CN110456104A - A kind of method and system of lack sampling raster scanning atomic force microscope high speed imaging - Google Patents
A kind of method and system of lack sampling raster scanning atomic force microscope high speed imaging Download PDFInfo
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- CN110456104A CN110456104A CN201910765767.6A CN201910765767A CN110456104A CN 110456104 A CN110456104 A CN 110456104A CN 201910765767 A CN201910765767 A CN 201910765767A CN 110456104 A CN110456104 A CN 110456104A
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- atomic force
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
- G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
- G01Q60/24—AFM [Atomic Force Microscopy] or apparatus therefor, e.g. AFM probes
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Abstract
The present invention relates to a kind of method and system of lack sampling raster scanning atomic force microscope high speed imaging, design the raster scan pattern of lack sampling first, and generate lack sampling raster scanning pattern with this；Then corresponding calculation matrix is constructed according to the lack sampling raster scanning pattern of generation；Atomic force microscope images are finally reconstructed according to calculation matrix and compressive sensing theory.The present invention can be improved the speed of atomic force microscope imaging.
Description
Technical field
The present invention relates to atomic force microscope technical field of imaging, especially a kind of lack sampling raster scanning atomic force microscopy
The method and system of mirror high speed imaging.
Background technique
Atomic force microscope (AFM) plays increasingly important role in many research objects, because it can be
The non-conductive sample of nanoscale and conducting sample are measured in liquid or air environment.However, atomic force microscope exists
When scanning imagery piece image, it is to carry out AFM imaging by conventional raster scan pattern, this usually requires to spend about 10
The time of minute or more completes.In addition, probe tip is contacted with sample excessively will lead to probe abrasion and specimen breakdown.This
Outside, the interaction of probe tip and sample will lead into image distortion.
The current feasible method of four classes has been applied to AFM and has realized high speed imaging.The first solution, rises hardware
Grade, such as scanner of small cantilever, new-type actuator and high resonant frequency, can be with the movement of acceleration mechanical component.But it is complicated
Hardware design and additional cost will be brought to the modification of standard commercial AFM.Second of solution is using some new controls
System strategy, as iterative method, robust control and feedforward and feedback control combine.The third method is to change scan path or sampling
Strategy is to design for scanning probe microscopy, such as helical scanning and Lisa are as scanned there are many non-grating scan pattern.
Fourth method is introduced into some advanced technologies in AFM measurement, due to its simplicity in practice, is always in recent years
Focus concerned by people.
Currently, high speed atomic force microscope is the urgent need of nanometer manufacture instrument field.High speed atomic force microscope energy
It enough realizes quick dynamic imaging, continuous phenomenon can be captured in a very short period of time, be particularly suitable for some biological fields
Dynamic observation and monitoring and nanometer manufacturing process in real-time quality detection.Therefore, the high speed of atomic force microscope is realized
Imaging is the urgent need of nanometer manufacture instrument field.
Summary of the invention
In view of this, the purpose of the present invention is to propose to a kind of sides of lack sampling raster scanning atomic force microscope high speed imaging
Method and system can be improved the speed of atomic force microscope imaging.
The present invention is realized using following scheme: a kind of method of lack sampling raster scanning atomic force microscope high speed imaging,
The following steps are included:
The raster scan pattern of lack sampling is designed, and lack sampling raster scanning pattern is generated with this；
Corresponding calculation matrix is constructed according to the lack sampling raster scanning pattern of generation；
Atomic force microscope images are reconstructed according to calculation matrix and compressive sensing theory.
Further, the raster scan pattern of the lack sampling specifically: afm tip along first sampling row from head end to
Before be moved to end, move again to the end of next sampling row, and the head end of the sampling row be moved in opposite direction, with this
Form has sampled all sampling rows.
Further, the raster scan pattern of the lack sampling includes rule format and random basis；Under rule format,
All sampling rows be all it is equally distributed, the columns of starting point is arranged in order in sampling row；Under random basis, with
Machine selection sampling row and starting point.
Further, the lack sampling raster scan pattern according to generation constructs corresponding calculation matrix specifically:
N-M row is deleted from the unit matrix of N × N, the calculation matrix of M row is generated, so that every a line in the calculation matrix
In 1 with the known pixels position in lack sampling raster scanning pattern it is corresponding so that calculation matrix measure each time only
Obtain a pixel value and from the lack sampling grating pattern；Wherein, M is sampling total in lack sampling raster scanning pattern
Point number.
Further, described to be specifically included according to calculation matrix and compressive sensing theory reconstruct atomic force microscope images
Following steps:
Step S1: measurement process is described using calculation matrix Ф, obtains formula (1):
Y=Φ x (1)；
In formula, y indicate atomic force microscope images measured value, x indicate atomic force microscope images to be reconstructed arrange to
Amount；
Step S2: vector x is indicated using following formula:
X=Ψ α (2)；
In formula, Ψ is sparse transformation base, and α is the rarefaction representation of x；
Step S3: it brings formula (2) into formula (1), obtains following formula:
Y=Φ Ψ α=A α (3)；
In formula, A is perception matrix；It obtains reconstruct by solving following optimization problem according to compressive sensing theory and obtains
Estimation sparse coefficient
Or
In formula, ε is error threshold；
Step S4: the sparse coefficient that reconstruct is obtainedIn substitution formula (2), outgoing vector is calculatedAccording to vectorObtain original
Sub- force microscope image.
Further, in step S3, following optimization problem is solved using TVAL3 algorithm or GPSR algorithm.
The present invention also provides a kind of based on lack sampling raster scanning atomic force microscope high speed imaging described above
The system of method, including processor, memory are stored with computer instruction in the memory, which is running
When, so that the method that processor executes lack sampling raster scanning atomic force microscope high speed imaging described above.
Compared with prior art, the invention has the following beneficial effects: the imaging of lack sampling grating mode proposed by the present invention
Strategy is a kind of superior compressed sensing atomic force microscope measurement scheme, compared to traditional raster-scan-imaging mode, tool
There is the advantages that imaging time is short, and sampling efficiency is high, while smaller to the damage of tip and sample.
Detailed description of the invention
Fig. 1 is the scan pattern schematic diagram of the lack sampling raster scan pattern of the embodiment of the present invention.
Fig. 2 is two kinds of forms of the lack sampling raster scan pattern of the embodiment of the present invention.Wherein (a) is rule format, (b)
For random basis.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
It is noted that described further below be all exemplary, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
A kind of method for present embodiments providing lack sampling raster scanning atomic force microscope high speed imaging, including following step
It is rapid:
The raster scan pattern of lack sampling is designed, and lack sampling raster scanning pattern is generated with this；
Corresponding calculation matrix is constructed according to the lack sampling raster scanning pattern of generation；
Atomic force microscope images are reconstructed according to calculation matrix and compressive sensing theory.
In the present embodiment, the raster scan pattern of the lack sampling specifically: afm tip is gone along first sampling from head
End (from left to right) is moved to end forward, moves again to the end of next sampling row, and in opposite direction (from right to left)
It is moved to the head end of the sampling row, has sampled all sampling rows in this format.
Preferably, the mode be by each sampling row (fast scan direction) uniform design sampled point construct,
The points in line number and sampling row wherein sampled are determined by sample rate.When starting, needle point is contacted with samples vertical, and
It will be lifted thereon after measuring at least one sample row.In mobile needle point on sampling row, it is contemplated that any two neighbouring sample point foot
It is enough close, it is not necessary that it is lifted from sample.
In the present embodiment, the raster scan pattern of the lack sampling includes rule format and random basis, such as Fig. 2 institute
Show；Under rule format, all sampling rows be all it is equally distributed, the columns of starting point is to be arranged in order in sampling row
's；Under random basis, random selection sampling row and starting point.
