Patent Publication Number: US-11656119-B2

Title: High density optical measurement systems with minimal number of light sources

Description:
RELATED APPLICATIONS 
     The present application is a continuation of U.S. patent application Ser. No. 17/202,641, filed on Mar. 16, 2021, which claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 62/992,516, filed on Mar. 20, 2020, and to U.S. Provisional Patent Application No. 63/052,609, filed on Jul. 16, 2020. These applications are incorporated herein by reference in their respective entireties. 
    
    
     BACKGROUND INFORMATION 
     Detecting neural activity in the brain (or any other turbid medium) is useful for medical diagnostics, imaging, neuroengineering, brain-computer interfacing, and a variety of other diagnostic and consumer-related applications. For example, it may be desirable to detect neural activity in the brain of a user to determine if a particular region of the brain has been impacted by reduced blood irrigation, a hemorrhage, or any other type of damage. As another example, it may be desirable to detect neural activity in the brain of a user and computationally decode the detected neural activity into commands that can be used to control various types of consumer electronics (e.g., by controlling a cursor on a computer screen, changing channels on a television, turning lights on, etc.). 
     Neural activity and other attributes of the brain may be determined or inferred by measuring responses of tissue within the brain to light pulses. One technique to measure such responses is time-correlated single-photon counting (TCSPC). Time-correlated single-photon counting detects single photons and measures a time of arrival of the photons with respect to a reference signal (e.g., a light source). By repeating the light pulses, TCSPC may accumulate a sufficient number of photon events to statistically determine a histogram representing the distribution of detected photons. Based on the histogram of photon distribution, the response of tissue to light pulses may be determined in order to study the detected neural activity and/or other attributes of the brain. 
     A photodetector capable of detecting a single photon (i.e., a single particle of optical energy) is an example of a non-invasive detector that can be used in an optical measurement system to detect neural activity within the brain. An exemplary photodetector is implemented by a semiconductor-based single-photon avalanche diode (SPAD), which is capable of capturing individual photons with very high time-of-arrival resolution (a few tens of picoseconds). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings illustrate various embodiments and are a part of the specification. The illustrated embodiments are merely examples and do not limit the scope of the disclosure. Throughout the drawings, identical or similar reference numbers designate identical or similar elements. 
         FIG.  1    shows an exemplary optical measurement system. 
         FIG.  2    illustrates an exemplary detector architecture. 
         FIG.  3    illustrates an exemplary timing diagram for performing an optical measurement operation using an optical measurement system. 
         FIG.  4    illustrates a graph of an exemplary temporal point spread function that may be generated by an optical measurement system in response to a light pulse. 
         FIG.  5    shows an exemplary non-invasive wearable brain interface system. 
         FIG.  6    shows a high density digital optical tomography system. 
         FIG.  7    shows an exemplary optical measurement system. 
         FIGS.  8 - 14    illustrate various modular assemblies that may implement one or more of the optical measurement systems described herein. 
         FIGS.  15 A- 15 B  illustrate spatial and time dependent optical path regions between a light source and a plurality of detectors. 
         FIGS.  16 A- 16 B  show illustrative configurations that include a processing unit. 
         FIG.  17    illustrates an exemplary implementation of a processing unit. 
         FIGS.  18 - 23    illustrate embodiments of a wearable device that includes elements of the optical detection systems described herein. 
         FIG.  24    illustrates an exemplary computing device. 
     
    
    
     DETAILED DESCRIPTION 
     High density optical measurement systems with a minimal number of light sources are described herein. For example, an optical measurement system may include a wearable assembly configured to be worn by a user and including a plurality of light sources each configured to emit light directed at a target and a plurality of detectors configured to detect arrival times for photons of the light after the light is scattered by the target. A ratio of a total number of the detectors to a total number of the light sources is at least two to one. 
     As described herein, a physical positioning of the detectors and light sources within the wearable assembly may result in both spatial and temporal overlapping of light source/detector pairs (also referred to herein as “S-D pairs”), where the same light source is included in more than one S-D pair. This, together with the time-of-flight measurement techniques described herein, may result in optical measurements that have an effective spatial resolution that is relatively high even without a dedicated light source for every detector, as is found in conventional high density digital optical tomography (HD DOT) systems. 
     These and other advantages and benefits of the present systems, circuits, and methods are described more fully herein. 
       FIG.  1    shows an exemplary optical measurement system  100  configured to perform an optical measurement operation with respect to a body  102 . Optical measurement system  100  may, in some examples, be portable and/or wearable by a user. Optical measurement systems that may be used in connection with the embodiments described herein are described more fully in U.S. patent application Ser. No. 17/176,315, filed Feb. 16, 2021; U.S. patent application Ser. No. 17/176,309, filed Feb. 16, 2021; U.S. patent application Ser. No. 17/176,460, filed Feb. 16, 2021; U.S. patent application Ser. No. 17/176,470, filed Feb. 16, 2021; U.S. patent application Ser. No. 17/176,487, filed Feb. 16, 2021; U.S. patent application Ser. No. 17/176,539, filed Feb. 16, 2021; U.S. patent application Ser. No. 17/176,560, filed Feb. 16, 2021; and U.S. patent application Ser. No. 17/176,466, filed Feb. 16, 2021, which applications are incorporated herein by reference in their entirety. 
     In some examples, optical measurement operations performed by optical measurement system  100  are associated with a time domain-based optical measurement technique (e.g., a time-of-flight measurement technique). Example time domain-based optical measurement techniques include, but are not limited to, TCSPC, time domain near infrared spectroscopy (TD-NIRS), time domain diffusive correlation spectroscopy (TD-DCS), and time domain Digital Optical Tomography (TD-DOT). 
     As shown, optical measurement system  100  includes a detector  104  that includes a plurality of individual photodetectors (e.g., photodetector  106 ), a processor  108  coupled to detector  104 , a light source  110 , a controller  112 , and optical conduits  114  and  116  (e.g., light pipes). However, one or more of these components may not, in certain embodiments, be considered to be a part of optical measurement system  100 . For example, in implementations where optical measurement system  100  is wearable by a user, processor  108  and/or controller  112  may in some embodiments be separate from optical measurement system  100  and not configured to be worn by the user. 
     Detector  104  may include any number of photodetectors  106  as may serve a particular implementation, such as 2 n  photodetectors (e.g., 256, 512, . . . , 16384, etc.), where n is an integer greater than or equal to one (e.g., 4, 5, 8, 10, 11, 14, etc.). Photodetectors  106  may be arranged in any suitable manner. 
