CN109373918A - A kind of high effective optical measurement method for two-dimensional material measured film thickness - Google Patents
A kind of high effective optical measurement method for two-dimensional material measured film thickness Download PDFInfo
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Abstract
A kind of high effective optical measurement method for two-dimensional material measured film thickness.Belong to color calculating and technical field of image processing based on thin film interference effects.The method of the present invention include under the conditions of specified value the color calculating process of substrate and different-thickness two-dimensional material film to be measured and it is subsequent based on color calculated result under the conditions of specified value be standard, to the calibration process of actual imaging result.The method of the present invention has the advantages that high-efficient, highly reliable, applied widely.
Description
Technical field
The present invention relates to a kind of color calculating and technical field of image processing based on thin film interference effects, and in particular to
A kind of high effective optical measurement method for two-dimensional material measured film thickness.
Background technique
All kinds of two-dimensional materials, such as graphene, hexagonal boron nitride, using molybdenum disulfide and tungsten disulfide as the transition metal of representative
Two sulfur family category compounds and black phosphorus etc., because its excellent photoelectricity and mechanical performance progress into the visual field of people.Two-dimensional material
Thickness be closely connected with its physical property, so the thickness characterization of two-dimensional material sample is mostly important with common measurement
Project.
Currently, the most common two-dimensional material thickness accurate Characterization method is atomic force microscope and Raman spectrum.But by
Slower in atomic force microscope and raman spectroscopy measurement imaging, efficiency is lower, and costly, sample has substrate certain equipment
Sensibility, therefore it is still necessary to improve for these methods.
The two-dimensional material of different-thickness is in common substrate, such as SiO2It, can be obvious by optical microscopy in/Si substrate
Ground, which observes, can be presented different colors, therefore can be using the relationship between color and the thickness of two-dimensional material to two-dimensional material
Thickness characterized.It is far high that efficiency can be completed only by the ordinary optical microscope for having digital camera based on this theory
In the two-dimensional material thickness measure of atomic force microscope and Raman spectrum.However, in actual operation, due to current existing light
Learning measurement method must carry out in the case where fixed lighting source, camera color matching functions and other relevant parameters are set
Measurement, and these parameters are often different due to different measurement situations and are difficult to determine；In addition, can determine light source and phase
Machine color matching functions, most of digital camera can also automatically process image, this becomes the extraneous factors such as fixed light source
There is no practical significance, therefore existing measuring method is not particularly suited for all measuring conditions, it is difficult to apply to practical reality
It tests and produces.In view of the color of the substrate of known oxides coating thickness can be calculated in advance, therefore ginseng can be passed through
The deviation for examining substrate actual color calibrates the color of general image, obtains being similar to the imaging knot under the conditions of specified value
Fruit, and then the image after calibration is applied to the thickness measure of two-dimensional material.
Summary of the invention
The purpose of the present invention is to solve inefficient, optical measurement that existing two-dimensional material film thickness often uses measurement means
The problem of low reliability of method, proposes a kind of high effective optical measurement method for two-dimensional material measured film thickness.
A kind of high effective optical measurement method for two-dimensional material measured film thickness, under the conditions of specified value substrate with
The color calculating process of different-thickness two-dimensional material film to be measured and subsequent color calculated result under the conditions of being based on specified value
For standard, to the calibration process of actual imaging result.
