CN105423948A - Splicing-interference-detection aspheric surface shape apparatus using distorting lens and method thereof - Google Patents

Abstract

The device and method for splicing and interfering detecting aspheric surface shapes using deformable mirrors belong to the technical field of optical detection. The present invention includes an interference detection system, a deformable mirror compensation system, a mechanical adjustment mechanism and a computer data processing module; specifically, the following steps are included: Step 1: Build a mosaic interference detection device using a deformable mirror; Step 2: Divide the sub-aperture; Step 3: Move to the position of the sub-aperture to be detected, and adjust the shape or refractive index of the deformed mirror according to the modeling and interference fringes; Step 4: Sub-aperture interferogram Acquisition and processing; step five, sub-aperture backhaul error correction; step six, full-aperture surface stitching. The invention combines the deformable mirror with the sub-aperture splicing interference detection method, which can effectively reduce the number of sub-apertures required to cover the full aperture, increase the effective area of each sub-aperture and the overlapping area, and solve the problem of affecting the splicing accuracy due to the small overlapping area problem.

Description

Device and method for detecting aspherical surface shape by splicing interference of deformable mirrors

technical field

The invention belongs to the technical field of optical detection, and in particular relates to a device and method for detecting an aspheric surface shape by splicing and interfering deformable mirrors.

Background technique

Interference detection technology is a commonly used surface shape detection technology, which is the relative detection of the surface to be measured and the reference surface. The reference surfaces are generally flat or spherical, and there will not be more interference fringes when using them to test the polished plane and spherical surface, while using spherical reference surfaces to detect aspheric surfaces, when the slope of the aspheric surface is larger, the density of interference fringes is also higher. many. When the interference fringe density exceeds the Nyquist frequency of the interferometer detector, the interference fringe cannot be resolved by the detector, resulting in the aspheric surface being unable to be measured. For the aspheric surface with a large slope, the sub-aperture splicing interference detection method is used to divide the aspheric surface with a large slope into multiple small-aperture sub-apertures, so that the interference fringes in each sub-aperture can be detected and resolved.

However, when the slope of the aspheric surface is too large, the detectable area of each sub-aperture from the center to the edge becomes smaller and smaller. At this time, more sub-apertures are needed to cover the entire aspheric surface, which reduces the detection efficiency and increases the mechanical error, detection time and data processing volume, etc.

Contents of the invention

The purpose of the present invention is to propose a device and method for detecting aspheric surface shape by splicing and interference of deformable mirrors, so as to solve the problems of low detection efficiency, large mechanical error, long detection time and large data processing capacity in the prior art. Combining deformable mirror technology with annular sub-aperture splicing interference detection method can effectively reduce the number of sub-apertures required to cover the full aperture, increase the effective area of each sub-aperture, and solve the problem of affecting splicing accuracy due to small overlapping areas.

In order to achieve the above object, the device of the present invention that adopts the splicing interference detection of deformable mirrors to detect aspheric surface shape includes a deformable mirror compensation system, an interference detection system, a mechanical adjustment mechanism and a computer data processing module;

The computer data processing module includes a deformable mirror control unit, a multi-dimensional adjustment table control unit, an interferogram acquisition processing unit, a backhaul error correction unit and a sub-aperture splicing algorithm unit;

The aspheric surface to be detected is fixed on the mechanical adjustment mechanism, and the interference detection system compensates the optical path difference with the reflected light of the aspheric surface to be detected through a deformation mirror compensation system. device connection;

The interferogram acquisition processing unit is connected with the deformable mirror control unit and the return error correction unit, and the deformable mirror control unit performs closed-loop feedback on the adjustment of the deformable mirror according to the interferogram, and controls the multidimensional adjustment table control unit to perform the motion of the multidimensional adjustment table. Closed-loop feedback control, each sub-aperture interferogram collected by the detector is processed by the interferogram acquisition and processing unit to obtain the return wavefront phase of each sub-aperture, and the return wavefront phase of each sub-aperture is obtained by the return error correction unit. The shape information of each sub-aperture is processed by the sub-aperture splicing algorithm unit to obtain the full-aperture shape information.