     Photodetectors  106  may each be implemented by any suitable circuit configured to detect individual photons of light incident upon photodetectors  106 . For example, each photodetector  106  may be implemented by a single photon avalanche diode (SPAD) circuit and/or other circuitry as may serve a particular implementation. 
     Processor  108  may be implemented by one or more physical processing (e.g., computing) devices. In some examples, processor  108  may execute instructions (e.g., software) configured to perform one or more of the operations described herein. 
     Light source  110  may be implemented by any suitable component configured to generate and emit light. For example, light source  110  may be implemented by one or more laser diodes, distributed feedback (DFB) lasers, super luminescent diodes (SLDs), light emitting diodes (LEDs), diode-pumped solid-state (DPSS) lasers, super luminescent light emitting diodes (sLEDs), vertical-cavity surface-emitting lasers (VCSELs), titanium sapphire lasers, micro light emitting diodes (m LEDs), and/or any other suitable laser or light source. In some examples, the light emitted by light source  110  is high coherence light (e.g., light that has a coherence length of at least 5 centimeters) at a predetermined center wavelength. 
     Light source  110  is controlled by controller  112 , which may be implemented by any suitable computing device (e.g., processor  108 ), integrated circuit, and/or combination of hardware and/or software as may serve a particular implementation. In some examples, controller  112  is configured to control light source  110  by turning light source  110  on and off and/or setting an intensity of light generated by light source  110 . Controller  112  may be manually operated by a user, or may be programmed to control light source  110  automatically. 
     Light emitted by light source  110  may travel via an optical conduit  114  (e.g., a light pipe, a light guide, a waveguide, a single-mode optical fiber, and/or or a multi-mode optical fiber) to body  102  of a subject. In cases where optical conduit  114  is implemented by a light guide, the light guide may be spring loaded and/or have a cantilever mechanism to allow for conformably pressing the light guide firmly against body  102 . 
     Body  102  may include any suitable turbid medium. For example, in some implementations, body  102  is a head or any other body part of a human or other animal. Alternatively, body  102  may be a non-living object. For illustrative purposes, it will be assumed in the examples provided herein that body  102  is a human head. 
     As indicated by arrow  120 , the light emitted by light source  110  enters body  102  at a first location  122  on body  102 . Accordingly, a distal end of optical conduit  114  may be positioned at (e.g., right above, in physical contact with, or physically attached to) first location  122  (e.g., to a scalp of the subject). In some examples, the light may emerge from optical conduit  114  and spread out to a certain spot size on body  102  to fall under a predetermined safety limit. At least a portion of the light indicated by arrow  120  may be scattered within body  102 . 
     As used herein, “distal” means nearer, along the optical path of the light emitted by light source  110  or the light received by detector  104 , to the target (e.g., within body  102 ) than to light source  110  or detector  104 . Thus, the distal end of optical conduit  114  is nearer to body  102  than to light source  110 , and the distal end of optical conduit  116  is nearer to body  102  than to detector  104 . Additionally, as used herein, “proximal” means nearer, along the optical path of the light emitted by light source  110  or the light received by detector  104 , to light source  110  or detector  104  than to body  102 . Thus, the proximal end of optical conduit  114  is nearer to light source  110  than to body  102 , and the proximal end of optical conduit  116  is nearer to detector  104  than to body  102 . 
     As shown, the distal end of optical conduit  116  (e.g., a light pipe, a light guide, a waveguide, a single-mode optical fiber, and/or a multi-mode optical fiber) is positioned at (e.g., right above, in physical contact with, or physically attached to) output location  126  on body  102 . In this manner, optical conduit  116  may collect at least a portion of the scattered light (indicated as light  124 ) as it exits body  102  at location  126  and carry light  124  to detector  104 . Light  124  may pass through one or more lenses and/or other optical elements (not shown) that direct light  124  onto each of the photodetectors  106  included in detector  104 . 
     Photodetectors  106  may be connected in parallel in detector  104 . An output of each of photodetectors  106  may be accumulated to generate an accumulated output of detector  104 . Processor  108  may receive the accumulated output and determine, based on the accumulated output, a temporal distribution of photons detected by photodetectors  106 . Processor  108  may then generate, based on the temporal distribution, a histogram representing a light pulse response of a target (e.g., brain tissue, blood flow, etc.) in body  102 . Example embodiments of accumulated outputs are described herein. 
       FIG.  2    illustrates an exemplary detector architecture  200  that may be used in accordance with the systems and methods described herein. As shown, architecture  200  includes a SPAD circuit  202  that implements photodetector  106 , a control circuit  204 , a time-to-digital converter (TDC)  206 , and a signal processing circuit  208 . Architecture  200  may include additional or alternative components as may serve a particular implementation. 
     In some examples, SPAD circuit  202  includes a SPAD and a fast gating circuit configured to operate together to detect a photon incident upon the SPAD. As described herein, SPAD circuit  202  may generate an output when SPAD circuit  202  detects a photon. 
     The fast gating circuit included in SPAD circuit  202  may be implemented in any suitable manner. For example, the fast gating circuit may include a capacitor that is pre-charged with a bias voltage before a command is provided to arm the SPAD. Gating the SPAD with a capacitor instead of with an active voltage source, such as is done in some conventional SPAD architectures, has a number of advantages and benefits. For example, a SPAD that is gated with a capacitor may be armed practically instantaneously compared to a SPAD that is gated with an active voltage source. This is because the capacitor is already charged with the bias voltage when a command is provided to arm the SPAD. This is described more fully in U.S. Pat. Nos. 10,158,038 and 10,424,683, which are incorporated herein by reference in their respective entireties. 
     In some alternative configurations, SPAD circuit  202  does not include a fast gating circuit. In these configurations, the SPAD included in SPAD circuit  202  may be gated in any suitable manner or be configured to operate in a free running mode with passive quenching. 
     Control circuit  204  may be implemented by an application specific integrated circuit (ASIC) or any other suitable circuit configured to control an operation of various components within SPAD circuit  202 . For example, control circuit  204  may output control logic that puts the SPAD included in SPAD circuit  202  in either an armed or a disarmed state. 
