CN102620683A - Aspheric surface adjustment error compensation method for sub-aperture stitching detection - Google Patents

Abstract

An aspheric surface adjustment error compensation method for sub-aperture stitching detection relates to the field of optical detection, and includes the steps: setting an interferometer to lead the curvature radius of a reference sphere wave front of the interferometer to be matched with the closest spherical radius of a central area of a to-be-detected aspheric surface; adjusting the relative position relation of the interferometer with the to-be-detected aspheric surface, so that the standard spherical wave front of the interferometer is aligned with a to-be-detected aspheric surface area; by means of a pattern search error compensation method, eliminating adjustment errors generated when the standard spherical surface detects the to-be-detected aspheric surface with large deviation amount; and realizing full-aperture stitching detection to obtain a precise surface-shaped result by means of the sub-aperture stitching detection technology. By means of the pattern search error compensation method, the adjustment errors resulting from nonalignment of stitching measurement positions can be effectively eliminated from measured sub-aperture phase data, so that stitching of multiple sub-apertures can be effectively realized, and aspheric surface full-aperture surface-shaped stitching detection can be precisely completed.

Description

Sub-aperture stitching detects aspheric surface adjustment error compensating method

Technical field

The present invention relates to the optical detection field, be specifically related to a kind of sub-aperture stitching and detect aspheric surface adjustment error compensating method.

Background technology

In optical system and optical instrument, utilize non-spherical element can correct aberration; Improve picture element; And can reduce the size and the weight of optical system; Therefore non-spherical element is used to fields such as astronomy, space optics, military and national defense, high-tech is civilian just more and more, and the detection of aspheric surface element has also received concern gradually.

Sub-aperture stitching is to utilize the small-bore standard sphere of interferometer reference wavefront that each regional phase place on the aperture aspherical is measured one by one, can obtain the unified face shape information of aspheric surface through the sub-aperture stitching algorithm.The sub-aperture stitching technology has been widened the aspheric horizontal and vertical dynamic range of interferometer measurement, makes aspheric bore of interferometer measurement and relative aperture that very big increase all arranged.In addition, be identical because the sub-aperture area of fritter is measured the interferometer CCD elemental area that is utilized with the interferometer CCD elemental area that unified interferometry is utilized, so sub-inside diameter measurement can obtain the information of the medium-high frequency section of aspheric surface.

Because the sub-aperture stitching method is to utilize the standard ball ground roll to go to detect aspheric surface; Measurement for single sub-aperture phase data; Need the radius-of-curvature of interferometer emerging wavefront and coincideing near spherical radius of sub-aperture area to be measured, therefore bearing accuracy and the repeatable accuracy to the splicing adjusting mechanism has very high requirement.But in the splicing measuring process, the relative position relation that interferometer and aspheric surface to be measured are actual is certain to exist deviation with theoretical relative position relation.

Summary of the invention

In order to solve the problem that exists in the prior art; The invention provides a kind of sub-aperture stitching and detect aspheric surface adjustment error compensating method; This method can well be eliminated and compensate in the sub-aperture stitching measuring process and not aim at the error of being brought owing to adjusting mechanism, thereby accomplish well aspheric sub-aperture stitching is detected.

The technical scheme that technical solution problem of the present invention is adopted is following:

Sub-aperture stitching detects aspheric surface adjustment error compensating method, and this method comprises the steps:

Step 1: set interferometer, make the radius-of-curvature of its reference sphere wavefront and coincideing near spherical radius of aspheric surface to be measured central area;

Step 2: adjustment interferometer and aspheric relative position relation to be measured make interferometer standard spherical wave front aim at aspheric surface zone to be measured;

Step 3:, eliminate the adjustment error that produces when the standard sphere detects the bigger aspheric surface to be measured of bias through the pattern search error compensating method;

Step 4:, realize that unified splicing detects, and obtains accurate face type result through the sub-aperture stitching detection technique.

The invention has the beneficial effects as follows: the present invention utilizes the pattern search error compensating method can well the adjustment error that have aligning to bring owing to the splicing measuring position not eliminated from the sub-aperture phase data of measuring; Thereby realize the splicing in a plurality of sub-apertures well, accomplish unified shape splicing of aspheric surface accurately and detect.

Description of drawings

Fig. 1 sub-aperture stitching of the present invention detects the sub-aperture of aspheric surface adjustment error compensating method and divides figure.

Fig. 2 sub-aperture stitching of the present invention detects the process flow diagram of aspheric surface adjustment error compensating method.

Fig. 3 sub-aperture stitching of the present invention detects aspheric surface adjustment error compensating method coordinate system definition figure.

Fig. 4 does not originally carry out optimizing complementary area shape error map to the adjustment error.

Fig. 5 sub-aperture stitching of the present invention detects spliced shape of aspheric surface adjustment error compensating method and distributes.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is explained further details.

