Apparatus for characterizing particles

Abstract

An apparatus (100) is provided for characterizing particles using nanoparticle tracking analysis. The apparatus includes a cell (101) for containing a sample containing a plurality of particles suspended in a fluid, a light source (102) configured to illuminate the sample, an imaging system (103) configured to collect light scattered or fluorescently emitted by particles moving within the cell (101) and within a detection region (111) of the imaging system (103) and to capture video of the particles moving within the detection region (111), and a computer (104). The computer is configured to process the video to automatically determine the depth of the detection region (111). Determining the depth of the detection region (111) includes tracking particles moving within the detection region (111) to thereby generate trajectories for each of the particles, and analyzing how measured characteristics of the trajectories within subsections of the video change as the size of the subsection changes.

Description

[Technical Field]

[0001] The present invention relates to nanoparticle tracking analysis, and more particularly to an apparatus and method for measuring particle properties without instrument calibration.

[0002] Nanoparticle Tracking Analysis (NTA) is a method for characterizing particles suspended in a fluid by tracking the movement of individual particles. Typically, the method involves illuminating a sample containing a plurality of particles suspended in the fluid, collecting light scattered or fluoresced by the particles, and capturing video of the particles as they move through the fluid. The video is analyzed frame by frame to track particle movement caused by Brownian motion and / or bulk flow. The fluid may be a liquid (e.g., water or other liquid) or a gas (e.g., air).

[0003] It is sometimes necessary to determine the particle concentration in a fluid. To calculate the concentration, the number of particles within the detection region of the NTA device (a three-dimensional space within the videotaped sample) can be counted. If the volume of the detection region is known, the concentration can be determined from the ratio of particle number and detection region. However, it is difficult to identify the depth of the detection region. The depth depends, for example, on the imaging system itself, environmental factors, and differences in the optical properties of the sample.

[0004] Therefore, conventional NTA devices require instrument calibration to determine the detection volume. Calibration involves first using a calibration sample to analyze the particle intensity at different depths within the detection volume. An example of an NTA calibration method is disclosed in EP 3071944.

[0005] However, this can require additional steps and time (often several hours), accurate calibration samples, and may need to be performed periodically to maintain accuracy. Therefore, NTA methods and apparatus that do not require calibration would be of great advantage.

[0006] Some progress has been made in developing calibration-free NTA methods. In some calibration-free methods, computational modeling of particle transport is used in combination with a priori knowledge of particle size (M. Roeding et al., Physics Review E 84, 031920, September 20, 2011).

[0007] Further improvements in calibration-free NTA techniques are needed. Summary of the Invention

[0008] According to a first aspect of the present invention, there is provided an apparatus for characterising particles using nanoparticle tracking analysis, comprising: a cell for containing a sample including a plurality of particles suspended in a fluid; a light source configured to illuminate the sample; an imaging system configured to collect light scattered or fluoresced by particles moving within the cell and within a detection region of the imaging system and to capture video of the particles moving within the detection region; a computer configured to process the video to automatically determine the depth of the detection region; Equipped with Determining the depth of the detection region includes: tracking the movement of the particles within the detection region and generating a trajectory for each of the particles; Analyzing how the measurement characteristics of trajectories within a subsection of a video change as the size of the subsection changes; and Includes.

[0009] The approach allows for accurate determination of the detection region without being computationally intensive. A trajectory may be defined as a set of vectors that define the change in particle position from frame to frame of the video.

[0010] The subsections may be strips taken across the video, where the strips are defined by a pair of parallel faces. The strips may have the shape of a parallelogram or a rectangle. If the pair of parallel faces spans the width of the video, the strip also spans the width of the video. Alternatively, if the strip does not span the full width of the video, it has a second pair of parallel faces perpendicular to the first pair of parallel faces, resulting in a rectangle within the video. The strips may be taken in the x or y direction (vertical or horizontal).

[0011] The size of the subsections may be varied between a pair of faces by varying the width of the strip. The computer may be further configured to record measured characteristics of the trajectory as a function of strip width.

