CN103792288A - Sparse array ultrasound phased array detection method of concrete dam disease - Google Patents

Abstract

The invention discloses a sparse array ultrasound phased array detection method of a concrete dam disease. The sparse array ultrasound phased array detection method combines a propagation characteristic of an ultrasound beam, a dynamic space focusing characteristic of a phased array technology and a large volume hydraulic concrete structure deep disease characteristic, optimally designs phased array element arrangement through an immune algorithm by adopting a sparse array ultrasound phase control probe according to the apriori information of a concrete dam disease position, thus reducing the probe process cost; and a data collecting system stimulates an ultrasound wave beam, and finishes the data collection and storage treatment, and thus realizing the scene detection for a large volume hydraulic concrete structure disease; and meanwhile, a phased array ultrasound detecting image is rebuilt through a two-dimension grey-scale map rebuilding method to obtain a high loading capacity detection image, and thus obtaining the characteristic information of the large volume hydraulic concrete structure deep disease.

Description

The thinned array ultrasonic phase array detection method of concrete dam disease

Technical field

The present invention relates to belong to the large volume Hydro-concrete Structures disease Detection Techniques fields such as concrete dam, be specifically related to a kind of thinned array ultrasonic phase array detection method of concrete dam disease.

Background technology

The common disease of large volume Hydro-concrete Structures comprises crack, corrosion, freeze thawing, temperature fatigue, carbonization, steel bar corrosion, alkali etc., in these diseases separately or under acting in conjunction, the surface damage of xoncrete structure and inherent vice form and constantly accumulation, have a strong impact on stability, permanance and the load-bearing capacity of structure, thereby reduced the safe running performance of Hydro-concrete Structures.At present, safety monitoring analysis adopts the mode of burying sensor inside and outside dam body underground to measure concrete dam operational factor, by the safe condition at the each position of the mode such as statistical study and calculating comprehensive evaluation concrete dam, this method can be found as early as possible dam body operation exception under comparatively economic condition, but accurately judging in the disease situation that whole dam all sites may occur, still needing further to be improved.The detection level of current concrete dam disease is comparatively backward.

Hyperacoustic penetration capacity is strong, and ultrasonic detection equipment is simple, operate more convenient, the fault of construction such as crackle, weld seam that is all the time all widely used in metal detects, and obtain good effect, be one of focus of domestic and international Structural defect field of detecting research, but the application of ultrasonic listening technology on concrete dam is also less.Main cause is: the volume of concrete dam or Hydro-concrete Structures is generally all comparatively huge, in the process that ultrasound wave is propagated in concrete, there is the phenomenons such as energy attenuation, sound scattering and reflection, make ultrasonic applications in the time that concrete dam disease detects, produce investigation depth little (being generally less than 500mm), and the mutual interference of reception ripple phase also limit by force the application prospect of ultrasound wave in concrete dam disease is surveyed.

Phased array ultrasonic detection technology is based on conventional ultrasound and Huygens's theory, form array energy transducer by multiple separate piezoelectric chips, each wafer is called a unit, excite unit by certain rule and sequential electricity consumption subsystem controls, make the ultrasound wave stack of each unit transmitting in array form a new wave front; Out of phase by pulse daley resulting from triggering is interfered, regulate ultrasonic beam angle or the depth of focus, thereby reach the object that produces the phased effects such as wave beam focusing, deflection at different depth, diverse location, survey image and high-precision Disease Characters information thereby carry out the high-resolution disease of a series of processing by the echoed signal that data acquisition instrument is gathered.In Non-Destructive Testing, phased array supersonic technology can be controlled the parameters such as axis, yawing moment, focal position and the focal spot size of probe generation ultrasonic beam flexibly, easily, can greatly improve signal to noise ratio (S/N ratio), detection sensitivity and detection efficiency, be one of Hot spots for development of ultrasonic detecting technology.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of thinned array ultrasonic phase array detection method of concrete dam disease, according to the prior imformation of large volume Hydro-concrete Structures disease, adopt Artificial Immune Algorithm optimal design to there is the two-dimensional random thinned array transducer of sparse characteristic, adopt two dimensional gray figure reconstructing method to build disease detection image, realize the in-situ measurement of large volume Hydro-concrete Structures disease.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

