CN111127473A - High-speed high-precision region block wavefront reconstruction method based on optimization strategy - Google Patents

High-speed high-precision region block wavefront reconstruction method based on optimization strategy Download PDF

Info

Publication number
CN111127473A
CN111127473A CN201911082211.3A CN201911082211A CN111127473A CN 111127473 A CN111127473 A CN 111127473A CN 201911082211 A CN201911082211 A CN 201911082211A CN 111127473 A CN111127473 A CN 111127473A
Authority
CN
China
Prior art keywords
sub
phase
subblocks
block
region
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201911082211.3A
Other languages
Chinese (zh)
Other versions
CN111127473B (en
Inventor
张晓芳
纪钟晔
郑志立
董冰
任虹禧
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN201911082211.3A priority Critical patent/CN111127473B/en
Publication of CN111127473A publication Critical patent/CN111127473A/en
Application granted granted Critical
Publication of CN111127473B publication Critical patent/CN111127473B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/11—Region-based segmentation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/187—Segmentation; Edge detection involving region growing; involving region merging; involving connected component labelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10004—Still image; Photographic image

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Image Analysis (AREA)

Abstract

The invention discloses a high-speed high-precision region blocking wavefront reconstruction method based on an optimization strategy, which reduces the total calculation amount of a high-sampling-rate self-adaptive optical system, improves the wavefront reconstruction speed and improves the bandwidth of the self-adaptive optical system by a region blocking splicing mode according to a certain optimization strategy on the premise of ensuring the reconstruction precision.

