CN115077727B - Method for online detection of front and rear surface shapes of transparent element - Google Patents
Method for online detection of front and rear surface shapes of transparent element Download PDFInfo
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- 238000005259 measurement Methods 0.000 claims abstract description 5
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
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Abstract
The invention provides a phase measurement deflection operation based on ray tracing and power spectrum estimation, which can be used for on-line detection of the front and back surface shapes of a transparent element. Firstly, a display displays sinusoidal fringe patterns with different frequencies, and after reflection on the front and rear surfaces of a transparent element, the sinusoidal fringe patterns are collected by a pinhole camera; then, solving display coordinates corresponding to the front surface and the rear surface by using a power spectrum estimation method; finally, the surface shape information of the front surface and the rear surface of the transparent element is obtained by utilizing ray tracing and nonlinear optimization. The method can realize the on-line detection of the front and rear surface shapes of the transparent element, and avoid the measurement error caused by the movement of the transparent element in the off-line detection.
Description
Technical field:
The invention relates to the field of on-line detection of the front and rear surface profiles of transparent elements by phase measurement deflection (Phase Measuring Deflectometry, PMD).
The background technology is as follows:
the high-precision transparent element has wide application, and the surface shape has great influence on the performance. And therefore the processing and inspection of the components is particularly important. The process from processing to detection of the transparent element is a repeated iterative process, and the surface shape deviation and the surface roughness are beyond the detection range of the interferometer from grinding to rough polishing. PMD with high dynamic range is a more efficient method to achieve link processing and detection. Moreover, the PMD can also realize online detection of the surface shape, thereby realizing integration of processing and detection, reducing precision loss and avoiding measurement errors caused by movement of the transparent element in offline detection.
The PMD is used as a non-contact surface shape detection method and consists of a pinhole camera, a component to be detected and a display, and the detection equipment is simple and has a large dynamic range, so that the rapid development is achieved. However, when PMD is used to detect the transparent element, the display displays sinusoidal fringes, and the reflection at the back surface may produce spurious fringes, resulting in a phase shift algorithm that fails to solve for the correct phase, and thus in a decrease in the accuracy of the detected surface shape. In order to separate the phases of the front and rear surfaces of the transparent element from the parasitic fringes, existing methods such as ultraviolet deflection, scanning line shift deflection and polarized light detection, which require the use of special light sources and polarizing filters, are expensive in equipment, and have complicated detection procedures. In the patents CN108489422B and CN110411376a, the front surface shape of the transparent element is finally reconstructed by displaying sinusoidal fringe patterns with different frequencies, solving the phase distribution corresponding to the front and rear surfaces by using a least square iterative algorithm. But the algorithm has poor convergence, and only a single surface shape of the transparent element can be obtained by single detection, so that the detection efficiency is reduced.
The invention comprises the following steps:
in view of the above problems, the invention provides a method for detecting the front and rear surface shapes of a transparent element on line, which combines ray tracing with power spectrum estimation to realize separation of parasitic stripes of the transparent element and simultaneous reconstruction of the front and rear surface shapes.
The method adopts sine fringe patterns with different frequencies, the sine fringe patterns are collected by a pinhole camera after being reflected by the front surface and the rear surface of the transparent element, the display coordinates corresponding to the front surface and the rear surface of the transparent element can be solved through power spectrum estimation. And reconstructing the front and back surface shapes of the transparent element by utilizing ray tracing and nonlinear optimization. The method comprises the following specific steps:
Step one: sinusoidal fringes with different display frequencies are collected by a pinhole camera after being reflected by the front surface and the rear surface of a transparent element, and the light intensity distribution of any pixel point on the CCD can be expressed as:
I(f)＝If+Mf·cos(2π·xsf·f)+Ib+Mb·cos(2π·xsb·f) (1)
Wherein I f and I b respectively represent background light intensities corresponding to the front and rear surfaces, x sf and x sb respectively represent abscissa in display coordinates corresponding to the front and rear surfaces, M f and M b respectively represent modulation degrees corresponding to the front and rear surfaces, and f is a sinusoidal fringe frequency.
Step two: performing Fourier transform on the light intensity distribution of the pixel point to obtain a power spectrum function G (x s) of I (f), as shown in formula (2):
Wherein the method comprises the steps of The representation is fourier transformed for I (f), w (f) being the window function. And according to the peak value of the power spectrum function, obtaining the abscissa x sf and x sb in the display coordinates. Similarly, the ordinate y sf and y sb in the display coordinates can be obtained in the same way.
