CN107479335A - The optical imagery quick calculation method decomposed based on light source interaural crosscorrelation function - Google Patents

The optical imagery quick calculation method decomposed based on light source interaural crosscorrelation function Download PDF

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CN107479335A
CN107479335A CN201710820261.1A CN201710820261A CN107479335A CN 107479335 A CN107479335 A CN 107479335A CN 201710820261 A CN201710820261 A CN 201710820261A CN 107479335 A CN107479335 A CN 107479335A
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function
light source
orthogonal basis
basis functions
frequency domain
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贡顶
沈忱
崔绍春
毛智彪
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SUZHOU COGENDA ELECTRONIC CO Ltd
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    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
    • G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
    • G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus

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  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)

Abstract

The invention discloses a kind of optical imagery quick calculation method decomposed based on light source interaural crosscorrelation function, it comprises the following steps：1) the light source function of imaging system is obtainedAnd pupil functionBy light source functionProject on one on frequency domain group of orthogonal basis function；3) light source interaural crosscorrelation function on solution room domainCorresponding basic functionProjection coefficient αpq,st；4) by projection coefficient apq,stEstablish the projection matrix A=[α of symmetric positive definitepq,st], and carry out eigendecomposition A=UU*；5) to light source interaural crosscorrelation functionCarry out variables separation, and the intersection transmission function established in spatial domainKernel function6) kernel function is calculatedWith mask plate figureConvolution, obtain image plane on exposing patternsThe present invention utilizes the Fourier function transform pairs in one group of spatial domain and frequency domain, and the integral transformation of complexity is calculated according to Defined, so as to quickly obtain corresponding kernel function so that light distribution calculating is quick and efficient, so as to meet actual photoetching process design requirement.

