CN101241000A - High steepness convex quadric aspherical aberration-free point Sub-Aperture Stitching measurement method - Google Patents

Abstract

The invention discloses a measuring method of non-aberration-point sub-aperture stitching for a high and steep convex second non-spherical surface, which divides the measured second non-spherical surface into a plurality of sub-apertures so that the test beam emitted by a surface wave interferometer roughly irradiates a divided first sub-aperture region thereof, measures the surface error of the sub-aperture with the surface wave interferometer under the test condition of non-aberration-point and saves the data, measures the second sub-aperture region and all the remaining sub-apertures in the same way and inputs all the measured data of the sub-apertures to process, and reconstructs the all-caliber face through non-aberration-point stitching algorithm so as to obtain the surface error of the measured second non-spherical surface. The invention needs no non-spherical surface compensator, and is a measuring method for high and steep convex second non-spherical surface with low cost and high precision.

Description

The aberrationless point method aperture splicing measuring method of high steepness convex secondary aspherical

Technical field

The invention belongs to the optical testing technology field, relate generally to a kind of aberrationless point method aperture splicing measuring method of high steepness convex secondary aspherical.

Background technology

Aspheric surface has aberration correction, improves picture element, enlarges outstanding advantages such as visual field, simplied system structure, has obtained widespread use in the contemporary optics system.Move towards high-end applications gradually along with optical system in recent years and optical design software constantly strengthens, various optical mirror planes novel, special-shaped, complicated surface continue to bring out, and wherein the most representative is exactly high steepness aspheric surface.

Conformal (conformal) optical surface is a kind of typical high steepness aspheric surface, its outstanding feature be in design process except that satisfying imaging requirements, more lay particular emphasis on and improve aspheric aerodynamic performance, to satisfy the requirement of various strategy and tactics guided missiles.Replace the target seeker of traditional semispherical surface with it as guided missile, can significantly reduce air resistance, improve the aerodynamic performance of guided missile, thereby obtain higher flying speed, farther range and mobility more flexibly, therefore the high fighting efficiency of final acquisition has caused the attention of countries in the world.1996, U.S. national defense advanced technology project agency (DARPA, Defense Advanced Research Projects Agency) took the lead in supporting relevant university and company to study high steepness conformal optical mirror plane characteristics, application places and feasibility.Under the guidance of DARPA, formed conformal optical research group-PCOT (Precision ConformalOptics Technology) in 1998.Raytheon company had succeeded in developing first conformal optical seeker in the world in 1999.Compare with traditional aspheric mirror, the conformal optical mirror plane can not use conventional relative aperture and aspherical degree to characterize, its common characterization parameter is bore and length-diameter ratio, be the ratio of vertical discrepancy in elevation and bore, the length-diameter ratio of typical conformal optical surface is more than 1.0, and hemispherical length-diameter ratio is 0.5.Consider the complicacy of making and measuring at present, the conformal optical surface on the target seeker is normal to adopt protruding secondary aspherical, and mainly is ellipsoid.Secondary aspherical comprises ellipsoid, hyperboloid and parabola.

Detect at aspheric face shape error of polishing stage wavefront interferometer commonly used.For high steepness secondary aspherical because aspherical degree is too big, head and shoulders above the vertical survey scope of wavefront interferometer, cause the interference fringe that forms too close and can't resolve.Adopt compensator the test sphere wavefront transform of interferometer can be become the non-spherical wavefront of mating with tested aspheric surface, thereby realize interfering the purpose that detects, but for high steepness secondary aspherical, its compensator itself also is aspheric surface usually, and problem is made, detected and debug to same the existence.

Liu and Lawrence etc. are at " Subaperture testing of aspheres with annularZones ", Y.M.Liu, G.N.Lawrence, and C.L.Koliopoulo, AppliedOptics, 27 (21): 4504-4513, propose in 1988 to adopt the method for endless belt sub-aperture stitching to measure heavy caliber and turn round symmetrical aspheric surface, need not compensator and increased the vertical survey scope.Hou Xi etc. propose to utilize the part compensator to carry out the endless belt sub-aperture stitching in the embodiment of Chinese patent application number " 200510116819.5 " " a kind of deep aspherical mirror detection system with big bore " and measure, and can solve the many problems of the sub-aperture of the heavy caliber required endless belt of dark type aspheric surface number.Above method can only increase the vertical survey scope to a certain extent, and for high steepness secondary aspherical, the sub-aperture of required endless belt is very many and sub-aperture is too narrow, seriously reduces the reliability of sub-aperture stitching algorithm and inapplicable.

