CN106091978A - The joining method of interference fringe image in inclined in type measurements by laser interferometry - Google Patents

Abstract

The joining method of interference fringe image in inclined in type measurements by laser interferometry disclosed by the invention, particularly as follows: with the helical gear flank of tooth for measuring object, tested surface is divided into W part in the X-axis direction, it is divided in the Y-axis direction on H part, i.e. tested surface and is divided into the individual mesh point of (W+1) × (H+1)；Any one mesh point be designated as G (h, w), h=0,1 ..., H, w=0,1 ..., W, its space coordinates is denoted as D_(h,w)；(h, normal direction w) is designated as n to arbitrary mesh point G_(h,w), particularly as follows: with the locus of tested curved surface for splicing benchmark, each width interference fringe image is registrated with tested curved surface；Carry out process reliability based on width of fringe to judge；Set up transformed coordinate system model；To tested curved surface shape error resampling, complete the splicing of interference fringe image.The joining method of the present invention realizes the splicing reconstruct of form error information in the interference fringe image that several primary optical axis positions are different.

Description

The joining method of interference fringe image in inclined in type measurements by laser interferometry

Technical field

The invention belongs to image processing method technical field, be specifically related in a kind of inclined in type measurements by laser interferometry interfere The joining method of stripe pattern.

Background technology

Laser interferometry has quickly, noncontact and high-precision advantage, be measure complex-curved (such as: gear teeth Face, dynamic and hydrostatic bearing inner surface etc.) effective ways of form error.

In existing technology, have based on the Mach-Zehnder laser interferometer improved, optical path can be built also Shoot the interference fringe picture of tested surface；When tested curved surface is wide or difference in height is bigger, object light path and ginseng in measurement system Examining the path difference between light path and change very big in whole tested surface region, in optical axis center position, path difference change is less, therefore Interference fringe is wider herein；In the position away from optical axis center, acutely, therefore interference fringe is narrow and dense in path difference change.Dry The processing accuracy relating to stripe pattern is inversely proportional to width of fringe, and its processing accuracy is when width of fringe is less than four pixels Incredible.In interference fringe image, the regional processing precision away from primary optical axis reduces, and can affect whole tested surface form error The overall accuracy measured, this just greatly limit the application of inclined in type laser interferometry, and to complexity When curved surface measures, the densest interference fringe image is nearly unavoidable, the most how in striped dense Region Inside obtain ensure that the shape information of certainty of measurement, be the key issue in inclined in type laser interferometry, but, current phase The achievement in research closed is the most few.

Japanese researchers once inserted special parameter lens in reference path, made reference path light path be more nearly measurement Light path light path, thus reduce the fringe density of regional area.The method is capable of the modulation to width of fringe, however it is necessary that root Select different modulation lens according to different tested curved surfaces, when tested curve form is changeable, need to be replaced as frequently as modulation thoroughly Mirror, causes measurement error.The operation and maintenance of the most high-precision lenses is also a considerable expense.Therefore, the method is also The most highly satisfactory.

Regulation reflecting mirror pose can regulate primary optical axis position on tested curved surface in an experiment, can interferometric modulator striped The position of the widest striped in image, is therefore considered as the method for interference fringe image splicing to solve this problem: first clap Take the photograph the interference fringe image that many group primary optical axis positions are different；Then the region that wherein can meet certainty of measurement is found out；? It is spliced into the form error of whole tested curved surface eventually.Therefore, bar is interfered in the local how splicing corresponding different tested curved surface areas Print image, is the key technology ensureing striped dense Region certainty of measurement.

Recent decades, occurs in that many merging algorithm for images in image processing field.In general these algorithms can divide It is two classes: stitching algorithm based on region (Ares-based method) and feature based (Feature-based method) Stitching algorithm.The former is also referred to as correlation method (correlation-like methods) or template matching (template Matching), the general calculation window using fixed size or whole image carry out correlation estimation.Actual measure in along with The movement of wide fringe position, all fringe distributions in interference fringe image change the most therewith, and therefore the method is difficult to use in dry Relate to the splicing of stripe pattern.The latter is based on the extraction of feature in image to be spliced, such as: characteristic area, characteristic curve, characteristic point Deng.Interference fringe image is different from the picture in our daily life, and it occurs serious compression relative to tested surface, and And one the interference fringe of rule gray scale gradual change there is no feature for stitching algorithm identification, therefore such algorithm also cannot be used directly for Interference fringe image splices.Moreover, the form error that primary optical axis position difference interference fringe image calculates is not one Under individual identical coordinate system, it is impossible to directly splice.

