CN102620683B - Aspheric adjustment error compensation method for sub-aperture splicing detection - Google Patents

Abstract

The sub-aperture splicing detection aspheric adjustment error compensation method relates to the field of optical detection, and the method includes the following steps: setting the interferometer so that the curvature radius of the wavefront of the reference sphere coincides with the closest spherical radius of the central area of the aspheric surface to be measured; The relative positional relationship between the interferometer and the aspheric surface to be measured makes the wavefront of the standard spherical surface of the interferometer align with the area to be measured on the aspheric surface; through the mode search error compensation method, the error generated when the standard sphere detects the aspheric surface with a large deviation is eliminated Adjust the error; through the sub-aperture splicing detection technology, realize the full-aperture splicing detection and obtain accurate surface shape results. The present invention uses the mode search error compensation method to well eliminate the adjustment error caused by the misalignment of the splicing measurement position from the measured sub-aperture phase data, so as to well realize the splicing of multiple sub-apertures and accurately complete the Spherical full aperture surface splicing detection.

Description

Aspheric adjustment error compensation method for sub-aperture splicing detection

technical field

The invention relates to the field of optical detection, in particular to a sub-aperture splicing detection aspheric adjustment error compensation method.

Background technique

The use of aspheric elements in optical systems and optical instruments can correct aberrations, improve image quality, and reduce the size and weight of optical systems. Therefore, aspheric elements are increasingly being used in astronomy, space optics, and military National defense, high-tech civil and other fields, the detection of aspherical components has gradually attracted attention.

The sub-aperture stitching is to use the small-aperture standard spherical reference wavefront of the interferometer to measure the phase of each area on the large-aperture aspheric surface successively, and the full-aperture surface information of the aspheric surface can be obtained through the sub-aperture stitching algorithm. The sub-aperture splicing technology broadens the lateral and vertical dynamic range of the interferometer to measure the aspheric surface, and greatly increases the aperture and relative aperture of the interferometer to measure the aspheric surface. In addition, since the interferometer CCD pixel area used for the measurement of the small sub-aperture area is the same as the area of the interferometer CCD pixel used for the full-aperture interferometry, the sub-aperture measurement can obtain the mid-high frequency of the aspheric surface. segment information.

Since the sub-aperture splicing method uses standard spherical waves to detect aspheric surfaces, for the measurement of phase data of a single sub-aperture, it is necessary that the curvature radius of the interferometer outgoing wavefront coincides with the closest spherical radius of the sub-aperture area to be measured, so the splicing adjustment The positioning accuracy and repeatability of the mechanism have high requirements. However, in the splicing measurement process, the actual relative positional relationship between the interferometer and the aspheric surface to be measured will definitely deviate from the theoretical relative positional relationship.

Contents of the invention

In order to solve the problems existing in the prior art, the present invention provides a method for compensating the aspheric adjustment error of the sub-aperture splicing detection, which can well eliminate and compensate for the misalignment of the adjustment mechanism during the sub-aperture splicing measurement process. error, so that the sub-aperture splicing detection of the aspheric surface is well completed.

The technical solution adopted by the present invention to solve technical problems is as follows:

A sub-aperture splicing detection aspheric adjustment error compensation method, the method includes the following steps:

Step 1: Set the interferometer so that the radius of curvature of the reference spherical wavefront coincides with the radius of the closest spherical surface in the central area of the aspheric surface to be measured;

Step 2: Adjust the relative positional relationship between the interferometer and the aspheric surface to be tested, so that the standard spherical wavefront of the interferometer is aligned with the aspheric surface to be tested;

Step 3: Eliminate the adjustment error generated when the standard spherical surface detects the aspheric surface to be tested with a large deviation by the method of pattern search error compensation;

Step 4: Through sub-aperture splicing detection technology, full-aperture splicing detection is realized, and accurate surface shape results are obtained.

The beneficial effects of the present invention are: the present invention can well eliminate the adjustment error caused by the misalignment of the splicing measurement positions from the measured sub-aperture phase data by using the mode search error compensation method, thereby well realizing multiple sub-apertures Splicing, accurate completion of the aspherical full-aperture surface splicing detection.

Description of drawings

Fig. 1 is a sub-aperture division diagram of the sub-aperture splicing detection aspheric surface adjustment error compensation method of the present invention.

Fig. 2 is a flow chart of the method for compensating the adjustment error of the sub-aperture splicing detection aspheric surface of the present invention.

Fig. 3 is a definition diagram of the coordinate system of the sub-aperture splicing detection aspheric surface adjustment error compensation method of the present invention.