Sub-aperture stitching detects aspheric surface adjustment error compensating method, and this method comprises the steps:

Step 1: set interferometer, make the radius-of-curvature of its reference sphere wavefront and coincideing near spherical radius of aspheric surface to be measured central area, promptly measure the PHASE DISTRIBUTION in the sub-aperture of center reference;

Step 2: adjustment interferometer and aspheric relative position relation to be measured, make interferometer standard spherical wave front aim at aspheric surface zone to be measured, promptly measure the PHASE DISTRIBUTION in other sub-apertures;

Step 3:, eliminate the adjustment error that produces when the standard sphere detects the bigger aspheric surface to be measured of bias through the pattern search error compensating method;

Step 4:, realize that unified splicing detects, and obtains accurate face type result through the sub-aperture stitching detection technique.

In order to verify the feasibility of adjustment error compensating method mathematical model, we are that the off-axis aspheric surface of 64.1 μ m has carried out the splicing test experience to a bias.This aspheric clear aperture is 230mm * 141mm, and vertex curvature radius is-1358.8mm that the quadric surface coefficient is-1.59, is-88.44mm from the axle amount.

Aspheric surface to be measured is placed on the four-dimensional adjusting mechanism; Can accurately adjust aspheric surface on X axle, Z-direction translation and along the inclination of X axle and Y direction; Interferometer is installed on the accurate elevating mechanism; Can regulate its translation on directions X, all test equipment all are placed on the shockproof platform of air supporting, and sub-aperture is divided as shown in Figure 1.

At first, regulate interferometer, make it with reference to the radius-of-curvature of spherical wave front and coincideing near spherical radius of aspheric surface to be measured central area (the sub-aperture 0 of center reference).

Adjust the relative position between aspheric surface to be measured and the interferometer, make the interferometer emerging wavefront aim at zone (sub-aperture 1) and lower area (sub-aperture 2) on the aspheric surface to be measured respectively, and make sub-aperture 1 and sub-aperture 2 certain overlapping region arranged respectively with the sub-aperture 0 of benchmark.

Next adjust error compensating method, as shown in Figure 2, to remove the RMS value of the phase place after the error of non-altogether road be objective function f to the sub-aperture phase data of definition in the algorithm.General aspheric surface to be measured all is the revolution symmetry; Need not rotation around the Z axle; Therefore for the position adjustment in single sub-aperture, only need consider the adjustment of 5 directions, be respectively along the translation of X axle, Y axle and Z axle and around the rotation of X axle and Y axle; Have 5 parameters optimization in the adjustment error compensation model, respectively d _x, d _y, d _z, α and β: d _xExpression is along the translation of X-direction; d _yExpression is along the translation of Y direction; d _zExpression is along the translation of Z-direction; α representes the rotation around the X axle; β representes the rotation around the Y axle.According to the planning of sub-inside diameter measurement, find the solution when measuring a certain sub-aperture the theoretical adjustment amount d of the relative position between aspheric surface to be measured and the interferometer _X0, d _Y0, d _Z0, α ₀And β ₀

Set up aspheric female mirror coordinate system to be measured (x, y, z) and with certain sub-aperture geometric center be true origin rectangular coordinate system (x '; Y ', z '), as shown in Figure 3; Z is an optical axis direction, and o is aspheric female mirror coordinate origin to be measured, and o ' measures the geometric center in sub-aperture for certain.Coordinate system (x ', y ', z ') (z) translation and rotation are respectively d to relative coordinate system for x, y _x, d _y, d _z, α and β.

If (coordinate under z) is that (z), the vector of A is A=(x y z 1) to A for x, y to arbitrfary point A for x, y at coordinate system on the minute surface ^T, the coordinate of adjustment back A under coordinate (x ', y ', z ') is A ' (x ', y ', z '), the vector of A ' is: and A '=(x ' y ' z ' 1) ^TCan get two transformation matrix of coordinates between the vector by the rigid motion theorem is:

$T=\left[\begin{array}{cccc}\cos \mathrm{\β}& \sin \mathrm{\α}\sin \mathrm{\β}& -\sin \mathrm{\β}\cos \mathrm{\α}& 0\\ 0& \cos \mathrm{\α}& \sin \mathrm{\α}& 0\\ \sin \mathrm{\β}& -\sin \mathrm{\α}\cos \mathrm{\β}& \cos \mathrm{\α}\cos \mathrm{\β}& 0\\ d_x& d_y& d_z& 1\end{array}\right]$

Female mirror of secondary aspherical coordinate system (x, y, z) under, be expressed as:

x ²+y ²＝2R ₀z-(1+k)z ²

Utilize space coordinate transformation Matrix Solving aspheric surface equation expression formula under the new coordinate system that with sub-aperture area center is true origin to be:

Az’ ²+Bz’+C＝0

Wherein:

A＝sin ²β+sin ²αcos ²β+(1+k)cos ²αcos ²β

B＝-kx’sin(2β)cos ²α+2d _xsin?β-2d _ysinαcos?β+ky’sin(2α)cos?β+2(d _z+kd _z-R ₀)cosαcosβ

C＝x’ ²cos ²β+d _x ²+2x’d _xcosβ+x’ ²sin ²αsin ²β+y’ ²cos ²α+d _y ²+x’y’sin(2α)sinβ+2x’sinαsin?βd _y+2y’d _ycosα+(1+k)[x’ ²sin ²βcos ²α+y’ ²sin ²α+d _z ²