Preferably, the measurement method is realized by following steps:
Step 1: specified value condition, by the spectral power distribution of lighting source and camera or the color-match of observer
Function is as the preset parameter under standard conditions；
Step 2: by reflectance spectrum caused by film interference, the two-dimensional material to be measured for calculating corresponding different-thickness is thin
The theoretical color of film, as substrate under standard conditions and different-thickness；And by theoretical color by CIE XYZ color space
It is converted into CIE Lab color space；
Wherein, by reflectance spectrum caused by film interference, the two-dimensional material film to be measured of corresponding different-thickness is calculated
Theoretical color, specifically: pass through the spectral power distribution of the lighting source as preset parameter and camera or the face of observer
The weighted sum of color matching function integral or discrete values obtains the theoretical color accordingly in CIE XYZ color space；
Step 3: seeking the color of the substrate in CIE Lab color space and the two-dimensional material film to be measured of different-thickness
Color color difference, using the color difference sought as both in CIE Lab color space coordinate distance；
Step 4: choosing the base part in the actual imaging color image of two-dimensional material film to be measured, and selected by calculating
Take average value of the color in region in CIE XYZ color space；Wherein, by the practical optical microscopy of the algorithm picks that flood at
As the base part in gained color image；
Step 5: substrate is in CIE XYZ color space under the conditions of calculating the average value and specified value that step 4 obtains
The color difference of theoretical color；Color difference in actual imaging image with substrate under the conditions of specified value is brought into calibration equation, is led to
It crosses calibration equation and calibrates actual imaging image pixel-by-pixel, then image is transformed into CIE Lab color sky by CIE XYZ color space
Between；
Step 6: calibration after image in color of each pixel in CIE Lab color space and the image after calibration
The color difference of middle base color average value is with the color difference of two-dimensional material film to be measured under the conditions of specified value compared with the relationship of thickness
Compared with, obtain respective pixel color representative two-dimensional material film thickness.
Beneficial effects of the present invention:
The high effective optical measurement method of two-dimensional material film thickness proposed by the present invention, has the beneficial effect that
1, the measuring method have the advantages that it is high-efficient with it is highly reliable；
2, the measuring method is applied widely, may be directly applied to unknown and unlocked lighting source
Optical imagery image in the case of the external parameters such as spectral power distribution and camera or the color matching functions of observer；
3, the measuring method requires measuring device lower, and only the ordinary optical with color digital camera is aobvious
Micro mirror effectively controls cost, realizes the practical of high effective optical measurement method；
4, measuring method calculation amount of the invention is smaller, therefore can be applied to the real-time measurement under real time scan.
5, in addition, under conditions of realizing close precision, compared to conventional atom force microscope and Raman spectrum, the present invention
The high effective optical measurement method of the two-dimensional material film thickness of proposition has efficiency outstanding and cost advantage, this is greatly convenient
The measurement of large area, extensive two-dimensional material film thickness provides convenience for the accurate measurement of two-dimensional material film thickness.Together
When, since its calculation amount is smaller, the real-time measurement being equally applicable under real time scan, measuring, two-dimensional material of the same area is thin
Under the premise of film thickness, the method all has significant advantage in efficiency, reliability and cost control.
Detailed description of the invention
Fig. 1 is model of the single thin film of the present invention in the medium of two kinds of semo-infinites.
Fig. 2 is of the present invention in 300nm oxide layer SiO2It include 1-3 layers of molybdenum disulfide film in/Si substrate
Practical original optical image.
Fig. 3 is Fig. 2 calibration conversion gained image of the present invention.
Fig. 4 be before and after conversion of the present invention and the molybdenum disulfide film thickness and substrate of given standard conditions with
The relationship of molybdenum disulfide color difference.
Fig. 5 is 1 process of embodiment of the present invention.
Under the conditions of Fig. 6 is D65 standard sources of the present invention and CIE standard Observer color matching functions, in 300nm
Oxide layer SiO2It include the calculated value image of 1-5 layers of molybdenum disulfide film in/Si substrate.
Fig. 7 is Fig. 6 calibration conversion gained image of the present invention.
Fig. 8 is standard illuminant A of the present invention and MT9V032 CMOS (Edmund Optics) color matching functions item
Under part, in 300nm oxide layer SiO2It include the calculated value image of 1-5 layers of molybdenum disulfide film in/Si substrate.
Fig. 9 is Fig. 8 calibration conversion gained image of the present invention.
Figure 10 is standard illuminant A of the present invention and CIE standard Observer color matching functions, and uses Gray
Under conditions of the calibration of World automatic white balance algorithm, in 300nm oxide layer SiO2It include 1-5 layers of molybdenum disulfide in/Si substrate
The calculated value image of film.
Figure 11 is Figure 10 calibration conversion gained image of the present invention.
Figure 12 is molybdenum disulfide film thickness before embodiment 2-4 of the present invention conversion and substrate and molybdenum disulfide
The relationship of color difference.