U.S. QED company is at " An automated subaperture stitching interferometerworkstation for spherical and aspherical surfaces ", P.E.Murphy, andG.W.Forbes, Proc.SPIE, Vol.5188,296-307,2003 and United States Patent (USP) " US6956657B2 " in the sub-aperture stitching method of a kind of aspherical mirror shape error-detecting is proposed, adjust tested aspheric surface or interferometer by 6 motion platforms, detection is interfered in the antithetical phrase aperture, adopt stitching algorithm to obtain unified testing result then, algorithm has mainly compensated interferometer image deformation error, inclination between reference wave surface error and the sub-aperture, defocus error.Algorithm does not need iteration, by hardware accuracy guarantee reliability.Li Shengyi etc. have proposed a kind of aspheric mirror medium-high frequency error detecting apparatus and method in Chinese patent application number " 200710034359.0 " " heavy caliber object lens of large relative aperture aspheric mirror medium-high frequency error detecting apparatus and method ", adopt 5-axis movement to adjust the Platform Implementation subregional interferometry in tested aspheric mirror top, adopt the area data stitching algorithm, the grid scale error of the six degree of freedom position and attitude error in the compensating measure process, best-fit radius of a ball error and interferometer imaging.More than two kinds of methods require the face shape in tested sub-aperture can be approximately sphere, promptly the aspherical degree in sub-aperture is smaller, available spherical wave interferometer is directly measured, and is mainly used in low steepness aspheric surface.For high steepness secondary aspherical,, cause that interference fringe is too close can not resolve because along generatrix direction curvature acute variation.Ellipsoid bore 75mm for example, length-diameter ratio 1.2, the radius in the middle center aperture that wavefront interferometer can directly be measured is less than 10mm, and reduces sharply especially from the roller pore size.

Su Xianyu etc. propose mobile interferometer in Chinese patent application number " 200710048201.9 " " a kind of Omnibearing detection method for large-diameter aspherical mirror " carries out continuous sweep along the aspheric surface axis of symmetry and obtains the time dependent three-dimensional interference striped of the whole audience, carry out data processing and reconstruct the whole audience information of tested aspheric surface, need not the aspheric surface compensator, need not to carry out sub-aperture stitching, but Measurement Resolution is not high, measuring accuracy is subjected to the scanning motion accuracy limitations, and is difficult to realize for the high steepness convex secondary aspherical.

Summary of the invention

The objective of the invention is to:, propose the aberrationless point method aperture splicing measuring method of a kind of low cost, high-precision high steepness convex secondary aspherical at the technical matters that prior art exists.

The aberrationless point method aperture splicing measuring method of the high steepness convex secondary aspherical that the present invention proposes may further comprise the steps:

The first step: the geometric parameter according to tested secondary aspherical is divided the plurality of sub aperture with it, wavefront interferometer, tested secondary aspherical and sphere or plane mirror are installed on the corresponding platform, and the test beams that makes wavefront interferometer send roughly is radiated at first sub-aperture area of dividing on the tested secondary aspherical;

Second step: by adjusting the position and the attitude of wavefront interferometer or tested secondary aspherical, and the position of sphere or plane mirror and attitude, make and satisfy aberrationless point method test condition, be that the convergent point of the spherical wave test beams sent of wavefront interferometer and the center of curvature of spherical reflector are positioned on a pair of aberrationless point of tested secondary aspherical, for tested secondary aspherical is parabolic situation, the convergent point of the spherical wave test beams that wavefront interferometer sends overlaps with paraboloidal focus, and catoptron is plane and perpendicular to paraboloidal axis of symmetry;

The 3rd step: utilize wavefront interferometer to measure the face shape error in sub-aperture and data are deposited;