Fig. 4 is the distribution diagram of the surface shape error without optimizing and compensating the adjustment error.

Fig. 5 is the surface shape distribution after splicing by the sub-aperture splicing detection aspheric surface adjustment error compensation method of the present invention.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments.

A sub-aperture splicing detection aspheric adjustment error compensation method, the method includes the following steps:

Step 1: Set the interferometer so that the radius of curvature of the reference spherical wavefront coincides with the radius of the closest spherical surface in the central area of the aspheric surface to be measured, that is, to measure the phase distribution of the central reference sub-aperture;

Step 2: Adjust the relative positional relationship between the interferometer and the aspheric surface to be measured, so that the wavefront of the standard spherical surface of the interferometer is aligned with the area to be measured on the aspheric surface, that is, to measure the phase distribution of other sub-apertures;

Step 3: Eliminate the adjustment error generated when the standard spherical surface detects the aspheric surface to be tested with a large deviation by the method of pattern search error compensation;

Step 4: Through sub-aperture splicing detection technology, full-aperture splicing detection is realized, and accurate surface shape results are obtained.

In order to verify the feasibility of the mathematical model of the adjustment error compensation method, we conducted a splicing detection experiment on an off-axis aspheric surface with a deviation of 64.1 μm. The aspheric surface has a clear aperture of 230mm×141mm, a vertex curvature radius of -1358.8mm, a quadratic surface coefficient of -1.59, and an off-axis distance of -88.44mm.

The aspheric surface to be tested is placed on a four-dimensional adjustment mechanism, which can accurately adjust the translation of the aspheric surface in the X-axis and Z-axis directions and the inclination along the X-axis and Y-axis directions. The interferometer is installed on the precision lifting mechanism, which can adjust its For translation in the X direction, all test equipment is placed on the air-floating shock-proof platform, and the sub-aperture division is shown in Figure 1.

First, adjust the interferometer so that the radius of curvature of the reference spherical wavefront coincides with the closest spherical radius of the central area of the aspheric surface to be measured (center reference sub-aperture 0).

Adjust the relative position between the aspheric surface to be measured and the interferometer, so that the wavefronts emitted by the interferometer are respectively aligned with the surface area (sub-aperture 1) and the lower area (sub-aperture 2) of the aspheric surface to be measured, and make the sub-aperture 1 and sub-aperture 2 respectively Aperture 2 has a certain overlapping area with reference sub-aperture 0.

Next, adjust the error compensation method, as shown in Figure 2, define the RMS value of the sub-aperture phase data phase after removing the non-common path error in the algorithm as the objective function f. Generally, the aspheric surface to be tested is rotationally symmetrical, and there is no need to rotate around the Z axis. Therefore, for the position adjustment of a single sub-aperture, only five adjustments need to be considered, namely translation along the X axis, Y axis, and Z axis. As well as the rotation around the X-axis and Y-axis, there are five optimization parameters in the adjustment error compensation model, respectively d _x , d _y , d _z , α and β: d _x represents the translation along the X-axis direction; d _y represents the translation along the Y-axis Axis translation; d _z indicates translation along the Z axis; α indicates rotation around the X axis; β indicates rotation around the Y axis. According to the sub-aperture measurement plan, when measuring a certain sub-aperture, the theoretical adjustments d _x0 , d _y0 , d _z0 , α ₀ and β ₀ of the relative position between the aspheric surface to be measured and the interferometer are solved.

Establish the mother mirror coordinate system (x, y, z) of the aspheric surface to be measured and the Cartesian coordinate system (x', y', z') with a certain sub-aperture geometric center as the coordinate origin, as shown in Figure 3, Z is The direction of the optical axis, o is the origin of the coordinate system of the mother mirror of the aspheric surface to be measured, and o' is the geometric center of a certain sub-aperture to be measured. The translation and rotation of the coordinate system (x', y', z') relative to the coordinate system (x, y, z) are respectively d _x , d _y , d _z , α and β.