Figure 13 is molybdenum disulfide film thickness after embodiment 2-4 of the present invention conversion and substrate and molybdenum disulfide
The relationship of color difference.
Figure 14 is process principle figure of the invention.
Specific embodiment
Specific embodiment 1:
A kind of high effective optical measurement method for two-dimensional material measured film thickness of present embodiment, in specified value
Under the conditions of the color calculating process of substrate and different-thickness two-dimensional material film to be measured and subsequent based under the conditions of specified value
Color calculated result is standard, to the calibration process of actual imaging result.
Specific embodiment 2:
Unlike specific embodiment one, a kind of height for two-dimensional material measured film thickness of present embodiment
Measuring method is imitated, the measurement method includes:
Step 1: specified value condition, by the spectral power distribution of lighting source and camera or the color-match of observer
Function is as the preset parameter under standard conditions；
Step 2: calculating the two-dimensional material film to be measured of different-thickness by reflectance spectrum caused by film interference
Theoretical color, the color of the two-dimensional material film of color and different-thickness as the substrate under standard conditions；And it will
The theoretical color of calculating is converted into CIE Lab color space by CIE XYZ color space；Different layers of two-dimensional material films are
For the two-dimensional material film of different-thickness；
Wherein, by reflectance spectrum caused by film interference, the reason of the two-dimensional material film to be measured of different-thickness is calculated
By color, specifically: pass through the spectral power distribution of the lighting source as preset parameter and the color of camera or observer
Weighted sum with functional integration or discrete values obtains the theoretical color accordingly in CIE XYZ color space；
Step 3: seeking the color of the substrate in CIE Lab color space and the two-dimensional material film to be measured of different-thickness
Color color difference, and by its indicate different-thickness two-dimensional material film to be measured color difference and thickness relationship；
Step 4: choosing the base part in the actual imaging color image of two-dimensional material film to be measured, and selected by calculating
Take average value of the color in region in CIE XYZ color space；Wherein, by the practical optical microscopy of the algorithm picks that flood at
As the base part in gained color image；
Step 5: substrate is in CIE XYZ color space under the conditions of calculating the average value and specified value that step 4 obtains
The color difference of theoretical color；The color difference of substrate under the conditions of actual imaging image and specified value is brought into calibration equation, is passed through
Calibration equation calibrates actual imaging image pixel-by-pixel, then the actual imaging image after calibration is converted by CIE XYZ color space
To CIE Lab color space；
Step 6: calibration after actual imaging image in color and calibration of each pixel in CIE Lab color space
The color difference of two-dimensional material film to be measured and thickness under the conditions of the color difference and specified value of base color average value in image afterwards
Relationship compares, and obtains the thickness of the two-dimensional material film of respective pixel color representative.
Specific embodiment 3:
Unlike specific embodiment two, a kind of height for two-dimensional material measured film thickness of present embodiment
Imitate measuring method, in the step one, specified value condition, by the spectral power distribution of lighting source and camera or sight
The color matching functions of survey person is as the preset parameter under standard conditions, wherein the specified value condition refers to given one
A white light source and a camera are as reference standard；The spectral power distribution of the lighting source and camera or observer's
Color matching functions can be one of various white light sources and color matching functions；
It is described using the spectral power distribution of lighting source and camera or the color matching functions of observer as standard conditions
Under preset parameter, specifically:
It is (more since the color of thin-film material depends primarily on its entirety to the reflectivity of different wave length visible light
The reflectivity of layer film interference system is the key parameter that model color calculates.)
Firstly, the model (as shown in Figure 1) according to single thin film in the medium of two kinds of semo-infinites, is calculated by formula (1)
The reflectivity of substrate:
In formula, just like formula (2), formula (3) relationship:
Formula (1), formula (2), in formula (3), λ is lambda1-wavelength, niFor the refractive index of i-th layer of medium, diFor i-th layer of medium
Thickness, θiFor the incident light beam strikes angle for being incident on i-th layer of medium, it is generally the case that due to the lighting source of optical microscopy
Vertical incidence, therefore θi=0；
Then, the SiO in known thickness oxide layer plated film is calculated2The refractive index of two-dimensional material film in/Si substrate, such as
Shown in formula (4):
Specific embodiment 4:
Unlike specific embodiment three, a kind of height for two-dimensional material measured film thickness of present embodiment
Measuring method is imitated, in the step two, by reflectance spectrum caused by film interference, calculates the to be measured of different-thickness
The two-dimensional material of the theoretical color of two-dimensional material film, color and different-thickness as the substrate under standard conditions is thin
The color of film；And convert the theoretical color of calculating to by CIE XYZ color space the process of CIE Lab color space, specifically
Are as follows:
Firstly, calculating the theoretical color of the two-dimensional material film to be measured of the color and different-thickness of substrate under the conditions of specified value
It is color:
In CIE XYZ color space, there is the theoretical color of the two-dimensional material film to be measured of different-thickness shown in formula (5)
Relationship:
And Y value is normalized by formula (6):
In formula (5), (6), R (λ) is indicated with the reflectivity of a length of function of visible light wave, and I (λ) is the spectral power point of light source
Cloth,For CIE standard Observer's color matching functions；
Then, it is chosen at the color difference defined in CIE Lab color space, it, will by the function expression of formula (7) and (8)
Theoretical color is converted to CIE Lab color space by CIE XYZ color space, obtains CIE Lab color space coordinates numerical value:
In formula,Xn、Yn、ZnIt is CIE benchmark white point tristimulus values.
Specific embodiment 5:
Unlike specific embodiment four, a kind of height for two-dimensional material measured film thickness of present embodiment
Imitate measuring method, in the step three, seek the substrate in CIE Lab color space color and different-thickness to
The color difference of the color of two-dimensional material film is surveyed, and by the color difference and thickness of its two-dimensional material film to be measured for indicating different-thickness
The process of relationship, specifically:
After obtaining CIE Lab color space coordinates numerical value, the substrate in CIE Lab color space is calculated using formula (11)
The color difference of the color of the two-dimensional material film to be measured of color and different-thickness:
In formula (9),WithIt is two-dimensional material film and substrate respectively in CIE Lab color
The coordinate of color space；Utilize the CIELab of the two-dimensional material film of different-thickness under the conditions of formula (4)-formula (9) calculating specified value
Color space coordinates, gained are the relationship of the color difference of the two-dimensional material film of different-thickness and thickness under the conditions of specified value,
And in this, as subsequent measurement standard.
Specific embodiment 6:
Unlike specific embodiment five, a kind of height for two-dimensional material measured film thickness of present embodiment
Measuring method is imitated, in the step five, substrate is in CIE under the conditions of calculating the average value and specified value that step 4 obtains
The color difference of the theoretical color of XYZ color space；The color difference of substrate under the conditions of actual imaging image and specified value is brought into school
In quasi- formula, actual imaging image is calibrated pixel-by-pixel by calibration equation, then by the actual imaging image after calibration by CIE XYZ
Color space is transformed into the process of CIE Lab color space, specifically:
(1) substrate is in CIE XYZ color space under the conditions of average value and specified value that the calculating step 4 described in obtains
Theoretical color color difference process are as follows:
To simplify expression, with t=[X Y Z]TIndicate include the space CIEXYZ tristimulus values vector, therefore average value with
Substrate is in the color difference of the theoretical color of CIE XYZ color space under the conditions of specified value
Δ t=tspesub-trawsub (10)
In formula (10), tspesubIt is the tristimulus values vector of the calculated results of substrate under given standard conditions, trawsub
It is the average value of the tristimulus values vector of actual base in original image；
(2) color difference by substrate under the conditions of actual imaging image and specified value described in is brought into calibration equation, is led to
Cross the process that calibration equation calibrates actual imaging image pixel-by-pixel are as follows:
Firstly, wushu (5) is expressed as the form of formula (11) in the matrix form to simplify expression:
T=ALr (11)
In formula, t=[X Y Z]TIndicate the vector including the space CIEXYZ tristimulus values；A is the matrix of 3 × N, including phase
Machine or the color matching functions of observer；N is the quantity of various discrete wavelength data in visible-range；L is to include illumination light
The diagonal matrix of the Spectral power distribution data in source；R is the N-dimensional vector comprising observation object reflectance spectrum data；
Then, by formula (12), original image is converted to the imaging results being similar under given standard conditions:
trec=traw+αJΔt (12)
In formula (12), trecIt is the vector of gained tristimulus values after converting, trawIt is the tristimulus of original image to be converted
It is worth vector, α J is nonlinear transformation, under normal circumstances, can simplify and calculates gained by formula (10) for α J=1, Δ t；Original image
For the resulting original optical image of optical microscopy.
Case study on implementation:
Material therefor, instrument, method and data in following implementation are this field routine material without specified otherwise
Material, instrument, method and data can be obtained by commercial channel and open channel.
Embodiment 1:
Here one is chosen in 300nm oxide layer SiO2It include the practical light of 1-3 layers of molybdenum disulfide film in/Si substrate
Learn image as an example, original image is as shown in Figure 2.Standard illuminant A and CIE standard Observer color matching functions is taken to be used as to calibration
Floating screed part, by converting the image of available approximate given standard conditions, as shown in Figure 3.Conversion front and back and given standard
The molybdenum disulfide film thickness and substrate and the relationship of molybdenum disulfide color difference of condition are as shown in Figure 4.It can be seen that conversion so that
And the result for not meeting theoretical model can be close to specified criteria, and then is used for the precise measurement of molybdenum disulfide film thickness.It is whole
A process is as shown in Figure 5.
Embodiment 2:
Here under the conditions of choosing D65 standard sources and CIE standard Observer color matching functions, in 300nm oxide layer
SiO2It include the calculated value image of 1-5 layers of molybdenum disulfide film in/Si substrate, as shown in Figure 6.Take standard illuminant A with
CIE standard Observer's color matching functions is as given standard conditions, by converting available approximate given standard conditions
Image, as shown in Figure 7.Relationship such as Figure 12 of molybdenum disulfide film thickness and substrate and molybdenum disulfide color difference before and after converting,
Shown in Figure 13.
Embodiment 3:
Here under the conditions of choosing standard illuminant A and MT9V032 CMOS (Edmund Optics) color matching functions,
300nm oxide layer SiO2It include the calculated value image of 1-5 layers of molybdenum disulfide film in/Si substrate, as shown in Figure 8.Take A
Standard sources and CIE standard Observer color matching functions are available approximate given by converting as given standard conditions
The image of standard conditions, as shown in Figure 9.Convert the molybdenum disulfide film thickness of front and back and the pass of substrate and molybdenum disulfide color difference
System is as shown in Figure 12 and Figure 13.
Embodiment 4:
Here standard illuminant A and CIE standard Observer color matching functions are chosen, and automatic white flat using Gray World
Under conditions of accounting method calibration, in 300nm oxide layer SiO2The theoretical of molybdenum disulfide film in/Si substrate comprising 1-5 layers is counted
Calculation value image, as shown in Figure 10.It takes standard illuminant A and CIE standard Observer color matching functions as given standard conditions, leads to
The image for converting available approximate given standard conditions is crossed, as shown in figure 11.Convert front and back molybdenum disulfide film thickness with
And substrate and the relationship of molybdenum disulfide color difference it is as shown in Figure 12 and Figure 13.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications all should belong to this
The protection scope of invention the attached claims.
Claims (6)
1. a kind of high effective optical measurement method for two-dimensional material measured film thickness, it is characterised in that: the method is
The color calculating process of substrate and different-thickness two-dimensional material film to be measured under the conditions of specified value, and it is based on specified value
Under the conditions of color calculated result be standard, to the calibration process of actual imaging result.
2. a kind of high effective optical measurement method for two-dimensional material measured film thickness according to claim 1, special
Sign is: the measurement method includes:
Step 1: specified value condition, by the spectral power distribution of lighting source and camera or the color matching functions of observer
As the preset parameter under standard conditions；
Step 2: calculating the theory of the two-dimensional material film to be measured of different-thickness by reflectance spectrum caused by film interference
Color, the color of the two-dimensional material film of color and different-thickness as the substrate under standard conditions；And it will calculate
Theoretical color CIE Lab color space is converted by CIE XYZ color space；
Wherein, by reflectance spectrum caused by film interference, the theoretical color of the two-dimensional material film to be measured of different-thickness is calculated
Coloured silk, specifically: pass through the spectral power distribution and camera of the lighting source as preset parameter or the color-match letter of observer
The weighted sum of scalar product point or discrete values obtains the theoretical color accordingly in CIE XYZ color space；
Step 3: seeking the color of the color of the substrate in CIE Lab color space and the two-dimensional material film to be measured of different-thickness
Color color difference, and by the relationship of the color difference of its two-dimensional material film to be measured for indicating different-thickness and thickness；
Step 4: choosing the base part in the actual imaging color image of two-dimensional material film to be measured, and calculate selected area
Average value of the color in domain in CIE XYZ color space；Wherein, institute is imaged by the practical optical microscopy of the algorithm picks that flood
Obtain the base part in color image；
Step 5: theory of the substrate in CIE XYZ color space under the conditions of average value and specified value that calculating step 4 obtains
The color difference of color；The color difference of substrate under the conditions of actual imaging image and specified value is brought into calibration equation, calibration is passed through
Formula calibrates actual imaging image pixel-by-pixel, then the actual imaging image after calibration is transformed into CIE by CIE XYZ color space
Lab color space；
Step 6: calibration after actual imaging image in each pixel in CIE Lab color space color and calibration after
In image under the conditions of the color difference and specified value of base color average value the color difference of two-dimensional material film to be measured and thickness relationship
It compares, obtains the thickness of the two-dimensional material film of respective pixel color representative.
3. a kind of high effective optical measurement method for two-dimensional material measured film thickness according to claim 2, special
Sign is: in the step one, specified value condition, by the spectral power distribution of lighting source and camera or the face of observer
Color matching function is as the preset parameter under standard conditions, wherein the specified value condition refer to a given light source and
One camera is as reference standard；
It is described using the spectral power distribution of lighting source and camera or the color matching functions of observer as under standard conditions
Preset parameter, specifically:
Firstly, the model according to single thin film in the medium of two kinds of semo-infinites, the reflectivity of substrate is calculated by formula (1):
In formula, just like formula (2), formula (3) relationship:
Formula (1), formula (2), in formula (3), λ is lambda1-wavelength, niFor the refractive index of i-th layer of medium, diFor the thickness of i-th layer of medium
Degree, θiFor the incident light beam strikes angle for being incident on i-th layer of medium, it is generally the case that since the lighting source of optical microscopy is vertical
Incidence, therefore θi=0；
Then, the SiO in known thickness oxide layer plated film is calculated2The refractive index of two-dimensional material film in/Si substrate, such as formula (4)
It is shown:
4. a kind of high effective optical measurement method for two-dimensional material measured film thickness according to claim 3, special
Sign is: in the step two, by reflectance spectrum caused by film interference, calculating the two-dimensional material to be measured of different-thickness
The theoretical color of film, the color of the two-dimensional material film of color and different-thickness as the substrate under standard conditions
It is color；And convert the theoretical color of calculating to by CIE XYZ color space the process of CIE Lab color space, specifically:
Firstly, calculating the theoretical color of the two-dimensional material film to be measured of the color and different-thickness of substrate under the conditions of specified value:
In CIE XYZ color space, there is relationship shown in formula (5):
And Y value is normalized by formula (6):
In formula (5), (6), R (λ) indicates that, with the reflectivity of a length of function of visible light wave, I (λ) is the spectral power distribution of light source,For CIE standard Observer's color matching functions；
Then, it is chosen at the color difference defined in CIE Lab color space, it, will be theoretical by the function expression of formula (7) and (8)
Color is converted to CIE Lab color space by CIE XYZ color space, obtains CIE Lab color space coordinates numerical value:
In formula,Xn、Yn、ZnIt is CIE benchmark white point tristimulus values.