Description

Optical imaging rapid calculation method based on light source mutual intensity function decomposition
[ technical field ] A method for producing a semiconductor device
The invention belongs to the technical field of photoetching resolution enhancement in semiconductor device process simulation, and particularly relates to an optical imaging fast calculation method based on light source mutual intensity function decomposition.
[ background ] A method for producing a semiconductor device
In the production process of semiconductor devices, the photolithography process is the main means of industrial production at present. The photolithography process is based on diffraction optics to obtain a light intensity distribution of a specific pattern at an imaging plane. With the development of semiconductor technology, the size of semiconductor devices is getting smaller, when the feature size is close to or even smaller than the wavelength of light used in the photolithography process, the exposure pattern formed on the silicon wafer will have a certain distortion compared with the mask pattern used by the photolithography process due to optical diffraction, and as the feature size is further reduced, the difference of the pattern will be increased. This phenomenon causes distortion in the transfer of the lithography pattern, and ultimately affects the yield of the product. To suppress the negative effects of optical diffraction on semiconductor device production, fast calculations of the light intensity distribution at the image plane are used for process simulations of lithography. To accommodate the diversity, complexity of design, model-based optical imaging is increasingly being employed.
The photoetching process simulation technology mainly comprises a photoetching system imaging model and a reverse optimization process, wherein the reverse optimization is a repeated iteration process, the photoetching imaging model is required to be called for each iteration, and an image on a silicon chip is correctly estimated under a specific photoetching condition. The optical imaging model is the key of the photoetching process, the basic principle of the current photoetching imaging mainly comprises a Hopkins imaging principle and an Abbe imaging principle, an imaging fast algorithm based on the two imaging principles is developed for a long time, and the essence of the photoetching imaging model is a series of Fourier optical operation processes. With the increasing scale of integrated circuits, more and more devices are integrated on a single semiconductor chip, and the exposure patterns of a mask plate required by the corresponding photoetching process are more and more complex, so that the calculation of a photoetching imaging model is required to be fast and efficient, thereby reducing the cycle time of the whole optical proximity correction process, improving the production efficiency and reducing the production cost.
The photoetching system can be simplified into an imaging system, and comprises four basic elements of an illumination light source, a mask plate, a projection objective and photoresist on a silicon wafer imaging surface. There is a literature in the prior art (a.k. — k.wong, resolution enhancement techniques in optical Resolution, vol.47.Spie press, 2001.) discloses a lithography Resolution enhancement technique, which utilizes Hopkins imaging principle to establish a four-dimensional Cross transfer function (TCC for short) to characterize the optical parameters (light source, numerical aperture, phase difference, defocus, etc.) of an imaging system, and for the imaging system with the same optical parameters, the TCC only needs to be calculated once and can be reused. In addition, in the prior art, documents (n.b. cobb, fast Optical and Process Proximity Correction for Integrated Circuit Manufacturing, ph.d. display, university of California, berkeley, 1998) propose a Fast Optical and Process Proximity Correction algorithm for Integrated Circuit Manufacturing, which extracts a characteristic value and a characteristic vector of TCC by using a characteristic value analysis method, and can greatly reduce the number of fourier transforms required for calculating a light intensity distribution by retaining the characteristic value and the characteristic vector having a large influence on imaging, thereby realizing Fast calculation. However, according to the Hopkins optical imaging theory, a four-dimensional cross transfer function TCC is established, and calculation of the cross transfer function TCC involves quadruple integral operation, which is time-consuming. If the corresponding optical parameters change, the TCC has to be recalculated, which according to the normal calculation method will seriously affect the efficiency of the calculation of the light intensity distribution, thereby affecting the design efficiency of the lithography process.
Therefore, it is necessary to provide a new fast calculation method for optical imaging based on light source mutual intensity function decomposition to solve the above problems.
[ summary of the invention ]
The invention mainly aims to provide an optical imaging fast calculation method based on light source mutual intensity function decomposition, which can quickly and accurately obtain a TCC (cross-correlation coefficient) kernel function, so that the light intensity distribution calculation is fast and efficient, and the actual design requirement of a photoetching process is met.
The invention realizes the purpose through the following technical scheme: a fast calculation method of optical imaging based on light source mutual intensity function decomposition comprises the following steps:
step S101: obtaining light source functions for an imaging systemAnd pupil function
Step S102: function of the light sourceProjecting onto a set of orthogonal basis functions in the frequency domain;