[0012] The computer may be further configured to analyze the trajectories within the subsection and classify each of the trajectories as one of the following: (i) x / y trajectories: particle trajectories are observed to cross one of a pair of planes; (ii) z-trajectories: particle trajectories that start and / or end within the strip but are not observed to cross one of the pair of faces.

[0013] The computer may be further configured to record measured characteristics of the x / y trajectory and the z trajectory separately.

[0014] The computer may be further configured as follows: Comparing the measured characteristics of the x / y trajectory and the z trajectory for each strip width; and The depth of the detection area is determined by finding the strip width where the measurement characteristic of the x / y trajectory and the measurement characteristic of the z trajectory are equal to or closest to the strip width, and the determined depth of the detection area is equal to the strip width.

[0015] The measurement characteristics of the trajectory may be selected from the following: Counting the number of x / y trajectories and the number of z trajectories observed within a given time interval; Measurements of x / y trajectory length and z trajectory length, where each trajectory length is the distance traveled by the particle within the strip; or A measure of the number of steps in the x / y trajectory and the number of steps in the z trajectory, where the number of steps in each trajectory is the number of frames of video that the particle moves through the strip.

[0016] The measurement characteristic may be a count of the number of x / y trajectories and the number of z trajectories.

[0017] Multiple strips of each strip width may be analyzed and the measured trajectory characteristics of the multiple strips of each strip width may be mathematically combined.

[0018] Multiple strips can be covering most or all of the detection area; and / or the detection area to cover multiple areas with different detection area depths; It may be configured.

[0019] Tracking particles may include identifying particles from a current frame of video in subsequent frames of the video.

[0020] Identifying particles in subsequent frames of the video may include identifying nearest particles in the subsequent frames.

[0021] Identifying the nearest particle in the subsequent frame may include identifying the nearest particle within a tracking distance limit.

[0022] The computer may be configured to calculate a concentration of particles suspended in the fluid; Calculating the concentration is calculating a volume of the detection region using the determined depth; measuring the number of particles in the detection area; may include:

[0023] According to a second embodiment of the present invention, there is provided a computer-implemented method for determining a depth of a detection region from video data obtained by nanoparticle tracking analysis, comprising: The method is: tracking particles moving within the detection region, thereby generating a trajectory for each of the particles; measuring characteristics of a trajectory within a subsection of the video; analyzing how measurement characteristics of trajectories within a subsection of the video change as the size of the subsection changes; Includes.

[0024] According to a third aspect of the present invention there is provided a machine-readable non-volatile storage medium containing instructions for causing a processor to carry out a method, comprising: The method includes determining a depth of the detection region from video data obtained by nanoparticle tracking analysis; Determining the depth is tracking particles moving within the detection region, thereby generating a trajectory for each of the particles; measuring characteristics of a trajectory within a subsection of the video; Analyzing how the measurement characteristics of trajectories within a subsection of a video change as the size of the subsection changes; and Includes.

[0025] Features described in relation to the first aspect may also apply to either the second or third aspect, including any features. Features of each aspect may be combined with features of the exemplary embodiments, and vice versa.

[0026] An embodiment of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: FIG. [Brief explanation of the drawings]

[0027] [Figure 1] FIG. 1 shows an apparatus for characterizing particles using NTA according to an embodiment of the present invention. [Figure 2] FIG. 2 shows the detection area obtained by the NTA device. [Figure 3] FIG. 3 shows a current frame and a subsequent frame of video, illustrating how 2D particle tracking determines the distance traveled by a particle due to Brownian motion in a known NTA process. [Figure 4] Figure 4 shows the trajectories of particles caused by Brownian motion. [Figure 5] FIG. 5 shows an example of the trajectory of a particle moving inside or outside the detection region. [Figure 6] Figure 6 shows particles moving within a subsection of the video, forming in-plane and out-of-plane trajectories. [Figure 7] FIG. 7 shows subsections of a video, the subsections having variable widths. [Figure 8] FIG. 8 shows an experimental test method used to validate the method according to an embodiment of the present invention. [Figure 9] FIG. 9 shows the results of the experimental test method shown in FIG. [Figure 10] FIG. 10 shows the results of the experimental test method shown in FIG. [Figure 11] FIG. 11 shows the results of a method for calculating particle concentration according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0028] 1 shows an apparatus 100 for characterizing particles using particle tracking analysis (NTA) according to an embodiment of the present invention. The apparatus comprises a cell 101 for containing a plurality of particles suspended in a fluid, a light source 102 configured to illuminate the sample, and an imaging system 103 configured to collect light scattered or fluoresced by particles moving within the cell and within a detection region, and to capture video of the particles moving within the detection region.

