System for determining the shape of particles in motion using an event-based camera

1 . A method for measuring attributes of a particle in motion, the method comprising:

observing a region of interest with an event-based sensor oriented such that lines of a pixel array of the sensor lie across an expected trajectory of the particle through the region of interest, wherein the event-based sensor comprises pixels that asynchronously generate events in response to changes in brightness;

defining two reference lines of pixels separated by a spatial distance;

sampling a first group of events produced by a first of the two reference lines;

sampling a second group of events produced by a second of the two reference lines;

determining a temporal distance between the second and first groups of events;

calculating a longitudinal speed factor of the particle by dividing the spatial distance by the temporal distance, wherein longitudinal refers to a direction perpendicular to the reference lines, wherein the particles have a size spanning multiple adjacent pixels in a line;

analyzing one of the first and second groups of events over multiple time steps in order to produce an outline of the particle in space-time coordinates including spatial components based on positions of event-triggered pixels in the lines and temporal components based on the time steps; and

converting the space-time coordinates of the outline to spatial coordinates by multiplying the time steps of the space-time coordinates by the longitudinal speed factor to obtain a first spatial coordinate while a second spatial coordinate is derived from the spatial component.

2 . The method of claim 1 , comprising:

measuring respective event rates produced by the two reference lines over multiple time steps;

storing a first time step where the event rate measured for the first group of events exceeds a threshold;

storing a second time step where the event rate measured for the second group of events exceeds the threshold; and

providing the temporal distance as a difference between the second and first time steps.

3 . The method of claim 2 , comprising the step of measuring each event rate by aggregating events produced by a group of multiple adjoining lines including the corresponding reference lines.

4 . The method of claim 1 , comprising:

analyzing the first and second groups of events over multiple time steps in order to produce respective first and second outlines of the particle in space-time coordinates; and

cross-correlating the first and second outlines to determine the temporal distance used for calculating the longitudinal speed factor.

5 . The method of claim 4 , comprising:

in cross-correlating the outlines, also determining a transverse spatial shift between the outlines in a direction of the lines;

providing a transverse speed factor by dividing the transverse spatial shift by the temporal distance; and

in converting the space-time coordinates to spatial coordinates, correcting the spatial components of the space-time coordinates based on the time steps and the transverse speed factor.

6 . The method of claim 1 , comprising the step of determining size attributes of the particle based on the outline in spatial coordinates.

7 . The method of claim 1 , comprising the step of determining a volume of the particle by:

(a) assuming the particle has a cross-section of revolution shape perpendicular to the longest axis of the outline; and

(b) calculating volume based on the outline dimensions in spatial coordinates and the assumed revolution shape using integration of cross-sectional areas along the longest axis.

8 . The method of claim 2 , comprising:

using multiple thresholds to determine multiple corresponding temporal distances; and

averaging the temporal distances.

9 . A droplet attribute analysis arrangement, comprising:

a nozzle configured to project droplets on a surface;

an event-based camera fixedly attached to the nozzle, wherein the event-based camera comprises pixels that asynchronously generate events in response to changes in brightness; and

an optical device attached to the nozzle, oriented such that it allows the camera to observe a region of interest between the nozzle and the surface;

wherein the camera includes a processor programmed to:

observe the region of interest with an event-based sensor oriented such that lines of a pixel array of the sensor lie across an expected trajectory of a particle through the region of interest;

define two reference lines of pixels separated by a spatial distance;

sample a first group of events produced by a first of the two reference lines;

sample a second group of events produced by the second of the two reference lines;

determine a temporal distance between the second and first groups of events; and

calculate a longitudinal speed factor of the particle by dividing the spatial distance by the temporal distance, wherein longitudinal refers to a direction perpendicular to the reference lines.