CN107993273A - The computer graphics device and drawing practice of a kind of single-particle Mie scattering properties - Google Patents

The computer graphics device and drawing practice of a kind of single-particle Mie scattering properties Download PDF

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CN107993273A
CN107993273A CN201711250334.4A CN201711250334A CN107993273A CN 107993273 A CN107993273 A CN 107993273A CN 201711250334 A CN201711250334 A CN 201711250334A CN 107993273 A CN107993273 A CN 107993273A
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module
particle
mie scattering
function
computer graphics
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方伟
高鑫
王玉鹏
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/20—Drawing from basic elements, e.g. lines or circles
    • G06T11/203—Drawing of straight lines or curves

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
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Abstract

The invention discloses a kind of computer graphics device of single-particle Mie scattering properties.The computer graphics device of the single-particle Mie scattering properties of the present invention includes：Processing module, graphics module, memory module and output module.The processing module is handled the complicated function in the Mie scattering formulas, and is expressed as the manageable iteration function form of computer；The graphics module is drawn according to iteration function form；The memory module is stored the drawing of the graphics module；The output module carries out the output and data call of image.The invention also discloses a kind of drawing practice of the computer graphics device of single-particle Mie scattering properties.The computer graphics device and drawing practice of single-particle Mie scattering properties provided by the invention have the advantages that applied widely.

Description

The computer graphics device and drawing practice of a kind of single-particle Mie scattering properties
Technical field
The present invention relates to numerical value processing drawing technique field, more particularly to a kind of computer of single-particle Mie scattering properties Plotter and drawing practice.
Background technology
Mie scatterings are to solve for spherical scatterer and the classic algorithm of electromagnetic wave field interaction analytic solution.Mie scatterings are mesh The most frequently used most basic algorithm of preceding widely used KPT Scatter, has other on the problem of handling wavelength magnitude KPT Scatter Theoretical unrivaled precision.Ironically, Mie scatterings are not an independent theories, it is that spherical medium exists Analytic solutions under maxwell equation group.But due to the complexity of solution itself, so first perfect completion solution task Gustav Mie become classics, his derivation algorithm is named as Mie theory.
Mie scattering theories give scattering light each physical quantity of the uniform spherome under plane monochromatic light exposure is tried to achieve it is tight Lattice mathematical solution.In theory can according to its complete formula, strictly obtain different scale, different refractivity particle scattering it is special Property.But due to containing a series of complex letters such as the first kind, three classes Bessel functions and Legendre functions in formula Number, calculation amount are very big so that numerical computations are very difficult.Although there are some Mie at present to scatter numerical computation method, lack Necessary code description, uses and is inconvenient.
The content of the invention
It is contemplated that overcoming defect existing in the prior art, the present invention uses following technical scheme：
On the one hand, an embodiment of the present invention provides a kind of computer graphics device of single-particle Mie scattering properties.The simple grain The computer graphics device of sub- Mie scattering properties includes：
Processing module, the processing module is handled the complicated function in the Mie scattering formulas, and is expressed as counting The manageable iteration function form of calculation machine；
Graphics module, the iteration function form after the processing that the graphics module is conveyed according to the processing module are painted Figure；
Memory module, the memory module are stored the drawing of the graphics module；
Output module, the output module issue output in the processing module and refer to according to the drawing of the memory module The output and data call of image are carried out when making.
In certain embodiments, the processing module includes calculating sub module, and controller；
The calculating sub module includes an/bnComputing module and πn/τnComputing module；
The an/bnComputing module is iterated calculating, exports a using birefringence Coefficient m, scale parameter α as inputn/ bnArray,
And according on an/bnFunctional relation, the extinction coefficient Q of single-particle is calculatedext, scattering coefficient Qsca；
The πn/τnComputing module is by birefringence Coefficient m, scale parameter α, an/bnThe a of computing module outputn/bnNumber Group, extinction coefficient Qext, scattering coefficient QscaAs input, with reference to scatteringangleθ, calculating is iterated, exports πn/τnArray, and root According to scattered light intensity function and phase function on πn/τnFunctional relation, calculate, output single-particle scattered light intensity function S, Xiang Han Number P；
The controller is connected with the calculating sub module, and carries out instruction input and output to the calculating sub module.