The mechanical adjustment mechanism includes a clamping mechanism and a multi-dimensional adjustment table, and the aspheric surface to be tested is fixed on the multi-dimensional adjustment table through the clamping mechanism.

The interference detection system is a Tieman-Green type interferometer or a Fizeau type interferometer.

The method for detecting aspheric surface shape by splicing interference of deformable mirrors comprises the following steps:

Step 1: Build a device that uses splicing and interference detection of deformable mirrors to detect aspheric surface shapes;

Step 2: System modeling, sub-aperture division, and reference files for each sub-aperture, specifically:

1) Carry out subaperture planning according to the radius of curvature of the best fitting sphere of the aspheric surface to be detected, the aperture of the best fitting sphere, the radius of curvature of the reference sphere, the aperture of the reference sphere and the subaperture overlapping area;

2) According to the specific device parameters of the aspheric surface interference detection system in the detection device, the aspheric surface interference detection system is modeled in the optical design software to obtain the system model;

3) carry out sub-aperture division in the system model obtained in step 2) according to the planning carried out to the sub-aperture in step 1);

4) The high-precision spherical surface with known surface error ε is detected by the interferometer, and the measured value W _sphere-test of the high-precision spherical surface shape is obtained; the ideal reference sphere is simulated in the Zemax optical design software to detect the high-precision spherical surface, and the high-precision spherical surface is tested. The test result of precision spherical surface shape precision is W _sphere-ideal , and the interferometer system error E _I and collimator manufacturing and assembly error E _F are obtained by formula (1):

E _I +E _F ＝W _sphere-teat -W _sphere-ideal -2ε(1)

5) Detect any sub-aperture surface shape _{Wasphere-ideal} of the ideal aspheric surface through system model simulation; use any sub-aperture surface shape _{Wasphere-ideal} as the error caused by the deviation of the aspheric surface from the reference spherical surface, and obtain the sub-aperture according to formula (2) The reference phase W _reference :

W _reference =W _{asphere-ideal} +W _sphere-test -W _sphere-ideal -2ε(2);

Step 3: According to the division of the sub-apertures, the movement amount of each axis of the multi-dimensional adjustment table required for the detection of each sub-aperture is obtained, and the aspheric surface is accurately positioned, and the shape or refractive index of the deformed mirror is adjusted according to the system model and interference fringes until the interference fringe pattern meets the detection requirements. Require;

Step 4: collect each sub-aperture interferogram through the interferogram acquisition processing unit, use the unwrapping algorithm to demodulate the phase of the interferogram, and obtain the wavefront phase _{Wasphere-test} of each sub-aperture received by the detector in the experiment;

Step 5: Calculate and obtain the surface shape ε _asphere of each sub-aperture according to the formula (3):

${\mathrm{\ϵ}}_{a\mathrm{the\; s}phere}=\frac{1}{2}\[W_{a\mathrm{the\; s}phere-te\mathrm{the\; s}t}-W_{refere\mathrm{no}ce}\]$ (3)

Where: _{Wasphere-test} is the sub-aperture wavefront phase

W _reference is the reference phase of the sub-aperture;

Step 6: According to the sub-aperture surface ε _asphere obtained in step 5, the influence of mechanical errors on the splicing result is reduced through the splicing algorithm, and finally the sub-aperture surface data are spliced to obtain the full-aperture surface.

The interference detection system is a Tieman-Green type interferometer or a Fizeau type interferometer.