Description

High-speed high-precision region block wavefront reconstruction method based on optimization strategy
Technical Field
The invention belongs to the technical field of adaptive optics, and particularly relates to a high-speed high-precision regional block wavefront reconstruction method based on an optimization strategy.
Background
The earliest researchers of the regional wavefront reconstruction method were Fried, the proposed Fried model laid a good foundation for fast and accurate wavefront reconstruction and elimination of the problem of pathological solution, and the Hudgin model and the Southwell model were proposed later by Hudgin and Southwell et al. Based on the three models, the existing method focuses on the reconstruction model and the improvement and optimization of the reconstruction method so as to improve the reconstruction precision of the method and expand the application range of the method. As in 2014, Biswajit Pathak et al improved the model by introducing four data points in the oblique direction based on the Southwell model. The improved model is shown in fig. 1.
Compared with the original Southwell model, each mathematical relation has two more phase reconstruction points to be solved and two slope data. The simulation result shows that the improved model has higher reconstruction precision.
In 2015, li lovely sun et al introduced a weight factor into the reconstruction model and improved the reconstruction model, so as to realize the area-method wavefront reconstruction of pupils and non-square apertures in any shapes. And the algorithm is verified through simulation experiments, and the experimental result shows that the reconstruction effect of the improved model on the non-square domain is higher than that of the traditional Southwell model algorithm.
As another example, in 2016, Sylvain Bonnefond et al studied the wavefront reconstruction of the region method in the case of unconnected domains, and concluded that the minimum variance method has the highest recovery effect in the case of unconnected domains.
In 2017, LEI HUANG et al improve the region method model according to the full differential concept, so that the region method can be applied to wavefront reconstruction under the condition of any quadrilateral aperture. As shown in fig. 2.
Experiments verify that the reconstruction error of the improved model integrated with the full differential thought for the non-square aperture is far lower than that of the common Southwell model and the interpolation model.
However, the research on the solving speed of the existing method is almost blank in recent years, and a few articles are published. With the expansion of the application field of the adaptive optics system, the requirements on the precision and the speed of the reconstruction method become higher and higher. Although the wang wave of Beijing technology university has been proposed to reduce the amount of calculation by using blocks in the past 90 s, the total number of sampling points needs to be known in advance, and an inverse matrix needs to be calculated and stored, which has a problem of poor versatility.
Disclosure of Invention
In view of this, the invention provides a high-speed high-precision region blocking wavefront reconstruction method based on an optimization strategy, which can reduce the total calculation amount of a high-sampling-rate adaptive optical system, improve the wavefront reconstruction speed and improve the bandwidth of the adaptive optical system on the premise of ensuring the reconstruction precision.
The technical scheme for realizing the invention is as follows:
a high-speed high-precision region blocking wavefront reconstruction method based on an optimization strategy comprises the following steps:
step one, carrying out region segmentation on an optical wave phase point matrix to be reconstructed, and dividing obtained sub-regions into three types according to the distribution condition of phase points: connected sub-blocks, semi-connected sub-blocks and non-connected sub-blocks;
performing wavefront reconstruction on the connected subblocks and the semi-connected subblocks;
decomposing the non-connected subblocks into a plurality of semi-connected subblocks, finding the real phase heights of the plurality of semi-connected subblocks by utilizing the common areas of the plurality of semi-connected subblocks, and obtaining the phase distribution of the non-connected subblocks by taking a union set to realize the wavefront reconstruction of the non-connected subblocks;
adjusting the phase heights of the connected sub-blocks and the semi-connected sub-blocks to enable the sum of absolute values of phase differences of each phase point in the public area and the phase point corresponding to the phase point to be minimum;
step three, performing mean value smoothing treatment on the phases in the public areas of the two adjacent sub-block areas after adjustment;
step four, according to the phase in the common area after the smoothing treatment, the sum of absolute values of phase differences between each phase point in the common area of the semi-connected subblocks obtained by decomposing the non-connected subblocks and the phase point corresponding to the phase point is minimized, so that the translation amount of the semi-connected subblocks obtained by decomposing the non-connected subblocks is obtained, and the non-connected subblocks are filled in the position corresponding to the wavefront in a translation manner;
and fifthly, performing mean value smoothing treatment on the phases in the public areas of the filled non-connected sub-blocks to complete block wavefront reconstruction of the area to be reconstructed.
Further, the translation amount in the fourth step is specifically:
the phase of a common region on a semi-connected sub-block obtained by decomposing a non-connected sub-block is assumed to be A1To AnN in total, the corresponding phase in the common region after smoothing process is B1To BnThen, the process of the present invention,
Figure BDA0002264317560000031
and m when the minimum value is obtained is the translation amount.
Further, when the phase point matrix of the optical wave to be reconstructed is N × N and the size of the sub-region obtained after the region division is N × N, the solution rate of the wavefront reconstruction is expressed as:
Figure BDA0002264317560000032
find n when Sp | n takes a minimum valueminThen n ismin×nminI.e. the optimal partition size, where Compro|n＝Cominv|n+Commul|n+Compis|n，
Cominv|n＝[(n+1)4(2n2+2n+1)+(n+1)6]+[(nm+m)2(2nm+m-n)+(nm+m)3]×2+[m4(2m2-2m+1)+m6]，
Figure BDA0002264317560000033
Figure BDA0002264317560000041
Figure BDA0002264317560000042
Comcla＝3N6-2N5+8N4-6N3+3N2；
Wherein the content of the first and second substances,