Problem for above-mentioned existence, it is achieved the splicing of the multi-frame interferometry stripe pattern that optical axis position is different is extremely important , need to be developed further and perfect.

Summary of the invention

It is an object of the invention to provide the joining method of interference fringe image in a kind of inclined in type measurements by laser interferometry, The splicing reconstruct of form error information in the interference fringe image that several primary optical axis positions are different can be realized, solve prior art The striped dense Region processing accuracy of middle interference fringe image is low and the problem that affects ultimate measurement accuracy.

The technical solution adopted in the present invention is, the splicing side of interference fringe image in inclined in type measurements by laser interferometry Method, specifically implements according to following steps: with the helical gear flank of tooth for measuring object, tested surface is divided into W part in the X-axis direction, at Y It is divided on direction of principal axis on H part, i.e. tested surface and is divided into the individual mesh point of (W+1) × (H+1)；

Any one mesh point be designated as G (h, w), h=0,1 ..., H, w=0,1 ..., W, its space coordinates is denoted as D_(h,w)；

(h, normal direction w) is designated as n to any one mesh point G_(h,w), specifically implement according to following steps:

Step 1, with the locus of tested curved surface for splicing benchmark, each width interference fringe image is carried out with tested curved surface Registration；

Step 2, after step 1 completes, carry out process reliability based on width of fringe judge；

Step 3, after step 2, set up transformed coordinate system model；

Step 4, after step 3 completes, to tested curved surface shape error resampling, complete the splicing of interference fringe image.

The feature of the present invention also resides in:

Step 1 is specifically implemented according to following steps:

Step 1.1, in simulation software to each mesh point on tested surface, whole optical path carries out light and chases after Mark calculates until CCD imaging plane, make each tested surface mesh point G (h, w) corresponding only one simulation imaging point S (h, w), institute Formed a width emulation flank of tooth picture by simulation imaging point, i.e. obtain the mapping relations between simulation image and the tested curved surface of reality；

Step 1.2, after step 1.1, simulation image is carried out integral transformation；

Variation includes: translates, scale and rotates so that it is overlap with actual measurement interference fringe image as far as possible；

So can make each simulation imaging point S (h, w) only one pixel I in corresponding interference fringe image (h, w), i.e. The mapping relations between simulation image and interference fringe image can be set up；

Step 1.3, after step 1.2, with simulation image as bridge, set up between interference fringe image and the tested curved surface of reality Mapping relations, on the corresponding tested curved surface of pixel on each interference fringe image unique the most a bit.

Step 2 is concrete to be judged in accordance with the following methods:

After step 1, by pseudo-coherence factor, width of fringe is identified, and then determine can in interference fringe image Ensure the reliable area of processing accuracy；

Pseudo-coherence factor obtains according to following algorithm:

In above formula, ψ_i,jBe in wrapped phase figure coordinate figure for (i, j) wrapped phase at place, k be with pixel (x, y) Centered by the size of calculation window, general k value is 3；

In the pseudo-coherence factor Quality Map generated, determine threshold value Γ_PSD, produce one in order to indicate interference according to algorithm The bianry image of reliable area in stripe pattern, specifically implements according to following algorithm:

White is reliable area, and the unreliable region of black, only reliable area are used for ensuing splicing.

