A surface micro-defect reconstruction method based on time-of-flight difference of scattered light

Abstract

The present application belongs to the technical field of optical surface defect detection, and particularly relates to a surface micro-defect reconstruction method based on scattered light flight time difference. The present application is directed to the problems that the current dark field scattering defect detection system has low utilization rate of multi-dimensional information of light field, cannot directly measure the defect size, classify the defects, and avoid the crosstalk caused by the secondary or multiple reflections of incident light on the surface, and proposes a calculation method for reconstructing the geometric characteristics of surface micro-defects based on scattered light flight time and a corresponding three-dimensional reconstruction model. According to the relative spatial pose relationship of the light source-defect-detection point, the present application focuses the source of calculation data on the process that the light beam is first contacted with the object surface from the light source, and skillfully uses the scattered light flight time difference to avoid the discussion of multiple interactions such as multiple scattering of the light beam and the object surface, thereby improving the detection capability of the dark field scattering detection system for the geometric characteristics of surface defects from the principle level.

Description

Technical Field

[0001] This invention relates to the field of optical surface defect detection technology, and specifically to a method for reconstructing minute surface defects based on the time-of-flight difference of scattered light. Background Technology

[0002] Dark-field scattering is a commonly used technique for surface defect detection. Dark-field illumination systems offer higher detection sensitivity than bright-field systems. While bright-field systems can detect defects with sizes close to their resolution, dark-field systems can detect defects much smaller than the resolution. This advantage is inherent to the properties of the optical imaging system itself. Imaging systems are diffraction-limited, thus inherently subject to aberrations and optical diffraction effects. This causes the object-side emission point to diffuse and broaden on the image plane. In bright-field systems, the emission point is the normal surface area surrounding the defect, which, after broadening, obscures the defect signal. However, in dark-field systems, the emission point is the defect itself, and the detector receives the scattered light from the defect. Therefore, the broadening effect makes the defect more prominent in the image, resulting in a high-contrast image.

[0003] However, current mainstream dark-field scattering detection technology still relies on the spatial distribution of scattered light intensity to identify defect types and sizes. One common method is to use electromagnetic simulations to obtain far-field diffraction intensity distributions of known defect types, forming a database, and then indirectly comparing it with images obtained from actual experiments to identify defect types and sizes. Current dark-field scattering defect detection systems suffer from low utilization of multi-dimensional optical field information, inability to directly measure defect size or classify defects, and inability to avoid crosstalk caused by secondary or multiple reflections of incident light on the surface. Summary of the Invention

[0004] This invention addresses the problems of low utilization of multi-dimensional optical field information in current dark-field scattering defect detection systems, inability to directly measure defect size and classify defects, and inability to avoid crosstalk caused by secondary or multiple reflections of incident light on the surface. It proposes a computational method and a three-dimensional reconstruction model for reconstructing the geometric features of minute surface defects based on dark-field scattering time-of-flight. This computational method cleverly utilizes the time-of-flight difference of scattered light, based on the geometric relationship between multiple light sources and surface defects and the relative pose relationship between single-path surface defects and detector sampling points, to avoid discussing the complex propagation process of the beam from the defect to the detector. It locks the defect's characteristic information into the linear propagation path from the light source to the surface defect, thereby improving the detection capability of dark-field scattering detection systems for the geometric features of surface defects.

[0005] The technical solution of the present invention is described in detail below.