Figure BDA0002264317560000043
representing the phase points remaining after the segmentation to the end because of the inability to divide exactly.
Has the advantages that:
1. according to the method, through a mode of region block splicing, on the premise of ensuring the reconstruction accuracy, although the calculation amount of matrix multiplication in the solving process is increased, the calculation amount of matrix inversion is greatly reduced compared with the prior art, and the total calculation amount is effectively reduced, so that the wavefront reconstruction speed is increased, and the bandwidth of the adaptive optical system is improved.
2. The block optimization strategy provided by the method solves the size of the optimal segmentation area based on the computation complexity theory, thereby ensuring the maximum compression of the computation amount.
Drawings
FIG. 1 is a schematic diagram of a modified Southwell model; (a) a model diagram of 9 adjacent grid points, and (b) a slope information diagram used.
FIG. 2 is a schematic representation of a region method model before and after modification; (a) in the original model, the distance between sampling points cannot be determined; (b) and improving the model, and decomposing the distance between sampling points in the horizontal direction and the vertical direction.
FIG. 3 is a flow chart of the method of the present invention.
FIG. 4 is a schematic diagram of a connected sub-block, a semi-connected sub-block, and a non-connected sub-block of the present invention; (a) a connected subblock region, (b) a semi-connected subblock region, and (c) a non-connected subblock region.
FIG. 5 is an exploded view of a non-connected sub-block region.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a high-speed high-precision area blocking wavefront reconstruction method based on an optimization strategy, which specifically comprises the following steps as shown in figure 3:
step one, carrying out region segmentation on an optical wave phase point matrix to be reconstructed, and dividing obtained sub-regions into three types according to the distribution condition of phase points: connected sub-blocks, semi-connected sub-blocks and non-connected sub-blocks;
decomposing a non-connected subblock into a plurality of semi-connected subblocks, finding the real phase heights of the plurality of semi-connected subblocks by utilizing the common areas of the plurality of semi-connected subblocks, and taking a union to obtain the phase distribution of the non-connected subblocks;
1. region segmentation
The reconstruction region is divided in order to reduce the operation scale in wavefront reconstruction and increase the solving speed. When the reconstruction region is divided, the size and the number of the sub-block regions have a mutual restriction relationship, and simultaneously, the size and the number jointly determine the solving time. If the subblock area is small, the time for solving the inverse matrix is less, but the number of subblocks is increased, so that the operation times of matrix multiplication are increased when the phase of the subsequent subblock area is recovered, and the time consumed in the matrix multiplication is increased; on the contrary, if the sub-block area is large, it takes long time to solve the inverse matrix, but the number of sub-blocks is reduced, so that the time consumption of matrix multiplication in the subsequent operation is reduced.
Now, a specific method of region segmentation is described, assuming that the size of the phase point matrix to be obtained in the reconstruction region is a × b. The sub-block area is n × n, so that in the vertical direction, the sub-block area is divided every n rows, and after division, in the vertical direction, the number c of the sub-blocks satisfies:
Figure BDA0002264317560000061
(
Figure BDA0002264317560000062
indicating upward rounding)
Similarly, in the horizontal direction, the division is performed once every n columns, and after the division, in the horizontal direction, the number d of blocks satisfies:
Figure BDA0002264317560000063
the blocks which are increased due to rounding up are used for storing the phase points to be solved which are divided to the end and are not evenly divided by n. For a simple example, if the partitioned area size is 11 × 11 and the sub-block area size is 10 × 10, the partitioned area will be divided into 2 blocks in the horizontal direction, where the first block column number is 10 and the remaining 1 column is placed in the second block. The same applies to the vertical direction.
After the preliminary region segmentation is completed, each sub-block region can be regarded as an element in a matrix, all sub-block regions jointly form a block matrix with the size of C × d, the matrix is marked as C, and each sub-block region can be expressed as Ci，jWherein i and j represent subblock regions C, respectivelyi，jThe position of the rows and columns in the block matrix.
After the total number of the blocks is determined, then expanding the sub-block area, specifically operating as follows: subblock region C1～c-1，1～d-1Respectively expanding a row and a column downwards and rightwards; subblock region Cc，1～d-1Expanding a column to the right; subblock region C1～c-1，dExpanding one row downwards; subblock region Cc，dNo expansion processing is performed. Thereby resulting in a final subblock region.
2. Wavefront restoration
After the region segmentation is completed, the wavefront reconstruction needs to be performed on each sub-block region by using a region method. Since the pupil of the optical system may have any shape, there may be invalid regions in the phase point matrix, and therefore, after the region division, the phase points to be acquired are not necessarily distributed over the whole sub-block region. According to the distribution of the phase points to be obtained, the subblock regions can be divided into three types, namely a connected subblock region, a semi-connected subblock region and a non-connected subblock region, as shown in fig. 4.
In the communicated subblock region, phase points to be solved are distributed in the whole subblock region; in the semi-connected sub-block area, an invalid area without a phase point to be solved exists; in the non-connected sub-block area, the invalid area divides the phase point to be solved into several independent clusters. The following describes how to use the region method to realize the wavefront reconstruction of the three different types of sub-block regions.
2.1 connected subblock region reconstruction
Reconstruction of the connected sub-block region is based on the Southwell model, and the solution thereof can be expressed as:
Figure BDA0002264317560000071
