погрешностью ≤2,2·10^-4 воспроизводить профиль предыскажений (1). По оценкам, приведенным в работе /1/, относительная интенсивность в плоскости цели при априорной компенсации теплового нелинейного искажения на трассе длиной 16 км в виде предыскажения (1) увеличивается более чем в 8 раз.Thus, the design of the deformable mirror ensures the reproduction of the function $$e^{-{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="00000046.png"\; state="\{\{state\}\}">y</figure-callout>}}^2/a^2}$$

along the y axis and function $$\mathrm{1,022}+\left(\frac{x}{a}\right)0.6888$$

along the X axis, which allows reproducing the predistortion profile (1) with an error of ≤2.2 · 10 ^-4 . According to the estimates given in / 1 /, the relative intensity in the target plane, while a priori compensating for thermal nonlinear distortion along a 16 km path in the form of predistortion (1), increases by more than 8 times.

Thus, the design of the inventive deformable mirror allows the same number of deforming drives to improve the quality of phase correction, which allows more than 6 times to increase the intensity of laser radiation on the target when it passes a disturbing atmospheric layer. In addition, in the claimed device, the effective corrective aperture is equal to the transverse size of the laser beam, while in the prototype device it should be twice as large.

The proposed deforming mirror can be widely used in transmitting laser optical systems, space communication systems and locations, where it is necessary to compensate for non-linear thermal distortions limiting the range and efficiency of these systems.

Used Books

1. V.P. Lukin, “Atmospheric adaptive optics”, Science, Sib. Dep., 1986, pp. 207 ÷ 209.

Claims (1)

A deformable mirror containing a reflecting elastic plate, the profile of which on the back is made of variable thickness, peripherally connected with the bearing housing, plate deformation means made in the form of a piezoceramic column located on the bearing housing, characterized in that, in order to improve the accuracy of phase compensation of thermal distortion of the laser beam in the atmosphere and reduce the size, the elastic plate is made square with sides 2 a × 2 a ,
where a is the radius of the corrected beam, and is connected with the supporting body along two parallel sides, while the thickness of the elastic plate in sections parallel to these sides is constant, and in the perpendicular direction is made according to the law
$$\frac{dz}{dx}=-\frac{8x{\text{e}}^{{\text{x}}^{\text{2}}}-(8x^3-12x){(\alpha +\beta \sin z)}^3}{2(\mathrm{one}-2x^2)\beta \cos z}$$

Where $$z=\frac{h(x)}{h_{\max }}$$

$$x=\frac{r}{a}$$

h (x) is the variable plate thickness;
h _max - structurally specified maximum plate thickness;
r is the current coordinate along the surface of the elastic plate;
$$\alpha =0.5\frac{h_{\max }+h_{\min }}{h_{\max }}$$

; $$\beta =0.5\frac{h_{\max }-h_{\min }}{h_{\max }}$$

h _min - the minimum allowable plate thickness,
wherein in the center of the elastic plate fixed parallel to the sides of the rib is set to the height l≥h _max, is rigidly connected to the plate, one end of which is pivotally connected to the carrier body and the elastic plate is removed from the center to 1,484 a, wherein a piezoceramic column hingedly connected to an edge at the point coinciding with the center of the elastic plate, and a rotary motion drive and a fixed base are additionally introduced into it, and the axis of the rotational motion drive coincides with the center of the elastic plate, and the bearing body is connected to the drive m of rotational motion and a fixed base with the possibility of rotation around an axis passing through the center of the elastic plate.

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