CN108648239A - The scaling method of phase height mapping system based on segmented fitting of a polynomial - Google Patents
The scaling method of phase height mapping system based on segmented fitting of a polynomial Download PDFInfo
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- G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
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Abstract
The invention discloses a kind of scaling methods of the Phase-height mapping system based on segmented fitting of a polynomial, fitting of a polynomial is used to carry out the segmented calibration of Phase-height mapping system, the method proposed according to this case, interval division is carried out to range ability, fitting of a polynomial calibration is carried out using different fitting orders in range at various height, to keep the relative error of each position in measurement range minimum, reconstruction accuracy in this case under the calibration of segmented fitting of a polynomial is than the reconstruction accuracy higher under the calibration of 1~6 order fitting of a polynomial, process is more simplified.
Description
Technical field
The present invention relates to phase measuring profilometers, and in particular to a kind of phase height based on segmented fitting of a polynomial
The scaling method of mapped system.
Background technology
In phase measuring profilometer, due to the effect that the height of object under test modulates sinusoidal grating, cause grating phase
Position changes, and the elevation information of object under test three-D profile is implied in phase change.Therefore, the height letter of object under test is measured
Breath, it is important to establish the correspondence between height and phase change, the especially mathematical relationship between height and phase, i.e. phase
Position-height mapping mathematical model.In existing phase height mapping mathematical model, it is broadly divided into two classes：Explicit phase height
Mapping model and implicit phase height mapping model.Wherein, explicit phase height mapping model needs during calculating
The accurately design parameter of measuring projector-camera chain structure in advance, such as digital light processing (DLP) device and Charged Couple
Horizontal distance, DLP between device (CCD) are to the folder between vertical range, DLP optical axises and the CCD optical axises between reference planes
Angle etc.；On the contrary, implicit phase height mapping model does not need accurate measuring projector-video camera system during calculating
The design parameter value for structure of uniting, it is only necessary to calibrate the correspondence between phase and height by demarcating object.
Fitting of a polynomial is that by one group there is the experimental data for the relationship of hiding to be found out according to error sum of squares minimum principle
The process of the polynomial function of these data best match.Fitting of a polynomial scaling method is simple with calibration process, calibration is smart
Exactness is high, avoids the advantages that projector calibrating and is widely studied and applies, and existing research is concentrated mainly on fitting of a polynomial
In terms of influence of the order to stated accuracy, in terms of the influence for fitting data quantity within the scope of certain altitude to stated accuracy simultaneously
There is no a correlative study, data bulk has emphatically the process complexity of fitting of a polynomial scaling method, result accuracy etc.
It influences.
Invention content
For the shortcomings of the prior art, the present invention proposes to divide by dividing different height range
Segmentation fitting of a polynomial scaling method to simplify calibration process, and improves result precision.
The present invention provides a kind of scaling method of the phase height mapping system based on segmented fitting of a polynomial,
It is characterized in that, includes the following steps：
1) several height values and corresponding position phase difference for obtaining object under test, to height value and phase difference described in every group
Multistage order polynomial fitting is carried out respectively, obtains each order fitting parameter successively；To each rank fitting parameter into line displacement, put
Big processing, saves as image data；
2) three-dimensional reconstruction and detection are carried out to Standard adjustable board using each order fitting parameter described in step 1), obtained each
Order fitting calibrating parameter, while calculating fitting of each protrusion under each order in Standard adjustable board and measuring height value, with
And the fitting measures the absolute error of height value and standard value, wherein with the fitting order of absolute error minimum for the first order；
3) phase difference value for extracting one group of equal difference interval in range to be calibrated, carries out the fitting of a polynomial of first order
Calibration, obtains the calibrating parameters at each interval and carries out precision test to it, wherein the interval with minimum average B configuration relative error
For the first fit interval；
4) each order fitting calibrating ginseng described in step 2) is carried out respectively at the theoretical level that object under test has equal difference
Height detection under several, and calculate the relative error between actually detected value and theoretical level value；
5) according to relative error obtained by step 4), the height of object under test is divided into several sections, wherein each section is adopted
With the minimum relative error of appearance when specific order fitting of a polynomial；
6) first order is used to each section divided in step 5) by calibrating parameters described in step 3)
Fitting of a polynomial simultaneously carries out three-dimensional reconstruction and detection, and the best fit order in each section is judged according to the detected value；
7) it according to best fit order described in step 6), calculates the system calibrating parameter in each section and carries out three dimensional detection
With reconstruction, and then measuring targets carry out segmented fitting of a polynomial calibration.