wherein A iseAnd DeFor the expansion coefficient matrix, S is the wavefront slope vector, d is the sampling interval,
Figure BDA0002264317560000072
is the vector formed by the phases to be solved.
2.2 semi-connected sub-Block region reconstruction
The reconstruction of the semi-connected sub-block region is also based on the Southwell model, but the Southwell model needs to be improved, and the improved model is as follows:
Figure BDA0002264317560000073
Figure BDA0002264317560000074
Figure BDA0002264317560000075
Figure BDA0002264317560000076
wherein the content of the first and second substances,
Figure BDA00022643175600000710
and
Figure BDA0002264317560000078
the slopes of (i, j) in the x-direction and the y-direction, respectively,
Figure BDA0002264317560000079
for the phase to be determined at (i, j), the factor sigma is determinedi，jIs defined as σ when the valid phase point to be found at (i, j)i，j1 is ═ 1; when (i, j) is located in the invalid region, σi，jThe result of the operation of nan, nan and any parameters is still nan, which indicates that there is no phase point to be found at (i, j). In the above four equations, the equation is valid only when all the decision factors have values of 1, otherwise, it needs to be eliminated.
After the improvement of the model is completed, when the phase distribution in the semi-connected sub-block area is solved, the vector S and the vector S are still needed to be firstly used
Figure BDA0002264317560000081
The matrix A and the matrix D are constructed by the arrangement mode, then invalid relational expressions in the matrix A and the matrix D are removed according to the value of a judgment factor, then the matrix A and the matrix D are expanded and complemented according to the limiting condition that the sum of the phases of all reconstruction points is zero, and finally the phase distribution condition in the area is obtained through inversion and matrix multiplication operation.
In the semi-connected sub-block region, assuming that the size of the phase point matrix including the invalid phase points to be solved is a × b, the modified Southwell model has the following same points as the original Southwell model:
Figure BDA0002264317560000082
there are still a × b elements in the vector, and 2 × a × b elements in the S vector. In the improved model, the elements in the matrix D satisfy:
Figure BDA0002264317560000083
Figure BDA0002264317560000084
the remaining elements in matrix D are 0, in which case matrix D is (2ab-a-b) x (2 ab).
The elements in matrix a satisfy:
Figure BDA0002264317560000085
Figure BDA0002264317560000086
the remaining elements in matrix A are all 0, in which case matrix A is (2ab-a-b) x (ab).
After the construction of the matrixes D and A is completed, the rows and columns of the D matrix and the A matrix, the value of which is nan, are found and removed from the matrixes, and simultaneously, the vectors are also removed
Figure BDA0002264317560000096
Elements with subscripts in S identical to the nan decision factor subscript are removed. Respectively recording the matrix and the vector after eliminating the invalid elements as Dres、Ares、
Figure BDA0002264317560000091
And Sres。
For AresIn the case of rank lacking 1, the same processing manner as the original Southwell model is adopted. Recording the related variable after the rank is complemented as
Figure BDA0002264317560000092
And
Figure BDA0002264317560000093
then vector on semi-connected sub-block region
Figure BDA0002264317560000094
Satisfies the following conditions:
Figure BDA0002264317560000095
2.3 non-connected sub-block region reconstruction
For a non-connected sub-block region, it can be decomposed into a plurality of mutually independent semi-connected sub-block regions, as shown in fig. 5.
For each semi-connected sub-block region forming the non-connected sub-block region, the wave front on the semi-connected sub-block region can be reconstructed by adopting a method in 2.2 subsections, and the reconstructed wave front piston and the actual wave front piston have deviation due to the introduction of a limiting condition that the sum of phases of all reconstruction points is zero, so that the reconstructed wave front piston and the actual wave front piston cannot be directly superposed to be used as the wave front on the non-connected sub-block region. However, considering the characteristic that the non-connected wave fronts in the block areas are connected with the wave fronts on the adjacent sub-block areas, if the piston on the adjacent sub-block areas is accurately known, each wave front on the non-connected sub-block areas can be independently translated to a correct piston position according to the piston in the translation reference area on the adjacent sub-block areas, and then the translated wave fronts are superposed to finally realize the reconstruction of the non-connected sub-block areas. Therefore, in the block region method, reconstruction and splicing of the connected sub-block region and the semi-connected sub-block region are required to be completed, and then reconstruction of the non-connected sub-block region is required.
Adjusting the phase heights of the connected sub-blocks and the semi-connected sub-blocks to enable the sum of absolute values of phase differences of each phase point in the public area and the phase point corresponding to the phase point to be minimum;
3. sub-block translation
As can be seen from the sub-block region expansion method introduced in section "region segmentation", the phase points of two adjacent sub-block regions in the common region have a one-to-one correspondence relationship. Let the phase point of a certain block of sub-block region in the common region be
Figure BDA0002264317560000101
The phase point in the common area corresponding thereto on the other sub-block area is
Figure BDA0002264317560000102
And because the constraint condition that the sum of the phases of all reconstruction points to be solved is 0 is used when the connected sub-block region and the semi-connected sub-block region are reconstructed, an unknown pixel deviation exists between the calculated phase distribution and the actual phase distribution in each reconstructed sub-block region. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002264317560000103
the piston deviation from its actual phase can be expressed as
Figure BDA0002264317560000104
In the same way, the method for preparing the composite material,
Figure BDA0002264317560000105
the piston deviation from its actual phase can be expressed as
Figure BDA0002264317560000106
Thus, the method can obtain the product,
Figure BDA0002264317560000107
and
Figure BDA0002264317560000108
with a piton deviation of
Figure BDA0002264317560000109
If the sub-block region is translated, it can be reduced
