CN114858090A - Surface shape error measurement method of array structure optical element - Google Patents
Surface shape error measurement method of array structure optical element Download PDFInfo
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- CN114858090A CN114858090A CN202210451951.5A CN202210451951A CN114858090A CN 114858090 A CN114858090 A CN 114858090A CN 202210451951 A CN202210451951 A CN 202210451951A CN 114858090 A CN114858090 A CN 114858090A
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- G01—MEASURING; TESTING
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- 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
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Abstract
The invention relates to the technical field of optical measurement, in particular to a surface shape error measurement method of an array structure optical element. The method is used for solving the problems of measurement and evaluation of the surface shape of the array structure optical element. The method comprises the following steps: 1) detecting the array structure optical element by using a three-dimensional surface topography detection device to obtain surface topography point cloud data of the array structure optical element; 2) performing translational rotation of six-dimensional freedom on the measured surface topography point cloud data of the array structure optical element to enable the point cloud data to be optimally matched with a theoretical design shape; 3) and (3) completely matching the matched measurement data with the transverse coordinates of the theoretical data by adopting a nearest neighbor interpolation algorithm, and then performing point-to-point subtraction on the longitudinal coordinates to enable the longitudinal coordinates to be optimally matched with a theoretical design shape, so that the surface shape error of the measured array optical element can be obtained.
Description
Technical Field
The invention relates to the technical field of optical measurement, in particular to a surface shape error measurement method of an array structure optical element.
Background
Because the array structure optical element has incomparable advantages in the aspects of realizing specific optical functions, improving system performance, simplifying system structure and the like, more and more optical systems begin to adopt microstructure free-form surfaces, such as application to illumination, beam shaping, sensors, imaging, fingerprint identification and the like.
The optical microstructure array processing method is more, and mainly comprises single-point diamond lathe processing (such as fast tool servo, fly-cutting and milling), micro-injection molding, photoetching, femtosecond laser micro-nano processing and the like. However, due to the complexity of the microstructure array, there is no uniform processing precision detection method for detecting the processing surface shape of the optical microstructure array.
In the detection process of the actual processing surface shape, because the microstructure array has repeatability, multiple analyses are usually adopted, one microstructure is analyzed each time, then a comprehensive evaluation method is adopted, and a certain profile is manually selected to be evaluated in the evaluation process of a single microstructure, but the overall appearance of a processing element cannot be completely reflected by the adoption of the profile evaluation mode.
Therefore, the invention provides the array structure optical element surface shape measuring method aiming at the problem that no three-dimensional error surface shape evaluation exists in the existing array structure optical element surface shape evaluation.
Disclosure of Invention
In view of this, the present invention provides a method for measuring a surface shape error of an array structure optical element, in order to solve the problems of measuring and evaluating the surface shape of the array structure optical element.
In order to achieve the purpose, the invention adopts the technical scheme that: a surface shape error measurement method of an array structure optical element is characterized in that: the method comprises the following steps:
1) detecting the array structure optical element by using a three-dimensional surface topography detection device to obtain surface topography point cloud data of the array structure optical element;
2) performing translational rotation of six-dimensional freedom on the measured surface topography point cloud data of the array structure optical element to enable the point cloud data to be optimally matched with a theoretical design shape;
3) and (3) completely matching the matched measurement data with the transverse coordinates of the theoretical data by adopting a nearest neighbor interpolation algorithm, and then performing point-to-point subtraction on the longitudinal coordinates to enable the longitudinal coordinates to be optimally matched with a theoretical design shape, so that the surface shape error of the measured array optical element can be obtained.