Preferably, the formula of fitting of a polynomial described in step 1) is：
H (x, y)=anΔφn(x,y)+an-1Δφn-1(x,y)+…+a1Δφ(x,y)+a0；
Wherein, n is fitting order, and H (x, y) is the fitting height value of the position (x, y), and Δ φ (x, y) is the position (x, y)
Phase difference, an,an-1,…,a0For coefficient of polynomial fitting.
Preferably, there are 16 protrusions, including rectangular preiection and circular protrusions in the centre of correcting plate described in step 2)；Institute
It states each order fitting calibrating parameter and passes through 30 reperformance tests that height is rebuild and detected respectively.
Preferably, multistage order polynomial described in step 1) is fitted to 1~6 order fitting of a polynomial, it is described several
The range of height value is at -250~+250 μm；First order described in step 2) is 2 ranks.
Preferably, range to be calibrated described in step 3) is at -250~+250 μm, be divided between one group of equal difference 10 μm,
20μm、30μm、40μm、50μm、60μm、70μm、80μm、90μm、100μm；First fit interval is 90 μm, the minimum
Average relative error is δ=1.06%, system calibrating time t=33.884s.
Preferably, the theoretical level described in step 4) be 10 μm, 20 μm, 30 μm ..., 500 μm.
Preferably, several sections described in step 5) be 0~90 μm, 100~190 μm, 190~480 μm, 480~500
μm。
Preferably, the best fit order in step 6) each section is：0~90 μm is selected 4 order multinomials quasi-
Conjunction, 100~190 μm of 3 order fitting of a polynomials of selection, 190~480 μm of 1 order fitting of a polynomials of selection, 480~500 μm of selections
4 order fitting of a polynomials.
The beneficial effects of the invention are as follows：Scaling method proposed by the invention is to carry out phase-height using fitting of a polynomial
The segmented calibration of mapped system is spent, the method proposed according to this case carries out interval division, in different height to range ability
Fitting of a polynomial calibration is carried out using different fitting orders in degree range, to make the opposite of each position in measurement range miss
It is poor minimum, i.e., under the reconstruction accuracy in this case under the calibration of segmented fitting of a polynomial is demarcated than 1~6 order fitting of a polynomial
Reconstruction accuracy higher, process is more simplified.
Description of the drawings
Fig. 1 is the comparative analysis figure that measured value and standard value are fitted under 1~6 order；
Fig. 2 is the absolute error comparison diagram that measured value and standard value are fitted under 1~6 order；
Fig. 3 is the standard deviation that measured value is fitted under 1~6 order；
Fig. 4 is the average relative error under different fit interval calibration；
Fig. 5 is the system calibrating time under different fit interval calibration；
Fig. 6 is the lower relative error comparative analysis of 1~6 order fitting；
Fig. 7 is the fitting order variation diagram under minimum relative error；
Fig. 8 is segmented fitting and the lower relative error analysis of each order fitting；
Fig. 9 is segmented fitting and the lower average relative error of each order fitting.
Specific implementation mode
Present invention will be described in further detail below with reference to the accompanying drawings, to enable those skilled in the art with reference to specification text
Word can be implemented according to this.
It should be appreciated that such as " having ", "comprising" and " comprising " term used herein are not discharged one or more
The presence or addition of a other elements or combinations thereof.
It is further illustrated the present invention below by way of specific embodiment.But the detail of embodiment is only used for explaining this hair
It is bright, it should not be construed as limited overall technical solution.
Step 1: each height of phase difference of corresponding position is obtained in the present embodiment by extraneous high-precision mobile device
Value, then obtains the fitting of a polynomial parameter between phase difference and height by the method for fitting of a polynomial, fitting of a polynomial
Formula is：
H (x, y)=anΔφn(x,y)+an-1Δφn-1(x,y)+…+a1Δφ(x,y)+a0；
Wherein, n is fitting order, and H (x, y) is the fitting height value of the position (x, y), and Δ φ (x, y) is the position (x, y)
Phase difference, an,an-1,…,a0For coefficient of polynomial fitting.
