CN105043988B - Single-point based on scanning galvanometer deconvolutes microscopic system and imaging method - Google Patents
Single-point based on scanning galvanometer deconvolutes microscopic system and imaging method Download PDFInfo
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Abstract
The single-point based on scanning galvanometer of the invention microscopic system of deconvoluting belongs to optical microphotograph fields of measurement with imaging method；The microscopic system element such as including spiral phase plate；First directional light and the second directional light finally form ring-shaped light spot and circular light spot respectively on fluorescent samples；The fluorescence that fluorescent samples surface excitation goes out is received by a photoelectric detector and is imaged；The imaging method realized in said system, obtains the gray value for the object point that coordinate is (i, j) first, then by adjusting two scanning galvanometers, travels through i and j all values, using the gray value information of all object points, constructs complete two dimensional image；The difference of the present invention and tradition STED technologies are do not irradiating two beam wavelength identical laser beams in the same time, and seek difference to reduce the scope of area-of-interest using two images, computing of deconvoluting is introduced simultaneously, go unless fuzzy on focal plane, reduce the measurement error that the convolution effect of detector is brought, the final resolution ratio for improving imaging system.
Description
Technical field
The single-point based on scanning galvanometer of the invention microscopic system of deconvoluting belongs to optical microphotograph fields of measurement with imaging method.
Background technology
Among the research of nanometer technology and biotechnology, high-resolution micro-imaging technique serves vital work
With.Particularly in life science, in order to more fully understand the mechanism of human life and the mechanism of production of disease, it is necessary to
The three-dimensional space position and distribution in three-dimensional cell such as cell (intracellular organ), virus are observed, it is necessary to accurate in the cell
Specific protein is positioned to study the relation of its position and function.And reflect the characteristic dimension of these system properties all in nanometer
Magnitude.Optical microscopy can realize fast imaging, long-time Imaging for Monitoring by non-contacting mode, not interfere with simultaneously
The activity of biosystem.In recent years, with the appearance of new fluorescence probe and imaging theory, the resolution ratio of light microscope is able to
Optical diffraction limit is broken through, the precision that can be compared favourably with electron microscope is reached, it is possible to a nanometer chi is seen on living cells
The protein of degree.The microtechnic that these resolution ratio break through optical diffraction limit is referred to as super-resolution microscopy.Wherein, it is most famous
The stimulated radiation loss (Stimulated Emission Depletion, STED) for surely belonging to obtain the Nobel Prize in 2014 show
Microtechnology.
STED technologies propose (Hell, S.W.and Wichmann, J. (1994), ' Breaking by Stefan W.Hell
the diffraction resolution limit by stimulated emission:Stimulated-emission-
Depletion fluorescence microscopy ', Optics Letters, 19 (11):780-782), its basic thought
It is while irradiating two beams has the picosecond pulse laser light beam of different wave length, wherein a branch of picosecond pulse laser light beam is in sample table
Face is converged to the first focal beam spot of donut-like, and a branch of picosecond pulse laser light beam is converged to second in sample surfaces and gathered in addition
Burnt hot spot, two spot centers is overlapped, wherein the fluorescent material positioned at spot center region inspires fluorescence, in hot spot
But de excitation hair occurs for the fluorescent material not in spot center region, fluorescence is not sent, so as to realize super-resolution imaging.
The content of the invention
The present invention has the laser beam of phase co-wavelength on the basis of traditional STED technologies not irradiating two beams in the same time,
Deconvolution algorithm is employed simultaneously, the resolution ratio of microscopic system is further improved.
The object of the present invention is achieved like this：
Single-point based on scanning galvanometer deconvolutes microscopic system, including spiral phase plate, Amici prism, polarization beam apparatus, X
Axle scanning galvanometer, Y axis scanning galvanometer, scanning lens, Guan Jing, focusing objective len, long wave pass filter, collection object lens and photodetection
Device；
First directional light sequentially passes through Amici prism and polarization beam apparatus transmission after spiral phase plate is modulated, and X-axis is swept
Galvanometer and Y axis scanning vibration mirror reflected, scanning lens and the transmission of pipe mirror are retouched, is converged in by focusing objective len on fluorescent samples, forms ring
Shape hot spot；
Described spiral phase plate makes the first directional light additional spiral phase factor exp (il θ)；Wherein, i is imaginary number list
Position, l is the topological charge number of spiral phase plate, and θ is rotational orientation angle；The X-axis scanning galvanometer is driven by X-axis motor, watched by X-axis
Dress system is controlled, and Y axis scanning galvanometer is driven by y-axis motor, by Y-axis servo system control, and X-axis scanning galvanometer shakes with Y axis scanning
Mirror cooperates, and realizes the point by point scanning that XY faces are carried out to sample；
Second directional light sequentially passes through polarization beam apparatus transmission, X-axis scanning galvanometer and Y-axis after Amici prism reflects
Scanning galvanometer reflects, scanning lens and the transmission of pipe mirror, is converged in by focusing objective len on fluorescent samples, forms circular light spot；
First directional light optical wavelength parallel with second is identical, is coaxially transmitted after Amici prism, by fluorescence sample
Product surface excitation goes out fluorescence, and the fluorescence sequentially passes through focusing objective len, Guan Jing and scanning lens transmission, Y axis scanning galvanometer, X-axis
Scanning galvanometer and polarization beam apparatus reflection, long wave pass filter transmission are converged to by collection object lens and carried out on photodetector
Picture.
The above-mentioned single-point based on scanning galvanometer deconvolutes microscopic system, and described polarization beam apparatus replaces with dichroscope.
The above-mentioned single-point based on scanning galvanometer deconvolutes microscopic system, and described long wave pass filter replaces with bandpass filter
Piece.
The above-mentioned single-point based on scanning galvanometer deconvolutes microscopic system, and the cutoff wavelength λ of the long wave pass filter chooses
It should meet：λ1＜ λ ＜ λ2, wherein, λ1For excitation wavelength, λ2The wavelength of fluorescence gone out for fluorescent samples surface excitation.
It is a kind of to be deconvoluted the imaging method realized in microscopic system in the above-mentioned single-point based on scanning galvanometer, sat first
It is designated as the gray value sum of the object point of (i, j)i,j, then by adjusting the angle of X-axis scanning galvanometer and Y axis scanning galvanometer, traversal i and
J all values, using the gray value information of all object points, construct complete two dimensional image.
Above-mentioned imaging method, described coordinate is the gray value information of the object point of (i, j), is obtained by following steps：
Step a, only irradiating the first directional light, do not irradiating under conditions of the second directional light, photodetector with coordinate (i,
J) fluorescent samples are imaged centered on, the first image Image1 that resolution ratio is m × n is obtainedm,n；
Step b, only irradiating the second directional light, do not irradiating under conditions of the first directional light, photodetector with coordinate (i,
J) fluorescent samples are imaged centered on, the second image Image2 that resolution ratio is m × n is obtainedm,n；
Step c, according to below equation to the first image Image1m,nWith the second image Image2m,nCarry out computing：
Temp1m,n=deconv (Image1m,n)
Temp2m,n=deconv (Image2m,n)
In formula, deconv represents computing of deconvoluting；
Step d, according to below equation calculate obtain central region of interest domain information Tempm,n：
In formula, n is more than 0；
Step e, according to below equation to center interested area information Tempm,nCarry out summation operation：
In formula, sumi,jDenotation coordination is the gray value of the object point of (i, j).
Above-mentioned imaging method, constructs complete two dimensional image and is obtained by following steps：
Step a, one blank matrix of construction；
Step b, by sumi,jCorresponding element position is filled out successively.
Beneficial effect：
Firstth, two laser beam wavelengths of tradition STED technical requirements are differed, while irradiation, and application claims two
Individual laser beam wavelength is identical, and asynchronously irradiates, and seeks difference to reduce the scope of area-of-interest using two images, these
Distinguishing feature can improve the resolution ratio of imaging system.
Secondth, present invention employs computing of deconvoluting, and then it can go unless obscuring on focal plane, reduces detector
The measurement error that convolution effect is brought, the technical characteristic can further improve the resolution ratio of imaging system.
3rd, the present invention is provided with caliber, forms telecentric beam path, for coordinating X-axis scanning galvanometer and Y axis scanning galvanometer,
Realize on axle as matter is consistent with off-axis image matter, improve the uniformity of beam lighting on scanning plane, reduction is distributed not because of laser irradiation
Measurement error caused by.
Brief description of the drawings
Fig. 1 is that the single-point based on scanning galvanometer of the invention deconvolutes the structural representation of microscopic system.
Fig. 2 is by sumi,jThe schematic diagram filled out successively behind corresponding element position.
In figure：1 spiral phase plate, 2 Amici prisms, 3 polarization beam apparatus, 4X axles scanning galvanometer, 5Y axles scanning galvanometer, 6 are swept
Retouch lens, 7 pipe mirrors, 8 focusing objective lens, 9 long wave pass filters, 10 collection object lens, 11 photodetectors.
Embodiment
The specific embodiment of the invention is described in further detail below in conjunction with the accompanying drawings.
Specific embodiment one
The present embodiment is that the single-point based on scanning galvanometer deconvolutes microscopic system embodiment.
The single-point based on scanning galvanometer of the present embodiment deconvolutes microscopic system, and structural representation is as shown in Figure 1.This is based on
The single-point of scanning galvanometer deconvolutes microscopic system including spiral phase plate 1, Amici prism 2, polarization beam apparatus 3, X-axis scanning galvanometer
4th, Y axis scanning galvanometer 5, scanning lens 6, pipe mirror 7, focusing objective len 8, long wave pass filter 9, collection object lens 10 and photodetector
11；
First directional light sequentially passes through Amici prism 2 and polarization beam apparatus 3 is transmitted, X after the modulation of spiral phase plate 1
Axle scanning galvanometer 4 and Y axis scanning galvanometer 5 are reflected, and scanning lens 6 and pipe mirror 7 are transmitted, and fluorescent samples are converged in by focusing objective len 8
On, form ring-shaped light spot；
Described spiral phase plate 1 makes the first directional light additional spiral phase factor exp (il θ)；Wherein, i is imaginary number list
Position, l is the topological charge number of spiral phase plate 1, and θ is rotational orientation angle；The X-axis scanning galvanometer 4 is driven, by X-axis by X-axis motor
Servo system control, Y axis scanning galvanometer 5 is driven by y-axis motor, by Y-axis servo system control, and X-axis scanning galvanometer 4 is swept with Y-axis
Retouch galvanometer 5 to cooperate, realize the point by point scanning that XY faces are carried out to sample；
Second directional light sequentially passes through polarization beam apparatus 3 and transmitted after the reflection of Amici prism 2, X-axis scanning galvanometer 4 and Y
Axle scanning galvanometer 5 is reflected, and scanning lens 6 and pipe mirror 7 are transmitted, and are converged in by focusing objective len 8 on fluorescent samples, forms circular light
Spot；
First directional light optical wavelength parallel with second is identical, is coaxially being transmitted after Amici prism 2, by fluorescence sample
Product surface excitation goes out fluorescence, and the fluorescence sequentially passes through focusing objective len 8, pipe mirror 7 and scanning lens 6 and transmitted, Y axis scanning galvanometer 5,
X-axis scanning galvanometer 4 and polarization beam apparatus 3 are reflected, and long wave pass filter 9 is transmitted, and photodetector is converged to by collection object lens 10
It is imaged on 11.
Specific embodiment two
The present embodiment is that the single-point based on scanning galvanometer deconvolutes microscopic system embodiment.
The single-point based on scanning galvanometer of the present embodiment deconvolutes microscopic system, is with the difference of specific embodiment one,
Described polarization beam apparatus 3 replaces with dichroscope.
Specific embodiment three
The present embodiment is that the single-point based on scanning galvanometer deconvolutes microscopic system embodiment.
The single-point based on scanning galvanometer of the present embodiment deconvolutes microscopic system, is with the difference of specific embodiment one,
Described long wave pass filter 9 replaces with bandpass filter.
The single-point of above example deconvolutes microscopic system, and the cutoff wavelength λ of the long wave pass filter 9 chooses and should expired
Foot：λ1＜ λ ＜ λ2, wherein, λ1For excitation wavelength, λ2The wavelength of fluorescence gone out for fluorescent samples surface excitation；Long wave pass filter
9 cutoff wavelength λ is limited to excitation wavelength λ1The wavelength of fluorescence λ gone out with fluorescent samples surface excitation2Between, this parameter limit
Surely the light of laser can be filtered out, retains fluorescence and contains sample surface type information, positive work is played to improving microscopic system resolution ratio
With.
Specific embodiment four
The present embodiment for more than the single-point based on scanning galvanometer deconvolute the imaging method implementation realized in microscopic system
Example.
The imaging method of the present embodiment, obtains the gray value sum for the object point that coordinate is (i, j) firsti,j, then by adjusting X
The angle of axle scanning galvanometer 4 and Y axis scanning galvanometer 5, travels through i and j all values, using the gray value information of all object points,
The complete two dimensional image of construction.
Specific embodiment five
The present embodiment for more than the single-point based on scanning galvanometer deconvolute the imaging method implementation realized in microscopic system
Example.
The imaging method of the present embodiment, on the basis of specific embodiment four, further limits object point of the coordinate as (i, j)
Gray value information, obtained by following steps：
Step a, the first directional light is only being irradiated, do not irradiated under conditions of the second directional light, photodetector 12 is with coordinate
Fluorescent samples are imaged centered on (i, j), the first image Image1 that resolution ratio is m × n is obtainedm,n；
Step b, the second directional light is only being irradiated, do not irradiated under conditions of the first directional light, photodetector 12 is with coordinate
Fluorescent samples are imaged centered on (i, j), the second image Image2 that resolution ratio is m × n is obtainedm,n；
Step c, according to below equation to the first image Image1m,nWith the second image Image2m,nCarry out computing：
Temp1m,n=deconv (Image1m,n)
Temp2m,n=deconv (Image2m,n)
In formula, deconv represents computing of deconvoluting；
Step d, according to below equation calculate obtain central region of interest domain information Tempm,n：
In formula, n is more than 0；
Step e, according to below equation to center interested area information Tempm,nCarry out summation operation：
In formula, sumi,jDenotation coordination is the gray value of the object point of (i, j).
Specific embodiment six
The present embodiment for more than the single-point based on scanning galvanometer deconvolute the imaging method implementation realized in microscopic system
Example.
The imaging method of the present embodiment, on the basis of specific embodiment four, further limits the complete X-Y scheme of construction
As being obtained by following steps：
Step a, one blank matrix of construction；
Step b, by sumi,jCorresponding element position is filled out successively, as shown in Figure 2.
It should be noted that the technical scheme of specific embodiment five and specific embodiment six can merge.
Claims (2)
- The microscopic system 1. single-point based on scanning galvanometer deconvolutes, it is characterised in that including spiral phase plate (1), Amici prism (2), polarization beam apparatus (3), X-axis scanning galvanometer (4), Y axis scanning galvanometer (5), scanning lens (6), Guan Jing (7), focusing objective len (8), long wave pass filter (9), collection object lens (10) and photodetector (11)；First directional light sequentially passes through Amici prism (2) and polarization beam apparatus (3) transmission after spiral phase plate (1) modulation, X-axis scanning galvanometer (4) and Y axis scanning galvanometer (5) reflection, scanning lens (6) and Guan Jing (7) transmissions, are converged by focusing objective len (8) On fluorescent samples, ring-shaped light spot is formed；Described spiral phase plate (1) makes the first directional light additional spiral phase factor exp (il θ)；Wherein, i is imaginary unit, L is the topological charge number of spiral phase plate (1), and θ is rotational orientation angle；The X-axis scanning galvanometer (4) is driven, by X by X-axis motor Axle servo system control, Y axis scanning galvanometer (5) drives by y-axis motor, by Y-axis servo system control, X-axis scanning galvanometer (4) with Y axis scanning galvanometer (5) cooperates, and realizes the point by point scanning that XY faces are carried out to sample；Second directional light sequentially passes through polarization beam apparatus (3) transmission, X-axis scanning galvanometer (4) after Amici prism (2) reflection With Y axis scanning galvanometer (5) reflection, scanning lens (6) and Guan Jing (7) transmissions are converged on fluorescent samples by focusing objective len (8), Form circular light spot；First directional light optical wavelength parallel with second is identical, in the coaxial transmission after Amici prism (2), by fluorescent samples Surface excitation goes out fluorescence, and the fluorescence sequentially passes through focusing objective len (8), Guan Jing (7) and scanning lens (6) transmission, and Y axis scanning shakes Mirror (5), X-axis scanning galvanometer (4) and polarization beam apparatus (3) reflection, long wave pass filter (9) transmission are converged by collection object lens (10) Gather and be imaged on photodetector (11)；The cutoff wavelength λ of the long wave pass filter (9) chooses and should met：λ1＜ λ ＜ λ2, wherein, λ1For excitation wavelength, λ2For The wavelength of fluorescence that fluorescent samples surface excitation goes out；The gray value sum for the object point that coordinate is (i, j) is obtained firsti,j, then by adjusting X-axis scanning galvanometer (4) and Y axis scanning The angle of galvanometer (5), travels through i and j all values, using the gray value information of all object points, constructs complete two dimensional image；Described coordinate is the gray value information of the object point of (i, j), is obtained by following steps：Step a, only irradiating the first directional light, do not irradiating under conditions of the second directional light, photodetector (11) with coordinate (i, J) fluorescent samples are imaged centered on, the first image Image1 that resolution ratio is m × n is obtainedm,n；Step b, only irradiating the second directional light, do not irradiating under conditions of the first directional light, photodetector (11) with coordinate (i, J) fluorescent samples are imaged centered on, the second image Image2 that resolution ratio is m × n is obtainedm,n；Step c, according to below equation to the first image Image1m,nWith the second image Image2m,nCarry out computing：Temp1m,n=deconv (Image1m,n)Temp2m,n=deconv (Image2m,n)In formula, deconv represents computing of deconvoluting；Step d, according to below equation calculate obtain central region of interest domain information Tempm,n：<mrow> <msub> <mi>Temp</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>2</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mi>n</mi> <mo>&times;</mo> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>1</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>2</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>></mo> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>1</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>2</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>&le;</mo> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>1</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>In formula, n is more than 0；Step e, according to below equation to center interested area information Tempm,nCarry out summation operation：<mrow> <msub> <mi>sum</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mi>m</mi> </munder> <munder> <mo>&Sigma;</mo> <mi>n</mi> </munder> <msub> <mi>Temp</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow>In formula, sumi,jDenotation coordination is the gray value of the object point of (i, j)；The complete two dimensional image of construction is obtained by following steps：Step a, one blank matrix of construction；Step b, by sumi,jCorresponding element position is filled out successively.
- The microscopic method 2. single-point based on scanning galvanometer deconvolutes, the used single-point based on scanning galvanometer deconvolutes micro- system System include spiral phase plate (1), Amici prism (2), polarization beam apparatus (3), X-axis scanning galvanometer (4), Y axis scanning galvanometer (5), Scanning lens (6), Guan Jing (7), focusing objective len (8), long wave pass filter (9), collection object lens (10) and photodetector (11)；First directional light sequentially passes through Amici prism (2) and polarization beam apparatus (3) transmission after spiral phase plate (1) modulation, X-axis scanning galvanometer (4) and Y axis scanning galvanometer (5) reflection, scanning lens (6) and Guan Jing (7) transmissions, are converged by focusing objective len (8) On fluorescent samples, ring-shaped light spot is formed；Described spiral phase plate (1) makes the first directional light additional spiral phase factor exp (il θ)；Wherein, i is imaginary unit, L is the topological charge number of spiral phase plate (1), and θ is rotational orientation angle；The X-axis scanning galvanometer (4) is driven, by X by X-axis motor Axle servo system control, Y axis scanning galvanometer (5) drives by y-axis motor, by Y-axis servo system control, X-axis scanning galvanometer (4) with Y axis scanning galvanometer (5) cooperates, and realizes the point by point scanning that XY faces are carried out to sample；Second directional light sequentially passes through polarization beam apparatus (3) transmission, X-axis scanning galvanometer (4) after Amici prism (2) reflection With Y axis scanning galvanometer (5) reflection, scanning lens (6) and Guan Jing (7) transmissions are converged on fluorescent samples by focusing objective len (8), Form circular light spot；First directional light optical wavelength parallel with second is identical, in the coaxial transmission after Amici prism (2), by fluorescent samples Surface excitation goes out fluorescence, and the fluorescence sequentially passes through focusing objective len (8), Guan Jing (7) and scanning lens (6) transmission, and Y axis scanning shakes Mirror (5), X-axis scanning galvanometer (4) and polarization beam apparatus (3) reflection, long wave pass filter (9) transmission are converged by collection object lens (10) Gather and be imaged on photodetector (11)；The cutoff wavelength λ of the long wave pass filter (9) chooses and should met：λ1＜ λ ＜ λ2, wherein, λ1For excitation wavelength, λ2For The wavelength of fluorescence that fluorescent samples surface excitation goes out；Characterized in that,The gray value sum for the object point that coordinate is (i, j) is obtained firsti,j, then by adjusting X-axis scanning galvanometer (4) and Y axis scanning The angle of galvanometer (5), travels through i and j all values, using the gray value information of all object points, constructs complete two dimensional image；Described coordinate is the gray value information of the object point of (i, j), is obtained by following steps：Step a, only irradiating the first directional light, do not irradiating under conditions of the second directional light, photodetector (11) with coordinate (i, J) fluorescent samples are imaged centered on, the first image Image1 that resolution ratio is m × n is obtainedm,n；Step b, only irradiating the second directional light, do not irradiating under conditions of the first directional light, photodetector (11) with coordinate (i, J) fluorescent samples are imaged centered on, the second image Image2 that resolution ratio is m × n is obtainedm,n；Step c, according to below equation to the first image Image1m,nWith the second image Image2m,nCarry out computing：Temp1m,n=deconv (Image1m,n)Temp2m,n=deconv (Image2m,n)In formula, deconv represents computing of deconvoluting；Step d, according to below equation calculate obtain central region of interest domain information Tempm,n：<mrow> <msub> <mi>Temp</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>2</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mi>n</mi> <mo>&times;</mo> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>1</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>2</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>></mo> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>1</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>2</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>&le;</mo> <mi>T</mi> <mi>e</mi> <mi>m</mi> <mi>p</mi> <msub> <mn>1</mn> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>In formula, n is more than 0；Step e, according to below equation to center interested area information Tempm,nCarry out summation operation：<mrow> <msub> <mi>sum</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mi>m</mi> </munder> <munder> <mo>&Sigma;</mo> <mi>n</mi> </munder> <msub> <mi>Temp</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow>In formula, sumi,jDenotation coordination is the gray value of the object point of (i, j)；The complete two dimensional image of construction is obtained by following steps：Step a, one blank matrix of construction；Step b, by sumi,jCorresponding element position is filled out successively.
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