Facebook Patent | Multi-speckle diffuse correlation spectroscopy and imaging

Patent: Multi-speckle diffuse correlation spectroscopy and imaging

Drawings: Click to check drawins

Publication Number: 20210338083

Publication Date: 20211104

Applicant: Facebook

Abstract

In some examples, an apparatus may include a laser, a source fiber that delivers the laser radiation to an object, and a detector fiber that receives scattered laser radiation and illuminates a detector array with the scattered laser radiation to form speckles on the detector array. In some examples, the object may be directed illuminated by a laser. The detector array may include a plurality of detectors, and may be positioned to receive the scattered laser radiation from the end of the detector fiber. The distance between the detector array and the end of the detector fiber may be adjustable. A controller may be configured to receive detector data from the detector array, determine a time-dependent intensity autocorrelation function for each detector of a plurality of detectors, and determine an ensemble average autocorrelation function. The apparatus may provide information relating to dynamic processes within the object. Various other methods, systems, and computer-readable media are also disclosed.

Claims

1. An apparatus comprising: a laser, configured to provide laser radiation; a detector fiber, having a collector end configured to receive scattered laser radiation and a detector end; a detector array comprising a plurality of detectors positioned to receive the scattered laser radiation from the detector end of the detector fiber; and a controller, configured to: receive detector data for each detector of the plurality of detectors; determine a time-dependent intensity autocorrelation function for each detector of the plurality of detectors; and determine an ensemble average autocorrelation function based on the time-dependent intensity autocorrelation function for each detector of the plurality of detectors.

2. The apparatus of claim 1, further comprising a distance adjuster configured to adjust a distance between the detector end of the detector fiber and the detector array.

3. The apparatus of claim 1, further comprising at least one optical element located between the detector end of the detector fiber and the detector array.

4. The apparatus of claim 1, wherein the plurality of detectors includes an arrangement of single-photon avalanche diodes.

5. The apparatus of claim 1, wherein the plurality of detectors comprises at least 1000 detectors.

6. The apparatus of claim 1 further comprising a source fiber, wherein: the source fiber has a source end configured to receive the laser radiation from the laser and a delivery end; and the source fiber includes a single-mode fiber.

7. The apparatus of claim 1, wherein the detector fiber includes a multimode fiber.

8. The apparatus of claim 1, wherein the apparatus is configured so that the scattered laser radiation emerges from the detector end of the detector fiber to form a plurality of speckles on the detector array.

9. The apparatus of claim 1, wherein the laser radiation has a wavelength of between 700 nm and 1200 nm.

10. The apparatus of claim 1, wherein the laser radiation has a coherence length of at least 1 m.

11. The apparatus of claim 1, further comprising a beam-splitter configured to direct unscattered laser radiation to the detector array.

12. The apparatus of claim 1, wherein the controller is configured to provide a controller output including time determination based on the ensemble average autocorrelation function.

13. The apparatus of claim 12, wherein the time determination is related to fluid flow dynamics within an object illuminated by the laser radiation.

14. The apparatus of claim 1, wherein the apparatus is a wearable apparatus configured to be worn by a user, and the apparatus is configured so that: the laser radiation is directed into a body part of the user when the apparatus is worn by the user; and the collector end of the detector fiber receives the scattered laser radiation from the body part of the user.

15. The apparatus of claim 14, wherein the apparatus is a head-mounted device and the body part is a head of the user.

16. The apparatus of claim 14, wherein the apparatus includes at least one band configured to attach the apparatus to the body part of the user.

17. A method, comprising: collecting scattered laser radiation using a detector fiber; illuminating a detector array using the scattered laser radiation to form a plurality of speckles on the detector array; and determining an ensemble average correlation function based on time-dependent intensity correlation functions for each of a plurality of detectors of the detector array.

18. The method of claim 17, further comprising adjusting a distance or a lens position between an end of the detector fiber and the detector array so that a speckle size on the detector array is approximately equal to a detector area within the plurality of detectors.

19. The method of claim 17, wherein the scattered laser radiation has a wavelength of between 700 nm and 1200 nm.

20. The method of claim 17, further including: Illuminating an object using laser radiation; and determining a characteristic time related to fluid flow within the object from the ensemble average correlation function.

Description

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No. 63/018,301 filed Apr. 30, 2020, the disclosure of which is incorporated, in its entirety, by this reference.

BRIEF DESCRIPTION OF THE DRAWINGS

[0002] The accompanying drawings illustrate a number of exemplary embodiments and are a part of the specification. Together with the following description, these drawings demonstrate and explain various principles of the present disclosure.

[0003] FIG. 1 is a diagram of the use of an example device for speckle correlation spectroscopy.

[0004] FIGS. 2A-2E further illustrate an example apparatus for speckle correlation spectroscopy and its operation.

[0005] FIG. 3 is a block diagram of an example system for fiber-based speckle contrast optical spectroscopy.

[0006] FIG. 4 shows an example optical fiber projecting a speckle field onto a detector array.

[0007] FIGS. 5A-5D show example improvements in the signal to noise ratio through formation of an ensemble average autocorrelation function.

[0008] FIGS. 6A and 6B show SNR improvements as a function of integration time and count rate per pixel, respectively.

[0009] FIG. 7A-7C further illustrates speckle formation on a detector array.

[0010] FIGS. 8A-8H illustrate speckle formation on a detector array and effects of adjusting the distance between the detector end of the fiber and the detector array.

[0011] FIGS. 9A-9F illustrate cluster sizes for projections of speckles onto a detector array.

[0012] FIGS. 10A-10C show that the cluster length may remain equal the speckle diameter even as the speckle diameter is increased.

[0013] FIGS. 11A-11F illustrate cluster and ensemble averaging in formation of an autocorrelation function, and associated noise characteristics.

[0014] FIGS. 12A and 12B illustrate the effect of fiber core diameter on SNR.

[0015] FIGS. 13A-13E show the effects of hot pixels in a detector array on the intensity autocorrelation function (g.sub.2) and SNR.

[0016] FIGS. 14A-14C further illustrate characteristics of hot pixels in a detector array.

[0017] FIGS. 15A and 15B show example fitting functions for an intensity autocorrelation function.

[0018] FIGS. 16A-16C illustrate the use of pulsed laser radiation to increase the intensity of laser pulses while maintaining the same average laser power.