Figure BDA00022643175600001010
When translating to
Figure BDA00022643175600001011
When it is, then
Figure BDA00022643175600001012
And
Figure BDA00022643175600001013
and the two adjacent sub-block regions are overlapped, and at the moment, the two adjacent sub-block regions are connected into a whole. If each sub-block area is positioned in the common area through translation, the phase point satisfies
Figure BDA00022643175600001014
All sub-block regions are connected as one entity, in this case
Figure BDA00022643175600001015
But due to the existence of errors during reconstruction, the method cannot lead to
Figure BDA00022643175600001016
At the same time, the fault block region passesWhen the translation is connected into a whole, the limitation condition is that
Figure BDA00022643175600001017
The minimum value is obtained.
Ideally, when the wavefronts in the sub-block regions are connected into a whole through translation splicing, the wavefronts in the common region are completely overlapped. However, in practice, the reconstructed wavefronts of the adjacent sub-blocks in the common region are not completely identical, i.e., the wavefronts in the common region are not necessarily completely coincident, because the reconstructed wavefronts have a slightly lower accuracy at the edges. In order to quantitatively describe the integrity of wave surfaces after splicing of adjacent wave fronts, a wave front photoston deviation E of a common region is introducedPAs evaluation indexes, it is expressed as:
Figure BDA00022643175600001018
wherein the content of the first and second substances,
Figure BDA00022643175600001019
phi is the phase distribution of the adjacent sub-blocks in the common area, and N is the number of phase points in the common area.
Thus, the problem of translation of the wavefront of the sub-block regions is essentially to find the appropriate amount of translation for each sub-block region, so that the total wavefront piston deviation of all common regions is minimized.
In the method, the translation amount of each sub-block area is determined by adopting a least square method. According to the previous blocking method, the common regions are located at the first row, the first column, the last row and the last column of each sub-block, and for convenience of subsequent description, the following symbols are defined:
Figure BDA0002264317560000111
in the block matrix, the pixel of the first column of the ith row and the jth column of the subblock area;
Figure BDA0002264317560000112
in the block matrix, i row and j columnThe last column of the block area is the piston;
Figure BDA0002264317560000113
in the block matrix, the pixel of the first row of the ith row and the jth column sub-block region;
Figure BDA0002264317560000114
in the block matrix, the last row of the subblock region of the ith row and the jth column;
Pi，jand (4) the translation amount of the ith row and jth column sub-block area.
Thus, all common area wavefront piston deviations can be expressed as:
Figure BDA0002264317560000115
wherein, L (i, j), R (i, j), U (i, j) and D (i, j) are weight factors of left, right, upper and lower four directions respectively, and satisfy:
Figure BDA0002264317560000116
Figure BDA0002264317560000121
Figure BDA0002264317560000122
Figure BDA0002264317560000123
let Delta pair Pi，jCalculating partial derivatives, obtaining:
Figure BDA0002264317560000124
according to the relevant knowledge of multivariate functional differential science, when Δ has a minimum value, it must have:
Figure BDA0002264317560000125
finishing to obtain:
Figure BDA0002264317560000126
order to
Figure BDA0002264317560000131
Figure BDA0002264317560000132
Figure BDA0002264317560000133
Then (1) can be abbreviated as:
Coef(i，j)Pi，j-[L(i，j)Pi，j-1+R(i，j)Pi，j+1+U(i，j)Pi-1，j+D(i，j)Pi+1，j]＝ΔCi，jits matrix form can be expressed as:
COEF×P＝ΔC (2)
if the total number of blocks (including the non-connected sub-block region) is c × d, the parameters in the matrix expression can be expressed as:
P＝[P1，1P2，1… Pc，1P1，2… Pc，d]T
ΔC＝[ΔC1，1ΔC2，1… ΔCc，1ΔC1，2… ΔCc，d]T
the matrix COEF has a size of (c × d) × (c × d), in which the elements satisfy:
Figure BDA0002264317560000134
in the matrix COEF, the values of the remaining elements are all 0.
Since the non-connected sub-block region is also counted when the matrix COEF is constructed, the calculation formula of the translation amount of the non-connected sub-block needs to be removed from the matrix after the construction of the matrix COEF is completed. At this time, the unconnected subblocks are not reconstructed, so the weighting factors in the calculation formula of the translation amount of the unconnected subblocks are all 0, that is, the calculation formula of the translation amount of the unconnected subblocks corresponds to all zero rows in the COEF matrix. After all zero rows are removed, the translation quantity parameters corresponding to the non-connected sub-blocks are also removed from the P vector.
After the processing of the matrix COEF is completed, equation (2) becomes:
COEFres×Pres＝ΔCres
because of COEFresRank lack of 1, to solve for PresVector, and an equation pair matrix COEF needs to be introducedresFor the order compensation, the method for solving the Southwell model may be referred to, that is, the sum of the translation amounts of all the sub-blocks is 0.
And recording the matrix expression after the order is complemented as follows:
Figure BDA0002264317560000141
then P isresThe solution of (a) is:
Figure BDA0002264317560000142
will calculate the obtained PresThe translation amount in the sub-block is added into the corresponding sub-block area, and then the translation of the sub-block can be completed.
Step three, performing mean value smoothing treatment on the phases in the public areas of the two adjacent sub-block areas after adjustment;
4. subblock edge smoothing
Based on the obtained calculation result PresAnd integrally translating the wave fronts of the corresponding sub-block regions, wherein the wave fronts in the common regions of the adjacent sub-blocks after translation are overlapped theoretically, but the wave front edges of the adjacent sub-blocks are not completely overlapped due to factors such as calculation errors and model errors. Therefore, the wavefront edge of each sub-block region needs to be smoothed.
The method adopts the mean value as a smoothing treatment means, and specifically comprises the following operations:
assuming that two sub-block regions adjacent to each other on the left and right are a and B, respectively, the column vector in the common region in a and B is recorded as:
Ar＝[a1a2… an]T
Bl＝[b1b2… bn]T
the smoothed wavefront in the common region is then:
Figure BDA0002264317560000151