5. a kind of high effective optical measurement method for two-dimensional material measured film thickness according to claim 4, special
Sign is: in the step three, seeking the color of the substrate in CIE Lab color space and the two-dimentional material to be measured of different-thickness
Expect the color difference of the color of film, and the mistake of the relationship by the color difference and thickness of its two-dimensional material film to be measured for indicating different-thickness
Journey, specifically:
After obtaining CIE Lab color space coordinates numerical value, the color of the substrate in CIE Lab color space is calculated using formula (11)
With the color difference of the color of the two-dimensional material film to be measured of different-thickness:
In formula (9),WithIt is that two-dimensional material film and substrate are empty in CIE Lab color respectively
Between coordinate；Utilize the CIE Lab color of the two-dimensional material film of different-thickness under the conditions of formula (4)-formula (9) calculating specified value
Space coordinate, gained are the relationship of the color difference of the two-dimensional material film of different-thickness and thickness under the conditions of specified value, and with
This is as subsequent measurement standard.
6. a kind of high effective optical measurement method for two-dimensional material measured film thickness according to claim 5, special
Sign is: in the step five, substrate is in CIE XYZ color under the conditions of calculating the average value and specified value that step 4 obtains
The color difference of the theoretical color in space；The color difference of substrate under the conditions of actual imaging image and specified value is brought into calibration equation
In, calibrate actual imaging image pixel-by-pixel by calibration equation, then the actual imaging image after calibration is empty by CIEXYZ color
Between be transformed into the process of CIE Lab color space, specifically:
(1) theory of the substrate in CIE XYZ color space under the conditions of average value and specified value that the calculating step 4 described in obtains
The process of the color difference of color are as follows:
To simplify expression, with t=[X Y Z]TIndicate include the space CIEXYZ tristimulus values vector, therefore average value and specified
Substrate is in the color difference of the theoretical color of CIE XYZ color space under standard conditions
Δ t=tspesub-trawsub (10)
In formula (10), tspesubIt is the tristimulus values vector of the calculated results of substrate under given standard conditions, trawsubIt is former
The average value of the tristimulus values vector of actual base in beginning image；
(2) color difference by substrate under the conditions of actual imaging image and specified value described in is brought into calibration equation, passes through school
Quasi- formula calibrates the process of actual imaging image pixel-by-pixel are as follows:
Firstly, wushu (5) is expressed as the form of formula (11) in the matrix form to simplify expression:
T=ALr (11)
In formula, t=[X Y Z]TIndicate the vector including the space CIEXYZ tristimulus values；A be 3 × N matrix, including camera or
The color matching functions of observer；N is the quantity of various discrete wavelength data in visible-range；L is to include lighting source
The diagonal matrix of Spectral power distribution data；R is the N-dimensional vector comprising observation object reflectance spectrum data；
Then, by formula (12), original image is converted to the imaging results being similar under given standard conditions:
trec=traw+αJΔt (12)
In formula (12), trecIt is the vector of gained tristimulus values after converting, trawBe original image to be converted tristimulus values to
Amount, α J is nonlinear transformation, can simplify and calculates gained by formula (10) for α J=1, Δ t.
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| US11562919B2 (en) | 2020-02-24 | 2023-01-24 | Yangtze Memory Technologies Co., Ltd. | Systems and methods for semiconductor chip surface topography metrology |
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| US11448499B2 (en) | 2020-02-24 | 2022-09-20 | Yangtze Memory Technologies Co., Ltd. | Systems and methods for semiconductor chip surface topography metrology |
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| CN113137930A (en) * | 2021-04-25 | 2021-07-20 | 西南石油大学 | Visual and quantitative determination method for thinning of foam liquid film |
| CN113137930B (en) * | 2021-04-25 | 2022-02-01 | 西南石油大学 | Visual and quantitative determination method for thinning of foam liquid film |
| CN114235752A (en) * | 2021-12-17 | 2022-03-25 | 江南大学 | Optical method for identifying two-dimensional material layer number in two-dimensional three-dimensional material heterojunction |
| CN114235752B (en) * | 2021-12-17 | 2024-02-09 | 江南大学 | Optical method for identifying number of layers of two-dimensional material in two-dimensional three-dimensional material heterojunction |
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