Let the coordinates of any point A on the mirror surface in the coordinate system (x, y, z) be A(x, y, z), the vector of A is A=(x y z 1) ^T , after adjustment, A is at the coordinates (x', y',z') is A'(x',y',z'), and the vector of A' is: A'=(x'y'z' 1) ^T . According to the rigid body motion theorem, the coordinate transformation matrix between two vectors can be obtained as:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]$

In the coordinate system (x, y, z), the mother mirror of the quadratic aspheric surface is expressed as:

x ² +y ² =2R ₀ z-(1+k)z ²

Using the space coordinate transformation matrix to solve the aspheric equation in the new coordinate system with the center of the sub-aperture area as the coordinate origin is as follows:

Az' ² +Bz'+C＝0

in:

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

B＝-kx'sin(2β)cos 2α+2d _x sinβ- ^2d _y sinαcosβ+ky'sin(2α)cosβ

+2(d _z +kd _z -R ₀ )cosαcosβ

C＝x' ² cos ² β+d _x ² +2x'd _x cosβ+x' ² sin ² αsin ² β+y' ² cos ² α+d _y ² +x'y'sin(2α)sinβ

+2x'sinαsinβd _y +2y'd _y cosα+(1+k)[x' ² sin ² βcos ² α+y' ² sin ² α+d _z ²

-x'y'sinβsin(2α)-2x'd _z sinβcosα+2y'd _z sinα]-2R ₀ (-x'sinβcosα+ysinα+d _z )

A known: $d_z=\frac{{d_x}^2+{d_{\mathrm{the\; y}}}^2}{R_0+\sqrt{{R_0}^2-(k+1)({d_x}^2+{d_{\mathrm{the\; y}}}^2)}}$

Then the vector height equation of the sub-aperture is:

The vector height equation of the reference spherical wavefront is: $S=r_0-\sqrt{r_0^2-x^{{,}^2}-{\mathrm{the\; y}}^{{,}^2}}---\left(1\right)$

The difference between the sagittal height F of the sub-aperture and the sagittal height S of the reference spherical wavefront is P:

P＝F(x’,y’)-S(x’,y’) (2)

Since the phase data values of each sub-aperture can be directly obtained by interferometer measurement, set the phase distribution measured by a certain sub-aperture as W, and define the phase distribution after eliminating the non-common path error in the phase data as U, then:

U=W-P

The objective function f is the formula: Where N is the number of sampling points in the sub-aperture data.

Initialize the program, and substitute the theoretical position adjustment initial value into the objective function f(d _x0 ,d _y0 ,d _z0 ,α ₀ ,β ₀ ). Give d _x0 , d _y0 , d _z0 , α ₀ and β ₀ five unknown constraints according to a certain value range and set their respective step sizes, and search in both forward and reverse directions to make the optimization result meet the actual requirements;

The basic idea of the pattern search algorithm is to search for a point with a smaller function value according to a certain step size near a certain point, and the step size decreases as the search process progresses. Through this algorithm, the maximum and minimum positive base patterns can be searched. It can handle boundary constraints, linear algebra, linear inequalities, and does not require continuous or differentiable functions, while most traditional optimization methods search for optimization points by using gradients or higher-order derivatives, which generally require continuous and differentiable functions.

When the search calculation value is greater than the base point function value, that is, this round of search fails, then the step size is halved and the search iteration is repeated.

Within the set threshold range, when the deviation of the objective function value calculated by two adjacent searches is less than 10 ^-5 nm, the search is stopped and the program ends.

At this time, the search result value can be regarded as the adjustment amount of the actual position, the new base point, and the final search result is brought into the equations (1) and (2), which can well compensate the adjustment error and accurately determine the non-common path Errors are separated from the subaperture data, allowing for good detection of full-aperture stitches.

Figure 4 shows the distribution of surface shape errors after full-aperture splicing after eliminating non-common path errors by using theoretical position adjustment parameter values. The PV and RMS values are 4.763λ and 0.682λ (λ=632.8nm), respectively. It can be seen that because the adjustment error is not optimized and compensated, the surface shape distribution has a large "scratch mark" at this time. The optimal position parameters of each sub-aperture are obtained by using the pattern search algorithm, as shown in Table 1.

Table 1 Theoretical location parameters and search optimization parameters

The three sub-apertures can converge to the optimal solution after about 70 iterations. Eliminate the non-common path error of the optimal position from each sub-aperture, and use the Fiducial calibration function module Fuducial calibration projection distortion in the Metropro software of the Zygo interferometer to unify the CCD pixel coordinates of each sub-aperture to the mirror coordinates, and the overlapping area Analyze and solve the data to obtain the adjustment error of each sub-aperture relative to the central reference sub-aperture, and obtain the spliced surface shape distribution through the comprehensive optimization splicing algorithm, as shown in Figure 5. There is no obvious "stitch mark" in the surface shape error distribution ", and its PV and RMS values are 4.087λ and 0.525λ, respectively.