[0029] The apparatus 100 further comprises a computer 104 configured to process the video. As described in more detail with reference to FIG. 3, processing the video comprises tracking particles across multiple subsequent frames of the video. The computer 104 is configured to track each of the multiple particles within the detection region and determine a trajectory of each particle's movement across the series of frames. The computer 104 is further configured to determine the depth of the detection region by analyzing measured characteristics of the trajectories.

[0030] The imaging system 103 may include a microscope and a camera configured to capture video through the microscope. The microscope may include, for example, a 20x magnification objective lens, and the camera may include a charge-coupled device (or CMOS device). The light source 102 may be a laser. In other embodiments, suitable alternative imaging systems and / or light sources may be used. For example, light may be refracted into the sample through a prism or other optical device, which may include other reflectors, lenses, prisms, etc.

[0031] The apparatus may further include a glass wall 106 and a metal surface 105 disposed between the glass wall 106 and the cell 101. The metal surface 105 is positioned to direct light scattered or fluoresced from the particles back toward the imaging system 103, thereby increasing the contrast of the particles. The glass wall 106 may include a portion of a prism configured to refract light from the light source 102 to form a thin sheet that is substantially parallel to the metal surface 105.

[0032] Figure 2 shows a sample volume containing particles suspended within a fluid dispersion 110. Although not labeled in Figure 2, the volume of particles in sample volume 110 may be surrounded by one or more cell walls.

[0033] The detection region 111 may include a sub-region of the sample volume 110. The detection region 111 is the region of the volume 110 where light 112 scattered or fluoresced by particles moving within the detection region 111 is detectable by an imaging system. The detection region 111 may be thought of as the three-dimensional "field of view" of the imaging system. The detection region 111 has a planar area in the xy plane and at a depth z.

[0034] FIG. 3 illustrates how tracking particles are used in NTA. FIG. 3 shows a current frame 1a of a video and a subsequent frame 1b of the video. Particle 2 is shown in current frame 1a. In subsequent frame 1b, particle 2 moves from its current position (shown by the dashed line) to a new position 2a. Between current frame 1a and subsequent frame 1b, particle 2 moves in two dimensions, i.e., in the x and y directions defined by the axes in FIG. 3. The Euclidean distance d traveled by particle 2 between frames 1a and 1b is considered the distance traveled by particle 2 due to Brownian motion.

[0035] For example, particle 2 is identified in subsequent frame 1b using two-dimensional particle tracking. Particle 2 is identified in subsequent frame 1b as the Euclidean nearest particle to the position of particle 2 in current frame 1a. The computer is configured to perform two-dimensional particle tracking of each of the plurality of particles within the detection region.

[0036] The computer may be configured to repeat the tracking process over a suitable number of frames of the video, and by tracking each particle across several frames, the computer generates a piecewise particle trajectory for each of the plurality of particles.

[0037] The computer may be configured to set a tracking distance limit once it has identified a particle 2 in a subsequent frame 1b. The tracking distance limit means that once the computer has identified the Euclidean nearest particle, it will only consider areas within a certain distance from the initial particle position 2a. This may mean that particle identification and tracking will be performed more efficiently.

[0038] Figure 4 shows an example of a particle trajectory 15 formed by a particle as it moves through a fluid. Because the movement is caused by Brownian motion, the particle appears to "random walk" between a start position 11 and a subsequent end position 12. In a first frame, the particle is at a first position 13. In a second subsequent frame, the particle is at a second position 14. Thus, each vector between successive pairs of vectors in the particle trajectory 15 corresponds to the movement of the particle between two successive frames of the video (each vertex corresponds to a position within a frame).

[0039] As shown in Figure 5, examples of particle trajectories of particles entering / exiting the detection region 111 in the z direction are shown. Particle trajectory 3a shows a particle leaving the detection region 111 through the bottom surface. Particle trajectory 3b shows a particle leaving the detection region 111 through the top surface. Particle trajectory 3c shows a particle entering the detection region 111 through the bottom surface and then leaving the detection region 111 through the same bottom surface. Particle trajectory 3d shows a particle entering the detection region 111 through the top surface and then exiting the detection region 111 through the opposing bottom surface.

[0040] However, the video is by definition a two-dimensional image and cannot be used to determine particle position in the z-direction, so the particle trajectories shown in Figure 5 are seen in the video as particles appear / disappear from the video as they enter / exit the detection region 111 in the Z-direction.

[0041] Particles similarly enter and exit the detection region in the x and y directions by passing through the sides of the detection region. Particle motion is not limited to motion along the x, y, and z axes. In fact, particle motion is a three-dimensional "random walk," with each "step" having an x, y, and z component.

[0042] Figure 6 shows how measured characteristics of particle trajectories can be used to determine the depth of a detection region according to an embodiment of the present invention. Figure 6 shows a schematic diagram of a video image 1. Video 1 may include a number of frames to show the movement of particles.

[0043] Similar to conventional NTA, a computer is configured to analyze the particle's motion to determine the particle's trajectory. A subsection 4 of video 1 is defined. The subsection may be a vertical x-strip 4 across video 1, as shown in FIG. 6, and may have a variable strip width Δx. The x-strip 4 is defined by a pair of parallel vertical planes across video 1 in the y direction and a pair of parallel horizontal planes across video 1 in the x direction. In this example, the horizontal planes are at the edges of the video, and the vertical planes are the full height of the video. Other shapes of strips may also be used.

[0044] FIG. 6 shows an example of particle trajectories of two particles moving within strip 4. A first particle is shown moving from a start position 2 within strip 4 to a subsequent position 2a outside strip 4 at an end time. In this example, the first particle moves primarily in the x-direction, generating a first particle trajectory 5a. The first particle moves in the x-direction and remains within the volume of the detection area captured by video 1. It can consequently be determined by the computer that the first particle trajectory 5a crosses one of the faces of strip 4.

[0045] The computer is configured to classify the first particle trajectory 5a as an "x trajectory." An x trajectory is a particle trajectory observed to cross one of the parallel perpendicular planes of the strip 4 and corresponds to a particle observed by the device entering or exiting the strip 4.

[0046] A second particle is shown moving from a starting position 2b within strip 4. The particle moves along a second particle trajectory 6. The second particle has a z-axis movement component and enters strip 4 through either the top or bottom face before the end time. Therefore, the second particle is not visible at the end time. The second particle trajectory 6 is observed to terminate without passing through a face of strip 4.

[0047] The computer is configured to classify the second particle trajectory 6 as a "z trajectory" or an "unobserved trajectory." A z trajectory is a particle trajectory that passes through the top or bottom of the detection region and corresponds to a particle whose trajectory enters or exits the strip 4 without passing through one of the faces of the strip 4.

[0048] The computer is configured to track multiple particles within the strip 4 or classify all particle trajectories as x-trajectories and z-trajectories.

[0049] In some embodiments of the present invention, the parallel pairs of vertical faces of the strips may span the full height of the video, as shown in Figure 6. In other embodiments, the strips may not span the full height of the video; instead, each strip may have four faces that fit entirely within the video. This may improve the accuracy of determining the depth of the detection region by reducing false trajectory classifications.

[0050] For example, consider the case where an x-strip is captured across the entire height of a video, and a particle is very close to the top edge of the strip. If the particle moves in the y-direction, it may move to the top of the image (outside the detection region) and not appear in subsequent video frames. The computer may misidentify this particle as a z-trajectory because it is not observed to leave the strip, but the particle has disappeared. However, if the dimensions of the strip are constrained within the video image (there is a "boundary region" on all four sides of the strip), the particle will be observed to have moved in the y-direction in subsequent frames. A computer configured to classify into x-trajectories and z-trajectories may be further configured to exclude this particle trajectory from analysis. The dimensions of the boundary region may be selected to correspond to the maximum expected movement of the particle between successive frames.

[0051] The computer is further configured to analyze a characteristic of the x and z trajectories as the width Δx of the strip 4 is varied. The characteristic may be the number of x trajectories and the number of z trajectories observed in a defined time interval.

[0052] For example, the computer may be configured to analyze a strip width of 100 pixels. The computer records the number of x-trajectories and the number of z-trajectories observed over a period of time. This process is repeated for different strip widths, for example, in steps of 1 pixel, 10 pixels, or 50 pixels.

[0053] By analyzing the changes in the number of x-trajectories and the number of z-trajectories recorded, the computer is configured to automatically determine the depth of the detection region.

[0054] If a very narrow strip is used (e.g., width Δx<< depth z), many particle trajectories will exit the strip in the x direction before they have a chance to exit the detection region in the z direction. Thus, the number of x trajectories will be large and the number of z trajectories will be small. Conversely, if a very wide strip is used (e.g., Δx >> z), very few particles will exit the strip in the x direction before first exiting the detection region in the z direction. In such a case, the number of z trajectories will be small and the number of z trajectories will be large.

[0055] The computer is configured to find strips where the number of x-trajectories and the number of z-trajectories are equal (or at least more similar), and therefore the depth z of the detection region is determined to be the same as this intermediate strip width.

[0056] Because particle movement is due to Brownian motion, particle movement is random (statistical) and tends to be equal to the average of the x, y, and z directions over a sufficient sample of trajectories. Statistically, when the strip width Δx is equal to the depth of the detection area, the number of x trajectories tends to be equal to the number of z trajectories. This is because when Δx = z, the surface areas of the two perpendicular strip faces and the top and bottom of the strip are equal. Therefore, the "flux" of particles moving through these faces is equal, meaning the number of x trajectories and the number of z trajectories are equal.

[0057] In many NTA instruments, the sample is flowed through a sample cell during measurement. This generates a component of sample movement that is not Brownian motion. It is known to correct for such particle drift in NTA analysis. Measured particle trajectories referred to in the specification are understood to have particle drift corrected. One way to correct for particle drift is to subtract the average velocity of the particles. Since the average Brownian motion is zero for all particles, this leaves only the Brownian motion component of the particles.

[0058] In other embodiments of the invention, the measured characteristics of the particle trajectories may be characteristics other than the number of trajectories. For example, the average lengths of the x and z trajectories before the particle exits the strip may be measured and compared. Alternatively, the average number of strips in the x and z trajectories before the particle exits the strip may be measured. The number of steps may be equal to the number of frames over which the particle's movement is observed. Like the number of trajectories, the trajectory length and number of steps are random in three directions, and once the intermediate strip width is found, it is predicted to be equal to the x and z trajectories.

[0059] In some embodiments of the present invention, the computer may be configured to analyze multiple strips of each strip width, which may improve the analysis of depth measurements. The multiple strips may be separate from one another, may be directly adjacent to one another, or may partially or fully overlap.

[0060] Multiple strips may be configured to encompass the entire image area. For example, five 100-pixel wide strips may be used to analyze a 500-pixel wide image. As another example, 400 different 100-pixel wide strips may be generated by placing 100-pixel wide strips on a 500-pixel wide image, offset by one pixel. In some embodiments, avoiding the edges of the image allows particles to be reliably tracked across the x and y edges of the strips. For example, exclusion boundaries may be defined around the edges of the image based on the maximum expected particle movement between successive frames.

[0061] Alternatively, the strips may not cover the entire detection area, but may be selected to cover important areas within the image. For example, a strip may be taken across the center of the image, and additional strips may be taken closer to the corners / edges of the image. Many imaging systems have optical aberrations, which can cause the depth of the detection area (e.g., depth of focus) to be different at the corners / edges of the image than in the center of the image. With strips in different areas of the image, the computer may be configured to account for differences in the depth of the detection area across the image.

