Method of determining a changing spatial distribution of particles at multiple points in time
First Claim
1. A method of determining a changing spatial distribution of particles at multiple points in time following to each other at intervals, the method comprising the following steps for each of the points in time:
- recording real two-dimensional images of the particles with different mapping functions at the respective one of the points in time;
providing an estimated spatial distribution of the particles;
calculating virtual two-dimensional images of the estimated spatial distribution applying the different mapping functions;
determining differences between the virtual two-dimensional images and the real two-dimensional images of the same mapping functions; and
varying the estimated spatial distribution of the particles for reducing the differences to obtain an approximated spatial distribution which is approximated to the actual spatial distribution of the particles at the respective one of the points in time;
wherein the estimated spatial distribution of the particles for at least one of the points in time is provided in that the locations of the individual particles in an approximated spatial distribution obtained for one other of the points in time are shifted dependently on how the locations of the individual particles have changed between at least two approximated spatial distributions obtained for at least two others of the points in time.
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Abstract
For determining a changing spatial distribution of particles at each of multiple points in time, real two-dimensional images of the particles are recorded with different mapping functions. An estimated spatial distribution of the particles is provided. Virtual two-dimensional images of the estimated spatial distribution are calculated applying the different mapping functions. Differences between the virtual and the real two-dimensional images are determined; and the estimated spatial distribution of the particles are varied for reducing the differences to obtain a spatial distribution approximated to the actual spatial distribution of the particles. The estimated spatial distribution of the particles is provided in that the locations of the individual particles in a spatial distribution approximated for one other point in time are shifted dependently on how the locations of the individual particles have changed between at least two spatial distributions approximated for at least two other points in time.
9 Citations
22 Claims
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1. A method of determining a changing spatial distribution of particles at multiple points in time following to each other at intervals, the method comprising the following steps for each of the points in time:
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recording real two-dimensional images of the particles with different mapping functions at the respective one of the points in time; providing an estimated spatial distribution of the particles; calculating virtual two-dimensional images of the estimated spatial distribution applying the different mapping functions; determining differences between the virtual two-dimensional images and the real two-dimensional images of the same mapping functions; and varying the estimated spatial distribution of the particles for reducing the differences to obtain an approximated spatial distribution which is approximated to the actual spatial distribution of the particles at the respective one of the points in time; wherein the estimated spatial distribution of the particles for at least one of the points in time is provided in that the locations of the individual particles in an approximated spatial distribution obtained for one other of the points in time are shifted dependently on how the locations of the individual particles have changed between at least two approximated spatial distributions obtained for at least two others of the points in time. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. A method of determining a changing spatial distribution of particles at multiple points in time following to each other at intervals, the method comprising the following steps for each of the points in time:
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recording real two-dimensional images of the particles with different mapping functions at the respective one of the points in time; providing an estimated spatial distribution of the particles; calculating virtual two-dimensional images of the estimated spatial distribution applying the different mapping functions; determining differences between the virtual two-dimensional images and the real two-dimensional images of the same mapping functions; and varying the estimated spatial distribution of the particles for reducing the differences to obtain an approximated spatial distribution which is approximated to the actual spatial distribution of the particles at the respective one of the points in time; wherein the estimated spatial distribution of the particles for at least one of the points in time is provided in that the locations of the individual particles in an approximated spatial distribution obtained for one other of the points in time are shifted dependently on how the locations of the individual particles have changed between at least two approximated spatial distributions obtained for at least two others of the points in time; wherein the estimated spatial distribution of the particles is provided for at least one of the points in time in that trajectories of the individual particles are determined from the approximated spatial distributions obtained for the at least two others of the points in time and in that these trajectories are extrapolated for the at least one of the points in time; wherein the trajectories are determined from the approximated spatial distributions obtained for more than two others of the points in time; and wherein particles with trajectories which deviate from Navier-Stokes solutions for a flow of a fluid seeded with the particles by more than a preset limit value are identified and eliminated from the approximated spatial distributions.
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15. A method of determining a changing spatial distribution of particles at multiple points in time following to each other at intervals, the method comprising the following steps for each of the points in time:
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recording real two-dimensional images of the particles with different mapping functions at the respective one of the points in time; providing an estimated spatial distribution of the particles; calculating virtual two-dimensional images of the estimated spatial distribution applying the different mapping functions; determining differences between the virtual two-dimensional images and the real two-dimensional images of the same mapping functions; and varying the estimated spatial distribution of the particles for reducing the differences to obtain an approximated spatial distribution which is approximated to the actual spatial distribution of the particles at the respective one of the points in time; wherein the estimated spatial distribution of the particles for at least one of the points in time is provided in that the locations of the individual particles in an approximated spatial distribution obtained for one other of the points in time are shifted dependently on how the locations of the individual particles have changed between at least two approximated spatial distributions obtained for at least two others of the points in time; and wherein the spatial distributions of the particles for those of the points in time between a first one of the points in time and a much later second one of the points in time are once determined starting from the first one of the points in time for succeeding points in time and once starting from the second one of the points in time for preceding points in time. - View Dependent Claims (16, 17, 18, 19, 20, 21, 22)
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Specification