the same mean smoothing process is also performed on the line vectors in the common area.
After the smoothing is finished, filling of the wave front of the non-connected sub-block area can be carried out to obtain the phase distribution on the whole area.
Step four, according to the phase in the common area after the smoothing treatment, the sum of absolute values of phase differences between each phase point in the common area of the semi-connected subblocks obtained by decomposing the non-connected subblocks and the phase point corresponding to the phase point is minimized, so that the translation amount of the semi-connected subblocks obtained by decomposing the non-connected subblocks is obtained, and the non-connected subblocks are filled in the position corresponding to the wavefront in a translation manner;
5. non-connected sub-block padding
The wave fronts on the two sub-block regions are spliced into a whole through the translation and edge smoothing of the wave fronts on the connected sub-block region and the semi-connected sub-block region, and the wave fronts on the non-connected sub-block region can be filled in the corresponding correct positions by using the whole wave front information. The specific implementation method is as follows.
As described in subsection 2.3, the non-connected sub-block regions are first decomposed into a plurality of semi-connected sub-block regions. And respectively reconstructing the wave fronts on the semi-connected regions obtained by decomposition by using a semi-connected sub-block region wave front reconstruction method. And then, judging whether the wave front on the semi-connected sub-block region and the wave front which is spliced at present have at least one common region. If so, non-connected sub-block region padding can be completed according to the method described in section 2.3. Otherwise, the non-connected sub-block region is skipped over, other non-connected sub-block regions are filled until each wave front on the non-connected sub-block region and the wave front completing splicing have at least one common region, and then the non-connected sub-block region is filled. This process is repeated until all the non-connected sub-block regions are filled.
The filling process of the non-connected subblock region actually translates the wavefront bordering the non-connected subblock region by using the phase information in the common region in the whole wavefront, and assumes that the phase of the common region on the semi-connected subblock obtained by decomposing the non-connected subblock is A1To AnN in total, the phase corresponding to the n in the common region on the whole wave front is B1To BnThen, when the translation amount m satisfies:
Figure BDA0002264317560000161
when the minimum value is obtained, m is the translation amount of the semi-connected subblock obtained by decomposing the non-connected subblock.
And fifthly, performing mean value smoothing treatment on the phases in the public areas of the filled non-connected sub-blocks to complete block wavefront reconstruction of the area to be reconstructed.
6. Filling subblock edge smoothing
After the translation is completed, the wavefront edge on the non-connected sub-block region is smoothed according to the method in section 4.
And filling the wave fronts on all the non-connected sub-block areas into the whole wave front to obtain the wave front phase distribution condition on the whole reconstruction area.
The block optimization strategy is specifically derived as follows:
the size of the divided sub-block area is related to the size of the phase point matrix to be solved, and in order to solve the optimal size of the sub-block area, the solution can be carried out based on the computation complexity of matrix inversion and matrix multiplication.
Assuming that the matrix size of the phase points to be solved is N × N, the size selected when the sub-block regions are divided is N × N, and the wavefront to be solved is continuous, the inversion of the matrix with size of α × α requires α operations according to the related knowledge of the computational complexity3The multiplication operation is carried out on a matrix with the size of α multiplied by β and a matrix with the size of α multiplied by gamma, and the required operation number is αβ gamma.
Based on the above assumptions, the total number of sub-block regions is
Figure BDA0002264317560000171
And because the sub-block region is expanded, then
Figure BDA0002264317560000172
The final size of the sub-block region is (n +1) × (n + 1);
Figure BDA0002264317560000173
and
Figure BDA0002264317560000174
wherein the final sizes of the sub-block regions are (n +1) × m and m × (n +1), respectively,
Figure BDA0002264317560000175
Figure BDA0002264317560000176
representing the phase points remaining from the segmentation to the end because of the impossibility of the integer division;
Figure BDA0002264317560000177
in (3), the final size of the subblock region is m × m.
According to the relevant steps in the flow chart, the total computation complexity in the method can be expressed as:
Compro|n＝Cominv|n+Commul|n+Compis|n
wherein Cominv|n，Commul| n and Compis| n is matrix calculation when the subblock regions are n × nAnd (4) calculating complexity in inverse multiplication, matrix multiplication and solution of translation quantity of the subblocks.
1. Inversion computation complexity Cominv|n
For Cominv| n, of
Figure BDA0002264317560000178
And
Figure BDA0002264317560000179
the sum of the inverse complexity of the medium matrix. In the four types of sub-regions, the sizes of the sub-regions are the same, so that each type of sub-region only needs to perform matrix inversion operation once.
In that
Figure BDA00022643175600001710
In (2) due to coefficient matrix AeIs [2n (n +1) +1]×(n+1)2Then, then
Figure BDA00022643175600001711
The computational complexity of the matrix multiplication is therefore:
Figure BDA00022643175600001712
due to the fact that
Figure BDA00022643175600001713
Has a size of (n +1)2×(n+1)2Therefore, the computational complexity of its inversion can be expressed as:
Figure BDA0002264317560000181
thus, can obtain
Figure BDA0002264317560000182
In that
Figure BDA0002264317560000183
The total computational complexity in (a) is:
Figure BDA0002264317560000184
in the same way, in
Figure BDA0002264317560000185
And
Figure BDA0002264317560000186
in (3), the computational complexity can be expressed as:
Figure BDA0002264317560000187
Figure BDA0002264317560000188
Figure BDA0002264317560000189
this gives:
Figure BDA00022643175600001810
2. matrix multiplication computation complexity Commul|n
Solving expression by Southwell model
Figure BDA00022643175600001811
To minimize the computational complexity of the matrix multiplication, D should be calculated firsteX S, recalculating
