CN103258075A - Accurate calculation method for primary surface accuracy and primary and secondary surface adjustment of shaped Cassegrain antenna - Google Patents

Abstract

The invention relates to an accurate calculation method for primary surface accuracy and primary and secondary surface adjustment of a shaped Cassegrain antenna, and belongs to the technical field of antennas. The accurate calculation method can be used for accurately calculating the primary surface accuracy of the shaped Cassegrain antenna, can accurately guide adjustment of secondary surface positions and gestures and active adjustment of a primary reflecting surface panel and is particularly applicable to the field of the antennas of large radio telescopes. The idea of the accurate calculation method includes that under the condition of aplanatism, an optimal identical reflecting surface is calculated through respectively adoption of translation along directions of an x-axis, a y-axis and a z-axis, rotation around an x1-axis and a y2-axis, and least square fit of six degrees of freedom of optical distance variation, so that the primary surface accuracy of the shaped Cassegrain antenna can be calculated. Meanwhile, calculated results of the accurate calculation method can guide the adjustment of the secondary surface positions and gestures and the active adjustment of the primary reflecting surface panel, so that influences of primary reflecting surface deformation on antenna performance can be reduced, and antenna efficiency is improved.

Description

The Method for Accurate Calculation that a kind of figuration cassette antenna interarea precision and major-minor face are adjusted

Technical field

The present invention relates to antenna technical field, is the Method for Accurate Calculation that a kind of figuration cassette antenna interarea precision and major-minor face are adjusted.The present invention is applicable to the calculating of figuration cassette antenna interarea precision, can be used for instructing the adjustment of subreflector position and attitude and the active adjustment of primary reflection surface panel simultaneously, to reduce the distortion of subreflector position and attitude sum of errors primary reflection surface to the influence of antenna performance.

Background technology

Figuration cassette antenna is with its higher gain and good sidelobe performance and be widely used in fields such as satellite communication, survey of deep space, radio astronomy.Behind the antenna major-minor reflecting surface figuration, its bus no longer is typical curve but the curve be made up of discrete data point.

The interarea precision is one of the key technical indexes of antenna, and it directly affects the electric property of antenna.Especially for the design of large-scale radio telescope antenna, realize that the high precision of primary reflection surface face type becomes one of its gordian technique of succeeding in developing.Along with the increase of antenna aperture, load factor especially gravity factor causes the distortion of antenna more and more serious, thereby has caused the antenna efficiency loss bigger.Iff being that rigidity by improving reflecting body guarantees that the interarea precision of antenna in range of observation is impracticable, therefore need pass through surface fitting method, simulate a new primary reflection surface according to the primary reflection surface of antenna after the distortion under the different elevations angle, primary reflection surface deviation minimum after making it with respect to distortion, be that the interarea precision is the highest, thereby improve antenna efficiency.

At present, the computing method of interarea precision have following several, but they are inapplicable for figuration cassette antenna.

1, to have proposed best-fit parabolic theoretical for the monograph " antenna structure design " delivered in 1980 of Zhu Zhonggan, leaf Shang Hui, this method is only applicable to calculate the interarea precision of forward-feed type parabolic antenna or standard Bimirror antenna, and to calculate the result of the interarea precision of figuration cassette antenna be inaccurate and use this theory.

2, Chinese patent publication number CN102013576A, open day on April 13rd, 2011, the name of innovation and creation is called " the secondary face method of adjustment of correction type Cassegrain formula antenna ", and this application case discloses the interarea precision that a kind of piecewise fitting para-curve method is calculated figuration cassette antenna.The step of this method is: figuration cassette antenna interarea bus discrete point is carried out the sectional parabola match, obtain a set of segmentation standard para-curve; The para-curve of match rotated a circle around common axis obtain one group of parabolic torus; Parabolic torus is carried out least square fitting calculating to the primary reflection surface after being out of shape just can obtain the interarea precision.Though this method represents that with sectional parabola figuration cassette antenna main reflector bus than method 1 accurately, but the Microwave Optics of the parabolic torus of match and subreflector relation is unmatched, this be this section primary reflection surface bus correspondence corresponding because every segment standard para-curve of match has only a focus be one section Jiao Qu, electromagnetic wave just can not focus on a focus again through the parabolic torus reflection of match after the subreflector reflection of figuration like this, therefore this method is a kind of method of approximate treatment figuration cassette antenna interarea precision, and is consequently inaccurate.

Summary of the invention

Order of the present invention is to be to avoid the weak point in the above-mentioned background technology and the Method for Accurate Calculation that provides a kind of figuration cassette antenna interarea precision and major-minor face to adjust, set up mathematical model according to the aplanatism condition, the interarea precision of accurate Calculation figuration cassette antenna can accurately instruct the adjustment of subreflector position and attitude and the active adjustment of primary reflection surface panel simultaneously.

The object of the present invention is achieved like this, and the Method for Accurate Calculation that a kind of figuration cassette antenna interarea precision and major-minor face are adjusted is characterized in that may further comprise the steps:

Suppose that (1) figuration cassette antenna theory design major-minor reflecting surface coordinate is xoyz; Coordinate system xoyz is carried out translation along x axle, y axle, z direction of principal axis respectively, afterwards more respectively around x ₁Axle, y ₂Axle, z ₃Direction of principal axis is rotated, and obtains describing the coincide coordinate system x of reflecting surface of secondary face and the best corresponding with the secondary face after the movement after mobile ₄O ₄y ₄z ₄Described x ₁Axle refers to coordinate system xoyz and carries out the coordinate system x that forms after the translation along x axle, y axle, z direction of principal axis respectively ₁o ₁y ₁z ₁Transverse axis; y ₂Axle refers to coordinate system x ₁o ₁y ₁z ₁Around x ₁The coordinate system x that axle rotation back forms ₂O ₂y ₂z ₂The longitudinal axis; z ₃Axle refers to coordinate system x ₂O ₂y ₂z ₂Around y ₂The coordinate system x that axle rotation back forms ₃O ₃y ₃z ₃Vertical pivot;

(2) because the load factor causes theoretical design primary reflection surface to produce distortion, the primary reflection surface expression formula after obtaining being out of shape by measurement or mechanics finite element analysis software;

Suppose that (3) the normal direction deviation between the primary reflection surface after best coincide reflecting surface and the distortion is δ, the primary reflection surface expression formula in the integrating step (2) after the distortion is calculated the best reflecting surface expression formula of coincideing;

(4) the secondary face expression formula after calculating is moved;