[0006] This invention provides a method for reconstructing minute surface defects based on the time-of-flight difference of scattered light. It utilizes a dark-field scattered light time-of-flight measurement system to reconstruct defects on the surface of the sample. Two incident light beams are time-domain modulated and applied to the surface of the sample, where they are scattered by minute defects. The scattered light then passes through a single-path optical microscope system and enters a photodetector to acquire the signal. By collecting scattered light signals from different spatial points on the sample, analyzing the time of flight of the scattered light signals from multiple beams, and calculating the time-of-flight difference, the surface gradient of the sample in three-dimensional space is determined, thereby reconstructing the surface morphology. The specific steps are as follows:

[0007] 1) Perform periodic time-domain modulation on each light source, and represent the time-domain signal of the light source as I. s ;

[0008] 2) The optical signal data collected from different spatial points under time-domain modulated radiation from two of the light sources are organized into a matrix form. The signal data are regarded as two data cubes with dimensions [W,H,n] and a spatial resolution of W×H. W,H,n are determined by the photodetector parameters and the actual experimental shooting duration. The photodetector is H pixels long and W pixels wide, and each spatial resolution point has n frames of data:

[0009]

[0010] The last dimension of each data cube represents the temporal distribution of the scattered light signal from the i-th pixel of the photodetector. i∈(1,W*H), compare it with the time-domain distribution of the scattered light signals of the neighboring spatial points. Perform cross-correlation calculations to determine the time delay τ between two signals scattered from a beam of light to adjacent spatial points separated by a pixel. l Defined as taking the maximum value of the cross-correlation function:

[0011]

[0012] According to Huygens' law of diffraction, the flight time t of the scattered beam l It involves two processes: the first is the process from the light source to the object, and the second is the process from the object to the observation point. and For the incident directions of two beams at the same spatial point, since the relative spatial position of the observation point and the sample remains unchanged, therefore It is a certain value, and The time delay τ for the two beams is determined by the incident direction and position of the incident light source. l1 τ l2 And the flight time corresponding to the first process in each of them, namely the time of flight from the light source to the first point of contact with the object's surface being measured. satisfy:

[0013]

[0014] Where τ l1 , τ l2 Solving by formula (3), we can see that the time delay between two adjacent spatial points in the two beams is respectively represented;

[0015] Furthermore, the time difference of flight of scattered light between two adjacent spatial points under the illumination of two beams is defined.

[0016]

[0017] In two-dimensional Cartesian coordinate space, the time delay corresponding to the first process in a beam of light, i.e., the time delay from the light source to the first point of contact with the object. The geometric features of the surfaces corresponding to the two spatial points satisfy the following constraints:

[0018]

[0019] Where α is the angle between the time-modulated equiphase surface of the incident light source and the normal to the macroscopic surface of the sample under test. When the light source is regarded as a plane wave incident, the equiphase surface at each point in space is regarded as a spatial plane; c is the speed of light. It is the ratio of the flight time of the light beam from the source to the first point of contact on the object surface to its lateral offset; It is the ratio of the longitudinal depth of adjacent spatial points to the lateral offset. When the lateral offset is small enough, this ratio is also called the surface gradient.

[0020] To apply this to three-dimensional Cartesian coordinate space, the constraint relationship between the time-of-flight difference of scattered light and the geometry of the sample under test in two-dimensional Cartesian coordinate space is extended to a certain extent, specifically as follows:

[0021] ① In three-dimensional space, it has direction (cosθ) x cosθ y cosθ z The incident rays may not lie on the XZ section, even though they fall on that section; this indicates that the energy transfer length corresponding to the phase shift is Instead Right now:

[0022]

[0023] ②The corresponding incident angle parameter α is corrected to:

[0024]

[0025] ③ When dealing with the YZ section, θ y and θ x The position before the change;

[0026] Therefore, substituting equations (7) and (8) into equation (6), the three-dimensional spatial relationship between the time-of-flight difference and the surface gradient of the sample to be tested is expressed as:

[0027]

[0028] Then, substituting formulas (4) and (5) into formula (9), the surface gradient of the sample under test in three-dimensional space is calculated based on the time difference of flight of the two incident beams:

[0029]

[0030] Where Δt represents the time difference of flight of scattered light between two adjacent spatial points under two-beam illumination, which is obtained by solving formulas (3), (4), and (5), (cosθ) x1 cosθ y1 cosθ z1 ), (cosθ x2 cosθ y2 cosθ z2 ) are the incident direction cosines of the two beams, Δx is the transverse offset of the sample under test, and Δz is the longitudinal depth offset of the sample under test.