[0019] FIGS. 17A-17B show the effects of speckle tracking using object detection.

[0020] FIGS. 18A-18J show further example characteristics of an ensemble average autocorrelation function.

[0021] FIG. 19 is a flow diagram of an example method for fiber-based speckle contrast optical spectroscopy.

[0022] FIG. 20 is a flow diagram of a further example method for fiber-based speckle contrast optical spectroscopy.

[0023] FIG. 21 is an illustration of exemplary augmented-reality glasses that may be used in connection with embodiments of this disclosure.

[0024] FIG. 22 is an illustration of an exemplary virtual-reality headset that may be used in connection with embodiments of this disclosure.

[0025] Throughout the drawings, identical reference characters and descriptions indicate similar, but not necessarily identical, elements. While the exemplary embodiments described herein are susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and is described in detail herein. However, the exemplary embodiments described herein are not intended to be limited to the particular forms disclosed. Rather, the present disclosure covers all modifications, equivalents, and alternatives falling within the scope of the appended claims.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0026] The present disclosure is generally directed to object characterization using light scattering. As is explained in greater detail below, embodiments of the present disclosure may include an apparatus that includes a laser, a source fiber that delivers the laser radiation to an object, and a detector fiber that receives scattered laser radiation and illuminates a detector array with the scattered laser radiation to form speckles on the detector array. The detector array may include a plurality of detectors, and may be positioned to receive the scattered laser radiation from the end of the detector fiber. The distance between the detector array and the end of the detector fiber may be adjustable, and may be coupled optically by additional optical elements such as lenses, polarizers, filters, splitters, and combiners. A controller may be configured to receive detector data from the detector array, determine a time-dependent intensity autocorrelation function for each detector of a plurality of detectors, and determine an ensemble average autocorrelation function. The apparatus may provide information relating to dynamic processes within the object, such as fluid flow. In some examples, blood flow within a body part of a user may be characterized using multi-speckle diffuse correlation spectroscopy (mDCS).

[0027] Blood flow in specific areas of the brain may correlate with neuronal activity in those areas, indicating specific brain functions (such as the use of particular words, an emotion, an intent to select or interact with an object within a real or virtual environment, a desire to select an option such as a menu option, a desire to control a real or virtual device, a desire to operate a computer interface device such as a mouse, a desire to enter one or more alphanumeric characters, or other brain function). Thus, observing blood flow may provide the basis for a brain-computer interface. Light directed at a point of a person’s head may penetrate and diffuse through that area of the head, creating a speckle field. Changes in the speckle field over time may provide information about blood flow in the targeted area, providing a non-invasive method for a brain-computer interface. An imaging array fed by a corresponding array of multi-mode fibers can penetrate hair and thus collect light to observe the speckle field with minimal interference from a user’s hair. In addition, correlating speckles in the speckle field to pixels in the imaging array on a N:1 speckle-to-pixel basis may provide a high signal-to-noise ratio. In some approaches, an apparatus may be configured to obtain an approximately 1:1 speckle-to-pixel ratio, and then the speckle diameter may be adjusted to at least approximately optimize the signal-to-noise ratio (SNR). This may lead to an N:1 speckle-to-pixel ratio, where N may be greater than 1 (e.g., approximately 2, 3, or 4, or within the range 1.5-5, such as between approximately 2 and approximately 4), depending on background noise. An example apparatus may be operated with a 1:1 speckle-to-pixel ratio at the detector array, or may operate with a N:1 speckle-to-pixel ratio at the detector array, where N.gtoreq.1 (e.g., where N is between approximately 2 and approximately 4). In some examples, identification of a brain function may be correlated with an eye-tracking system to identify an object or virtual representation that the person desires to interact with.

[0028] In some examples, the imaging array may be large (e.g., 32.times.32, or N.times.M where N and M are both integers and N.times.M>1000). In some examples, an apparatus may include a 128.times.128 detector array (e.g., a SPAD array), such as a 512.times.512 detector array (e.g., a SPAD array).

[0029] Features from any of the embodiments described herein may be used in combination with one another in accordance with the general principles described herein. These and other embodiments, features, and advantages will be more fully understood upon reading the following detailed description in conjunction with the accompanying drawings and claims.

[0030] The following provides, with reference to FIGS. 1-22, detailed descriptions of apparatus and data analysis approaches related to multi-speckle diffuse correlation spectroscopy. FIGS. 1-4 show example apparatus configurations. FIGS. 5A-6B illustrate improvements in the signal to noise ratio through formation of an ensemble average autocorrelation function. FIGS. 7A-10C further illustrate speckle formation on a detector array and methods to characterize the diameter of the speckles. FIGS. 11A-12B illustrate noise reduction using ensemble averaging in the formation of an autocorrelation function, and the effects of fiber core diameter. FIGS. 13A-14C illustrate the effects of hot pixels in a detector array. FIGS. 15A-17B show example fitting functions, the use of pulsed laser radiation, and the effects of speckle tracking using object detection. FIGS. 18A-18J shows further example characteristics of an ensemble average autocorrelation function. FIGS. 19 and 20 are flow diagrams of example methods for fiber-based speckle contrast optical spectroscopy, and FIGS. 21-22 illustrate exemplary augmented reality/virtual reality applications.

[0031] Speckle correlation spectroscopy, such as diffuse correlation spectroscopy (DCS), measures the dynamics of scatterers deep within a scattering medium, such as blood-perfused tissue, by collecting the diffused laser light from the object illuminated by a source fiber and detecting the laser speckle fluctuations. The source fiber may have a source end configured to receive the laser radiation from the laser and a delivery end configured to illuminate the object with laser radiation. Since the penetration depth of laser radiation collected by the detector can be controlled by increasing the source-detector separation (.rho.), DCS may enable the monitoring of deep tissue dynamics such as the cerebral blood flow noninvasively. However, in some implementations, the sensitivity of DCS to cerebral hemodynamics may be limited by the low photon fluxes (N.sub.ph) detected at large .rho., since N.sub.ph decays exponentially with p. Values of .rho. for DCS on the adult human head may typically not exceed 25-29 mm, corresponding to a mean sensitivity depth which is roughly one-third to one-half of .rho. (.sup..about.10 mm), which may be insufficient to effectively probe through scale and skull. To address this issue, systems and methods of the present disclosure include high-sensitivity multi-speckle DCS (mDCS), which can extend .rho. by detecting thousands of speckles in parallel to boost the signal-to-noise ratio (SNR).