A thinned array ultrasonic phase array detection method for concrete dam disease, concrete steps are as follows:

Step 1, for the prior imformation of concrete dam disease, employing Artificial Immune Algorithm optimal design has the two-dimensional random thinned array transducer of sparse characteristic, obtains the arrangement form of thinned array phased array ultrasonic detection array element; Be specially:

101, the Sparse parameter that reflects redundance is set, full battle array redundant system linear transducer array is carried out to immune algorithm simulation;

102, it is k that coding parameter is set, and establishes k=0 and carries out initialization, and select at random the initialization antibody P of colony (k);

103, the initialization antibody P of colony (k) is carried out to affinity check assessment with antigen;

104, the initialization antibody P of colony (k) is assessed to big or small descending sort according to affinity, select the front 50% higher P of antibody colony of affinity sequence _h(k) carry out the amplification of self-adaptation clonal propagation, obtain the P of antibody colony _m(k) fitness function of, constructing is:

$\mathrm{Fit}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="1401261400234.png,1401261400235.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{ML}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="1401261400232.png,1401261400233.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\mathrm{SL}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="1401261400234.png,1401261400235.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{BM}}_0-{\mathrm{BM}}_i|/{\mathrm{BM}}_0)+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="1401261400232.png,1401261400233.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{BS}}_0-{\mathrm{BS}}_i|/{\mathrm{BS}}_0)$

In formula, ML and SL are respectively main lobe and the sidelobe performance of array pulse echo response; k ₁and k ₂be respectively the weighted value of main lobe and sidelobe performance; BM ₀and BS ₀represent respectively pulse echo main lobe and the secondary lobe width of full battle array redundant system; BM _iand BS _ibe respectively main lobe and the secondary lobe width of thinned array in i direction; N is the judge direction number of the corresponding effect in thinned array space;

105, utilize mutation operator to the clonal propagation antibody P of colony _m(k) make a variation, produce antibody population P of new generation _n(k);

106, from antibody population PN of new generation (k), select a certain amount of antibody to replace rear 50% lower antibody colony of affinity sequence in the initialization antibody P of colony (k), produce population P of new generation (k+1);

107, be optimized criterion and pass judgment on, if do not meet, return to step 103; If meet, loop termination, thus obtain the arrangement form of thinned array phased array ultrasonic detection array element;

Step 2, according to the arrangement form of thinned array ultrasonic phase array detection array element, arranges phased array supersonic linear transducer array on concrete dam surface;

Step 3, computer control system calculates the time delay of ultrasonic array element, is sent to signal transmitting device; Signal transmitting device produces the ultrasonic signal of different carryover effects, is sent to ultrasonic probe array; Ultrasound wave in concrete dam conducted inside, adopts the mode of sector display to carry out disease detection to concrete dam by ultrasonic probe array; The feedback signal of ultrasonic scanning transfers to computer control system after by the collection of ultrasonic signal collector;

Described sector display is specially: according to the fineness requirement of the structure of concrete dam and disease detection, u root sweep trace is set, v sampled point is set on every sweep trace, after the complete sweep trace of every collection, carries out the collection of next root sweep trace, thereby obtain u × v sampled data;

Step 4, computer control system receives after the feedback signal of ultrasonic scanning, adopt { (r, θ), the polar form of g} is carried out data storage, utilize 2-D gray image reconstructing method to rebuild phased array ultrasonic detection gray level image simultaneously, thereby obtain the two dimensional gray hum pattern of concrete dam, to differentiate position and the order of severity of disease; Wherein, (r, θ) is the positional information of sampled point in sector display, and θ is the angle between sweep trace and the 1st sweep trace at this sampled point place, and r is that on this sampled point and place sweep trace, the distance between the 1st sampled point is; The gray scale normalization degree of disease that g is ultrasound data that this sampled point gathers;