In certain embodiments, the value range of the scatteringangleθ is 0~180 °.
In certain embodiments, the scale parameter α includes α<3 thin mode and the roughcast state of α >=3.
In certain embodiments, the controller judges that the scale parameter α is α<3 thin mode or the roughcast of α >=3 State, and instruction input is carried out to the calculating sub module according to different scale parameter α and calls different algorithms to calculate an/bnNumber Group.
On the other hand, the embodiment of the present invention additionally provides a kind of painting for computer graphics device of single-particle Mie scattering properties Drawing method, the drawing practice of the computer graphics device of the single-particle Mie scattering properties include step：
Complicated function in the Mie scattering formulas is handled, and is expressed as the manageable iteration letter of computer Number form formula；
Drawn according to the iteration function form after the processing；
The drawing is stored；
According to the drawing of the storage, the output and data call of image are carried out when issuing output order.
In certain embodiments, the step：Complicated function in the Mie scattering formulas is handled, and is expressed For the manageable iteration function form of computer, it is specially：
Using birefringence Coefficient m, scale parameter α as input, calculating is iterated, exports an/bnArray,
And according on an/bnFunctional relation, the extinction coefficient Q of single-particle is calculatedext, scattering coefficient Qsca；
By birefringence Coefficient m, scale parameter α, an/bnArray, extinction coefficient Qext, scattering coefficient QscaAs input, with reference to Scatteringangleθ, is iterated calculating, exports πn/τnArray, and according to scattered light intensity function and phase function on πn/τnFunction close System, calculates, scattered light intensity function S, the phase function P of output single-particle.
In certain embodiments, the value range of the scatteringangleθ is 0~180 °.
In certain embodiments, the scale parameter α includes α<3 thin mode and the roughcast state of α >=3.
In certain embodiments, a is being calculatedn/bnArray, when α is α<3 thin mode or the roughcast state when α >=3, calling Algorithm is different.
The technique effect of the present invention：The computer graphics device of single-particle Mie scattering properties disclosed by the invention and drawing Complicated function (Bessel functions/Legendre functions etc.) in Mie scattering formulas is converted into computer and can handled by method Iteration form, solve the problems, such as that such complicated function directly cannot ask calculation using computer, overcome and deposited in numerical computations Difficulty.By key parameter an/bn/πn/τn, extinction coefficient, scattering coefficient, scattered light intensity function, phase function calculating integrate Onto the computer graphics device of same single-particle Mie scattering properties, this single-particle Mie scattering properties has largely been expanded The scope of application of computer graphics device, improves the applicability of Mie scattering numerical computation methods.Simple grain provided in an embodiment of the present invention The computer graphics device of sub- Mie scattering properties, because having output module, there are data output function, and provides number According to subsequent applications interface.
Brief description of the drawings
Fig. 1 is a kind of principle of the computer graphics device of single-particle Mie scattering properties according to an embodiment of the invention Block diagram；
Fig. 2 is a kind of drawing of the computer graphics device of single-particle Mie scattering properties according to an embodiment of the invention The flow diagram of method；
Fig. 3 is that a kind of institute of the computer graphics device of single-particle Mie scattering properties according to an embodiment of the invention is defeated The schematic diagram of the figure gone out；
Fig. 4 is that a kind of institute of the computer graphics device of single-particle Mie scattering properties according to an embodiment of the invention is defeated The schematic diagram of the figure gone out；
Fig. 5 is that a kind of institute of the computer graphics device of single-particle Mie scattering properties according to an embodiment of the invention is defeated The schematic diagram of the figure gone out.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, below in conjunction with attached drawing and specific implementation Example, the present invention will be described in further detail.It should be appreciated that specific embodiment described herein is only explaining this hair It is bright, without being construed as limiting the invention.
Refering to what is shown in Fig. 1, an embodiment of the present invention provides a kind of computer graphics device 100 of single-particle Mie scattering properties. The computer graphics device 100 of the single-particle Mie scattering properties includes：
Processing module 10, the processing module is handled the complicated function in the Mie scattering formulas, and is expressed as The manageable iteration function form of computer；
Graphics module 20, the iteration function form after the processing that the graphics module is conveyed according to the processing module carry out Draw；
Memory module 30, the memory module are stored the drawing of the graphics module；
Output module 40, the output module issue output according to the drawing of the memory module in the processing module The output and data call of image are carried out during instruction.
In certain embodiments, the processing module 10 includes calculating sub module 101, and controller 102；
The calculating sub module 101 includes an/bnComputing module and πn/τnComputing module；
The an/bnComputing module is iterated calculating, exports a using birefringence Coefficient m, scale parameter α as inputn/ bnArray,
And according on an/bnFunctional relation, the extinction coefficient Q of single-particle is calculatedext, scattering coefficient Qsca；
The πn/τnComputing module is by birefringence Coefficient m, scale parameter α, an/bnThe a of computing module outputn/bnNumber Group, extinction coefficient Qext, scattering coefficient QscaAs input, with reference to scatteringangleθ, calculating is iterated, exports πn/τnArray, and root According to scattered light intensity function and phase function on πn/τnFunctional relation, calculate, output single-particle scattered light intensity function S, Xiang Han Number P；
The controller 102 is connected with the calculating sub module 101, and the calculating sub module 101 instruct defeated Enter and export.
In certain embodiments, the value range of the scatteringangleθ is 0~180 °.
In certain embodiments, the scale parameter α includes α<3 thin mode and the roughcast state of α >=3.
In certain embodiments, the controller 102 judges that the scale parameter α is α<3 thin mode or α >=3 Roughcast state, and instruction input is carried out to the calculating sub module 101 according to different scale parameter α and calls different algorithms to calculate an/bnArray.
In certain embodiments, the computer graphics device 100 of the single-particle Mie scattering properties can also include display mould Block, to be shown to the information exported in the output module 40.Such as the display module is computer monitor, put down Display screen of plate, mobile phone etc. etc..
In schematic diagram as in Figure 3-5, the computer graphics device 100 of the single-particle Mie scattering properties can be drawn Two figures：
One is polar diagrams of the scattered light intensity function S on angle of scattering, characterizes the scattering pattern of single-particle：Its pole is sat Parameter is angle of scattering, and polar value characterizes scattering strength.If particle size is smaller, Rayleigh scattering signatures, forward direction are embodied Scattering is symmetrical (as shown in Fig. 3 left parts) with back scattering, and scattering pattern is relatively simple；If particle size increases, embody Mie and dissipate Feature is penetrated, forward scattering is compared with back scattering bigger, and scattering pattern is increasingly complex (as shown in Fig. 4 left parts and Fig. 5 left parts)；
One is rectangular coordinate systems of the phase function P on angle of scattering, characterizes the scattering strength under different angle of scatterings.It is horizontal Coordinate is angle of scattering, and ordinate is phase function value, good (such as symmetry at left and right sides of boundary with 90 ° if particle size is smaller Shown in Fig. 3 right parts)；If particle size is larger, phase function value nearby has maximum at 0 °, and there is no obvious symmetry (such as Fig. 4 Shown in right part and Fig. 5 right parts).
On the other hand, as shown in Fig. 2, the embodiment of the present invention additionally provides a kind of computer of single-particle Mie scattering properties The drawing practice of plotter, the drawing practice of the computer graphics device of the single-particle Mie scattering properties include step：
S1, the complicated function in the Mie scattering formulas is handled, and is expressed as the manageable iteration of computer Functional form；
S2, draws according to the iteration function form after the processing；
S3, the drawing is stored；
S4, according to the drawing of the storage, the output and data call of image are carried out when issuing output order.
In certain embodiments, the step S1：Complicated function in the Mie scattering formulas is handled, and table Up to for the manageable iteration function form of computer, it is specially：
Using birefringence Coefficient m, scale parameter α as input, calculating is iterated, exports an/bnArray,
And according on an/bnFunctional relation, the extinction coefficient Q of single-particle is calculatedext, scattering coefficient Qsca；
By birefringence Coefficient m, scale parameter α, an/bnArray, extinction coefficient Qext, scattering coefficient QscaAs input, with reference to Scatteringangleθ, is iterated calculating, exports πn/τnArray, and according to scattered light intensity function and phase function on πn/τnFunction close System, calculates, scattered light intensity function S, the phase function P of output single-particle.