The 4th step: by adjusting the position and the attitude of wavefront interferometer or tested secondary aspherical, and the position of sphere or plane mirror and attitude, the test beams that makes wavefront interferometer send is radiated at second sub-aperture area of dividing on the tested secondary aspherical and satisfies aberrationless point method test condition, utilizes wavefront interferometer to measure the face shape error in sub-aperture and data are deposited;

The 5th step: repeated for the 4th step and measure up to the face shape error in all sub-apertures of realizing dividing on the tested aspheric surface, each sub-inside diameter measurement data input computing machine is handled, carry out unified shape reconstruct by aberrationless point method aperture splicing algorithm, obtain the face shape error of tested secondary aspherical.

The plurality of sub aperture is made of different piece zone on the tested secondary aspherical, has overlappingly between the sub-aperture mutually, and sub-aperture set covers the unified of tested secondary aspherical.

Aberrationless point method aperture splicing algorithm comprises that initial pose determines method, overlapping sub-aperture data extraction algorithm and sub-inside diameter measurement parameter optimization algorithm.Initial pose is determined position and the attitude adjustment amount of exercise of method according to wavefront interferometer in the measuring process or tested secondary aspherical, calculates the initial pose of the tested relatively secondary aspherical of wavefront interferometer automatically; Overlapping sub-aperture data extraction algorithm to the containment relationship between the subpoint of nominal secondary aspherical, is determined the overlapped data between any two tested sub-apertures according to data point automatically; Sub-inside diameter measurement parameter optimization algorithm passes through iteration optimization, six degree of freedom position and attitude error in the compensating measure process, best-fit secondary aspherical parameter error, make inconsistency minimum between all overlapped data, all data points and nominal secondary aspherical optimum matching simultaneously.

This measuring method need not the aspheric surface compensator, by aberrationless point method aperture splicing algorithm plurality of sub inside diameter measurement data splicing is obtained unified face shape error, resolution than unified interferometry is higher, algorithm requires the position adjustment precision of wavefront interferometer or tested secondary aspherical and sphere or plane mirror to reach 0.1mm, and attitude is adjusted precision and reached 1 '.

Compared with prior art, the invention has the advantages that:

1, the aberrationless point method aperture splicing measuring method of high steepness convex secondary aspherical of the present invention is by carrying out the zero-bit interferometry to the plurality of sub aperture on aberrationless point, avoided the glancing incidence problem of unified measuring method at tested secondary aspherical edge, by the unified face shape error of aberrationless point method aperture splicing algorithm reconstruct, improved lateral resolution;

2, aberrationless point method aperture splicing algorithm of the present invention requires the position adjustment precision of wavefront interferometer or tested secondary aspherical and sphere or plane mirror to reach 0.1mm, and attitude adjustment precision reaches 1 ' and gets final product, thereby has reduced cost;

3, aberrationless point method aperture splicing algorithm of the present invention can be determined the overlapped data between any two tested sub-apertures automatically, compensated six degree of freedom position and attitude error and the best-fit secondary aspherical parameter error in the measuring process, thereby do not need measurement data is carried out pre-service, do not need accurate priori, just can obtain high-precision unified face shape error expeditiously.

Below in conjunction with accompanying drawing the present invention is described in further details.

Description of drawings

Fig. 1 is the system and device synoptic diagram that the inventive method adopts.

Fig. 2 is that synoptic diagram is divided in unified sub-aperture of going up the high steepness convex secondary aspherical.

Fig. 3 is the coordinate graph of a relation of the inventive method actual spot of measurement.

Fig. 4 is three coordinate system figure that the inventive method aberrationless point method sub-aperture stitching relates to.

Fig. 5 is the inventive method aberrationless point method aperture splicing algorithm flow chart.

Embodiment

As shown in Figure 1, the system and device of measuring method employing of the present invention mainly is made up of wavefront interferometer (for example Fizeau type spherical wave interferometer) 1, tested secondary aspherical 2, sphere or plane mirror 3, main control computer and corresponding position and attitude motion adjusting mechanism.

In order to reduce the influence of ambient vibration to detecting, suggestion is placed on the whole measuring system device on the air supporting vibration-isolating platform.