Step three: display coordinates S 1(xsf,ysf) and S 2(xsb,ysb corresponding to the front and rear surfaces are obtained by power spectrum estimation in the second step). Substituting the display coordinates S 1 corresponding to the front surface into the formula (3) to calculate the front surface slope, and fitting to obtain the front surface shape.
Determining refracted light rays according to the law of refractionAs in formula (4):
Wherein n 0 is the refractive index of the transparent element, n is the refractive index of air, Represents the direction of the incident light, and the M 1 point represents/>Intersection with front surface,/>Representing the front surface normal vector.
Further, it is assumed that the rear surface shape is formedWherein M 2 is/>Intersection coordinates with the back surface Zern (x M2,yM2) is an expression of a Zernike polynomial,/>The ray trace can obtain the M 2 point coordinates as the coefficients of the Zernike polynomials.
After determining the coordinates of the point M 2, the reflected light is determined according to the law of reflectionAs in formula (5):
wherein, The reflected ray/>, as the normal vector of the back surface, can be calculated from ray tracingIntersection point M 3 with the front surface. Refraction occurs at the point M 3, and/>, is determined according to the law of refractionAs in formula (6):
wherein, Is the normal vector of the front surface. Obtain/>After that, the display coordinates/>, can be obtained by utilizing the ray traceDisplay coordinates/>Is related to/>Is a function of (a) as follows equation (7):
Obtained by nonlinear optimization Thereby fitting to obtain the surface shape of the rear surface, and further realizing the detection of the surface shape of the front and rear surfaces of the transparent element.
Description of the drawings:
Fig. 1 is a schematic diagram of a transparent element back surface calculation method.
The specific embodiment is as follows:
The invention will now be described in more detail by way of example with reference to the accompanying drawings, in order to make the objects and aspects of the invention more apparent. It is noted that the following examples are given for the purpose of illustration only and are not to be construed as limiting the scope of the invention, since numerous insubstantial modifications and adaptations of the invention will be within the scope of the invention as viewed by one skilled in the art from the foregoing disclosure.
Referring to fig. 1, the invention provides a method for detecting the front and back surface shape of a transparent element on line, which consists of a pinhole camera 1, a front surface 2 and a back surface 3 of the transparent element and a display 4. The display 4 displays sine fringe patterns with different frequencies, after being reflected by the front surface 2 and the rear surface 3 of the transparent element, the sine fringe patterns are collected by the pinhole camera 1, then coordinates of the display 4 corresponding to the front surface 2 and the rear surface 3 of the transparent element can be solved through power spectrum estimation, and then the surface shapes of the front surface 2 and the rear surface 3 of the transparent element are reconstructed by utilizing ray tracing and nonlinear optimization. The method comprises the following specific steps:
Step one: the display 4 displays sinusoidal fringes with different frequencies, after being reflected by the front surface 2 and the rear surface 3 of the transparent element, the light intensity distribution of any pixel point on the CCD can be expressed as:
I(f)＝If+Mf·cos(2π·xsf·f)+Ib+Mb·cos(2π·xsb·f) (1)
Wherein I f and I b are the background light intensities corresponding to the front surface 2 and the rear surface 3, x sf and x sb respectively represent the coordinates of the display 4 corresponding to the front surface 2 and the rear surface 3, M f and M b are the modulation degrees corresponding to the front surface 2 and the rear surface 3, and f is the sinusoidal fringe frequency.
Step two: performing Fourier transform on the light intensity distribution of the pixel points to obtain a power spectrum function G (x s) of I (f), as shown in formula (2):
Wherein the method comprises the steps of The representation is fourier transformed for I (f), w (f) being the window function. From the peaks of the power spectrum function, the abscissas x sf and x sb in the coordinates of the display 4 are obtained. Similarly, the ordinate y sf and y sb in the display coordinates can be obtained in the same way.
Step three: the coordinates S 1(xsf,ysf) and S 2(xsb,ysb of the display 4 corresponding to the front surface 2 and the rear surface 3 are obtained by power spectrum estimation in the second step). Substituting the display 4 coordinates S 1 corresponding to the front surface 2 into the formula (3) can calculate the slope of the front surface 2 and fit to obtain the surface shape of the front surface 2.