     In some examples, control circuit  204  may control a gate delay, which specifies a predetermined amount of time control circuit  204  is to wait after an occurrence of a light pulse (e.g., a laser pulse) to put the SPAD in the armed state. To this end, control circuit  204  may receive light pulse timing information, which indicates a time at which a light pulse occurs (e.g., a time at which the light pulse is applied to body  202 ). Control circuit  204  may also control a programmable gate width, which specifies how long the SPAD is kept in the armed state before being disarmed. 
     Control circuit  204  is further configured to control signal processing circuit  208 . For example, control circuit  204  may provide histogram parameters (e.g., time bins, number of light pulses, type of histogram, etc.) to signal processing circuit  208 . Signal processing circuit  208  may generate histogram data in accordance with the histogram parameters. In some examples, control circuit  204  is at least partially implemented by controller  112 . 
     TDC  206  is configured to measure a time difference between an occurrence of an output pulse generated by SPAD circuit  202  and an occurrence of a light pulse. To this end, TDC  206  may also receive the same light pulse timing information that control circuit  204  receives. TDC  206  may be implemented by any suitable circuitry as may serve a particular implementation. 
     Signal processing circuit  208  is configured to perform one or more signal processing operations on data output by TDC  206 . For example, signal processing circuit  208  may generate histogram data based on the data output by TDC  206  and in accordance with histogram parameters provided by control circuit  204 . To illustrate, signal processing circuit  208  may generate, store, transmit, compress, analyze, decode, and/or otherwise process histograms based on the data output by TDC  206 . In some examples, signal processing circuit  208  may provide processed data to control circuit  204 , which may use the processed data in any suitable manner. In some examples, signal processing circuit  208  is at least partially implemented by processor  108 . 
     In some examples, each photodetector  106  (e.g., SPAD circuit  202 ) may have a dedicated TDC  206  associated therewith. For example, for an array of N photodetectors  106 , there may be a corresponding array of N TDCs  206 . Alternatively, a single TDC  206  may be associated with multiple photodetectors  106 . Likewise, a single control circuit  204  and a single signal processing circuit  208  may be provided for a one or more photodetectors  106  and/or TDCs  206 . 
       FIG.  3    illustrates an exemplary timing diagram  300  for performing an optical measurement operation using optical measurement system  100 . Optical measurement system  100  may be configured to perform the optical measurement operation by directing light pulses (e.g., laser pulses) toward a target within a body (e.g., body  102 ). The light pulses may be short (e.g., 10-2000 picoseconds (ps)) and repeated at a high frequency (e.g., between 100,000 hertz (Hz) and 100 megahertz (MHz)). The light pulses may be scattered by the target and then detected by optical measurement system  100 . Optical measurement system  100  may measure a time relative to the light pulse for each detected photon. By counting the number of photons detected at each time relative to each light pulse repeated over a plurality of light pulses, optical measurement system  100  may generate a histogram that represents a light pulse response of the target (e.g., a temporal point spread function (TPSF)). The terms histogram and TPSF are used interchangeably herein to refer to a light pulse response of a target. 
     For example, timing diagram  300  shows a sequence of light pulses  302  (e.g., light pulses  302 - 1  and  302 - 2 ) that may be applied to the target (e.g., tissue within a brain of a user, blood flow, a fluorescent material used as a probe in a body of a user, etc.). Timing diagram  300  also shows a pulse wave  304  representing predetermined gated time windows (also referred as gated time periods) during which photodetectors  106  are gated ON to detect photons. Referring to light pulse  302 - 1 , light pulse  302 - 1  is applied at a time t 0 . At a time a first instance of the predetermined gated time window begins. Photodetectors  106  may be armed at time t 1 , enabling photodetectors  106  to detect photons scattered by the target during the predetermined gated time window. In this example, time t 1  is set to be at a certain time after time t 0 , which may minimize photons detected directly from the laser pulse, before the laser pulse reaches the target. However, in some alternative examples, time t 1  is set to be equal to time t 0 . 
     At a time t 2 , the predetermined gated time window ends. In some examples, photodetectors  106  may be disarmed at time t 2 . In other examples, photodetectors  106  may be reset (e.g., disarmed and re-armed) at time t 2  or at a time subsequent to time t 2 . During the predetermined gated time window, photodetectors  106  may detect photons scattered by the target. Photodetectors  106  may be configured to remain armed during the predetermined gated time window such that photodetectors  106  maintain an output upon detecting a photon during the predetermined gated time window. For example, a photodetector  106  may detect a photon at a time t 3 , which is during the predetermined gated time window between times t 1  and t 2 . The photodetector  106  may be configured to provide an output indicating that the photodetector  106  has detected a photon. The photodetector  106  may be configured to continue providing the output until time t 2 , when the photodetector may be disarmed and/or reset. Optical measurement system  100  may generate an accumulated output from the plurality of photodetectors. Optical measurement system  100  may sample the accumulated output to determine times at which photons are detected by photodetectors  106  to generate a TPSF. 
     As mentioned, in some alternative examples, photodetector  106  may be configured to operate in a free-running mode such that photodetector  106  is not actively armed and disarmed (e.g., at the end of each predetermined gated time window represented by pulse wave  304 ). In contrast, while operating in the free-running mode, photodetector  106  may be configured to reset within a configurable time period after an occurrence of a photon detection event (i.e., after photodetector  106  detects a photon) and immediately begin detecting new photons. However, only photons detected within a desired time window (e.g., during each gated time window represented by pulse wave  304 ) may be included in the TPSF. 
       FIG.  4    illustrates a graph  400  of an exemplary TPSF  402  that may be generated by optical measurement system  100  in response to a light pulse  404  (which, in practice, represents a plurality of light pulses). Graph  400  shows a normalized count of photons on a y-axis and time bins on an x-axis. As shown, TPSF  402  is delayed with respect to a temporal occurrence of light pulse  404 . In some examples, the number of photons detected in each time bin subsequent to each occurrence of light pulse  404  may be aggregated (e.g., integrated) to generate TPSF  402 . TPSF  402  may be analyzed and/or processed in any suitable manner to determine or infer detected neural activity. 
     Optical measurement system  100  may be implemented by or included in any suitable device. For example, optical measurement system  100  may be included, in whole or in part, in a non-invasive wearable device (e.g., a headpiece) that a user may wear to perform one or more diagnostic, imaging, analytical, and/or consumer-related operations. The non-invasive wearable device may be placed on a user&#39;s head or other part of the user to detect neural activity. In some examples, such neural activity may be used to make behavioral and mental state analysis, awareness and predictions for the user. 