In order to verify and compare the accuracy of the sub-aperture splicing inspection, we designed a compensation lens, and used the zero compensation interferometry to measure the full-port mirror shape of the off-axis aspheric surface. The PV value and RMS value of the surface shape error distribution were respectively are 4.064λ and 0.511λ. It can be obtained by comparison: the surface shape error distribution obtained by the two test methods is consistent, the deviations of the PV value and the RMS value are 0.023λ and 0.014λ respectively, and the relative deviations of the PV value and the RMS value are only 0.57% and 2.74% respectively .

Claims (1)

1. sub-aperture stitching detects the compensation method of aspheric surface alignment error, and it is characterized in that, the method comprises the steps:

Step one: setting interferometer, makes the best-fit sphere radius of the radius-of-curvature of its reference sphere wavefront and aspheric surface central area to be measured coincide;

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

Step 3: by pattern search error compensating method, eliminates the alignment error produced when standard sphere detects bias larger aspheric surface to be measured; Pattern search algorithm be by the less point of certain step length searching functional value near certain point, and step-length carrying out and reduce with search procedure, can search out minimax positive group pattern by this algorithm; When search calculated value is greater than basic point functional value, when being search failure that this takes turns, then step-length reduces by half and re-starts search iteration; In the threshold range of setting, the deviation of searching calculating target function value when adjacent twice is less than 10 ^-5nm, then stop searching, EOP (end of program), wherein the definition of objective function and concrete establishment step as follows:

Defining aspheric female mirror coordinate to be measured is (x, y, z) and with the rectangular coordinate that certain sub-aperture geometric center is true origin be (x ', y ', z '), Z is optical axis direction, and o is aspheric female mirror coordinate origin to be measured, and o ' is the geometric center of certain measurement sub-aperture.Coordinate system (x ', y ', z ') relative coordinate system (x, y, z) is along the translation of X-axis, Y-axis and Z axis and be respectively d around the rotation of X-axis and Y-axis _x, d _y, d _z, α and β;

If to be the vector of Q (x, y, z), Q be the coordinate of arbitrfary point Q under coordinate system (x, y, z) on minute surface $\stackrel{\&OverBar;}{Q}={\left(\begin{array}{cccc}x& y& z& 1\end{array}\right)}^T,$ After adjustment, the coordinate of Q under coordinate (x ', y ', z ') is is Q ' (x ', y ', z '), and the vector of Q ' is: $\stackrel{\&OverBar;}{Q^{\&prime;}}={\left(\begin{array}{cccc}{x}^{\&prime;}& y^{\&prime;}& z^{\&prime;}& 1\end{array}\right)}^T;$ The transformation matrix of coordinates that can be obtained between two vectors by rigid motion theorem is:

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

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

x ²+y ²＝2R ₀z-(1+k)z ²

Space coordinate transformation Matrix Solving aspherical equation expression formula under the new coordinate system being true origin with sub-aperture regional center is utilized 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 _xsinβ-2d _ysinαcosβ+ky’sin(2α)cosβ

+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’sinαsinβd _y+2y’d _ycosα+(1+k)[x’ ²sin ²βcos ²α+y’ ²sin ²α+d _z ²

-x’y’sinβsin(2α)-2x’d _zsinβcosα+2y’d _zsinα]-2R ₀(-x’sinβcosα+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 of sub-aperture is:

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

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

P＝F(x’，y’)-S(x’,y’) (2)

Because the phase data values of each sub-aperture directly can be obtained by interferometer measurement, the PHASE DISTRIBUTION setting certain sub-aperture measurement gained is W, and the PHASE DISTRIBUTION in definition phase data after the error of cancellation non-co-road is U, then:

U＝W-P

Objective function f is formula: wherein N is the number of sampled point in sub-aperture data;

Can obtain objective function is thus about d _x, d _y, d _z, α and β function, be f (d _x, d _y, d _z, α, β),

Theoretical position is adjusted initial value and substitute into objective function f (d _x0, d _y0, d _z0, α ₀, β ₀); To d _x0, d _y0, d _z0, α ₀and β ₀five unknown quantity constraints also set respective step-length respectively according to certain span, and both forward and reverse directions is searched for simultaneously, to make the realistic requirement of optimum results;

When search calculated value is greater than basic point functional value, when being search failure that this takes turns, then step-length reduces by half and re-starts search iteration;

In the threshold range of setting, the deviation of searching calculating target function value when adjacent twice is less than 10 ^-5nm, then stop searching, EOP (end of program);

Search result value is now the adjustment amount of physical location, new basic point, final search result is brought into equation (1) and (2), can compensation adjustment error, non-co-road error is separated from sub-aperture data;

Step 4: by sub-aperture stitching detection technique, realizes unified splicing and detects, obtain accurate face type result.