Further, the method for matching the measurement data of the step 2) with the theoretical design shape comprises the following steps:
as known, the coordinate Q of any point in the surface shape measurement data of the optical element with the array structure is (x, y, z), and the coordinate P of any point in the theoretical design shape is (x) 0 ,y 0 ,z 0 ) Wherein z is 0 ＝f(x 0 ,y 0 ) And adopting a corresponding algorithm to convert the measurement data Q into Q ' by performing translation rotation with six degrees of freedom, so that the measurement data Q can be optimally matched with a theoretical design shape, and the measurement data point Q and the data point Q ' (x ', y ', z ') after translation rotation satisfy the following relation:
in the formula, unknown numbers alpha, beta, gamma, tx, ty and tz are respectively the anticlockwise rotation angle and the translation displacement of the measuring surface around an X, Y, Z axis in the rotation and translation process, and R is 3×3 Is a 3 × 3 rotation matrix expressed as:
constructing an objective function, determining six translational rotation amounts of alpha, beta, gamma, tx, ty and tz,
Δz＝z 0 -z′
wherein z 'is a longitudinal coordinate value of the point Q', and z is 0 Theoretical shape point P (x) matched for point Q 0 ,y 0 ,z 0 ) Performing multi-parameter optimization solution on the coordinate values, namely calculating to obtain position parameters alpha, beta, gamma, tx, ty and tz when the measured data is optimally matched with the theoretical design shape, so that the two groups of data are optimally matched;
the relation between the measurement surface Q' point and the corresponding point P is as follows:
compared with the prior art, the invention has the following advantages and effects:
1) the method adopts a surface area measurement mode for the processed array structure optical element, compared with a linear mode, the result is more real, technical support is provided for high-precision manufacturing of the array structure optical element, and the method has wide engineering application prospect.
2) The method adopts a high-precision three-dimensional surface topography measuring device to obtain the actual surface topography distribution condition of the processed array structure optical element, and then carries out data processing calculation on the surface topography obtained by the measurement and the theoretical topography so as to obtain the surface shape error of the processed array structure optical element; by constructing the multi-degree-of-freedom target function, the best matching between the measurement result and the theoretical morphology is realized, the translational rotation amount of the coordinate system during the best matching is obtained, and the calculation precision of the surface shape error is ensured.
3) Compared with the currently common sectioning line evaluation mode, the method has comprehensiveness and intuition, and can provide technical support for surface shape error measurement and compensation correction processing (the manufacturing accuracy of the array structure optical element is generally improved) of the array structure optical element.
Drawings
FIG. 1 is a flow chart of the surface shape error detection of the present invention;
FIG. 2 is a diagram illustrating a relative spatial position relationship between the actually processed micro pyramid structure array surface shape and the theoretical surface shape;
FIG. 3 is a spatial position relationship between a measured surface shape and a theoretical surface shape after matching according to the present invention;
fig. 4 is an error surface shape detected by the micro pyramid structure array actually processed by the present invention.
Description of the labeling: (1) is a theoretical surface shape, and (2) is a measurement surface shape;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
This example provides a method for measuring the surface shape error of an array structure optical element, wherein the measured and evaluated array structure optical element is a 2 × 2 micro pyramid structure array, the bottom side is 1170 microns, and the height is 40 microns, as shown in fig. 1,
1. according to the parameters of the optical element of the array structure to be measured, considering the measuring area range and the inclination angle, and combining the condition of a white light interferometer, selecting a proper field lens and an interference objective lens; detecting the array structure optical element by using a three-dimensional surface topography detection device, and obtaining the surface topography point cloud data (x, y, z) of the array structure optical element;
2. as shown in fig. 2, in order to measure the relative relationship between the surface shape and the theoretical surface shape, there is a six-dimensional degree of freedom misalignment between two sets of three-dimensional data, including the amount of translation along the X, Y, Z axis and the amount of rotation around the three axes, so that a corresponding algorithm is required to be adopted to perform six-degree of freedom translational rotation on the measurement data Q to change the measurement data Q into Q' so that the measurement data Q can be optimally matched with the theoretical design shape;
the specific method comprises the following steps:
1) and processing the cloud data of the measured points according to the following steps to obtain matched measured surface shape point cloud data (x ', y ', z ') containing parameters alpha, beta, gamma, tx, ty and tz.