The specific steps for adjusting the shape or refractive index of the deformed mirror according to the system model and interference fringes described in step three until the interference fringe pattern meets the detection requirements are:

1) According to the Zernike aberration at the detector obtained by simulation in the optical design software, when the interference detection system uses a Tieman-Green interferometer, the surface shape of the deformable mirror is set to 1 of the Zernike aberration /2; when the interference detection system chooses Fizeau interferometer, use the "inversion" method to calculate the refractive index distribution required to compensate the aspheric surface, calculate the phase required to compensate the aspheric surface, P is any point on the aspheric surface, The normal line of the aspheric surface is made through P, and the rear surface of the deformable mirror is M; after the light PM is diffracted by the deformable mirror, the front surface of the deformable mirror is N, and the final convergence point of refraction is F; the refractive index of the deformable mirror is ng, The refractive index of the surrounding air is na; the distance between the aspheric surface and the rear surface of the deformable mirror is d1, the thickness of the deformable mirror is d, and the distance between F and the front surface of the deformable mirror is d2;

According to Fermat's principle, to make the light emitted from any point on the aspheric surface along the normal converge to point F, then:

n _a |PM|+n _g |MN|+n _a |NF|＝n _a d ₁ +n _g d+n _a d ₂

The refractive index ng of the deformable mirror is calculated by the formula (4):

${\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

2) Detect the sub-aperture through the interference detection system to obtain the interference fringe pattern;

3) Perform feedback adjustment on the deformable mirror in step 1) according to the interference fringe pattern obtained in step 2), until the interference fringe pattern meets the detection requirements, and the adjustment of the deformable mirror is completed.

The splicing algorithm described in step six is specifically:

1) Calculate the sub-aperture surface shape after introducing the compensation amount according to formula (5)

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ...</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where: f _k (x, y) is the compensation factor of the sub-aperture;

L is the number of compensation factors;

is the surface shape of the ith sub-aperture obtained in step five;

F _ik is the compensation coefficient of the sub-aperture compensation factor, and the compensation coefficient F _ik of each sub-aperture is obtained by the least square method shown in formula (6);

$\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1...</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0...</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&cap;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Wherein, N is the number of sub-apertures;

The sub-aperture counts from zero, that is, the 0th sub-aperture is the central sub-aperture;

Indicates that only the j-th sub-aperture that overlaps with the i-th sub-aperture is calculated;

2) Each sub-aperture surface obtained according to step 1) Stitching to get a full-diameter surface shape, that is, all In addition, the surface shape of the overlapping area takes the weighted average of the data of each sub-aperture, and the weight is related to the accuracy of the measurement data.

The optical design software is Zemax software.

The beneficial effects of the present invention are: the present invention combines the deformable mirror and sub-aperture splicing interference detection method, uses the deformable mirror to generate aspheric wavefronts to match the different sub-aperture areas of the measured surface, so that the number of sub-apertures required for full-aperture detection is greatly reduced, The sub-aperture area is increased, thereby increasing the overlapping area of adjacent sub-apertures, reducing detection time and accumulation of mechanical errors, and improving detection efficiency and accuracy. It effectively solves the problem of low splicing accuracy caused by too low sub-aperture area, and at the same time increases the splicing efficiency.

Description of drawings

Fig. 1 is the structure schematic diagram when adopting Teiman-Green type interferometer in the device of splicing interference detection aspheric surface shape that adopts deformable mirror of the present invention;

Fig. 2 is a structural schematic diagram when a Fizeau-type interferometer is used in the device for splicing interference detection aspheric surface shape using deformable mirrors of the present invention;

Fig. 3 is the detection flowchart of the method for detecting the aspheric surface shape using splicing interference detection of deformable mirrors of the present invention;

Fig. 4 is the neutron aperture planning structure schematic diagram of the method for splicing interference detection aspheric surface shape using deformable mirrors of the present invention;

Fig. 5 is a schematic diagram of the deformable mirror surface shape or refractive index adjustment structure in the method for splicing and interfering detecting aspheric surface shape using deformable mirrors according to the present invention;

Among them: 1. Frequency stabilized laser, 2. Collimating beam expander system, 3. Beam splitting prism, 4. Deformable mirror, 5. Imaging mirror, 6. Detector, 7. Converging mirror group, 8. Aspheric surface, 9. Clip Holding mechanism, 10. Computer, 11. Multi-dimensional adjustment table, 12. Deformable mirror control unit, 13. Multi-dimensional adjustment table control unit, 14. Interferogram acquisition and processing unit, 15. Mirror, 16. Standard mirror, 17. Reference surface .