Determining refracted light rays according to the law of refractionAs in formula (4):
Wherein n 0 is the refractive index of the transparent element, n is the refractive index of air, Represents the direction of the incident light, and the M 1 point represents/>Intersection with front surface,/>Representing the normal vector of the front surface 2.
Further, assume that the rear surface 3 is formedWherein M 2 is/>Intersection coordinates with the back surface 3, zern (x M2,yM2) is an expression of a Zernike polynomial,/>The ray trace can obtain the M 2 point coordinates as the coefficients of the Zernike polynomials.
After determining the coordinates of the point M 2, the reflected light is determined according to the law of reflectionAs in formula (5):
wherein, For the normal vector of the rear surface 3, the reflected ray/>, can be calculated from ray tracingIntersection point M 3 with front surface 2. Refraction occurs at the point M 3, and/>, is determined according to the law of refractionAs in formula (6):
wherein, Is the normal vector of the front surface 2. Obtain/>After that, ray tracing can obtain the display 4 coordinates/>Display 4 coordinates/>Is related to/>As shown in equation (7):
Obtained by nonlinear optimization Fitting the surface shape of the rear surface 3, and detecting the surface shape of the front surface 2 and the rear surface 3 of the transparent element.
Claims (1)
1.A method for detecting the front and back surface shape of a transparent element on line is characterized in that: based on phase measurement deflection operation, sinusoidal fringe patterns with different frequencies are adopted, reflected by a transparent element and collected by a pinhole camera; then solving display coordinates corresponding to the front surface and the rear surface of the transparent element through power spectrum estimation; reconstructing the front and rear surface shapes of the transparent element by utilizing ray tracing and nonlinear optimization; the method comprises the following specific steps:
Step one: sinusoidal stripes with different frequencies are adopted, after being reflected by the front surface and the rear surface of the transparent element, the light is collected by a pinhole camera, and the light intensity distribution of any pixel point on the CCD is expressed as:
I(f)＝If+Mf·cos(2π·xsf·f)+Ib+Mb·cos(2π·xsb·f)
Wherein, I f and I b are respectively the background light intensities corresponding to the front and back surfaces, x sf and x sb respectively represent the abscissa in the display coordinates corresponding to the front and back surfaces, M f and M b are respectively the modulation degrees corresponding to the front and back surfaces, and f is the sinusoidal fringe frequency;
Step two: performing Fourier transform on the light intensity distribution of the pixel points to obtain a power spectrum function G (x s) of I (f), wherein the power spectrum function G (x s) is as follows:
Wherein the method comprises the steps of Representing the fourier transform of I (f), w (f) being a window function; according to the peak value of the power spectrum function, the abscissa x sf and x sb in the display coordinates are obtained; similarly, the ordinate y sf and y sb in the display coordinates are obtained in the same way;
Step three: obtaining display coordinates S 1(xsf,ysf) and S 2(xsb,ysb corresponding to the front surface and the rear surface through power spectrum estimation in the second step; substituting the display coordinate S 1 point corresponding to the front surface into the following formula, calculating the slope of the front surface, and fitting to obtain the front surface shape;
Determining refracted light rays according to the law of refraction The formula is as follows:
Wherein n 0 is the refractive index of the transparent element, n is the refractive index of air, Represents the direction of the incident light, and the M 1 point represents/>Intersection with front surface,/>Representing a front surface normal vector;
further, it is assumed that the rear surface shape is formed Wherein M 2 is/>Intersection coordinates with the back surface Zern (x M2,yM2) is an expression of a Zernike polynomial,/>Obtaining M 2 point coordinates by ray tracing for the coefficients of the Zernike polynomials;
after determining the coordinates of the point M 2, the reflected light is determined according to the law of reflection The formula is as follows:
wherein, For the normal vector of the rear surface, the reflected ray/>, is calculated from the ray traceIntersection point M 3 with front surface; refraction occurs at the point M 3, and/>, is determined according to the law of refractionThe formula is as follows:
wherein, Is the normal vector of the front surface; obtain/>Then, the display coordinates/>, are obtained by utilizing the ray traceDisplay coordinatesIs related to/>Is a function of (a) as follows:
Obtained by nonlinear optimization Thereby fitting to obtain the surface shape of the rear surface, and further realizing the detection of the surface shape of the front and rear surfaces of the transparent element.
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| EP1882916A1 (en) * | 2006-07-20 | 2008-01-30 | Interuniversitair Microelektronica Centrum | Compact catadioptric spectrometer |
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