Figure BDA00022643175600001812
By DeS, finally, calculating
Figure BDA00022643175600001813
Multiplication by
Figure BDA00022643175600001814
And CommulN is
Figure BDA00022643175600001815
And
Figure BDA00022643175600001817
all matrix multiplications in (a) sum the complexity.
In that
Figure BDA0002264317560000191
In, S, De，
Figure BDA0002264317560000192
And
Figure BDA0002264317560000193
are respectively 2(n +1)2×1，[2n(n+1)+1]×2(n+1)2，(n+1)2×[2n(n+1)+1]And (n +1)2×(n+1)2. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002264317560000194
the total computational complexity of the matrix multiplication is:
Figure BDA0002264317560000195
in that
Figure BDA0002264317560000196
In, due to S, De，
Figure BDA0002264317560000197
And
Figure BDA0002264317560000198
are 2(n +1) m.times.1, [ nm + (n +1) (m-1) +1]×2(n+1)m，(n+1)m×[nm+(n+1)(m-1)+1]With (n +1) m × (n +1) m, one can obtain:
Figure BDA0002264317560000199
due to the fact that
Figure BDA00022643175600001910
And
Figure BDA00022643175600001911
the situation is exactly the same, and it is possible to obtain:
Figure BDA00022643175600001912
finally, in
Figure BDA00022643175600001913
In, S, De，
Figure BDA00022643175600001914
And
Figure BDA00022643175600001915
are respectively 2m in size2X 1, [2m (m-1) +1]×2m2，m2×[2m(m-1)+1]And m2×m2. Then there are:
Figure BDA0002264317560000201
therefore, the computational complexity due to the matrix multiplication is:
Figure BDA0002264317560000202
3. calculating complexity Com for solving translation amount of subblockpis|n
As can be seen from the relevant content in 3,
Figure BDA0002264317560000203
and
Figure BDA0002264317560000204
respectively has the size of
Figure BDA0002264317560000205
And
Figure BDA0002264317560000206
therefore, the temperature of the molten metal is controlled,
Figure BDA0002264317560000207
in (2), the computational complexity of matrix multiplication is:
Figure BDA0002264317560000208
the computational complexity of the matrix inversion is:
Figure BDA0002264317560000211
therefore, the method comprises the following steps:
Figure BDA0002264317560000212
4. computational complexity of traditional Southwell model
The computational complexity of the traditional Southwell model is practically equal to
Figure BDA0002264317560000213
The same applies to
Figure BDA0002264317560000214
Replacing m in the computational complexity expression with N, the computational complexity expression of the traditional Soutwell model can be obtained, and therefore:
Comcla＝3N6-2N5+8N4-6N3+3N2
5. optimal split area size
After obtaining the computational complexity expression of the present method and the conventional method, when the size of the partition area is n × n, the solution rate can be expressed as:
Figure BDA0002264317560000215
when the size NxN of the solved wavefront is determined, the value N when the Sp | N is the minimum value is the size of the optimal segmentation area.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A high-speed high-precision region blocking wavefront reconstruction method based on an optimization strategy is characterized by comprising the following steps:
step one, carrying out region segmentation on an optical wave phase point matrix to be reconstructed, and dividing obtained sub-regions into three types according to the distribution condition of phase points: connected sub-blocks, semi-connected sub-blocks and non-connected sub-blocks;
performing wavefront reconstruction on the connected subblocks and the semi-connected subblocks;
decomposing the non-connected subblocks into a plurality of semi-connected subblocks, finding the real phase heights of the plurality of semi-connected subblocks by utilizing the common areas of the plurality of semi-connected subblocks, and obtaining the phase distribution of the non-connected subblocks by taking a union set to realize the wavefront reconstruction of the non-connected subblocks;
adjusting the phase heights of the connected sub-blocks and the semi-connected sub-blocks to enable the sum of absolute values of phase differences of each phase point in the public area and the phase point corresponding to the phase point to be minimum;
step three, performing mean value smoothing treatment on the phases in the public areas of the two adjacent sub-block areas after adjustment;
step four, according to the phase in the common area after the smoothing treatment, the sum of absolute values of phase differences between each phase point in the common area of the semi-connected subblocks obtained by decomposing the non-connected subblocks and the phase point corresponding to the phase point is minimized, so that the translation amount of the semi-connected subblocks obtained by decomposing the non-connected subblocks is obtained, and the non-connected subblocks are filled in the position corresponding to the wavefront in a translation manner;
and fifthly, performing mean value smoothing treatment on the phases in the public areas of the filled non-connected sub-blocks to complete block wavefront reconstruction of the area to be reconstructed.
2. The high-speed high-precision area blocking wavefront reconstruction method based on the optimization strategy as claimed in claim 1, wherein the translation amount in the fourth step is specifically:
the phase of a common region on a semi-connected sub-block obtained by decomposing a non-connected sub-block is assumed to be A1To AnN in total, the corresponding phase in the common region after smoothing process is B1To BnThen, the process of the present invention,
Figure FDA0002264317550000011
and m when the minimum value is obtained is the translation amount.
3. The method according to claim 1, wherein when the phase point matrix of the optical wave to be reconstructed is nxn and the size of the sub-region obtained after the region segmentation is nxn, the solution rate of the wavefront reconstruction is expressed as:
Figure FDA0002264317550000021
find n when Sp | n takes a minimum valueminThen n ismin×nminI.e. the optimal partition size, where Compro|n＝Cominv|n+Commul|n+Compis|n，
Cominv|n＝[(n+1)4(2n2+2n+1)+(n+1)6]+[(nm+m)2(2nm+m-n)+(nm+m)3]×2+[m4(2m2-2m+1)+m6]，
Figure FDA0002264317550000022
Figure FDA0002264317550000023
Comcla＝3N6-2N5+8N4-6N3+3N2；
Wherein the content of the first and second substances,
Figure FDA0002264317550000024
representing the phase points remaining after the segmentation to the end because of the inability to divide exactly.
CN201911082211.3A 2019-11-07 2019-11-07 High-speed high-precision area blocking wavefront reconstruction method based on optimization strategy Active CN111127473B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911082211.3A CN111127473B (en) 2019-11-07 2019-11-07 High-speed high-precision area blocking wavefront reconstruction method based on optimization strategy