[0062] The results of the measurement characteristics of each of the multiple strips of each width may be mathematically combined. For example, the number of trajectories across the multiple strips of each width may be summed (if the same number of strips are used for each width), or the average or median trajectory length may be calculated for each strip width. Alternatively, the results of strips taken in different regions of the image may be kept separate, and depths calculated for multiple regions of the detection area. This may allow differences in depth of the detection area (e.g., differences due to optical aberrations) to be calculated.

[0063] 7 shows that the process described in FIG. 6 is equally applicable to the y direction. As described, vertical x strips 4a of video 1 can be analyzed as varying in width Δx. Similarly, however, horizontal y strips 4b are analyzed as varying in width Δy. Although y trajectory 5b is classified by the computer as not being an x ​​trajectory 5a, all of the processes described for the x direction apply equally. In some embodiments, the computer may be configured to capture a combination of x and y strips and combine the results to determine the depth of the detection region.

[0064] Figure 8 shows a variation of the process described in Figure 7. This modified process was used in experimental tests to demonstrate the effectiveness of the depth measurement technique. A computer is configured to analyze video 1 of particles moving in a detection area. However, rather than attempting to detect depth (which is not observable in the z direction), the analysis is performed in the observable z and y directions.

[0065] The width of the strip 4a is set by the estimated value x. Accordingly, substrips 4b are sampled across the strip 4a, with the substrips having a variable width Δy. The computer is configured to count the number of observed x trajectories 5a and the number of observed y trajectories 5b in each of the multiple substrips 4b sampled from the strip 4a as Δy is varied. If the width of the y strip is smaller than the total height of the x strip (e.g., the y strips are aligned so that they do not overlap, or are moved over the x strips if they overlap), multiple y strips within the strip can be defined. Due to the small height Δy, many substrips 4b are sampled from the strip 4a. Using the same logic as above, the number of x trajectories and y trajectories is equal to x, which can be experimentally determined as Δy=x.

[0066] Figure 9 shows a plot of the number of x and y trajectories as a function of Δy. In this test, the width x of the strip 4a is set to 200 pixels, and all possible sub-strips 4b are sampled from the strip 4a for each sub-strip width Δy. Figure 9 shows, as expected, that the number of x and y trajectories is approximately equal to 200 pixels.

[0067] As expected, the number of y trajectories is very high when Δy is small and decreases as Δy increases. The number of x trajectories initially increases as Δy increases, as expected, but then decreases at high values ​​of Δy. This is because the number of trajectories shown in Figure 9 is the cumulative total taken across all possible strips of each Δy width. As the strips become wider, fewer substrips 4b can be sampled from the strip 4a, resulting in a decrease in the cumulative total trajectories at high values ​​of Δy.

[0068] Figure 10 shows a plot in which the process described in Figure 9 is repeated for a number of different x widths. Figure 10 shows that the cumulative value of x approaches the known value for x = 100, 200, 300, and 400 pixels. The error between the estimated x width and the expected value is made to be 6.5%.

[0069] According to another embodiment of the invention, the computer is further configured to calculate the concentration of particles in the fluid. The computer is configured to count the number of particles N in the video (corresponding to the number of particles in the detection region). The volume V of the detection region can be calculated from the planar area of ​​the detection region (known from the area of ​​the sample imaged by the imaging system) and the detection depth. The pixel-wise measurements may be translated into physical dimensions using the known particles of the device. Thus, the concentration C may be calculated as N / V.

[0070] Figure 11 shows the experimental concentrations obtained for several samples with different particle sizes using an apparatus according to an embodiment of the present invention and following the approach described above. The concentrations are given in parts per million (ppm). Figure 11 shows that the estimated concentrations obtained using the apparatus of the present invention are very similar to the known concentrations of the samples.

[0071] While exemplary embodiments have been described, they do not limit the scope of the invention, which should be determined with reference to the appended claims.

