Transparent element surface shape decoupling method based on ROOT-MUSIC

Abstract

The invention provides a transparent element surface shape decoupling method based on ROOT-MUSIC, and the method comprises the steps: employing a pinhole camera and a display to form a reflection deflection technology detection system, enabling a plurality of groups of fringe patterns to be projected to the display based on the principle of phase measurement deflection technology, and enabling the fringe patterns to be reflected by a detected element and then to be received by the camera; according to the collected data, a shot superposed fringe pattern is separated by using a ROOT-MUSIC algorithm to obtain corresponding display coordinates; and obtaining the front surface shape of the transparent element according to a light reflection principle and a least square optimization algorithm. The method has the advantages of rapidness, flexibility, low cost and large detection dynamic range.

Description

TECHNICAL FIELD

[0001] The application relates to a transparent element surface shape decoupling method based on ROOT-MUSIC, and particularly relates to a phase measuring deflectometry implementation. BACKGROUND

[0002] In the field of modern precision manufacturing and optical engineering, surface shape measurement of optical elements is an important link to ensure the quality of optical systems. Among them, transparent elements are widely used in consumer electronics, optical instruments, aerospace and medical equipment and many other fields, so the requirement for the surface precision of the transparent elements is higher and higher. As an advanced optical measurement technology, phase measuring deflectometry (PMD) has the advantages of high resolution, non-contact in-situ measurement and stable anti-interference. PMD projects structured light onto the surface of the measured element, and uses phase shift technology to accurately measure the deflection and reflection of light on the surface, so as to reconstruct the surface shape. However, due to the birefringence of light passing through the transparent element, parasitic fringes are generated, which leads to the failure to correctly obtain the phase information of the front and back surfaces.

[0003] The special light source method uses the characteristics of the ultraviolet light band to realize the measurement of the transparent element. When the ultraviolet light source is irradiated to the transparent element, only the reflection occurs on the front surface of the transparent element, so that the surface shape is obtained alone. However, the method is expensive and requires high stability of the light source. The multi-frequency fringe method projects a series of fringe patterns with equal interval changes in frequency, and uses the least square iteration algorithm to solve the corresponding phase distribution of the front and back surfaces. However, the method involves power spectrum estimation. Due to the frequency spectrum leakage, the traditional estimation method needs to increase the number of projection to achieve high accuracy, which reduces the detection efficiency. SUMMARY

[0004] In order to overcome the problems existing in the above-mentioned technologies, the application provides a transparent element surface shape decoupling method based on ROOT-MUSIC. The phase information of the front and back surfaces is separated by using the characteristic decomposition idea of the ROOT-MUSIC algorithm to reconstruct the surface shape information. The method is fast, flexible, low-cost and has a large dynamic range.

[0005] The technical scheme adopted by the application is a transparent element surface shape decoupling method based on ROOT-MUSIC. The method uses a pinhole camera and a display to form a reflection deflectometry detection system. Based on the principle of phase measuring deflectometry, a plurality of fringe patterns are projected onto the display. The fringe patterns are reflected by the measured element and then received by the camera. The collected data is used to separate the superimposed fringe patterns by using the ROOT-MUSIC algorithm to obtain the corresponding display coordinates. According to the principle of light reflection and the least square optimization algorithm, the front surface shape of the transparent element is obtained. The specific steps of the method are as follows:

[0006] Step 1: Play on the monitor A fringe pattern with equally spaced frequencies is captured by a camera. The camera receives the fringe pattern after reflection from the measured element. The light intensity value of the same pixel in each fringe pattern on the camera is extracted, forming a light intensity sequence:

[0007] (1)

[0008] in: This represents the DC component, i.e., the background light intensity of the projected fringe pattern; and These represent the modulation levels corresponding to the front and rear surface signals, respectively. and The signals corresponding to the front and rear surfaces are respectively The orientation display coordinates correspond to the frequency information of the sine wave signal. The frequency of the projected sinusoidal fringes corresponds to the time series value of a common sinusoidal signal;

[0009] Step 2: Construct the covariance matrix of the light intensity sequence obtained in Step 1 using the ROOT-MUSIC algorithm. Represented as:

[0010] (2)

[0011] Using algebraic theory of covariance matrix It can be decomposed into a signal subspace and noise subspace :

[0012] (3)

[0013] P = [ E [ | s 1 | 2 ] … … … … E [ | s 2 | 2 ] … … … … … … … … … E [ | s N | 2 ] ] (4)

[0014] In the formula: The autocorrelation matrix represents the signal and reflects its characteristics; The autocorrelation matrix represents the noise, assuming the noise is white noise with a uniform power spectrum; It represents The eigenvector matrix is ​​composed of the direction and amplitude information of the sinusoidal signal; Indicates the noise variance. for The identity matrix; as shown in equation (4) is This is the signal power matrix, representing the power of each sinusoidal signal;

[0015] Since the signal subspace and the noise subspace are orthogonal to each other under ideal conditions, frequency estimation can be completed based on this principle and the eigenvectors of the separated noise subspace.

[0016] Step 3: Adjust the covariance matrix Perform eigenvalue decomposition to obtain the eigenvector matrix. and eigenvalue matrix :

[0017] (5)

[0018] A = [ A 1 0 … 0 0 A 2 … . . . … … … 0 0 … 0 A N ] (6)

[0019] In formula (6): Given eigenvalues ​​arranged in descending order, the eigenvector is divided into signal subspaces based on the magnitude of the eigenvalues. and noise subspace The signal subspace corresponds to larger eigenvalues, and the noise subspace corresponds to smaller eigenvalues. Given the display coordinates corresponding to the front and rear surfaces, the eigenvectors corresponding to the two largest eigenvalues ​​constitute the signal subspace. The remaining feature vectors constitute the noise subspace. ;

[0020] Step 4: Construct the signal vector as follows:

[0021] e ( Ω ) = [ 1 e j Ω ... e j ( N − 1 ) Ω ] T (7)

[0022] Due to the noise subspace in step three Since the signal vectors in the same signal space are orthogonal, they satisfy the following relationship:

[0023] (8)

[0024] Will In Treat as a complex number Equation (8) can be transformed into:

[0025] (9)

[0026] The frequency estimation result is obtained by solving the equation, that is, the front and rear surface displays are separated. Similarly, the orientation coordinates are obtained from the display. Direction coordinates;

[0027] Step 5: Set the display coordinates corresponding to the front surface Substitute the points into the following formula to calculate the slope of the front surface, and then fit the shape of the front surface.

[0028] (10) Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the system device of the present invention.

[0030] Figure 2 This is a flowchart of the data processing algorithm of the present invention. Detailed Implementation

[0031] To make the objectives and solutions of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and examples. It should be noted that the following embodiments are only for further illustration and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description are still within the scope of protection of this invention.

[0032] Reference Appendix Figure 1 This invention provides a root-music-based method for decoupling the surface shape of a transparent element, comprising a pinhole camera 1, a front surface 2 and a rear surface 3 of a transparent element, and a display 4. The display 4 shows sinusoidal fringe patterns with different frequencies. After reflection from the front surface 2 and the rear surface 3 of the transparent element, the patterns are captured by the pinhole camera 1. The coordinates of the display 4 corresponding to the front surface 2 and the rear surface 3 of the transparent element can then be calculated using the root-music algorithm. Detailed steps for calculating the display coordinates are provided in the appendix. Figure 2 Then, using ray tracing and nonlinear optimization, the front surface 2 and back surface 3 of the transparent element are reconstructed. The specific steps are as follows:

[0033] Step 1: Play on monitor 4 A fringe pattern with equally spaced frequencies is received by camera 1 after reflection from the measured element. The light intensity value of the same pixel in each fringe pattern on camera 1 is extracted, forming a light intensity sequence:

[0034] (1)

[0035] In the formula: This represents the DC component, i.e., the background light intensity of the projected fringe pattern; and These represent the modulation levels corresponding to the front and rear surface signals, respectively. and The signals corresponding to the front and rear surfaces are respectively The orientation display coordinates correspond to the frequency information of the sine wave signal. The frequency of the projected sinusoidal fringes corresponds to the time-domain sampling of the sinusoidal signal;

[0036] Step 2: Construct the covariance matrix of the light intensity sequence obtained in Step 1 using the ROOT-MUSIC algorithm. Represented as:

[0037] (2)

[0038] Using algebraic theory of covariance matrix It can be decomposed into a signal subspace and noise subspace :

[0039] (3)

[0040] P = [ E [ | s 1 | 2 ] … … … … E [ | s 2 | 2 ] … … … … … … … … … E [ | s N | 2 ] ] (4)

[0041] In the formula: The autocorrelation matrix represents the signal and reflects its characteristics; The autocorrelation matrix represents the noise, assuming the noise is white noise with a uniform power spectrum; It represents The eigenvector matrix is ​​composed of the direction and amplitude information of the sinusoidal signal; Indicates the noise variance. for The identity matrix; as shown in equation (4) is This is the signal power matrix, representing the power of each sinusoidal signal;

[0042] Since the signal subspace and the noise subspace are orthogonal to each other under ideal conditions, frequency estimation can be completed based on this principle and the eigenvectors of the separated noise subspace.

[0043] Step 3: Adjust the covariance matrix Perform eigenvalue decomposition to obtain the eigenvector matrix. and eigenvalue matrix :

[0044] (5)

[0045] A = [ A 1 0 … 0 0 A 2 … . . . … … … 0 0 … 0 A N ] (6)

[0046] In formula (6): Given eigenvalues ​​arranged in descending order, the eigenvector is divided into signal subspaces based on the magnitude of the eigenvalues. and noise subspace The signal subspace corresponds to larger eigenvalues, and the noise subspace corresponds to smaller eigenvalues. Given the display coordinates corresponding to the front and rear surfaces, the eigenvectors corresponding to the two largest eigenvalues ​​constitute the signal subspace. The remaining feature vectors constitute the noise subspace. ;

[0047] Step 4: Construct the signal vector as follows:

[0048] e ( Ω ) = [ 1 e j Ω ... e j ( N − 1 ) Ω ] T (7)

[0049] Due to the noise subspace in step three Since the signal vectors in the same signal space are orthogonal, they satisfy the following relationship:

[0050] (8)

[0051] Will In Treat as a complex number Equation (8) can be transformed into:

[0052] (9)

[0053] The frequency estimation result is obtained by solving the equation, that is, the front and rear surface displays are separated. Similarly, the orientation coordinates are obtained from the display. Direction coordinates;

[0054] Step 5: Set the display coordinates corresponding to front surface 2. Substitute the points into the following formula to calculate the slope of the front surface, and then fit the two-sided shape of the front surface.

[0055] (10)

Claims

1. A ROOT-MUSIC based decoupling method for surface shape of a transparent element, characterized in that: Based on the principle of phase measuring deflectometry, multiple sets of fringe patterns are projected onto the display, and the reflected fringe patterns are received by the camera after being reflected by the measured element. The collected data is used to separate the superimposed fringe patterns using the ROOT-MUSIC algorithm to obtain the corresponding display coordinates. According to the principle of light reflection and the least squares optimization algorithm, the front surface profile of the transparent element is obtained. The specific steps are as follows: Step one: play on the display The fringe pattern with equal interval variation of spatial frequency is played on the display. The camera receives the fringe pattern reflected by the measured element. The light intensity values of the same pixel point in each fringe pattern are extracted to form a light intensity sequence: (1) wherein: is the direct current component, i.e. the background light intensity of the projected fringe pattern; and are the modulation depths of the front and back surface signals, respectively; and are the phase shifts of the front and back surface signals, respectively; is the direction display coordinate, corresponding to the frequency information of the sinusoidal signal, is the projected sinusoidal fringe frequency, corresponding to the time domain sampling of the sinusoidal signal; Step two: Construct the covariance matrix based on the light intensity sequence obtained in step one according to the ROOT-MUSIC algorithm is represented as: (2) Covariance matrix by algebraic theory Decomposable into signal subspace and noise subspace : (3) (4) In the formula: The autocorrelation matrix of the signal, reflecting the characteristics of the signal; The autocorrelation matrix of the noise, assuming that the noise is white noise, has a uniform power spectrum; The characteristic vector matrix of , composed of the direction and amplitude information of the sinusoidal signal; The noise variance, The unit matrix of ; formula (4) is The signal power matrix, representing the power of each sinusoidal signal; Since the signal subspace and the noise subspace are orthogonal to each other under ideal conditions, the frequency estimation is completed according to the principle and the characteristic vectors of the separated noise subspace; Step three: Eigenvalue decomposition of the covariance matrix to obtain the eigenvector matrix and the eigenvalue matrix : (5) (6) In formula (6): Given eigenvalues ​​arranged in descending order, the eigenvector is divided into signal subspaces based on the magnitude of the eigenvalues. and noise subspace The signal subspace corresponds to larger eigenvalues, and the noise subspace corresponds to smaller eigenvalues. Given the display coordinates corresponding to the front and rear surfaces, the eigenvectors corresponding to the two largest eigenvalues ​​constitute the signal subspace. The remaining feature vectors constitute the noise subspace. ; Step four: construct the signal vector as: (7) Due to the noise subspace of step three The signal vectors in the same signal space are orthogonal, thus satisfying the following relationship: (8) Consider in as complex , equation (8) becomes: (9) The frequency estimation result is obtained by solving the equation, i.e. separating the front and rear surface displays Direction coordinates, and the display is obtained in the same way Direction coordinates Step five: Substitute the front surface corresponding display coordinates into the following equation; (10) The front surface slope is calculated, and the front surface profile is fitted.

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