[0031] 3) Reconstruct the surface morphology by gradient integration based on the obtained surface gradient.

[0032] In this invention, in step 1), cosine modulation is performed on each light source.

[0033] In this invention, the incident light speed is replaced by more than two paths. When there are more than two paths, the beam is divided into two beams as a group and calculated according to step 2), and a weighted average is taken to finally obtain the surface gradient of the sample under test in three-dimensional space.

[0034] In this invention, in step 3), the surface morphology is reconstructed using the least squares method.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] Based on the relative spatial pose relationship between the light source, the defect, and the detection point, this invention focuses the source of the calculation data on the process of the light beam originating from the light source and making its first contact with the object surface. It cleverly utilizes the time difference of flight of scattered light to avoid the discussion of multiple scattering interactions between the light beam and the object surface, thereby improving the ability of the dark field scattering detection system to detect the geometric features of surface defects from a principle level.

[0037] The method proposed in this invention solves the surface gradient of the sample based on the time-of-flight difference, which provides an additional information dimension compared with traditional methods. By using this dimension of information and combining it with traditional information, the characteristics of various defects can be compared, and then classified and categorized, which helps to determine the size and classification of defects. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of a surface micro-defect reconstruction method based on the time-of-flight difference of scattered light.

[0039] Figure 2 This is a schematic diagram of the principle of a two-dimensional Cartesian coordinate system relating the time delay of beam flight between adjacent spatial points to the gradient of the sample surface. Figure 2 (a) The surface gradient is defined as a positive value. Figure 2 (b) The surface gradient is defined as negative. In the figure, Δx is the transverse offset of the sample under test, Δz is the longitudinal depth offset of the sample under test, Δl is the beam propagation distance corresponding to the time difference of flight between adjacent spatial points, angle α is the beam incident angle parameter, and angles β and γ are defined as follows: and

[0040] Figure 3 This is a schematic diagram illustrating the principle of extending the two-dimensional Cartesian coordinate system to three-dimensional space. The cube in the upper left corner represents the direction cosine of a light beam in three-dimensional space. In the diagram, Δx, Δz, and Δl are related to... Figure 2 Consistent with the definition, the subscript 's' represents the correction value of the corresponding parameter. Angle and Representing l1 and l2 to l respectively s1 and l s2 The spatial angle corresponding to the projection.

[0041] Figure 4 This is a schematic diagram and result of a surface micro-defect reconstruction calculation based on the time-of-flight difference of scattered light using ray tracing. Detailed Implementation

[0042] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0043] Please refer to the following first. Figure 1 , Figure 1 This is a schematic diagram of a surface micro-defect reconstruction method based on the time-of-flight difference of scattered light. The specific method is as follows:

[0044] 1) By applying cosine modulation (or other periodic time-domain modulation) to each light source, the time-domain signal of the light source can be expressed as:

[0045]

[0046] 2) Organize the optical signal data collected from different spatial points under time-domain modulated radiation from two light sources into a matrix form. The signal data can be regarded as two data cubes with dimensions [W,H,n], that is, the spatial resolution is W×H, and each spatial resolution point has n frames of data. W, H, and n can all be determined by the parameters of the experimental detector and the experimental shooting time. W and H refer to the spatial resolution of the detector, which can be regarded as the detector (or camera) being H pixels long and W pixels wide. n represents the number of frames captured by the detector. For example, if a 60fps detector is used for shooting, then 120 frames of images can be obtained in 2 seconds. In this case, n is 120.