The face shape error that obtains tested secondary aspherical can carry out according to following measuring method of the present invention.

See Fig. 2, at first tested secondary aspherical 2 is divided into some overlapping sub-apertures that have mutually, main consider sub-aperture overlap coefficient (between the sub-aperture overlapping region ratio of area in sub-aperture changes), requirements such as unified covering power and structural constraint, by calculating incident beam 4 and the marginal ray of folded light beam 5 and the intersection point of tested secondary aspherical 2, determine the scope in tested sub-aperture, with a bore 75mm, length-diameter ratio 1.2 (vertex curvature radius 15.5612mm, secondry constants-0.8278) ellipsoid is an example, interferometer is selected f/7 sphere lens group, can with minute surface therefrom mind-set be divided into outward 3 the circle, each circle comprises 6 successively, 12,18 and 24 sub-apertures, one has 60 from the roller aperture, middle center aperture can be approximately sphere, need not adopt method of the present invention, can directly use interferometer measurement; The test beams that wavefront interferometer is sent roughly is radiated at first sub-aperture area of dividing on the tested secondary aspherical;

See Fig. 1, adjust the position and the attitude of wavefront interferometer 1 or tested secondary aspherical 2, and the position and the attitude of sphere or plane mirror 3, make the convergent point 6 of the spherical wave test beams 4 that wavefront interferometer sends and the center of curvature 7 of spherical reflector 3 be positioned on a pair of aberrationless point of tested secondary aspherical 2, test beams 4 is at first shone to spherical reflector 3 along normal direction after tested secondary aspherical 2 reflections, the reverse extending congruence accumulation that is folded light beam 5 overlaps with the center of curvature 7 of spherical reflector 3, folded light beam 5 shines on the tested secondary aspherical 2 after reflecting through spherical reflector 3 once more, after tested secondary aspherical 2 reflections, return wavefront interferometer 1 again along former road, meeting with the reference beam of interferometer reference surface reflection interferes, and realizes the aberrationless point method interferometry in sub-aperture on the tested secondary aspherical 2; For tested secondary aspherical 2 are parabolic situations, and the convergent point 6 of the spherical wave test beams 4 that wavefront interferometer sends overlaps with paraboloidal focus, and catoptron 3 is plane and perpendicular to paraboloidal axis of symmetry;

Utilize wavefront interferometer to measure the face shape error in sub-aperture and data are deposited;

Adjust the position and the attitude of wavefront interferometer 1 or tested secondary aspherical 2, and the position and the attitude of sphere or plane mirror 3, aberrationless point method interferometry finished to other sub-apertures on the tested secondary aspherical;

Measurement data input computing machine with position in the measuring process and attitude motion amount and interferometer 1, utilize the Measurement and Data Processing algorithm to calculate the initial pose of the tested relatively secondary aspherical of interferometer in each sub-inside diameter measurement process automatically, automatically determine the overlapped data between any two tested sub-apertures, pass through iteration optimization at last, six degree of freedom position and attitude error in the compensating measure process, best-fit secondary aspherical parameter error, thus realize that error surface shape figure with a plurality of sub-apertures is spliced into the error surface shape figure on unified.

The principle that the present invention adopts is the interferometry of aberrationless point method, all is nonnormal incidence for each sub-aperture, determines the object coordinates of actual spot of measurement by method shown in Figure 3.At first, be different from the normal incidence interferometry, the incident angle of aberrationless point method interferometry changes on whole bore, thereby the scale factor of interferometer (scale factor) is not a constant.Suppose that the tested surface equation is

$\frac{x^2+y^2}{a^2}+\frac{{(z+b)}^2}{b^2}=1$

Wherein x, y and z are the parameter of surface equation, and a and b are that the major semi-axis of ellipsoid is long and minor semi-axis is long.