Step 3 is concrete to be set up in accordance with the following methods:

In interference fringe image, the center of the widest striped is optical axis center position, in Practical Calculation, with closest to reason Pixel I (the h of opinion position₀, W/2) and it is optical axis center, 0 < h₀<H；With this pixel as starting point in Phase-un-wrapping, phase value It is set to 0；The interference fringe image that two groups of primary optical axis positions are different, Phase-un-wrapping starting point is different, the form error calculated Datum mark is the most different, coordinate transform to be carried out；

Setting pixel I (H/2, W/2) in interference fringe image, the data in all interference fringe images are all put with this and are Optical axis reference center carries out coordinate transform；

Set one group of interference fringe image optical axis center as I (h₀, W/2), define a three-dimensional matrice N_(h,w)For coordinate Conversion, N_(h,w)=[x, y, f], wherein, x, y be pixel I (h, w) corresponding to tested net surfaces lattice point G (h, w) at X-axis, Y Spatial value on axle, as it is shown in figure 1, wherein, f is optical path difference to tested curved space coordinate system, uses following algorithm through meter Calculate and obtain:

In above formula, l is Laser Measurement wavelength,Being the phase value after solving parcel, β is to measure angle of light；

After coordinate transform, optical path difference f ' specifically is computed obtaining by following algorithm:

In above formula,Vers θ=(1-cos θ), θ is two normal n_(H/2,W/2)WithBetween angle, specifically by following algorithm be computed obtain:

In above formula, (n_x,n_y,n_z) it is normal direction n_(H/2,W/2)Coordinate figure, (n_0x,n_0y,n_0z) it is normal directionCoordinate figure；K is normal n_(H/2,W/2)WithThe normal direction of the space plane of composition, specifically by following Algorithm is computed obtaining:

Optical path difference is after coordinate transform, and the form error Δ f of tested curved surface is specifically obtained by following algorithm, specific algorithm As follows:

Δ f=f_obj-f_ref(8)；

In above formula, f_objIt is the optical path difference of tested curved surface, f_refIt it is the optical path difference of reference surface.

Step 4 is specifically implemented according to following steps:

The form error that will be located in reliable area is designated as: R_i(h, w), i=1,2 ..., it is used to refer to the volume of interference fringe Number；The part overlapped in two groups of interference fringe image reliable area is designated as L_i(h,w)；

The splicing of two groups of interference fringe images, specifically implements according to following steps:

Step 4.1, at R₁(h, w) and R₂(h, w) in extract overlapping region L₁(h, w) and L₂(h,w)；

Step 4.2, after step 4.1, search splicing boundary point:

Step 4.3, after step 4.2, according to following algorithm splice data R₁(h, w) and R₂(h, w) be R (h, w), the most right The data at two ends, border carry out resampling, it is then determined that the form error value of border each point, complete the splicing of interference fringe image, The algorithm being specifically related to is:

Step 4.2 is specifically implemented according to following steps:

First, in the first row data of overlapping region, the point differing minimum between two groups of form error data is found, as Splicing starting point, is designated as B (0)；

Then, calculate the difference of two grouping error data at three pixels adjacent thereto in next column data, find The pixel at minima place is designated as B (1), and searches the boundary point in next column with this as the starting point；

The like, until finding out all of boundary point, and these boundary points are designated as B (w), w=0,1 ..., W.

The beneficial effects of the present invention is:

(1) joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention, it is achieved several primary optical axis In the interference fringe image that position is different, the splicing reconstruct of form error information, solves interference fringe image in prior art Striped dense Region processing accuracy is low, the problem affecting ultimate measurement accuracy.

(2) joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention, it is ensured that whole tested song The form error information in face both is from interference fringe image region that is sparse in striped and that ensure that processing accuracy, Jin Erbao Hinder overall certainty of measurement.

Accompanying drawing explanation

Fig. 1 is tested gear teeth face coordinate system in optical path；

Fig. 2 is that tested surface mesh point divides schematic diagram；

Fig. 3 is interference fringe picture in the joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention Registration process schematic diagram between picture and tested curved surface；

Fig. 4 is tested curved surface imitative in the joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention True image；

Fig. 5 is image resampling in the joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention Flow chart；

Fig. 6 is that in inclined in type measurements by laser interferometry of the present invention, in the joining method of interference fringe image, boundary point selected The schematic diagram of journey；

Fig. 7 is the inclined in type used in the joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention The structural representation of laser interference system.