[0047]

[0048] 3) The last dimension of each data cube This represents the time-domain distribution of the scattered light signal of the i-th pixel of the photodetector. If i∈(1,W*H), then This array represents the data of each frame of pixels in the first row and first column of the detector for the first beam. Cross-correlation is performed between the cross-correlation function and the time-domain distribution of the scattered light signals from neighboring spatial points, and the maximum value of the cross-correlation function is taken as the time delay τ between the two signals. l :

[0049]

[0050] It should be noted that the two signals mentioned here are the signal time delays of each beam scattered to adjacent spatial points. The pixel in the first row and first column of the detector and the pixel in the first row and second column belong to the neighboring spatial points. That is, the interval between them is called the adjacent spatial points. In formula (3), τ′ is the horizontal axis of the cross-correlation function, which is an intermediate variable. The purpose of formula (3) is to calculate the signal time delay of one beam scattered to the adjacent spatial points.

[0051] 4) According to Huygens' diffraction law, the flight time t of the scattered beam... l It involves two processes: the journey from the light source to the object, and the journey from the object to the observation point. and For the incident directions of two beams at the same spatial point, since the relative spatial position of the observation point and the sample remains unchanged, therefore It is a certain value, and The time delay τ is determined by the incident direction and position of the incident light source. Therefore, the time delay difference τ between the two beams is calculated. l1 τ l2 And the first process in each of them, namely the flight time from the light source to the object. and satisfy:

[0052]

[0053] These refer to the flight time of the two beams from the light source plane to the first contact point on the surface under test. The difference between these two quantities is the flight time difference.

[0054] 5) Based on equation (4), the time difference of flight of scattered light between two adjacent spatial points under the illumination of two beams is further defined. Right now:

[0055]

[0056] Time difference of flight The solution can be obtained by combining formula (3).

[0057] 6) such as Figure 2 As shown, consider the relationship between the surface gradient along the XZ axes and the time of flight of a light beam between two points during its journey from the light source to the object's surface in a two-dimensional case. Using a unified dimension, let Δl be the spatial distance the light beam energy travels during this time-of-flight difference. Figure 2 The angle between the propagation direction of the light source and the Z-axis (incident angle) is α; where γ satisfies β satisfies Based on geometric relationships, it is easy to know Figure 2 In (a), the light source direction angle α, the optical path difference gradient angle β, and the object surface gradient angle γ satisfy the relationship |α|+|β|=|γ|. Similarly, Figure 2 In (b), the relation |α|-|β|=-|γ| is satisfied. Furthermore, for the object plane and the light source plane, the lengths Δx and Δx′ are... Figure 2 In (a) and (b), Δx′=(Δx+|Δz|tanα)cosα and Δx′=(Δx-|Δz|tanα)cosα, respectively. According to the chain rule of differential operations, we have:

[0058]

[0059] Considering Δl and satisfying the time delay Therefore, the time delay in the first process of a beam of light, i.e., the time delay from the light source to the first point of contact with the object. The geometric features of the surfaces corresponding to the two spatial points satisfy the following relationship in the two-dimensional Cartesian XZ coordinate system:

[0060]

[0061] Where α is the angle between the time-modulated equiphase surface of the incident light source and the normal to the macroscopic surface of the sample under test. When the light source can be regarded as a plane wave incident, the equiphase surface at each point in space can be regarded as a spatial plane; c is the speed of light. It is the ratio of the flight time of the light beam from the source to the first point of contact on the object surface to the lateral offset. It is the ratio of the longitudinal depth of adjacent spatial points to the lateral offset. When the lateral offset is small enough, this ratio is also called the surface gradient.

[0062] 7) such as Figure 3 As shown, the constraint relationship between the time-of-flight difference of scattered light and the geometry of the sample under test in two-dimensional Cartesian coordinate space can be extended to three-dimensional Cartesian coordinate space by making certain modifications. In three-dimensional space, the direction (cosθ) is... x cosθ y cosθ z The incident rays may not lie on the XZ section, even though they fall on that section. This indicates that the energy transfer length corresponding to the phase shift is Instead Right now:

[0063]

[0064] The corresponding incident angle parameter α should also be corrected:

[0065]

[0066] Note that when dealing with the YZ section, θ y and θ x The previous positions need to be swapped.