In certain embodiments, the value range of the scatteringangleθ is 0~180 °.
In certain embodiments, the scale parameter α includes α<3 thin mode and the roughcast state of α >=3.
In certain embodiments, a is being calculatedn/bnArray, when α is α<3 thin mode or the roughcast state when α >=3, calling Algorithm is different.
Key parameter an/bn, an/bnArray derives from scattering intensity distribution function i1/i2, expression formula is：
an/bnIt is wavelength X, particle radii r, the function of birefringence Coefficient m, by the first kind and three classes Bessel function tables Reach.an/bnComputing module is using m the and α values that user gives as input, according to iterative calculation an/bn, and according to formula：
Extinction coefficient, the scattering coefficient of single-particle are calculated respectively.
In the present embodiment, the scale parameter of particle is divided into α<3 thin mode and the roughcast state of α >=3, respectively with difference Algorithm calculate an/bn。
Such as it is divided into α in the scale parameter of particle<When 3, the algorithm is：
In above formula, α is scale parameter, and m is birefringence coefficient, AnBnFor the iteration parameter of introducing, no physical meaning；DnFor The iteration parameter of Bessel functions, is the function of α and m α.
In the α >=3, the algorithm is：
In above formula, α is scale parameter, and m is birefringence coefficient,For the iteration parameter of introducing, no physical meaning；DnFor The iteration parameter of Bessel functions, is the function of α and m α.
This two kinds of algorithms have differences in the selection of iteration parameter, and the main distinction is that applicable range scale is to differ Cause.The former iteration precision higher under small scale, no longer sets up under large scale；The latter is on the contrary.Two kinds of iterative algorithms are distinguished Run in applicable range scale, it is thus possible to make result more accurate.
In certain embodiments, the process calculated in the computer graphics device 100 of the single-particle Mie scattering properties In, iterations n initial assignments are 1.5 α+10, but are run in the computer graphics device 100 of the single-particle Mie scattering properties In to judge an/bnValue, work as an/bnWhen having value more than 10156, main program will be returned to immediately, this operation is mainly used for preventing Numerical value overflows, and causes operation mistake.Further improve the accuracy of computing.
In certain embodiments, πn/τnIt is the function of scatteringangleθ, by Legendre function representations.In computer graphics device It is middle that scatteringangleθ is arranged to 0~180 °.πn/τnThe Q that computing module is exported with above-mentioned moduleext/QscaFor input, meter is iterated Calculate πn/τn, and according to formula：
S=| S1|2+|S2|2
To calculate scattered light intensity function S, further according to：
Calculate KPT Scatter phase function P.So far, the Mie scattering properties of single-particle is all calculated and completed.
User can define birefringence Coefficient m, the scale parameter α of single-particle, software respectively by two values input frame Support plural number input, it is not necessary to which user carries out nuisance operation.Then " calculating/drawing " button is clicked on, will appear from the middle part of interface Single-particle scattering pattern and phase function two images, actual effect is referred to attached drawing 3, and (m=1.33-0.01i, α=1, represents Thin mode), attached drawing 4 (m=1.33-0.01i, α=5, represent roughcast state), (m=1.33-0.01i, α=20, represent thick attached drawing 5 Mode).Empirical tests, it is accurate to calculate mapping result.
In certain embodiments, after calculating drawing and terminating, drawing and result of calculation can store in a storage module, For example, operation result can be saved on local computer with Excel forms, file will automatically with " the local computer date- Time " (" yyyymmdd-hhmmss.xls ") title preserves, and user consults will be very convenient.