detailed description

Embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

The device of the present invention adopting splicing interference detection of deformable mirrors to detect aspheric surface shape comprises a deformable mirror compensation system, an interference detection system, a mechanical adjustment mechanism and a computer data processing module;

The computer data processing module includes a deformable mirror control unit 12, a multi-dimensional adjustment table control unit 13, an interferogram acquisition processing unit 14, a backhaul error correction unit and a sub-aperture splicing algorithm unit;

The aspherical surface 8 to be detected is fixed on the mechanical adjustment mechanism, and the interference detection system compensates the optical path difference with the reflected light from the aspheric surface 8 to be detected through a deformation mirror compensation system. The interferogram acquisition processing unit 14 and the interference detection system Probe 6 connection in;

The interferogram acquisition processing unit 14 is connected with the deformable mirror control unit 12 and the backhaul error correction unit, and the deformable mirror control unit 12 performs closed-loop feedback on the adjustment of the deformable mirror 4 according to the interferogram, and controls the multidimensional adjustment table control unit 13 to perform multidimensional adjustment. The movement of the adjustment table 11 is controlled by closed-loop feedback. The interferograms of each sub-aperture collected by the detector 6 are processed by the interferogram acquisition and processing unit 14 to obtain the return wavefront phase of each sub-aperture. The error correction unit obtains the surface information of each sub-aperture, and the surface information of each sub-aperture is processed by the sub-aperture splicing algorithm unit to obtain the full-aperture surface information.

The mechanical adjustment mechanism includes a clamping mechanism 9 and a multi-dimensional adjustment table 11 , and the aspheric surface 8 to be tested is fixed on the multi-dimensional adjustment table 11 through the clamping mechanism 9 .

Referring to Figure 1, the interferometric detection system is a Tieman-Green interferometer, and the thin beam emitted by the frequency-stabilized laser 1 is expanded into a wide-beam parallel light by a collimator beam-expanding system 2, and the wide-beam parallel light propagates forward It is divided into two paths at the beam-splitting prism 3; one of them is reflected by the beam-splitting prism 3 and transmitted to the deformable mirror 4, and then returns to the original path as a reference wave; Divergence, the divergent light is reflected by the aspheric surface 8 and passes through the converging lens group 7 again to form a detection wave. The reference wave and the detection wave are imaged at the detector 6 through the imaging mirror 5 after interference.

Referring to accompanying drawing 2, described interferometric detection system is Fizeau type interferometer, and the light beam that the frequency stabilization laser 1 exits passes the light after collimating beam expander system 2 and propagates forward to beam-splitting prism 3 places, and beam-splitting prism 3 reflects and propagates to Mirror 15, through standard mirror 16, a part is reflected by reference surface 17 as reference wave, and the other part is transmitted and propagated forward to deformable mirror 4, after being reflected by aspheric surface 8 and passing through deformable mirror 4 again, a detection wave is formed. The reference wave and the detection wave are imaged at the detector 6 through the imaging mirror 5 after interference.

The work of the deformable mirror compensation system needs to be completed jointly by the deformable mirror drive system, the interference detection system, and the computer control system. The closed-loop feedback control of the deformable mirror 4 is performed through the interference fringe pattern measured by the interferometer. The deformable mirror compensation system mainly includes the deformable mirror 4 and the deformable mirror control unit 12 in the computer data processing module. According to the simulation results of the computer 10 or the measurement results of the interference detection system, the required amount of deformation of the deformable mirror 4 is obtained, and the deformation is controlled by the computer 10. The mirror driver deforms the deformable mirror 4 .

The mechanical adjustment mechanism includes a multi-dimensional adjustment table 11, a positioning device such as a grating ruler, and a multi-dimensional adjustment table control unit 13 in the computer data processing module. The aspheric surface 8 is fixed on the clamping mechanism 9 , and the clamping mechanism 9 is fixed on the multi-dimensional adjustment table 11 . The position and orientation of the mirror to be measured required for detecting each sub-aperture is given by the sub-aperture planning, and the computer 10 can drive the multi-dimensional adjustment table 11 to make the clamping mechanism 9 translate along the x, y, and z axes, tilt the x, y axes, and rotate around the z axis , The position of multi-dimensional movement can be controlled by closed-loop feedback by positioning devices such as grating rulers in each direction.

The interferogram acquisition and processing unit 14 processes the image collected by the detector 6 through the computer 10, and outputs the result to the backhaul error correction unit, and then obtains the full-aperture surface information through the sub-aperture splicing unit.

Referring to accompanying drawing 3, the method for detecting the aspheric surface shape by splicing interference of deformable mirrors comprises the following steps:

Step 1: Build a device that uses splicing and interference detection of deformable mirrors to detect aspheric surface shapes;

Step 2: System modeling, sub-aperture division, and reference files for each sub-aperture, specifically:

1) Carry out sub-aperture planning according to the radius of curvature of the best fitting sphere of the aspheric surface 8 to be detected, the aperture of the best fitting sphere, the radius of curvature of the reference sphere, the aperture of the reference sphere and the sub-aperture overlapping area;

See Figure 4, for example, the aspheric surface 8 best fitting sphere, reference sphere, and overlapping area are as follows:

The sub-aperture distribution is as follows:

2) According to the specific device parameters of the aspheric 8 interference detection system in the detection device, the aspheric 8 interference detection system is modeled in the optical design software to obtain the system model;

Taking the Tieman-Green type interference detection system as an example, the parameters of the specific device include: the laser wavelength emitted by the frequency-stabilized laser 1, the aperture and magnification of the collimator beam expander system 2, the parameters of the beam splitter 3, The caliber of the deformable mirror 4, the caliber and the surface radius of curvature and the thickness of the imaging mirror 5, the nominal surface shape equation and the caliber of the measured aspheric surface 8;

3) carry out sub-aperture division in the system model that obtains in step 2) according to the planning that step 1) carries out to sub-aperture;

4) The high-precision spherical surface with known surface error ε is detected by the interferometer, and the measured value W _sphere-test of the high-precision spherical surface shape is obtained; the ideal reference sphere is simulated in the Zemax optical design software to detect the high-precision spherical surface, and the high-precision spherical surface is tested. The test result of precision spherical surface shape precision is W _sphere-ideal , and the interferometer system error E _I and collimator manufacturing and assembly error E _F are obtained by formula (1):

E _I +E _F ＝W _sphere-test -W _sphere-ideal -2ε(1)

5) Through system model simulation, detect any sub-aperture surface shape _{Wasphere-ideal} of the ideal aspheric surface 8; use any sub-aperture surface shape _{Wasphere-ideal} as the error caused by the aspheric surface 8 deviating from the reference spherical surface, and obtain according to formula (2) The reference phase W _reference of the sub-aperture:

W _reference =W _{asphere-ideal} +W _sphere-test -W _sphere-ideal -2ε(2);

Step 3: According to the division of the sub-apertures, obtain the movement amount of each axis of the multi-dimensional adjustment table 11 required to detect each sub-aperture, accurately position the aspheric surface 8, and adjust the shape or refractive index of the deformation mirror 4 according to the system model and interference fringes until the interference The fringe pattern meets the detection requirements;

Step 4: collect each sub-aperture interferogram by the interferogram acquisition processing unit 14, utilize the unwrapping algorithm to carry out interferogram phase demodulation, obtain each sub-aperture wavefront phase _{Wasphere-test} that detector 6 receives in the experiment;

Step 5: Calculate and obtain the surface shape ε _asphere of each sub-aperture according to the formula (3):

${\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Where: _{Wasphere-test} is the sub-aperture wavefront phase

W _reference is the reference phase of the sub-aperture;

Step 6: According to the sub-aperture surface ε _asphere obtained in step 5, the influence of mechanical errors on the splicing result is reduced through the splicing algorithm, and finally the sub-aperture surface data are spliced to obtain the full-aperture surface.

The interference detection system is a Tieman-Green type interferometer or a Fizeau type interferometer.

According to the system model and interference fringes described in step 3, the specific steps for adjusting the 4-surface shape or refractive index of the deformable mirror until the interference fringe pattern meets the detection requirements are:

1) According to the Zernike aberration at the detector 6 obtained by the simulation detection in the optical design software, when the interferometric detection system selects the Tieman-Green interferometer, the surface shape of the deformable mirror 4 is set to the Zernike aberration 1/2; when the interference detection system selects the Fizeau interferometer, the "inversion" method is used to calculate the refractive index distribution required to compensate the aspheric surface 8, and calculate the phase required to compensate the aspheric surface 8, see Figure 5, P is any point on the aspheric surface 8, the normal line of the aspheric surface 8 passes through P, and the back surface of the deformable mirror 4 is M; after the light PM is diffracted by the deformable mirror 4, the front surface of the cross deformable mirror 4 is N, and finally refracted The converging point is F; the refractive index of the deformable mirror 4 is _{n g} , and the refractive index of the surrounding air is na; the distance between the aspheric surface 8 and the rear surface of the deformable mirror 4 is d ₁ , the thickness of the deformable mirror 4 is d, and the distance between F and the deformable mirror 4 is d1. The distance from the front surface of the mirror 4 is d ₂ ;

According to Fermat's principle, to make the light emitted from any point on the aspheric surface 8 along the normal converge to point F, then:

n _a |PM|+n _g |MN|+n _a |NF|＝n _a d ₁ +n _g d+n _a d ₂

The refractive index n _g of the deformable mirror 4 is calculated by formula (4):

${\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

2) Detect the sub-aperture through the interference detection system to obtain the interference fringe pattern;

3) Perform feedback adjustment on the deformable mirror 4 in step 1) according to the interference fringe pattern obtained in step 2), until the interference fringe pattern meets the detection requirements, and the adjustment of the deformable mirror 4 is completed.

The splicing algorithm described in step six is specifically:

1) Calculate the sub-aperture surface shape after introducing the compensation amount according to formula (5)

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ...</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where: f _k (x, y) is the compensation factor of the sub-aperture;

L is the number of compensation factors;

is the surface shape of the ith sub-aperture obtained in step five;

F _ik is the compensation coefficient of the sub-aperture compensation factor, and obtains the compensation coefficient F _ik of each sub-aperture by the least square method as shown in formula (6);

$\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1...</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0...</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&cap;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{{\mathrm{<span\; class="notranslate">\; asphere</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Wherein, N is the number of sub-apertures;

The sub-aperture counts from zero, that is, the 0th sub-aperture is the central sub-aperture;

Indicates that only the j-th sub-aperture that overlaps with the i-th sub-aperture is calculated;

2) According to each sub-aperture surface obtained in step 1) Stitching to get a full-diameter surface, which will be used In addition, the surface shape of the overlapping area takes the weighted average of the data of each sub-aperture, and the weight is related to the accuracy of the measurement data.

The optical design software is Zemax software, which is an optical design software developed by American RadiantZemax Company.

Claims (8)

1. adopt the stitching interferometer of distorting lens to detect the device of aspheric surface, it is characterized in that, comprise distorting lens bucking-out system, interfere detection system, mechanical adjusting mechanism and computer digital animation module;

Described computer digital animation module comprises distorting lens control module (12), multidimensional adjusting table control module (13), interferogram sampling processing unit (14), hysterisis error correcting unit and sub-aperture stitching algorithm unit;

Aspheric surface to be detected (8) is fixed on described mechanical adjusting mechanism, described interference detection system compensates the optical path difference with aspheric surface to be detected (8) reflected light by distorting lens bucking-out system, and described interferogram sampling processing unit (14) is connected with the detector (6) of interfering in detection system;

Described interferogram sampling processing unit (14) is connected with described distorting lens control module (12) and hysterisis error correcting unit, distorting lens control module (12) carries out close-loop feedback according to the adjustment of interferogram to distorting lens (4), control multidimensional adjusting table control module (13) motion to multidimensional adjusting table (11) and carry out close-loop feedback control, each sub-aperture interferogram that detector (6) collects processes through described interferogram sampling processing unit (14), obtain each sub-aperture and return Wave-front phase, each sub-aperture returns Wave-front phase and obtains each sub-aperture diametric plane shape information through hysterisis error correcting unit, each sub-aperture diametric plane shape information obtains unified shape information through the process of sub-aperture stitching algorithm unit.

