CN115144373A - Reflective laminated diffraction imaging method, device and system based on angle self-calibration - Google Patents
Reflective laminated diffraction imaging method, device and system based on angle self-calibration Download PDFInfo
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Abstract
The invention discloses a reflective laminated diffraction imaging method, device and system based on angle self-calibration, and belongs to the field of laminated diffraction imaging. The method is used for establishing a reflection type optical field propagation model based on a light field rotation mode, acquiring reconstructed images of a low-resolution sample and a probe by using a reflection type laminated diffraction algorithm, rotating the sample to find an angle with highest definition to realize rapid positioning of the angle of the sample to be detected, finally setting an angle interval of the sample and the detector, converging the angle interval to the direction with the smallest diffraction light intensity distribution error, completing angle error self calibration, realizing high-resolution reconstruction of the sample and the probe, and having the advantages of high calibration sensitivity, high operation speed, no need of additional information and the like.
Description
Technical Field
The invention belongs to the field of stacked diffraction imaging, and particularly relates to a reflective stacked diffraction imaging method, device and system based on angle self-calibration.
Background
The laminated diffraction imaging is a lens-free calculation imaging technology, utilizes the superposed scanning of a real space and the diffraction light intensity of a frequency space as constraints, and utilizes a laminated diffraction algorithm to iteratively reconstruct the amplitude and phase information of a sample, thereby generating larger influence in the field of X-ray and electron beam high-resolution imaging. Compared with the traditional transmission type laminated diffraction imaging system, the reflection type optical path system can be suitable for an opaque reflection type sample and has application prospect in an extreme ultraviolet band.
The principle of the reflective laminated diffraction imaging system is basically the same as that of the transmission system, but in a reflective optical path, a sample and an optical axis are obliquely arranged, and a diffraction propagation model between parallel planes is not applicable any more. The light field forward and backward diffraction propagation model between the inclined planes needs to know the included angle between the source plane and the observation plane in the model, the angle between the sample and the detector relative to the optical axis is difficult to accurately measure, and the quality of a reconstructed image can be directly influenced by the error of the assembly angle. The existing method for solving the angle error is to measure and calibrate the installation angle of the device before each experiment, and has the disadvantages of complex operation and limited precision.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a reflection type laminated diffraction imaging method, a device and a system based on angle self-calibration, and aims to solve the problems that the quality of a reconstructed image is poor and a calibration installation angle needs to be measured before each experiment due to angle errors between a sample to be measured, a detector and an optical axis in the existing imaging method.
In order to achieve the above object, in a first aspect, the present invention provides a reflective stacked diffraction imaging method based on angular self-calibration, the method being applied to a reflective stacked diffraction imaging system, and the method including:
s1, obtaining scanning position information and diffraction light field intensity information of a sample to be measured, a current angle theta to be calibrated between the sample to be measured and an optical axis, and a current angle alpha to be calibrated between a detector and the optical axis, and inputting the theta, alpha into a reflective laminated diffraction imaging algorithm to obtain an uncalibrated reconstructed sample and a probe;
s2, sampling an initial calibration range [ theta-delta theta ] at equal intervals 1 ,θ+Δθ 1 ]，Δθ 1 Representing an initial calibration offset resulting in a plurality of sampling angles { theta } m H, and theta are m Inputting the data into a rotation propagation model to simulate an uncalibrated reconstructed sample to rotate to each sampling angle plane, performing phase compensation on the rotated reconstructed sample, calculating the definition of the compensated reconstructed sample, and updating the current angle theta to be calibrated into a sampling angle corresponding to the maximum definition;
s3, sampling at equal intervals and accurately calibrating the range [ theta-delta theta ] 2 ,θ+Δθ 2 ]And detector angle interval [ alpha-delta alpha, alpha + delta alpha ]]，Δθ 2 Expressing the accurate correction offset to obtain multiple groups of sampling angle combinations { [ theta ] i ,α j ]Will each group [ theta ] i ,α j ]Inputting the data into a reflective laminated diffraction imaging algorithm, calculating the error between each group of simulated diffraction light intensity and actual diffraction light intensity, and acquiring a sampling angle combination corresponding to the minimum error;
and S4, updating the current angle theta to be calibrated and the current angle alpha to be calibrated into a sampling angle combination with the minimum error, correspondingly updating the reconstructed sample and the probe, judging whether the minimum error is smaller than a set threshold value, if so, outputting the corresponding reconstructed sample and the probe, otherwise, adjusting the accurate calibration range and the detector angle interval, and entering the step S3.
It should be noted that, the invention compares the error between each group of simulated diffraction light intensity and the actually measured light intensity through the multiple groups of independent angle combined reflective laminated diffraction iteration, gradually approaches the actual value of the angle between the sample and the detector and the optical axis, realizes the self calibration of the angle between the sample and the detector, and further realizes the high-quality reconstruction of the sample and the probe.