[0032] FIG. 1 is a schematic representation of an example device 100 for fiber-based speckle contrast optical spectroscopy. The device 100 may be, for example, a medical device, wearable device, analytical instrument (e.g., a spectrometer), or other device. As shown in FIG. 1, device 100 may include a source light 110 (e.g., a laser) directing light toward a point on a user (e.g., on the user’s head), illustrated by object cross-section 102. In some examples, the object 102 may represent a head. The surface of a head may be curved, but the schematic representation is simplified. The light from source light 110 may diffuse through the user’s head, as represented by diffusion paths 122, 124, 126, 128, and 129. As illustrated, the greater the distance between the entry point of source light 110 on the user and an exit point of diffused light, the greater the depth reached by the diffusion path. Thus, for example, diffusion path 122 has an exit point relatively near the entry point of source light 110 and has a relatively shallow depth, while diffusion path 129 has an exit point relatively distant from the entry point of source light 110 and has a relatively greater depth. As shown in FIG. 1, device 100 may also include optical fibers (detector fibers) 132, 134, 136, 138, and 139, which may gather the light diffused through diffusion paths 122, 124, 126, 128, and 129, respectively. Device 100 may also include detector arrays (which may also be referred to as cameras) 142, 144, 146, 148, and 149, onto which light gathered by optical fibers 132, 134, 136, 138, and 139, respectively, are projected.

[0033] In some examples, an apparatus may also include an optical configuration configured to direct a portion of the unscattered laser radiation around the object. Scattered and unscattered radiation may be incident together on the detector array, and interference effects may further help increase an SNR. This is represented schematically in FIG. 1 by beam-splitter 150, which re-directs a fraction of laser radiation (before the laser radiation reaches the object, which may be termed incident laser radiation or unscattered laser radiation) as beam 152. The unscattered radiation is then recombined with scattered radiation using beam combiner 154, so that both scattered and unscattered radiation are incident on detector array (camera) 142. Other optical configurations may be used, for example, using one or more optical components such as beam-splitters, prisms, reflectors, lenses, optical fibers, apertures, and the like. In some examples, the path of the unscattered radiation may be configured so that it is approximately the same length as that of the scattered radiation. In some examples, a laser configured to provide laser radiation with a long coherence length (e.g., >1 m, or >10 m) may be used, as a longer coherence length may facilitate obtaining interference at the detector array.

[0034] FIG. 1 illustrates a number of aspects, one or more of which may be used in an example apparatus. For example, an apparatus may include one or more source fibers and one or more detector fibers. Different source fibers may receive laser radiation from the same laser, or, in some examples, one or more lasers may be used. Scattered laser radiation may probe dynamic processes within a scattering portion of the object, and the location of the scattering portion within the object may be adjusted by adjusting one or more of the following: the distance between the source and detector fibers, the angle of the source and/or detector fibers to the surface of the object, the wavelength of the laser radiation, or one or more other parameters that may be adjusted. For example, the depth of the scattering portion may be increased by increasing the distance between source and detector fibers. The figure shows the object as having a generally planar surface. In some examples, the object may have a curved surface (e.g., the head of a user) and one or more source fibers and/or one or more detector fibers may be arranged around the surface of the head. In some examples, a fiber may be generally normal to the local surface orientation. In some examples, the term source fiber may refer to a bundle of fibers configured to deliver laser radiation to the object, and the term detector fiber may refer to a bundle of fibers configured to collect scattered laser radiation from the object and illuminate to detector array with the scattered laser radiation. In some examples, one or more source fibers and/or one or more detector fibers may be positioned closer to a user’s body in a wearable device, as discussed further below. In this context, one or more source fibers may refer to one or more fiber bundles delivering light to one or more locations on the object, and one or more source fibers may refer to one or more fiber bundles collecting light from one or more locations on the object.

[0035] FIG. 2A shows an example apparatus 200 that may include an mDCS system based on a single-photon avalanche diode (SPAD) array. The apparatus 200 includes light source 202, source fiber 204 (e.g., a single-mode fiber) having source end 206 and delivery end 208, detector fiber 214 (e.g., a multi-mode fiber) having a collector end 216 and detector end 218, detector array 220, and controller 230. The detector array 220 may include a plurality of detectors and may, for example, include an arrangement of single-photon avalanche diodes (SPADs), such as a 32.times.32 array of SPADs. In some examples, the detector array 220 may include a SPAD array configured to detect a plurality of speckles. The object 210 is the object to be imaged, and may include object components 212 (e.g., fluid components, blood cells, or other components) engaged in a dynamic process such as diffusive motion. Scattered laser radiation, such as scattered pulsed laser radiation, emerges from the detector end 218 of the detector fiber 214 as light cone 222. The dashed lines within the object 210 approximately represents the path of incident and scattered laser light between the source fiber 204 and detector fiber 214, and this may be adjusted by adjusting the distance (.rho.) between the source and detector fibers.

[0036] In some examples, the detector array 220 may detect 1024 speckles, or approximately one speckle per detector. This offered a 32-fold increase in signal-to-noise ratio over a single-speckle DCS. The light source 202 may be a laser, such as a long-coherence (e.g., >9 m) continuous wave (CW) laser. The laser may have an emission wavelength within visible or IR wavelengths, such as a red or near-IR wavelength. In some examples, the laser emission wavelength may in the range 700 nm-1200 nm, for example, 700 nm-900 nm, and example results were obtained using an emission wavelength of 785 nm. Source fiber 204 may direct laser radiation from the light source to the object 212, and the light may be coupled into the object 210 by delivery end 208 of source fiber 204. Detected light, such as scattered and/or diffused light, is collected from the object 210 by collector end 216 and directed along detector fiber 214 to detector end 218 and emerges as light cone 222 to form speckles on the receiving surface of the detector array 220. The detected light is then detected by the detector array 220, and electronic signals from the detector array 220 may be provided to the controller 230.

[0037] In some experiments, the object 210 included an equilibrium homogeneous liquid phantom, and the detector array 220 was a 32.times.32 SPAD array detector. The object may be any object to be imaged, such as a human head, other bodily organ or component, animal, or any other object to be imaged. The source-detector separation (.rho.) may be adjusted, and in some experiments was set to 11 mm. The fiber-SPAD distance (z) may also be adjusted, for example, by rotating an adjustable lens tube.