In the present embodiment, the lack sampling raster scanning pattern according to generation is specific to construct corresponding calculation matrix
Are as follows:
N-M row is deleted from the unit matrix of N × N, the calculation matrix of M row is generated, so that every a line in the calculation matrix
In 1 with the known pixels position in lack sampling raster scanning pattern it is corresponding so that calculation matrix measure each time only
Obtain a pixel value and from the lack sampling grating pattern；Wherein, M is sampling total in lack sampling raster scanning pattern
Point number.Every row of the calculation matrix only one 1 and N-1 0, it assures that compressed sensing measurement only needs image array every time
In an element.In addition, such a sparse matrix will not occupy too many memory.When calculation matrix Φ form such as
When lower, corresponding lack sampling raster scan pattern is as shown in Figure 1:
In the present embodiment, described specific according to calculation matrix and compressive sensing theory reconstruct atomic force microscope images
The following steps are included:
Step S1: measurement process is described using calculation matrix Ф, obtains formula (1):
Y=Φ x (1)；
In formula, y indicate atomic force microscope images measured value, x indicate atomic force microscope images to be reconstructed arrange to
Amount；
Step S2: vector x is indicated using following formula:
X=Ψ α (2)；
In formula, Ψ is sparse transformation base, and α is the rarefaction representation of x；Wherein, sparse transformation base can choose DCT base, FFT
Base, DWT base etc.；
Step S3: it brings formula (2) into formula (1), obtains following formula:
Y=Φ Ψ α=A α (3)；
In formula, A is perception matrix；For formula (1), due to the problem of dimension of Φ, i.e., the quantity of equation is less than unknown quantity
Quantity, solving in the case where known y and Φ is a underdetermined problem, and solution has nonuniqueness.But for formula (3), due to α
Be it is sparse, that is, have many 0, meet compressive sensing theory reconstruction condition；
The estimation sparse coefficient that reconstruct obtains is obtained by solving following optimization problem according to compressive sensing theory
Or
In formula, ε is error threshold；
Step S4: the sparse coefficient that reconstruct is obtainedIn substitution formula (2), outgoing vector is calculatedAccording to vectorObtain original
Sub- force microscope image, i.e., will be again by vectorIt is rearranged into the matrix form of n × n, i.e., by a column vector side of being converted into
Battle array, n are determined according to the actual situation.
In the present embodiment, in step S3, following optimization problem is solved using TVAL3 algorithm or GPSR algorithm.
For TVAL3, according to its two-dimensional structure restructuring matrix in the spatial domain, it is ensured that any sampled point to it most
The distance of Neighbor Points is short enough, particularly, due to can determine distance between the adjacent sampling row of any two, ensure that whole
In a scanning process, inserting needle is primary, therefore is most suitable for for rule format, can be with lower sample rate, high speed, high quality
Successfully restore afm image in ground.And for the random basis in lack sampling raster scan pattern, it is more suitable for using GPSR algorithm.
Wherein, two kinds of the detailed of restructing algorithm are expressed as follows:
(1) TVAL3 effectively combines alternating direction technology with Non-monotone linear search, when minimizing each iteration
Augmented Lagrangian Functions.The uniqueness of TV regularization is on condition that the gradient of original signal is sparse.It is rebuild for compressed sensing
The discrete TV model of noiseless can be write as:
In most cases, preferred isotropism TV, it may be assumed that
Wherein, Ii,jThe value for being matrix element at (i, j).
(2) GPSR algorithm solves the quadratic programming reconstruction of a kind of convex Non-smooth surface unconstrained optimization problem, these are asked
Topic is as caused by other inverse problems in compression sensing and signal processing and statistics.Specific formula is as follows:
In formula, τ is a non-negative parameter.
The present embodiment additionally provides a kind of based on lack sampling raster scanning atomic force microscope high speed imaging described above
Method system, including processor, memory be stored with computer instruction in the memory, which is transporting
When row, so that the method that processor executes described in any item lack sampling raster scanning atomic force microscope high speed imagings above.
The above described is only a preferred embodiment of the present invention, being not that the invention has other forms of limitations, appoint
What those skilled in the art changed or be modified as possibly also with the technology contents of the disclosure above equivalent variations etc.
Imitate embodiment.But without departing from the technical solutions of the present invention, according to the technical essence of the invention to above embodiments institute
Any simple modification, equivalent variations and the remodeling made, still fall within the protection scope of technical solution of the present invention.
Claims (7)
1. a kind of method of lack sampling raster scanning atomic force microscope high speed imaging, which comprises the following steps:
The raster scan pattern of lack sampling is designed, and lack sampling raster scanning pattern is generated with this；
Corresponding calculation matrix is constructed according to the lack sampling raster scanning pattern of generation；
Atomic force microscope images are reconstructed according to calculation matrix and compressive sensing theory.
2. a kind of method of lack sampling raster scanning atomic force microscope high speed imaging according to claim 1, feature
It is, the raster scan pattern of the lack sampling specifically: afm tip moves forward to end from head end along first sampling row
End, moves again to the end of next sampling row, and is moved to the head end of the sampling row in opposite direction, has sampled in this format
All sampling rows.
3. a kind of method of lack sampling raster scanning atomic force microscope high speed imaging according to claim 1, feature
It is, the raster scan pattern of the lack sampling includes rule format and random basis；Under rule format, all sampling rows
All be it is equally distributed, the columns of starting point is arranged in order in sampling row；Under random basis, random selection sampling row
And starting point.
4. a kind of method of lack sampling raster scanning atomic force microscope high speed imaging according to claim 1, feature
It is, the lack sampling raster scanning pattern according to generation constructs corresponding calculation matrix specifically:
From the unit matrix of N × N delete N-M row, generate M row calculation matrix so that in the calculation matrix in every a line 1
With with the known pixels position in lack sampling raster scanning pattern it is corresponding so that calculation matrix measures each time has to one
A pixel value and from the lack sampling grating pattern；Wherein, M is sampled point total in lack sampling raster scanning pattern
Number.
5. a kind of method of lack sampling raster scanning atomic force microscope high speed imaging according to claim 1, feature
Be, it is described according to calculation matrix and compressive sensing theory reconstruct atomic force microscope images specifically includes the following steps:
Step S1: measurement process is described using calculation matrix Ф, obtains formula (1):
Y=Φ x (1)；
In formula, y indicates that the measured value of atomic force microscope images, x indicate atomic force microscope images column vector to be reconstructed；
Step S2: vector x is indicated using following formula:
X=Ψ α (2)；
In formula, Ψ is sparse transformation base, and α is the rarefaction representation of x；
Step S3: it brings formula (2) into formula (1), obtains following formula:
Y=Φ Ψ α=A α (3)；
In formula, A is perception matrix；According to compressive sensing theory, by solving following optimization problem, obtain that reconstruct obtains estimates
Count sparse coefficient
S.t.y=Φ Ψ α；
Ors.t.||y-ΦΨα||2≤ε；
In formula, ε is error threshold；
Step S4: the sparse coefficient that reconstruct is obtainedIn substitution formula (2), outgoing vector is calculatedAccording to vectorObtain atomic force
MIcrosope image.
6. a kind of method of lack sampling raster scanning atomic force microscope high speed imaging according to claim 1, feature
It is, in step S3, following optimization problem is solved using TVAL3 algorithm or GPSR algorithm.
7. a kind of method based on lack sampling raster scanning atomic force microscope high speed imaging described in any one of claims 1-6
System, which is characterized in that including processor, memory, be stored with computer instruction in the memory, the computer instruction
At runtime, so that processor perform claim requires the described in any item lack sampling raster scanning atomic force microscope high speeds of 1-6
The method of imaging.
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