For 1 Q on the actual tested surface, its corresponding optical path difference is

O wherein ₁And O ₂Be ellipsoid perifocus and over focus, O ₁Q and O ₂The intersection point of Q and nominal ellipsoid is respectively P ₁And P ₂So measurement point Q is positioned on the ellipsoid (being called the error ellipsoid face)

Wherein $c=\sqrt{b^2-{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="S2008100308197E00011.png,S2008100308197E00021.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}.$

Measurement and Data Processing algorithm flow of the present invention is (is example with tested protruding ellipsoid) as shown in Figure 5:

The first step: the input data, determine initial pose and best-fit secondary aspherical parameter.Each sub-aperture is in measuring process, and all to a best-fit ellipsoid 8 should be arranged, owing to have face shape error and alignment error, the best-fit ellipsoid does not overlap with nominal ellipsoid 2 actual tested surface 9.It is as follows to set up three coordinate systems: { TS} is based upon on the transmission ball summit of wavefront interferometer 1, and the Z axle is the optical axis of test beams; The local coordinate system of sub-aperture i i} in the best-fit ellipsoid in the heart, and model coordinate systems { M} is based upon on the summit of nominal ellipsoid (referring to Fig. 4).Model coordinate systems { { the relative local coordinate system of M} is determined according to position in the measuring process and attitude motion amount by the initial pose of i}; Because the convergence range of detection data processing algorithm of the present invention is big, the initial value of best-fit ellipsoid parameter can be taken as the parameter of nominal ellipsoid.

Second step: overlapping sub-aperture data extract.The measurement data of supposing interferometer 1 on i the sub-aperture is { w _{J, i}=(u _{J, i}, v _{J, i}, φ _{J, i}), j=1 ..., N _i, φ wherein _{J, i}Be pixel coordinates (u _{J, i}, v _{J, i}) on the phase differential scale factor of interferometer (this moment be set to 1), N _iBe i the sampling number on the sub-aperture.{ coordinate among the i} is (to omit subscript i, j) to corresponding measurement point at coordinate system

$\left[\begin{array}{c}{t}_1\\ t_2\\ {\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="S2008100308197E00011.png"\; state="\{\{state\}\}">t</figure-callout>}}_3\\ 1\end{array}\right]=T_1{\mathrm{<figure-callout\; id="2"\; label="RT"\; filenames="S2008100308197E00011.png,S2008100308197E00021.png"\; state="\{\{state\}\}">RT</figure-callout>}}_2\left[\begin{array}{c}\mathrm{\&beta;u}\\ \mathrm{\&beta;v}\\ \sqrt{r_{\mathrm{ts}}^2-{\mathrm{\&beta;}}^2{u}^2-{\mathrm{\&beta;}}^2{v}^2}-r_{\mathrm{ts}}\\ 1\end{array}\right]$

Wherein β is the lateral coordinates scale factor, r _TsThe transmission radius of a ball for interferometer

$T_1=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& -\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="S2008100308197E00012.png"\; state="\{\{state\}\}">c</figure-callout>}\\ 0& 0& 0& 1\end{array}\right],$ ${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="S2008100308197E00011.png,S2008100308197E00021.png"\; state="\{\{state\}\}">T</figure-callout>}}_2=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& {\mathrm{<figure-callout\; id="0"\; label="r\; ts"\; filenames="S2008100308197E00012.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{ts}}\\ 0& 0& 0& 1\end{array}\right]$

R is the 3 d pose matrix that homogeneous coordinates are represented.Error ellipsoid face and mistake point (t ₁, t ₂, t ₃) and the intersection point of the line of best-fit ellipsoid over focus be actual spot of measurement, (x, y z) obtain by separating following equation its coordinate

$\frac{x}{t_1}=\frac{\mathrm{<figure-callout\; id="2"\; label="y\; t"\; filenames="S2008100308197E00011.png,S2008100308197E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}{t_{}}=\frac{z+c}{{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="S2008100308197E00011.png"\; state="\{\{state\}\}">t</figure-callout>}}_3+c}$

Wherein

{ coordinate is measurement point among the M} at coordinate system

${[{}^{M}x,{}^{M}y,{}^{M}z,1]}^T=g_i^{-1}{[x,y,z,1]}^T$

Wherein $g_i=\exp \left({\mathrm{\&Sigma;}}_{h=1}^5{m}_{h,i}{\widehat{\mathrm{\&xi;}}}_h\right){\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="S2008100308197E00012.png"\; state="\{\{state\}\}">G</figure-callout>}}_0,$ For coordinate system M} relatively the position shape of i},

Be spinor, ξ _h∈ R ⁶Be vector of unit length, its h component is 1, and other components are 0.m _{H, i}Be correspondence Coordinate, G ₀For turning round symmetrical subgroup.