The height of reference plane is set as 0, is downwards negative (-), is upwards positive (+), is driven by high-precision servo motor
Optical texture (being made of projecting apparatus and video camera) carries out up and down equidistantly mobile (spacing is 50 μm), and obtains height (unit：
μm) be equal to -250, -200 ..., at 200,250 positions relative to the phase differential of reference plane be Δ φ-250、Δφ200、…、Δ
φ250、Δφ200Totally 11 groups of data pair.By 11 groups of data of fitting polynomial formulas pair to carrying out 1~6 order multinomial respectively
Fitting, due to being relatively independent between pixel, shown each pixel fitting of a polynomial parameter is also mutual indepedent, finally to each
A order fitting parameter is handled (offset 100,100 times of method), and saves as image data (PNG format), quasi- with 2 orders
It is combined into example, height reconstruction formula is：
H (x, y)=p2(x,y)×Δφ2(x,y)+p1(x,y)Δφ(x,y)+p0(x,y)；
Wherein, p2(x, y), p1(x, y), p0(x, y) is respectively the constant term coefficient of 2 orders fitting, Monomial coefficient and two
Secondary term coefficient；H (x, y) is the three-dimensional reconstruction height of the position (x, y), and Δ φ (x, y) is the phase difference of the position (x, y), remaining rank
It is secondary to analogize.
Step 2: carrying out three-dimensional reconstruction and detection to Standard adjustable board using 1~6 obtained order fitting parameter, obtain
Each order fitting calibrating parameter, while calculating fitting of each protrusion under each order in Standard adjustable board and measuring height value,
And the fitting measures the absolute error of height value and standard value, wherein with the fitting order of absolute error minimum for the first rank
It is secondary.
Specifically, Standard adjustable board has been subjected to third-party authentication, there are 16 protrusions in the centre of correcting plate, and (1~No. 8 is circle
Shape protrusion, 9~No. 16 be rectangular preiection), table 1 lists corresponding height value.It is quasi- using 1~6 order multinomial in step 1
It closes parameter and three-dimensional reconstruction is carried out to Standard adjustable board, and detect height value of 1~No. 16 protrusion under 1~6 order, be listed in table 1
Among.
The standard value of 1. Standard adjustable board of table and measured value (unit：μm)
| No. 1 | No. 2 | No. 3 | No. 4 | No. 5 | No. 6 | No. 7 | No. 8 | |
| Standard value | 100.8 | 101.1 | 101.3 | 101.8 | 101.5 | 101.5 | 101.9 | 101.9 |
| 1 rank | 96.098 | 99.764 | 99.709 | 100.6 | 100.95 | 101.86 | 101.38 | 102.14 |
| 2 ranks | 97.846 | 100.46 | 100.28 | 101.5 | 101.56 | 102.59 | 102.1 | 102.63 |
| 3 ranks | 96.543 | 97.704 | 98.243 | 100.99 | 99.816 | 100.79 | 100.51 | 100.13 |
| 4 ranks | 98.553 | 96.402 | 97.268 | 98.585 | 97.402 | 98.313 | 97.591 | 100.11 |
| 5 ranks | 117.78 | 123.21 | 160.05 | 108.62 | 140.01 | 163.83 | 128.23 | 132.26 |
| 6 ranks | 504.33 | 340.07 | 600.83 | 343.46 | 346.54 | 314 | 392.55 | 344.11 |
| No. 9 | No. 10 | No. 11 | No. 12 | No. 13 | No. 14 | No. 15 | No. 16 | |
| Standard value | 100.7 | 100.7 | 100.7 | 101.2 | 101.2 | 100.8 | 101.6 | 101.9 |
| 1 rank | 101.15 | 101.89 | 102.12 | 101.69 | 102.73 | 103.22 | 102.63 | 103.36 |