Preferably, the reflective stacked diffraction imaging algorithm is as follows:
(1) The point multiplication result is obtained by point multiplication of the probe and the reconstructed sample at the c scanning position so as to simulate the effect of the reconstructed sample on the probe;
(2) Rotating the point multiplication result to 0 degrees from theta 'by adopting a rotation propagation model to obtain a reflected light field function of a plane vertical to the optical axis, wherein the theta' is an included angle between the sample to be detected and the optical axis input in the algorithm;
(3) Simulating reflected light to be transmitted to the surface of the detector by adopting a light transmission model to obtain simulated diffraction optical field distribution of the target surface of the detector;
(4) Inputting [0 °, α' ] to a rotational propagation model to simulate a rotational diffracted light field; replacing the amplitude of the diffraction light field distribution simulated by the detection target surface with actually measured diffraction light intensity distribution, wherein the phase information is unchanged; after the amplitude value is replaced, inputting alpha ',0 degree into a rotation propagation model to simulate the inverse process of the diffraction light field rotation, wherein alpha' is an included angle between a detector input in an algorithm and an optical axis;
(5) Simulating the updated diffraction light field to reversely propagate to the position of the sample to be detected by adopting a light propagation model to obtain updated reflected light;
(6) Calculating the difference value of the reflected light field before and after updating, and rotating the difference value of the reflected light field from 0 degree to theta' by adopting a rotation propagation model to obtain the difference value of the reflected light field after rotation;
(7) Updating a sample and probe reconstruction image based on the rotated reflected light field difference value;
(8) Repeating (1) - (7) until the updating of all scanning positions is completed;
(9) And (3) calculating the root mean square error between the simulated diffraction light field distribution of all the scanning positions and the measured diffraction light field intensity, outputting the reconstructed sample and the probe after iteration when the root mean square error is smaller than a preset threshold value, and otherwise, turning to the step (1).
It should be noted that, the invention simulates the angle error between the target surface and the optical axis of the detector based on the rotation propagation model, further corrects the simulated diffraction light field obtained in the reflective stacked diffraction imaging algorithm, so that the amplitude constraint of the reciprocal space is more effective, after the angle error of the detector is compensated, the reconstruction quality of the probe and the sample can be further improved, and the assembly of the detector at any angle can be realized. The model is the basis of angle correction, and high-quality reconstruction of the sample and the probe can be realized through real space overlapping constraint and reciprocal space detector amplitude constraint through angle correction.
Preferably, the rotational propagation model is expressed as T β,β ', β represents the angle between the optical axis and the optical field plane before rotation, β' represents the angle between the optical axis and the optical field plane after rotation, and the specific details are as follows:
1) Calculating the frequency domain coordinate (u) of the reference plane according to the uniform sampling coordinate of the reference plane 0 ,v 0 ) Calculating the frequency domain coordinate of the reference plane along the optical axis direction
Wherein λ is a wavelength, the reference plane is a plane perpendicular to the optical axis;
2) Rotation matrix R y (beta) and (u) 0 ,v 0 ,w 0 ) T Multiplying to obtain the frequency domain coordinate of the source plane and rotating the matrix R y (β') and (u) 0 ,v 0 ,w 0 ) T Multiplying to obtain the frequency domain coordinate of the observation plane, wherein R y (β) represents a rotation matrix for rotating β about the Y-axis;
3) Acquiring a source plane light field, and calculating the frequency domain distribution of a reference plane according to non-uniform two-dimensional Fourier transform;
4) And converting the frequency domain distribution of the reference plane into the light field distribution of the observation plane according to the non-uniform two-dimensional inverse Fourier transform.
It should be noted that, at present, two methods of uniform interpolation and non-uniform fourier transform after rotation of frequency domain coordinates are mainly used for solving the problem of light field propagation between inclined planes, the former method is complex in process and low in precision, and the latter method is high in precision but high in calculation overhead. In addition, both methods use the source plane or the observation plane as a reference plane, and when both planes are not perpendicular to the optical axis, the high-frequency tilt phase may undersample the optical field and distort the optical field, subject to limited discrete sampling frequency. According to the method, a plane perpendicular to an optical axis is taken as a reference plane, and the non-uniform Fourier transform is used for associating the frequency domain distribution of the reference plane with a source plane and an observation plane in a real space, so that the precision loss caused by interpolation is avoided, and the sampling distortion when the reference plane is not perpendicular to the optical axis is also avoided. The light field rotation method has clear forward modeling process, is suitable for a source plane and an observation plane at any angle, has high operation speed, can realize the quick and accurate calculation of a sample reflected light diffraction light field at any angle, completes the self calibration of the reflective laminated diffraction imaging angle error, and further realizes the high-quality reconstruction of the sample and the probe.
Preferably, the calculation formula of the frequency domain distribution of the reference surface in step 3) is as follows:
Gd(u 0 ,v 0 )＝∫∫U 1 (x 1 ,y 1 )exp[-2πi(x 1 u 1 +y 1 v 1 )]dx 1 dy 1
wherein, U 1 (x 1 ,y 1 ) Representing a source planar light field, (x) 1 ,y 1 ) Represents the coordinates of the uniform sampling point of the source plane (u) 1 ,v 1 ) Representing the source plane frequency domain coordinates.
Preferably, the calculation formula of the light field distribution of the observation surface in step 4) is as follows:
U 2 (x 2 ,y 2 )＝∫∫Gd(u 0 ,v 0 )exp[2πi(x 2 u 2 +y 2 v 2 )]du 2 dv 2
wherein Gd (u) 0 ,v 0 ) Represents the frequency domain distribution of the reference plane (x) 2 ,y 2 ) Represents the coordinate of the uniform sampling point of the observation surface, (u) 2 ,v 2 ) Representing the observation plane frequency domain coordinates.