     Mental state described herein refers to the measured neural activity related to physiological brain states and/or mental brain states, e.g., joy, excitement, relaxation, surprise, fear, stress, anxiety, sadness, anger, disgust, contempt, contentment, calmness, focus, attention, approval, creativity, positive or negative reflections/attitude on experiences or the use of objects, etc. Further details on the methods and systems related to a predicted brain state, behavior, preferences, or attitude of the user, and the creation, training, and use of neuromes can be found in U.S. Provisional Patent Application No. 63/047,991, filed Jul. 3, 2020. Exemplary measurement systems and methods using biofeedback for awareness and modulation of mental state are described in more detail in U.S. patent application Ser. No. 16/364,338, filed Mar. 26, 2019, published as US2020/0196932A1. Exemplary measurement systems and methods used for detecting and modulating the mental state of a user using entertainment selections, e.g., music, film/video, are described in more detail in U.S. patent application Ser. No. 16/835,972, filed Mar. 31, 2020, published as US2020/0315510A1. Exemplary measurement systems and methods used for detecting and modulating the mental state of a user using product formulation from, e.g., beverages, food, selective food/drink ingredients, fragrances, and assessment based on product-elicited brain state measurements are described in more detail in U.S. patent application Ser. No. 16/853,614, filed Apr. 20, 2020, published as US2020/0337624A1. Exemplary measurement systems and methods used for detecting and modulating the mental state of a user through awareness of priming effects are described in more detail in U.S. patent application Ser. No. 16/885,596, filed May 28, 2020, published as US2020/0390358A1. These applications and corresponding U.S. publications are incorporated herein by reference in their entirety. 
       FIG.  5    shows an exemplary non-invasive wearable brain interface system  500  (“brain interface system  500 ”) that implements optical measurement system  100  (shown in  FIG.  1   ). As shown, brain interface system  500  includes a head-mountable component  502  configured to be attached to a user&#39;s head. Head-mountable component  502  may be implemented by a cap shape that is worn on a head of a user. Alternative implementations of head-mountable component  502  include helmets, beanies, headbands, other hat shapes, or other forms conformable to be worn on a user&#39;s head, etc. Head-mountable component  502  may be made out of any suitable cloth, soft polymer, plastic, hard shell, and/or any other suitable material as may serve a particular implementation. Examples of headgears used with wearable brain interface systems are described more fully in U.S. Pat. No. 10,340,408, incorporated herein by reference in its entirety. 
     Head-mountable component  502  includes a plurality of detectors  504 , which may implement or be similar to detector  104 , and a plurality of light sources  506 , which may be implemented by or be similar to light source  110 . It will be recognized that in some alternative embodiments, head-mountable component  502  may include a single detector  504  and/or a single light source  506 . 
     Brain interface system  500  may be used for controlling an optical path to the brain and for transforming photodetector measurements into an intensity value that represents an optical property of a target within the brain. Brain interface system  500  allows optical detection of deep anatomical locations beyond skin and bone (e.g., skull) by extracting data from photons originating from light source  506  and emitted to a target location within the user&#39;s brain, in contrast to conventional imaging systems and methods (e.g., optical coherence tomography (OCT)), which only image superficial tissue structures or through optically transparent structures. 
     Brain interface system  500  may further include a processor  508  configured to communicate with (e.g., control and/or receive signals from) detectors  504  and light sources  506  by way of a communication link  510 . Communication link  510  may include any suitable wired and/or wireless communication link. Processor  508  may include any suitable housing and may be located on the user&#39;s scalp, neck, shoulders, chest, or arm, as may be desirable. In some variations, processor  508  may be integrated in the same assembly housing as detectors  504  and light sources  506 . 
     As shown, brain interface system  500  may optionally include a remote processor  512  in communication with processor  508 . For example, remote processor  512  may store measured data from detectors  504  and/or processor  508  from previous detection sessions and/or from multiple brain interface systems (not shown). Power for detectors  504 , light sources  506 , and/or processor  508  may be provided via a wearable battery (not shown). In some examples, processor  508  and the battery may be enclosed in a single housing, and wires carrying power signals from processor  508  and the battery may extend to detectors  504  and light sources  506 . Alternatively, power may be provided wirelessly (e.g., by induction). 
     In some alternative embodiments, head mountable component  502  does not include individual light sources. Instead, a light source configured to generate the light that is detected by detector  504  may be included elsewhere in brain interface system  500 . For example, a light source may be included in processor  508  and coupled to head mountable component  502  through optical connections. 
     Optical measurement system  100  may alternatively be included in a non-wearable device (e.g., a medical device and/or consumer device that is placed near the head or other body part of a user to perform one or more diagnostic, imaging, and/or consumer-related operations). Optical measurement system  100  may alternatively be included in a sub-assembly enclosure of a wearable invasive device (e.g., an implantable medical device for brain recording and imaging). 
     A conventional HD DOT system is characterized by a regular grid of light sources and detectors (e.g., photodetectors). For example,  FIG.  6    shows an HD DOT system  600  that includes a grid of alternating light sources (labeled “S”) and detectors (labeled “D”) such that a ratio of light sources to detectors is one to one. This provides a relatively high number of overlapping S-D pairs, which means that light from a particular light source can be detected by multiple detectors that are located near the light source. This may provide relatively high density spatial information. However, such a configuration disadvantageously requires a relatively high number of light sources, which can make the HD DOT system  600  physically large and/or consume a relatively high amount of power. 
     In contrast,  FIG.  7    shows an exemplary optical measurement system  700  in accordance with the principles described herein. Optical measurement system  700  may be an implementation of optical measurement system  100  and, as shown, includes a wearable assembly  702 , which includes N light sources  704  (e.g., light sources  704 - 1  through  704 -N) and M detectors  706  (e.g., detectors  706 - 1  through  706 -M). Optical measurement system  700  may include any of the other components of optical measurement system  100  as may serve a particular implementation. 
     Light sources  704  are each configured to emit light and may be implemented by any of the light sources described herein. Detectors  706  may each be configured to detect arrival times for photons of the light emitted by one or more light sources  704  after the light is scattered by the target. For example, a detector  706  may include a photodetector configured to generate a photodetector output pulse in response to detecting a photon of the light and a TDC configured to record a timestamp symbol in response to an occurrence of the photodetector output pulse, the timestamp symbol representative of an arrival time for the photon. 