| 2 ranks | 101.9 | 102.65 | 102.53 | 102.35 | 103.27 | 103.82 | 103.06 | 104.02 |
| 3 ranks | 100.51 | 100.74 | 100.91 | 100.75 | 101.96 | 102.55 | 101.93 | 102.47 |
| 4 ranks | 100.92 | 99.506 | 95.702 | 99.053 | 100.6 | 101.49 | 99.752 | 100.34 |
| 5 ranks | 139.93 | 141.75 | 136.95 | 128.88 | 153.75 | 125.57 | 125.57 | 129.34 |
| 6 ranks | 518.46 | 430.12 | 508.57 | 630.38 | 402.41 | 486.93 | 486.93 | 488.84 |
Fig. 1 is the comparison diagram of the standard value of measured value and Third Party Authentication under 1~6 order, and Fig. 2 is to be measured under 1~6 order
The comparison diagram of value and the standard value absolute error of Third Party Authentication.It can be obtained by Fig. 1 and Fig. 2, under 1~4 order, absolute error Δ
5 μm of ＜ (height value is at 100 μm or so)；5, the absolute error of 6 orders fitting greatly deviates from respectively at 40 μm and 300 μm or so
Detection height.So the fitting of 1~4 order is relatively more suitable for fitting of a polynomial calibration, in the fitting of 1~4 order, 1,3,4 ranks
4 μm of 5 μm of ＜ Δs ＜ of absolute error obtained by secondary fitting；2 orders are fitted obtained 3 μm of absolute error Δ ＜, and it is average
Relative errorSo in the fitting of 1~4 order, the fitting of 2 orders can obtain smaller absolute error, Three-dimensional Gravity
Build precision higher.
For the stability that fitting of a polynomial under 1~6 order of verification is demarcated, the parameter under 1~6 order fitting calibrating is distinguished
30 reperformance tests that height is rebuild and detected are carried out, the standard deviation (Fig. 3) of measured value under each order and average standard deviation are obtained
(note is in table 2).
2. average of table is poor
As shown in figure 3 and table 2, the standard deviation sigma ＜ 1 under 1~4 order；0.5 ＜ σ ＜ 2.5 of standard deviation under 5 orders；6 ranks
2.5 ＜ σ ＜ 9.5 of standard deviation under secondary.In table 2, the average under 1~2 order is poorIt is flat under 3~4 orders
Equal standard deviationAverage under 5~6 orders is poorStandard deviation is smaller, and stability is better, by
Known to this：Multiple ounce fitting calibrating stability under 1~2 order is best；3~4 order stability inferiors take second place；Under 5~6 orders
Stability is worst.It is rebuild with three-dimensional height by the fitting of a polynomial calibration under 1~6 order, it is found that when it is 1~4 to be fitted order
Higher reconstruction precision (5 μm of absolute error Δ ＜) can be obtained.To the fitting of a polynomial calibration coefficient of 1~4 order into traveling
The analysis and research of one step find, when it is 2 to be fitted order, to possess higher reconstruction precision (absolute error：Δ=1.36 μm；Phase
To error：δ=1.34%) and stability (average is poor：)。
Step 3: extracting the phase difference value at one group of equal difference interval in range to be calibrated, the multinomial of first order is carried out
Formula fitting calibrating obtains the calibrating parameters at each interval and carries out precision test to it, wherein having minimum average B configuration relative error
Between be divided into the first fit interval.
