CN106091978B - The joining method of interference fringe image in inclined in type measurements by laser interferometry - Google Patents
The joining method of interference fringe image in inclined in type measurements by laser interferometry Download PDFInfo
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- CN106091978B CN106091978B CN201610382967.XA CN201610382967A CN106091978B CN 106091978 B CN106091978 B CN 106091978B CN 201610382967 A CN201610382967 A CN 201610382967A CN 106091978 B CN106091978 B CN 106091978B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2416—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures of gears
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformation in the plane of the image
- G06T3/40—Scaling the whole image or part thereof
- G06T3/4038—Scaling the whole image or part thereof for image mosaicing, i.e. plane images composed of plane sub-images
Abstract
The joining method of interference fringe image in inclined in type measurements by laser interferometry disclosed by the invention, specifically: using the helical gear flank of tooth as measurement object, tested surface is divided into W parts in the X-axis direction, it is divided into H parts in the Y-axis direction, i.e., is divided into a mesh point of (W+1) × (H+1) on tested surface；Any one mesh point is designated as G (h, w), h=0,1 ..., H, w=0,1 ..., W, and space coordinate is denoted as D(h,w)；The normal direction of any mesh point G (h, w) is denoted as n(h,w), specifically: to be tested the spatial position of curved surface as splicing benchmark, each width interference fringe image is registrated with tested curved surface；Carry out the processing reliability judgement based on width of fringe；Establish transformed coordinate system model；To tested curved surface shape error resampling, the splicing of interference fringe image is completed.Joining method of the invention realizes the splicing reconstruct of form error information in the different interference fringe image of several key light shaft positions.
Description
Technical field
The invention belongs to image processing method technical fields, and in particular to interfere in a kind of inclined in type measurements by laser interferometry
The joining method of stripe pattern.
Background technique
Laser interferometry have the advantages that it is quick, non-contact and high-precision, be measurement it is complex-curved (such as: gear teeth
Face, dynamic and hydrostatic bearing inner surface etc.) form error effective ways.
In existing technology, have based on improved Mach-Zehnder laser interferometer, optical path can be built simultaneously
Shoot the interference fringe picture of tested surface；When tested curved surface is wide or difference in height is larger, object optical path and ginseng in measuring system
It examines the path difference between optical path to change in entire tested surface region very greatly, in optical axis center position, path difference variation is smaller, therefore
Interference fringe is wider herein；In the position far from optical axis center, path difference variation is violent, therefore interference fringe is narrow and dense.It is dry
The processing accuracy and width of fringe for relating to stripe pattern are inversely proportional, and its processing accuracy is when width of fringe is less than four pixels
It is incredible.Regional processing precision in interference fringe image far from primary optical axis reduces, and will affect entire tested surface form error
The overall accuracy of measurement, this just greatly limits the application of inclined in type laser interferometry, and to complexity
When curved surface measures, the dense interference fringe image in part is nearly unavoidable, therefore how in striped dense Region
The shape information for inside obtaining to guarantee measurement accuracy is the critical issue in inclined in type laser interferometry, still, phase at present
The research achievement of pass is simultaneously few.
Japanese researchers are once inserted into special parameter lens in reference path, and reference path light path is made to be more nearly measurement
Optical path light path, to reduce the fringe density of regional area.This method can be realized the modulation to width of fringe, but need root
Different modulation lens are selected according to different tested curved surfaces, and when tested curve form is changeable, it is saturating to need to be replaced as frequently as modulation
Mirror causes measurement error.The operation and maintenance of so more high-precision lenses is also a considerable expense.Therefore, this method is simultaneously
It is not highly satisfactory.
Reflecting mirror pose is adjusted in an experiment is adjustable position of the primary optical axis on tested curved surface, it can interferometric modulator striped
The position of most wide striped in image, therefore the method for interference fringe image splicing is considered as to solve the problems, such as this: it claps first
Take the photograph the different interference fringe image of multiple groups key light shaft position；Then the region that can satisfy measurement accuracy is found out wherein；Most
It is spliced into the form error of entire tested curved surface eventually.Therefore, how splicing correspondence difference, which is tested the local of curved surface area, is interfered item
Print image is the key technology for ensureing striped dense Region measurement accuracy.