     Wearable assembly  702  may be implemented by any of the wearable devices, wearable module assemblies, and/or wearable units described herein. For example, wearable assembly  702  may be implemented by a wearable device configured to be worn on a user&#39;s head. Wearable assembly  702  may additionally or alternatively be configured to be worn on any other part of a user&#39;s body. 
     In accordance with the principles described herein, a ratio of the total number of detectors  706  (i.e., M) to the total number of light sources (i.e., N) is at least two to one. In other words, there are at least twice as many detectors in wearable assembly  702  as there are light sources. 
     As described herein, a physical positioning of detectors  706  and light sources  704  within wearable assembly  702  may result in both spatial and temporal overlapping of S-D pairs, where the same light source is included in more than one S-D pair. This, in combination with the time-of-flight measurement techniques described herein, may result in optical measurements that have an effective spatial resolution that is relatively high even without a dedicated light source for every detector, as is found in conventional HD DOT systems (e.g., HD DOT system  600  shown in  FIG.  6   ). This in turn allows for the implementations of optical measurement system  700  described to have fewer light sources and/or detectors than conventional HD DOT systems while still having at least the same effective spatial resolution. 
     Optical measurement system  700  may be modular in that one or more components of optical measurement system  700  may be removed, changed out, or otherwise modified as may serve a particular implementation. As such, optical measurement system  700  may be configured to conform to three-dimensional surface geometries, such as a user&#39;s head. Exemplary modular multimodal measurement systems are described in more detail in U.S. patent application Ser. No. 17/176,460, filed Feb. 16, 2021, U.S. patent application Ser. No. 17/176,470, filed Feb. 16, 2021, U.S. patent application Ser. No. 17/176,487, filed Feb. 16, 2021, U.S. Provisional Patent Application No. 63/038,481, filed Jun. 12, 2020, and U.S. patent application Ser. No. 17/176,560, filed Feb. 16, 2021, which applications are incorporated herein by reference in their respective entireties. 
     To illustrate, various modular assemblies that implement optical measurement system  700  are described in connection with  FIGS.  8 - 14   . The modular assemblies described herein are merely illustrative of the many different implementations of optical measurement system  700  that may be realized in accordance with the principles described herein. Each of the modular assemblies described herein may include one or more modules and may be worn on the head or any other suitable body part of the user. 
     In  FIGS.  8 - 14   , the illustrated modules may, in some examples, be physically distinct from each other. For example, as described herein, each module may be configured to be removably attached to a wearable assembly (e.g., by being inserted into a different slot of the wearable assembly). This may allow the modular assemblies to conform to three-dimensional surface geometries, such as a user&#39;s head. 
     In  FIGS.  8 - 14   , each illustrated module may include one or more light sources labeled “S” and a set of detectors each labeled “D”. Some specific light sources and detectors are also referred to by specific reference numbers. Each light source depicted in  FIGS.  8 - 14    may be implemented by one or more light sources similar to light source  110  and may be configured to emit light directed at a target (e.g., the brain). Each detector depicted in  FIGS.  8 - 14    may implement or be similar to detector  104  and may include a plurality of photodetectors (e.g., SPADs) as well as other circuitry (e.g., TDCs), and may be configured to detect arrival times for photons of the light emitted by one or more light sources after the light is scattered by the target. 
       FIG.  8    shows an illustrative modular assembly  800  that may implement optical measurement system  700 . As shown, modular assembly  800  includes a plurality of modules  802  (e.g., modules  802 - 1  through  802 - 3 ). While three modules  802  are shown to be included in modular assembly  800 , in alternative configurations, any number of modules  802  (e.g., a single module up to sixteen or more modules) may be included in modular assembly  800 . 
     Each module  802  includes a light source (e.g., light source  804 - 1  of module  802 - 1  and light source  804 - 2  of module  802 - 2 ) and a plurality of detectors (e.g., detectors  806 - 1  through  806 - 6  of module  802 - 1 ). In the particular implementation shown in  FIG.  8   , each module  802  includes a single light source and six detectors such that a ratio of detectors to light sources in modular assembly  800  is six to one. 
     Each light source (e.g., light source  804 - 1  or light source  804 - 2 ) depicted in  FIG.  8    may be located at a center region of a surface of the light source&#39;s corresponding module. For example, light source  804 - 1  is located at a center region of a surface  808  of module  802 - 1 . In alternative implementations, a light source of a module may be located away from a center region of the module. 
     The detectors of a module may be distributed around the light source of the module. For example, detectors  806  of module  802 - 1  are distributed around light source  804 - 1  on surface  808  of module  802 - 1 . In some examples, the detectors of a module may all be equidistant from the light source of the same module. In other words, the spacing between a light source (i.e., a distal end portion of a light source optical conduit) and the detectors (i.e., distal end portions of optical conduits for each detector) are maintained at the same fixed distance on each module to ensure homogeneous coverage over specific areas and to facilitate processing of the detected signals. The fixed spacing also provides consistent spatial (lateral and depth) resolution across the target area of interest, e.g., brain tissue. Moreover, maintaining a known distance between the light source, e.g., light emitter, and the detector allows subsequent processing of the detected signals to infer spatial (e.g., depth localization, inverse modeling) information about the detected signals. Detectors of a module may be alternatively disposed on the module as may serve a particular implementation. 
     In  FIG.  8   , modules  802  are shown to be adjacent to and touching one another. Modules  802  may alternatively be spaced apart from one another. For example,  FIGS.  9 A- 9 B  show an exemplary implementation of modular assembly  800  in which modules  802  are configured to be inserted into individual slots  902  (e.g., slots  902 - 1  through  902 - 3 , also referred to as cutouts) of a wearable assembly  904 . In particular,  FIG.  9 A  shows the individual slots  902  of the wearable assembly  904  before modules  802  have been inserted into respective slots  902 , and  FIG.  9 B  shows wearable assembly  904  with individual modules  802  inserted into respective individual slots  902 . 
     Wearable assembly  904  may implement wearable assembly  702  and may be configured as headgear and/or any other type of device configured to be worn by a user. 
     As shown in  FIG.  9 A , each slot  902  is surrounded by a wall (e.g., wall  906 ) such that when modules  802  are inserted into their respective individual slots  902 , the walls physically separate modules  802  one from another. In alternative embodiments, a module (e.g., module  802 - 1 ) may be in at least partial physical contact with a neighboring module (e.g., module  802 - 2 ). 