Specifically, be divided between height of the extraction (depth) respectively 10 μm, 20 μm, 30 μm ..., the phase difference value under 100 μm,
And corresponding fitting of a polynomial calibration (fitting order is 2) is carried out, obtain 10 groups of calibrating parameters.Calibration range be -250 μm~
250 μm, when being divided into 10 μm between height (depth), there are 51 pairs of fitting data (phase difference+height), and so on, when height is (deep
Degree) between when be divided into 100 μm, have 6 pairs of fitting data.Precision test is carried out respectively to 10 pairs of calibrating parameters, in theoretical level
For 20 μm, 40 μm, 60 μm ..., be detected respectively at 500 μm, and calculate the average relative error under every group of detection, such as scheme
Described in 4, smaller average relative error can be obtained when fit interval is 90 μmFig. 5 is different fittings
The system calibrating time under interval, with the increase at interval, the system calibrating required time is fewer and fewer, whole to become in decline
Gesture.It follows that in 500 μm of range ability, fitting of a polynomial order is 2, and fit interval not only may be used when being 90 μm
To obtain smaller average relative errorAnd possess the higher system calibrating speed (nominal timet=
33.884s)。
Step 4: being carried out respectively under each order fitting calibrating parameter at the theoretical level that object under test has equal difference
Height detection, and calculate the relative error between actually detected value and theoretical level value；
Step 5: according to gained relative error, the height of object under test is divided into several sections, wherein each section uses
Occurs minimum relative error when specific order fitting of a polynomial；
Step 6: using the fitting of a polynomial of first order simultaneously to each section divided by the calibrating parameters
Three-dimensional reconstruction and detection are carried out, the best fit order in each section is judged according to the detected value；
Step 7: according to the best fit order, calculate the system calibrating parameter in each section and carry out three dimensional detection with
It rebuilds, and then measuring targets carry out segmented fitting of a polynomial calibration；
Step 1~step 3 is pre-preparation process, and step 4~step 7 is that measuring targets carry out segmented multinomial
Fitting calibrating process.
Specifically, theoretical level be 10 μm, 20 μm, 30 μm ..., 500 μm place respectively carry out 1~6 order fitting mark
Determine the height detection under parameter, and calculates the relative error between actually detected value and theoretical level value, it is opposite under each order
For error change as shown in fig. 6, Fig. 6 is the relative error variation diagram at each theoretical level position under 1~6 order, Fig. 7 is each reason
By the fitting order variation diagram corresponding to relative error minimum at height, as seen from the figure, when height is less than 90 μm, 4 ranks
Minimum relative error is obtained under secondary fitting calibrating；When height is when between 100 μm~190 μm, taken under 3 order fitting calibratings
Obtain minimum relative error；When height is when between 190 μm~480 μm, acquirement is minimum relatively accidentally under 1 order fitting calibrating
Difference；Minimum relative error is obtained when height is when between 480 μm~500 μm, under 4 order fitting calibratings.Relative error is got over
Small, reconstruction accuracy is higher.
It, can be in range ability, according to Fig. 7's in order to all obtain higher reconstruction precision in 500 μm of range ability
Information carries out fitting of a polynomial calibration in range using different fitting orders at various height, to reach each in measurement
The purpose of the relative error minimum of position；Intended using 4 order multinomials when being highly less than when height is less than 90 μm according to Fig. 7
Close calibration；When height is at 100 μm~190 μm, demarcated using 3 order fitting of a polynomials；When height is at 190 μm~480 μm,
It is demarcated using 1 order fitting of a polynomial；When height is at 480 μm~500 μm, demarcated using 4 order fitting of a polynomials.In reality
Detection in, can first pass through the systematic parameter under the 2 order fitting calibratings that step 2 obtains it is carried out three-dimensional reconstruction with detection,
Then the best fit order in each section is judged according to detected value, finally carries out three using the system calibrating parameter in each section
Dimension is rebuild and detection.
According to section above, segmented fitting of a polynomial calibration is carried out to system, then theoretical level be 20 μm, 40
μm, 60 μm ..., carry out the lower height of segmented fitting of a polynomial calibration at 500 μm and rebuild and detection, rebuild highly and theory height
Relative error between degree is as shown in figure 8, in fig. 8, dotted line, which is that the calibration of segmented fitting of a polynomial is lower, rebuilds height and theory
The relative error variation diagram of height, solid line are respectively the lower phase for rebuilding height and theoretical level of 1~6 order fitting of a polynomial calibration
To error change figure, it follows that the reconstruction accuracy under the calibration of segmented fitting of a polynomial is more quasi- than 1~6 order multinomial
Close the reconstruction accuracy higher under calibration.
Fig. 9 be segmented fitting with 1~6 order fitting under, 20 μm, 40 μm, 60 μm ..., 500 μm place rebuild highly with
The average relative error of theoretical level, as shown in Figure 9, the average relative error under 5 and 6 ordersUnder 2 and 3 orders
Average relative errorAverage relative error under 1 and 4 ordersAnd being averaged under segmented fitting
Relative errorSo under 1~6 order fitting of a polynomial of ratio of precision under the calibration of segmented fitting of a polynomial is demarcated
Precision higher.