There are many merging algorithm for images in field of image processing in recent decades.In general these algorithms can divide
For two classes: stitching algorithm (Ares-based method) based on region and being based on feature (Feature-based method)
Stitching algorithm.The former is also referred to as correlation method (correlation-like methods) or template matching (template
Matching), correlation estimation is generally carried out using the calculation window of fixed size or whole image.With most in actual measurement
The movement of wide fringe position, all fringe distributions in interference fringe image all change correspondingly, thus this method be difficult to use in it is dry
Relate to the splicing of stripe pattern.The latter is the extraction based on 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 lifes, and serious compressive deformation occurs relative to tested surface in it, and
And one the interference fringe of rule gray scale gradual change there is no feature to identify that therefore such algorithm also cannot be used directly for doing for stitching algorithm
Relate to stripe pattern splicing.Moreover, key light shaft position different dry relates to the calculated form error of stripe pattern not at one
Under identical coordinate system, cannot directly it be spliced.
In view of the above problems, realize that the splicing of the different multi-frame interferometry stripe pattern of optical axis position is extremely important
, need further develop and it is perfect.
Summary of the invention
The purpose of the present invention is to provide a kind of joining method of interference fringe image in inclined in type measurements by laser interferometry,
It is able to achieve the splicing reconstruct of form error information in the different interference fringe image of several key light shaft positions, solves the prior art
The problem of striped dense Region processing accuracy of middle interference fringe image is low and influences ultimate measurement accuracy.
The technical scheme adopted by the invention is that in inclined in type measurements by laser interferometry interference fringe image splicing side
Method is specifically implemented according to the following steps: using the helical gear flank of tooth as measurement object, tested surface is divided into W parts in the X-axis direction, in Y
It is divided into H parts in axis direction, i.e., is divided into a mesh point of (W+1) × (H+1) on tested surface；
Any one mesh point is designated as G (h, w), h=0,1 ..., H, w=0,1 ..., W, and space coordinate is denoted as
D(h,w)；
The normal direction of any one mesh point G (h, w) is denoted as n(h,w), it is specifically implemented according to the following steps:
Step 1 with the spatial position for being tested curved surface is splicing benchmark, and each width interference fringe image and tested curved surface are carried out
Registration；
Step 2, after the completion of step 1, carry out based on width of fringe processing reliability judgement；
Step 3, after step 2, establish transformed coordinate system model；
Step 4, after the completion of step 3, to tested curved surface shape error resampling, complete the splicing of interference fringe image.
The features of the present invention also characterized in that:
Step 1 is specifically implemented according to the following steps:
Step 1.1, in simulation software to each mesh point on tested surface, carry out light in entire optical path and chase after
Mark is calculated up to CCD imaging plane, keeps each tested surface mesh point G (h, w) corresponding only one simulation imaging point S (h, w),
All simulation imaging points form width emulation flank of tooth picture to get the mapping relations between curved surface are tested to simulation image and reality；
Step 1.2, after step 1.1, to simulation image carry out integral transformation；
Variation includes: translation, scaling and rotation are overlapped it as far as possible with actual measurement interference fringe image；
It can make only one pixel I (h, w) in the corresponding interference fringe image of each simulation imaging point S (h, w) in this way, i.e.,
The mapping relations between simulation image and interference fringe image can be established；
Step 1.3, after step 1.2, using simulation image as bridge, establish between interference fringe image and practical tested curved surface
Mapping relations, on the corresponding tested curved surface of pixel on each interference fringe image it is unique a bit.