     Each of the modular assemblies described herein may be inserted into appropriately shaped slots or cutouts of a wearable assembly, as described in connection with  FIGS.  9 A- 9 B . However, for ease of explanation, such wearable assemblies are not shown in the figures. 
     As shown in  FIGS.  8  and  9 B , modules  802  may have a hexagonal shape. Modules  802  may alternatively have any other suitable geometry (e.g., in the shape of a pentagon, octagon, square, rectangular, circular, triangular, free-form, etc.). 
     To illustrate,  FIG.  10    shows another illustrative modular assembly  1000  that may implement optical measurement system  700 . As shown, modular assembly  1000  includes a plurality of modules  1002  (e.g., modules  1002 - 1  through  1002 - 4 ) that are each in the shape of a diamond. While four modules  1002  are shown to be included in modular assembly  1000 , in alternative configurations, any number of modules  1002  (e.g., a single module up to sixteen or more modules) may be included in modular assembly  1000 . 
     Modular assembly  1000  is similar to modular assembly  800  in that each module  1002  of modular assembly  1000  includes a light source “S” surrounded by a plurality of detectors “D”. In the particular implementation shown in  FIG.  10   , each module  1002  includes a single light source and four detectors such that a ratio of detectors to light sources in modular assembly  1000  is four to one. 
       FIG.  11    shows another illustrative modular assembly  1100  that may implement optical measurement system  700 . As shown, modular assembly  1100  includes a plurality of modules  1102  (e.g., modules  1102 - 1  through  1102 - 4 ) that are each in the shape of a square. While four modules  1102  are shown to be included in implementation  1100 , in alternative configurations, any number of modules  1102  (e.g., a single module up to sixteen or more modules) may be included in modular assembly  1100 . 
     Modular assembly  1100  is similar to modular assembly  800  in that each module  1102  of modular assembly  1100  includes a light source “S” surrounded by a plurality of detectors “D”. In the particular implementation shown in  FIG.  11   , each module  1102  includes a single light source and eight detectors such that a ratio of detectors to light sources in modular assembly  1100  is eight to one. 
       FIG.  12    shows another illustrative modular assembly  1200  that may implement optical measurement system  700 . As shown, modular assembly  1200  includes a plurality of modules  1202  (e.g., modules  1202 - 1  through  1202 - 4 ) that are each in the shape of a hexagon. While four modules  1202  are shown to be included in modular assembly  1200 , in alternative configurations, any number of modules  1202  (e.g., a single module up to sixteen or more modules) may be included in modular assembly  1200 . 
     Modular assembly  1200  is similar to modular assembly  800  in that each module  1202  of modular assembly  1200  includes a light source “S” surrounded by a plurality of detectors “D”. In the particular implementation shown in  FIG.  12   , each module  1202  includes a single light source and twelve detectors such that a ratio of detectors to light sources in modular assembly  1200  is twelve to one. As shown, some of the detectors (e.g., detector  1204 - 1 ) of a module (e.g., module  1202 - 1 ) are closer to a light source (e.g., light source  1206 ) of the module than other detectors (e.g., detector  1204 - 2 ) of the same module. 
       FIG.  13    shows another illustrative modular assembly  1300  that may implement optical measurement system  700 . As shown, modular assembly  1300  includes a plurality of modules  1302  (e.g., modules  1302 - 1  through  1302 - 6 ) that are each in the shape of a triangle. While six modules  1302  are shown to be included in modular assembly  1300 , in alternative configurations, any number of modules  1302  (e.g., a single module up to sixteen or more modules) may be included in modular assembly  1300 . 
     Modular assembly  1300  is similar to modular assembly  800  in that each module  1302  of modular assembly  1300  includes a light source “S” and a plurality of detectors “D”. However, in the particular implementation shown in  FIG.  13   , the light source for each module  1302  is located away from a center region of the module  1302 . For example, the light source for each module  1302  is located towards one of the vertices of the module  1302 . 
       FIG.  14    shows another illustrative modular assembly  1400  that may implement optical measurement system  700 . As shown, modular assembly  1400  includes a plurality of modules  1402  (e.g., modules  1402 - 1  through  1402 - 4 ) that are each in the shape of a hexagon. While three modules  1402  are shown to be included in modular assembly  1400 , in alternative configurations, any number of modules  1402  (e.g., a single module up to sixteen or more modules) may be included in modular assembly  1400 . 
     Modular assembly  1400  is similar to modular assembly  800 , except that in modular assembly  1400  each module  1402  includes two light sources “S” (instead of one light source) and a plurality of detectors “D”. For example, module  1402 - 1  includes a first light source  1404 - 1  and a second light source  1404 - 2 . As shown, each pair of light sources may be co-located (e.g., right next to each other) on their respective module  1402 . In this configuration, light source  1404 - 1  may emit light having a first wavelength and light source  1404 - 2  may emit light having a second wavelength different than the first wavelength. Any of the other modular assemblies described herein may include multiple light sources per module as may serve a particular implementation. 
     The dual light source configuration shown in  FIG.  14    may be used when it is desired for an optical measurement system to concurrently measure or detect different properties. For example, pairs of lights sources operating at different wavelengths may be used to measure the concentrations of oxygenated and deoxygenated hemoglobin, which are at different wavelengths. 
     In each of the modular assemblies described in connection with  FIGS.  8 - 14   , a positioning of the modules may cause one or more detectors of a first module to not only detect arrival times for photons of light emitted by a light source of the first module, but to also detect arrival times for photons of light emitted by a light source of a second module. 
     For example, with reference to modular assembly  800  of  FIG.  8   , detector  806 - 3  is located on a side of module  802 - 1  that is adjacent to module  802 - 2 . As such, detector  806 - 3  of module  802 - 1  may be configured to detect photons of light emitted by the light source of module  802 - 1  and photons of light emitted by the light source of module  802 - 2 . Likewise, detector  810  of module  802 - 2  may be configured to detect photons of light emitted by the light source  804 - 2  of module  802 - 2  and photons of light emitted by the light source of module  802 - 1 . Other detectors (e.g., detectors  806 - 1 ,  806 - 2 , and  806 - 4  through  806 - 6 ) may be too far from the light source  804 - 2  of module  802 - 2  to detect photons of light emitted by the light source  804 - 2  of module  802 - 2 . 