[0067] Furthermore, based on the above modifications, substituting formulas (7) and (8) into formula (6), the three-dimensional spatial relationship between the time-of-flight difference and the surface gradient of the sample under test can be expressed as:

[0068]

[0069] 8) The data obtained from the actual experiment is the time delay τ l Non-flight time Therefore, to solve for the surface gradient of the sample under test based on formula (9), further transformation is required, which necessitates data obtained from fixed observation directions and multi-angle illumination. Let two different incident directions (cosθ) be considered. x1 cosθ y1 cosθ z1 ), (cosθ x2 cosθ y2 cosθ z2 The time delays obtained under the illumination observation experiment are τ l1 and τ l2 Combining with formula (9), we have:

[0070]

[0071] Substituting formula (4) into formula (10), we get:

[0072]

[0073] Combining equations (5) and (11), the surface gradient of the surface to be measured along the X and Y axes of the Cartesian coordinate system can be expressed as:

[0074]

[0075] Where Δt represents the time difference of flight of scattered light between two adjacent spatial points under two-beam illumination, which is obtained by solving formulas (3), (4), and (5), (cosθ) x1 cosθ y1 cosθ z1 ), (cosθ x2 cosθ y2 cosθ z2 ) are the incident direction cosines of the two beams, Δx is the transverse offset of the sample under test, and Δz is the longitudinal depth offset of the sample under test.

[0076] 9) The obtained surface gradient is used to reconstruct the surface morphology by gradient integration, specifically by methods such as least squares.

[0077] The above steps allow for convenient simulation calculations using ray tracing algorithms, such as... Figure 4 As shown, when using two beams, the simulation results show that the proposed calculation method has an error of less than 0.25 nm compared with the real surface in a local area of ​​10 mm for the reconstruction results of planes, higher-order aspherical surfaces, and non-axisymmetric and non-rotational symmetric surfaces. Moreover, the error of the plane can even reach less than 0.00000001 nm. This indirectly shows that the reconstruction accuracy of the model is greatly affected by the gradient and the accuracy of the gradient reconstruction algorithm, that is, the proposed calculation has a reliable surface morphology reconstruction capability.

[0078] In this invention, more than two beams can be incident on the surface to be tested. By analyzing the flight time of the scattered light signals from multiple beams and calculating the flight time difference, the surface gradient of the sample under test in three-dimensional space can be obtained and the surface morphology can be reconstructed. For the calculation method of the surface gradient of more than two beams, they can be divided into two beams as a group for calculation and weighted average can be taken. The method is the same as the calculation method of two beams, and will not be repeated here.