Above-mentionedly transform to from w that { transformation of coordinates note is f the M}

[ ^Mx， ^My， ^Mz，1] ^T＝fw

Pose { the g that utilizes the first step to determine _i, attitude matrix { R _i, best-fit ellipsoid parameter { b _i, c _iAfter, by following formula measurement data points is transformed to model coordinate systems { under the M}.Then all measurement data points in k sub-aperture and the individual sub-aperture of i are all projected on the nominal secondary aspherical, produce homolographic projection point set { x _{J, k}And { x _{J, i}.Claim k the some f in the sub-aperture _kw _{Jo, k}Drop in the overlay region, if its subpoint x _{Jo, k}Projection on the XY plane is positioned at projection point set { x _{J, i}In the convex closure of projection on the XY plane (can with reference to " IterativeAlgorithm for Subaperture Stitching Interferometry for General Surfaces " J.OSA.A.22 (9): 1929-1936 such as Chinese patent application such as Li Shengyi number " 200710034359.0 " and Chen, 20005).

After having extracted overlapping sub-aperture data, calculate the root-mean-square value σ of the deviation of the distance of its corresponding measurement data points to the nominal secondary aspherical _o, calculate the root-mean-square value σ of the distance of all measurement data points to the nominal secondary aspherical simultaneously, wherein σ and σ _oBe about pose { g _i, attitude matrix { R _iAnd best-fit ellipsoid parameter { b _i, c _iNonlinear function

${\mathrm{\&sigma;}}^2=\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}{\&lang;f_i{w}_{j,i}-x_{j,i},n_{j,i}\&rang;}^2/N$

${\mathrm{\&sigma;}}_o^2=\underset{i=1}{\overset{s-1}{\mathrm{\&Sigma;}}}\underset{k=i+1}{\overset{s}{\mathrm{\&Sigma;}}}\underset{\mathrm{jo}=1}{\overset{{}^{\mathrm{ik}}N_o}{\mathrm{\&Sigma;}}}{(\&lang;f_k\&CenterDot;{}^{\mathrm{ik}}w_{\mathrm{jo},k}-{}^{\mathrm{ik}}x_{\mathrm{jo},k},{}^{\mathrm{ik}}n_{\mathrm{jo},k}\&rang;-\&lang;f_i\&CenterDot;{}^{\mathrm{ik}}w_{\mathrm{jo},i}-{}^{\mathrm{ik}}x_{\mathrm{jo},k},{}^{\mathrm{ik}}n_{\mathrm{jo},k}\&rang;)}^2/N_o$

Wherein $N=\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{N}_i$ Be total number of sample points, s is a sub-aperture number, and x and n are the unit normal vector of sampled point at lip-deep subpoint of name and subpoint place; $N_o={\mathrm{\&Sigma;}}_{i=1}^{s-1}{\mathrm{\&Sigma;}}_{k=i+1}^s{}^{\mathrm{ik}}N_o$ To sum, pre-super ik represents it is the overlapping region of sub-aperture k and sub-aperture i for overlapping.Note overlapping to identical closest approach is arranged ^Ikx _{Jo, k}And normal vector ^Ikn _{Jo, k}

The 3rd step: calculating target function value.Objective function is the linear combination of binocular target

$F={\mathrm{\&mu;}}_1{\mathrm{\&sigma;}}^2+{\mathrm{\&mu;}}_2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="o"\; filenames="S2008100308197E00011.png,S2008100308197E00021.png"\; state="\{\{state\}\}">o</figure-callout>}}^2$

μ wherein ₁And μ ₂Weight coefficient for positive satisfies μ ₁+ μ ₂=1.