Described 2-D gray image reconstructing method is specially: first the sampled point of j sampled point on each root sweep trace is carried out to interpolation arithmetic, obtain the gray scale measured value of each interpolation point, i.e. ultrasonic echo wave height; Then obtain phased array ultrasonic detection gray level image by the coordinate conversion between polar coordinates and planimetric coordinates; Wherein

The gray scale measured value g of described interpolation point G _gcomputing formula is as follows:

$\begin{array}{c}{g}_G=g_a\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_b(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\\ g_a=g_{i,j}\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_{i+1,j}(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\\ g_b=g_{i,j+1}\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_{i+1,j+1}(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\end{array}$

In formula, g _a, g _bbe respectively the interpolation of j and j+1 article of length of scanning line direction; g _i,j, g _{i+1, j}, g _{i, j+1}, g _{i+1, j+1}represent respectively the gray-scale value of adjacent four sampled points of interpolation point G, g _i,jrepresent the gray-scale value of the sampled point that on j article of sweep trace of sector display, radius is i; Δ r is two spacing in sampled point sample radius; R ' is the spacing of interpolation point and previous sampled point.

As further prioritization scheme of the present invention, described computer control system, signal transmitting device and signal picker composition data acquisition system (DAS); Wherein, described signal transmitting device is connected with computer control system with ultrasonic probe array respectively by data conductive bus; Described ultrasonic signal collector is arranged on the opposite side of concrete dam, and is connected to computer control system by data transmission line.

As further prioritization scheme of the present invention, sampled point described in step 3 be provided with two kinds of situations, one is to be uniformly distributed on sweep trace; One is to be encrypted distribution according to disease prior imformation at regional area.

The present invention adopts above technical scheme compared with prior art, has following technique effect:

1) in conjunction with the propagation characteristic of ultrasonic beam, dynamic space focus characteristics and the large volume Hydro-concrete Structures deep Disease Characters of phased-array technique, adopt thinned array ultrasound phase-control probe, while is according to the prior imformation of concrete dam disease position, arrange by the phased array element of immune algorithm optimal design, reduce Probe technology cost;

2) data acquisition system (DAS) being made up of computer control system, signal transmitting device and signal picker is set, encourages ultrasonic beam data acquisition and stores processor, realize the in-situ measurement of large volume Hydro-concrete Structures disease;

3) the present invention rebuilds phased array ultrasonic detection image by two dimensional gray figure reconstructing method, obtains accordingly high information carrying amount and surveys image, the i.e. characteristic information of large volume Hydro-concrete Structures disease.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is the array element arrangenent diagram of full battle array redundant system linear transducer array.

Fig. 3 is the phased array supersonic probe array element arrangenent diagram that the degree of rarefication of Artificial Immune Algorithm optimal design is 0.25.

Fig. 4 is sector display schematic diagram.

Fig. 5 is the two-dimensional linear interpolation graphs of sector display sampled point.

Fig. 6 is the structural representation of data acquisition system (DAS).

Wherein: 1-computer control system; 2-signal transmitting device; 3-signal picker; 4-ultrasonic probe array.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

As shown in Figure 1, a kind of thinned array ultrasonic phase array detection method of concrete dam disease, concrete steps are as follows:

Step 1, for the prior imformation of concrete dam disease, employing Artificial Immune Algorithm optimal design has the two-dimensional random thinned array transducer of sparse characteristic, obtains the arrangement form of thinned array phased array ultrasonic detection array element;

Array element quantity and degree of rarefication depend on Hydro-concrete Structures form or test specimen form, and full battle array redundant system linear transducer array is as shown in Figure 2 example, is made up of altogether 208 array elements.The Sparse parameter that reflection redundance is set is K=0.25, this array is carried out to the optimal design of the Artificial Immune Algorithm of thinned array.Idiographic flow is:

101, the Sparse parameter that reflects redundance is set, full battle array redundant system linear transducer array is carried out to immune algorithm simulation;

102, it is k that coding parameter is set, and establishes k=0 and carries out initialization, and select at random the initialization antibody P of colony (k);

103, the initialization antibody P of colony (k) is carried out to affinity check assessment with antigen;

104, the initialization antibody P of colony (k) is assessed to big or small descending sort according to affinity, select the front 50% higher P of antibody colony of affinity sequence _h(k) carry out the amplification of self-adaptation clonal propagation, obtain the P of antibody colony _m(k) fitness function of, constructing is:

$\mathrm{Fit}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="1401261400234.png,1401261400235.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\mathrm{ML}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="1401261400232.png,1401261400233.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\mathrm{SL}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="1401261400234.png,1401261400235.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{BM}}_0-{\mathrm{BM}}_i|/{\mathrm{BM}}_0)+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="1401261400232.png,1401261400233.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{BS}}_0-{\mathrm{BS}}_i|/{\mathrm{BS}}_0)$

In formula, ML and SL are respectively main lobe and the sidelobe performance of array pulse echo response; k ₁and k ₂be respectively the weighted value of main lobe and sidelobe performance; BM ₀and BS ₀represent respectively pulse echo main lobe and the secondary lobe width of full battle array redundant system; BM _iand BS _ibe respectively main lobe and the secondary lobe width of thinned array in i direction; N is the judge direction number of the corresponding effect in thinned array space;

105, utilize mutation operator to the clonal propagation antibody P of colony _m(k) make a variation, produce antibody population P of new generation _n(k);

106, from antibody population PN of new generation (k), select a certain amount of antibody to replace rear 50% lower antibody colony of affinity sequence in the initialization antibody P of colony (k), produce population P of new generation (k+1);

107, be optimized criterion and pass judgment on, if do not meet, return to step 103; If meet, loop termination, thus obtain the arrangement form of thinned array phased array ultrasonic detection array element, as shown in Figure 3.

Step 2, according to the arrangement form of thinned array ultrasonic phase array detection array element, arranges phased array supersonic linear transducer array on concrete dam surface.

Step 3, computer control system calculates the time delay of ultrasonic array element, is sent to signal transmitting device; Signal transmitting device produces the ultrasonic signal of different carryover effects, is sent to ultrasonic probe array; Ultrasound wave in concrete dam conducted inside, adopts the mode of sector display to carry out disease detection to concrete dam by ultrasonic probe array; The feedback signal of ultrasonic scanning transfers to computer control system after by the collection of ultrasonic signal collector;

As shown in Figure 4, described sector display is specially: according to the fineness requirement of the structure of concrete dam and disease detection, u root sweep trace is set, v sampled point is set on every sweep trace, after the complete sweep trace of every collection, carry out the collection of next root sweep trace, thereby obtain u × v sampled data.

Step 4, computer control system receives after the feedback signal of ultrasonic scanning, adopt { (r, θ), the polar form of g} is carried out data storage, utilize 2-D gray image reconstructing method to rebuild phased array ultrasonic detection gray level image simultaneously, thereby obtain the two dimensional gray hum pattern of concrete dam, to differentiate position and the order of severity of disease; Wherein, (r, θ) is the positional information of sampled point in sector display, and θ is the angle between sweep trace and the 1st sweep trace at this sampled point place, and r is that on this sampled point and place sweep trace, the distance between the 1st sampled point is; The gray scale normalization degree of disease that g is ultrasound data that this sampled point gathers.

In sector display, and the 1st sampled point distance is for spacing between two neighbouring sample points of r is along with the increase of r increases, therefore need the sampled point in remote sector display region to carry out interpolation encryption, to eliminate far field image " Moire fringe " phenomenon because the difference of data coordinate system causes.