[0038] Since N.sub.ph decays by about a factor of 10 per 10 mm, the systems and methods described herein may give a .sup..about.15 mm extension of .rho. and a .sup..about.6 mm increase in depth sensitivity over a single-speckle DCS. Greater improvements may also be achieved. This approach may be scalable to even more speckles (e.g., 10,000, 100,000, or more) with the use of large pixel count SPAD arrays, which may extend .rho. to .sup..about.50 mm or more and depth sensitivity to .sup..about.21 mm or more, reaching the cortex.

[0039] FIG. 2B shows a rotating diffuser phantom setup in which a laser (not shown) provides laser radiation to a source fiber 246, and the rotating diffuser phantom 240 is illuminated by laser radiation emerging from the delivery end 242 of the source fiber 246. Scattered laser radiation may be received by the collector end 244 of detector fiber 248 and delivered to a detector array (not shown). The rotating diffuser phantom 240 may be rotated between the fiber ends. In some configurations, an object to be imaged may be rotated (where practical) and located in place of the rotating diffuser phantom 240. The fiber ends may be arranged in a transmission geometry as shown, though other geometries may be used. This apparatus may be used to measure the diameter of the speckles.

[0040] FIG. 2C shows images of speckle pattern on the SPAD array at varying distance z. Such images may be recorded using a rotating diffuser phantom to visualize the speckles at a higher photon count rate. By adjusting the fiber-SPAD distance (z=106, 59, or 30 mm), the projected speckle diameter may be tuned (d=8, 4, or 2 pixels). The input laser power may be adjusted to avoid saturating the detector. Replacing the phantom with a milk phantom may keep the speckle diameter unchanged, as long as the same fiber core diameter (D) and fiber-SPAD distance (z) is used.

[0041] FIG. 2D shows a photon counts time series from a single pixel as shown in FIG. 2C. This shows an example raw signal for calculating the intensity autocorrelation function g.sub.2(.tau.) and the decorrelation time .tau..sub.c.

[0042] FIG. 2E shows the autocorrelation function g.sub.2(.tau.) of the photon counts shown in FIG. 2D.

[0043] The autocorrelation function is described in more detail below, along with an extensive discussion of the advantages of using a SPAD array.

[0044] FIG. 3 is a block diagram of an example system 300 for fiber-based speckle contrast optical spectroscopy. As shown in FIG. 3, system 300 may include a wearable device 310 (worn, e.g., by a user 302). In some examples, wearable device 310 may correspond to wearable device 100 of FIG. 1. System 300 may also include a subsystem 320. Additionally, system 300 may include a computing system 340 (e.g., that receives control input). In some examples, subsystem 320 may form a part of wearable device 310. In some examples, subsystem 320 may form a part of computing system 340. In some examples, subsystem 320 may represent an intermediate subsystem separate from wearable device 310 and computing system 340.

[0045] As shown in FIG. 3, a source light 312 of wearable device 310 may direct light at user 302 (e.g., a point of the head of user 302), which light may diffuse through the blood-perfused tissue of user 302. The diffused light may exit from the blood-perfused tissue at various points, and optical fibers 314(1)-(n) may collect diffused light from some points. Optical fibers 314(1)-(n) may project the collected light onto corresponding cameras 316(1)-(n). The light projected onto cameras 316(1)-(n) may appear as speckle fields. Subsystem 320 may be configured to perform various steps executed by a processor 321. For example, subsystem 320 may receive speckle fields 322(1)-(n) from cameras 316(1)-(n). Subsystem 320 may generate contrast values (and/or autocorrelation functions) 324(1)-(n), which describe the speckle contrast (and/or the correlation times) observed in respective speckle fields 322(1)-(n). Subsystem 320 may explicitly or implicitly model, calculate, and/or derive blood movement 330 based on observed contrast values (and/or autocorrelation functions) 324(1)-(n). Subsystem 320 may then determine brain activity 332 based on blood movement 330. Subsystem 320 may apply an activity-to-input map 334 to map observed brain activity 332 to an input 336. Subsystem 320 may then provide input 336 to computing system 340, thereby performing a control operation on computing system 340 initiated by mental activity of user 302.

[0046] Contrast values may be determined in laser speckle contrast imaging. For diffuse correlation spectroscopy (DCS), the correlation time may be determined and used to estimate the speed of the blood flow. In DCS, the variation in contrast values may affect the amplitude of the autocorrelation function (.beta.), but not the correlation time (.tau.).

[0047] FIG. 4 illustrates a detector fiber 402 (e.g., an optical fiber) having a collector end 422 configured to receive scattered laser radiation and a detector end 420 configured to project scattered laser radiation onto a detector array 412 to form a plurality of speckles. The detector array 412 may also be referred to as a camera. The detector end 420 may be mechanically coupled to a distance adjuster 426 and may be mediated by additional optical elements, which may be used to adjust the distance between the detector end 420 of the detector fiber 402 and the detector array 412. As shown in FIG. 4, the distance between the detector fiber 402 and detector array 412 may impact the size of a projection 414 of the speckle field on the light receiving surface of detector array 412. By adjusting the distance using distance adjuster 426, the average size of speckles in the speckle field may be adjusted. The distance adjuster may include any suitable mechanical adjustment, and may include one or more of a threaded engagement, actuator, slider, or other mechanical adjustment. In some examples, a source and/or a detector fiber may be generally normal to the local surface orientation, but in some examples, the orientation of the source and/or detector fiber may be oblique (e.g., non-normal) to the local surface, and the orientation (e.g., angle relative to the local object surface normal) may be adjustable.

[0048] The configuration shown in FIG. 4 may be used to project the speckles onto the detector array and to adjust the speckle diameters using the distance adjuster. In some examples, the form factor may be reduced using one or more optical elements (e.g., lenses, filters, polarizers, splitters, or combiners) between the end of the detector optical fiber and the detector array, sometimes referred to as the camera. These optical elements can be miniaturized as needed for the application (e.g., for use in AR glasses or an AR/VR headset).

