JP2007114130A - Position analyzing method and position analyzer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position analyzing method which enhances the frame rate of an image reader and prevents the calculation precision of a position from decreasing when the position of fluorescent particles or the like smaller than a diffraction limit is calculated using the image data acquired by an optical microscope using an image data acquired by an optical microscope using the image reader for reading an image using a plurality of line sensors or area sensors subjected to binning operation. <P>SOLUTION: The intensity distribution of light of a material straddling a plurality of the pixels of a projection element is positionally analyzed in a uniaxial direction on the basis of a predetermined distribution function and the correlation table of the position of light with respect to the difference of the light intensity in a plurality of theoretical pixels is calculated from the intensity distribution straddling a plurality of the pixels with respect to the axial direction crossing the analyzed uniaxial direction at a right angle and, from the difference between the light intensities in a plurality of actually projected pixels, position is calculated from the correlation table. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a position analysis method capable of calculating the position of particles using image information acquired by an optical microscope and tracking the passage of time, and a material such as particles by using this position analysis method. The present invention relates to a position analysis apparatus that analyzes and tracks a position.

Proteins that are too small to be seen with the naked eye can be obtained from fluorescent signals such as evanescent fluorescence microscopes and confocal fluorescence microscopes. By detecting the position of the particle, that is, the position of the protein over time, the behavior and state of the protein are analyzed.
This analysis method is disclosed in Patent Document 1. In the above method, the fluorescent particles should be as small as possible so as not to disturb the behavior of the protein. As a substance for fluorescently labeling a protein, a fluorescent dye molecule is generally used. In particular, when a fluorescent protein is used as the fluorescent dye molecule, it can be fused to the target protein by genetic engineering.

A method for calculating the position of fluorescent particles or fluorescent dye molecules is given in Non-Patent Document 1. In Non-Patent Document 1, under the optical microscope, the position of a particle having a diameter smaller than the diffraction limit is calculated from the digital image data using the fact that the fluorescence intensity distribution approximately follows a two-dimensional Gaussian distribution. Calculated as the center of gravity position as the weight. According to Non-Patent Document 1, approximate calculation with a two-dimensional Gaussian function is said to be the most accurate method for calculating the position of the center of gravity of the fluorescent particle or fluorescent dye molecule.
In many cases, a line sensor or an area sensor is used to take a fluorescent image of the fluorescent particles or fluorescent dye molecules. A line sensor is an optical sensor in which projection elements made of a semiconductor that converts received light information into electrical signals are arranged in only one row. In a video camera using a line sensor, a two-dimensional video signal is output by capturing an image in a line field and performing scanning averaged at a certain pitch. In the area sensor, the projection elements are two-dimensionally arranged, and a video camera using the area sensor does not need to scan the sensor. The frame rate of an image reading apparatus that reads an image using a line sensor or an area sensor such as a digital CCD camera is determined by the exposure time and the read time. Accordingly, by processing (binning) a plurality of pixels of the digital image data as one pixel (bin), the resolution of the image is reduced, but the frame rate is improved. However, in the digital CCD camera, the frame rate cannot be improved by binning in the serial register direction because of the structure of the CCD chip.

When the position of the fluorescent particle or fluorescent dye molecule is calculated by the method of Non-Patent Document 1, the position accuracy is expressed by the following formula written in Non-Patent Document 2.
Here, s is the standard deviation of the point spread function, a is the pixel size (distance of one side of one pixel on the image), N is the total number of photons, and b is the background light (where s> a ).

  According to the mathematical expression represented by [Equation 1] (hereinafter described in the same manner), the decrease in the number of pixels does not significantly affect the decrease in accuracy. In the case of s <a, it is necessary to represent an image of fluorescent particles or fluorescent dye molecules with only a few pixels. In fact, a two-dimensional Gaussian function approximation by a computer is impossible. Therefore, when calculating the barycentric position of fluorescent particles or fluorescent dye molecules by the two-dimensional Gaussian function approximation method described in Non-Patent Document 1, the pixel size does not exceed the standard deviation of the point spread function. Only binning can be done.

Japanese Patent Laid-Open No. 2003-294631 Cheezum, M.C. K. , W.M. F. Walker, and W.W. H. Guilford. Quantitative comparison of algorithms for tracking single fluorescent particles. Boophys. j. (2001), 81: 2378-2388. Thompson, R.A. E. Larson, D .; R. Webb, W .; W. Precise nanometer localization analysis for individual fluorescens probes. Biophys. J. et al. (2002), 82, 2775-2783.

  Therefore, in the present invention, a plurality of line sensors that perform a binning operation, or an image reading device that reads an image using an area sensor, and using image information acquired by an optical microscope, fluorescent particles smaller than the diffraction limit are used. Or, when calculating the barycentric position of the fluorescent dye molecule, binning exceeding the standard deviation of the point spread function is performed, the frame rate of the image reading device is improved, and the calculation accuracy of the barycentric position is further reduced. It is an object of the present invention to provide a position analysis method that does not provide a position analysis method, and that uses the principle to analyze the position of a moving fluorescent particle or fluorescent dye molecule and further track it.

As means for solving the above problems, the present invention has the following features.
The present invention uses one or a plurality of line sensors in which projection elements that receive light are arranged in only one row, or an area sensor in which the projection elements are two-dimensionally arranged. Fluorescence whose diameter is smaller than the diffraction limit from image information read from the image reading device by an optical microscope equipped with an image processing device capable of analyzing (binning) the number of elements of the image pickup device as one pixel (bin). A method of calculating a position of a particle or a fluorescent dye molecule, wherein pixel data of only the y-axis of the image information is binned so that a fluorescent image of the fluorescent particle or the fluorescent dye molecule is projected on two bins. The intensity distribution of the fluorescent image of the fluorescent particle or fluorescent dye molecule whose diameter is smaller than the diffraction limit should approximately follow a Gaussian distribution by a predetermined function, for example, a Gaussian function. The x-axis coordinate position is calculated by approximating the x-axis pixel data sequence in the image information of the fluorescent particles by a Gaussian function, and the intensity distribution in the y-axis direction of the fluorescent image is calculated, From the intensity distribution, a correlation table of the y-axis coordinate position of the fluorescent image with respect to the difference in the fluorescence intensity in the two bins on the theoretical y-axis is calculated, and from the difference in the fluorescence intensity in the two bins on the y-axis actually projected. A position analysis method for calculating a y-axis coordinate position using the correlation table is provided.

  Also, two line sensors, a CCD register for holding two output information corresponding to the line sensor, and the line sensor and the CCD register are arranged on the light receiving surface to drive the light receiving surface in a two-dimensional manner. In order to achieve this, approximation is performed using a Gaussian function with two driving devices connected to two sides perpendicular to the light receiving surface, two control devices for controlling the driving device, and the diameter on the light receiving surface is diffracted. An image processing device for calculating the x-axis coordinate position of fluorescent particles or fluorescent dye molecules smaller than the limit, two circuits for adding all the values of the CCD register, and a difference for extracting a difference between output signals of the two addition circuits A calculation process for calculating a y-axis coordinate position of the fluorescent particle or fluorescent dye molecule on the light receiving surface by using a circuit, an output signal from the image processing apparatus, and an output signal from the difference circuit; And a recording device for recording the x-axis coordinate position, the y-axis coordinate position, and the current position of the two control devices, and the x-axis coordinate position of the fluorescent particles or fluorescent dye molecules at the center position of the light-receiving surface Provided is a position analysis device that enables tracking of moving fluorescent particles or fluorescent dye molecules by controlling the control device and the drive device so that the y-axis coordinate position is positioned.

  By means for solving the above-mentioned problems, the position analysis method of the present invention analyzes the positions of fluorescent particles and fluorescent dye molecules having a size less than the diffraction limit, and further improves the time resolution when tracking the passage of time. Can be made. Further, in the position analysis method of the present invention, the image processing time is reduced because the image information is reduced when performing the image processing. The position analysis apparatus of the present invention uses a fluorescence microscope such as an evanescent fluorescence microscope or a confocal fluorescence microscope to observe and track the behavior and state of proteins with an accuracy of nm (nanometers) and ms (milliseconds). Thus, protein function analysis can be performed.

  The best mode for carrying out the present invention will be described with reference to the drawings. However, these are merely embodiments, and do not limit the scope of the claims of the present invention.

First, a method for calculating the positions of the fluorescent particles or fluorescent dye molecules shown in Non-Patent Documents 1 and 2 in the xy coordinate system will be described below. An image of fluorescent particles or fluorescent dye molecules (hereinafter simply referred to as fluorescent particles) smaller than the diffraction limit approximately follows the two-dimensional Gaussian distribution shown below.
Here, (x ₀ , y ₀ ) is the centroid position of the fluorescent particle in the coordinate system consisting of x and y axes, σ _xy is the standard deviation, I is the fluorescence intensity emitted by the particle at the centroid position of the fluorescent particle, and C is the background Represents light.
When performing digital processing, this distribution is discretized. By approximating the digital image data of the fluorescent particles obtained from the optical microscope with [Equation 2], the position of the fluorescent particles obtained in the xy coordinate system can be obtained.

In this embodiment, a digital CCD camera is used as an image reading apparatus that reads an image using a plurality of line sensors or an area sensor that perform a binning operation. In the optical microscope used here, the standard deviation of the point spread function is 238 nm, and the size of the pixel is 49 nm. The diameter of the fluorescent particles is about 10 nm, the emitted photons are about 3500 photons / ms, and the camera frame rate is 2 ms (frame transfer type).
FIG. 1 shows the correlation between the number of binning and the accuracy of actual approximate calculation in this embodiment. Binning was performed on the x and y axes, i.e. both the parallel register (x) and the serial register (y) in the CCD camera. In FIG. 1, for example, the binning number of 5 represents that the five pixels on the x and y axes are processed as one pixel, and the amount of information is reduced to 1/25. In FIG. 1, the horizontal axis indicates the number of binning, and the vertical axis indicates the standard deviation when approximate calculation is performed for 300 images (Δx in [Expression 1]). The standard deviation represents the position accuracy in the approximate calculation. When the number of binning exceeds 4, the accuracy decreases. Therefore, when binning is performed while maintaining the calculation accuracy of the calculation of the gravity center position of the fluorescent particles by approximation of [Equation 2], binning can be performed for up to four pixels, and therefore binning is not performed during the readout time from the CCD camera. Compared to the case, the maximum is four times.

Next, the position analysis method according to the present invention will be described with reference to the flowchart of FIG.
First, binned image information is acquired from a digital CCD camera. When an image is acquired by a digital CCD camera, only the y-axis direction, that is, the serial register is binned. FIG. 3 shows a binning method in this embodiment. FIG. 3A is a fluorescent image of fluorescent particles having a diameter of 10 nm. Each pixel has 256 gradations. FIG. 3B is a contour graph in which the fluorescence values shown in FIG. FIG. 3B is approximated by a two-dimensional Gaussian function. If in focus, the standard deviation in the two-dimensional Gaussian function is equal to the standard deviation of the point spread function. When FIG. 3B is approximated by a two-dimensional Gaussian function, the standard deviation is 4.85 pixels (238 nm). The binning number is 3 to 4 times the standard deviation of the point spread function in the optical system used so that the above point spread is projected only on two bins in the y-axis direction. To a degree. As shown in FIG. 3C, in this embodiment, 16 pixels in the y-axis direction were binned. FIG. 3D is a graph in which the value of each pixel on the y-axis in FIG. 3C is plotted on the vertical axis and the pixel number on the x-axis is plotted on the horizontal axis. In this embodiment, since the binning of 16 pixels is performed in the serial register direction, the readout time of the digital CCD camera is 16 times faster than the case where no binning is performed. In the digital CCD camera according to the present embodiment, the analog signal output from the CCD chip is converted to digital, and the data is transferred to the computer. Further, since the digital CCD camera used in this embodiment is a frame transfer type, the exposure time does not have to be added to the frame rate. Therefore, the frame rate of the digital CCD camera in this embodiment is the addition of the readout time and the data transfer time to the computer. In this embodiment, the frame rate is improved by 6 times by binning 16 pixels. From the image information obtained by the above method, the x-coordinate position and the y-coordinate position of the fluorescent particles are respectively calculated.

First, the position of the fluorescent particle in the x coordinate is obtained. The images shown in FIG. 3C are added in the y-axis direction to form a one-dimensional data string. This is equivalent to projecting the Gaussian distribution shown in FIG. 3b in the x-axis direction. The data sequence is approximated by a one-dimensional Gaussian function shown below.
Here, x ₀ is the center of gravity along the x-axis of the fluorescent particles, sigma is the standard deviation, I is the fluorescence intensity emitted by the particles in the center of gravity of the fluorescent particles, C is representative of the background light. Thereby, the center-of-gravity position on the x-axis of the fluorescent particles is obtained.

Next, the position of the fluorescent particle in the y coordinate is obtained. In this embodiment, as shown in FIG. 3D, the image of the fluorescent particles projected on the two bins is represented by a one-dimensional Gaussian distribution in each bin. The images of the fluorescent particles projected on the two bins are approximated by a one-dimensional Gaussian function of [Equation 3], respectively, and the approximation parameter I is recorded as I _A and I _B. In the approximate calculation, the approximate parameters other than I _A and I _B are substituted with the values of the approximate solution obtained when obtaining the position in the x coordinate and fixed values, thereby improving the speed of the iterative calculation process. Since the fluorescent image of the fluorescent particles is projected onto two pixels on the y axis, theoretically, I _A and I _B follow the following equations.
Here, y ₀ is the position of the center of gravity of the fluorescence on the y-axis, σ is the standard deviation, and bin is the binning number. Further, when bin is sufficiently larger than σ, bin = ∞ may be set.

Since I = I _A + I _B , the difference diff (y ₀ ) between I _A and I _B is
It is defined as

The inverse function is
Thus, the center-of-gravity position on the y-axis of the fluorescent particles can be calculated from I _A and I _B.
Due to a slight defocus, the value of σ changes and deviates from the standard deviation of the point spread function. FIG. 4 shows a graph plotting [Equation 4], which is a theoretical correlation between (I _A −I _B ) / (I _A + I _B ) and y ₀ when σ is changed. Kyaribure the graph of FIG. 4 - Shonte - used as a table, I _A, the I _B, can be obtained centroid position y ₀ on the y-axis of the fluorescent particles.

However, it is very difficult to analytically obtain [Equation 5] and [Equation 6]. Therefore, in order to simplify the expression and speed up the calculation process, [Expression 6] is obtained in advance by numerical calculation, and an expression approximated by a quintic function is used. This operation is equivalent to the Taylor expansion of [Equation 6]. Since [Equation 6] is point-symmetric, even number terms are omitted, and [Equation 7] is an approximate expression of [Equation 6].
In [Expression 7], -8 to 8 pixels are linearly converted to 0 to 1 for the sake of simplicity. Each of g ₁ , g ₂ , and g ₃ is a function of σ. FIG. 5 is a graph showing the correlation between g ₁ , g ₂ , and g _{3 and} σ. g ₁ , g ₂ , and g ₃ can also be approximated as a quintic function.

In this example, g ₁ , g ₂ , and g ₃ were set to [Equation 8] shown below.
However, [xi] = [sigma] / 16pixels, and the number of significant digits is shown only up to five digits. The plot in FIG. 5 is a theoretical value, and the solid line indicates a function represented by [Equation 8]. The R-squared value of the approximate curve of [Equation 8] with respect to the theoretical value of FIG. 5 is 1.0 (7 decimal places are raised), and [Equation 8] substantially matches the theoretical value within the rounding error range. . As described above, [Equation 6] can be approximated as a higher-order polynomial of σ and (I _A −I _B ) / (I _A + I _B ) represented by [Equation 7] and [Equation 8]. FIG. 6 is calculated using the theoretical value of the relationship between (I _A −I _B ) / (I _A + I _B ) and y ₀ when [sigma] is changed, and [Equation 7] and [Equation 8]. It is the figure which showed the value. ◯ Δ □ in FIG. 6 is a plot obtained by discretizing FIG. 4, and three lines are values calculated using [Equation 7] and [Equation 8] while changing σ. Since the R-squared value of the approximate curve is 0.9996 to 1.0 (7 digits below the decimal point), it can be said that [Equation 7] and [Equation 8] are substantially equal to [Equation 6].

In the optical microscope used in this example, the position accuracy of measuring the position of the fluorescent particles in FIG. 3 using the above method was 3 nm in the x-axis direction and 3 nm in the y-axis direction. The position accuracy obtained by measuring the position of the same bright spot by a conventional method (approximation using a two-dimensional Gaussian function) was 3 nm in both the x-axis direction and the y-axis direction. In the present invention, since the fluorescence intensity emitted by the fluorescent particles is used to calculate the position of the y coordinate, blinking and anisotropy of the fluorescent particles reduce the positional accuracy in the y-axis direction. However, in the present invention, as shown in [Equation 5], the fluorescence intensity term is removed by dividing the difference (I _A −I _B ) by the addition (I _A + I _B ). There is no effect on the positional accuracy in the y-axis direction, and the positional accuracy does not decrease in spite of the fact that the information in the y-axis direction is reduced to 1/16 compared to the conventional method. . The spatio-temporal resolution of the image acquisition time of the digital CCD camera is improved by a factor of 6 in this embodiment, so that 3 nm / ms → 1.2 nm / ms in both the x and y axes (conventional method → the present invention). And has improved.

The position accuracy of this method also depends on the total number of photons emitted by the fluorescent particles, as in the conventional method. When the total number of photons was sufficiently large (such as a dark field image of a polyester bead smaller than the diffraction limit), the positional accuracy of this method was 0.6 nm in both the x-axis direction and the y-axis direction. The positional accuracy obtained by measuring the position of the same bright spot by the conventional method was 0.6 nm in both the x-axis direction and the y-axis direction. As described above, according to the present invention, the calculation accuracy of the position measurement of the fluorescent particles is not lowered regardless of the reduction of the image information acquired by the digital CCD camera by the binning.
By using the calculation method described above, the movement of the fluorescent particle can be tracked by calculating the position of the fluorescent particle in the xy coordinates for each frame. FIG. 7 is a graph obtained by tracking fluorescent particles having a diameter of about 10 nm that are driven stepwise every 10 nm in the optical microscope used in this example. The number of photons emitted from the fluorescent particles was 5000 photonms, and the positional accuracy under these conditions was 1.9 nm in the x-axis direction and 2.0 nm in the y-axis direction. FIG. 7a is a graph showing the time course of tracking the fluorescent particles driven along the x-axis, and FIG. 7b is the time course of tracking the fluorescent particles driven along the y-axis. According to the graph of FIG. 7, in this embodiment, the movement of the fluorescent particles can be acquired with a frame rate of 330 μs and with an accuracy of several nm using a CCD camera with a frame rate of 2 ms at the fastest without binning.

  Next, a position analysis apparatus that tracks fluorescent particles using the analysis method of the present invention will be described with reference to FIG. Two line sensors 801 and 802 and corresponding CCD registers 803 and 804 are arranged on one stage 805. The stage which is the light receiving surface can be driven two-dimensionally along the X and Y axes by the two driving devices 806 and 807. The line sensor 801 sends a signal to the CCD register 803, and the line sensor 802 sends a signal to the CCD register 804. Signals from the CCD registers 803 and 804 are approximated by a Gaussian function [Equation 3] after the respective pixels are added by the image processing device 808.

The image processing device 808 calculates the position (X) of the fluorescent particle on the stage 805 on the x coordinate. The adder circuits 809 and 810 add the signals of the CCD registers 803 and 804, respectively, and pass the voltage signal to the difference circuit 811. The difference circuit 811 passes the voltage signal obtained by subtracting the voltage signal passed from the adder circuits 809 and 810 to the calculation device 812. The calculation device 812 receives parameters obtained from the result of the Gaussian function approximation from the image processing device 808, and uses the [Equation 6] and [Equation 7] to calculate the stage from the difference voltage passed by the difference circuit 811. The position (Y) on the y coordinate of the fluorescent particle on 805 is calculated. X and Y are recorded by the recording device 813. Control devices 814 and 815 that control the drive devices 806 and 807 send the current stage position to the recording device 813. Thereafter, the control device 814 that controls the drive device 806 receives X and controls the drive device 806 so that the center of the stage is at the center of the bright spot (a feedback circuit may be used).
Similarly, the control device 815 that controls the drive device 807 receives Y and controls the drive device 806 so that the center of the stage is at the center of the bright spot. The recording device 813 records the current position of the stage and the position of the fluorescent bright spot on the stage for each loop described above. By using the above apparatus, it is possible to keep track of the center position of the moving fluorescent bright spot. The driving devices 806 and 807 move the stage 805, that is, the light receiving surface, but may move the specimen to be microscopically observed by moving the microscope stage.

The application of the present invention is not limited to the tracking of fluorescent particles or fluorescent dye molecules whose diameter under the microscope is smaller than the diffraction limit. For example, it can be used for calculating the center of gravity of a star bright spot in astronomical observation. Binning speeds up the calculation process and apparently increases the number of pixels, so that more photons can be collected and background light is reduced. Furthermore, in this embodiment, the fluorescent particles are assumed to be smaller than the diffraction limit of the optical system. For this reason, the obtained fluorescence image approximately follows a Gaussian distribution.
The present invention is not limited to the case of fluorescent particles smaller than the diffraction limit of the optical system. If the obtained image is point-symmetric and line-symmetric, the calculation algorithm in the present invention can be used as long as a theoretical formula for approximating the image is prepared. Therefore, the present invention can be used for all digital calculation processing for calculating the center of gravity of particles.
In particular, the field of fluid mechanics that measures the flow of particles, and attaching a phosphor to the joint to capture movement (a technique used to capture baseball throwing motions, such as fluorescent light on elbows and wrists) This is effective when particles or phosphors move, such as in biomechanics and computer simulation.
In addition, although it can apply to various uses, a part is described below. In medicine, fossil and ore in minerals such as blood cell movement in the blood, analysis of cells, recent movements, analysis of DNA chips, etc., in manufacturing and inspection fields, such as inspection of scratches, dirt, discoloration, bubbles, other foreign substances, etc. For example, detection of a polished shape or bubbles.

  The center of gravity calculation method of fluorescent particles or fluorescent dye molecules developed by the present invention is a method for tracking a moving object based on moving image data that tracks moving particles that move in all moving images including a micro-aerial image. Can be used as

It is a graph which shows the correlation of the number of binning and calculation position accuracy by the conventional method. It is a flowchart of the calculation process which concerns on embodiment of this invention. (A) is the fluorescence image of the fluorescent particle which concerns on embodiment of this invention. (B) is a contour graph in which the fluorescence intensity of the fluorescent image of the fluorescent particles according to the embodiment of the present invention is plotted on the z-axis. (C) is the fluorescence image after the binning of the fluorescent particle which concerns on embodiment of this invention. (D) is a graph which shows the fluorescence intensity distribution in each bin of the fluorescence image after the binning of the fluorescent particles according to the embodiment of the present invention. It is a graph which shows the theoretical value of the position in the y coordinate of the fluorescent particle with respect to the difference of the fluorescence intensity in a bin based on embodiment of this invention. According to an embodiment of the present invention, and _{g 1,} g 2, _{g 3} Hano theoretical value for σ in Equation 6] is a graph showing the number 7. It is a graph which shows the theoretical value of the position in the y coordinate of the fluorescent particle with respect to the fluorescence intensity difference in the bin of the y-axis direction, and the approximate curve in this method based on embodiment of this invention. It is the graph which tracked the motion of the fluorescent particle of diameter 10nm which moves stepwise every 10 nm using the analysis method which concerns on embodiment of this invention. It is a block diagram of a particle position tracking device using the analysis technique concerning the embodiment of the present invention.

Explanation of symbols

801 Line sensor 802 Line sensor 803 CCD register corresponding to line sensor 801 804 CCD register corresponding to line sensor 802 805 Stage 806 Drive unit (for X axis)
807 Drive unit (for Y axis)
808 Image processing device 809 Adder circuit 810 Adder circuit 811 Difference circuit 812 Calculation device 813 Recording device 814 Control device for controlling drive device 806 (for X axis)
815 Control device for driving device 807 (for Y-axis)

Claims (8)

In a position analysis method for calculating the position of a material that emits light by processing a signal from a projection element that receives light through an optical microscope with an image processing device,
In the position analysis method, the light intensity distribution of the material spanning a plurality of pixels of the projection element is analyzed based on a predetermined distribution function in the uniaxial direction, and the analyzed axial direction is orthogonal to the uniaxial direction. Then, a correlation table of the light position with respect to the theoretical difference in light intensity in the plurality of pixels is calculated from the intensity distribution across the plurality of pixels, and the correlation table is calculated from the difference in light intensity in the plurality of pixels actually projected. A position analysis method characterized by using to calculate the position. The position analysis method according to claim 1,
The projection element is one or two line sensors or an area sensor arranged two-dimensionally. In the position analysis method according to claim 1 or 2,
The position analysis method, wherein the material is fluorescent particles or fluorescent dye molecules that emit fluorescence and is smaller than a diffraction limit. In the position analysis method according to any one of claims 1 to 3,
The position analysis method, wherein the predetermined distribution function is a Gaussian function. The position analysis method according to any one of claims 1 to 4,
The position analysis method characterized in that the difference in light intensity across the plurality of pixels is calculated by Taylor expansion. In a position analysis device including an image processing device that calculates a position of a material that emits light by processing a signal from a projection element that receives light through an optical microscope,
The image processing device analyzes the light intensity distribution of the material based on a Gaussian function in a uniaxial direction, and theoretically calculates the intensity distribution over a plurality of pixels with respect to the analyzed axial direction orthogonal to the uniaxial direction. The correlation table of the light position with respect to the difference in light intensity at a plurality of pixels is calculated, and the position of the material is calculated using the correlation table from the difference in light intensity at the plurality of pixels actually projected. A position analysis device. The position analysis apparatus according to claim 6,
The position analysis apparatus uses the position analysis method according to any one of claims 2 to 4. In the position analysis device according to claim 6 or 7,
The position analysis device includes two drive devices connected to two sides perpendicular to the light receiving surface including the sensor and a control device for controlling the drive device,
A position analysis apparatus that tracks the position of a moving material by storing the control apparatus and the drive apparatus, and stores the tracking information.