(5) according to the secondary face expression formula after the identical reflecting surface expression formula of the best of determining in step (3), (4) and the movement, choose x ₄O ₄y ₄Be the aplanatism reference surface, the expression formula of the normal direction deviation δ between the primary reflection surface after calculating best coincide reflecting surface and the distortion;

(6) according to the expression formula of the normal direction deviation δ that determines in the step (5), computing method is figuration cassette antenna interarea precision δ to the weighted mean square value of deviation δ _mExpression formula;

(7) according to the figuration cassette antenna interarea precision δ that determines in the step (6) _mExpression formula, use least square method and calculate 6 degree of freedom parameters finding the solution the best reflecting surface that coincide.Coincide 6 degree of freedom parameters of reflecting surface of described the best are specially: respectively along the translational movement of x axle, y axle, z axle, respectively around x ₁Axle, y ₂Rotation amount and the change in optical path length amount of axle;

(8) the best of obtaining in the step (7) the is coincide expression formula of the normal direction deviation δ that obtains in 6 degree of freedom parameter substitution steps (5) of reflecting surface obtains the numerical value of normal direction deviation δ; The figuration cassette antenna interarea precision δ that obtains in the numerical value substitution step (6) with normal direction deviation δ again _mExpression formula, obtain figuration cassette antenna interarea accurate values, finish the calculating of figuration cassette antenna interarea precision;

(9) the best of obtaining in the step (7) is coincide secondary face expression formula after the movement that obtains in 5 degree of freedom parameter substitution steps (4) of reflecting surface just can obtain the exact position that secondary face is adjusted, and finishes the adjustment of secondary face.5 degree of freedom parameters of the identical reflecting surface of described the best are specially respectively along the translational movement of x axle, y axle, z axle with respectively around x ₁Axle, y ₂The rotation amount of axle;

(10) the normal direction deviation δ expression formula of the best of obtaining in the step (7) being coincide obtaining in 6 degree of freedom parameter substitution steps (5) of reflecting surface, the primary reflection surface that the numerical value that obtains normal direction deviation δ is about to distortion is adjusted into the adjustment amount of the best reflecting surface that coincide, and finishes the adjustment of interarea.

Wherein, the identical reflecting surface of described the best refers to: after the distortion of figuration cassette antenna theory design primary reflection surface, the error of the primary reflection surface relative theory design primary reflection surface after the distortion is bigger, therefore can seek a new primary reflection surface, it has mobile with respect to theory design primary reflection surface and rotates, light path has the variation of trace simultaneously, this new primary reflection surface that satisfies the aplanatism condition has numerous, yet a new primary reflection surface is arranged wherein, primary reflection surface after the distortion is its root-mean-square error minimum relatively, and this new primary reflection surface is referred to as the best reflecting surface that coincide.

Wherein, x in the step (1) ₄O ₄y ₄z ₄The expression formula of coordinate system is:

$\left\{\begin{array}{c}{x}_4^{\′}=x^{\′}-u_x+{\mathrm{\α}}_z{y}^{\′}-{\mathrm{\α}}_y{z}^{\′}\\ y_4^{\′}=y^{\′}-u_y-{\mathrm{\α}}_z{x}^{\′}+{\mathrm{\α}}_x{z}^{\′}\\ z_4^{\′}=z^{\′}-u_z+{\mathrm{\α}}_y{x}^{\′}-{\mathrm{\α}}_x{y}^{\′}\end{array}\right.$

In the formula: x ' ₄, y ' ₄, z ' ₄Be respectively x ₄O ₄y ₄z ₄X under the coordinate system ₄Axle, y ₄Axle, z ₄The coordinate figure of axle; X ＇, y ＇, z ＇ are respectively the coordinate figure of x axle under the xoyz coordinate system, y axle, z axle; u _x, u _y, u _zBe respectively along the translational movement of x axle, y axle, z axle; α _x, α _y, α _zBe respectively around x ₁Axle, y ₂Axle, z ₃The anglec of rotation of axle.

Wherein, the primary reflection surface expression formula after the distortion is in the step (2):

$\left\{\begin{array}{c}{x_{\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">m</figure-callout>}0}}^{\&prime;}=x_m+{\mathrm{\&epsiv;}}_x\\ {{\mathrm{<figure-callout\; id="0"\; label="y\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">y</figure-callout>}}_m}^{\&prime;}=y_m+{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="y\; z\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">y</figure-callout>}}& \\ {z_m}^{}{0_{}}^{\&prime;}=z_m+{\mathrm{\&epsiv;}}_z\end{array}\right.$

In the formula: x ' _M0, y ' _M0, z ' _M0Be respectively the coordinate figure of x axle under the xoyz coordinate system of primary reflection surface after the distortion, y axle, z axle; x _m, y _m, z _mBe respectively the coordinate figure of the x axle of theoretical design primary reflection surface under the xoyz coordinate system, y axle, z axle; ε _x, ε _y, ε _zBe respectively theoretical design primary reflection surface at the deflection of xoyz coordinate system lower edge x axle, y axle, z axle.

Wherein, calculating the best reflecting surface expression formula of coincideing in the step (3) is:

$\left\{\begin{array}{c}{x_m}^{\&prime;}={{\mathrm{<figure-callout\; id="0"\; label="x\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">x</figure-callout>}}_m}^{\&prime;}+n_x\mathrm{\&delta;}=x_m+{\mathrm{\&epsiv;}}_x+n_x\mathrm{\&delta;}\\ {y_m}^{\&prime;}={{\mathrm{<figure-callout\; id="0"\; label="y\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">y</figure-callout>}}_m}^{\&prime;}+n_y\mathrm{\&delta;}=y_m+{\mathrm{\&epsiv;}}_y+n_y\mathrm{\&delta;}\\ {z_m}^{\&prime;}={{\mathrm{<figure-callout\; id="0"\; label="z\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">z</figure-callout>}}_m}^{\&prime;}+n_z\mathrm{\&delta;}=z_m+{\mathrm{\&epsiv;}}_z+n_z\mathrm{\&delta;}\end{array}\right.$

In the formula: x ' _m, y ' _m, z ' _mBe respectively the coordinate figure of best coincide the x axle of reflecting surface under the xoyz coordinate system, y axle, z axle; n _x, n _y, n _zBe respectively the normal vector of theoretical design primary reflection surface at x axle, y axle, the axial component of z; δ is the primary reflection surface after being out of shape and best normal direction deviation of coincideing between the reflecting surface.