[0049] In some examples, a wearable device (such as the example device of FIG. 1) may be configured such that the average size of speckles in the speckle field is approximately one pixel. For example, the distance adjuster 426 may be adjusted so that the average size of speckles in the speckle field is approximately one pixel. In some examples, the detector end of the detector fiber 402 may include a lens that modifies the effective distance between detector end 420 and detector array 412 such that the average size of speckles in the speckle field is approximately one pixel. As used herein, “approximately” one pixel in size may indicate, for example, that the mean speckle size is between 0.5 and 2 pixels, that at least 68% of observed speckles are between 0.5 and 2 pixels in size, and/or that at least 95% of observed speckles are between 0.5 and 2 pixels in size. In some examples, the detector end 420 may be a plane surface. In some examples, detector end may include a curved surface, such as a concave surface or a convex surface. In some examples, the detector end 420 may be associated with one or more optical elements (such as an external lens) that may be adjusted to modify the speckle size. In some examples, an objective lens, adjustable tube lens, or any other suitable lens may be used. FIG. 4 shows an optional optical element, in this example lens 430 (e.g., a converging lens). The position of lens 430 may be adjustable, for example, using a threaded element (e.g., a knurled knob), slider, or any other suitable adjustment mechanism. For example, a distance between the lens 430 and the detector end 420 may be adjusted using the distance adjuster 426. The distance may be determined between the detector end 420 and the optical center of the lens 430, measured along the fiber axis and/or the optical axis of the lens (which may be parallel and may coincide). A lens distance adjuster 428, which may be similar to and/or combined with distance adjuster 426, may be used to adjust the position of the lens 430. The lens distance adjuster 428 may be in mechanical connection with at least part of the edge portion of lens 430. In some examples, one or more of the lens 430, lens distance adjuster 428, or distance adjuster 426 may be omitted from the apparatus.

[0050] In some examples, the distance between the detector end of a detector fibers and the detector array (and/or a lens configuration associated with the optical fiber) may be fixed (e.g., such that the average size of the speckles in the speckle fields is approximately one pixel). In some examples, the distance and/or the lenses may be adjustable (e.g., such that the average size of the speckles in the speckle fields is approximately one pixel). The adjustment may be performed manually by a user and/or may be performed by the systems described herein during a calibration process (e.g., until the average speckle size is identified as approximately one pixel).

[0051] Further discussion of autocorrelation function characteristics now follows, including a detailed discussion of signal-to-noise (SNR) characteristics. When an example apparatus injects coherent light into a dynamic scattering medium (such as that shown in FIG. 2A or 2B), a dynamic speckle pattern emerges as previously shown in FIG. 2C. A DCS system may estimate the speed of the scatterers by measuring the average turnover time of the speckles (.tau..sub.c), which is inversely related to the speed of the scatterers. An example apparatus may estimate a speed (or speed distribution) of the scatterers by measuring a speckle intensity vs. time and calculating the corresponding autocorrelation function (g.sub.2), for example, as previously illustrated in FIGS. 2D and 2E.

[0052] Even though the SNR of g.sub.2 may be increased by having longer integration times (the time over which the speckle intensity is recorded for each g.sub.2 calculation, T.sub.int) and higher photon count rates (N.sub.ph), these parameters are limited by the time scales of the dynamics used to measure and the laser maximum permissible exposure (MPE) on skin. In one approach, a single-mode fiber (SMF) may be used as the detection fiber to ensure coupling of only one speckle onto a single-photon detector (called “single-speckle DCS”). In another approach, a multi-mode fiber (MMF) may be used to couple multiple (M) speckles onto the single-photon detector. However, although the detection count rate increases (N.sub.ph.varies.M), the magnitude of g.sub.2 decreases with the number of speckles arriving at the detector (.beta..varies.1/M), effectively resulting in no gain of the g.sub.2 SNR.

[0053] Multi-speckle DCS (mDCS) allows significant improvements in the SNR, compared to single-speckle DCS, using parallel DCS measurements of M>1 speckles to provide M independent photon-counting channels. Parallel DCS measurements of M=1024 speckles may be achieved by using a kilopixel SPAD array. While coupling one speckle on every pixel in the SPAD array gave an SNR gain of 32.times., pulsing a CW laser source may give an additional SNR gain. For example, an experimentally obtained SNR gain of 3.2.times. from using pulsed laser radiation resulted in a total SNR gain of more than 100. The additional SNR gain due to pulsing the laser may be increased by reducing the duty cycle of the laser. For example, the SNR gain may be related to the inverse of the square-root of the duty cycle. If the duty cycle is 1, the SNR gain may be 1 (corresponding to no SNR improvement). If the duty cycle is 0.25, then the SNR gain may be 2. The duty cycle may be adjusted to obtain a desired SNR gain. Systems and methods implementing this approach (e.g., pulsed laser operation) may provide a scalable implementation of DCS that allows both high SNR and high sensitivity to the cortex.

[0054] An example apparatus may include a laser, such as a semiconductor laser, such as a visible (e.g., red-emitting) or near-IR CW laser diode. In some experiments, a 780 nm CW laser may be coupled to an object using a source optical fiber (such as a single-mode fiber). The object may include a dynamic scattering medium. A detector optical fiber (e.g., a multimode fiber) may be used to direct scattered light to a detector, such as a SPAD array. The scattered light may include light diffusing out of the scattering medium. In some experiments, for evaluation purposes, the object may include an equilibrium homogeneous liquid phantom. For example, a phantom may be used to determine the SNR for a particular apparatus configuration. In some examples, the object may be a static or a rotating diffuser, which may be used to determine the diameter of the speckles.

[0055] In some examples, the detector array may include 1024 SPADs arranged in a 32.times.32 array, with a pixel pitch of 50.times.50 .mu.m and an active area of 6.95 .mu.m in diameter at each pixel. In some examples, the pixels may be generally square pixels, but other pixel shapes are possible, such as circles. Each pixel may have its own photon counting electronics, for example, that may run at greater than 250,000 frames per second. Operation at 625 kfps was obtained using a 32.times.32 detector array (in this example, a SPAD detector array that may be referred to as a SPAD camera or SPAD array) The SPAD detector array enables simultaneous detection of a plurality of speckles, and this results in an appreciable SNR improvement of the autocorrelation function (g.sub.2). In some examples, an apparatus may ensure that each SPAD pixel detects one or more speckles by adjusting the speckle size to be equal or smaller than the pixel active area.

[0056] The average diameter of a speckle (d) obeys the relationship of Equation (1):

d=.lamda.z/D (Equation 1)

[0057] Here, .lamda. is the wavelength of the light (785 nm), z is the distance between the detection fiber and the SPAD array (3.5-10 mm) and D is the fiber core diameter (e.g., 200-910 .mu.m). In some examples, apparatus configurations may allow a reduction in d by decreasing z, and/or by using a larger fiber core diameter D.

[0058] A high-contrast image of the speckles may be formed on the SPAD array, and the diameter of the speckles at varying distance z may be determined. This may use a high-throughput rotating diffuser phantom, such as shown in FIG. 2B, with source (SMF) and detection (MMF) fiber ends arranged in the transmission geometry shown in FIG. 2B. FIG. 2C shows static images of the speckles illustrating that the speckle diameter (d) can be made smaller by decreasing z. As the diffuser phantom is rotating, the time trace of the photon counts on each pixel can be recorded, and g.sub.2 can be calculated (as previously illustrated in FIG. 2E). In this way the measured g.sub.2 curves and their SNRs for several values of d may be compared.

[0059] In other experiments, an equilibrium milk phantom in a reflection geometry with a .rho. of 11 mm may be used in a configuration similar to that shown above in FIG. 2A. A milk-based phantom may better represent the fast decorrelation time (.ltoreq.200 .mu.s) and low photon count rate seen in typical human tissue studies. The condition of one speckle per pixel active area may be satisfied using a fiber core diameter of 910 .mu.m and a fiber-SPAD distance of 8.1 mm. Other configurations may be used. In these measurement, the SPAD camera may record photon counting time traces on every pixel with a frame exposure time of 4 .mu.s (T.sub.bin) for up to 2 million frames (8.0 seconds).

[0060] From each pixel (e.g., each detector of a detector array), the g.sub.2 function as a function of time lag r may be calculated. Then a comparison may be made with the g.sub.2 curve obtained in a single run from a single pixel (“the pixel g.sub.2”) as in Equation 2:

g 2 i .function. ( .tau. ) = < .times. n .function. ( t ) .times. n .function. ( t + .tau. ) .times. > < .times. n .function. ( t ) .times. >< .times. n .function. ( t + .tau. ) .times. > ( Equation .times. .times. 2 ) ##EQU00001##

[0061] The curve obtained from the ensemble average of all 1024 pixels (“the ensemble g.sub.2”) is given by Equation 3:

g _ 2 .function. ( .tau. ) = 1 M .times. .SIGMA. i M .times. .times. g 2 i .function. ( .tau. ) ( Equation .times. .times. 3 ) ##EQU00002##

[0062] Here, n(t) is the number of photons counts in time bin t, the square bracket ( … ) denotes the average over an integration time T.sub.int, and M is the number of independent speckle field measurements.

[0063] FIGS. 5A-5C show measurements of R=160 runs with an integration time of T.sub.int=50 ms in each run, calculating the time statistics over all runs. A symmetric normalization may be adopted in these calculations.

[0064] FIG. 5A shows the time statistics (mean and standard deviation) of a pixel g.sub.2.

[0065] FIG. 5B shows the time statistics for an ensemble g.sub.2. As can be seen from a comparison of FIGS. 5A and 5B, the standard deviation (STD) is significantly reduced for the ensemble average autocorrelation function g.sub.2.

[0066] FIG. 5C shows the measured signal-to-noise (SNR) ratio (g.sub.2/STD) at increasing ensemble size (shown as points) accompanied by the calculated SNR from the mDCS noise model (shown as continuous lines) discussed further below. The SNR shows an overall increase with larger ensemble size, which matches the theoretical predictions. The SNR gain (comparing the ensemble g.sub.2 and the pixel g.sub.2) is calculated by taking the ratio of the measured ensemble g.sub.2 to the pixel g.sub.2 of the first bin (T=4 .mu.s).

[0067] FIG. 5D shows that the measured SNR gain increases as M increases and reaches a maximum value of 32 when the full array is used.

[0068] The SNR of g.sub.2 in single-speckle DCS is determined by a number of parameters that includes bin time, integration time, count rate, decorrelation time, and coherence factor. In order to evaluate mDCS, a noise model that may be applied to single-speckle DCS may be extended to mDCS. Under the assumption of ergodicity, this may be accomplished by incorporating the number of speckles together with the integration time in the model. In this new model, the g.sub.2 STD at each time lag may be estimated according to Equation 4 below:

.sigma. .function. ( .tau. ) = T tM .function. [ .beta. 2 * ( 1 + e - 2 .times. .GAMMA. .times. .times. T ) .times. ( 1 + e - 2 .times. .GAMMA..tau. ) + 2 .times. m .function. ( 1 - e - 2 .times. .GAMMA. .times. .times. T ) .times. ( e - 2 .times. .GAMMA..tau. ) ( 1 - e - 2 .times. .GAMMA. .times. .times. T ) + 2 .times. < .times. n .times. > - 1 .times. .beta. .function. ( 1 + e - 2 .times. .GAMMA..tau. ) + < .times. n .times. > - 2 .times. ( 1 + .beta. .times. .times. e - 2 .times. .GAMMA..tau. ) ] 1 .times. / .times. 2 ( Equation .times. .times. 4 ) ##EQU00003##

[0069] Here, T (=T.sub.bin) is the correlator time bin interval, t (=T.sub.int) is the averaging integration time, M is the number of detected speckles, .beta. is the coherence factor g.sub.2(0), 2.GAMMA. is the decay rate, m is the delay time bin index, and (=N.sub.ph.times.T.sub.bin) is the count rate within T.sub.bin per pixel. The multi-speckle factor M plays the same role statistically with T.sub.int. This results from the ergodicity of a random process in the system. To validate the mDCS noise model, a comparison of the measured g.sub.2 SNR at increasing T.sub.int or N.sub.ph to increasing the ensemble size M at short T.sub.int or low N.sub.ph is performed.

[0070] FIGS. 6A and 6B shows SNR improvements as a function of integration time and count rate per pixel, respectively.

[0071] FIG. 6A shows the SNR comparison at increasing integration time (T.sub.int) with different numbers of individual detectors, sometimes referred to as pixels (where M=1, 32, or 1024). By increasing the ensemble size at short T.sub.int (10 ms) the same SNR gain is obtained that would be achieved by one pixel at 103 times longer T.sub.int (10 s).

[0072] FIG. 6B shows the SNR comparison at increasing count rate by increasing the laser input power, and demonstrates that increasing the ensemble size is equivalent to increasing the count rate of one pixel by 30 times. As can be seen from these plots, the mDCS noise model (in solid line) is in close agreement with the experimental results (shown as points), even in the absence of any fitting parameters. In particular, there is a linear dependence of the SNR with respect to N.sub.ph in the low count rate regime. This is well predicted by the mDCS noise model (Equation 4), which is dominated by the third term in the low count rate limit and approximated as in Equation (5) below:

.sigma. .function. ( 0 ) = 1 < .times. n .times. > .times. T tM .times. ( 1 + .beta. ) ( Equation .times. .times. 5 ) ##EQU00004##

[0073] This leads directly to Equation (6):

SNR .function. ( 0 ) = < .times. n .times. > .times. tM T .times. .beta. 2 ( 1 + .beta. ) ( Equation .times. .times. 6 ) ##EQU00005##

[0074] The square-root dependence of SNR(0) to t (=T.sub.int) and M arises from the ergodicity of the measured system. In this way, a higher SNR beyond the T.sub.int and N.sub.ph limits is achieved by using larger M. DCS measurements may be configured to detect tissue dynamics at longer .rho. (or larger penetration depths) at the expense of count rates. Therefore, this comparison validates the mDCS noise model in the low count rate regime. The ensemble averaging allows the recovery of some gains of the SNR even when the total count rate is approaching the SPAD’s dark count rate (DCR) of <100 Hz per pixel.

[0075] FIG. 6B further illustrates how the ensemble averaging technique is applicable to photon-starved applications, such as the detection of deep-tissue dynamics. FIG. 6B shows that when the photon flux was as low as .sup..about.4 counts per pixel per T.sub.int (point D), ensemble averaging resulted in the same SNR as with only one pixel with .sup..about.100 counts per T.sub.int (point E). mDCS reached the predicted SNR gain even in the case of an unprecedentedly small number of counts available to calculate g.sub.2 in each pixel.

[0076] In addition to capturing more speckles, the SNR may be further increased by pulsing the laser at higher peak power (N.sub.ph) at the expense of shorter pulse width (Tit), as long as the average power is below the MPE on skin. This approach results in a net SNR gain because the SNR is linear in N.sub.ph and square-root in T.sub.int. This approach may be validated by comparing the usual SNR from using a CW laser to the SNR that would be obtained from 15.times. laser input peak power at 1/15 duty cycle, which results in a 3.5.times. SNR gain. The combination of this pulsed mode (3.5.times. SNR gain) with the kilopixel SPAD array (32.times. SNR gain) leads to a total of >100.times. SNR gain.

[0077] Accordingly, examples of the present disclosure include a scalable approach for mDCS using a kilopixel SPAD array, and with a pulsed mode, to enhance the SNR gain by a factor of greater than 100 times compared to the single-speckle CW-DCS. This means that this technique may be used to measure signal changes on significantly faster time scales and/or longer penetration depth. Thus, if a conventional technique would allow a .rho. for DCS measurement on the adult human head as high as 29 mm using M=14 channels, the techniques discussed herein may allow an increase of .rho. by .sup..about.15 mm or more and an increase in depth sensitivity by about .sup..about.6 mm or more. A noise model for mDCS may be established by assuming speckle ergodicity (which assumptions are supported quantitatively with experimental results), where the SNR is approximately proportional to N.sub.ph.times. T.sub.int.times. M in the shot noise limit. In addition, the mDCS model may be applied in the low photon limit. The kilopixel SPAD array offers a significant increase of channels (M=1024) by a factor of 36 times as compared to M=4-28.

[0078] With the advent of LIDAR technology, high-sensitivity kilopixel SPAD arrays with small dark count rates and high frame rates are commercially available, and detector arrays having larger numbers of pixels may be fabricated. This allows further increases in SNR using SPAD arrays having greater than at least 10,000, or at least 100,000, and in some examples at least 1 million pixels. Using a larger number of pixels, a larger fiber core diameter may be used to accommodate more speckles and faster data transfer and processing rates for real-time mDCS measurements. As is explained in greater detail below, this technique can also be implemented in the time-domain mDCS to enable enhanced depth sensitivity.

[0079] The approaches described herein for mDCS can also be implemented in the time-domain to enhance sensitivity to deep tissue. As discussed above, the steady-state operation of mDCS may use a continuous wave (CW) laser light source. A challenge with steady-state DCS measurements is that the total signal includes the desired signals from deep tissues (e.g., the brain) in addition to the unwanted signals from the intervening superficial tissues (e.g., the scalp and skull). This problem occurs because, in steady-state DCS, all photons are detected from the source point which reaches the detector point regardless of the path the photons took through the tissue. Employing pulsed laser light source, improved multi-speckle time-domain diffuse correlation spectroscopy (mTD-DCS) may be achieved. The time-domain approach enables systems and methods described herein to selectively capture different photons that have traveled along different path lengths through tissue. As a rule of thumb, photons are injected from the source point and capture the returning photons at the detector point, and photons that have traveled through deep tissue have longer path lengths as compared to photons that have traveled through superficial tissue. In other words, photons that have traveled through deep tissues may arrive a few hundreds of picoseconds to a few nanoseconds later as compared to the photons that have only traveled through superficial tissues. By applying time-gated strategies to the DCS signal, systems described herein can differentiate between short and long photon path lengths through the tissue and determine the tissue dynamics for different depths. This technique involves picosecond pulsed laser sources, and a time-correlated single-photon counting (TCSPC) to time-tag each detected photons with two values, the time-of-flight from the source to the detector points to obtain the temporal point-spread function (TPSF), and the absolute arrival time to calculate the temporal autocorrelation function for DCS. By evaluating the correlation functions over different time gates of the TPSF, TD-DCS may differentiate between early and late arriving photons and evaluate the dynamics at different depths within the tissue. The mDCS approach described herein using a kilopixel to megapixel SPAD arrays may enable parallel independent measurements of TD-DCS signals and further increase the instrument sensitivity.

[0080] The number of speckles that are projected on a SPAD array may determine the maximum SNR enhancement factor that is achieved with the mDCS technique. However, the instantaneous number of speckles may change over time because the speckles from dynamical scattering media are constantly changing over time (i.e., appearing and disappearing across time). Accordingly, an object detection technique to locate every speckle and count the number of speckles per frame is used. The number of speckles per frame increases as the speckle size decreases.

[0081] An example configuration may use a rotating diffuser phantom in transmission geometry with a 785 nm CW laser source, a SMF source fiber end (4.4 .mu.m core diameter, 0.13 NA), and a MMF detector fiber end (400 .mu.m core diameter, 0.5 NA). The speckle diameter and the number of speckles can be adjusted by tuning the fiber-SPAD distance.

[0082] FIG. 7A shows the speckle pattern on an example SPAD array with about 21 speckles identified, and each speckle is about 5 pixels in diameter. The time statistics of the number of speckles per frame can be obtained by recording the image and performing the speckle tracking on every frame.

[0083] FIG. 7B shows the time trace of the number of speckles with 10 .mu.s frame exposure time for up to 500 frames. The speckle tracking detects 21 speckles on the frame by identifying their peak intensity characteristics across the array, and each speckle is about 5 pixels in diameter. The speckle turnover time is about 1 ms, adjustable by the rotation speed. FIG. 7B shows the time trace of the number of speckles per frame at fiber-SPAD distance of 82 mm (solid line) and 158 mm (dashed line). As shown in the figure, the number of speckles per frame varies over time.

[0084] FIG. 7C shows the histogram of the number of speckles over time around the mean value of 22 (upper histogram) and 12 (lower histogram) speckles per frame. This speckle tracking technique alone may fail when the speckle size is too small (comparable with the pixel size) or too large (comparable with the camera size). If the speckle size becomes too large, the diameter can be measured using a 2D autocorrelation technique. If the speckle size becomes too small, its diameter may be estimated using a pixel clustering method.

[0085] FIGS. 8A-8H illustrate speckle formation on a detector array, and the effects of adjusting the distance between the detector end of the fiber and the detector array.

[0086] FIGS. 8A-8C show that the speckle size gets larger by increasing the fiber to detector array distance (z). In these examples, a detection fiber core diameter of 400 .mu.m and a numerical aperture of 0.50 may be used.

[0087] FIGS. 8D-8F show that, by calculating the 2D autocorrelation function of each multi-speckle image, the average speckle size may be quantified.

[0088] FIG. 8G shows the linecut of the 2D spatial autocorrelation image at z=106 mm.

[0089] FIG. 8H shows that the diameter of the speckles scales linearly with z, which can be expressed as d=.lamda.z/D, where d is the average diameter of the speckles, .lamda. is the laser wavelength, z is the fiber-SPAD distance, and D is the detection (MMF) fiber core diameter.

[0090] A pixel clustering method may be used to determine the diameter of the speckles. This method may use the decrease in magnitude of the coherence factor .beta. as the photon counts from more speckles are summed up prior to calculating g.sub.2.

[0091] An example apparatus may include a rotating diffuser phantom in transmission geometry with a 785 nm CW laser source, a SMF source fiber end (4.4 .mu.m core diameter, 0.13 NA), and an MMF detector fiber end (400 .mu.m core diameter, 0.5 NA). The speckle diameter and the number of speckles can be adjusted by tuning the fiber-SPAD distance.

[0092] FIGS. 9A-9F illustrate cluster sizes for projections of speckles onto a detector array.

[0093] FIG. 9A shows that multiple speckles may be projected on a SPAD array, where the speckle diameter may span more than one pixel. One or both of two methods may be used to determine the temporal autocorrelation function g.sub.2 from this type of image data. One method is to calculate g.sub.2 from each pixel, where 1024.times.g.sub.2 is obtained from each repetition. Another method is to first perform a pixel clustering such that the size of each cluster is comparable to the speckle size and then calculate g.sub.2 from each cluster.

[0094] FIGS. 9B-9D show that, for example, with 2.times.2, 4.times.4, or 16.times.16 pixels in each clusters (respectively), and 256.times., 64.times., or 4.times. g.sub.2 is obtained from each repetition. For example, in a more accurate representation, the shaded region in the 4.times.4 case may be twice as large as the shaded region in the 2.times.2 case.

[0095] FIG. 9E shows that the magnitude of the g.sub.2 clusters may decrease as more than one speckle per cluster is detected.

[0096] FIG. 9F shows that the number of speckles per cluster may be determined form the coherence factor (.beta.) that appears in the Siegert relation for multimode detection

.beta. = .beta. max K , ##EQU00006##

where .beta..sub.max=0.67 in this configuration and K is the number of speckles per cluster. .beta. decreases as the cluster length is increased. The crossing at

.beta. = .beta. max 2 ##EQU00007##

corresponds to the cluster length where two speckles per cluster are detected.

[0097] FIGS. 10A-10C show that the cluster length (obtained using the method discussed above in relation to FIG. 9F) is equal to the speckle diameter even when the speckle diameter is increased. FIG. 10A shows the relationship of coherence length (.beta.) to cluster length in pixels. FIG. 10B shows the relationship of coherence length (.beta., normalized to 1) to cluster length in pixels. FIG. 10C shows the cluster length at half-.beta..sub.max to fiber-SPAD distance in millimeters, showing an approximately linear relationship.

[0098] FIGS. 11A-11F illustrate cluster and ensemble averaging in formation of an autocorrelation function, with reduced signal-to-noise for ensemble averaging.

[0099] FIG. 11A illustrates how, at every repetition R, g.sub.2 may be calculated from each cluster (called a “g.sub.2 cluster”). Individual clusters may be represented by squares, such as squares 1100. Multiple measurements may be summed for individual clusters. The second layer 1102 represents a second repetition. FIG. 11B shows how the ensemble average of all g.sub.2 clusters at every repetition R can also be calculated (called a “g.sub.2 ensemble”). This is represented by the shaded area 1100, covering a plurality of clusters (e.g., all clusters) as represented by the ensemble of individual squares. In these examples, measurements up to R=19 repetitions were taken (T.sub.int=65 ms in each repetition), where the mean g.sub.2 cluster and its standard deviation over all repetitions is obtained to calculate the SNR of the cluster. Similarly for the ensemble, the mean g.sub.2 ensemble and its standard deviation may be obtained over all repetition to calculate the SNR of the ensemble.

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