Described 2-D gray image reconstructing method is specially: first the sampled point of j sampled point on each root sweep trace is carried out to interpolation arithmetic, as shown in Figure 5, obtain the gray scale measured value of each interpolation point, i.e. ultrasonic echo wave height; Then obtain phased array ultrasonic detection gray level image by the coordinate conversion between polar coordinates and planimetric coordinates; Wherein

The gray scale measured value g of described interpolation point G _gcomputing formula is as follows:

$\begin{array}{c}{g}_G=g_a\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_b(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\\ g_a=g_{i,j}\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_{i+1,j}(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\\ g_b=g_{i,j+1}\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_{i+1,j+1}(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\end{array}---\left(1\right)$

In formula, g _a, g _bbe respectively the interpolation of j and j+1 article of length of scanning line direction; g _i,j, g _{i+1, j}, g _{i, j+1}, g _{i+1, j+1}represent respectively the gray-scale value of adjacent four sampled points of interpolation point G, g _i,jrepresent the gray-scale value of the sampled point that on j article of sweep trace of sector display, radius is i; Δ r is two spacing in sampled point sample radius; R ' is the spacing of interpolation point and previous sampled point.

Computer control system 1 of the present invention, signal transmitting device 2 and signal picker 3 form data acquisition system (DAS), as shown in Figure 6; Wherein, described signal transmitting device 2 is connected with computer control system 1 with ultrasonic probe array 4 respectively by data conductive bus; Described ultrasonic signal collector 3 is arranged on the opposite side of concrete dam, and is connected to computer control system 1 by data transmission line.

The above; it is only the embodiment in the present invention; but protection scope of the present invention is not limited to this; any people who is familiar with this technology is in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprise scope within, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (5)

1. a thinned array ultrasonic phase array detection method for concrete dam disease, is characterized in that, concrete steps are as follows:

Step 1, for the prior imformation of concrete dam disease, employing Artificial Immune Algorithm optimal design has the two-dimensional random thinned array transducer of sparse characteristic, obtains the arrangement form of thinned array phased array ultrasonic detection array element;

Step 2, according to the arrangement form of thinned array ultrasonic phase array detection array element, arranges phased array supersonic linear transducer array on concrete dam surface;

Step 3, is calculated time delay of ultrasonic array element by computer control system, be sent to signal transmitting device; Signal transmitting device produces the ultrasonic signal of different carryover effects, is sent to ultrasonic probe array; Ultrasound wave in concrete dam conducted inside, adopts the mode of sector display to carry out disease detection to concrete dam by ultrasonic probe array; The feedback signal of ultrasonic scanning transfers to computer control system after by the collection of ultrasonic signal collector;

Described sector display is specially: according to the fineness requirement of the structure of concrete dam and disease detection, u root sweep trace is set, v sampled point is set on every sweep trace, after the complete sweep trace of every collection, carries out the collection of next root sweep trace, thereby obtain u × v sampled data;

Step 4, computer control system receives after the feedback signal of ultrasonic scanning, adopt { (r, θ), the polar form of g} is carried out data storage, utilize 2-D gray image reconstructing method to rebuild phased array ultrasonic detection gray level image simultaneously, thereby obtain the two dimensional gray hum pattern of concrete dam, to differentiate position and the order of severity of disease; Wherein, (r, θ) is the positional information of sampled point in sector display, and θ is the angle between sweep trace and the 1st sweep trace at this sampled point place, and r is the distance between the 1st sampled point on this sampled point and place sweep trace; The gray scale normalization degree of disease that g is ultrasound data that this sampled point gathers.