Step 2 is specific to be judged in accordance with the following methods:
After step 1, width of fringe is identified by pseudo- coherence factor, and then determining can in interference fringe image
Guarantee the reliable area of processing accuracy；
Pseudo- coherence factor is obtained according to following algorithm:
In above formula, ψi,jIt is the wrapped phase that coordinate value is at (i, j) in wrapped phase figure, k is with pixel (x, y)
Centered on calculation window size, general k value be 3；
In the pseudo- coherence factor Quality Map of generation, threshold value ΓPSD, one, which is produced, according to algorithm interferes to indicate
The bianry image of reliable area in stripe pattern is specifically implemented according to following algorithm:
White is reliable area, and the unreliable region of black, only reliable area are used for next splicing.
Step 3 is specific to be established in accordance with the following methods:
It is optical axis center position at the center of most wide striped in interference fringe image, in actually calculating, with closest reason
By the pixel I (h of position0, W/2) and it is optical axis center, 0 < h0<H；Using the pixel as starting point in Phase- un- wrapping, phase value
It is set to 0；The different interference fringe image of two groups of key light shaft positions, Phase- un- wrapping starting point is different, calculated form error
Datum mark is also different, to be coordinately transformed；
Pixel I (H/2, W/2) in interference fringe image is set, the data in all interference fringe images, which are all put with this, is
Optical axis reference center is coordinately transformed；
One group of interference fringe image optical axis center is set as I (h0, W/2), define a three-dimensional matrice N(h,w)For coordinate
Transformation, N(h,w)=[x, y, f], wherein x, y are tested net surfaces lattice point G (h, w) corresponding to pixel I (h, w) in X-axis, Y
Spatial value on axis it is as shown in Figure 1 to be tested curved space coordinate system, wherein f is optical path difference, using following algorithm through counting
It calculates and obtains:
In above formula, l is measurement optical maser wavelength,It is the phase value after unpacking, β is measurement angle of light；
After coordinate transform, optical path difference f ' is specifically computed acquisition by following algorithm:
In above formula,Vers θ=(1-cos
θ), θ is two normal n(H/2,W/2)WithBetween angle, acquisition is specifically computed by following algorithm:
In above formula, (nx,ny,nz) it is normal direction n(H/2,W/2)Coordinate value, (n0x,n0y,n0z) it is normal directionCoordinate value；K is normal n(H/2,W/2)WithThe normal direction of the space plane of composition, specifically by following calculation
Method is computed acquisition:
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
It is as follows:
Δ f=fobj-fref(8)；
In above formula, fobjIt is the optical path difference of tested curved surface, frefIt is the optical path difference of reference surface.
Step 4 is specifically implemented according to the following steps:
The form error for being located at reliable area is denoted as: Ri(h, w), i=1,2 ..., it is used to refer to the volume of interference fringe
Number；The part to overlap in two groups of interference fringe image reliable areas is denoted as Li(h,w)；
The splicing of two groups of interference fringe images, is specifically implemented according to the following steps:
Step 4.1, in R1(h, w) and R2Overlapping region L is extracted in (h, w)1(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) is R (h, w), first right
The data at boundary both ends carry out resampling, then determine the form error value of boundary each point, complete the splicing of interference fringe image,
The algorithm being specifically related to are as follows:
Step 4.2 is specifically implemented according to the following steps:
First, it is found in the first column data of overlapping region and differs the smallest point between two groups of form error data, as
Splice starting point, is denoted as B (0)；
Then, the difference for calculating two grouping error data at three pixels adjacent thereto in next column data, finds
Pixel where minimum value is denoted as B (1), and searches the boundary point in next column with this as the starting point；
And so on, until finding out all boundary points, and these boundary points are denoted as B (w), w=0,1 ..., W.
The beneficial effects of the present invention are:
(1) in inclined in type measurements by laser interferometry of the present invention interference fringe image joining method, realize several primary optical axis
The splicing reconstruct of form error information, solves interference fringe image in the prior art in the different interference fringe image in position
The problem of striped dense Region processing accuracy is low, influences ultimate measurement accuracy.
(2) in inclined in type measurements by laser interferometry of the present invention interference fringe image joining method, guarantee entire tested song
The form error information in face both is from and interference fringe image that can guarantee processing accuracy region sparse in striped, Jin Erbao
Hinder overall measurement accuracy.