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911082211.3A CN111127473B (en) 2019-11-07 2019-11-07 High-speed high-precision area blocking wavefront reconstruction method based on optimization strategy

Publications (2)

Publication Number Publication Date
CN111127473A true CN111127473A (en) 2020-05-08
CN111127473B CN111127473B (en) 2023-11-07

Family

ID=70495752

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911082211.3A Active CN111127473B (en) 2019-11-07 2019-11-07 High-speed high-precision area blocking wavefront reconstruction method based on optimization strategy

Country Status (1)

Country Link
CN (1) CN111127473B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103714516A (en) * 2013-12-03 2014-04-09 西安交通大学 Point diffusion function estimation method in self-adaptive optical imaging
US20150073752A1 (en) * 2013-09-11 2015-03-12 Canon Kabushiki Kaisha Wavefront measuring apparatus, wavefront measuring method, method of manufacturing optical element, and assembly adjustment apparatus of optical system
CN108489445A (en) * 2018-03-12 2018-09-04 四川大学 One kind is for arbitrary not equidistant area surface shape integration method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150073752A1 (en) * 2013-09-11 2015-03-12 Canon Kabushiki Kaisha Wavefront measuring apparatus, wavefront measuring method, method of manufacturing optical element, and assembly adjustment apparatus of optical system
CN103714516A (en) * 2013-12-03 2014-04-09 西安交通大学 Point diffusion function estimation method in self-adaptive optical imaging
CN108489445A (en) * 2018-03-12 2018-09-04 四川大学 One kind is for arbitrary not equidistant area surface shape integration method

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
LEI HUANG 等: "Spline based least squares integration for two-dimensional shape or wavefront reconstruction" *
ZHONGYE JI 等: "Fitting relationship between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam" *
王映波: "一种区域波前重构的快速算法" *
王棪 等: "基于稀疏孔径的波前重构算法" *

Also Published As

Publication number Publication date
CN111127473B (en) 2023-11-07

Similar Documents

Publication Publication Date Title
Johannessen et al. Isogeometric analysis using LR B-splines
Liu et al. The interacting correlated fragments model for weak interactions, basis set superposition error, and the helium dimer potential
Greco et al. An efficient blended mixed B-spline formulation for removing membrane locking in plane curved Kirchhoff rods
Li et al. Displacement minimization of thermoelastic structures by evolutionary thickness design
CN107016649A (en) A kind of vision data complementing method estimated based on local low-rank tensor
CN104268934A (en) Method for reconstructing three-dimensional curve face through point cloud
CN110084756A (en) A kind of image de-noising method based on the overlapping sparse full variation of group of high-order
CN112465713B (en) Tensor low-rank model non-smooth three-dimensional image completion method based on manifold optimization
CN110139046A (en) A kind of video frame synthetic method based on tensor
CN110334450B (en) Method for repairing object plane projection error in multi-block structure grid generation
CN104765948B (en) Three-dimensional acoustic wave method for numerical simulation based on PML absorbing boundary
Hubeli et al. Fairing of non-manifolds for visualization
CN115017773A (en) Dimension reduction method of three-dimensional grid model, electronic equipment and medium
CN111127473A (en) High-speed high-precision region block wavefront reconstruction method based on optimization strategy
Kimbell et al. On the solution of general equilibrium models
WO2002093412A1 (en) Parallel infinite element method calculation system
CN109856673B (en) High-resolution Radon transformation data separation technology based on dominant frequency iterative weighting
CN114119928A (en) Grid operation-based lung organ three-dimensional model optimization method and system
Ge et al. Blending isogeometric and Lagrangian elements in three-dimensional analysis
CN103440680A (en) Polycube controllable generation method based on norm optimization
CN105528763A (en) Self-adaptive region sensing mask generation method based on multi-grid approximate algorithm
CN108072899B (en) Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm
CN109584369A (en) Actual formation all-hexahedral element mesh generation method and device
CN113362465B (en) Non-rigid three-dimensional shape point-by-point correspondence method and human heart motion simulation method
CN115374567B (en) She Panlun hub processing path generation method and device, medium and electronic equipment

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant