Cross-correlation tomography

Abstract

Methods and systems are described for performing cross-correlational analysis. An example method may comprise receiving sensor data indicative of a subject region. The example method may comprise determining signal data indicative of change in the sensor data. The example method may comprise determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location in the subject region. The example method may comprise determining change data based on the mapping data, the signal data, and a cross-correlation process. The example method may comprise causing output of the change data.

Description

1003-0007W01CROSS-CORRELATION TOMOGRAPHYCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of and priority to United States Patent Provisional Application No. 63 / 724,764 filed November 25, 2024, which is hereby incorporated by reference for any and all purposes.FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

[0002] This invention was made with government support under Grant Nos. FA9550-19-1- 0167 and FA9550-23-1-0221 awarded by the Air Force Office of Scientific Research (AFOSR). The government has certain rights in the invention.BACKGROUND OF THE INVENTION

[0003] Conventional measurement techniques for measuring turbulence, flow, and other similar physical phenomena often rely on seeding flows with tracer particles for Particle Image Velocimetry (PIV), which is intrusive and impractical in many real-world environments. Alternative optical methods, such as schlieren and Background-Oriented Schlieren (BOS), eliminate the need for tracers but can only provide two-dimensional projections, resulting in poor depth resolution. Multi-camera BOS tomography can recover 3D information but requires numerous cameras, making systems complex, expensive, and prone to alignment and synchronization errors. Even with multiple viewpoints, reconstruction accuracy is constrained by diffraction, multiple scattering, and focus mismatch, limiting applicability in dynamic or uncontrolled settings. Thus, there is a need for more sophisticated techniques for measuring flow, turbulence, and other physical phenomena.SUMMARY OF THE INVENTION

[0004] Disclosed herein are devices, methods, and systems for performing cross- correlational analysis for physical phenomena. An example method may comprise receiving sensor data indicative of a subject region, wherein the sensor data comprises at least first data based on a first field of view capturing the subject region from a first angle and second data1003-0007W01 based on a second field of view capturing the subject region from a second angle different than the first angle. The example method may comprise determining, based on the first data and the second data, signal data indicative of change in the sensor data. The example method may comprise determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location in the subject region. The example method may comprise determining change data based on the mapping data, the signal data, and a cross-correlation process. The example method may comprise causing output of the change data.

[0005] An example system may comprise a plurality of sensors comprising at least a first sensor configured to capture signals from a subject region from a first field of view at a first angle thereby generating first data and a second sensor configured to capture signals from the subject region from a second field of view at a second angle thereby generating second data. The example system may comprise a computing device comprising one or more processors and a memory, wherein the memory stores instructions that, when executed by the one or more processors, cause the computing device to perform receiving sensor data indicative of a subject region, wherein the sensor data comprises at least first data based on a first field of view capturing the subject region from a first angle and second data based on a second field of view capturing the subject region from a second angle different than the first angle. The computing device may be caused to perform determining, based on the first data and the second data, signal data indicative of change in the sensor data. The computing device may be caused to perform determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three- dimensional spatial location in the subject region. The computing device may be caused to perform determining change data based on the mapping data, the signal data, and a crosscorrelation process. The computing device may be caused to perform causing output of the change data.

[0006] An example device may comprise one or more processors and a memory storing instructions that, when executed by the one or more processors, cause the device to perform: receiving sensor data indicative of a subject region, wherein the sensor data comprises at least first data based on a first field of view capturing the subject region from a first angle and second data based on a second field of view capturing the subject region from a second angle different1003-0007W01 than the first angle. The device may be caused to perform determining, based on the first data and the second data, signal data indicative of change in the sensor data. The device may be caused to perform determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location in the subject region. The example device may be caused to perform determining change data based on the mapping data, the signal data, and a cross-correlation process. The device may be caused to perform causing output of the change data.

[0007] An example non-transitory computer-readable medium may store instructions that, when executed by one or more processors, cause a device to perform receiving sensor data indicative of a subject region, wherein the sensor data comprises at least first data based on a first field of view capturing the subject region from a first angle and second data based on a second field of view capturing the subject region from a second angle different than the first angle. The device may be caused to perform determining, based on the first data and the second data, signal data indicative of change in the sensor data. The device may be caused to perform determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location in the subject region. The example device may be caused to perform determining change data based on the mapping data, the signal data, and a cross-correlation process. The device may be caused to perform causing output of the change data.

[0008] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Furthermore, the claimed subject matter is not limited to limitations that solve any or all disadvantages noted in any part of this disclosure.

[0009] Additional advantages will be set forth in part in the description which follows or may be learned by practice. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive.1003-0007W01BRIEF DESCRIPTION OF DRAWINGS

[0010] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments and together with the description, serve to explain the principles of the methods and systems.

[0011] FIG. 1 A shows an example system for performing cross-correlation analysis.

[0012] FIG. IB shows a flow chart of an example method in accordance with the present disclosure.

[0013] FIG. 1C shows an example system for background-oriented Schlieren.

[0014] FIG. ID shows another example of background-oriented schlieren tomography.

[0015] FIG. IE shows an example of stereo background-oriented schlieren with 3D localization of turbulence recoverable through time-averaged intensity correlations.

[0016] FIG. 2 shows a setup for cross-correlation BOS using axial displacements.

[0017] FIG. 3 is an illustration of an experimental setup to test correlation stereo camera turbulence imaging including prisms used to project viewpoints onto one half of the same camera sensor.

[0018] FIG. 4A shows experimental measurement of heat plume from a soldering iron, with setup and transverse correlations.

[0019] FIG. 4B shows graphs showing peaks of cross-correlations giving axial distance from background.

[0020] FIG. 5 shows image showing experimental result showing 3D profiles of two flow patterns.

[0021] FIG. 6 is an illustration of the Principle of Time Correlation Tomography, showing that rays passing through different points acquire uncorrelated shifts in time.

[0022] FIG. 7 shows example results of ray reconstruction for a round turbulent jet.

[0023] FIG. 8 shows an example reconstructed speed map and gaussian fit for a slice passing through the center of circular nozzle in an x-y plane and an x-z plane.

[0024] FIG. 9 shows velocity decay as a function of axial distance from the nozzle for four different experimental flow speeds.

[0025] FIG. 10 is a block diagram illustrating an example computing device.1003-0007W01DETAILED DESCRIPTION OF THE INVENTION

[0026] Disclosed herein are devices, methods, and systems for performing cross- correlational analysis for physical phenomena. Disclosed herein are systems and methods for detecting and characterizing changes within a subject region using multi -view sensor data and cross-correlation analysis. In general, the disclosed techniques include receiving sensor data from at least two different fields of view capturing the subject region from distinct angles. Based on this data, the system determines signal data indicative of changes in the region, such as variations in refractive index, intensity, or other physical properties. The disclosed techniques may compute mapping data to associate sensor coordinates from the different views with corresponding three-dimensional spatial locations, enabling volumetric analysis. Using this mapping data and a cross-correlation process, the system may generate change data that represents dynamic behavior in three (e.g., or more) dimensions over time. The resulting change data may be stored, transmitted, or displayed for visualization and / or further analysis. In some scenarios, the resulting change data may be used to update a parameter for a machine, such as a system parameter for operating a machine (e.g., or other device, substance) that creates a flow in the subject region, a manufacturing parameter for changing the physical properties of a device manufactured, a combination thereof, and / or the like. These techniques provide improved depth resolution and non-intrusive measurement of complex phenomena such as turbulence, flow dynamics, and other physical changes in transparent or semi-transparent media. The disclosed techniques also include the ability to perform a large number of parallel cross-correlations.

[0027] FIG. 1A shows a block diagram of an example system 100 for performing crosscorrelation analysis. The system 100 may comprise a computing device 102, a user device 104, an analysis device 106, an application device 108 (e.g., an application server), or a combination thereof. It should be noted that while the singular term device is used herein, it is contemplated that some devices may be implemented as a single device or a plurality of devices (e.g., via load balancing). The computing device 102, the user device 104, the analysis device 106, the application device 108 may each be implemented as one or more computing devices. Any device disclosed herein may be implemented using one or more computing nodes, such as virtual machines, executed on a single device and / or multiple devices.

[0028] The computing device 102, the user device 104, the analysis device 106, and / or the application device 108 may be communicatively coupled via one or more networks, such as the1003-0007W01 network 110 (e.g., a wide area network). The network 110 may comprise wired links, wireless links, a combination thereof, and / or the like. The network 110 may comprise routers, switches, nodes, gateways, servers, modems, and / or the like.

[0029] The application device 108 may be configured to provide one or more services, such as application services associated with a user interface. The application device 108 may comprise services for one or more applications on or accessible by the user device 104. The application device 108 may generate application data associated with the one or more application services. The application data may comprise data for a user interface, data to update a user interface, data for an application session associated with the user device 104, and / or the like. The application data may comprise data used for cross-correlation analysis.

[0030] The user device 104 may comprise a computing device, a smart device (e.g., smart glasses, smart watch, smart phone), a mobile device, a tablet, a computing station, a laptop, a television, and / or the like. In some scenarios, a user may have multiple user devices, such as a mobile phone, a smart watch, smart glasses, a combination thereof, and / or the like. The user device 104 may be configured to communicate with the computing device 102, the analysis device 106, the application device 108, and / or the like. The user device 104 may be configured to output a user interface. The user interface may be output via the user interface via an application, service, and / or the like, such as an application for analysis for sensor data. The user interface may receive application data from the application device 108. The application data may be processed by the user device 104 to cause display of the user interface. The user interface may be displayed on a display of the user device 104. The display may comprise a television, screen, monitor, projector, and / or the like.

[0031] The computing device 102 may be configured to receive sensor data indicative of a subject region 116. The sensor data may be generated based on signals and / or radiation passing through the subject region 116. The sensor data may comprise at least first data 112 based on a first field of view capturing the subject region 116 from a first angle and second data 114 based on a second field of view capturing the subject region 116 from a second angle different than the first angle. The sensor data may comprise data captured by a plurality of sensors 118 (e.g., such as photodiodes generating data based on the radiation and / or signals that passed through the subject region 116). The first data may be captured by a first sensor 120 of the plurality of sensors and the second data may be captured by a second sensor 122 of the plurality of sensors1003-0007W01118. The plurality of sensors 118 may be implemented in a variety of ways. For example, the plurality of sensors 118 may be integrated into a single device, such as a camera (e.g., such as shown in FIG. 3). The plurality of sensors 118 may be physically distributed across multiple separate devices (e.g., multiple cameras and / or sensor arrays, such as shown in FIG. IE).

[0032] In the case of a single device, such as a camera, the sensor data may comprise an image captured with a camera. The first data may comprise a first portion of the image and the second data may comprise a second portion of the image. The first sensor 120 may be configured to capture the first data 112 (e.g., a first pixel or group of pixels in the image). The second sensor 122 may be configured to capture the second data (e.g., corresponding to a second pixel or group of pixels in the image).

[0033] The sensor data may comprise a time sequence of data representing signals captured over time. The time sequence may comprise a video and / or sequence of images. The time sequence may include other data collected, measured, and / or calculated at each point in time.

[0034] The system 100 may comprise one or more control elements 124. The one or more control elements may be configured to control the direction and / or properties of signals to and / or from the subject region 116. In the case of light, the one or more control elements may comprise an optical subsystem. The one or more control elements 124 may be configured based on the type of sensors and / or the location of the plurality of sensors 118. For example, in the case of a single camera comprising the plurality of sensors 118, the one or more control elements 124 may comprise one or more refractive elements (e.g., two right angle prisms) and one or more reflective elements (e.g., two mirrors) configured to direct the path of different signals and / or radiation to different sensors (e.g., the first sensor, the second sensor) in a single device (e.g., as shown in FIGs. 3, 4A, and 6). The reflective elements may be configured to direct radiation and / or signals from the subject region 116 to the one or more refractive elements. The one or more refractive elements may direct the radiation and / or signals to the plurality of sensors 118. It should be understood that other optical elements may be used, such as diffractive elements, modulating elements, polarizing elements, filtering elements, diffusion elements, a combination thereof, and / or the like. For other types of physical properties and / or radiation other control elements may be used to manipulate and / or control the relevant signals between the subject region 116 and the plurality of sensors 118.1003-0007W01

[0035] The sensor data may be indicative of a background pattern 126. The subject region 116 may be between the plurality of sensors 118 and the background pattern 126. The background pattern may comprise one or more of a printed background, a horizon, an array of lights, background scenery, or a geographic pattern. The background pattern 126 may be selected and / or optimized for measurement of changes of appearance of the background pattern 126 due to signals passing through the subject region 116. Flow in the subject region 116 may cause the background pattern 126 to appear different, though the background pattern 126 may not actually be changing.

[0036] The subject region 116 may comprise a flow region (e.g., liquid or gas flow), a fluid region, an engine flow region, a combustion zone, a heat plume region, a thermal gradient region, a turbulent flow region, a chaotic flow region, a laminar flow region, a boundary layer region, a shear layer region, a jet flow region, a fluid mixing layer, a shock wave region, an acoustic propagation region, a plasma region, a gas-liquid interface, a microfluidic channel, an atmospheric turbulence region, an aquatic flow region, a cryogenic fluid region, a chemical reaction zone, an aerodynamic wage region, a cooling flow region, a fluid region in a biological cell, a combination thereof, and / or the like.

[0037] The computing device 102 may be configured to store the first data 112 and the second data 114 for processing, such as any combination of the steps and features of the method of FIG. IB or any other process or method described herein. In some scenarios, the computing device 102 may send the first data 112 and / or the second data 114 via the network 110 to another device, such as the analysis device 106 for processing. The analysis device 106 may perform any combination of the steps and features of the method of FIG. IB or any other process or method described herein. In some scenarios, the computing device 106 and the analysis device 106 may each perform a corresponding portion of the steps and features of the method of FIG. IB or any other process or method described herein. The application device 108 may access the results of the processing and provide them via a user interface, which may be accessible via the user device 104.

[0038] FIG. IB shows a flow chart of an example method 101 in accordance with the present disclosure. The method 101 may comprise a computer implemented method for providing a data analysis service (e.g., cross-correlation analysis service). A system and / or computing environment, such as the system 100 of FIG. 1 A and / or the computing environment of FIG. 10,1003-0007W01 may be configured to perform the method 101 . The method 101 may be performed in connection with the system illustrated in FIG. 1. Any step or combination of steps of the method 101 may be performed by a computing device, user device, application device, and / or analysis device, such as any of the devices shown in FIG. 1A. Any of the features of the methods described in the other figures herein may be combined with any of the features and / or steps of the method 101 of FIG. IB.

[0039] At step 103, sensor data indicative of a subject region may be received (e.g., or determined, accessed). The sensor data may comprise at least first data based on a first field of view capturing the subject region from a first angle and second data based on a second field of view capturing the subject region from a second angle different than the first angle. The sensor data may comprise data captured by a plurality of sensors. The first data may be captured by a first sensor of the plurality of sensors. The second data may be captured by a second sensor of the plurality of sensors. The sensor data may comprise an image captured with a camera. The first data may comprise a first portion of the image and the second data comprises a second portion of the image. The sensor data may comprise a time sequence of data representing signals captured over time.

[0040] The sensor data may be indicative of a background pattern. The subject region may be between a sensor detecting the sensor data and a background pattern. The background pattern may comprise one or more of a printed background, a horizon, an array of lights, background scenery, or a geographic pattern. Determining the signal data may comprise determining apparent displacement of the background pattern for the first data and the second data. Determining apparent displacement of the background pattern for the first data and the second data may comprise comparing at least a portion of the first data in a first frame captured at a first time with corresponding portions of the first data in a second frame captured at a second time.

[0041] At step 105, signal data indicative of change in the sensor data may be determined. The signal data indicative of change in the sensor data may be determined based on the first data, the second data, or a combination thereof. Determining the signal data may comprise determining displacement (e.g., or other change) of the background pattern for the first data and / or the second data. The signal data may be indicative of changes in one or more of refractive index, intensity, contrast, phase, polarization, or apparent displacement of background features. The signal data may comprise displacement data (e.g., or data indicative of other changes)1003-0007W01 indicative of movement in the subject region. The signal data may be indicative of density, velocity, pressure, temperature, refractive index, absorption, or a combination thereof. The signal data may comprise one or more of a probability distribution, at least one peak of a probability distribution, at least one moment of a probability distribution, a higher order correlation, a correlation of more than two pixels, a correlation of a random combination of pixels, a subset of video frames, a periodic subset of frames, an aperiodic subset of frames, a random set of frames, or any combination thereof.

[0042] At step 107, mapping data may be determined. The mapping data may associate a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location (e.g., or spatial location, such as a multi-dimensional spatial location with more or less than three dimensions of data) in the subject region may be determined. The three-dimensional spatial location may comprise a voxel location in three dimensional space, a point location in three-dimensional space, a plane in three-dimensional space, and / or the like. Determining the mapping data may comprise determining an intersection of radiation (e.g., or line of sight) from the first field of view with radiation from the second field of view thereby defining a voxel indicative of the three-dimensional spatial location.

[0043] Determining the mapping data may be based on calibration data. The calibration data may comprise an image capturing a pattern in the subject region. Determining the mapping data may comprise inputting the pattern into a stereo camera calibrator process. Determining the mapping data may comprise applying epipolar geometry to associate sensor coordinates from the first field of view and corresponding sensor coordinates from the second field of view with corresponding three dimensional spatial locations.

[0044] At step 109, change data may be determined. The change data may be determined based on the mapping data, the signal data (e.g., the signal data from step 107 or signal data from step 107 that is further processed, such as by reducing noise or irrelevant signal data to the objective), a cross-correlation process, or any combination thereof. Determining the change data may comprise identifying a spatial location corresponding to a peak in the cross-correlation metric between signals in the signal data. In some scenarios, change data be multi-dimensional, including, for example, spatial location (in three dimensions), time, and / or other properties, such as polarization, color, and / or the like.1003-0007W01

[0045] The cross-correlation process may comprise computing a time-averaged correlation of signals in the signal data associated with the first field of view with signals in the signal data associated with the second field of view. The cross-correlation process may comprise using the mapping data to identify sensor coordinates corresponding to lines of sight from the first field of view and the second field of view that intersect at a common three-dimensional spatial location. The cross-correlation process may comprise generating a correlation value for that spatial location by comparing signals in the signal data associated with the identified sensor coordinates. The cross-correlation process may comprise determining a velocity of change at the three- dimensional spatial location based on computing a time-delayed correlation of signals in the signal data.

[0046] The change data may comprise a time series of at least three dimensions (e.g., three spatial dimensions, time dimension, other data dimensions) representing changes in the subject region. The change data may comprise a representation of a fluid property may comprise one or more of density, speed, velocity, temperature, pressure, or a representation of multiple fluids or phases in the subject region. The change data may be indicative of changes in one or more of a gas or plasma.

[0047] At step 111, output of the change data may be caused. Causing output of the change data may comprise causing one or more of: storage of the change data, sending the change data via a network to a computing device (e.g., the application device 108, the analysis service 106, the user device 105), output of the change data (e.g., via a display and / or user interface), or output of data calculated based on the change data.

[0048] The method may comprise processing the signal data (e.g., prior to generating the change data) to reduce contributions from one or more of time-invariant or quasi-static components thereby enhancing detection of localized changes in the subject region. Processing the signal data may comprise subtracting one or more of a moving mean or a mean value from the signal data prior to applying the cross-correlation process.

[0049] The following paragraphs provide further examples and illustrations of the example devices, systems, and methods of FIG. 1 A-B. It should be understood that the methods, devices, and systems are not limited to the specific examples provided below. Instead, these specific examples provide additional features and details, any one or any combination of which, may be implemented by the method of FIG.1B and / or the device 100 of FIG. 1A.1003-0007W01

[0050] Background-oriented schlieren (BOS) typically measures a refractive index change in a region of interest (ROI) by taking the difference of two images of a background plane: one without an object in the ROI to serve as a reference and one with an object in the ROI to record distortions caused by it (e.g., as shown in FIG. 1C). Most BOS configurations use a random array of discrete points as a background, but periodic arrays and continuous patterns have been used as well. Conventional BOS cannot determine the refractive index profile of the object in 3D, as all changes along the optical path from the background to the camera are projected onto a 2D detection plane. There are also issues of axial resolution, as the camera cannot be focused on the background and the object at the same time.

[0051] BOS tomography can localize a refractive index change in 3D by using many cameras to record a large number of different viewpoints (e.g., as shown in FIG. ID). Numerical reconstruction follows from standard techniques, such as (filtered) back-projection. The need for many cameras makes the system complex, expensive, and subject to alignment and synchronization issues. The accuracy of the reconstruction is limited by the number of cameras, the reconstruction algorithm, diffraction, multiple scattering, and blur from the focus mismatch.

[0052] Here, correlations are introduced as a new parameter that overcomes many of the previous issues. The simplest embodiment is a two-point cross-correlation that includes only two cameras, or two halves of a single camera (e.g., as shown in FIG. IE). The object in the ROI is a phase object containing a plurality of points that fluctuate randomly in time. In a preferred embodiment, the object is a region of turbulence in a transparent medium, such as air or water.

[0053] In another preferred embodiment, the illumination is incoherent, such as white light. Any meaningful statistics recorded in the detectors comes only from fluctuations from the object within the ROI.

[0054] Using detectors in stereo allows the simultaneous recording of different optical paths; paths that sample the same point in space, i.e. those that cross each other, will be highly correlated. By measuring the time-varying intensity in each detector, these cross-correlations can be measured and traced back to their common source.

[0055] Importantly, each pixel in the camera(s) may act as an individual and independent detector, so an enormous number of optical paths can be recorded. For example, a megapixel detector can record ~1012different pairs.1003-0007W01

[0056] Further, the system is not limited to two-point correlations. Higher-order statistics, such as 3-, 4-, and N-point correlations, can be performed. Full statistical distributions in the ROI can then be reconstructed using post-processing.

[0057] One embodiment of the invention relies on a series of background images taken with 2 different view angles. One can find the shift of the background pattern numerically, e.g. using well-known particle image velocimetry algorithms, and create a shift vector for each background point. One can then find the average cross correlation of these shift vectors for each pixel. Each pixel pair gives a single location in 3D space using epipolar geometry. The correlation value is proportional to the time average of the turbulence at that point. The contribution of all other points may be neglected because their shifts are uncorrelated (the optical paths don’t cross) for different points in space.

[0058] In another embodiment, the cross-correlation is taken for two points along the optical axis, e.g. one in-focus picture and one out-of-focus picture (e.g., as shown in FIG. 2). For small displacements the two measured images differ by a scale factor from each other (i.e. one is a magnified / diffracted version of the other).

[0059] In another embodiment, the illuminating radiation is patterned using non-intensity properties of the radiating field (the original patterned background can viewed as an amplitude modulation for an initially uniform incident radiation). For example, in light illumination, optical properties suitable for modulation include polarization, wavelength, and phase. In acoustics, sound or ultrasound properties include temperature and pressure.

[0060] In these examples, the background screen can appear of uniform intensity. If the imaging system has a small enough depth of focus, a physical screen may not be necessary, as the focusing condition provides an object distance.

[0061] In a preferred embodiment, the non-amplitude properties are patterned to highlight subregion of the ROI. A prime example is the shear boundary between a turbulent jet and the ambient air, e.g. by using one polarization to illuminate the jet and a perpendicular one to illuminate its surroundings. Since polarization can be identified and tracked individually by the sensors, e.g. with polarizer filters, the separate initial conditions of “outside” and “inside” the jet have been effectively tagged as a two-phase fluid.

[0062] For an experimental demonstration, the setup shown schematically in FIGs. 2 and 3 was used. First, a random background of points was illuminated with an incoherent light source.1003-0007W01A single Sony Rxl0-M4 camera was used to image this background. For stereo imaging, 2 different viewing angles are created using 2 mirrors and 2 right-angle prisms.

[0063] Airflow patterns were created by placing a heat source between the background plane and detector plane. For laminar flow, the heat plume from a soldering iron was used, while for turbulence flow hair dryers were used. A video of the dynamics was recorded and the apparent shift at each pixel location was found using Particle Image Velocimetry PIV) algorithm for each frame. Finally, cross-correlations of each pair of pixels were taken, over time, to reconstruct the flow dynamics. Results are shown in FIGs. 4A-B and 5.

[0064] In one preferred embodiment, a background pattern may be utilized. Resolution may be limited because there is ambiguity in determining which points moved (e.g. is the source of a deflected point one from the left that has moved right or one from the right that has moved left). This may be ameliorated by optimizing the background pattern for a given sensor and fluid configuration. Resolution may also be improved numerically by using a different algorithm. For example, instead of a PIV algorithm, which uses correlating a sub-region of the pattern, optical flow can be used, which correlates the measured images point-by-point.

[0065] In various embodiments, the method relies on a time averaging of intensity. For fast scales, this may use high video frame rates to prevent evolution of the pattern during the acquisition exposure. In the test example above, the air exited the dryer at ~25m / s, and video rates of 10-1500 frames per second were used. In some embodiments, the frame rates are controlled by the user, while in others it is set automatically. Importantly, the frame rate may vary over the course of the recording. In some preferred embodiments, the time interval between frames may not be constant, e.g. increasing or decreasing monotonically (giving a frequency chirp) or having an aperiodic structure.

[0066] If two (or more) cameras are used, there may be issues with synchronization. Projecting the perspectives onto two halves (or separate regions) of the same camera, as shown in FIG. 3, can avoid this issue.

[0067] In other preferred embodiments, a relative time delay is introduced between the cameras. This can be done by triggering recording at different starting times; the resulting time difference is a separate parameter from the time interval between video frames (determined by frame rate of each camera). For example, if each camera has a video rate of 1000 frames per second (giving a time interval of 1ms), the time offset between the cameras may be Ips, or Ins.1003-0007W01In one preferred embodiment, this time offset remains constant and is repeated at the video frame rate of each camera.

[0068] Inter alia, the disclosed techniques can be used to measure fundamental fluid, air, and heat flow. Example properties include density, velocity, pressure, and temperature variations over a 3D volume. Direct applications include imaging heat flow in buildings to prevent loss, measuring air flow around a wind turbine to optimize power, remote sensing of turbulence strength to estimate smooth or rough transport, and the observation of separating flow as an (early) warning of wing stall in aircraft. Applications that use the measurements as a baseline for further action include adaptive optics (e.g. for receiving signals or directing energy) and for adaptive aerodynamics.

[0069] In various aspects, a method for cross-correlation imaging may be provided. The method may include receiving at least one pair of images (which may be in any appropriate form, such as that of plain images, frames from video, etc.). This may include receiving a plurality of pairs of images captured over a period of time.

[0070] Each image of the pair of images may be taken from different view angles. The different view angles may be configured to capture radiation passing through an overlapping volume of space. The overlapping volume of space may include a fluid. The fluid may be a gas. The fluid may be a liquid. The fluid may be free of reflective particles. The fluid may be free of particles opaque to whatever wavelengths of radiation are otherwise passing through the fluid. The radiation may include optical / visible light (e g., light having one or more wavelengths of 400 nm - 700 nm), and / or infrared light (e g., light having one or more wavelengths of 700 nm - 1 mm).

[0071] Each pair of images may include two images that are captured simultaneously, or may include a first image captured at a first time point and a second image captured at a later time point. The time between the first and second time point may be any appropriate time difference. In some instances, this is a constant value. In some instances, this may vary. In some instances, the later time point may be no more than 1 ps later than the first time point. In some embodiments, a time between capturing each pair of images is constant (e.g., a time between capturing a first image in a one pair of images and a first image in the following pair of images is constant). In some embodiments, a time between capturing each pair of images varies.

[0072] Each image may include relatively light portion(s) and relatively dark portion(s).1003-0007W01

[0073] These relatively light portion(s) and relatively dark portion(s) may be from a background behind the overlapping volume of space. In some cases, the background may be an organized array or random pattern of light dots on a black background. In some cases, the background may be perfectly uniform, e.g. a white screen, and the cameras record intensity variations made by shadows. Outdoor references include city or runway lights, brick walls, asphalt roads, and sandy or rocky terrain. Another importance reference is a line of separation, such as the rim of a smoke stack or cooling tower, the edge of a building, the boundary of an animal or vehicle, and the horizon distinguishing earth from sky. The sensor(s) used to capture the pairs of images may preferably be focused on that background.

[0074] If an additional image is introduced individually, so that the total number of images captured is odd, then they can be correlated in pairs. In a preferred embodiment, there are three images { 1,2,3} and the set correlations {(1,2), (1,3), (3,2)} is measured. As before, there is a dominant cross-correlation when each path in the image crosses. For one megapixel detectors, the number of crossover points can increase from about 1012combinations for two images to about 1018crossover points for three images.

[0075] In a preferred embodiment with three sensors, one sensor defines an axis to the background plane while the other two sensors are placed symmetrically on either side, i.e. at equal distances and opposite angles from the axis.

[0076] In another preferred embodiment, the sensors are cameras and the flow in the region of interest is caused by a solid body moving through the ROI, e.g. an airplane or swimming fish. Each camera records a different view of both the object and the flow around it. In the final reconstructed image, the image of the body can provide context for an observer in that perspective, to better convey the flow information obtained.

[0077] The method may include cropping the received images.

[0078] The method may include creating a shift vector for each pixel of the image. This may be done using any appropriate technique known in the art for doing so. Such may include, e.g., using OpenPIV or other open-sourced software packages for particle image velocimetry.

[0079] The method may include, for each pixel within each image, determining an average cross-correlation of the shift vectors of n pixels, where n > 2. That is, determining correlations between the shift vector for a pixel on the first image of a pair of images and the shift vector for at least one other pixel, with the caveat that it may include at least one pixel on the second image1003-0007W01 of the pair of images. In some cases, n=2; that is, this only involves correlations between one pixel on a first image and one pixel on a second image. In some cases, n > 2; that is, this may be correlations between each pixel on the first image and two or more pixels on the second image. In some cases, this may be correlations between each pixel on the first image, one or more other pixels on the first image, and one or more pixels on the second image.

[0080] Typically, the number of pixels involved in each correlation may be determined by a desired speed of calculation - fewer pixels use less processing time, while more pixels use more processing time. In some cases, more pixels may result in a higher degree of accuracy. Thus, this may be a trade-off between accuracy and speed. However, as will be understood, almost any number of pixels may be involved as part of the correlation determination. In the limit of all possible correlations, the full distribution function of the statistics may be reconstructed.

[0081] The simplest case of two-point correlations still contains much more information than a single-point measurement. In conventional (single-viewpoint) BOS, each pixel in the recording camera can only register the intensity integrated over the entire (optical) path from pixel to background. In the preferred embodiment of a stereo system, the introduction of a second detector creates a second path that crosses the first one. Triangulation of the intersection provides a three-dimensional localization inside the volume of interest, but something extra is needed to isolate its contribution to the line-integrated intensity recorded in each camera pixel.

[0082] As discussed above, the long-time average of the pixel cross-correlation is dominated by the point where the paths cross, as the (turbulent) fluid varies randomly throughout the volume of interest. The cross-correlation peaks at the intersection, which samples the same region of fluid, and falls off as the paths diverge from this point. In the limit of totally random fluid motion, continuous space-time points, and infinite time average, the cross-correlation becomes a delta function.

[0083] For real systems, none of these idealizations occur. The fluid motion has finite correlations in space and time (e.g. coherent structures in turbulence), the measurement space is discretized by pixels, the time sampling is determined by the video frame rate, and the measurement time is finite. In practice, these parameters set the resolution of the voxel reconstruction, and the cross-correlation peak becomes more prominent as the recording time increases.1003-0007W01

[0084] The most important consequence of this growth is that the cross-correlation peak can be localized in three dimensions after recording a finite number of frames. This peak is an identifiable feature whose motion can be tracked by observing subsequent frames.

[0085] In a preferred embodiment, the cross-correlation peak is determined by a set of N frames, i.e. { 1, ... ,N), and the next recorded frame (N+l) gives a new peak determined by moving the time average to the set {2, ... , N+l }. If the position of the peak moves, then its velocity can be calculated by dividing its spatial shift by the time interval between frames.

[0086] Since every pair of pixels on the camera(s) corresponds to a unique point in space, the time evolution in the entire (discretized) volume of interest can be reconstructed.

[0087] While the time behavior of the measured correlations can be used to design sensors, there is a still a disconnect between the shifts in optical intensity and the underlying fluid dynamics that causes them. To establish the link, we have to explore the light-matter interactions that couple the two fields.

[0088] Neglecting diffraction, rays in the optical path deviate from straight lines because Snell’s law of refraction causes their direction to change. That is, the interstitial fluid between the background and detector has spatial variations in the index of refraction, which is ultimately determined by spatial gradients in the fluid density. Unfortunately, there can be many causes for a change in density, e.g. pressure and / or temperature differences (as in the ideal gas law). Even worse, all of these parameters are coupled and can be altered by the fluid velocity. On the other hand, their inter-relations are usually well represented by a set of transport equations, e g. the Navier-Stokes equations.

[0089] As an example of how the parameters might be deconvolved, let’s return to our test experiment of a turbulent jet from a hair dryer. The initial conditions are known and include the geometry of the dryer nozzle (circular with a given diameter), the initial temperature and velocity of the flowing air, and the temperature, density, and pressure of the ambient air. Measuring the intensity correlations gives the 3D gradients of the refractive index, which gives the corresponding gradients of the fluid density. Because we know the baseline density from the ambient air (the boundary conditions), we can use the gradients to approximate the density within the volume of interest.

[0090] As a consistency check, we can perform a numerical simulation of light propagation from the background to the cameras, to match the estimated intensity patterns with the observed1003-0007W01 ones; if they are different, we can iterate the reconstruction process using well-known tomographic techniques.

[0091] After this calculation, we can look at the next frame (of the moving average) and repeat the analysis. Any changes in density as a function of position can be used to estimate a local velocity.

[0092] The fluid density and velocity are related by conservation of mass. More specifically, any change in density over time may result from a divergence in momentum. Using the previous estimates, this equation gives an expression for the gradient of the velocity.

[0093] Changes in momentum over time result from forces, given by Newton’s second law. In the case of fluids, the dominant forces are given by turbulent Reynolds’ stresses from fluctuating velocity components and an overall gradient of pressure. Through a similar iteration of dynamics, again bounded by the ambient fluid, the local pressure can be estimated from its gradient.

[0094] While the point-by-point reconstruction of the underlying fluid parameters gives the relevant physics, these field functions are usually not the most informative. Rather, the dynamics are best represented by particular modes of the system. Examples of dynamical mode decomposition include Fourier and wavelet modes, Koopman analysis, and principal component analysis [known as proper orthogonal decomposition (POD) in fluids]. Each of these representations can be used in either the spatial or temporal domain (or both). This versatility is especially important for transitional features, such as shear waves from the Kelvin-Helmholtz instability and pressure waves from the Orr-Somerfeld mechanism, and for coherent structures, which by definition persist in both space time. Important examples of the latter include vortices, helices, and acoustic waves.

[0095] Note that the turbulent jet contains all of these transient and coherent states, and the stereo tomography experiment described above observed all of them. As the system was calibrated, both spatial and temporal dynamics were quantified.

[0096] Nearly all efforts to identify the more advanced dynamical modes, ie. PODs and spectral PODs, have been performed in computation or in very controlled laboratory experiments. Both are idealizations that try to limit the variety of real-world conditions.

[0097] Our method of stereo recording enables direct sensing and imaging of real flows. In a preferred embodiment, two cameras are placed on a body segment and used for cross-correlation1003-0007W01 tomography of flow around the body. Examples include airflow over wings and water flow around aquatic vehicles and animals.

[0098] With real-world data, in three spatial dimensions and time, the individualized dynamical modes can be determined. While the identification of these modes can be guided by theory, they are in fact data-driven by experiment.

[0099] Introducing other elements to the ray paths, either before or after the ROI, increases the information diversity of the system. For example, standard optical include polarizers, shutters, flash and stroboscopic lights, amplitude and phase masks, and spatial light modulators. Since sensors record information over the entire ray path, prior knowledge of these elements can transfer to more information about the object in the ROI, leading to broader and more accurate measurements.

[0100] In a preferred embodiment, the computational sensing / imaging system includes both the physical devices used to manipulate the light and the algorithms used to determine the modes. That is, the best system performance arises from a joint optimization of both the physical and computational components together. In practice, a small number of these modes characterizes the dynamics of interest, e.g. energy, vorticity, and pressure distributions. Interestingly, the dominant modes of the average dynamics (or statistically steady state) are not necessarily the same ones that characterize the resolvent modes from (applied) forces and their response.

[0101] Once these modes are identified, the system can be modified to search specifically for them. This can be done using standard methods of adaptive optics.

[0102] Similar feedback can be used to modify the system, e.g. to amplify or suppress certain modes. For example, cross-flow from a second jet could excite particular density, temperature, or velocity modes generated by the first.

[0103] Thus, the method may include estimating turbulence based on the average cross correlation of the pair of pixels associated with the three-dimensional location. As disclosed herein, the correlation value may be proportional to the time average of the turbulence at that location.

[0104] The method may include creating one or more images representative of the 3D turbulence within the overlapping volume of space. The method may include creating a video1003-0007W01 representative of the 3D flow of a fluid within the overlapping volume of space (if there are multiple pairs of images).

[0105] Systems that use this technique may be provided. The systems may include a sensor subsystem, the sensor subsystem configured to capture the radiation passing through an overlapping volume of space from the two different view angles. One or more processing units may be configured to receive images from the sensor subsystem. The processing unit(s) may be operably coupled to a non-transitory computer-readable storage device containing instructions that, when executed by the one or more processing units, causes the processing unit(s) to, collectively, perform an embodiment of a method as disclosed herein.

[0106] The sensor subsystem may include a single sensor, a prism, and two mirrors (see, e.g., FIG. 3). The two different viewing angles define the paths that radiation takes as it passes through the overlapping volume of space and eventually reaches the sensor. The sensor subsystem may include two sensors (e.g., one sensor for each path of radiation). The sensor subsystem may be configured to capture images at a frame rate of 10-1500 frames / second.

[0107] A system may be provided, that includes one or more processing units. The processing unit(s) may be operably coupled to a non-transitory computer-readable storage device containing instructions that, when executed by the one or more processing units, causes the processing unit(s) to, collectively, perform an embodiment of a method as disclosed herein. For example, a remote device may receive the images from the sensors, and may send the images to the processing unit(s). The processing unit(s) may perform the necessary determinations, and may optionally create images or video representative of the turbulence or flow within the overlapping volume of space, and may transmit some or all of this information to the same (or different) remote device.

[0108] Further, a non-transitory computer-readable storage device may be provided. The storage device may include instructions that, when executed by the one or more processing units, causes the one or more processing units to, collectively, perform a method as disclosed herein.

[0109] Additional Examples

[0110] The following description provides further information and examples for implementing the disclosed techniques.[OHl] Turbulence is the stochastic motion of fluids and remains a fundamental topic in fluid dynamics with wide-ranging applications, including drag reduction, stall prevention in aircraft,1003-0007W01 and enhanced wind farm efficiency. Conventional experimental approaches of measuring turbulence often rely on seeding the flow with resolvable tracer particles to estimate local streamlines and velocities. Although effective for 3D flow reconstruction, these methods require specialized equipment and are limited in real-world applicability due to their intrusive nature. Alternative remote sensing techniques, such as multi-camera systems, are sensitive to environmental vibrations and heavily depend on the stability of the experimental setup. In this study, we introduce a stereo-camera Background-Oriented Schlieren (BOS) technique capable of reconstructing turbulent structures and average flow velocities in 3D by capturing a sequence of images and exploiting the stochasticity of turbulence. The method is validated through experiments and simulations on a free jet, successfully capturing the inner potential core, the 1 / r axial velocity decay, and Gaussian radial velocity profiles in both cases.

[0112] Introduction

[0113] Turbulence plays a critical role in many life-sustaining and industrial processes. Understanding it enables control over the transport and dispersion of heat, momentum, and chemical species in fluids. Despite its importance, turbulence remains notoriously difficult to measure and model. Its inherently chaotic, three-dimensional, and multiscale nature challenges both experimental and computational approaches. Measurements are further complicated by the need for high spatial and temporal resolution, often in harsh or inaccessible environments. These difficulties make the accurate characterization and prediction of turbulent flows one of the most persistent and complex problems in science and engineering.

[0114] A major breakthrough in turbulence research occurred in the early 20th century, enabled by advances in photography that allowed visualization of complex flows. Early methods use smoke to trace streamlines [1-3], while more sophisticated techniques employed dual flashes to measure particle displacements [4], enabling the reconstruction of local velocity fields [5], This technique, known as Particle Image Velocimetry (PIV), provides quantitative data on the evolution of turbulent flows [6], Despite its maturity and widespread use, PIV’s reliance on tracer particles is impractical or unfeasible in some environments because of seeding these particles are challenging.

[0115] In sufficiently turbulent flows, refractive index variations caused by eddies can be visualized without tracers using shadowgraphy or schlieren techniques. By tracking the average displacement of these label-free features, local instantaneous velocity can be estimated in a1003-0007W01 manner similar to PIV [7-9], Although Schlieren PIV eliminates the need for tracers, it still lacks depth resolution, as total ray deflections results from integration of transverse density-gradients along the ray path. Focusing schlieren addresses this limitation by rejecting out-of-focus light, thereby restricting integration to the system’s depth of field [10, 11], However, its performance depends on precise alignment between the light source and the cutoff grid. While self-aligned setups

[0012] alleviate this requirement, the mirror needed for such systems imposes constraints on the measurable object size.

[0116] A more flexible alternative, known as synthetic schlieren or Background Oriented Schlieren (BOS), offers a computational approach to classical schlieren imaging [13, 14], BOS uses a random background pattern imaged with and without the turbulent medium. The apparent displacement of background points reveals ray deviations due to refractive index gradients. Like traditional schlieren, BOS lacks inherent 3D resolution, since ray deflections result from integration along the ray path.

[0117] To achieve three-dimensional measurements, Bauknecht et al. added a second camera to observe the object from an additional viewpoint. Using this second field of view (FoV), they successfully localized sharp refractive index gradients, such as rotor-tip vortices, through epipolar geometry [15, 16], Grauer et al. extended this approach to 23 FoVs to reconstruct the flow field from an open flame

[0017] , Such multi -view systems are crucial for capturing more diffuse turbulent structures, as stereo methods are primarily effective for resolving sharp features. Recent simulation-based studies have shown that modeling the problem in continuous time and incorporating fluid dynamics constraints can improve reconstruction accuracy even with fewer FoVs [18-20],

[0118] An alternative method that uses only two FoVs, Crossed Beam Correlation (CBC), exploits the spatial randomness of turbulence to measure local turbulent properties by computing the correlation between two absorption signals along separate 2 optical paths [21, 22], Although each absorption signal contains information integrated along the entire path from source to detector, their correlation localizes the measurement to the region where the optical paths intersect. Moreover, by analyzing time-delayed cross-correlations, it is possible to recover local flow velocity at the intersection point. CBC requires only two FoVs; however, its reliance on intensity fluctuations demands careful experimental design to minimize the influence of schlieren and shadowgraphy effects. Similar correlation-based concepts have also been1003-0007W01 implemented using laser shadow or deflectometry techniques [23, 24], though these methods typically restrict analysis to a single spatial point just like CBC.

[0119] Here, we propose a stereo-camera BOS system capable of reconstructing the three- dimensional distribution of turbulence using a correlation-based approach. By capturing the flow from two distinct viewpoints, the system independently measures displacement fields from each camera. Correlating these fields enables the localization of refractive index variance at approximately 25 million points in space simultaneously. Flow velocity at each 3D location is then estimated using time-delayed cross-correlations, following principles similar to those used in PIV and CBC. The proposed technique has been validated through both simulations and experiments. In both cases, we successfully recovered the conical envelope, the expected 1 / r axial velocity decay, and Gaussian radial velocity profiles of a round turbulent jet.

[0120] FIG. 6 shows an illustration of Time Correlation Tomography. The left side of FIG. 6 shows rays acquiring shifts according to their location in space. Rays passing through different points acquire uncorrelated shifts in time. Cross-correlation of two rays in time removes the effect of other layers in the ray’s optical path. Only the contribution from the intersection point of rays survives after the time correlation. The value of cross correlation is proportional to the variance of refractive index gradient at the intersection of 2 rays. By doing this for every ray pair in 2 FoV, turbulence in 3D space can be reconstructed. The right side of FIG. 6 shows an example measured displacement field that is synchronously measured with the experimental setup.

[0121] Methods

[0122] Principles

[0123] Turbulent flow can be described as spatially varying refractive index fluctuations that evolve stochastically over time, causing corresponding variations in ray deflection through the flow. Measuring the apparent displacement of a single background point provides information about the integrated deflection along the line of sight and can be determined using conventional Background-Oriented Schlieren (BOS) algorithms. However, since the rays are projected onto a two-dimensional sensor, classical BOS systems inherently lose depth information, capturing only the integrated effect of the refractive index gradients along the optical path. This limitation is evident in Eq. 1, which shows that the measured displacement is a line integral of the refractive1003-0007W01 index gradient field, thereby collapsing the three-dimensional structure into a two-dimensional measurement.

[0124] Here, the beam is assumed to propagate along the z-axis, and n is the refractive index of the medium which is modified by the flow. To overcome this limitation, Time Correlation Tomography uses a stereo camera system to observe the same turbulent region (e.g., as shown in FIG. 6). After stereo camera calibration, the intersection of two rays, each corresponding to a different FoV, defines a voxel in 3D space. Although the apparent displacement along each ray is integrated over its entire propagation path, the time correlation of these displacements is proportional to the variance of refractive index gradient at their intersection point. Contributions from other regions cancel out due to the zero-mean nature of turbulent fluctuations. This method leverages time as an additional measurement dimension, reducing the need for multiple FoVs and simplifying the experimental setup. By computing the time correlation for all ray pairs along the baseline camera separation direction, the 3D distribution of refractive index fluctuations can be reconstructed.

[0125] The flow velocity can also be estimated in 3D by invoking Taylor’s frozen flow hypothesis, similar to Schlieren velocimetry. The average movement of a refractive index fluctuation within a voxel can be determined by calculating the time-delayed cross-correlation of its projected displacements in FoV 1 and FoV 2. The spatial shift of the correlation peak indicates the average velocity of the turbulent structure at that voxel.

[0126] Experimental Setup

[0127] To test our assumptions, we constructed the experimental setup shown in FIG. 6. In this configuration, two different views of the same scene, used for correlation calculations, are generated using two right-angle prisms (e.g., Thorlabs PS910) and two mirrors (e.g., Thorlabs BB2-E02). To enable synchronized image acquisition, two opposite halves of a single digital camera sensor are used. The camera’s direct line of sight is blocked by a beam blocker to prevent overlap between the two optical paths.

[0128] The background pattern is designed to provide high spatial feature density. It is generated by dividing the background into 4x4 pixel tiles, then randomly selecting one white1003-0007W01 pixel per tile. This approach ensures sufficient local contrast for measuring apparent displacement in 8*8 interrogation windows. The pattern is printed on a transparency film (3M) using a laser printer.

[0129] The background is imaged along the two optical paths using a high-speed digital camera (Photron Mini R5-4K) equipped with a 135 mm lens (TS-E 135 mm f / 4L Macro). Images are recorded at 2000 frames per second with 12-bit depth and a resolution of 2304 x 2432 pixels. The epipolar geometry between the two fields of view is calibrated using the Stereo Camera Calibrator App in MATLAB 2024a. Background point displacements are computed using the GPU-accelerated OpenPIV package

[0025] , To remove motion-induced bias, the global displacement due to camera movement is subtracted from each displacement map. Turbulent phase targets are generated using a commercially available heat gun with a 13 mm diameter nozzle.

[0130] To remove the effects of mean refractive index gradients and slowly varying non- turbulent contributions, a moving mean is subtracted from the measured pixel displacements. This preprocessing step also eliminates the need to capture a reference background image without the phase object. The 3D distribution of refractive index variance is reconstructed by computing the cross-correlation of all pixel pairs along the camera separation direction, as described in Eq. 2. Each Ay value corresponds to a different reconstruction slice in 3D.

[0131] Here di and d2 corresponds to displacements measured on first and second camera Respectively. Similarly, the local flow speed can be reconstructed by identifying the peak of the time-delayed cross-correlation function, (Axp), as shown in Eq. 3. For each slice set by Ay, a range of Ax shifts are evaluated across time delays At. The velocity at a specific point (x, y) is then given by v (x, y) = Axp / At.1003-0007W01

[0132] The original FoV allows for recording up to 20 x / D, where x is the streamwise distance from the nozzle and D is the nozzle diameter. To capture the full range from 0 to 30 x / D, the bottom portion of the flow was recorded first. Then, the nozzle was moved downward by a known amount, and the top portion of the flow was recorded. The 3D reconstructions of refractive index fluctuations and mean flow velocity, calculated separately for the bottom and top sections, were subsequently stitched together by maximizing the similarity in the overlapping regions to identify the best match and ensure continuity. To achieve a smooth transition between the two regions, a weighting matrix with linearly varying weights across the overlap zone was applied during stitching.

[0133] For the velocity reconstruction, a time delay of At and 3At was used for the bottom and top portions, respectively. While longer delay times improve velocity resolution, they also reduce the correlation amplitude. These values were chosen to ensure a sufficient signal -to-noise ratio for reliable velocity estimation in both sections. Regions with low correlation strength were masked out during the reconstruction process to reduce the influence of noise on the final velocity field.

[0134] Simulation

[0135] The time-correlation approach has been validated using a simulation of an isothermal Mach 0.9 turbulent jet generated by the Charles solver

[0026] , This simulation is one of the few comprehensive datasets of free turbulent jets that is also publicly available as part of a larger database

[0027] , Readers are referred to Br'es et al.

[0026] for details on the LES simulation strategy and to Br es et al.

[0028] for further validation of the dataset. The dataset consists of 10,000 uniformly sampled time points. For each time point, the 3D density and velocity fields (in cylindrical coordinates) are provided on a structured grid with dimensions { 138, 128, 656} corresponding to {r, 0, x}.

[0136] To compute BOS displacements, the 3D density field is interpolated onto a Cartesian grid with uniform spacing in the y and z directions, while keeping x fixed. After calculating transverse density gradients, the idealized total displacement is computed by summing the gradients along the optical axis. Although this synthetic projection does not account for ray-path integration or optical effects such as Gaussian blurring which are present in experimental measurements, it produces idealized BOS-like images that depend on fluid density gradients in a manner similar to actual BOS observations.1003-0007W01

[0137] Results

[0138] FIG. 7 shows an example of the results of reconstruction for a round turbulent jet. The left panel shows an example of the center slice in the XY plane. The center panel shows an example of the center slice in the XZ plane. The right panel provides examples of slices in the YZ plane for cases where X=2.5, X=7.5, and X=12.5.

[0139] The proposed method is applied to reconstruct a free turbulent jet generated by a heat gun with a round nozzle. The reconstruction result for the mid-plane slice parallel to the camera plane is shown in FIG. 7 on the left and middle, while the right side of FIG. 7 displays the midplane slice along the optical axis, which is perpendicular to the former. As expected, the variance in density is minimal within the potential core region, leading to very low correlation values, which are clearly visible in FIG. 7, left, middle, and right sides. A noticeable difference in resolution is also evident, as the resolution along the optical axis is given by 5z = 3y / 0, where 3y is the spatial resolution in the y-direction, and 0 is the angle between the two FoVs.

[0140] Even though the measured flow is cylindrically symmetric, the diameter of the potential core region appears smaller in the x-z plane compared to the y-z plane. This discrepancy can be attributed to the lower resolution along the z-axis and the fluid’s correlation length. Since the proposed method employs varying Ax values to reconstruct correlation values across different slices, the thickness of correlation structures in the camera plane, particularly along the direction of baseline, introduces a shadowing effect. This effect causes correlation to “leak” into slices where the actual structure is not present, thereby limiting the achievable resolution. This shadowing represents a fundamental constraint in the reconstruction process, as discussed by Kolhe and Agrawal

[0029] ,

[0141] FIG. 8 shows an example of a reconstructed speed map with Gaussian fit. The left most panel shows the reconstructed speed map for a slice passing through the center of the circular nozzle in the XY plane. The center-left panel shows the XZ plane. The center-right panel shows the Gaussian fit to speed decay in radial direction for the XY plane. The right most panel shows the Gaussian fit to speed decay in the radial direction for YZ axis. The values along the Z axis are selected by selecting the line which passes along the midpoint of fit in the center-left panel.

[0142] The local flow speed was measured using time-delayed cross-correlation, as described by Fisher and Krause

[0021] , The slice cuts used for velocity reconstruction, which pass1003-0007W01 through the center of the flow, are shown in FIG. 8 (left most panel) for the x-y plane and FIG. 8 (center left panel) for the x-z plane.

[0143] To verify the speed measurements, one-dimensional Gaussian profiles were fitted to the velocity data in the transverse direction at various distances from the nozzle. Only data points with non-zero velocity were used in the fit to avoid effect coming from masking. The fits in the x and z directions for these distances are shown in the two right most panels of FIG. 8, respectively. The close agreement between the two directions is consistent with the expected symmetry of a circular nozzle. Nozzle distances smaller than y = 5D is not included in this plot as potential core of flow does not create any measurable signal generated in that region.

[0144] To verify the velocity measurements, one-dimensional Gaussian profiles were fitted to the transverse velocity distributions at various axial distances from the nozzle. Only data points with non-zero velocity were included in the fits to avoid artifacts introduced by masked or noise-dominated regions. Axial positions closer than y = 5D were excluded from the analysis, as the potential core in this region does not produce significant measurable signal due to the lack of turbulent fluctuations. The fitted profiles in the x and z directions are shown in FIG. 8 (center right panel) and FIG. 8 (left most panel), respectively. The close agreement between these two directions confirms the expected cylindrical symmetry of the flow produced by the circular nozzle.

[0145] FIG. 9 shows an example of centerline velocity decay and transverse Gaussian widths. The left panel shows the normalized centerline velocity, v0 / v(x), as a function of axial distance from the nozzle for four different experimental flow speeds. The right panel shows onedimensional Gaussian widths in the Y and Z directions plotted against the axial distance from the nozzle.

[0146] The velocity decay along the centerline of the flow is analyzed by plotting the ratio of the nozzle speed, vO, to the measured velocity, v(y), at various axial distances from the nozzle for four different experimental flow speeds (e.g., as shown in FIG. 9 left panel). For a cylindrically symmetric turbulent jet, the centerline velocity is expected to decay as 1 / r, implying that the inverse normalized centerline velocity should follow a linear trend which is supported by the results shown in FIG. 9 left panel.

[0147] In addition, the normalized half-widths obtained from one-dimensional Gaussian fits to the velocity profiles in the x and z directions are plotted against axial distance in FIG. 9 right1003-0007W01 panel. For distances less than 15D, there is good agreement between the half-widths measured in the x and z directions. For y > 15D, the half-widths in the x direction continue to follow a linear trend, as expected for a circular turbulent jet. However, the half-widths in the z direction deviate from this linear behavior. This discrepancy may be attributed to the shadowing effect of thicker coherent structures, which effectively reduces resolution along the z-axis, as previously discussed.

[0148] Conclusion

[0149] In this study, we introduced a novel time correlation tomography technique based on stereo-camera Background-Oriented Schlieren imaging for three-dimensional reconstruction of turbulent flow structures and velocity fields. By exploiting the inherent randomness of turbulence and leveraging time-delayed cross-correlation between displacement fields measured from two distinct viewpoints, our method successfully localizes refractive index fluctuations in 3D space and estimates local flow velocities. Validation against both simulations and experiments on a free turbulent jet demonstrated the capability of the approach to recover key turbulent features, including the inner potential core, the characteristic 1 / r axial velocity decay, and Gaussian radial velocity profiles consistent with classical turbulent jet theory. The observed symmetry in velocity profiles across different axes further supports the robustness of the reconstruction.

[0150] While the technique shows promising results, resolution anisotropy caused by the shadowing effect and camera geometry presents a limitation that can be addressed through future refinements. The ability to reconstruct 3D turbulent fields with only two optical views and without seeding particles highlights the potential for broader applicability in scenarios where traditional velocimetry methods are challenging.

[0151] Future work will focus on improving spatial resolution, extending the approach to more complex turbulent flows, and integrating physics-based models to enhance reconstruction accuracy. Overall, time correlation tomography offers a powerful, nonintrusive tool for advancing turbulence measurement and analysis in both laboratory and field environments.

[0152] FIG. 10 depicts a computing device that may be used in various aspects, such as the sensor arrays, modules, and / or devices depicted in FIGs. 1A-E, 3, 4A, 5, and 6. With regard to the example architecture of FIG. 1A, the computing device 102, the user device 104, the analysis device 106, the application device 108 may each be implemented (e.g., controlled by1003-0007W01 management component 1010) in an instance of a computing device 1000 of FIG. 10. The computer architecture shown in FIG. 10 shows a conventional server computer, workstation, desktop computer, laptop, tablet, network appliance, PDA, e-reader, digital cellular phone, or other computing node, and may be utilized to execute any aspects of the computers described herein, such as to implement the methods described in relation to FIG. IB or elsewhere described herein.

[0153] The computing device 1000 may include a baseboard, or “motherboard,” which is a printed circuit board to which a multitude of components or devices may be connected by way of a system bus or other electrical communication paths. One or more central processing units (CPUs) 1004 may operate in conjunction with a chipset 1006. The CPU(s) 1004 may be standard programmable processors that perform arithmetic and logical operations necessary for the operation of the computing device 1000.

[0154] The CPU(s) 1004 may perform the necessary operations by transitioning from one discrete physical state to the next through the manipulation of switching elements that differentiate between and change these states. Switching elements may generally include electronic circuits that maintain one of two binary states, such as flip-flops, and electronic circuits that provide an output state based on the logical combination of the states of one or more other switching elements, such as logic gates. These basic switching elements may be combined to create more complex logic circuits including registers, adders-subtractors, arithmetic logic units, floating-point units, and the like.

[0155] The CPU(s) 1004 may be augmented with or replaced by other processing units, such as GPU(s) 1005. The GPU(s) 1005 may comprise processing units specialized for but not necessarily limited to highly parallel computations, such as graphics and other visualization- related processing.

[0156] A chipset 1006 may provide an interface between the CPU(s) 1004 and the remainder of the components and devices on the baseboard. The chipset 1006 may provide an interface to a random access memory (RAM) 1008 used as the main memory in the computing device 1000. The chipset 1006 may further provide an interface to a computer-readable storage medium, such as a read-only memory (ROM) 1020 or non-volatile RAM (NVRAM) (not shown), for storing basic routines that may help to start up the computing device 1000 and to transfer information between the various components and devices. ROM 1020 or NVRAM may also store other1003-0007W01 software components necessary for the operation of the computing device 1000 in accordance with the aspects described herein.

[0157] The computing device 1000 may operate in a networked environment using logical connections to remote computing nodes and computer systems through local area network (LAN) 1016. The chipset 1006 may include functionality for providing network connectivity through a network interface controller (NIC) 1022, such as a gigabit Ethernet adapter. A NIC 1022 may be capable of connecting the computing device 1000 to other computing nodes over a network 1016. It should be appreciated that multiple NICs 1022 may be present in the computing device 1000, connecting the computing device to other types of networks and remote computer systems.

[0158] The computing device 1000 may be connected to a mass storage device 1028 that provides non-volatile storage for the computer. The mass storage device 1028 may store system programs, application programs, other program modules, and data, which have been described in greater detail herein. The mass storage device 1028 may be connected to the computing device 1000 through a storage controller 1024 connected to the chipset 1006. The mass storage device 1028 may consist of one or more physical storage units. A storage controller 1024 may interface with the physical storage units through a serial attached SCSI (SAS) interface, a serial advanced technology attachment (SATA) interface, a fiber channel (FC) interface, or other type of interface for physically connecting and transferring data between computers and physical storage units.

[0159] The computing device 1000 may store data on a mass storage device 1028 by transforming the physical state of the physical storage units to reflect the information being stored. The specific transformation of a physical state may depend on various factors and on different implementations of this description. Examples of such factors may include, but are not limited to, the technology used to implement the physical storage units and whether the mass storage device 1028 is characterized as primary or secondary storage and the like.

[0160] For example, the computing device 1000 may store information to the mass storage device 1028 by issuing instructions through a storage controller 1024 to alter the magnetic characteristics of a particular location within a magnetic disk drive unit, the reflective or refractive characteristics of a particular location in an optical storage unit, or the electrical characteristics of a particular capacitor, transistor, or other discrete component in a solid-state1003-0007W01 storage unit. Other transformations of physical media are possible without departing from the scope and spirit of the present description, with the foregoing examples provided only to facilitate this description. The computing device 1000 may further read information from the mass storage device 1028 by detecting the physical states or characteristics of one or more particular locations within the physical storage units.

[0161] In addition to the mass storage device 1028 described above, the computing device 1000 may have access to other computer-readable storage media to store and retrieve information, such as program modules, data structures, or other data. It should be appreciated by those skilled in the art that computer-readable storage media may be any available media that provides for the storage of non-transitory data and that may be accessed by the computing device 1000.

[0162] By way of example and not limitation, computer-readable storage media may include volatile and non-volatile, transitory computer-readable storage media and non-transitory computer-readable storage media, and removable and non-removable media implemented in any method or technology. Computer-readable storage media includes, but is not limited to, RAM, ROM, erasable programmable ROM (“EPROM”), electrically erasable programmable ROM (“EEPROM”), flash memory or other solid-state memory technology, compact disc ROM (“CD- ROM”), digital versatile disk (“DVD”), high definition DVD (“HD-DVD”), BLU-RAY, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage, other magnetic storage devices, or any other medium that may be used to store the desired information in a non- transitory fashion.

[0163] A mass storage device, such as the mass storage device 1028 depicted in FIG. 10, may store an operating system utilized to control the operation of the computing device 1000. The operating system may comprise a version of the LINUX operating system. The operating system may comprise a version of the WINDOWS SERVER operating system from the MICROSOFT Corporation. According to further aspects, the operating system may comprise a version of the UNIX operating system. Various mobile phone operating systems, such as IOS and ANDROID, may also be utilized. It should be appreciated that other operating systems may also be utilized. The mass storage device 1028 may store other system or application programs and data utilized by the computing device 1000.1003-0007W01

[0164] The mass storage device 1028 or other computer-readable storage media may also be encoded with computer-executable instructions, which, when loaded into the computing device 1000, transforms the computing device from a general -purpose computing system into a specialpurpose computer capable of implementing the aspects described herein. These computerexecutable instructions transform the computing device 1000 by specifying how the CPU(s) 1004 transition between states, as described above. The computing device 1000 may have access to computer-readable storage media storing computer-executable instructions, which, when executed by the computing device 1000, may perform the methods described in relation to FIG. IB or elsewhere described herein.

[0165] A computing device, such as the computing device 1000 depicted in FIG. 10, may also include an input / output controller 1032 for receiving and processing input from a number of input devices, such as a keyboard, a mouse, a touchpad, a touch screen, an electronic stylus, or other type of input device. Similarly, an input / output controller 1032 may provide output to a display, such as a computer monitor, a flat-panel display, a digital projector, a printer, a plotter, or other type of output device. It will be appreciated that the computing device 1000 may not include all of the components shown in FIG. 10, may include other components that are not explicitly shown in FIG. 10, or may utilize an architecture completely different than that shown in FIG. 10.

[0166] As described herein, a computing device may be a physical computing device, such as the computing device 1000 of FIG. 10. A computing node may also include a virtual machine host process and one or more virtual machine instances. Computer-executable instructions may be executed by the physical hardware of a computing device indirectly through interpretation and / or execution of instructions stored and executed in the context of a virtual machine.

[0167] It is to be understood that the methods and systems are not limited to specific methods, specific components, or to particular implementations. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

[0168] As used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value1003-0007W01 and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0169] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0170] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other components, integers or steps.“Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal embodiment. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0171] The term “or” when used with “one or more of’ is used in its inclusive sense (and not in its exclusive sense) so that when used, for example, to connect a list of elements, the term “or” means one, some or all of the elements in the list. The term “or” when used with “at least one of’ is used in its inclusive sense (and not in its exclusive sense) so that when used, for example, to connect a list of elements, the term “or” means one, some or all of the elements in the list. For example, the phrases “one or more of A, B, or C” includes any of the following: A, B, C, A andB, A and C, B and C, and A and B and C. Similarly the phrase “one or more of A, B, and C” includes any of the following: A, B, C, A and B, A and C, B and C, and A and B and C. The phrase “at least one of A, B, or C” includes any of following: A, B, C, A and B, A and C, B andC, and A and B and C. Similarly, the phrase “at least one of A, B, and C” includes any of following: A, B, C, A and B, A and C, B and C, and A and B and C.

[0172] Components are described that may be used to perform the described methods and systems. When combinations, subsets, interactions, groups, etc., of these components are described, it is understood that while specific references to each of the various individual and collective combinations and permutations of these may not be explicitly described, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application including, but not limited to, operations in described methods. Thus, if there are a variety of additional operations that may be performed it is understood that each of1003-0007W01 these additional operations may be performed with any specific embodiment or combination of embodiments of the described methods.

[0173] As will be appreciated by one skilled in the art, the methods and systems may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the methods and systems may take the form of a computer program product on a computer-readable storage medium having computer- readable program instructions (e.g., computer software) embodied in the storage medium. More particularly, the present methods and systems may take the form of web-implemented computer software. Any suitable computer-readable storage medium may be utilized including hard disks, CD-ROMs, optical storage devices, or magnetic storage devices.

[0174] Embodiments of the methods and systems are described herein with reference to block diagrams and flowchart illustrations of methods, systems, apparatuses and computer program products. It will be understood that each block of the block diagrams and flowchart illustrations, and combinations of blocks in the block diagrams and flowchart illustrations, respectively, may be implemented by computer program instructions. These computer program instructions may be loaded on a general-purpose computer, special-purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions which execute on the computer or other programmable data processing apparatus create a means for implementing the functions specified in the flowchart block or blocks.

[0175] These computer program instructions may also be stored in a computer-readable memory that may direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including computer-readable instructions for implementing the function specified in the flowchart block or blocks. The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions that execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks.

[0176] The various features and processes described above may be used independently of one another, or may be combined in various ways. All possible combinations and sub-1003-0007W01 combinations are intended to fall within the scope of this disclosure. In addition, certain methods or process blocks may be omitted in some implementations. The methods and processes described herein are also not limited to any particular sequence, and the blocks or states relating thereto may be performed in other sequences that are appropriate. For example, described blocks or states may be performed in an order other than that specifically described, or multiple blocks or states may be combined in a single block or state. The example blocks or states may be performed in serial, in parallel, or in some other manner. Blocks or states may be added to or removed from the described example embodiments. The example systems and components described herein may be configured differently than described. For example, elements may be added to, removed from, or rearranged compared to the described example embodiments.

[0177] It will also be appreciated that various items are illustrated as being stored in memory or on storage while being used, and that these items or portions thereof may be transferred between memory and other storage devices for purposes of memory management and data integrity. Alternatively, in other embodiments, some or all of the software modules and / or systems may execute in memory on another device and communicate with the illustrated computing systems via inter-computer communication. Furthermore, in some embodiments, some or all of the systems and / or modules may be implemented or provided in other ways, such as at least partially in firmware and / or hardware, including, but not limited to, one or more application-specific integrated circuits (“ASICs”), standard integrated circuits, controllers (e.g., by executing appropriate instructions, and including microcontrollers and / or embedded controllers), field-programmable gate arrays (“FPGAs”), complex programmable logic devices (“CPLDs”), etc. Some or all of the modules, systems, and data structures may also be stored (e.g., as software instructions or structured data) on a computer-readable medium, such as a hard disk, a memory, a network, or a portable media article to be read by an appropriate device or via an appropriate connection. The systems, modules, and data structures may also be transmitted as generated data signals (e.g., as part of a carrier wave or other analog or digital propagated signal) on a variety of computer-readable transmission media, including wireless-based and wired / cable- based media, and may take a variety of forms (e.g., as part of a single or multiplexed analog signal, or as multiple discrete digital packets or frames). Such computer program products may also take other forms in other embodiments. Accordingly, the present invention may be practiced with other computer system configurations.1003-0007W01

[0178] While the methods and systems have been described in connection with preferred embodiments and specific examples, it is not intended that the scope be limited to the particular embodiments set forth, as the embodiments herein are intended in all respects to be illustrative rather than restrictive.

[0179] It will be apparent to those skilled in the art that various modifications and variations may be made without departing from the scope or spirit of the present disclosure. Other embodiments will be apparent to those skilled in the art from consideration of the specification and practices described herein. It is intended that the specification and example figures be considered as exemplary only, with a true scope and spirit being indicated by the following claims.

[0180] Aspects

[0181] The following Aspects are illustrative only and do not limit the scope of the present disclosure or the appended claims. Any part or parts of any one or more Aspects can be combined with any part or parts of any one or more other Aspects.

[0182] Aspect 1. A method comprising, consisting of, or consisting essentially of receiving sensor data indicative of a subject region, wherein the sensor data comprises at least first data based on a first field of view capturing the subject region from a first angle and second data based on a second field of view capturing the subject region from a second angle different than the first angle; determining, based on the first data and the second data, signal data indicative of change in the sensor data; determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location in the subject region; determining change data based on the mapping data, the signal data, and a cross-correlation process; and causing output of the change data.

[0183] Aspect 2. The method of Aspect 1, wherein the sensor data comprises data captured by a plurality of sensors, and wherein the first data is captured by a first sensor of the plurality of sensors and the second data is captured by a second sensor of the plurality of sensors.

[0184] Aspect 3. The method of any one of Aspects 1-2, wherein the sensor data comprises an image captured with a camera, and wherein the first data comprises a first portion of the image and the second data comprises a second portion of the image.1003-0007W01

[0185] Aspect 4. The method of any one of Aspects 1-3, wherein the sensor data comprises a time sequence of data representing signals captured over time.

[0186] Aspect 5. The method of any one of Aspects 1-5, wherein the sensor data is indicative of a background pattern, and wherein the subject region is between a sensor detecting the sensor data and a background pattern, and wherein determining the signal data comprises determining apparent displacement of the background pattern for the first data and the second data.

[0187] Aspect 6. The method of Aspect 5, wherein the background pattern comprises one or more of a printed background, a horizon, an array of lights, background scenery, or a geographic pattern.

[0188] Aspect 7. The method of any one of Aspects 5-6, wherein determining apparent displacement of the background pattern for the first data and the second data comprises comparing at least a portion of the first data in a first frame captured at a first time with corresponding portions of the first data in a second frame captured at a second time.

[0189] Aspect 8. The method of any one of Aspects 1-7, wherein the signal data is indicative of changes in one or more of refractive index, intensity, contrast, phase, polarization, or apparent displacement of background features.

[0190] Aspect 9. The method of any one of Aspects 1-8, wherein the signal data comprises displacement data indicative of movement in the subject region.

[0191] Aspect 10. The method of any one of Aspects 1-9, wherein the signal data is indicative of one or more of density, velocity, pressure, temperature, refractive index, or absorption.

[0192] Aspect 11. The method of any one of Aspects 1-10, further comprising processing the signal data to reduce contributions from one or more of time-invariant or quasi-static components, thereby enhancing detection of localized changes in the subject region.

[0193] Aspect 12. The method of Aspect 11, wherein processing the signal data comprises subtracting one or more of a moving mean or a mean value from the signal data prior to applying the cross-correlation process.

[0194] Aspect 13. The method of any one of Aspects 1-12, wherein the signal data comprises one or more of a probability distribution, at least one peak of a probability distribution, at least one moment of a probability distribution, a higher order correlation, a correlation of more than1003-0007W01 two pixels, a correlation of a random combination of pixels, a subset of video frames, a periodic subset of frames, an aperiodic subset of frames, or a random set of frames.

[0195] Aspect 14. The method of any one of Aspects 1-13, wherein determining the mapping data comprises determining an intersection of radiation from the first field of view with radiation from the second field of view, thereby defining a voxel indicative of the three-dimensional spatial location.

[0196] Aspect 15. The method of any one of Aspects 1-14, wherein determining the mapping data is based on calibration data, and wherein the calibration data comprises an image capturing a pattern in the subject region, and wherein determining the mapping data comprises inputting the pattern into a stereo camera calibrator process.

[0197] Aspect 16. The method of any one of Aspects 1-15, wherein determining the mapping data comprises applying epipolar geometry to associate sensor coordinates from the first field of view and corresponding sensor coordinates from the second field of view with three dimensional spatial location (e.g., corresponding three dimensional locations).

[0198] Aspect 17. The method of any one of Aspects 1-16, wherein the cross-correlation process comprises computing a time-averaged correlation of signals in the signal data associated with the first field of view with signals in the signal data associated with the second field of view.

[0199] Aspect 18. The method of any one of Aspects 1-17, wherein the cross-correlation process comprises using the mapping data to identify sensor coordinates corresponding to lines of sight from the first field of view and the second field of view that intersect at a common three- dimensional spatial location, and generating a correlation value for that spatial location by comparing signals in the signal data associated with the identified sensor coordinates.

[0200] Aspect 19. The method of any one of Aspects 1-18, wherein determining the three- dimensional change data comprises identifying a spatial location corresponding to a peak in the cross-correlation metric between signals in the signal data.

[0201] Aspect 20. The method of any one of Aspects 1-19, wherein the cross-correlation process comprises determining a velocity of change at the three-dimensional spatial location based on computing a time-delayed correlation of signals in the signal data.

[0202] Aspect 21. The method of any one of Aspects 1-20, wherein the change data comprises a time series of at least three dimensions representing changes in the subject region.1003-0007W01

[0203] Aspect 22. The method of any one of Aspects 1 -21 , wherein the change data comprises a representation of a fluid property comprising one or more of density, speed, velocity, temperature, pressure, or a representation of multiple fluids or phases in the subject region.

[0204] Aspect 23. The method of any one of Aspects 1-22, wherein the change data is indicative of changes in one or more of a gas or plasma.

[0205] Aspect 24. The method of any one of Aspects 1-23, wherein the subject region comprises a fluid region in a biological cell.

[0206] Aspect 25. The method of any one of Aspects 1-24, wherein causing output of the change data comprises causing one or more of: storage of the change data, sending the change data via a network to a computing device, output of the change data, or output of data calculated based on the change data.

[0207] Aspect 26. A system comprising, consisting of, or consisting essentially of: a plurality of sensors comprising at least a first sensor configured to capture signals from a subject region from a first field of view at a first angle thereby generating first data and a second sensor configured to capture signals from the subject region from a second field of view at a second angle thereby generating second data; and a computing device comprising one or more processors and a memory, wherein the memory stores instructions that, when executed by the one or more processors, cause the computing device to perform the methods of any one of Aspects 1-25.

[0208] Aspect 27. A device comprising, consisting of, or consisting essentially of: one or more processors; and a memory storing instructions that, when executed by the one or more processors, cause the device to perform the methods of any one of Aspects 1-25.

[0209] Aspect 28. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause a device to perform the methods of any one of Aspects 1-25.

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Claims

1003-0007W01Claims1. A method comprising: receiving sensor data indicative of a subject region, wherein the sensor data comprises at least first data based on a first field of view capturing the subject region from a first angle and second data based on a second field of view capturing the subject region from a second angle different than the first angle; determining, based on the first data and the second data, signal data indicative of change in the sensor data; determining mapping data associating a sensor coordinate associated with the first field of view and a sensor coordinate associated with the second field of view with a corresponding three-dimensional spatial location in the subject region; determining change data based on the mapping data, the signal data, and a cross-correlation process; and causing output of the change data.

2. The method of claim 1, wherein the sensor data comprises data captured by a plurality of sensors, and wherein the first data is captured by a first sensor of the plurality of sensors and the second data is captured by a second sensor of the plurality of sensors.

3. Tire method of claim 1, wherein the sensor data comprises an image captured with a camera, and wherein the first data comprises a first portion of tire image and the second data comprises a second portion of the image.

4. The method of claim 1 , wherein the sensor data comprises a time sequence of data representing signals captured over time.

5. The method of claim 1, wherein the sensor data is indicative of a background pattern, and wherein the subject region is between a sensor detecting the sensor data and a background pattern, and wherein determining the signal data comprises determining apparent displacement of the background pattern for the first data and the second data.

6. Tire method of claim 5, wherein the background pattern comprises one or more of a printed background, a horizon, an array of lights, background scenery, or a geographic pattern.1003-0007W017. The method of claim 5, wherein detennining apparent displacement of the background pattern for the first data and the second data comprises comparing at least a portion of the first data in a first frame captured at a first time with corresponding portions of the first data in a second frame captured at a second time.

8. The method of claim 1, wherein the signal data is indicative of changes in one or more of refractive index, intensity, contrast, phase, polarization, or apparent displacement of background features.

9. Tire method of claim 1, wherein tire signal data comprises displacement data indicative of movement in the subject region.

10. The method of claim 1, wherein the signal data is indicative of one or more of density, velocity, pressure, temperature, refractive index, or absorption.

11. Tire method of claim 1, further comprising processing tire signal data to reduce contributions from one or more of time-invariant or quasi-static components, thereby enhancing detection of localized changes in the subject region.

12. The method of claim 11, wherein processing the signal data comprises subtracting one or more of a moving mean or a mean value from the signal data prior to applying the cross-correlation process.

13. The method of claim 1, wherein the signal data comprises one or more of a probability distribution, at least one peak of a probability distribution, at least one moment of a probability distribution, a higher order correlation, a correlation of more than two pixels, a correlation of a random combination of pixels, a subset of video frames, a periodic subset of frames, an aperiodic subset of frames, or a random set of frames.

14. The method of claim 1, wherein detennining the mapping data comprises determining an intersection of radiation from the first field of view with radiation from the second field of view, thereby defining a voxel indicative of the three-dimensional spatial location.

15. The method of claim 1, wherein determining the mapping data is based on calibration data, and wherein the calibration data comprises an image capturing a pattern in the subject region, and wherein determining the mapping data comprises inputting the pattern into a stereo camera calibrator process.1003-0007W0116. The method of claim 1, wherein determining the mapping data comprises applying epipolar geometry to associate sensor coordinates from the first field of view and corresponding sensor coordinates from the second field of view with three dimensional spatial location.

17. The method of claim 1, wherein the cross-correlation process comprises computing a time- averaged correlation of signals in the signal data associated with the first field of view with signals in the signal data associated with the second field of view.

18. Tire method of claim 1, wherein the cross-correlation process comprises using the mapping data to identify sensor coordinates corresponding to lines of sight from the first field of view and the second field of view that intersect at a common three-dimensional spatial location, and generating a correlation value for that spatial location by comparing signals in the signal data associated with the identified sensor coordinates.

19. The method of claim 1, wherein determining the three-dimensional change data comprises identifying a spatial location corresponding to a peak in the cross-correlation metric between signals in the signal data.

20. The method of claim 1, wherein the cross-correlation process comprises determining a velocity of change at the three-dimensional spatial location based on computing a time-delayed correlation of signals in the signal data.

21. The method of claim 1, wherein the change data comprises a time series of at least three dimensions representing changes in the subject region.

22. Tire method of claim 1, wherein tire change data comprises a representation of a fluid property comprising one or more of density, speed, velocity, temperature, pressure, or a representation of multiple fluids or phases in the subject region.

23. The method of claim 1, wherein the change data is indicative of changes in one or more of a gas or plasma.

24. The method of claim 1, wherein the subject region comprises a fluid region in a biological cell.1003-0007W0125. The method of claim 1, wherein causing output of the change data comprises causing one or more of: storage of the change data, sending the change data via a network to a computing device, output of the change data, or output of data calculated based on the change data.

26. A system comprising: a plurality of sensors comprising at least a first sensor configured to capture signals from a subject region from a first field of view at a first angle thereby generating first data and a second sensor configured to capture signals from tire subject region from a second field of view at a second angle thereby generating second data; and a computing device comprising one or more processors and a memory, wherein the memory stores instructions that, when executed by the one or more processors, cause the computing device to perform the methods of any one of claims 1-25.

27. A device comprising: one or more processors; and a memory storing instructions that, when executed by the one or more processors, cause the device to perform the methods of any one of claims 1-25.

28. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause a device to perform the methods of any one of claims 1-25.

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