Although the embodiments of the present invention have been disclosed as above, but its is not only in the description and the implementation listed
With.It can be applied to various suitable the field of the invention completely.It for those skilled in the art, can be easily
Realize other modification.Therefore without departing from the general concept defined in the claims and the equivalent scope, the present invention is simultaneously unlimited
In specific details and embodiment shown here.
Claims (8)
1. a kind of scaling method of the phase height mapping system based on segmented fitting of a polynomial, which is characterized in that including under
State step：
1) several height values and corresponding position phase difference for obtaining object under test, distinguish height value described in every group and phase difference
Multistage order polynomial fitting is carried out, obtains each order fitting parameter successively；To each rank fitting parameter at line displacement, amplification
Reason, saves as image data；
2) three-dimensional reconstruction and detection are carried out to Standard adjustable board using each order fitting parameter described in step 1), obtains each order
Fitting calibrating parameter, while calculating fitting of each protrusion under each order in Standard adjustable board and measuring height value, and should
Fitting measures the absolute error of height value and standard value, wherein with the fitting order of absolute error minimum for the first order；
3) phase difference value for extracting one group of equal difference interval in range to be calibrated, carries out the fitting of a polynomial mark of first order
It is fixed, it obtains the calibrating parameters at each interval and precision test is carried out to it, wherein with being divided between minimum average B configuration relative error
First fit interval；
4) it is carried out respectively under each order fitting calibrating parameter described in step 2) at the theoretical level that object under test has equal difference
Height detection, and calculate the relative error between actually detected value and theoretical level value；
5) according to relative error obtained by step 4), the height of object under test is divided into several sections, wherein each section is using special
Determine occur minimum relative error when order fitting of a polynomial；
6) the multinomial of first order is used to each section divided in step 5) by calibrating parameters described in step 3)
Formula is fitted and carries out three-dimensional reconstruction and detection, and the best fit order in each section is judged according to the detected value；
7) according to best fit order described in step 6), calculate the system calibrating parameter in each section and carry out three dimensional detection with again
It builds, and then measuring targets carry out segmented fitting of a polynomial calibration.
2. scaling method according to claim 1, which is characterized in that the formula of fitting of a polynomial described in step 1) is：
H (x, y)=anΔφn(x,y)+an-1Δφn-1(x,y)+…+a1Δφ(x,y)+a0；
Wherein, n is fitting order, and H (x, y) is the fitting height value of the position (x, y), and Δ φ (x, y) is the phase of the position (x, y)
Difference, an,an-1,…,a0For coefficient of polynomial fitting.
3. scaling method according to claim 1, which is characterized in that the centre of correcting plate described in step 2) have 16 it is convex
It rises, including rectangular preiection and circular protrusions；Each order fitting calibrating parameter is passed through 30 height and is rebuild and detection respectively
Reperformance test.
4. scaling method according to claim 1, which is characterized in that multistage order polynomial described in step 1) is fitted to 1
~6 order fitting of a polynomials, the range of several height values is at -250~+250 μm；First order described in step 2) is
2 ranks.
5. scaling method according to claim 4, which is characterized in that range to be calibrated described in step 3) -250~+
250 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm are divided between one group of equal difference；Institute
It is 90 μm to state the first fit interval, and the minimum average B configuration relative error is δ=1.06%, system calibrating time t=33.884s.
6. scaling method according to claim 5, which is characterized in that the theoretical level described in step 4) is 10 μm, 20 μ
m、30μm、…、500μm。
7. scaling method according to claim 6, which is characterized in that several sections described in step 5) be 0~90 μm,
100~190 μm, 190~480 μm, 480~500 μm.
8. scaling method according to claim 7, which is characterized in that the best fit order in step 6) each section
For：0~90 μm is selected 4 order fitting of a polynomials, 100~190 μm of 3 order fitting of a polynomials of selection, 190~480 μm of 1 ranks of selection
Order polynomial fitting, 480~500 μm of 4 order fitting of a polynomials of selection.
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