2. the thinned array ultrasonic phase array detection method of concrete dam disease according to claim 1, it is characterized in that, described in step 1, adopt Artificial Immune Algorithm optimal design to there is the two-dimensional random thinned array transducer of sparse characteristic, the arrangement form that obtains thinned array phased array ultrasonic detection array element, is specially:

101, the Sparse parameter that reflects redundance is set, full battle array redundant system linear transducer array is carried out to immune algorithm simulation;

102, it is k that coding parameter is set, and establishes k=0 and carries out initialization, and select at random the initialization antibody P of colony (k);

103, the initialization antibody P of colony (k) is carried out to affinity check assessment with antigen;

104, the initialization antibody P of colony (k) is assessed to big or small descending sort according to affinity, select the front 50% higher P of antibody colony of affinity sequence _h(k) carry out the amplification of self-adaptation clonal propagation, obtain the P of antibody colony _m(k) fitness function of, constructing is:

$\mathrm{Fit}=k_1\mathrm{ML}+k_2\mathrm{SL}=k_1\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{BM}}_0-{\mathrm{BM}}_i|/{\mathrm{BM}}_0)+k_2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\right|{\mathrm{BS}}_0-{\mathrm{BS}}_i|/{\mathrm{BS}}_0)$

In formula, ML and SL are respectively main lobe and the sidelobe performance of array pulse echo response; k ₁and k ₂be respectively the weighted value of main lobe and sidelobe performance; BM ₀and BS ₀represent respectively pulse echo main lobe and the secondary lobe width of full battle array redundant system; BM _iand BS _ibe respectively main lobe and the secondary lobe width of thinned array in i direction; N is the judge direction number of the corresponding effect in thinned array space;

105, utilize mutation operator to the clonal propagation antibody P of colony _m(k) make a variation, produce antibody population P of new generation _n(k);

106, from antibody population PN of new generation (k), select a certain amount of antibody to replace rear 50% lower antibody colony of affinity sequence in the initialization antibody P of colony (k), produce population P of new generation (k+1);

107, be optimized criterion and pass judgment on, if do not meet, return to step 103; If meet, loop termination, thus obtain the arrangement form of thinned array phased array ultrasonic detection array element.

3. the thinned array ultrasonic phase array detection method of concrete dam disease according to claim 1, is characterized in that, computer control system described in step 3, signal transmitting device and signal picker composition data acquisition system (DAS); Wherein, described signal transmitting device is connected with computer control system with ultrasonic probe array respectively by data conductive bus; Described ultrasonic signal collector is arranged on the opposite side of concrete dam, and is connected to computer control system by data transmission line.

4. the thinned array ultrasonic phase array detection method of concrete dam disease according to claim 1, is characterized in that, sampled point described in step 3 be provided with two kinds of situations, one is to be uniformly distributed on sweep trace; One is to be encrypted distribution according to disease prior imformation at regional area.

5. the thinned array ultrasonic phase array detection method of concrete dam disease according to claim 1, it is characterized in that, the reconstructing method of 2-D gray image described in step 4 is specially: first the sampled point of j sampled point on each root sweep trace is carried out to interpolation arithmetic, obtain the gray scale measured value of each interpolation point, i.e. ultrasonic echo wave height; Then obtain phased array ultrasonic detection gray level image by the coordinate conversion between polar coordinates and planimetric coordinates; Wherein

Wherein, the gray scale measured value g of interpolation point G _gcomputing formula is as follows:

$\begin{array}{c}{g}_G=g_a\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_b(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\\ g_a=g_{i,j}\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_{i+1,j}(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\\ g_b=g_{i,j+1}\frac{r^{\&prime;}}{\mathrm{\&Delta;r}}+g_{i+1,j+1}(1-\frac{r^{\&prime;}}{\mathrm{\&Delta;r}})\end{array}$

In formula, g _a, g _bbe respectively the interpolation of j and j+1 article of length of scanning line direction; g _i,j, g _{i+1, j}, g _{i, j+1}, g _{i+1, j+1}represent respectively the gray-scale value of adjacent four sampled points of interpolation point G, g _i,jrepresent the gray-scale value of the sampled point that on j article of sweep trace of sector display, radius is i; Δ r is two spacing in sampled point sample radius; R ' is the spacing of interpolation point and previous sampled point.

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