In figure, 1. reflecting mirror a, 2. half-reflecting half mirror, 3. imaging len, 4.CCD camera, 5. reference path, 6. object light Road, 7. wedge a, 8. helical gear, 9. wedge b, 10. beam expanding lens a, 11. piezoelectric ceramics, 12. reflecting mirror b, 13. Amici prism a, 14. Amici prism b, 15.He-Ne laser instrument, 16.1/4 wave plate, 17. beam expanding lens b.

Detailed description of the invention

The present invention is described in detail with detailed description of the invention below in conjunction with the accompanying drawings.

The joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention, specifically real according to following steps Execute:

First, with the helical gear flank of tooth for measuring object, measuring system coordinate system can be as it is shown in figure 1, tested surface be in X-direction On be divided into W part, be divided into H part in the Y-axis direction, say, that on tested surface, be divided into the individual grid of (W+1) × (H+1) Point, as shown in Figure 2；Any one mesh point be labeled as G (h, w), h=0,1 ..., H, w=0,1 ..., W, its space coordinates remember Make D_(h,w)；(h, normal direction w) is designated as n to any one mesh point G_(h,w), all algebraic symbols used collect in Table 1, Concrete as shown in table 1.

Table 1 identification list

Step 1, with the locus of tested curved surface for splicing benchmark, each width interference fringe image is carried out with tested curved surface Registration, wherein method for registering is concrete as it is shown on figure 3, specifically implement according to following steps:

In the interference fringe image that several optical axis positions are different, although respective fringe distribution is different from, but they The most corresponding same tested curved surface；Owing to measuring the big angle of incidence of light, interference fringe image is heavy compression relative to tested curved surface Distortion, need special method for registering to determine mapping relations between the two；

Step 1.1, in simulation software to each mesh point on tested surface, whole optical path carries out light and chases after Mark calculates until CCD imaging plane, the most each tested surface mesh point G (h, w) corresponding only one simulation imaging point S (h, w), All simulation imaging points form a width emulation flank of tooth picture, as shown in Figure 4, i.e. obtain the mapping between simulation image and the tested curved surface of reality Relation；

Step 1.2, after step 1.1, simulation image is carried out integral transformation, variation includes: translates, scale and revolves Turn so that it is overlap with actual measurement interference fringe image as far as possible；

So can make each simulation imaging point S (h, w) only one pixel I in corresponding interference fringe image (h, w), i.e. The mapping relations between simulation image and interference fringe image can be set up；

Step 1.3, after step 1.2, with simulation image as bridge, set up between interference fringe image and the tested curved surface of reality Mapping relations, on the corresponding tested curved surface of pixel on each interference fringe image unique the most a bit.

Step 2, after step 1 completes, carry out process reliability based on width of fringe judge, the most in accordance with the following methods Judge:

After step 1, by pseudo-coherence factor (PSD), width of fringe is identified, and then determines interference fringe image In ensure that the reliable area of processing accuracy；

Pseudo-coherence factor is embodied as following algorithm:

In above formula, ψ_i,jBe in wrapped phase figure coordinate figure for (i, j) wrapped phase at place, k be with pixel (x, y) Centered by the size of calculation window, general k value is 3；

In the pseudo-coherence factor Quality Map generated, determine threshold value Γ_PSD, produce one in order to indicate interference according to algorithm The bianry image of reliable area in stripe pattern, specifically implements according to following algorithm:

Wherein, white is reliable area, and the unreliable region of black, only reliable area are used for ensuing splicing.

Step 3, after step 2, set up transformed coordinate system model, set up the most in accordance with the following methods:

In theory: in interference fringe image, the center of the widest striped is optical axis center position, in Practical Calculation In, with the pixel I (h closest to theoretical position₀, W/2) and it is optical axis center, 0 < h₀<H；Phase-un-wrapping with this pixel is Starting point, phase value is set to 0；The interference fringe image that two groups of primary optical axis positions are different, Phase-un-wrapping starting point is different, calculates The form error datum mark gone out is the most different, coordinate transform to be carried out；

Setting pixel I (H/2, W/2) in interference fringe image, the data in all interference fringe images are all put with this and are Optical axis reference center carries out coordinate transform；