Claims

1. A surface micro-defect reconstruction method based on time-of-flight difference of scattered light, characterized in that, It is based on the dark field scattering light time of flight measurement system to the surface of the sample to be measured defect reconstruction, it will be two-way incident beam after time domain modulation on the surface of the sample to be measured and scattered by subtle defects, then through a single optical microscopy into the photodetector to obtain signal, by collecting the scattering light signal of different spatial points of the sample to be measured, analysis of the flight time of the multi-channel light scattering signal and calculate the flight time difference, to obtain the surface gradient of the sample to be measured in three-dimensional space and then reconstruct the surface topography; The specific steps are as follows: 1) Periodic time domain modulation is performed on each light source, the time domain signal of the light source is represented as ; 2) The optical signal data collected at different spatial points under the 2-path light source time-domain modulation radiation are arranged in matrix form, and the signal data are regarded as two data cubes with specifications of The spatial resolution is WxH, The photoelectric detector parameters and the actual experimental shooting duration determine that the photoelectric detector has H pixels in length and W pixels in width, and each spatial resolution point has n frames of data: ， The last dimension data of each data cube represents the time domain distribution of the scattered light signal of the i-th pixel of the photodetector , The time delay between the two signals of the adjacent spatial points with one pixel interval to which the scattered light signal time domain distribution of the adjacent spatial points is correlated The time delay between the two signals of the adjacent spatial points with one pixel interval to which the scattered light signal time domain distribution of the adjacent spatial points is correlated The time delay between the two signals of the adjacent spatial points with one pixel interval to which the scattered light signal time domain distribution of the adjacent spatial points is correlated ， According to Huygens diffraction law, the time of flight of the scattered light beam contains two processes, one is the process of light source to object, the second is the process of object to observation point, respectively and , and for the same spatial point of 2 light beam incident direction, because the observation point and the relative spatial position of the sample to be measured is unchanged, therefore is a constant, and is determined by the incident direction and incident position of the incident light source, so the time delay of 2 light beams and their respective processes, the first process, that is, the time of flight of the light source to the first contact point on the surface of the object to be measured , satisfies: ， wherein Solving equation (3), the time delay of two adjacent spatial points in two beams is represented respectively; equation (4) illustrates the internal relationship between the time delay and the flight time of the scattered light, and further defines the flight time difference of the scattered light under the illumination of two adjacent spatial points and two beams : ， In a two-dimensional Cartesian coordinate space, a first process in a light beam corresponds to a time of flight from a light source to a first contact point of an object Geometric features of surfaces corresponding to the two spatial points satisfy the following constraint relationship: ， wherein is the angle between the time-modulated equiphase surface of the light source and the normal to the macroscopic surface of the sample under test, when the light source is considered as a plane wave incident; c is the speed of light; is the ratio of the time-of-flight of the light beam from the source to the first point of contact on the surface of the object and the lateral displacement in the direction of the displacement; is the ratio of the longitudinal depth of adjacent points in space to the lateral displacement in the direction of the displacement, which is also referred to as the surface gradient when the lateral displacement is sufficiently small; In order to be applied to three-dimensional Cartesian coordinate space, the constraint relationship between the flight time difference of the scattering light and the geometric topography of the sample to be measured in two-dimensional Cartesian coordinate space is expanded, specifically: ① In three-dimensional space, having a direction of an incident light ray that falls on the XZ section, but whose origin is either inside or outside the XZ section; this indicates that the energy transport length corresponding to the phase shift is c , not c , i.e.: ， 2. The method of claim 1, wherein the step of determining the corresponding incident angle parameter comprises: determining the corresponding incident angle parameter based on the first and second received signals. Correct ， ③ In processing the YZ section, and positions before alternation; Therefore, formula (7), formula (8) are substituted into formula (6), the flight time difference and the three-dimensional space relationship of the surface gradient of the sample to be measured are represented as: ， Further, formula (4), (5) are substituted into formula (9), and the surface gradient of the sample to be measured in three-dimensional space is obtained according to the flight time difference of the two incident light beams: ， wherein represents the difference of the time of flight of the scattered light of two adjacent spatial points under the illumination of two light beams, which is obtained by formula (3), (4), (5), , are the incident direction cosine of two light beams respectively, is the lateral offset of the sample to be measured, is the longitudinal depth offset of the sample to be measured; 3) Based on the obtained surface gradient, the surface topography is reconstructed by gradient integration.

2. The surface microdefect reconstruction method according to claim 1, wherein In step 1), each light source is cosine modulated.

3. The method of claim 1, wherein the surface microdefect reconstruction is performed by a computer. The incident light speed is replaced by more than 2, when more than 2, the light beam is divided into 2 light beams as a group, which is calculated according to step 2) and weighted average, and finally the surface gradient of the sample to be measured in three-dimensional space is obtained.

4. The method of claim 1, wherein the surface fine defect reconstruction method is characterized by, In step 3), the least square method is used to reconstruct the surface topography.

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