step S103: solving a source-to-source mutual intensity function over a spatial domainCorresponding basis functionsProjection coefficient a of pq,st ；
Step S104: from the projection coefficient alpha pq,st Establishing a projection matrix A = [ alpha ] pq,st ]And performing eigenvector decomposition A = UU * ；
Step S105: a pair of light source mutual intensity functions based on the projection matrix ASeparating variables and establishing cross transfer function in space domainKernel function of
Step S106: computing kernel functionsPattern with maskObtaining an exposure pattern on the image plane
Compared with the prior art, the optical imaging fast calculation method based on the light source mutual intensity function decomposition has the beneficial effects that: a group of Fourier function transformation pairs on a space domain and a frequency domain are utilized, and complex integral transformation is calculated according to convolution definition, so that a corresponding kernel function is quickly obtained, the calculation of light intensity distribution is quick and efficient, and the design requirement of an actual photoetching process is met. In particular, the method comprises the following steps of,
1) Built upAndis a set of Fourier function transformation pairs in the space domain and the frequency domain satisfying the orthogonal relationship, so that if there is a frequency domain function asLinear combination of (2), then the Fourier transform is alsoA linear combination of (a); the orthogonal basis function projection method of the embodiment is suitable for all orthogonal basis functions, such as Zernike polynomials, orthogonal Legendre polynomials, fourier-Bessel basis functions and the like;
2) Projection coefficient alpha in the form of quadruple integral in calculation pq,st In the meantime, the very difficult quadruple integral is converted into a simple analytical expression by using convolution definition and the properties of the orthogonal basis fourier transform pair. In the projection coefficientAnd beta nm,st,pq Easy to obtain, and because of the orthogonal relation, the calculation of the projection coefficient is simplified to only calculate the projection coefficient alpha of a specific bit pq,st Namely, the calculation steps are greatly reduced, and the calculation efficiency is improved.
[ description of the drawings ]
FIG. 1a is a schematic diagram illustrating a calculation flow of a kernel function of a cross transfer function according to an embodiment of the present invention;
FIG. 1b is a schematic diagram illustrating a calculation process of light intensity distribution according to an embodiment of the present invention;
FIG. 2a is a schematic diagram of a light sourceNumber ofThe two-pole fan-shaped light source schematic diagram of (1);
FIG. 2b is a diagram of the light source function in an embodiment of the present inventionDistribution along the section and parameter schematic diagram;
FIG. 3 is a light source function in an embodiment of the present inventionA Zernike transformed schematic of (a);
FIG. 4 is a cross intensity function of light sources in an embodiment of the present inventionThe schematic diagram of the separation variable method space sampling;
FIGS. 5a, 5b, 5c, 5d, 5e, and 5f are fast decomposition kernel functions of cross transfer function tcc in an embodiment of the present inventionA schematic diagram of (a);
FIGS. 6a and 6b are schematic diagrams illustrating the light intensity distribution of the mask pattern according to the embodiment of the present invention;
FIGS. 7a and 7b are schematic diagrams illustrating actual light intensity distributions on the imaging plane of various mask patterns according to an embodiment of the present invention.
[ detailed description ] embodiments
Example (b):
based on the imaging theory of Hopkins diffraction optics, the imaging light intensity distribution function formula is as follows:
wherein i is an imaginary unit, M (F, g) = F [ M (x, y) ] is a two-dimensional Fourier Transform (FFT) of the spatial distribution of the mask, TCC is a corresponding four-dimensional cross transfer function, which is defined as:
TCC(f 1 ,g 1 ；f 2 ,g 2 )＝∫∫J(f,g)·P(f+f 1 ,g+g 1 )·P * (f+f 2 ,g+g 2 )dfdg (2)
wherein J (f, g) is a light source function, P (f, g) is a pupil function of the imaging system, P * (f, g) is the complex conjugate of P (f, g) of the pupil function, representing the optical parameters of the optical imaging system. According to the decomposition algorithm of Cobb, then the singular value decomposition for TCC exists as follows:
wherein, ker i (f, g) is the kernel function of TCC, the light intensity distribution of the imaging system can be calculated quickly as follows:
referring to fig. 1a, the present embodiment is a method for fast calculating optical imaging based on light source mutual intensity function decomposition, that is, performing fast decomposition calculation on formula (1), and includes the following steps:
step S101: obtaining optical parameters, in particular light source functions, of an imaging systemAnd pupil function
Step S102: light source function to be acquiredProjection (projector)Onto a set of orthogonal basis functions in the frequency domain.
Specifically, the method comprises the following steps:
1) Establishing a set of orthogonal basis functions in the frequency domainThe orthogonal basis functionsAny orthogonal basis function can be selected, the orthogonal basis functionIncluding but not limited to Zernike polynomials, orthogonal Legendre polynomials, fourier-Bessel basis functions. The orthogonal basis functions described in the present embodimentIs a Zernike polynomial.
Within a unit circle, a set of orthogonal basis functions described in polar coordinates is established in the frequency domain, which is expressed as follows:
wherein m and n are positive integers satisfying the condition that n is more than or equal to m,is the azimuth angle of the polynomial, rho is the radial distance, and rho is more than or equal to 0 and less than or equal to 1. In the optical imaging model, the light source function is usually described in the frequency domain, and all coordinates are normalized, that is, the highest frequency of the light source satisfies f max ≤1。
2) Function of light sourceUsing the above-mentioned orthogonal basis functionsThe linear combination of (c) is described.
Since the light source function is a smooth function on the unit circle, the light source function is controlled by the unit circleAs orthogonal bases, the light source function is described by a linear combination of orthogonal bases as follows:
wherein the content of the first and second substances,as a function of the light sourceAnd orthogonal basis functionsInner product operation of two functions<·&And the corresponding projection coefficient has the following expression:
wherein the content of the first and second substances,is an orthogonal basis functionThe die of (1).
3) Establishing orthogonal basis functions in the frequency domainOrthogonal basis functions corresponding to spatial domain
Due to the fact thatIs an orthogonal basis function in the frequency domain, thenThe corresponding orthogonal basis function on the space domain can be obtained through Fourier transformationUnder the condition of polar coordinatesThe expression of (c) is as follows:
and is provided withThe orthogonal relationship is satisfied.
Step S103: solving a source-to-source mutual intensity function over a spatial domainCorresponding basis functionsProjection coefficient alpha of pq,st . Projection coefficient alpha pq,st Is calculated as follows:
wherein the content of the first and second substances, is a basis functionThe moduli p, q, s, t are all integer orders of orthogonal basis functions, f < g > is the function inner product, and it is very time consuming to directly calculate the quadruple integral. The invention comprehensively considers convolution property and numerical integration method to quickly calculate projection coefficient alpha pq,st . The solving steps are as follows:
1) Changing the integration sequence of the integrals, solving one double integral to obtain the convolution definition
2) Convolving the aboveThe fourier transform and multiplication operations are performed, and the results are as follows:
3) Will be convolutedProjection onto orthogonal basis functionsThe above.
In particular, becauseIs an orthogonal basis function in the frequency domain, thenAvailable basis functionsTo describe, due to angular integrationAnd according to projection formula according to formula (5) and polynomialAnd obtaining the convolution operation according to the property of Fourier transform to orthogonal basis functionThe calculation results are as follows:
wherein the content of the first and second substances,β mn,st,(n+s)l are respectively asOrthogonal basis functions in the frequency domainThe projection coefficients of (a).
4) Convolving the aboveSubstituting the calculation result of (2) into the projection coefficient α pq,st Derivation in the expression
Due to the fact thatFor projection on orthogonal basis functionsThe above function only needs to calculate the number of the function according to the orthogonal property of the basis functionObtaining the projection coefficient a by p = n + s and l = q pq,st The results are as follows:
wherein the content of the first and second substances,representing orthogonal basis functionsThe die of (1).
Step S104: from the projection coefficient alpha pq,st Establishing a symmetric positive definite projection matrix A = [ alpha ] pq,st ]And performing eigenvector decomposition A = UU * And A is a sparse matrix. The integer order of the basis function is p, q, s, t, respectively, and if p is satisfied, s belongs to [0,N ]]And q, t ∈ [1,S]Then the size of matrix A is (2N + 1) S × (2N + 1) S, and the number of non-zero elements in A is (2N + 1) S × S.
Step S105: from the characteristic decomposition, the mutual intensity function of the light sourcesSeparating variables and establishing cross transfer function in space domainKernel function ofSpecifically, the cross transfer function TCC in the four-dimensional cross transfer function described in the formula (2) is transformed by fourier transform to obtain the corresponding cross transfer function in the spatial domainThe expression is as follows:
wherein the content of the first and second substances,for the expression of a vector in the spatial domain,as a function of pupilThe inverse fourier transform of (c). Step S103 is to the formula (6)Corresponding basis functionsProjection coefficient alpha of pq,st And (6) solving.
1) According to the separation variable theory, the projection matrix A is used for the light source mutual intensity function in the formula (6)Decomposition is carried out, and the decomposition result is as follows:
wherein the content of the first and second substances,is a vectorA related row matrix, andcorresponding to an orthogonal polynomial function in a spatial domainMatrix a = [ α = [ ] pq,st ]In which α is pq,st As a function of mutual intensity of light sourcesCorresponding basis functionsThe projection coefficients of (a) are calculated,u ij are elements of the matrix U.
2) The decomposed light source mutual intensity functionSubstituting into equation (6) yields:
therefore, the number of the first and second electrodes is increased,
step S106: computing kernel functionsPattern with maskObtaining an exposure pattern on the image planeIn particular, the method comprises the following steps of,
according to the kernel function obtained in step S105, the imaging light intensity distribution of the imaging system can be obtained according to the formula (4), and the result is as follows:
in order to verify the beneficial effects of the optical imaging fast calculation method based on the light source mutual intensity function decomposition in the present embodiment, the following embodiment performs the calculation of the light intensity distribution thereof by combining with a specific mask pattern, thereby further explaining the inventive content of the present embodiment in detail.
The optical parameters in the imaging system include:
two-pole fan-shaped light source sigma in ＝0.4，σ out ＝0.8，λ＝248nm，NA＝0.53。
Step S101: light source function please refer to the two-pole fan light source shown in FIG. 2a and FIG. 2bThe pupil function is an ideal pupil function.
Step S102: selecting Zernike polynomials as a set of orthogonal basis functionsProjection to Zernike polynomial orthogonal base, projection coefficient calculation involving inner product operation<·&Since the Zernike polynomial is separable in radial and angular directions, and the radial function is polynomial, the inner product can be rapidly calculated according to the numerical integration:
wherein, the first and the second end of the pipe are connected with each other,andthe corresponding projection coefficients are calculated by the inner product of two functions, and the expressions are respectively:
the source function after the above Zernike transformation is shown in fig. 3.
Step S103: for light source mutual intensity function in space domainProjecting onto orthogonal basisIn the above, a separation variable is implemented. According to the convolution and orthogonal relationship proposed in this embodiment, the projection coefficient can be calculated quickly
Step S104: from the projection coefficient alpha pq,st Establishing a projection matrix A = [ alpha ] pq,st ]And performing eigenvector decomposition A = UU * Establishing separation variable of light source mutual intensity function according to characteristic vector U
In the fast solution method for the separation variable proposed in this embodiment, i.e. steps S103 and S104, the real light source mutual intensity function is described by the separation variable, and the function is shown in fig. 4.
Step S105: since the pupil function itself is a separate variable, the kernel function of tcc can be obtained
The kernel function obtained in step S105 is shown in fig. 5a, 5b, 5c, 5d, 5e, 5 f.
Step S106: computing kernel functionsPattern with maskObtaining an exposure pattern on the image plane
Considering the relationship between the convolution operation and the fourier transform, step S106 includes:
step S201: kernel function ker of cross transfer function in spatial domain of input imaging system i (x, y) and the spatial distribution m (x, y) of the mask pattern;
step S202: calculating cross transfer kernel function Ker on frequency domain by FFT method i (f,g)＝F[ker i (x,y)]To reach the representation of the mask pattern in the frequency domain M (F, g) = F [ M (x, y)]；
Step S203: calculating the intensity distribution I (x, y) = ∑ Σ of the imaging plane i |F -1 [Ker i (f,g)·M(f,g)]| 2 。
The kernel function in step S201 is obtained in step S105 proposed in this embodiment, and the spatial distribution m (x, y) of the mask pattern is a spatial sample, and a part of the mask pattern is shown in fig. 6 a. In step S203, the light intensity distribution of the imaging plane is calculated according to formula (4), as shown in fig. 6 b. Fig. 7a and 7b show the light intensity distribution on the imaging plane of the mask plate for a plurality of mask patterns based on the fast decomposition method of the present invention. As can be seen from fig. 6a, 6b, 7a, and 7b, the fast algorithm of the present embodiment can quickly calculate the light intensity distribution of the mask pattern.
The invention content of the embodiment is mainly used for quickly calculating the mask pattern change caused by the process parameter change so as to meet the design requirement of the photoetching process. Referring to fig. 1a, the light intensity distribution of the image plane is rapidly calculated,
the optical imaging fast calculation method based on the light source mutual intensity function decomposition has the advantages that: a group of Fourier function transformation pairs on a space domain and a frequency domain are utilized, and complex integral transformation is calculated according to convolution definition, so that a corresponding kernel function is quickly obtained, the calculation of light intensity distribution is quick and efficient, and the design requirement of an actual photoetching process is met. In particular, the method comprises the following steps of,
1) Built upAndis a set of Fourier function transformation pairs in the space domain and the frequency domain satisfying the orthogonal relationship, so that if there is a frequency domain function asThe Fourier transform of the linear combination of (1) is alsoA linear combination of (a); the orthogonal basis function projection method of the embodiment is suitable for all orthogonal basis functions, such as Zernike polynomials, fourier-Bessel basis functions and the like;
2) Projection coefficient alpha in the form of quadruple integral in calculation pq,st In the process, the convolution definition and the property of the orthogonal base Fourier transform are utilized to convert the extremely difficult quadruple integral into a simple analytical expression, and the calculation of the projection coefficient is simplified into the projection coefficient alpha only needing to calculate a specific bit due to the orthogonal relation pq,st Namely, the calculation steps are greatly reduced, and the calculation efficiency is improved.
What has been described above are merely some embodiments of the present invention. It will be apparent to those skilled in the art that various changes and modifications can be made without departing from the inventive concept thereof, and these changes and modifications can be made without departing from the spirit and scope of the invention.