Set one group of interference fringe image optical axis center as I (h₀, W/2), define a three-dimensional matrice N_(h,w)For coordinate Conversion, N_(h,w)=[x, y, f], wherein, x, y be pixel I (h, w) corresponding to tested net surfaces lattice point G (h, w) at X-axis, Y Spatial value on axle, as it is shown in figure 1, wherein, f is optical path difference to tested curved space coordinate system, uses following algorithm through meter Calculate and obtain:

In above formula, λ is Laser Measurement wavelength,Being the phase value after solving parcel, β is to measure angle of light；

After coordinate transform, optical path difference f ' specifically is computed obtaining by following algorithm:

In above formula,Vers θ=(1-cos θ), θ is two normal n_(H/2,W/2)WithBetween angle, specifically by following algorithm be computed obtain:

In above formula, (n_x,n_y,n_z) it is normal direction n_(H/2,W/2)Coordinate figure, (n_0x,n_0y,n_0z) it is normal directionCoordinate figure；K is normal n_(H/2,W/2)WithThe normal direction of the space plane of composition, specifically by following Algorithm is computed obtaining:

Optical path difference is after coordinate transform, and the form error Δ f of tested curved surface is specifically obtained by following algorithm, specific algorithm As follows:

Δ f=f_obj-f_ref(8)；

In above formula, f_objIt is the optical path difference of tested curved surface, f_refIt it is the optical path difference of reference surface.

Step 4, after step 3 completes, to tested curved surface shape error resampling, complete the splicing of interference fringe image；

The form error that will be located in reliable area is designated as: R_i(h, w), i=1,2 ..., it is used to refer to the volume of interference fringe Number；The part overlapped in two groups of interference fringe image reliable area is designated as L_i(h,w)；

The splicing of two groups of interference fringe images is as it is shown in figure 5, specifically implement according to following steps:

Step 4.1, at R₁(h, w) and R₂(h, w) in extract overlapping region L₁(h, w) and L₂(h,w)；

Step 4.2, after step 4.1, search splicing boundary point, its flow process as shown in Figure 6, specifically comprises the following steps that

First, in the first row data of overlapping region, the point differing minimum between two groups of form error data is found, as Splicing starting point, is designated as B (0)；

Then, calculate the difference of two grouping error data at three pixels adjacent thereto in next column data, find The pixel at minima place is designated as B (1), and searches the boundary point in next column with this as the starting point；

The like, until finding out all of boundary point, and these boundary points are designated as B (w), w=0,1 ..., W；

Step 4.3, after step 4.2, according to following algorithm splice data R₁(h, w) and R₂(h, w) be R (h, w), the most right The data at two ends, border carry out resampling, it is then determined that the form error value of border each point, complete the splicing of interference fringe image, The algorithm being specifically related to is:

Inclined in type measurements by laser interferometry of the present invention relates in the joining method of interference fringe image inclined in type laser do Relating to system, its structure is as it is shown in fig. 7, optical path is made up of object light path 6 and reference path 5；Tested part is positioned over thing In body light path 6, object light path 6 and reference path 5 (two-way light path) interfere after half-reflecting half mirror 2, right by CCD camera 4 Interference fringe shoots.Piezoelectric ceramics 11 (PZT) is fixed on the phase shift realizing reference path 5 on reflecting mirror b12, this reflection The pose of mirror b12 can regulate, in order to change optical axis center position on tested surface, i.e. and the widest striped in interference fringe image Position.

Two flank of tooth of same helical gear 8 are counted as respectively with reference to the flank of tooth and the tested flank of tooth, and as example, this are described Bright joining method；Taking average phase-shifting method to change the phase place of reference path 5, phase shift step value pi/2, phase shift range is 0 to 2 π, Detailed process is as follows:

Step 1, shooting first group of interference fringe image, the widest striped is located adjacent to tooth top position, shoots five width with reference to teeth The phase shift interference fringe image in face, rotates tested helical gear, the phase shift interference fringe image of five tested flank of tooth of shooting；

Step 2, the pose of modulation reflecting mirror b12, make the widest fringe position close to root position, shoot five width references respectively The phase shift interference fringe image of the flank of tooth and the tested flank of tooth, and as second group of interference fringe image；

Step 3, joining method according to the present invention set up the mapping relations between interference fringe image and the actual flank of tooth, use Pseudo-coherence factor (PSD) identifies width of fringe, and the pixel window in calculating is 3 × 3, and threshold value is 0.3；

According to recognition result: the root portions of first group of interference fringe image and the tooth of second group of interference fringe image It is insecure that top is divided, although has some discrete noise spots in other regions of image, but can carry out it easily Filter and have no effect on final recognition result；

According to credibility recognition result, respectively by first group of interference fringe image tooth tip 2/3 region and second group of interference Stripe pattern tooth root end 2/3 region is considered as reliable area, is used for splicing；

Step 4, calculate the Phase Unwrapping Algorithm of each group of interference fringe image, and calculate the form error of the tested flank of tooth；

Owing to optical axis center is different, two groups of fringe distributions are different, and it is also inconsistent, through coordinate for solving the PHASE DISTRIBUTION after parcel Just can be used for after conversion splicing；

In first group and second group of image, tested flank of tooth optical path difference does difference respectively with reference to flank of tooth optical path difference, obtains two Organize tested tooth surface shape error to be spliced.

Automatically search for splicing boundary according in the joining method of the present invention, and two groups of form error data spliced, The splicing result of final tested surface form error is continually varying, and does not has obvious locus of discontinuity near splicing boundary Territory, thus demonstrate the feasibility of the method.With the help of this interference fringe picture spelicing profiles algorithm, all on tested curved surface Form error data both from the reliable fringe area of processing accuracy, this substantially increases the precision of measurement undoubtedly.

The joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention, can realize several primary optical axis positions Put the splicing reconstruct of form error information in different interference fringe images, solve the bar of interference fringe image in prior art Stricture of vagina dense Region processing accuracy is low and the problem that affects ultimate measurement accuracy.

Claims (6)

1. the joining method of interference fringe image in inclined in type measurements by laser interferometry, it is characterised in that be with the helical gear flank of tooth Measuring object, tested surface is divided into W part in the X-axis direction, is divided in the Y-axis direction on H part, i.e. tested surface and is divided into (W + 1) × (H+1) individual mesh point；

Any one mesh point be designated as G (h, w), h=0,1 ..., H, w=0,1 ..., W, its space coordinates is denoted as D_(h,w)；

(h, normal direction w) is designated as n to any one mesh point G_(h,w), specifically implement according to following steps:

Step 1, with the locus of tested curved surface for splicing benchmark, each width interference fringe image is joined with tested curved surface Accurate；

Step 2, after step 1 completes, carry out process reliability based on width of fringe judge；

Step 3, after step 2, set up transformed coordinate system model；

Step 4, after step 3 completes, to tested curved surface shape error resampling, complete the splicing of interference fringe image.

The joining method of interference fringe image, its feature in inclined in type measurements by laser interferometry the most according to claim 1 Being, described step 1 is specifically implemented according to following steps:

Step 1.1, in simulation software to each mesh point on tested surface, whole optical path carries out ray tracing meter Calculate until CCD imaging plane, make each tested surface mesh point G (h, w) corresponding only one simulation imaging point S (h, w), all imitative True imaging point forms a width emulation flank of tooth picture, i.e. obtains the mapping relations between simulation image and the tested curved surface of reality；

Step 1.2, after step 1.1, simulation image is carried out integral transformation；

Variation includes: translates, scale and rotates so that it is overlap with actual measurement interference fringe image as far as possible；

So can make each simulation imaging point S (h, w) only one pixel I in corresponding interference fringe image (h, w), Ji Nengjian Vertical mapping relations between simulation image and interference fringe image；

Step 1.3, after step 1.2, with simulation image as bridge, set up the mapping between interference fringe image and the tested curved surface of reality Relation, on the corresponding tested curved surface of pixel on each interference fringe image unique the most a bit.