Wherein, the secondary face expression formula of calculating after moving in the step (4) is:

$\left\{\begin{array}{c}{x}_{4s}^{\&prime;}=x_s^{\&prime;}-u_x+{\mathrm{\&alpha;}}_z{y}_s^{\&prime;}-{\mathrm{\&alpha;}}_y{z}_s^{\&prime;}\\ y_{4s}^{\&prime;}=y_s^{\&prime;}-u_y-{\mathrm{\&alpha;}}_z{x}_s^{\&prime;}+{\mathrm{\&alpha;}}_x{z}_s^{\&prime;}\\ z_{4s}^{\&prime;}=z_s^{\&prime;}-u_z+{\mathrm{\&alpha;}}_y{x}_s^{\&prime;}-{\mathrm{\&alpha;}}_z{\mathrm{\&alpha;}}_s^{\&prime;}\end{array}\right.$

In the formula: x _s, y _s, z _sBe respectively the coordinate figure of the x axle of the secondary face of theoretical design under the xoyz coordinate system, y axle, z axle; X ' _s, y ' _s, z ' _sThe coordinate figure of the x axle of the secondary face after mobile of being respectively under the xoyz coordinate system, y axle, z axle.

Wherein, the expression formula of the normal direction deviation δ between the primary reflection surface after best coincide reflecting surface and the distortion of calculating may further comprise the steps in the step (5):

(501) secondary face is less with respect to primary reflection surface, suppose it that translation and rotation are only arranged and not distortion, keep simultaneously after mobile feed and mobile after secondary face between distance and the distance between former feed and the secondary face of theoretical design remain unchanged, namely former feed need move to o ₄The place, calculate between the secondary face after feed and the movement after mobile apart from r _s＇;

(502) according to the best of determining in step (3), (4) coincide reflecting surface with mobile after the expression formula of secondary face, calculate best coincide reflecting surface with move after secondary face between apart from S ＇;

(503) feed after mobile with mobile after secondary face and the best reflecting surface that coincide constituted new Microwave Optics system, its aplanatism condition should be with x ₄O ₄y ₄The plane is reference surface, calculates the best reflecting surface that coincide at x ₄O ₄y ₄z ₄Z under the coordinate system ₄The value z ' of axle _4m

(504) the aplanatism equation of new Microwave Optics system is C ＇=r _s＇+S ＇-z ' _4m, C ＇ is the aplanatism constant of new Microwave Optics system, thereby can calculate primary reflection surface after the distortion and the expression formula of the best normal direction deviation δ between the reflecting surface that coincide.

The present invention compares with background technology has following advantage:

1, the present invention is based on the aplanatism condition and set up mathematical model, derived the computing method of figuration cassette antenna interarea precision, overcome the problem that existing theory can only approximate processing, result calculated is accurate.

2, result calculated of the present invention can instruct the adjustment of subreflector position and attitude, thereby can improve the performance of antenna.

3, result calculated of the present invention can instruct primary reflection surface initiatively to adjust, and reduces the workload of interarea debugging, thereby improves antenna performance.

Description of drawings

Fig. 1 is coordinate system transformational relation synoptic diagram of the present invention.

Fig. 2 is the major-minor reflecting surface corresponding relation synoptic diagram of the theoretical design of the present invention and new Microwave Optics system.

Geometric relationship synoptic diagram when Fig. 3 is cassette antenna theory of the present invention design major-minor reflecting surface figuration.

Embodiment

The Method for Accurate Calculation that a kind of figuration cassette antenna interarea precision and major-minor face are adjusted is characterized in that comprising step:

Suppose that (1) figuration cassette antenna theory design major-minor reflecting surface coordinate is xoyz; Coordinate system xoyz is carried out translation along x axle, y axle, z direction of principal axis respectively, afterwards more respectively around x ₁Axle, y ₂Axle, z ₃Direction of principal axis is rotated, and obtains describing the coincide coordinate system x of reflecting surface of secondary face and the best corresponding with the secondary face after the movement after mobile ₄O ₄y ₄z ₄Described x ₁Axle refers to coordinate system xoyz and carries out the coordinate system x that forms after the translation along x axle, y axle, z direction of principal axis respectively ₁o ₁y ₁z ₁Transverse axis; y ₂Axle refers to coordinate system x ₁o ₁y ₁z ₁Around x ₁The coordinate system x that axle rotation back forms ₂O ₂y ₂z ₂The longitudinal axis; z ₃Axle refers to coordinate system x ₂O ₂y ₂z ₂Around y ₂The coordinate system x that axle rotation back forms ₃O ₃y ₃z ₃Vertical pivot.

With reference to Fig. 1, calculate x ₄O ₄y ₄z ₄The expression formula of coordinate system can be carried out as follows:

(101) coordinate translation of xoyz coordinate system

With reference to Fig. 1 (a), the xoyz coordinate system carries out forming x after the translation along x axle, y axle, z direction of principal axis respectively ₁o ₁y ₁z ₁Coordinate system.Wherein, be respectively u along x axle, y axle, the axial translational movement of z _x, u _y, u _z, can get:

$\left\{\begin{array}{c}{x}_1^{\&prime;}=x^{\&prime;}-u_x\\ y_1^{\&prime;}=y^{\&prime;}-u_y\\ z_1^{\&prime;}=z^{\&prime;}-u_z\end{array}\right.$

In the formula: x ' ₁, y ' ₁, z ' ₁Be respectively x ₁o ₁y ₁z ₁X under the coordinate system ₁Axle, y ₁Axle, z ₁The coordinate figure of axle; X ＇, y ＇, z ＇ are respectively the coordinate figure of x axle under the xoyz coordinate system, y axle, z axle;

(102) x ₁o ₁y ₁z ₁Coordinate system is around x ₁The rotation of axle

With reference to Fig. 1 (b), x ₁o ₁y ₁z ₁Coordinate system is around x ₁Axle rotation back forms x ₂O ₂y ₂z ₂Coordinate system, the anglec of rotation are α _x, can get:

$\left\{\begin{array}{c}{x}_2^{\&prime;}=x_1^{\&prime;}\\ y_2^{\&prime;}=y_1^{\&prime;}\cos {\mathrm{\&alpha;}}_x+z_1^{\&prime;}\sin {\mathrm{\&alpha;}}_x\\ z_2^{\&prime;}=-y_1^{\&prime;}\sin {\mathrm{\&alpha;}}_x+z_y^{\&prime;}\cos {\mathrm{\&alpha;}}_z\end{array}\right.$

In the formula: x ' ₂, y ' ₂, z ' ₂Be respectively x ₂O ₂y ₂z ₂X under the coordinate system ₂Axle, y ₂Axle, z ₂The coordinate figure of axle;