Claims (10)

1. A rapid optical imaging calculation method based on light source mutual intensity function decomposition is characterized in that: which comprises the following steps of,
step S101: obtaining light source functions for an imaging systemAnd pupil function
Step S102: function of the light sourceProjecting onto a set of orthogonal basis functions in the frequency domain;
step S103: solving a source-to-source mutual intensity function over a spatial domainCorresponding basis functionsProjection coefficient a of pq,st ；
Step S104: from the projection coefficient alpha pq,st Establishing a symmetric positive definite projection matrix A = [ alpha ] pq,st ]And performing eigenvector decomposition A = UU * ；
Step S105: a pair of light source mutual intensity functions based on the projection matrix ASeparating variables and establishing cross transfer function in space domainKernel function of
Step S106: computing kernel functionsPattern with maskObtaining an exposure pattern on the image plane
2. The optical imaging fast calculation method based on light source mutual intensity function decomposition of claim 1, characterized in that: in the step S102, the method comprises the following steps,
1) Establishing a set of orthogonal basis functions in the frequency domain
2) Function of light sourceBy orthogonal basis functions in the frequency domainThe linear combination of (a);
3) Establishing orthogonal basis functions in the frequency domainOrthogonal basis functions corresponding to spatial domain
3. The method for optical imaging fast calculation based on light source mutual intensity function decomposition as claimed in claim 2, wherein: orthogonal basis functions in the frequency domainIs a Zernike polynomialThe Zernike polynomials are expressed as
Wherein the content of the first and second substances,is the azimuth angle of the polynomial, rho is the radial distance, and rho is more than or equal to 0 and less than or equal to 1.
4. The optical imaging fast calculation method based on light source mutual intensity function decomposition as claimed in claim 2, characterized in that: orthogonal basis functions in the frequency domainWith orthogonal basis functions in the spatial domainA pair of fourier transform pairs.
5. The optical imaging fast calculation method based on light source mutual intensity function decomposition of claim 1, characterized in that: light source function in the frequency domainIs expressed as
Wherein the content of the first and second substances,is composed ofIn the orthogonal basis functionThe projection coefficient of (c).
6. The method for optical imaging fast calculation based on light source mutual intensity function decomposition as claimed in claim 2, wherein: in the step S103, the projection coefficient α pq,st Is expressed as
Wherein the content of the first and second substances,is a basis functionP, q, s, t are integer orders of the orthogonal basis functions.
7. The method for optical imaging fast calculation based on light source mutual intensity function decomposition as claimed in claim 6, wherein: the projection coefficient alpha pq,st The step of calculating (a) comprises,
1) The projection coefficient alpha is measured pq,st The quadruple of integrals in (1) decomposes the convolution definition of one double integralThe expression is as follows:
wherein the content of the first and second substances,
2) Volume computation using Fourier transforms and multiplicationsProduct of large quantitiesTo obtain
3) Will be convolutedOrthogonal basis functions projected onto the spatial domainTo obtain
Wherein the content of the first and second substances,β mn,st,(n+s)l are respectively asOrthogonal basis functions in the frequency domainThe projection coefficient of (a) to (b),vector representation in the spatial domain, N (-) is the modulus of the function, < F, g > is the inner product of the function, and F is the Fourier transform.
8. The method for optical imaging fast calculation based on light source mutual intensity function decomposition as claimed in claim 7, wherein: the projection coefficient alpha pq,st And beta mn,st,(n+s)l In the calculation of (2), only a specific calculation is requiredProjection coefficients corresponding to bits p = n + s, l = q are sufficient.
9. The method for optical imaging fast calculation based on light source mutual intensity function decomposition as claimed in claim 8, wherein: the kernel functionWherein u is ij Are elements of the matrix U and are,as a function of pupilThe inverse fourier transform of (c).
10. The optical imaging fast calculation method based on light source mutual intensity function decomposition of claim 1, characterized in that: the projection matrix A is a sparse matrix.
CN201710820261.1A 2017-09-13 2017-09-13 The optical imagery quick calculation method decomposed based on light source interaural crosscorrelation function Withdrawn CN107479335A (en)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109164683A (en) * 2018-09-30 2019-01-08 墨研计算科学（南京）有限公司 Light distribution fast determination method and device based on mask graph processing
CN109212913A (en) * 2018-09-30 2019-01-15 墨研计算科学（南京）有限公司 Light distribution acquisition methods and device based on non-homogeneous calculating
CN109270802A (en) * 2018-09-30 2019-01-25 墨研计算科学（南京）有限公司 A kind of fast acquiring method and device of crystal column surface light distribution
CN113779928A (en) * 2021-09-03 2021-12-10 珠海市睿晶聚源科技有限公司 Calculation method and system for rapid simulation photoetching process

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109164683A (en) * 2018-09-30 2019-01-08 墨研计算科学（南京）有限公司 Light distribution fast determination method and device based on mask graph processing
CN109212913A (en) * 2018-09-30 2019-01-15 墨研计算科学（南京）有限公司 Light distribution acquisition methods and device based on non-homogeneous calculating
CN109270802A (en) * 2018-09-30 2019-01-25 墨研计算科学（南京）有限公司 A kind of fast acquiring method and device of crystal column surface light distribution
CN113779928A (en) * 2021-09-03 2021-12-10 珠海市睿晶聚源科技有限公司 Calculation method and system for rapid simulation photoetching process

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Application publication date: 20171215