The joining method of interference fringe image, its feature in inclined in type measurements by laser interferometry the most according to claim 1 Being, described step 2 is concrete to be judged in accordance with the following methods:

After step 1, by pseudo-coherence factor, width of fringe is identified, and then determines in interference fringe image and ensure that The reliable area of processing accuracy；

Pseudo-coherence factor obtains according to following algorithm:

$C(x,y)=\frac{\sqrt{{\left(\underset{i=x-k/2}{\overset{x+k/2}{\&Sigma;}}\underset{j=y-k/2}{\overset{y+k/2}{\&Sigma;}}{\mathrm{cos\&psi;}}_{i,j}\right)}^2+{\left(\underset{i=x-k/2}{\overset{x+k/2}{\&Sigma;}}\underset{j=y-k/2}{\overset{y+k/2}{\&Sigma;}}{\mathrm{sin\&psi;}}_{i,j}\right)}^2}}{k\&times;k}---\left(1\right);$

In above formula, ψ_i,jIt is that in wrapped phase figure, coordinate figure is that (i, j) wrapped phase at place, k is that (x, in y) being with pixel The size of the calculation window of the heart, general k value is 3；

In the pseudo-coherence factor Quality Map generated, determine threshold value Γ_PSD, produce one in order to indicate interference fringe according to algorithm The bianry image of reliable area in image, specifically implements according to following algorithm:

$Q_{PSD}(x,y)=\left\{\begin{array}{cccc}1& \left(reliable\right)& if& C(x,y)>{\mathrm{\&Gamma;}}_{PSD}\\ 0& \left(unreliable\right)& if& C(x,y)\&le;{\mathrm{\&Gamma;}}_{PSD}\end{array}\right.---\left(2\right);$

White is reliable area, and the unreliable region of black, only reliable area are used for ensuing splicing.

The joining method of interference fringe image, its feature in inclined in type measurements by laser interferometry the most according to claim 1 Being, described step 3 is concrete to be set up in accordance with the following methods:

In interference fringe image, the center of the widest striped is optical axis center position, in Practical Calculation, with closest to theoretical bits Pixel I (the h put₀, W/2) and it is optical axis center, 0 < h₀<H；With this pixel as starting point in Phase-un-wrapping, phase value is set to 0；The interference fringe image that two groups of primary optical axis positions are different, Phase-un-wrapping starting point is different, the form error benchmark calculated Point is also different, coordinate transform to be carried out；

Setting pixel I (H/2, W/2) in interference fringe image, the data in all interference fringe images are all with this point as optical axis Reference center carries out coordinate transform；

Set one group of interference fringe image optical axis center as I (h₀, W/2), define a three-dimensional matrice N_(h,w)For coordinate transform, N_(h,w)=[x, y, f], wherein, x, y be pixel I (h, w) corresponding to tested net surfaces lattice point G (h, w) in X-axis, Y-axis Spatial value, as it is shown in figure 1, wherein, f is optical path difference to tested curved space coordinate system, uses following algorithm to be computed obtaining:

In above formula, λ is Laser Measurement wavelength,Being the phase value after solving parcel, β is to measure angle of light；

After coordinate transform, optical path difference f ' specifically is computed obtaining by following algorithm:

${N^{\&prime;}}_{(h,w)}=(N_{(h,w)}-N_{(h_0,W/2)})R(k,\mathrm{\&theta;})---\left(4\right);$

$R(k,\mathrm{\&theta;})=\left[\begin{array}{ccc}{k}_x{k}_{x}Vers\mathrm{\&theta;}+\cos \mathrm{\&theta;}& k_y{k}_{x}Vers\mathrm{\&theta;}-k_z\sin \mathrm{\&theta;}& k_z{k}_{x}Vers\mathrm{\&theta;}+k_y\sin \mathrm{\&theta;}\\ k_x{k}_{y}Vers\mathrm{\&theta;}+k_z\sin \mathrm{\&theta;}& k_y{k}_{y}Vers\mathrm{\&theta;}+\cos \mathrm{\&theta;}& k_z{k}_{y}Vers\mathrm{\&theta;}-k_x\sin \mathrm{\&theta;}\\ k_x{k}_{z}Vers\mathrm{\&theta;}+k_y\sin \mathrm{\&theta;}& k_y{k}_{z}Vers\mathrm{\&theta;}+k_x\sin \mathrm{\&theta;}& k_z{k}_{z}Vers\mathrm{\&theta;}+\cos \mathrm{\&theta;}\end{array}\right]---\left(5\right);$