(103) x ₂O ₂y ₂z ₂Coordinate system is around y ₂The rotation of axle

With reference to Fig. 1 (c), x ₂O ₂y ₂z ₂Coordinate system is around y ₂The axle supination is changeed and is formed x ₃O ₃y ₃z ₃Coordinate system, the anglec of rotation are α _y, can get:

$\left\{\begin{array}{c}{x}_3^{\&prime;}=x_2^{\&prime;}\cos {\mathrm{\&alpha;}}_y-z_2^{\&prime;}\sin {\mathrm{\&alpha;}}_y\\ y_3^{\&prime;}=y_2^{\&prime;}\\ z_3^{\&prime;}=x_2^{\&prime;}\sin {\mathrm{\&alpha;}}_y+z_2^{\&prime;}\cos {\mathrm{\&alpha;}}_y\end{array}\right.$

In the formula: x ' ₃, y ' ₃, z ' ₃Be respectively x ₃o ₃y ₃z ₃X under the coordinate system ₃Axle, y ₃Axle, z ₃The coordinate figure of axle;

(104) x ₃O ₃y ₃z ₃Coordinate system is around z ₃The rotation of axle

With reference to Fig. 1 (d), x ₃o ₃y ₃z ₃Coordinate system is around z ₃Axle rotation back forms x ₄O ₄y ₄z ₄Coordinate system, the anglec of rotation are α _z, can get:

$\left\{\begin{array}{c}{x}_4^{\&prime;}=x_3^{\&prime;}\cos {\mathrm{\&alpha;}}_z+y_3^{\&prime;}\sin {\mathrm{\&alpha;}}_z\\ y_4^{\&prime;}={-x}_3^{\&prime;}\sin {\mathrm{\&alpha;}}_z+y_3^{\&prime;}\cos {\mathrm{\&alpha;}}_z\\ z_4^{\&prime;}=z_3^{\&prime;}\end{array}\right.$

In the formula: x ' ₄, y ' ₄, z ' ₄Be respectively x ₄O ₄y ₄z ₄X under the coordinate system ₄Axle, y ₄Axle, z ₄The coordinate figure of axle;

Above-mentioned three rotations are carried out according to right hand rule, and simultaneous step (101)～(104) can get:

Wherein, corner α _x, α _y, α _zFor in a small amount, can be similar to and think

$\left\{\begin{array}{c}\sin {\mathrm{\&alpha;}}_x={\mathrm{\&alpha;}}_x\\ \cos {\mathrm{\&alpha;}}_x=1\\ \sin {\mathrm{\&alpha;}}_y={\mathrm{\&alpha;}}_y\\ \cos {\mathrm{\&alpha;}}_y=1\\ \sin {\mathrm{\&alpha;}}_z={\mathrm{\&alpha;}}_z\\ \cos {\mathrm{\&alpha;}}_z=1\end{array}\right.$

Ignore second order during abbreviation in a small amount, can get x ₄O ₄y ₄z ₄The expression formula of coordinate system is:

$\left\{\begin{array}{c}{x}_4^{\&prime;}=x^{\&prime;}-u_x+{\mathrm{\&alpha;}}_z{y}^{\&prime;}-{\mathrm{\&alpha;}}_y{z}^{\&prime;}\\ y_4^{\&prime;}=y^{\&prime;}-u_y-{\mathrm{\&alpha;}}_z{x}^{\&prime;}+{\mathrm{\&alpha;}}_x{z}^{\&prime;}\\ z_4^{\&prime;}=z^{\&prime;}-u_z+{\mathrm{\&alpha;}}_y{x}^{\&prime;}-{\mathrm{\&alpha;}}_x{y}^{\&prime;}\end{array}\right.$

(2) because the load factor causes theoretical design primary reflection surface to produce distortion, the primary reflection surface expression formula after obtaining being out of shape by measurement or mechanics finite element analysis software;

With reference to Fig. 2, theoretical design primary reflection surface obtains theoretical design primary reflection surface by measurement or mechanics software analysis and is respectively ε at the deflection of xoyz coordinate system lower edge x axle, y axle, z axle because the load factor has produced distortion _x, ε _y, ε _z, the primary reflection surface expression formula after can being out of shape is:

$\left\{\begin{array}{c}{x_{\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">m</figure-callout>}0}}^{\&prime;}=x_m+{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="x\; y\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">x</figure-callout>}}& \\ {y_m}^{}{0_{}}^{\&prime;}=y_m+{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="y\; z\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">y</figure-callout>}}& \\ {z_m}^{}{0_{}}^{\&prime;}=z_m+{\mathrm{\&epsiv;}}_z\end{array}\right.$

In the formula: x ' _M0, y ' _M0, z ' _M0Be respectively the coordinate figure of x axle under the xoyz coordinate system of primary reflection surface after the distortion, y axle, z axle; x _m, y _m, z _mBe respectively the coordinate figure of the x axle of theoretical design primary reflection surface under the xoyz coordinate system, y axle, z axle;

Suppose that (3) the normal direction deviation between the primary reflection surface after best coincide reflecting surface and the distortion is δ, the primary reflection surface expression formula in the integrating step (2) after the distortion is calculated the best reflecting surface expression formula of coincideing;

With reference to Fig. 2, do vertical line, the normal direction deviation δ between the primary reflection surface after can getting best identical reflecting surface and being out of shape by the primary reflection surface after the distortion to the best reflecting surface that coincide.In addition, because malformation is small, can be similar to and thinks the normal vector approximately equal of theoretical design primary reflection surface and the best reflecting surface that coincide, wherein the normal vector of theoretical design primary reflection surface is

n _x, n _y, n _zBe respectively the normal vector of theoretical design primary reflection surface at x axle, y axle, the axial component of z.Can get, best expression formula of coincideing reflecting surface is:

$\left\{\begin{array}{c}{x_m}^{\&prime;}={{\mathrm{<figure-callout\; id="0"\; label="x\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">x</figure-callout>}}_m}^{\&prime;}+n_x\mathrm{\&delta;}=x_m+{\mathrm{\&epsiv;}}_x+n_x\mathrm{\&delta;}\\ {y_m}^{\&prime;}={y_{m0}}^{\&prime;}+n_y\mathrm{\&delta;}=y_m+{\mathrm{\&epsiv;}}_y+n_y\mathrm{\&delta;}\\ {z_m}^{\&prime;}={{\mathrm{<figure-callout\; id="0"\; label="z\; m"\; filenames="DEST\_PATH\_HSB00001102810400011.png"\; state="\{\{state\}\}">z</figure-callout>}}_m}^{\&prime;}+n_z\mathrm{\&delta;}=z_m+{\mathrm{\&epsiv;}}_z+n_z\mathrm{\&delta;}\end{array}\right.$

In the formula: x ' _m, y ' _m, z ' _mBe respectively the coordinate figure of best coincide the x axle of reflecting surface under the xoyz coordinate system, y axle, z axle;

(4) the secondary face expression formula after calculating is moved;

With reference to Fig. 2, the secondary face after moving is to design secondary face by theory to carry out translation along x axle, y axle, z direction of principal axis respectively, afterwards more respectively around x ₁Axle, y ₂Axle, z ₃Direction of principal axis is rotated and obtains.Integrating step (1), the secondary face after can moving is at x ₄O ₄y ₄z ₄Expression formula under the coordinate system is:

$\left\{\begin{array}{c}{x}_{4s}^{\&prime;}=x_s^{\&prime;}-u_x+{\mathrm{\&alpha;}}_z{y}_s^{\&prime;}-{\mathrm{\&alpha;}}_y{z}_s^{\&prime;}\\ y_{4s}^{\&prime;}=y_s^{\&prime;}-u_y-{\mathrm{\&alpha;}}_z{x}_s^{\&prime;}+{\mathrm{\&alpha;}}_x{z}_s^{\&prime;}\\ z_{4s}^{\&prime;}=z_s^{\&prime;}-u_z+{\mathrm{\&alpha;}}_y{x}_s^{\&prime;}-{\mathrm{\&alpha;}}_z{\mathrm{\&alpha;}}_s^{\&prime;}\end{array}\right.$

In the formula: x ' _s, y ' _s, z ' _sThe coordinate figure of the x axle of the secondary face after mobile of being respectively under the xoyz coordinate system, y axle, z axle; X ' _4s, y ' _4s, z ' _4sThe secondary face after mobile of being respectively is at x ₄O ₄y ₄z ₄X under the coordinate system ₄Axle, y ₄Axle, z ₄The coordinate figure of axle;

With reference to Fig. 2, because designing secondary face translation rotation by theory, the secondary face after mobile obtains same x ₄O ₄y ₄z ₄Coordinate system is also obtained by xoyz coordinate system translation rotation, and therefore, the secondary face after moving is at x ₄O ₄y ₄z ₄Position under the coordinate system is geostationary with the position of the theoretical secondary face of design under the xoyz coordinate system, and the secondary face after therefore moving is at x ₄O ₄y ₄z ₄Expression formula under the coordinate system also can be expressed as:

$\left\{\begin{array}{c}{x}_{4s}^{\&prime;}=x_s\\ y_{4s}^{\&prime;}=y_s\\ z_{4s}^{\&prime;}=z_s\end{array}\right.$

In the formula: x _s, y _s, z _sBe respectively the coordinate figure of the x axle of the secondary face of theoretical design under the xoyz coordinate system, y axle, z axle;

Therefore, can be got by above-mentioned two formulas:

$\left\{\begin{array}{c}{x}_s=x_s^{\&prime;}-u_x+{\mathrm{\&alpha;}}_z{y}_s^{\&prime;}-{\mathrm{\&alpha;}}_y{z}_s^{\&prime;}\\ y_s=y_s^{\&prime;}-u_y-{\mathrm{\&alpha;}}_z{x}_s^{\&prime;}+{\mathrm{\&alpha;}}_x{z}_s^{\&prime;}\\ z_s=z_s^{\&prime;}-u_z+{\mathrm{\&alpha;}}_y{x}_s^{\&prime;}-{\mathrm{\&alpha;}}_x{y}_s^{\&prime;}\end{array}\right.$

After the following formula conversion, the expression formula of the secondary face after can moving under theory design coordinate system xoyz is:

$\left\{\begin{array}{c}{x}_s^{\&prime;}=x_s+u_x-{\mathrm{\&alpha;}}_z{y}_s+{\mathrm{\&alpha;}}_y{z}_s\\ y_s^{\&prime;}=y_s+u_y+{\mathrm{\&alpha;}}_z{x}_s-{\mathrm{\&alpha;}}_x{z}_s\\ z_s^{\&prime;}=z_s+u_z-{\mathrm{\&alpha;}}_y{x}_s+{\mathrm{\&alpha;}}_x{y}_s\end{array}\right.$

(5) according to the secondary face expression formula after the identical reflecting surface expression formula of the best of determining in step (3), (4) and the movement, choose x ₄O ₄y ₄Be the aplanatism reference surface, the expression formula of the normal direction deviation δ between the primary reflection surface after calculating best coincide reflecting surface and the distortion;

(501) secondary face is less with respect to primary reflection surface, suppose it that translation and rotation are only arranged and not distortion, keep simultaneously after mobile feed and mobile after secondary face between distance and the distance between former feed and the secondary face of theoretical design remain unchanged, namely former feed need move to o ₄The place, calculate between the secondary face after feed and the movement after mobile apart from r _s＇;

During cassette antenna figuration, the distance between known former feed and the secondary face of theoretical design is

Therefore between the secondary face after the feed after mobile and the movement apart from r _s＇ is:

${r_s}^{\&prime;}=r_s=\sqrt{{x_s}^2+{y_s}^2+{z_s}^2}$

(502) according to the best of determining in step (3), (4) coincide reflecting surface with mobile after the expression formula of secondary face, calculate best coincide reflecting surface with move after secondary face between apart from S ＇;

$S^{\&prime;}=\sqrt{{({x_m}^{\&prime;}-{x_s}^{\&prime;})}^2+{({y_m}^{\&prime;}-{y_s}^{\&prime;})}^2+{({z_m}^{\&prime;}-{z_s}^{\&prime;})}^2}$

The following formula abbreviation can be got:

$S^{\&prime;}=S-\frac{u_x(x_m-x_s)+u_y(y_m-y_s)+u_z(z_m-z_s)}{S}+\frac{{\mathrm{\&alpha;}}_x(y_m{z}_s-z_m{y}_s)-{\mathrm{\&alpha;}}_y(x_m{z}_s-z_m{x}_s)}{S}$

$+\frac{(x_m-x_s)n_x+(y_m-y_s)n_y+(z_m-z_s)n_z}{S}\mathrm{\&delta;}+\frac{(x_m-x_s){\mathrm{\&epsiv;}}_x+(y_m-y_s){\mathrm{\&epsiv;}}_y+(z_m-z_s){\mathrm{\&epsiv;}}_z}{S}$

In the formula: $S=\sqrt{{(x_m-x_s)}^2+{(y_m-y_s)}^2{(z_m-z_s)}^2},$ Distance between the i.e. theory design major-minor reflecting surface.

With reference to Fig. 3, following geometric relationship is arranged during cassette antenna theory design major-minor reflecting surface figuration:

In the formula:

Feed and the line of secondary face respective point and the angle of z axle when θ is the figuration design;

The line of major-minor face respective point and the angle of z axle when θ is the figuration design;

Be the position angle;

Therefore, S ＇ can abbreviation be:

(503) feed after mobile with mobile after secondary face and the best reflecting surface that coincide constituted new Microwave Optics system, its aplanatism condition should be with x ₄O ₄y ₄The plane is reference surface, calculates the best reflecting surface that coincide at x ₄O ₄y ₄z ₄Z under the coordinate system ₄The value z ' of axle _4m

Integrating step (1) can get best identical reflecting surface at x ₄O ₄y ₄z ₄Z under the coordinate system ₄The value z ' of axle _4mFor:

z′ _4m＝z′ _m-u _z+α _yx′ _m-α _xy′ _m

Integrating step (3) with the expression formula substitution following formula of the identical reflecting surface of the best, is ignored second order in a small amount, and abbreviation can get:

z′ _4m＝z _m-u _z+α _yx _m-α _xy _m+ε _z+n _zδ

(504) the aplanatism equation of new Microwave Optics system is C ' _k=r _s＇+S ＇-z ' _4m, C ' _kBe the aplanatism constant of new Microwave Optics system, thereby can calculate primary reflection surface after the distortion and the expression formula of the best normal direction deviation δ between the reflecting surface that coincide;

The aplanatism equation of new Microwave Optics system is:

C′ _k＝r _s＇+S＇-z′ _4m

Integrating step (401)～(403), substitution aplanatism equation, abbreviation can get:

In the formula: the optical path difference Δ _Ck=C ' _k-C _kWherein, C _k=r _s+ S-z _m, C _kThe aplanatism constant of theoretical design during for cassette antenna figuration;

(6) according to the expression formula of the normal direction deviation δ that determines in the step (5), computing method is figuration cassette antenna interarea precision δ to the weighted mean square value of deviation δ _mExpression formula;

Consider the illumination coefficient F of theoretical design primary reflection surface sampling spot, its influence area is Δ S, then has:

Can get interarea precision δ _mExpression formula be:

(7) according to the figuration cassette antenna interarea precision δ that determines in the step (6) _mExpression formula, use least square method and calculate 6 degree of freedom parameters finding the solution the best reflecting surface that coincide.Coincide 6 degree of freedom parameters of reflecting surface of described the best are specially: respectively along the translational movement of x axle, y axle, z axle, respectively around x ₁Axle, y ₂Rotation amount and the change in optical path length amount of axle;

According to the definite figuration cassette antenna interarea precision δ of step (6) _mExpression formula, use least square method and calculate and can get:

$\frac{\&PartialD;{\mathrm{\&delta;}}_m^2}{\&PartialD;{\mathrm{\&Delta;}}_{\mathrm{ck}}}=\frac{\&PartialD;{\mathrm{\&delta;}}_m^2}{{\&PartialD;u}_x}=\frac{{\&PartialD;\mathrm{\&delta;}}_m^2}{{\&PartialD;u}_y}=\frac{{\&PartialD;\mathrm{\&delta;}}_m^2}{{\&PartialD;u}_z}=\frac{{\&PartialD;\mathrm{\&delta;}}_m^2}{{\&PartialD;\mathrm{\&alpha;}}_x}=\frac{{\&PartialD;\mathrm{\&delta;}}_m^2}{{\&PartialD;\mathrm{\&alpha;}}_y}=0$

Abbreviation can get, and the matrix of finding the solution of 6 degree of freedom parameters is:

$\left[\begin{array}{cccccc}{a}_{11}& a_{12}& a_{13}& a_{14}& a_{15}& a_{16}\\ a_{21}& a_{22}& a_{23}& a_{24}& a_{25}& a_{26}\\ a_{31}& a_{32}& a_{33}& a_{34}& a_{35}& a_{36}\\ a_{41}& a_{42}& a_{43}& a_{44}& a_{45}& a_{46}\\ a_{51}& a_{52}& a_{53}& a_{54}& a_{55}& a_{56}\\ a_{61}& a_{62}& a_{63}& a_{64}& a_{65}& a_{66}\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;}}_{\mathrm{ck}}\\ u_x\\ u_y\\ u_z\\ {\mathrm{\&alpha;}}_x\\ {\mathrm{\&alpha;}}_y\end{array}\right]=\left[\begin{array}{c}{c}_1\\ c_2\\ c_3\\ c_4\\ c_5\\ c_6\end{array}\right]$

In the formula:

$a_{11}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{A}_i$

Wherein:

(8) the best of obtaining in the step (7) the is coincide expression formula of the normal direction deviation δ that obtains in 6 degree of freedom parameter substitution steps (5) of reflecting surface obtains the numerical value of normal direction deviation δ; The figuration cassette antenna interarea precision δ that obtains in the numerical value substitution step (6) with normal direction deviation δ again _mExpression formula, obtain figuration cassette antenna interarea accurate values, finish the calculating of figuration cassette antenna interarea precision;

6 degree of freedom parameter Δs of best identical reflecting surface have been obtained in the step (6) _Ck, u _x, u _y, u _z, α _y, α _y, with the expression formula of the normal direction deviation δ that obtains in its substitution step (5), just can obtain the normal direction deviation of gross sample point, the figuration cassette antenna interarea precision δ that obtains in the numerical value substitution step (6) with normal direction deviation δ again _mExpression formula, can obtain figuration cassette antenna interarea accuracy value, finish the calculating of figuration cassette antenna interarea precision.

(9) the best of obtaining in the step (7) is coincide secondary face expression formula after the movement that obtains in 5 degree of freedom parameter substitution steps (4) of reflecting surface just can obtain the exact position that secondary face is adjusted, and finishes the adjustment of secondary face.5 degree of freedom parameters of the identical reflecting surface of described the best are specially respectively along the translational movement of x axle, y axle, z axle with respectively around x ₁Axle, y ₂The rotation amount of axle;

6 degree of freedom parameters of best identical reflecting surface have been obtained in the step (6), with 5 degree of freedom parameters u wherein _x, u _y, u _z, α _x, α _ySecondary face expression formula after the movement that obtains in the substitution step (4) is as follows:

$\left\{\begin{array}{c}{x}_s^{\&prime;}=x_s+u_x-{\mathrm{\&alpha;}}_z{y}_s+{\mathrm{\&alpha;}}_y{z}_s\\ y_s^{\&prime;}=y_s+u_y+{\mathrm{\&alpha;}}_z{x}_s-{\mathrm{\&alpha;}}_x{z}_s\\ z_s^{\&prime;}=z_s+u_z-{\mathrm{\&alpha;}}_y{x}_s+{\mathrm{\&alpha;}}_x{y}_s\end{array}\right.$

Wherein, with α _zBeing taken as 0 gets final product.This is around z because of secondary face ₃The axle rotation alpha _zDuring angle, it is about z ₃Axle is rotational symmetric, is equal to and do not rotate, therefore, can be with α _zAngle is taken as 0.Therefore, the accurate adjustment of secondary face position and attitude can be determined by following formula:

$\left\{\begin{array}{c}{x}_s^{\&prime;}=x_s+u_x+{\mathrm{\&alpha;}}_y{z}_s\\ y_s^{\&prime;}=y_s+u_y-{\mathrm{\&alpha;}}_x{z}_s\\ z_s^{\&prime;}=z_s+u_s-{\mathrm{\&alpha;}}_y{x}_s+{\mathrm{\&alpha;}}_x{y}_s\end{array}\right.$

Secondary face adjustment is finished like this: secondary face carries out translation u along x axle, y axle, z direction of principal axis respectively _x, u _y, u _z, and then around x ₁The axle rotation alpha _yThe angle is at last around y ₂The axle rotation alpha _ySubreflector can be adjusted to its position accurately in the angle, thereby finishes the adjustment of secondary face.

(10) the normal direction deviation δ expression formula of the best of obtaining in the step (7) being coincide obtaining in 6 degree of freedom parameter substitution steps (5) of reflecting surface, the primary reflection surface that the numerical value that obtains normal direction deviation δ is about to distortion is adjusted into the adjustment amount of the best reflecting surface that coincide, and finishes the adjustment of interarea.

6 degree of freedom parameter Δs of best identical reflecting surface have been obtained in the step (6) _Ck, u _x, u _y, u _z, α _y, α _y, with the expression formula of the normal direction deviation δ that obtains in its substitution step (5), just can obtain the adjustment amount of gross sample point, so just the primary reflection surface after the distortion can be adjusted into the best reflecting surface that coincide along normal orientation, so just finished the accurate adjustment of interarea.

Claims (7)

1. the Method for Accurate Calculation adjusted of a figuration cassette antenna interarea precision and major-minor face is characterized in that may further comprise the steps:

Suppose that (1) figuration cassette antenna theory design major-minor reflecting surface coordinate is xoyz; Coordinate system xoyz is carried out translation along x axle, y axle, z direction of principal axis respectively, afterwards more respectively around x ₁Axle, y ₂Axle, z ₃Direction of principal axis is rotated, and obtains describing the coincide coordinate system x of reflecting surface of secondary face and the best corresponding with the secondary face after the movement after mobile ₄O ₄y ₄z ₄Described x ₁Axle refers to coordinate system xoyz and carries out the coordinate system x that forms after the translation along x axle, y axle, z direction of principal axis respectively ₁o ₁y ₁z ₁Transverse axis; y ₂Axle refers to coordinate system x ₁o ₁y ₁z ₁Around x ₁The coordinate system x that axle rotation back forms ₂O ₂y ₂z ₂The longitudinal axis; z ₃Axle refers to coordinate system x ₂O ₂y ₂z ₂Around y ₂The coordinate system x that axle rotation back forms ₃O ₃y ₃z ₃Vertical pivot;

(2) because the load factor causes theoretical design primary reflection surface to produce distortion, the primary reflection surface expression formula after obtaining being out of shape by measurement or mechanics finite element analysis software;

Suppose that (3) the normal direction deviation between the primary reflection surface after best coincide reflecting surface and the distortion is δ, the primary reflection surface expression formula in the integrating step (2) after the distortion is calculated the best reflecting surface expression formula of coincideing;

(4) the secondary face expression formula after calculating is moved;

(5) according to the secondary face expression formula after the identical reflecting surface expression formula of the best of determining in step (3), (4) and the movement, choose x ₄O ₄y ₄Be the aplanatism reference surface, the expression formula of the normal direction deviation δ between the primary reflection surface after calculating best coincide reflecting surface and the distortion;

(6) according to the expression formula of the normal direction deviation δ that determines in the step (5), computing method is figuration cassette antenna interarea precision δ to the weighted mean square value of deviation δ _mExpression formula;

(7) according to the figuration cassette antenna interarea precision δ that determines in the step (6) _mExpression formula, use least square method and calculate 6 degree of freedom parameters finding the solution the best reflecting surface that coincide.Coincide 6 degree of freedom parameters of reflecting surface of described the best are specially: respectively along the translational movement of x axle, y axle, z axle, respectively around x ₁Axle, y ₂Rotation amount and the change in optical path length amount of axle;

(8) the best of obtaining in the step (7) the is coincide expression formula of the normal direction deviation δ that obtains in 6 degree of freedom parameter substitution steps (5) of reflecting surface obtains the numerical value of normal direction deviation δ; The figuration cassette antenna interarea precision δ that obtains in the numerical value substitution step (6) with normal direction deviation δ again _mExpression formula, obtain figuration cassette antenna interarea accurate values, finish the calculating of figuration cassette antenna interarea precision;

(9) the best of obtaining in the step (7) is coincide secondary face expression formula after the movement that obtains in 5 degree of freedom parameter substitution steps (4) of reflecting surface just can obtain the exact position that secondary face is adjusted, and finishes the adjustment of secondary face.5 degree of freedom parameters of the identical reflecting surface of described the best are specially respectively along the translational movement of x axle, y axle, z axle with respectively around x ₁Axle, y ₂The rotation amount of axle;

(10) the normal direction deviation δ expression formula of the best of obtaining in the step (7) being coincide obtaining in 6 degree of freedom parameter substitution steps (5) of reflecting surface, the primary reflection surface that the numerical value that obtains normal direction deviation δ is about to distortion is adjusted into the adjustment amount of the best reflecting surface that coincide, and finishes the adjustment of interarea.

2. the Method for Accurate Calculation adjusted of a kind of figuration cassette antenna interarea precision according to claim 1 and major-minor face, it is characterized in that: the identical reflecting surface of described the best refers to: after the distortion of figuration cassette antenna theory design primary reflection surface, the error of the primary reflection surface relative theory design primary reflection surface after the distortion is bigger, therefore can seek a new primary reflection surface, it has mobile with respect to theory design primary reflection surface and rotates, light path has the variation of trace simultaneously, this new primary reflection surface that satisfies the aplanatism condition has numerous, yet a new primary reflection surface is arranged wherein, primary reflection surface after the distortion is its root-mean-square error minimum relatively, and this new primary reflection surface is referred to as the best reflecting surface that coincide.

3. the Method for Accurate Calculation of a kind of figuration cassette antenna interarea precision according to claim 1 and major-minor face adjustment is characterized in that, x in the step (1) ₄o ₄y ₄z ₄The expression formula of coordinate system is:

$\left\{\begin{array}{c}{x}_4^{\&prime;}=x^{\&prime;}-u_x+{\mathrm{\&alpha;}}_z{y}^{\&prime;}-{\mathrm{\&alpha;}}_y{z}^{\&prime;}\\ y_4^{\&prime;}=y^{\&prime;}-u_y-{\mathrm{\&alpha;}}_z{x}^{\&prime;}+{\mathrm{\&alpha;}}_x{z}^{\&prime;}\\ z_4^{\&prime;}=z^{\&prime;}-u_z+{\mathrm{\&alpha;}}_y{x}^{\&prime;}-{\mathrm{\&alpha;}}_x{y}^{\&prime;}\end{array}\right.$

In the formula: x ' ₄, y ' ₄, z ' ₄Be respectively x ₄O ₄y ₄z ₄X under the coordinate system ₄Axle, y ₄Axle, z ₄The coordinate figure of axle; X ＇, y, z ＇ are respectively the coordinate figure of x axle under the xoyz coordinate system, y axle, z axle; u _x, u _y, u _zBe respectively along the translational movement of x axle, y axle, z axle; α _x, α _y, α _zBe respectively around x ₁Axle, y ₂Axle, z ₃The anglec of rotation of axle.

4. the Method for Accurate Calculation of a kind of figuration cassette antenna interarea precision according to claim 1 and major-minor face adjustment is characterized in that, the primary reflection surface expression formula in the step (2) after the distortion is:

$\left\{\begin{array}{c}{x_{m0}}^{\&prime;}=x_m+{\mathrm{\&epsiv;}}_x\\ {y_{m0}}^{\&prime;}=y_m+{\mathrm{\&epsiv;}}_y\\ {z_{m0}}^{\&prime;}=z_m+{\mathrm{\&epsiv;}}_z\end{array}\right.$

In the formula: x ' _M0, y ' _M0, z ' _M0Be respectively the coordinate figure of x axle under the xoyz coordinate system of primary reflection surface after the distortion, y axle, z axle; x _m, y _m, z _mBe respectively the coordinate figure of the x axle of theoretical design primary reflection surface under the xoyz coordinate system, y axle, z axle; ε _x, ε _y, ε _zBe respectively theoretical design primary reflection surface at the deflection of xoyz coordinate system lower edge x axle, y axle, z axle.

5. the Method for Accurate Calculation of a kind of figuration cassette antenna interarea precision according to claim 1 and major-minor face adjustment is characterized in that, calculates the best reflecting surface expression formula of coincideing in the step (3) to be:

$\left\{\begin{array}{c}{x_m}^{\&prime;}={x_{m0}}^{\&prime;}+n_x\mathrm{\&delta;}=x_m+{\mathrm{\&epsiv;}}_x+n_x\mathrm{\&delta;}\\ {y_m}^{\&prime;}={y_{m0}}^{\&prime;}+n_y\mathrm{\&delta;}=y_m+{\mathrm{\&epsiv;}}_y+n_y\mathrm{\&delta;}\\ {z_m}^{\&prime;}={z_{m0}}^{\&prime;}+n_z\mathrm{\&delta;}=z_m+{\mathrm{\&epsiv;}}_z+n_z\mathrm{\&delta;}\end{array}\right.$

In the formula: x ' _m, y ' _m, z ' _mBe respectively the coordinate figure of best coincide the x axle of reflecting surface under the xoyz coordinate system, y axle, z axle; n _x, n _y, n _zBe respectively the normal vector of theoretical design primary reflection surface at x axle, y axle, the axial component of z; δ is the primary reflection surface after being out of shape and best normal direction deviation of coincideing between the reflecting surface.

6. the Method for Accurate Calculation of a kind of figuration cassette antenna interarea precision according to claim 1 and major-minor face adjustment is characterized in that, the secondary face expression formula of calculating after moving in the step (4) is:

$\left\{\begin{array}{c}{x}_s^{\&prime;}=x_s+u_x-{\mathrm{\&alpha;}}_z{y}_s+{\mathrm{\&alpha;}}_y{z}_s\\ y_s^{\&prime;}=y_s+u_y+{\mathrm{\&alpha;}}_z{x}_s-{\mathrm{\&alpha;}}_x{z}_s\\ z_s^{\&prime;}=z_s+u_z-{\mathrm{\&alpha;}}_y{x}_s+{\mathrm{\&alpha;}}_x{y}_s\end{array}\right.$

In the formula: x _s, y _s, z _sBe respectively the coordinate figure of the x axle of the secondary face of theoretical design under the xoyz coordinate system, y axle, z axle; X ' _s, y ' _s, z ' _sThe coordinate figure of the x axle of the secondary face after mobile of being respectively under the xoyz coordinate system, y axle, z axle.

7. the Method for Accurate Calculation adjusted of a kind of figuration cassette antenna interarea precision according to claim 1 and major-minor face, it is characterized in that the expression formula of the normal direction deviation δ between the primary reflection surface in the step (5) after best coincide reflecting surface and the distortion of calculating may further comprise the steps:

(501) secondary face is less with respect to primary reflection surface, suppose it that translation and rotation are only arranged and not distortion, keep simultaneously after mobile feed and mobile after secondary face between distance and the distance between former feed and the secondary face of theoretical design remain unchanged, namely former feed need move to o ₄The place, calculate between the secondary face after feed and the movement after mobile apart from r _s＇;

(502) according to the best of determining in step (3), (4) coincide reflecting surface with mobile after the expression formula of secondary face, calculate best coincide reflecting surface with move after secondary face between apart from S ＇;

(503) feed after mobile with mobile after secondary face and the best reflecting surface that coincide constituted new Microwave Optics system, its aplanatism condition should be with x ₄O ₄y ₄The plane is reference surface, calculates the best reflecting surface that coincide at x ₄O ₄y ₄z ₄Z under the coordinate system ₄The value z ' of axle _4m

(504) the aplanatism equation of new Microwave Optics system is C ＇=r _s＇+S ＇-z ' _4m, C ＇ is the aplanatism constant of new Microwave Optics system, thereby can calculate primary reflection surface after the distortion and the expression formula of the best normal direction deviation δ between the reflecting surface that coincide.

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