Preferably, step S2 comprises:
s21, sampling an initial calibration range [ theta-delta theta ] at equal intervals 1 ,θ+Δθ 1 ]Obtaining M sampling angles theta m ；
S22, rotating the reconstructed sample O (r) to a corresponding angle plane by using a rotation propagation model to obtain a rotated reconstructed sample O m (r)：
S23. After the standard sample is subjected to the same rotating processThe image is used as a reference to compensate the inclined phase to obtain a compensated reconstructed sample O' m (r) the standard sample O 0 (r) has an amplitude of 1 and a phase of 0;
s24, calculating the definition of the reconstructed sample after each sampling angle is compensated;
and S25, updating the current angle theta to be calibrated to be the sampling angle when the definition is maximum.
It should be noted that the reconstructed sample image obtained without angle correction is the projection of the actual sample to be measured in the propagation model containing the angle error plane, the invention simulates the high-precision rotation of the reconstructed sample, theoretically, the definition of the reconstructed sample is the highest when the reconstructed sample rotates to the correct angle plane, and the rapid positioning of the sample angle is realized by evaluating the definition of the rotated sample.
Preferably, step S3 comprises:
s31, sampling at equal intervals and accurately calibrating range [ theta-delta theta ] 2 ,θ+Δθ 2 ]And the detector angle interval [ alpha-delta alpha, alpha + delta alpha]To obtain n 1 ×n 2 Group angle combination { [ theta ] i ,α j ]}，i＝1,…,n 1 ，j＝1,…,n 2 ；
S32, each group [ theta ] i ,α j ]Inputting the data into a reflective laminated diffraction imaging algorithm, and rotating alpha after acquiring a diffraction light field j Obtaining the compensated diffraction intensity by simulating the angle error of an actual detector;
s33, calculating errors between the simulated diffraction light intensity and the actual light intensity of each group;
and S34, obtaining the angle combination with the minimum error.
Preferably, in step S4, if the minimum error is not lower than the set threshold, continuously determining whether both angles have not changed, if yes, increasing the number of iterations of the next round, otherwise, decreasing the number of iterations of the next round; and after each iteration, the accurate calibration range of the sample and the angle interval of the detector in the next iteration are reduced.
Preferably, Δ θ 2 ＝0.95×Δθ 2 ，Δα＝0.95×Δα。
It should be noted that the invention avoids that the local optimal solution is difficult to jump out due to too few iteration times when the angle is not changed by dynamically adjusting the iteration times, and also avoids extra calculation amount caused by redundant iteration when the angle is changed; and each iteration reduces the angle calibration interval of the next iteration, so that the oscillation of the angle in the interval can be avoided, and the gradual fine convergence of the angle to the correct value is realized.
To achieve the above object, in a second aspect, the present invention provides a reflective stacked diffraction imaging device based on angular self-calibration, comprising: a processor and a memory;
the memory is for storing a computer program or instructions;
the processor is adapted to execute the computer program or instructions in the memory such that the method of the first aspect is performed.
To achieve the above object, in a third aspect, the present invention provides a reflective stacked diffraction imaging system based on angular self-calibration, comprising:
a light source, a plane reflector, a beam expander, a diaphragm, a scattering sheet, a spherical reflector and a detector are sequentially arranged along the direction of an optical axis;
and the angle self-calibration-based reflective laminated diffraction imaging device in the second aspect is used for simultaneously obtaining a probe function, a reconstructed sample, and an accurate included angle between a sample detector and an optical axis through iterative self-calibration based on the diffraction light intensity distribution of reflected light at each scanning position, wherein the sample to be detected is positioned between the spherical reflector and the detector.
Generally, compared with the prior art, the technical scheme conceived by the invention has the following beneficial effects:
the invention provides a reflection type laminated diffraction imaging method based on angle self-calibration, which is characterized in that a reflection type optical field propagation model is established based on an optical field rotation mode, a reconstructed image of a low-resolution sample and a probe is obtained by utilizing a reflection type laminated diffraction algorithm, the sample is rotated to find an angle with the highest definition to realize the rapid positioning of the angle of the sample to be measured, finally, an angle interval of the sample and the detector is set, the angle interval converges towards the direction with the minimum diffraction light intensity distribution error, the angle error self-calibration is completed, the high-resolution reconstruction of the sample and the probe is realized, and the method has the advantages of high calibration sensitivity, high operation speed, no need of additional information and the like, is mutually self-adaptive to other calibration methods, and can be applied to the fields of biological sample imaging, semiconductor defect detection, micro-nano structure characterization and the like.
Drawings
FIG. 1 is a schematic diagram of a reflective stacked diffraction optical path provided by the present invention;
FIG. 2 is a schematic view of a recording of light intensity of a reflective stacked scanning diffraction beam with an angle error according to the present invention;
FIG. 3 is a flow chart of a reflective stacked diffraction imaging reconstruction method provided by the present invention;
FIG. 4 is a flow chart of a method for self-calibration of the angle of reflective stacked diffraction imaging provided by the present invention;
FIG. 5 is a diagram of a sample under test and an illumination probe according to an embodiment of the present invention;
FIG. 6 shows a reconstruction result without angle calibration according to an embodiment of the present invention;
FIG. 7 is a reconstructed result after angle calibration according to an embodiment of the present invention;
FIG. 8 is a sample angle convergence curve for different initial angle values provided by an embodiment of the present invention;
the same reference numbers will be used throughout the drawings to refer to the same or like elements or structures, wherein:
1-light source, 2-plane reflector, 3-beam expander, 4-diaphragm, 5-scattering sheet, 6-spherical reflector, 7-sample to be measured, and 8-detector.