Claims

1. 1. An apparatus for characterizing particles using nanoparticle tracking analysis, comprising: a cell for containing a sample including a plurality of particles suspended in a fluid; a light source configured to illuminate the sample; an imaging system configured to collect light scattered or fluoresced by particles moving within the cell and within a detection area of ​​the imaging system and to capture video of the particles moving within the detection area; a computer configured to process the video to automatically determine the depth of the detection region; Equipped with Determining the depth of the detection region comprises: tracking the particles moving within the detection region, thereby generating a trajectory for each of the particles; analyzing how measurement characteristics of the trajectory within a subsection of the video change as the size of the subsection changes; Including, Device.

2. the subsection is a parallelogram strip taken across the video; The strip is defined by a pair of parallel surfaces.

10. The apparatus of claim 1.

3. the size of the subsection is varied by varying the width of the strip between the pair of faces; the computer is further configured to record the measured characteristic of the trajectory as a function of the strip width.

3. The apparatus of claim 2.

4. the computer is further configured to analyze the trajectory within the subsection; Each of the trajectories is (i) an x / y trajectory in which the particle trajectory is observed to cross one of the pair of faces; or (ii) a z-trajectory in which the particle trajectory begins and / or ends within the strip but is not observed to cross one of the pair of faces; are classified into the computer is further configured to record the measured characteristics of the x / y trajectory and the z trajectory separately.

4. The apparatus of claim 3.

5. the computer is configured to compare the measured characteristics of the x / y trajectory with the measured characteristics of the z trajectory for each strip width; the depth of the detection area is determined by finding the strip width at which the measurement characteristic of the x / y trajectory and the measurement characteristic of the z trajectory are equal or closest, and the determined depth of the detection area is equal to the strip width; 5. The apparatus of claim 4.

6. The measured characteristic of the trajectory is: Counting the number of x / y trajectories and the number of z trajectories observed within a given time interval; a measurement of the length of the x / y trajectory and the length of the z trajectory, where the length of each trajectory is the distance traveled by the particle within the strip; or a measurement of the number of steps in the x / y trajectory and the number of steps in the z trajectory, the number of steps in each trajectory being the number of frames of the video over which the particle moves within the strip; Selected from:

6. An apparatus according to claim 4 or 5.

7. the measurement characteristic is the count of the number of x / y trajectories and the number of z trajectories; 7. The apparatus of claim 6.

8. Multiple strips of each strip width are analyzed, the measured trajectory characteristics of the plurality of strips for each strip width are mathematically combined; 8. An apparatus according to any one of claims 3 to 7.

9. The plurality of strips include: covering most or all of the detection area; and / or the detection area to cover a plurality of areas having different detection area depths; Consists of 9. The apparatus of claim 8.

10. tracking the particles includes identifying particles from a current frame of the video in a subsequent frame of the video.

10. An apparatus according to any one of claims 1 to 9.

11. and identifying the particle in the subsequent frame of the video includes identifying a nearest neighbor particle in the subsequent frame.

11. The apparatus of claim 10.

12. and identifying the nearest particle in the subsequent frame includes identifying the nearest particle within a tracking distance limit.

13. The apparatus of claim 12.

13. the computer is configured to calculate a concentration of the particles suspended in the fluid; Calculating the concentration calculating a volume of the detection region using the determined depth; measuring the number of particles in the detection area; Including, 13. An apparatus according to any one of claims 1 to 12.

14. 1. A computer-implemented method for determining a depth of a detection region from video data obtained by nanoparticle tracking analysis, comprising: tracking particles moving within the detection region, thereby generating a trajectory for each of the particles; measuring a characteristic of the trajectory within a subsection of the video; analyzing how the measured characteristics of the trajectories within a subsection of the video change as the size of the subsection changes; Including, How computers are implemented.

15. A machine-readable non-volatile storage medium containing instructions for causing a processor to perform a method, comprising: The method includes determining a depth of a detection region from video data obtained by nanoparticle tracking analysis; Determining the depth is tracking particles moving within the detection region, thereby generating a trajectory for each of the particles; measuring a characteristic of the trajectory within a subsection of the video; analyzing how measurement characteristics of the trajectory within a subsection of the video change as the size of the subsection changes; Including, A machine-readable non-volatile storage medium.

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