     Such physical positioning of neighboring modules may result in the same light source being included in more than one S-D pair, thereby providing a relatively high effective spatial resolution. For example,  FIG.  15 A  illustrates an exemplary configuration  1500 - 1  in which a light source (labeled “S”) is included in two spatially overlapping S-D pairs. In particular, the light source is included in a first S-D pair with a first detector labeled “D 1 ” and a second S-D pair with a second detector labeled “D 2 ”. 
       FIG.  15 A  also illustrates a first optical path region (i.e., the region within solid banana path lines  1502 - 1  and  1502 - 2 ) associated with the first S-D pair and a second optical path region (i.e., the region within the dashed banana path lines  1504 - 1  and  1504 - 2 ) associated with the second S-D pair. The first optical path region represents possible spatially-dependent optical paths for photons between the light source S and the first detector D 1 . Likewise, the second optical path region represents possible spatially-dependent optical paths for photons between the light source S and the second detector D 2 . As shown, the first and second optical path regions partially overlap, thereby indicating that the first and second S-D pairs are spatially overlapping. 
       FIG.  15 B  shows an exemplary configuration  1500 - 2  in which a time-of-flight measurement technique is used by an optical measurement system that includes the light source S and detectors D 1  and D 2 . 
     In  FIG.  15 B , a first plurality of optical path regions (i.e., the regions between solid banana path lines  1506 - 1  through  1506 - 5 ) are associated with the first S-D pair. The first plurality of optical path regions represent possible time-dependent optical paths for photons between the light source S and the first detector D 1 . 
     Likewise, a second plurality of optical path regions (i.e., the regions between dashed banana path lines  1508 - 1  through  1508 - 4 ) are associated with the second S-D pair. The second plurality of optical path regions represent possible time-dependent optical paths for photons between the light source S and the second detector D 2 . As shown, the first and second plurality of optical path regions partially overlap, thereby indicating that the first and second S-D pairs are also temporally overlapping. 
     As illustrated by  FIGS.  15 A and  15 B , the optical measurement systems described herein provide both spatially and time dependent optical paths between a single light source and a plurality of detectors. In this manner, the optical measurement systems described herein may provide an effective spatial resolution that is relatively high even without a dedicated light source for every detector, as is found in conventional HD DOT systems. 
     In some examples, the optical measurement systems described herein may further include a processing unit configured to perform one or more operations based on arrival times detected by the detectors described herein. For example,  FIGS.  16 A- 16 B  show illustrative configurations  1600 - 1  and  1600 - 2  in accordance with the principles described herein. Each configuration  1600  includes the wearable assembly  702 , light sources  704  and detectors  706  described in connection with  FIG.  7   . In configuration  1600 - 1 , a processing unit  1602  is also included in wearable assembly  702 . In configuration  1600 - 2 , processing unit  1602  is not included in wearable assembly  702  (i.e., processing unit  1602  is located external to wearable assembly). Either configuration  1600 - 1  or  1600 - 2  may be used in accordance with the systems, circuits, and methods described herein. 
     Detectors  706  are configured to output signals representative of photon arrival times, as described herein. Processing unit  1602  is configured to receive the output signals and perform one or more operations based on the signals. For example, processing unit  1602  may generate one or more histograms based on the signals, as described herein. 
     As mentioned, in configuration  1600 - 2 , processing unit  1602  is not included in wearable assembly  702 . To illustrate, processing unit  1602  may be included in a wearable device separate from wearable assembly  702 . For example, processing unit  1602  may be included in a wearable device configured to be worn off the head while wearable assembly  702  is worn on the head. In these examples, one or more communication interfaces (e.g., cables, wireless interfaces, etc.) may be used to facilitate wearable assembly  702  and the separate wearable device. 
     Additionally or alternatively, in configuration  1600 - 2 , processing unit  1602  may be remote from the user (i.e., not worn by the user). For example, processing unit  1602  may be implemented by a stand-alone computing device communicatively coupled to wearable assembly  702  by way of one or more communication interfaces (e.g., cables, wireless interfaces, etc.). 
     Processing unit  1602  may be implemented by processor  108 , controller  112 , control circuit  204 , and/or any other suitable processing and/or computing device or circuit. 
     For example,  FIG.  17    illustrates an exemplary implementation of processing unit  1602  in which processing unit  1602  includes a memory  1702  and a processor  1704  configured to be selectively and communicatively coupled to one another. In some examples, memory  1702  and processor  1704  may be distributed between multiple devices and/or multiple locations as may serve a particular implementation. 
     Memory  1702  may be implemented by any suitable non-transitory computer-readable medium and/or non-transitory processor-readable medium, such as any combination of non-volatile storage media and/or volatile storage media. Exemplary non-volatile storage media include, but are not limited to, read-only memory, flash memory, a solid-state drive, a magnetic storage device (e.g., a hard drive), ferroelectric random-access memory (“RAM”), and an optical disc. Exemplary volatile storage media include, but are not limited to, RAM (e.g., dynamic RAM). 
     Memory  1702  may maintain (e.g., store) executable data used by processor  1704  to perform one or more of the operations described herein. For example, memory  1702  may store instructions  1706  that may be executed by processor  1704  to perform any of the operations described herein. Instructions  1706  may be implemented by any suitable application, program (e.g., sound processing program), software, code, and/or other executable data instance. Memory  1702  may also maintain any data received, generated, managed, used, and/or transmitted by processor  1704 . 
     Processor  1704  may be configured to perform (e.g., execute instructions  1706  stored in memory  1702  to perform) various operations described herein. For example, processor  1704  may be configured to perform any of the operations described herein as being performed by processing unit  1602 . 
       FIGS.  18 - 23    illustrate embodiments of a wearable device  1800  that includes elements of the optical detection systems described herein. In particular, the wearable devices  1800  shown in  FIGS.  18 - 23    include a plurality of modules  1802 , similar to any of the modules and module configurations described herein. For example, each module  1802  may include a light source and a plurality of detectors. The wearable devices  1800  may each also include a controller (e.g., controller  112 ) and a processor (e.g., processor  108 ) and/or be communicatively connected to a controller and processor. In general, wearable device  1800  may be implemented by any suitable headgear and/or clothing article configured to be worn by a user. The headgear and/or clothing article may include batteries, cables, and/or other peripherals for the components of the optical measurement systems described herein. 