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.
The invention provides a reflection type laminated diffraction imaging method based on angle self-calibration, which comprises the following steps:
Fig. 1 is a schematic diagram of a reflective stacked diffraction optical path provided by the present invention. As shown in fig. 1, a light source 1, a plane mirror 2, a beam expander 3, a diaphragm 4, a scattering sheet 5, a spherical mirror 6, a sample to be detected 7 and a detector 8 are sequentially arranged along an optical axis direction.
Preferably, the light source 1 is a high stability He-Ne laser with a wavelength of 632nm and a beam diameter (1/e) 2 ) 0.54mm, pointing drift less than 30urad, power of 1mW, and power fluctuation less than 0.1%.
Preferably, the plane mirror 2 is a broadband dielectric film mirror with reflectivity greater than 99%; the beam expander 3 selects a 10-time beam expander, and the light transmittance of the beam expander is greater than 95%; the diaphragm 4 adjusts the diameter of the light beam to 3mm; the diffusion angle of the scattering sheet 5 is selected to be 0.5 degree; the spherical reflector 6 is an aluminized parabolic reflector with an effective focal length of 152.4mm.
Preferably, the sample 7 to be tested is a reflective resolution test target, the highest line pair is 228lp/mm, and other micron-sized reflective samples to be tested can also be selected. The precise two-dimensional motion platform drives the sample 7 to move along a specific track, the stroke of the motion platform is 25 multiplied by 25mm, and the repeated positioning precision is 100nm.
Preferably, the detector 8 is a scientific research CCD camera, the size of the target surface is 18.1 multiplied by 13.6mm, the dynamic range is 14 bits, the quantum efficiency is 32 percent, the dark noise is about 1e-/s, and the detector with a refrigeration system can be selected, has smaller dark noise and larger dynamic range, and can greatly improve the imaging quality.
Adjusting the light path to ensure that: the beam expander 3, the diaphragm 4, the scattering sheet 5 and the spherical reflector 6 share the optical axis; the sample 7 to be measured is positioned behind the spherical reflector 6, the light field is slightly larger than the focal distance, 165mm is taken here, the incident angle is about 45 degrees, the distance between the reflector and the sample is adjusted, so that the incident beam is converged to the major axis of the elliptic illumination spot on the surface of the sample by the spherical reflector, the major axis is about 0.2mm-1mm, and 0.5mm is taken here; the detector 8 is positioned at the position of about 70mm of the light field behind the sample 7 to be detected, the angle of the sample 7 to be detected and the position of the detector 8 are finely adjusted, and the zero-order diffraction light is ensured to be in the central area of the target surface of the detector, and the target surface of the detector is approximately vertical to the main light.
FIG. 2 is a schematic diagram of a light intensity recording of a reflective stacked layer scanning diffraction with an angle error according to the present invention. After the optical path is adjusted, diffracted light is obtained through experiments, the process is shown in fig. 2, theta represents an included angle between the sample and the optical axis, and alpha represents an included angle between the detector and the optical axis. The precise two-dimensional displacement table drives the sample to move according to a preset scanning track, the common track comprises a linear grid, a spiral line, a concentric circle and the like, and the overlapping area of adjacent illumination light spots is ensured to be 70%. Preferably, a raster path with 10% random offset is set with a scan trajectory of 15 × 15, with a scan step size of 0.05mm. When the sample is moved to a preset position and is still, the detector records the diffraction light intensity of the position, and the sample is moved to the next position after exposure. The exposure time of all positions should be the same, the exposure time depends on the reflectivity of a sample to be detected, the brightest pixel of the target surface of the detector is required to be saturated as much as possible, preferably, the exposure time is set to be 1 second, multiple exposures can be carried out, and a high dynamic range diffraction light field is synthesized by using an HDR algorithm. Recording the information of the scanning track and the light intensity distribution I of the corresponding position c (r '), wherein c is a position serial number, and r' represents the reciprocal space coordinates of the detector plane.
And 2, initially guessing a probe function P (r) and a sample function O (r), wherein the initial value of the probe is an evenly distributed elliptical light field added with a 45-degree inclined phase, the initial value of the sample is a random number matrix with a proper size, the initial value of an included angle between an uncalibrated sample and an optical axis is set to be 45 degrees, and the initial value of an included angle between a target surface of the detector and the optical axis is set to be 0 degree. The method does not study the error of the scanning position and the error of the axial distance, so that the distance between the sample and the detector and the scanning position are assumed to be accurately known, and the angle calibration method provided by the invention is adaptive to other error calibration methods.