The technique effect of the present invention：The computer graphics device of single-particle Mie scattering properties disclosed by the invention and drawing Complicated function (Bessel functions/Legendre functions etc.) in Mie scattering formulas is converted into computer and can handled by method Iteration form, solve the problems, such as that such complicated function directly cannot ask calculation using computer, overcome and deposited in numerical computations Difficulty.By key parameter an/bn/πn/τn, extinction coefficient, scattering coefficient, scattered light intensity function, phase function calculating integrate Onto the computer graphics device of same single-particle Mie scattering properties, this single-particle Mie scattering properties has largely been expanded The scope of application of computer graphics device, improves the applicability of Mie scattering numerical computation methods.Simple grain provided in an embodiment of the present invention The computer graphics device of sub- Mie scattering properties, because having output module, there are data output function, and provides number According to subsequent applications interface.
Those skilled in the art should further appreciate that, be described with reference to the embodiments described herein Each exemplary unit and algorithm steps, can be realized with electronic hardware, computer software or the combination of the two, in order to clear Illustrate to Chu the interchangeability of hardware and software, generally describe each exemplary group according to function in the above description Into and step.These functions are performed with hardware or software mode actually, application-specific and design depending on technical solution Constraints.Professional technician can realize described work(using distinct methods to each specific application The software module that device performs, or the combination of the two are managed to implement.Software module can be placed in random access memory (RAM), memory, Read-only storage (ROM), electrically programmable ROM, electrically erasable ROM, register, hard disk, moveable magnetic disc, CD-ROM, Or in any other form of storage medium well known in technical field.
In the description of the present invention, it is to be understood that term " " center ", " longitudinal direction ", " transverse direction ", " length ", " width ", " thickness ", " on ", " under ", "front", "rear", "left", "right", " vertical ", " level ", " top ", " bottom " " interior ", " outer ", " up time The orientation or position relationship of the instruction such as pin ", " counterclockwise ", " axial direction ", " radial direction ", " circumferential direction " be based on orientation shown in the drawings or Position relationship, is for only for ease of and describes the present invention and simplify description, rather than indicates or imply that signified device or element must There must be specific orientation, with specific azimuth configuration and operation, therefore be not considered as limiting the invention.
In addition, term " first ", " second " are only used for description purpose, and it is not intended that instruction or hint relative importance Or the implicit quantity for indicating indicated technical characteristic.Thus, define " first ", the feature of " second " can be expressed or Implicitly include at least one this feature.
In the present invention, unless otherwise clearly defined and limited, term " installation ", " connected ", " connection ", " fixation " etc. Term should be interpreted broadly, for example, it may be fixedly connected or be detachably connected, or integrally；Can be that machinery connects Connect or be electrically connected；It can be directly connected, can also be indirectly connected by intermediary, can be in two elements The connection in portion or the interaction relationship of two elements, unless otherwise restricted clearly.For those of ordinary skill in the art For, the concrete meaning of above-mentioned term in the present invention can be understood as the case may be.
In the present invention, unless otherwise clearly defined and limited, fisrt feature can be with "above" or "below" second feature It is that the first and second features directly contact, or the first and second features pass through intermediary mediate contact.Moreover, fisrt feature exists Second feature " on ", " top " and " above " but fisrt feature are directly over second feature or oblique upper, or be merely representative of Fisrt feature level height is higher than second feature.Fisrt feature second feature " under ", " lower section " and " below " can be One feature is immediately below second feature or obliquely downward, or is merely representative of fisrt feature level height and is less than second feature.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show The description of example " or " some examples " etc. means specific features, structure, material or the spy for combining the embodiment or example description Point is contained at least one embodiment of the present invention or example.In the present specification, schematic expression of the above terms is not It must be directed to identical embodiment or example.Moreover, particular features, structures, materials, or characteristics described can be in office Combined in an appropriate manner in one or more embodiments or example.In addition, without conflicting with each other, the skill of this area Art personnel can be tied the different embodiments or example described in this specification and different embodiments or exemplary feature Close and combine.
Although the embodiment of the present invention has been shown and described above, it is to be understood that above-described embodiment is example Property, it is impossible to limitation of the present invention is interpreted as, those of ordinary skill in the art within the scope of the invention can be to above-mentioned Embodiment is changed, changes, replacing and modification.