Detailed description of the invention
Fig. 1 is tested coordinate system of the gear teeth face in optical path；
Fig. 2 is that tested surface mesh point divides schematic diagram；
Fig. 3 is interference fringe image 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 tested curved surface；
Fig. 4 is to be tested imitating for curved surface in inclined in type measurements by laser interferometry of the present invention in the joining method of interference fringe image
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 boundary point selected in the joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention
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 schematic diagram of laser interference system.
In figure, 1. reflecting mirror a, 2. half-reflecting half mirrors, 3. imaging lens, 4.CCD camera, 5. reference paths, 6. object lights
Road, 7. wedge a, 8. helical gears, 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, 16.1/4 wave plate, 17. beam expanding lens b.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention, it is specifically real according to the following steps
It applies:
Firstly, using the helical gear flank of tooth as measurement object, measuring system coordinate system can as shown in Figure 1, tested surface in X-direction
On be divided into W parts, be divided into H parts in the Y-axis direction, that is to say, that a grid of (W+1) × (H+1) is divided on tested surface
Point, as shown in Figure 2；Any one mesh point is labeled as G (h, w), h=0,1 ..., H, w=0,1 ..., W, space coordinate note
Make D(h,w)；The normal direction of any one mesh point G (h, w) is denoted as n(h,w), all algebraic symbols used are summarised in table 1, have
Body is as shown in table 1.
1 identification list of table
Step 1 with the spatial position for being tested curved surface is splicing benchmark, and each width interference fringe image and tested curved surface are carried out
Registration, wherein method for registering is specific as shown in figure 3, being specifically implemented according to the following steps:
In the different interference fringe image of several optical axis positions, although respective fringe distribution is different from, they
All correspond to same tested curved surface；Due to measuring the big incidence angle of light, interference fringe image is heavy compression relative to tested curved surface
Distortion, special method for registering is needed to determine mapping relations between the two；
Step 1.1, in simulation software to each mesh point on tested surface, carry out light in entire optical path and chase after
Mark is calculated up to CCD imaging plane, and tested surface mesh point G (h, w) each in this way is corresponding only one simulation imaging point S (h, w),
All simulation imaging points form a width and emulate flank of tooth picture, as shown in Figure 4 to get the mapping arrived between simulation image and practical tested curved surface
Relationship；
Step 1.2, after step 1.1, to simulation image carry out integral transformation, variation includes: translation, scaling and rotation
Turn, is overlapped it as far as possible with actual measurement interference fringe image；
It can make only one pixel I (h, w) in the corresponding interference fringe image of each simulation imaging point S (h, w) in this way, i.e.,
The mapping relations between simulation image and interference fringe image can be established；
Step 1.3, after step 1.2, using simulation image as bridge, establish between interference fringe image and practical tested curved surface
Mapping relations, on the corresponding tested curved surface of pixel on each interference fringe image it is unique a bit.
Step 2, after the completion of step 1, carry out based on width of fringe processing reliability judgement, specifically in accordance with the following methods
Judgement:
After step 1, width of fringe is identified by pseudo- coherence factor (PSD), and then determines interference fringe image
In can guarantee the reliable area of processing accuracy；
Pseudo- coherence factor is embodied as following algorithm:
In above formula, ψi,jIt is the wrapped phase that coordinate value is at (i, j) in wrapped phase figure, k is with pixel (x, y)
Centered on calculation window size, general k value be 3；
In the pseudo- coherence factor Quality Map of generation, threshold value ΓPSD, one, which is produced, according to algorithm interferes to indicate
The bianry image of reliable area in stripe pattern is specifically implemented according to following algorithm:
Wherein, white is reliable area, and the unreliable region of black, only reliable area are used for next splicing.