In the light path coordinate system established in the invention, the original point is the intersection point of the optical axis and the plane to be researched, the Z axis is the direction of the optical axis, the X axis is in the plane of the light beam and is vertical to the Z axis, and the Y axis is vertical to the XZ plane. Before introducing a detailed light field model, the method for calculating the diffraction propagation of the inclined plane, which is provided by the invention, is introduced, is suitable for the diffraction propagation among any inclined planes in the reflective stack diffraction, the core is the rotation transformation of any angle of the plane, and the method is frequently used subsequently, and the specific calculation method is as follows:
source plane uniform sampling point coordinate (x) 1 ,y 1 ) Reference plane uniform coordinate (x) perpendicular to the optical axis 0 ,y 0 ) Observation plane uniform observation coordinate (x) 2 ,y 2 ). It is generally recommended that the discrete sampling intervals of the local coordinate systems in the three real spaces are the same, the real space coordinate range should be more than twice the diameter of the light spot, and the discrete sampling frequency is required to contain more than 99% of energy in the frequency domain. From reference plane real space coordinates (x) 0 ,y 0 ) Calculating the corresponding frequency domain coordinates (u) 0 ,v 0 ) Frequency domain coordinates of the source plane and the observation plane are represented by (u) 0 ,v 0 ) The rotation change is obtained, and the transformation process is as follows:
(u,v,w) t ＝R·(u 0 ,v 0 ,w 0 ) t (1)
wherein, w 0 Representing the frequency domain coordinates of the source plane along the optical axis,
w represents the frequency domain coordinate of the observation plane along the optical axis direction, λ is the wavelength, R is the orthogonal rotation matrix, the rotation matrix of firstly rotating β around the Y axis and then rotating γ around the X axis is:
based on the above orthogonal rotation matrix, the frequency domain coordinate (u) of the reference plane 0 ,v 0 ) Calculating the frequency domain coordinates (u) of the source plane and the observation plane 1 ,v 1 ) And (u) 2 ,v 2 ). Because the frequency domain coordinates after rotation are non-uniform, the fast Fourier transform is not suitable, and according to the non-uniform two-dimensional Fourier transform, the plane light field U of the light source is formed by the light source 1 (x 1 ,y 1 ) Obtaining a frequency domain distribution Gd (u) of a reference plane 0 ,v 0 )：
Gd(u 0 ,v 0 )＝∫∫U 1 (x 1 ,y 1 )exp[-2πi(x 1 u 1 +y 1 v 1 )]dx 1 dy 1 (3)
Then according to the non-uniform two-dimensional inverse Fourier transform, the frequency domain of the reference plane is distributed with Gd (u) 0 ,v 0 ) Conversion to light field distribution of the observation plane:
U 2 (x 2 ,y 2 )＝∫∫Gd(u 0 ,v 0 )exp[2πi(x 2 u 2 +y 2 v 2 )]du 2 dv 2 (4)
the above method is a general rotation method, which can solve the rotation transformation of any angle plane, and for the sake of simplicity, only the rotation around the Y axis is considered in the subsequent propagation process, i.e. the case of γ =0, and the process of rotating the plane from β to β' is denoted as T β,β′ 。
Fig. 3 is a flowchart of a reflective stacked diffraction imaging reconstruction method provided by the present invention. As shown in fig. 3, in step 3, the c-th scanning position is selected, the sample is regarded as a thin sample, and the action process of the sample on the probe can be approximated as dot multiplication of two complex matrices, so that the physical meaning of each element in the complex matrix of the sample is as follows: the amplitude is the reflectivity to the incident light field, and the phase is the relative retardation to the phase of the incident light field. The sample reflected light is rotated through the optical field to be perpendicular to the optical axis (rotated from θ' to 0 °):
wherein the content of the first and second substances,
representing the emergent light field function of the c-th scanning position, theta' is the included angle between the sample to be measured and the optical axis input in the algorithm, P (r) represents the light field function of the incident probe, and O c (r) sample representing the c-th scanning position illuminated by the spotAnd (4) a product area function, wherein r represents real space coordinates and corresponds to (x, y).
Transmitting the reflected light field to far field to obtain the light field distribution phi of the detection target surface containing phase information c (r') the propagation mode is selected from a Fresnel diffraction propagation model, or a Fraunhofer propagation model which can be calculated faster can be selected,
representing the light field propagation model from the sample to the detector:
wherein phi is c (r ') represents the diffracted optical field distribution function for the detector plane at the c-th scan position, and r' represents the detector plane reciprocal space coordinates.
Using the actually measured light intensity I c (r') to Φ c (r') carrying out amplitude replacement without changing phase information, and carrying out inverse propagation to a plane perpendicular to the optical axis through a propagation model:
wherein the content of the first and second substances,
representing the function of the emergent light field after the c-th position update, I c (r') represents the actually measured diffracted light intensity distribution at the c-th scanning position.
The difference of the reflected light field before and after the update is calculated and the field is rotated to be parallel to the sample plane (from 0 ° to θ'), obtaining:
updating the selected region and the probe of the sample to be tested by using a public rPIE updating formula, wherein the updating formula containing specific coefficients is as follows:
wherein denotes the conjugate operation of the complex matrix, O c (r) and P (r) denote the sample and illumination probe at the c-th position before updating, O c '(r) and P' (r) denote a sample and an illumination probe at the c-th position after update, | calculation of luminance max Representing the maximum of the magnitudes of the elements in the matrix. The update coefficients 0.3 and 0.05 are usually 0-1, and the values affect the convergence speed and accuracy, and a set of empirical values are given here. 0.1 in the denominator is also an empirical value of the coefficient in the rPIE algorithm, and this value is adjusted according to actual conditions, generally speaking, the smaller the coefficient is, the higher the reconstruction accuracy is, but the algorithm robustness is low, and the empirical values in the two formulas are not required to be equal.