The embodiment of present invention described above, is not intended to limit the scope of the present invention..Any basis Various other corresponding changes and deformation made by the technical concept of the present invention, should be included in the guarantor of the claims in the present invention In the range of shield.

Claims (10)

  1. A kind of 1. computer graphics device of single-particle Mie scattering properties, it is characterised in that including：
    Processing module, the processing module is handled the complicated function in the Mie scattering formulas, and is expressed as computer Manageable iteration function form；
    Graphics module, the iteration function form after the processing that the graphics module is conveyed according to the processing module are drawn；
    Memory module, the memory module are stored the drawing of the graphics module；
    Output module, the output module is according to the drawing of the memory module, when the processing module issues output order Carry out the output and data call of image.
  2. 2. the computer graphics device of single-particle Mie scattering properties according to claim 1, it is characterised in that the processing Module includes calculating sub module, and controller；
    The calculating sub module includes an/bnComputing module and πn/τnComputing module；
    The an/bnComputing module is iterated calculating, exports a using birefringence Coefficient m, scale parameter α as inputn/bnNumber Group；
    And according on an/bnFunctional relation, the extinction coefficient Q of single-particle is calculatedext, scattering coefficient Qsca；
    The πn/τnComputing module is by birefringence Coefficient m, scale parameter α, an/bnThe a of computing module outputn/bnArray, Extinction coefficient Qext, scattering coefficient QscaAs input, with reference to scatteringangleθ, calculating is iterated, exports πn/τnArray, and according to Scattered light intensity function and phase function are on πn/τnFunctional relation, calculate, output single-particle scattered light intensity function S, phase function P；
    The controller is connected with the calculating sub module, and carries out instruction input and output to the calculating sub module.
  3. 3. the computer graphics device of single-particle Mie scattering properties according to claim 2, it is characterised in that the scattering The value range of angle θ is 0~180 °.
  4. 4. the computer graphics device of single-particle Mie scattering properties according to claim 2, it is characterised in that the scale Parameter alpha includes α<3 thin mode and the roughcast state of α >=3.
  5. 5. the computer graphics device of single-particle Mie scattering properties according to claim 4, it is characterised in that the control Device judges that the scale parameter α is α<3 thin mode or the roughcast state of α >=3, and according to different scale parameter α to described Calculating sub module carries out instruction input and calls different algorithms to calculate an/bnArray.
  6. 6. a kind of drawing practice of the computer graphics device of single-particle Mie scattering properties, it is characterised in that including step：
    Complicated function in the Mie scattering formulas is handled, and is expressed as the manageable iteration function shape of computer Formula；
    Drawn according to the iteration function form after the processing；
    The drawing is stored；
    According to the drawing of the storage, the output and data call of image are carried out when issuing output order.
  7. 7. the drawing practice of the computer graphics device of single-particle Mie scattering properties according to claim 6, its feature exist In the step：Complicated function in the Mie scattering formulas is handled, and it is manageable repeatedly to be expressed as computer For functional form, it is specially：
    Using birefringence Coefficient m, scale parameter α as input, calculating is iterated, exports an/bnArray；
    And according on an/bnFunctional relation, the extinction coefficient Q of single-particle is calculatedext, scattering coefficient Qsca；
    By birefringence Coefficient m, scale parameter α, an/bnArray, extinction coefficient Qext, scattering coefficient QscaAs input, with reference to scattering Angle θ, is iterated calculating, exports πn/τnArray, and according to scattered light intensity function and phase function on πn/τnFunctional relation, Calculate, scattered light intensity function S, the phase function P of output single-particle.
  8. 8. the drawing practice of the computer graphics device of single-particle Mie scattering properties according to claim 7, its feature exist In the value range of the scatteringangleθ is 0~180 °.
  9. 9. the drawing practice of the computer graphics device of single-particle Mie scattering properties according to claim 7, its feature exist In the scale parameter α includes α<3 thin mode and the roughcast state of α >=3.
  10. 10. the drawing practice of the computer graphics device of single-particle Mie scattering properties according to claim 9, its feature exist In in calculating an/bnDuring array, when α is α<3 thin mode or the roughcast state when α >=3, the algorithm of calling are different.
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