Given that the theoretical design surface shape z is f (x, y), the point Q (x, y, z) on the surface shape is measured, and the point Q ' of the matched measurement surface shape corresponds to the point Q ' (x ', y ', z '), then:
in the formula, alpha, beta, gamma, tx, ty and tz are unknown parameters, R 3×3 Is a 3 × 3 rotation matrix expressed as:
2) and obtaining the three-dimensional coordinates of the matched measurement point Q '(X', Y ', Z') corresponding to the theoretical point P (X, Y, Z) by the following method:
3) and obtaining the values of corresponding unknowns alpha, beta, gamma, tx, ty and tz when the measured surface shape is matched with the theoretical surface shape and the matched measured surface shape data point cloud (x ', y ', z ') without parameters.
The objective function is constructed as follows:
Δz＝Z-z′ (4)
and (3) bringing in each data point, obtaining the values of the parameters alpha, beta, gamma, tx, ty and tz when the optimal values are obtained, wherein the values are 0.00003282868260194414, -0.0001080211007972598, 0.007774062356098, -1240.719748404752, -1257.568817572882 and 13.532747410540406 in sequence, and bringing the obtained parameter values into the step (2) to obtain the matched measured surface shape data point cloud (x ', y ', z ') without the parameters.
3. Adopting a nearest neighbor interpolation algorithm to completely match the matched measured data with the horizontal coordinates of the theoretical data, wherein fig. 3 is the relative spatial position of the measured surface shape and the theoretical surface shape after matching without parameters, and the error surface shape E is the subtraction of the matched measured point Q and the corresponding point P on the theoretical surface shape on the vertical coordinate, namely:
E＝Z-z′ (7)
and obtaining the processing surface shape error of the array structure optical element, wherein fig. 4 is the surface shape error obtained by the example.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.
Claims (2)
1. A surface shape error measurement method of an array structure optical element is characterized in that: the method comprises the following steps:
1) detecting the array structure optical element by using a three-dimensional surface topography detection device to obtain surface topography point cloud data of the array structure optical element;
2) performing translational rotation of six-dimensional freedom on the measured surface topography point cloud data of the array structure optical element to enable the point cloud data to be optimally matched with a theoretical design shape;
3) and (3) completely matching the matched measurement data with the transverse coordinates of the theoretical data by adopting a nearest neighbor interpolation algorithm, and then performing point-to-point subtraction on the longitudinal coordinates to enable the longitudinal coordinates to be optimally matched with a theoretical design shape, so that the surface shape error of the measured array optical element can be obtained.
2. The method for measuring the surface shape error of the array structure optical element according to claim 1, wherein: the method for matching the measured data of the step 2) with the theoretical design shape comprises the following steps:
as known, the coordinate Q of any point in the surface shape measurement data of the optical element with the array structure is (x, y, z), and the coordinate P of any point in the theoretical design shape is (x) 0 ,y 0 ,z 0 ) Wherein, in the step (A),z 0 ＝f(x 0 ,y 0 ) And adopting a corresponding algorithm to convert the translation rotation of six degrees of freedom of the measurement data Q into Q ', so that the measurement data Q can be optimally matched with a theoretical design shape, and the measurement data point Q and the data point Q ' (x ', y ', z ') after the translation rotation satisfy the following relation:
in the formula, the unknown numbers alpha, beta, gamma, tx, ty and tz are respectively the anticlockwise rotation angle and the translation displacement of the measuring surface around the X, Y, Z axis in the rotation and translation process, and R 3×3 Is a 3 × 3 rotation matrix expressed as:
constructing an objective function, determining six translational rotation amounts of alpha, beta, gamma, tx, ty and tz,
Δz＝z 0 -z′
wherein z 'is a longitudinal coordinate value of the point Q', and z is 0 Theoretical shape point P (x) matched for point Q 0 ,y 0 ,z 0 ) Performing multi-parameter optimization solution on the coordinate values, namely calculating to obtain position parameters alpha, beta, gamma, tx, ty and tz when the measured data is optimally matched with the theoretical design shape, so that the two groups of data are optimally matched;
the relation between the measurement surface shape Q' point and the corresponding point P is as follows:
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