And 4, repeating the step 3 until all scanning positions are traversed, namely completing one iteration, and obtaining low-resolution reconstructed sample and probe images without angle calibration after 20 iterations, wherein the iteration times are not too high, otherwise, the local optimal solution is easy to fall into.
And step 5, the low-resolution sample and probe images obtained in the process are projections of the actual sample image on an angle error plane in the model, and the projections serve as uncorrected low-resolution P and O. FIG. 4 is a flow chart of a method for self-calibration of the angle of reflective stacked diffraction imaging provided by the present invention. As shown in fig. 4, θ can be preliminarily calibrated using this characteristic. The specific process is as follows:
setting an angle interval [ theta-delta theta ] in the left and right ranges of the angle theta to be calibrated 1 ,θ+Δθ 1 ]Within the interval, n angles are taken at equal intervals, wherein the mth angle is marked as theta m (m =1, 2.. N), preferably, Δ θ 1 The distance is 1 DEG (= 5 DEG), namely, 11 angles including theta are takenAnd (4) degree.
since the planar rotation introduces a tilt phase, the phase needs to be compensated. The amplitude information of the sample image can be directly sampled for the amplitude sample, and more generally, for the sample containing both amplitude and phase, a standard sample O with amplitude 1 and phase 0 can be introduced 0 (r) compensating the tilt phase by referring to the image of the standard sample subjected to the same rotation process, which can be expressed as a function of:
the method adopts a gray variance evaluation function to evaluate the image definition of n samples rotated to different angles, and can also evaluate the definition of the rotated samples by using methods such as information entropy, tenengrad function, FRC and the like. The gray variance was evaluated as follows, where θ =0.01,s m The greater the sharpness is:
step (ii) of 7, 7 finding the maximum S in the above steps except for the original plane that is not rotated m Entering a precise calibration step to determine the theta corresponding to the highest definition m Updating to the propagation model, i.e. updating epsilon, and rotating P (r) and O (r) to the angle plane correspondingly:
step 8, setting a sample angle interval [ theta-delta theta ] 2 ,θ+Δθ 2 ]And the detector angle interval [ alpha-delta alpha, alpha + delta alpha]And sequentially take n at equal intervals 1 ,n 2 An angle, denoted as θ i And alpha j And setting the initial iteration times. Preferably, Δ θ is set 2 ＝0.5°，Δα＝1°，n 1 ＝9，n 2 =3, initial number of iterations is 3.
Step 9, mixing different theta i And alpha j The angle is used as an input parameter of a reflective laminated diffraction reconstruction algorithm, and n is carried out 1 ×n 2 The groups are mutually independent, iterative reconstruction is realized, and the time consumption can be greatly reduced by using multi-thread parallel computing. The iterative process refers to step 3, but due to the introduction of the detector angle error, after the diffracted light field is obtained, the diffracted light field should be rotated by alpha j To simulate the angle error of the actual detector, equations (6) and (7) should be replaced with:
finding the sample angle theta corresponding to the minimum error i And the detector angle alpha j The sample angle θ and the detector angle α are updated, and the iteration results for the group are updated to sample O (r) and probe P (r). If the two angles are not changed, the number of times of next iteration is increased, otherwise, the number of times of next iteration is reduced, the range of the angle interval of the next iteration is reduced after each iteration, and the angle interval needs to be adjusted according to the actual conditionInter convergence speed determination, a preferred reference method is given here:
Δθ 2 ＝0.95×Δθ 2 ,Δa＝0.95×Δa (18)
and 11, repeating the steps 8 to 10 until the sample, the probe and the angle are completely converged, and finally obtaining a calibrated high-resolution sample reconstructed image and an accurate value of the actual angle of the sample and the detector.
For general laminated diffraction reconstruction, the convergence criterion is that the average Error of diffraction light intensity at each scanning position is less than 0.01, and because the structure of the reflective laminated diffraction probe is more complex, the convergence criterion selected in the embodiment is Error i,j <0.02 × 225=4.5. Wherein, error i,j For the error between the far field diffracted intensity and the actual measured intensity, 225 is the number of scan positions.
The reconstruction resolution can be estimated by the resolution formula:
in the formula, k is a coefficient, usually 0.5-1, lambda is a wavelength used for detection, NA is determined by the size of a target surface of the detector and the distance between the detector and a sample, and all line pairs (228 lp/mm) of a resolution target can be reconstructed in an experiment. The angle calibration algorithm can be converged to the range of +/-0.2 degrees around the correct angle under the condition that the initial angle error is within 10 degrees, and has higher sensitivity.
Examples
Fig. 5 is a diagram of a sample to be tested and an illumination probe according to an embodiment of the present invention, wherein (a) is an amplitude diagram of the sample to be tested used in a simulation process; (b) Is the light intensity distribution pattern of the probe used in the simulation process. The amplitude of a sample to be detected used in a simulation experiment is shown in a graph (a), the size of the sample is 332 multiplied by 332pixel, an angular momentum light beam with the light beam diameter of 128pixel and the wavelength of 632.8nm is constructed, the physical size corresponding to each element in the matrix is 3.4um, after the light beam is transmitted for 40mm through a spherical mirror (with the focal length of 25 mm), the light beam is incident on the surface of the sample to be detected at an incident angle of 45 degrees to form an elliptical initial illumination probe, the amplitude information of the initial illumination probe is shown in a graph (b), the probe is placed at a position 50mm after being displaced by the sample to be detected and is vertical to an optical axis, the pixels of the target surface of the probe are 128 multiplied by 128pixel, and the size of a single pixel is 72um. The sample is driven by a precise displacement platform to move along a preset track in two dimensions, the track is set to be a 15 x 15 grid path, the adjacent stepping amount is 8 pixels, the maximum random offset of 2 pixels is set to avoid periodic artifacts, and a total of 225 diffraction fields at different scanning positions are collected.
Fig. 6 shows the reconstruction results without angle calibration according to the embodiment of the present invention, in which (a) is the reconstruction result of the sample amplitude without angle calibration, (b) is the reconstruction result of the probe amplitude without angle calibration, and (c) is the error convergence curve without angle calibration. Random guessing is carried out on the illumination probe and the sample to be tested, the reflection type laminated diffraction imaging algorithm which is not subjected to angle calibration is adopted for iteration for 50 times, and the simulation result is shown in figure 6.
Fig. 7 is a reconstruction result after angle calibration according to an embodiment of the present invention, where (a) is a reconstruction result of an amplitude of a sample after angle calibration, (b) is a reconstruction result of an amplitude of a probe after angle calibration, and (c) is an error convergence curve after angle calibration. And then, randomly guessing the illumination probe and the sample to be detected, iterating for 50 times by adopting the angle self-calibration reflection type laminated diffraction imaging algorithm, wherein the simulation result is shown in fig. 7.
Fig. 8 is a sample angle convergence curve under different initial angle values according to an embodiment of the present invention. And finally, under the condition of different initial angle values, respectively using an angle self-calibration reflective laminated diffraction imaging algorithm to record different initial angle conditions and angle self-calibration convergence curves.
Simulation results show that when angle calibration is not carried out, the reconstruction quality of the illumination probe and the sample to be measured is poor, and obvious distortion occurs, so that the reconstructed sample provided by the invention is the projection of a real sample to be measured on a plane containing angle errors. After angle correction, the illumination probe and the sample to be measured are reconstructed by high resolution and high contrast, and the angle is converged to be close to a correct value. Finally, the result of fig. 8 shows that for the initial angle error up to 10 °, the angle self-calibration reflective stacked diffraction imaging method provided by the present invention can rapidly converge to the correct value, i.e. has strong robustness to the initial angle error.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A reflective stacked diffraction imaging method based on angle self-calibration is characterized in that the method is applied to a reflective stacked diffraction imaging system, and the method comprises the following steps:
s1, obtaining scanning position information and diffraction light field intensity information of a sample to be measured, a current angle theta to be calibrated between the sample to be measured and an optical axis, and a current angle alpha to be calibrated between a detector and the optical axis, and inputting the theta, alpha into a reflective laminated diffraction imaging algorithm to obtain an uncalibrated reconstructed sample and a probe;
s2, sampling an initial calibration range [ theta-delta theta ] at equal intervals 1 ,θ+Δθ 1 ]，Δθ 1 Representing the initial calibration offset, resulting in a plurality of sampling angles { theta } m H, and θ m Inputting the data to a rotation propagation model to simulate an uncalibrated reconstructed sample to rotate to each sampling angle plane, performing phase compensation on the rotated reconstructed sample, calculating the definition of the compensated reconstructed sample, and updating the current angle theta to be calibrated to a sampling angle corresponding to the maximum definition;
s3, sampling at equal intervals and accurately calibrating the range [ theta-delta theta ] 2 ,θ+Δθ 2 ]And detector angle interval [ alpha-delta alpha, alpha + delta alpha ]]，Δθ 2 Expressing the accurate correction offset to obtain multiple groups of sampling angle combinations { [ theta ] i ，α j ]Will each group [ theta ] i ，α j ]Inputting the data into a reflective laminated diffraction imaging algorithm, calculating the error between each group of simulated diffraction light intensity and actual diffraction light intensity, and obtaining the minimum errorCorresponding sampling angle combinations;
and S4, updating the current angle theta to be calibrated and the current angle alpha to be calibrated into a sampling angle combination with the minimum error, correspondingly updating the reconstructed sample and the probe, judging whether the minimum error is smaller than a set threshold value, if so, outputting the corresponding reconstructed sample and the probe, otherwise, adjusting the accurate calibration range and the detector angle interval, and entering the step S3.
2. The method of claim 1, wherein the reflective stacked diffraction imaging algorithm is specified as follows:
(1) The point multiplication result is obtained by point multiplication of the probe and the reconstructed sample at the c scanning position so as to simulate the effect of the reconstructed sample on the probe;
(2) Rotating the point multiplication result from theta 'to 0 degrees by adopting a rotation propagation model to obtain a reflected light field function of a plane perpendicular to the optical axis, wherein the theta' is an included angle between the sample to be detected and the optical axis input in the algorithm;
(3) Simulating reflected light to be transmitted to the surface of the detector by adopting a light transmission model to obtain simulated diffraction optical field distribution of the target surface of the detector;
(4) Inputting [0 °, α' ] to a rotational propagation model to simulate a rotational diffracted light field; replacing the amplitude of the diffraction light field distribution simulated by the detection target surface with actually measured diffraction light intensity distribution, wherein the phase information is unchanged; after the amplitude value is replaced, inputting alpha ',0 degree into a rotation propagation model to simulate the inverse process of the diffraction light field rotation, wherein alpha' is an included angle between a detector input in an algorithm and an optical axis;
(5) Simulating the updated diffraction light field to reversely propagate to the position of the sample to be detected by adopting a light propagation model to obtain updated reflected light;
(6) Calculating the difference value of the reflected light field before and after updating, and rotating the difference value of the reflected light field from 0 degree to theta' by adopting a rotation propagation model to obtain the difference value of the reflected light field after rotation;
(7) Updating a sample and probe reconstruction image based on the rotated reflected light field difference value;
(8) Repeating (1) - (7) until the updating of all scanning positions is completed;
(9) And (3) calculating the root mean square error between the simulated diffraction light field distribution of all scanning positions and the measured diffraction light field intensity, outputting the reconstructed sample and the probe after iteration when the root mean square error is smaller than a preset threshold value, and otherwise, turning to the step (1).
3. The method of claim 1 or 2, wherein the rotational propagation model is expressed as T β,β′ Beta represents an included angle between the light field plane and the optical axis before rotation, and beta' represents an included angle between the light field plane and the optical axis after rotation, and the specific steps are as follows:
1) Calculating the frequency domain coordinate (u) of the reference plane according to the uniform sampling coordinate of the reference plane 0 ,v 0 ) Calculating the frequency domain coordinates of the reference plane along the optical axis
Wherein λ is a wavelength, the reference plane is a plane perpendicular to the optical axis;
2) Rotation matrix R y (β) and (u) 0 ,v 0 ,w 0 ) T Multiplying to obtain the frequency domain coordinate of the source plane and rotating the matrix R y (β') and (u) 0 ,v 0 ,w 0 ) T Multiplying to obtain the frequency domain coordinate of the observation plane, wherein R y (β) represents a rotation matrix rotating β about the Y-axis;
3) Acquiring a source plane light field, and calculating reference plane frequency domain distribution according to non-uniform two-dimensional Fourier transform;
4) And converting the frequency domain distribution of the reference plane into the light field distribution of the observation plane according to the non-uniform two-dimensional inverse Fourier transform.
4. The method of claim 3, wherein the frequency domain distribution of the reference plane in step 3) is calculated as follows:
Gd(u 0 ,v 0 )＝∫∫U 1 (x 1 ,y 1 )exp[-2πi(x 1 u 1 +y 1 v 1 )]dx 1 dy 1
wherein, U 1 (x 1 ，y 1 ) Representing a source planar light field, (x) 1 ，y 1 ) Represents the coordinates of the source plane uniform sampling point (u) 1 ，v 1 ) Representing the source plane frequency domain coordinates.
5. The method according to claim 3, wherein the calculation formula of the light field distribution of the observation plane in step 4) is as follows:
U 2 (x 2 ,y 2 )＝∫∫Gd(u 0 ,v 0 )exp[2πi(x 2 u 2 +y 2 v 2 )]du 2 dv 2
wherein Gd (u) 0 ，v 0 ) Representing the frequency domain distribution of the reference plane, (x) 2 ，y 2 ) Represents the coordinate of the uniform sampling point of the observation surface (u) 2 ，v 2 ) Representing the observation plane frequency domain coordinates.
6. The method according to any of claims 1 to 5, wherein step S2 comprises:
s21, equal-interval sampling initialization calibration range [ theta-delta theta 1 ,θ+Δθ 1 ]Obtaining M sampling angles theta m ；
S22, rotating the reconstructed sample O (r) to a corresponding angle plane by using a rotation propagation model to obtain a rotated reconstructed sample O m (r)：
S23, compensating the tilt phase by taking the image of the standard sample subjected to the same rotation process as a reference to obtain a compensated reconstructed sample O' m (r) the standard sample O 0 (r) has an amplitude of 1 and a phase of 0;
s24, calculating the definition of the reconstructed sample after each sampling angle is compensated;
and S25, updating the current angle theta to be calibrated to be the sampling angle when the definition is maximum.
7. The method according to any one of claims 1 to 3, wherein in step S4, if the minimum error is not lower than the set threshold, it is continuously determined whether both angles have not changed, if so, the number of iterations of the next round is increased, otherwise, the number of iterations of the next round is decreased; and after each iteration, the accurate calibration range of the sample and the angle interval of the detector in the next iteration are reduced.
8. The method of claim 7, wherein Δ θ 2 ＝0.95×Δθ 2 ，Δα＝0.95×Δα。
9. A reflective stacked diffraction imaging device based on angular self-calibration, comprising: a processor and a memory;
the memory is for storing a computer program or instructions;
the processor is for executing the computer program or instructions in the memory, causing the method of any of claims 1-8 to be performed.
10. A reflective stacked diffraction imaging system based on angular self-calibration, comprising:
a light source, a plane reflector, a beam expander, a diaphragm, a scattering sheet, a spherical reflector and a detector are sequentially arranged along the direction of an optical axis;
the angle self-calibration based reflective stacked diffraction imaging device of claim 9, wherein the angle self-calibration based reflective stacked diffraction imaging device is configured to obtain a probe function, a reconstructed sample, and an accurate included angle between a sample detector and an optical axis through iterative self-calibration based on a diffraction light intensity distribution of reflected light at each scanning position, and the sample to be measured is located between the spherical reflector and the detector.
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