2. the stitching interferometer of employing distorting lens according to claim 1 detects the device of aspheric surface, it is characterized in that, described mechanical adjusting mechanism comprises clamping device (9) and multidimensional adjusting table (11), and described aspheric surface to be detected (8) is fixed on described multidimensional adjusting table (11) by clamping device (9).

3. the stitching interferometer of employing distorting lens according to claim 1 detects the device of aspheric surface, and it is characterized in that, described interference detection system is Tai Man-Green's type interferometer or Feisuo type interferometer.

4. the stitching interferometer of employing distorting lens according to claim 1 detects the detection method of the device of aspheric surface, it is characterized in that, comprises the following steps:

Step one: build the device adopting the stitching interferometer of distorting lens to detect aspheric surface;

Step 2: system modelling, divides sub-aperture, and makes the reference paper of each sub-aperture, be specially:

1) sub-aperture planning is carried out according to the bore of the radius-of-curvature of the best-fit ball of aspheric surface to be detected (8), best-fit ball, the radius-of-curvature with reference to sphere, the bore with reference to sphere and sub-aperture overlapping region;

2) interfere the parameter of the concrete device of detection system according to aspheric surface in pick-up unit, in optical design software, interfere detection system to carry out modeling to aspheric surface, obtain system model;

3) according to step 1) planning carried out sub-aperture is in step 2) in carry out sub-aperture division in the system model that obtains;

4) detect the known high precision sphere of face shape error ε by interferometer, obtain the measured value W of high precision spherical surface shape _sphere-test; In Zemax optical design software, faced by simulate ideal reference sphere, high precision sphere detects, and high precision sphere surface figure accuracy testing result is W _sphere-ideal, obtain interferometer system error E by formula (1) _irigging error E is manufactured with collimating mirror _f:

E _I+E _F＝W _sphere-test-W _sphere-ideal-2ε(1)

5) by any one sub-aperture diametric plane shape of system model analog detection desired aspheric (8) W _{asphere-ideal}; By any one sub-aperture diametric plane shape W _{asphere-ideal}depart from the error caused with reference to sphere as aspheric surface (8), obtain the fixed phase W of sub-aperture according to formula (2) _reference:

W _reference＝W _{asphere-ideal}+W _sphere-test-W _sphere-ideal-2ε(2)；

Step 3: divide according to sub-aperture and show that the amount of exercise detecting multidimensional adjusting table (11) each axle needed for each sub-aperture is accurately located aspheric surface (8), and adjust distorting lens (4) face shape or refractive index, until interference fringe picture meets testing requirement according to system model and interference fringe;

Step 4: gather each sub-aperture interferogram by interferogram sampling processing unit (14), utilizes unwrapping algorithm to carry out interferogram phase demodulating, obtains each sub-aperture Wave-front phase W that in testing, detector (6) receives _asphere-test;

Step 5: calculating each sub-aperture diametric plane shape ε according to formula (3) _asphere:

${\mathrm{\&epsiv;}}_{asphere}=\frac{1}{2}\&lsqb;W_{asphere-test}-W_{reference}\&rsqb;---\left(3\right)$

Wherein: W _asphere-testfor sub-aperture Wave-front phase

W _referencefor the fixed phase of sub-aperture;

Step 6: according to each sub-aperture diametric plane shape ε obtained in step 5 _asphere, reduce the impact of machine error on splicing result by stitching algorithm, the most each sub-aperture diametric plane graphic data splicing, draws unified shape.

5. the stitching interferometer of employing distorting lens according to claim 4 detects the device of aspheric surface, and it is characterized in that, described interference detection system is Tai Man-Green's type interferometer or Feisuo type interferometer.