-x’y’sin?βsin(2α)-2x’d _zsin?βcosα+2y’d _zsinα]-2R ₀(-x’sin?βcosα+ysinα+d _z)

Known: $d_z=\frac{{d_x}^2+{d_y}^2}{R_0+\sqrt{{R_0}^2-(k+1)({d_x}^2+{d_y}^2)}}$

Then the rise equation in sub-aperture is: $F=\frac{-B-\sqrt{B^2-4\mathrm{AC}}}{2A}$

Rise equation with reference to spherical wave front is a formula: $S=r_0-\sqrt{r_0^2-x^{,2}-y^{,2}}---\left(1\right)$

The rise F in sub-aperture is P with difference with reference to the rise S of spherical wave front:

P＝F(x’，y’)-S(x’，y’) (2)

Because the phase data value in each sub-aperture can directly obtain through interferometer measurement, the PHASE DISTRIBUTION of setting certain sub-inside diameter measurement gained is W, and the PHASE DISTRIBUTION in the definition phase data after the non-road error altogether of cancellation is U, then:

U＝W-P

Objective function f is a formula:

wherein N be the number of sampled point in the data of sub-aperture.

Initialize routine is adjusted initial value substitution objective function f (d with theoretical position _X0, d _Y0, d _Z0, α ₀, β ₀).Give d _X0, d _Y0, d _Z0, α ₀And β ₀Five unknown quantity constraints are also set step-length separately respectively according to certain span, and both forward and reverse directions is searched for simultaneously, so that Optimization result meets actual requirement;

The basic thought of pattern search algorithm be near certain point by the littler point of certain step length searching functional value, and step-length can search out minimax positive group pattern with the carrying out and reduce of search procedure through this algorithm.It can be handled boundary constraint, linear algebra, linear inequality and not need function continuously or can be little, and most of traditional optimization is searched optimized point through the method for using gradient or higher derivative, and it generally requires the function continuously differentiable.

When searching calculated value greater than the basic point functional value, when being this search of taking turns failure, then step-length reduces by half and carries out search iteration again.

In the preset threshold scope, when the deviation of searching the calculating target function value for adjacent twice less than 10 ^-5Nm then stops to search EOP (end of program).

The search result value of this moment is for regarding as the adjustment amount of physical location; New basic point is brought final search result into equation (1) and (2), gets final product good compensation adjustment error; Accurately non-road error is altogether separated from the data of sub-aperture, thereby realize that well unified splicing detects.

Utilize theoretical position adjustment parameter value to eliminate to carry out unified spliced face shape error after the non-road error altogether and distribute as shown in Figure 4; Its PV value and RMS value are respectively 4.763 λ and 0.682 λ (λ=632.8nm); Can find out; Owing to the adjustment error is not carried out the optimizing compensation, this moment, face shape was distributed with very big " assembly trace ".It is as shown in table 1 to utilize pattern search algorithm to find the solution the optimal location parameter in each sub-aperture.

Table 1 theoretical position parameter and search the most optimized parameter

Three sub-aperture just can converge to optimum solution through 70 left and right sides iteration.The non-road error altogether of cancellation optimal location from each sub-aperture; And utilize Fiducial calibrating function module Fuducial labeling projection distortion in the Metropro software of Zygo interferometer with the CCD pixel coordinate unification in each sub-aperture to the minute surface coordinate; The data of overlapping region are analyzed and found the solution; Try to achieve the adjustment error in the sub-aperture of relative center reference, each sub-aperture; Try to achieve spliced shape through the complex optimum stitching algorithm and distribute as shown in Figure 5ly, face shape error distributes not significantly " assembly trace ", and its PV value and RMS value are respectively 4.087 λ and 0.525 λ.

In order to verify and contrast the accuracy of sub-aperture stitching check; We have designed offset lens; Utilize the zero compensation interferometric method that this off-axis aspheric surface has been carried out full mouth mirror surface shape measurement, PV value and RMS value that its face shape error distributes are respectively 4.064 λ and 0.511 λ.Relatively can get: it is consistent that the face shape error of two kinds of method of testing gained distributes, and the deviation of its PV value and RMS value is respectively 0.023 λ and 0.014 λ, and the relative deviation of PV value and RMS value is merely 0.57% and 2.74% respectively.

Claims (1)

1. sub-aperture stitching detects aspheric surface adjustment error compensating method, it is characterized in that this method comprises the steps:

Step 1: set interferometer, make the radius-of-curvature of its reference sphere wavefront and coincideing near spherical radius of aspheric surface to be measured central area;

Step 2: adjustment interferometer and aspheric relative position relation to be measured make interferometer standard spherical wave front aim at aspheric surface zone to be measured;

Step 3:, eliminate the adjustment error that produces when the standard sphere detects the bigger aspheric surface to be measured of bias through the pattern search error compensating method;

Step 4:, realize that unified splicing detects, and obtains accurate face type result through the sub-aperture stitching detection technique.

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