Step 3, after step 2, establish transformed coordinate system model, specifically in accordance with the following methods establish:
In theory: in interference fringe image at the center of most wide striped be optical axis center position, in practical calculating
In, with closest to the pixel I (h of theoretical position0, W/2) and it is optical axis center, 0 < h0<H；It is with the pixel in Phase- un- wrapping
Starting point, phase value are set to 0；The different interference fringe image of two groups of key light shaft positions, Phase- un- wrapping starting point is different, calculates
Form error datum mark out is also different, to be coordinately transformed；
Pixel I (H/2, W/2) in interference fringe image is set, the data in all interference fringe images, which are all put with this, is
Optical axis reference center is coordinately transformed；
One group of interference fringe image optical axis center is set as I (h0, W/2), define a three-dimensional matrice N(h,w)For coordinate
Transformation, N(h,w)=[x, y, f], wherein x, y are tested net surfaces lattice point G (h, w) corresponding to pixel I (h, w) in X-axis, Y
Spatial value on axis it is as shown in Figure 1 to be tested curved space coordinate system, wherein f is optical path difference, using following algorithm through counting
It calculates and obtains:
In above formula, λ is measurement optical maser wavelength,It is the phase value after unpacking, β is measurement angle of light；
After coordinate transform, optical path difference f ' is specifically computed acquisition by following algorithm:
In above formula,Vers θ=(1-cos θ),
θ is two normal n(H/2,W/2)WithBetween angle, acquisition is specifically computed by following algorithm:
In above formula, (nx,ny,nz) it is normal direction n(H/2,W/2)Coordinate value, (n0x,n0y,n0z) it is normal directionCoordinate value；K is normal n(H/2,W/2)WithThe normal direction of the space plane of composition, specifically by following calculation
Method is computed acquisition:
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
It is as follows:
Δ f=fobj-fref(8)；
In above formula, fobjIt is the optical path difference of tested curved surface, frefIt is the optical path difference of reference surface.
Step 4, after the completion of step 3, to tested curved surface shape error resampling, complete the splicing of interference fringe image；
The form error for being located at reliable area is denoted as: Ri(h, w), i=1,2 ..., it is used to refer to the volume of interference fringe
Number；The part to overlap in two groups of interference fringe image reliable areas is denoted as Li(h,w)；
The splicing of two groups of interference fringe images is as shown in figure 5, be specifically implemented according to the following steps:
Step 4.1, in R1(h, w) and R2Overlapping region L is extracted in (h, w)1(h, w) and L2(h, w)；
Step 4.2, after step 4.1, search splicing boundary point, process is as shown in Figure 6, the specific steps are as follows:
First, it is found in the first column data of overlapping region and differs the smallest point between two groups of form error data, as
Splice starting point, is denoted as B (0)；
Then, the difference for calculating two grouping error data at three pixels adjacent thereto in next column data, finds
Pixel where minimum value is denoted as B (1), and searches the boundary point in next column with this as the starting point；
And so on, until finding out all boundary points, and these boundary points are denoted 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) is R (h, w), first right
The data at boundary both ends carry out resampling, then determine the form error value of boundary each point, complete the splicing of interference fringe image,
The algorithm being specifically related to are as follows:
Inclined in type laser involved in the joining method of interference fringe image is dry in inclined in type measurements by laser interferometry of the present invention
System is related to, structure is as shown in fig. 7, optical path is made of object optical path 6 and reference path 5；Tested part is placed in object
In body optical path 6, object optical path 6 and reference path 5 (two-way optical path) interfere after half-reflecting half mirror 2, right by CCD camera 4
Interference fringe is shot.Piezoelectric ceramics 11 (PZT) is fixed on reflecting mirror b12 to the phase shift for realizing reference path 5, the reflection
The pose of mirror b12 is adjustable, to change position of the optical axis center on tested surface, i.e., most wide 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 illustrate this hair as example
Bright joining method；Average phase-shifting method is taken to change the phase of reference path 5, phase shift step value pi/2, phase shift range is 0 to 2 π,
Detailed process is as follows:
First group of step 1, shooting interference fringe image, most wide striped are located adjacent to tooth top position, and five width of shooting refer to tooth
The phase shift interference fringe image in face, rotates tested helical gear, and five width of shooting are tested the phase shift interference fringe image of the flank of tooth；
Step 2, the pose for modulating reflecting mirror b12, make most wide fringe position close to root position, shoot the reference of five width 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 establishes the mapping relations between interference fringe image and the practical flank of tooth according to joining method of the invention, uses
Pseudo- coherence factor (PSD) identifies width of fringe, and the pixel window in calculating is 3 × 3, threshold value 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
Top part is insecure, although having some discrete noise spots in other regions of image, is carried out to it with can be convenient
It filters out and has no effect on final recognition result；
According to confidence level recognition result, respectively by first group of 2/3 region of interference fringe image tooth tip and second group of interference
2/3 region of stripe pattern tooth root end is considered as reliable area, for splicing；
Step 4, the Phase Unwrapping Algorithm for calculating each group interference fringe image, and calculate the form error of the tested flank of tooth；
Due to optical axis center difference, two groups of fringe distributions are different, the phase distribution after unpacking be also it is inconsistent, through coordinate
It just can be used for splicing after transformation；
In first group and second group of image, tested flank of tooth optical path difference makes the difference respectively with reference to flank of tooth optical path difference, obtains two
Group tested tooth surface shape error to be spliced.