The 4th step: judge whether convergence.The condition of convergence is target function value F＜ε ₁Or the target function value of adjacent twice iteration is poor | F _n-F _N-1|＜ε ₂, ε ₁And ε ₂It is constant given in advance.If satisfy the condition of convergence, then algorithm finishes, and the pose, attitude matrix and the best-fit ellipsoid parameter that obtain according to optimization transform to model coordinate systems with sub-aperture data and { among the M}, obtain unified face shape error; Otherwise continue next step.

The 5th step: adopt sub-inside diameter measurement parameter optimization algorithm, calculate new pose, attitude matrix and best-fit ellipsoid parameter.If l is an iterations, utilize following formula approximate

$g_i^{l+1}=g_i^l\exp \left(\underset{h=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_{h,i}{\widehat{\mathrm{\&xi;}}}_h\right)\&ap;g_i^l[I+\underset{h=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_{h,i}{\widehat{\mathrm{\&xi;}}}_h]$

υ wherein _{1, i}, υ _{2, i}And υ _{3, i}Be correspondence

With Coordinate, I is 4 * 4 unit matrixs, and objective function is carried out linearization process, with σ and σ _oIn inner product＜part is expressed as linear function about pose, attitude matrix and best-fit ellipsoid parameter

$d_{j,i}^{l+1}=\&lang;f_i{w}_{j,i}-x_{j,i},n_{j,i}\&rang;\&ap;d_{j,i}^l+{\&dtri;}_{j,i}^{T}m$

M=[υ wherein _1,1, υ _2,1, υ _3,1, m _1,1..., m _5,1, b ₁, c ₁..., υ _{1, s}, υ _{2, s}, υ _{3, s}, m _{1, s}..., m _{5, s}, b _s, c _s] ^TBe the variable parameter of expression pose, attitude matrix and best-fit ellipsoid, d ^l _{J, i}Be in the l time iteration sampled point to the distance on name surface,  ^T _{J, i}Distance function gradient for last j the measurement point of sub-aperture i.Thereby the objective function minimization problem turns to the linear least-squares problem, finds the solution system of linear equations and obtains new pose, attitude matrix and best-fit ellipsoid parameter.Make iterations l=l+1, algorithm jumped to for second step.

Claims (2)

1, a kind of aberrationless point method aperture splicing measuring method of high steepness convex secondary aspherical is characterized in that adopting following steps:

The first step: the geometric parameter according to tested secondary aspherical is divided the plurality of sub aperture with it, wavefront interferometer, tested secondary aspherical and sphere or plane mirror are installed on the corresponding platform, and the test beams that makes wavefront interferometer send roughly is radiated at first sub-aperture area of dividing on the tested secondary aspherical;

Second step: by adjusting the position and the attitude of wavefront interferometer or tested secondary aspherical, and the position of sphere or plane mirror and attitude, make and satisfy aberrationless point method test condition, be that the convergent point of the spherical wave test beams sent of wavefront interferometer and the center of curvature of spherical reflector are positioned on a pair of aberrationless point of tested secondary aspherical, for tested secondary aspherical is parabolic situation, the convergent point of the spherical wave test beams that wavefront interferometer sends overlaps with paraboloidal focus, and catoptron is plane and perpendicular to paraboloidal axis of symmetry;

The 3rd step: utilize wavefront interferometer to measure the face shape error in sub-aperture and data are deposited;

The 4th step: by adjusting the position and the attitude of wavefront interferometer or tested secondary aspherical, and the position of sphere or plane mirror and attitude, the test beams that makes wavefront interferometer send is radiated at second sub-aperture area of dividing on the tested secondary aspherical and satisfies aberrationless point method test condition, utilizes wavefront interferometer to measure the face shape error in sub-aperture and data are deposited;

The 5th step: repeated for the 4th step and measure up to the face shape error in all sub-apertures of realizing dividing on the tested aspheric surface, each sub-inside diameter measurement data input computing machine is handled, carry out unified shape reconstruct by aberrationless point method aperture splicing algorithm, obtain the face shape error of tested secondary aspherical.

2, the aberrationless point method aperture splicing measuring method of high steepness convex secondary aspherical according to claim 1 is characterized in that: have overlappingly between the described sub-aperture mutually, and sub-aperture set covers the unified of tested secondary aspherical.

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