       FIG.  18    illustrates an embodiment of a wearable device  1800  in the form of a helmet with a handle  1804 . A cable  1806  extends from the wearable device  1800  for attachment to a battery or hub (with components such as a processor or the like).  FIG.  19    illustrates another embodiment of a wearable device  1800  in the form of a helmet showing a back view.  FIG.  20    illustrates a third embodiment of a wearable device  1800  in the form of a helmet with the cable  1806  leading to a wearable garment  1808  (such as a vest or partial vest) that can include a battery or a hub. Alternatively or additionally, the wearable device  1800  can include a crest  1810  or other protrusion for placement of the hub or battery. 
       FIG.  21    illustrates another embodiment of a wearable device  1800  in the form of a cap with a wearable garment  1808  in the form of a scarf that may contain or conceal a cable, battery, and/or hub.  FIG.  22    illustrates additional embodiments of a wearable device  1800  in the form of a helmet with a one-piece scarf  1808  or two-piece scarf  1808 - 1 .  FIG.  23    illustrates an embodiment of a wearable device  1800  that includes a hood  1810  and a beanie  1812  which contains the modules  1802 , as well as a wearable garment  1808  that may contain a battery or hub. 
     In some examples, a non-transitory computer-readable medium storing computer-readable instructions may be provided in accordance with the principles described herein. The instructions, when executed by a processor of a computing device, may direct the processor and/or computing device to perform one or more operations, including one or more of the operations described herein. Such instructions may be stored and/or transmitted using any of a variety of known computer-readable media. 
     A non-transitory computer-readable medium as referred to herein may include any non-transitory storage medium that participates in providing data (e.g., instructions) that may be read and/or executed by a computing device (e.g., by a processor of a computing device). For example, a non-transitory computer-readable medium may include, but is not limited to, any combination of non-volatile storage media and/or volatile storage media. Exemplary non-volatile storage media include, but are not limited to, read-only memory, flash memory, a solid-state drive, a magnetic storage device (e.g. a hard disk, a floppy disk, magnetic tape, etc.), ferroelectric random-access memory (“RAM”), and an optical disc (e.g., a compact disc, a digital video disc, a Blu-ray disc, etc.). Exemplary volatile storage media include, but are not limited to, RAM (e.g., dynamic RAM). 
       FIG.  24    illustrates an exemplary computing device  2400  that may be specifically configured to perform one or more of the processes described herein. Any of the systems, units, computing devices, and/or other components described herein may be implemented by computing device  2400 . 
     As shown in  FIG.  24   , computing device  2400  may include a communication interface  2402 , a processor  2404 , a storage device  2406 , and an input/output (“I/O”) module  2408  communicatively connected one to another via a communication infrastructure  2410 . While an exemplary computing device  2400  is shown in  FIG.  24   , the components illustrated in  FIG.  24    are not intended to be limiting. Additional or alternative components may be used in other embodiments. Components of computing device  2400  shown in  FIG.  24    will now be described in additional detail. 
     Communication interface  2402  may be configured to communicate with one or more computing devices. Examples of communication interface  2402  include, without limitation, a wired network interface (such as a network interface card), a wireless network interface (such as a wireless network interface card), a modem, an audio/video connection, and any other suitable interface. 
     Processor  2404  generally represents any type or form of processing unit capable of processing data and/or interpreting, executing, and/or directing execution of one or more of the instructions, processes, and/or operations described herein. Processor  2404  may perform operations by executing computer-executable instructions  2412  (e.g., an application, software, code, and/or other executable data instance) stored in storage device  2406 . 
     Storage device  2406  may include one or more data storage media, devices, or configurations and may employ any type, form, and combination of data storage media and/or device. For example, storage device  2406  may include, but is not limited to, any combination of the non-volatile media and/or volatile media described herein. Electronic data, including data described herein, may be temporarily and/or permanently stored in storage device  2406 . For example, data representative of computer-executable instructions  2412  configured to direct processor  2404  to perform any of the operations described herein may be stored within storage device  2406 . In some examples, data may be arranged in one or more databases residing within storage device  2406 . 
     I/O module  2408  may include one or more I/O modules configured to receive user input and provide user output. I/O module  2408  may include any hardware, firmware, software, or combination thereof supportive of input and output capabilities. For example, I/O module  2408  may include hardware and/or software for capturing user input, including, but not limited to, a keyboard or keypad, a touchscreen component (e.g., touchscreen display), a receiver (e.g., an RF or infrared receiver), motion sensors, and/or one or more input buttons. 
     I/O module  2408  may include one or more devices for presenting output to a user, including, but not limited to, a graphics engine, a display (e.g., a display screen), one or more output drivers (e.g., display drivers), one or more audio speakers, and one or more audio drivers. In certain embodiments, I/O module  2408  is configured to provide graphical data to a display for presentation to a user. The graphical data may be representative of one or more graphical user interfaces and/or any other graphical content as may serve a particular implementation. 
     An illustrative optical measurement system may include a wearable assembly configured to be worn by a user and comprising a plurality of light sources each configured to emit light directed at a target and a plurality of detectors configured to detect arrival times for photons of the light after the light is scattered by the target, wherein a ratio of a total number of the detectors to a total number of the light sources is at least two to one. 
     An illustrative optical measurement system may include a headgear configured to be worn on a head of a user and having a plurality of slots; a first module configured to be located in a first slot of the plurality of slots and comprising a first light source configured to emit light directed at a target within the head of the user and a first set of detectors configured to detect arrival times for photons of the light emitted by the first light source; and a second module configured to be located in a second slot of the plurality of slots and comprising a second light source configured to emit light directed at the target within the head of the user, and a second set of detectors configured to detect arrival times for photons of the light emitted by the second light source. A positioning of the first and second modules in the slots of the headgear may be configured to cause one or more detectors of the first set of detectors to also detect arrival times for the photons of the light emitted by the second light source and one or more detectors of the second set of detectors to detect arrival times for the photons of the light emitted by the first light source. 
     An illustrative optical measurement system may include a plurality of light sources each configured to emit light directed at a target, a plurality of detectors configured to detect arrival times for photons of the light after the light is scattered by the target, wherein a ratio of a total number of the detectors to a total number of the light sources is at least two to one, and a processing unit configured to perform an operation based on the detected arrival times. 
     In the preceding description, various exemplary embodiments have been described with reference to the accompanying drawings. It will, however, be evident that various modifications and changes may be made thereto, and additional embodiments may be implemented, without departing from the scope of the invention as set forth in the claims that follow. For example, certain features of one embodiment described herein may be combined with or substituted for features of another embodiment described herein. The description and drawings are accordingly to be regarded in an illustrative rather than a restrictive sense.