Automatically splicing boundary is searched in joining method according to the present invention, and two groups of form error data are spliced,
The splicing result of final tested surface form error is consecutive variations, and without apparent locus of discontinuity near splicing boundary
Domain, to demonstrate the feasibility of this method.With the help of the interference fringe picture spelicing profiles algorithm, it is tested all on curved surface
For form error data both from the reliable fringe area of processing accuracy, this undoubtedly substantially increases the precision of measurement.
The joining method of interference fringe image in inclined in type measurements by laser interferometry of the present invention, is able to achieve several key light axle positions
The splicing reconstruct for setting form error information in different interference fringe images, solves the item of interference fringe image in the prior art
The problem of line dense Region processing accuracy is low and influences ultimate measurement accuracy.
Claims (5)
1. the joining method of interference fringe image in inclined in type measurements by laser interferometry, which is characterized in that be with the helical gear flank of tooth
Measurement object, tested surface are divided into W parts in the X-axis direction, are divided into H parts in the Y-axis direction, i.e., are divided into (W on tested surface
+ 1) × (H+1) a mesh point；
Any one mesh point is designated as G (h, w), h=0,1 ..., H, w=0,1 ..., W, space coordinate be denoted as D (h,
w)；
The normal direction of any one mesh point G (h, w) is denoted as n (h, w), is specifically implemented according to the following steps:
Step 1, be tested curved surface spatial position be splicing benchmark, each width interference fringe image is matched with tested curved surface
It is quasi-；
Step 2, after the completion of step 1, carry out based on width of fringe processing reliability judgement；
Step 3, after step 2, establish transformed coordinate system model；
Step 4, after the completion of step 3, to tested curved surface shape error resampling, complete the splicing of interference fringe image；
The step 4 is specifically implemented according to the following steps:
The form error for being located at reliable area is denoted as: Ri (h, w), i=1,2 ... are used to refer to the number of interference fringe；Two
The part to overlap in group interference fringe image reliable area is denoted as Li (h, w)；
The splicing of two groups of interference fringe images, is specifically implemented according to the following steps:
Step 4.1 extracts overlapping region L1 (h, w) and L2 (h, w) in R1 (h, w) and R2 (h, w)；
Step 4.2, after step 4.1, search splicing boundary point, these boundary points are denoted as B (w), w=0,1 ..., W；
Step 4.3, after step 4.2, splicing data R1 (h, w) and R2 (h, w) according to following algorithm is R (h, w), first to boundary
The data at both ends carry out resampling, then determine the form error value of boundary each point, complete the splicing of interference fringe image, specifically
The algorithm being related to are as follows:
2. the joining method of interference fringe image, feature in inclined in type measurements by laser interferometry according to claim 1
It is, the step 1 is specifically implemented according to the following steps:
Step 1.1, in simulation software to each mesh point on tested surface, ray tracing meter is carried out in entire optical path
It calculates until CCD imaging plane, keeps each tested surface mesh point G (h, w) corresponding only one simulation imaging point S (h, w), Suo Youfang
True imaging point forms width emulation flank of tooth picture to get the mapping relations between curved surface are tested to simulation image and reality；
Step 1.2, after step 1.1, to simulation image carry out integral transformation；
Variation includes: translation, scaling and rotation are overlapped it as far as possible with actual measurement interference fringe image；
It can make only one pixel I (h, w), Ji Nengjian in the corresponding interference fringe image of each simulation imaging point S (h, w) in this way
Mapping relations between vertical simulation image and interference fringe image；
Step 1.3, after step 1.2, using simulation image as bridge, establish the mapping between interference fringe image and practical tested curved surface
Relationship, on the corresponding tested curved surface of pixel on each interference fringe image it is unique a bit.