In above formula,Vers θ=(1-cos θ), θ is Two normal n_(H/2,W/2)WithBetween angle, specifically by following algorithm be computed obtain:

$\mathrm{\&theta;}=\arccos \frac{n_x{n}_{0x}+n_y{n}_{0y}+n_z{n}_{0z}}{\sqrt{{n_x}^2+{n_y}^2+{n_z}^2}\&CenterDot;\sqrt{{n_{0x}}^2+{n_{0y}}^2+{n_{0z}}^2}}---\left(6\right);$

In above formula, (n_x,n_y,n_z) it is normal direction n_(H/2,W/2)Coordinate figure, (n_0x,n_0y,n_0z) it is normal direction Coordinate figure；K is normal n_(H/2,W/2)WithThe normal direction of the space plane of composition, specifically by following algorithm through meter Calculate and obtain:

$\left\{\begin{array}{c}{k}_x=n_y{n}_{0z}-n_z{n}_{0y}\\ k_y=n_z{n}_{0x}-n_x{n}_{0z}\\ k_z=n_x{n}_{0y}-n_y{n}_{0x}\end{array}\right.---\left(7\right);$

Optical path difference is after coordinate transform, and the form error Δ f of tested curved surface is specifically obtained by following algorithm, and specific algorithm is such as Under:

Δ f=f_obj-f_ref(8)；

In above formula, f_objIt is the optical path difference of tested curved surface, f_refIt it is the optical path difference of reference surface.

The joining method of interference fringe image, its feature in inclined in type measurements by laser interferometry the most according to claim 1 Being, described step 4 is specifically implemented according to following steps:

The form error that will be located in reliable area is designated as: R_i(h, w), i=1,2 ..., it is used to refer to the numbering of interference fringe；Two groups The part overlapped in interference fringe image reliable area is designated as L_i(h,w)；

The splicing of two groups of interference fringe images, specifically implements according to following steps:

Step 4.1, at R₁(h, w) and R₂(h, w) in extract overlapping region L₁(h, w) and L₂(h,w)；

Step 4.2, after step 4.1, search splicing boundary point:

Step 4.3, after step 4.2, according to following algorithm splice data R₁(h, w) and R₂(h is w) that (h, w), first to border for R The data at two ends carry out resampling, it is then determined that the form error value of border each point, complete the splicing of interference fringe image, specifically The algorithm related to is:

$\left\{\begin{array}{cc}R(h,w)=R_1(h,w)& h<B\left(w\right)\\ R(h,w)=R_2(h,w)& h>B\left(w\right)\\ R(h,w)=R_1(h,w)& h=B\left(w\right)and{\mathrm{Diff}}_1\&le;{\mathrm{Diff}}_2\\ R(h,w)=R_2(h,w)& h=B\left(w\right)and{\mathrm{Diff}}_1>{\mathrm{Diff}}_2\end{array}\right.---\left(9\right);$

$\left\{\begin{array}{c}{\mathrm{diff}}_1=\&lsqb;L_1(h,w)-L(h,w-1)\&rsqb;+\&lsqb;L_1(h,w)-L(h,w+1)\&rsqb;\\ {\mathrm{diff}}_2=\&lsqb;L_2(h,w)-L(h,w-1)\&rsqb;+\&lsqb;L_2(h,w)-L(h,w+1)\&rsqb;\end{array}\right.---\left(10\right).$

The joining method of interference fringe image, its feature in inclined in type measurements by laser interferometry the most according to claim 5 Being, described step 4.2 is specifically implemented according to following steps:

First, in the first row data of overlapping region, the point differing minimum between two groups of form error data is found, as splicing Starting point, is designated as B (0)；

Then, calculate the difference of two grouping error data at three pixels adjacent thereto in next column data, find minimum The pixel at value place is designated as B (1), and searches the boundary point in next column with this as the starting point；

The like, until finding out all of boundary point, and these boundary points are designated as B (w), w=0,1 ..., W.