6. the stitching interferometer of employing distorting lens according to claim 5 detects the device of aspheric surface, it is characterized in that, described in step 3 according to system model and interference fringe adjustment distorting lens (4) face shape or refractive index, until the concrete steps that interference fringe picture meets testing requirement are:

1) the Zelnick aberration at detector (6) place obtained is detected according to emulation in optical design software, when interfering detection system to select Twyman Green Interferometer, the face shape of distorting lens (4) is set to 1/2 of Zelnick aberration; When interfering detection system to select Feisuo interferometer, the method of " inversion " is adopted to calculate the index distribution compensated needed for aspheric surface (8), phase place needed for calculation compensation aspheric surface (8), P is any point in aspheric surface (8), cross the normal that P does aspheric surface (8), hand over distorting lens (4) rear surface to be M; Light PM, after distorting lens (4) diffraction, hand over distorting lens (4) front surface to be N, then to reflect last convergent point is F; Wherein the refractive index of distorting lens (4) is n _g, the refractive index of surrounding air is n _a; Aspheric surface (8) is d apart from the distance of distorting lens (4) rear surface ₁, distorting lens (4) thickness is the distance of d, F distance distorting lens (4) front surface is d ₂;

According to Fermat principle, the upper any point of aspheric surface (8) be made all to converge to a F along the light of normal emergence, then have:

n _a|PM|+n _g|MN|+n _a|NF|＝n _ad ₁+n _gd+n _ad ₂

Distorting lens (4) refractive index ng is calculated by formula (4):

$n_g=\frac{n_a{d}_1+n_{g}d+n_a{d}_2-n_a\left|NF\right|-n_a\left|PM\right|}{\left|MN\right|}---\left(4\right)$

2) by interfering detection system to detect sub-aperture, interference fringe picture is obtained;

3) according to step 2) in the interference fringe picture that obtains distorting lens (4) carry out step 1) in feedback regulation, until interference fringe picture meets testing requirement, distorting lens (4) has regulated.

7. the stitching interferometer of employing distorting lens according to claim 4 detects the device of aspheric surface, and it is characterized in that, the stitching algorithm described in step 6 is specially:

1) according to sub-aperture diametric plane shape after formula (5) calculating introducing compensation rate

${E_{asphere}}_i={{\mathrm{\&epsiv;}}_{asphere}}_i+\underset{k=1}{\overset{L}{\&Sigma;}}{F}_{ik}{f}_k(x,y),k=1,2...L---\left(5\right)$

Wherein: f _kthe compensation factor that (x, y) is sub-aperture;

L is the number compensating factor;

for the face shape of i-th sub-aperture that step 5 obtains;

F _ikfor sub-aperture compensates the penalty coefficient of factor, obtain the penalty coefficient F of each sub-aperture by the such as least square method shown in (6) _ik;

$\min =\underset{i=1...N-1}{\&Sigma;}\underset{j=0...N-1}{\overset{j\&cap;i}{\&Sigma;}}{\left(\left({\mathrm{\&epsiv;}}_{{\mathrm{asphere}}_i}\left(x,y\right)+\underset{k=1}{\overset{L}{\&Sigma;}}{F}_{ik}{f}_k\left(x,y\right)\right)-\left({\mathrm{\&epsiv;}}_{{\mathrm{asphere}}_j}\left(x,y\right)+\underset{k=1}{\overset{L}{\&Sigma;}}{F}_{jk}{f}_k\left(x,y\right)\right)\right)}^2---\left(6\right)$

Wherein: N is the number of sub-aperture;

Sub-aperture counts from zero, i.e. sub-aperture centered by the 0th sub-aperture;

representing only has the jth of an overlapping region sub-aperture to calculate to i-th sub-aperture;

2) according to step 1) in each sub-aperture diametric plane shape of obtaining splicing obtains unified shape, by used be added, the face shape of overlapping region gets the weighted mean value of each sub-aperture data.

8. the stitching interferometer of employing distorting lens according to claim 4 detects the device of aspheric surface, and it is characterized in that, described optical design software is Zemax software.