3. the joining method of interference fringe image, feature in inclined in type measurements by laser interferometry according to claim 1
It is, the step 2 is specific to be judged in accordance with the following methods:
After step 1, width of fringe is identified by pseudo- coherence factor, and then can be guaranteed in determining interference fringe image
The reliable area of processing accuracy；
Pseudo- coherence factor is obtained according to following algorithm:
In above formula, ψi,jIt is the wrapped phase that coordinate value is at (i, j) in wrapped phase figure, k, which is with pixel (x, y), is
The size of the calculation window of the heart, k value are 3；
In the pseudo- coherence factor Quality Map of generation, threshold value ΓPSD, one is produced to indicate interference fringe according to algorithm
The bianry image of reliable area in image is specifically implemented according to following algorithm:
White is reliable area, and the unreliable region of black, only reliable area are used for next splicing.
4. the joining method of interference fringe image, feature in inclined in type measurements by laser interferometry according to claim 1
It is, the step 3 is specific to be established in accordance with the following methods:
It is optical axis center position at the center of most wide striped in interference fringe image, in actually calculating, with closest theoretical position
The pixel I (h0, W/2) set is optical axis center, 0 < h0 < H；Using the pixel as starting point in Phase- un- wrapping, phase value is fixed
It is 0；The different interference fringe image of two groups of key light shaft positions, Phase- un- wrapping starting point is different, calculated form error base
It is on schedule also different, it to be coordinately transformed；
Pixel I (H/2, W/2) in interference fringe image is set, the data in all interference fringe images are all using this point as optical axis
Reference center is coordinately transformed；
One group of interference fringe image optical axis center is set as I (h0, W/2), defines a three-dimensional matrice N(h,w)For coordinate transform,
N(h,w)=[x, y, f], wherein x, y are tested net surfaces lattice point G (h, w) corresponding to pixel I (h, w) in X-axis, Y-axis
Spatial value, wherein f is optical path difference, is computed acquisition using following algorithm:
In above formula, λ is measurement optical maser wavelength,It is the phase value after unpacking, β is measurement angle of light；
After coordinate transform, optical path difference f ' is specifically computed acquisition by following algorithm:
In above formula,Vers θ=(1-cos θ), θ are two normals
n(H/2,W/2)WithBetween angle, acquisition is specifically computed by following algorithm:
In above formula, (nx,ny,nz) it is normal direction n(H/2,W/2)Coordinate value, (n0x,n0y,n0z) it is normal direction
Coordinate value；K is normal n(H/2,W/2)WithThe normal direction of the space plane of composition, specifically by following algorithm through counting
It calculates and obtains:
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=fobj-fref(8)；
In above formula, fobjIt is the optical path difference of tested curved surface, frefIt is the optical path difference of reference surface.
5. the joining method of interference fringe image, feature in inclined in type measurements by laser interferometry according to claim 1
It is, the step 4.2 is specifically implemented according to the following steps:
First, it is found in the first column data of overlapping region and differs the smallest point between two groups of form error data, as splicing
Starting point is denoted as B (0)；
Then, the difference for calculating two grouping error data at three pixels adjacent thereto in next column data, finds minimum
Pixel where value is denoted as B (1), and searches the boundary point in next column with this as the starting point；
And so on, until finding out all boundary points.
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