Patent Publication Number: US-2023138571-A1

Title: Techniques for enhanced detection of distant objects

Description:
RELATED APPLICATION 
     This application is a continuation of U.S. Pat. Application No. 17/495,665, filed on Oct. 6, 2021, the entire contents of which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to optical detection, and more particularly to systems and methods for using array waveguide receivers and optical frequency shifting in a frequency-modulated continuous wave (FMCW) light detection and ranging (LIDAR) system to enhance detection of distant objects. 
     BACKGROUND 
     A LIDAR system includes an optical scanner to transmit an FMCW infrared (IR) optical beam and to receive a return signal from reflections of the optical beam; an optical processing system coupled with the optical scanner to generate a baseband signal in the time domain from the return signal, where the baseband signal includes frequencies corresponding to LIDAR target ranges; and a signal processing system coupled with the optical processing system to measure energy of the baseband signal in the frequency domain, to compare the energy to an estimate of LIDAR system noise, and to determine a likelihood that a signal peak in the frequency domain indicates a detected target. 
     SUMMARY 
     One aspect disclosed herein is directed to a system of array waveguide receivers and optical frequency shifting in a frequency-modulated continuous wave (FMCW) light detection and ranging (LIDAR) system to enhance detection of distant objects. In some embodiments, the system includes one or more waveguides, responsive to a transmission of a plurality of optical beams towards at least one target, to receive a first returned reflection having a first lag angle, and generate a first waveguide signal based on the first returned reflection, receive a second returned reflection having a second lag angle different from the first lag angle, and generate a second waveguide signal based on the second returned reflection. In some embodiments, the system includes one or more photodetectors to: generate, based on the first waveguide signal and a first local oscillator (LO) signal, a first output signal within a first frequency range; and generate, based on the second waveguide signal and a second LO signal, a second output signal within a second frequency range. In some embodiments, the system includes an optical frequency shifter (OFS) to shift a frequency of the second LO signal to cause the second output signal to shift from within the second frequency range to within the first frequency range to generate a shifted signal. In some embodiments, the system includes a processor, coupled to memory, to receive the shifted signal to produce one or more points in a point set. 
     In another aspect, the present disclosure is directed to a method for using array waveguide receivers and optical frequency shifting in an FMCW LIDAR system to enhance detection of distant objects. In some embodiments, the method includes receiving, responsive to a transmission of a plurality of optical beams into an environment, a first returned optical beam having a first lag angle. In some embodiments, the method includes generating a first waveguide signal based on the first returned optical beam. In some embodiments, the method includes receiving, responsive to the transmission of a plurality of optical beams into an environment, a second returned optical beam having a second lag angle. In some embodiments, the method includes generating a second waveguide signal based on the second returned optical beam. In some embodiments, the method includes generating, based on the first waveguide signal and a first local oscillator (LO) signal, a first output signal within a first frequency range. In some embodiments, the method includes generating, based on the second waveguide signal and a second LO signal, a second output signal within a second frequency range. In some embodiments, the method includes shifting a frequency of the second LO signal to cause the second output signal to shift from within the second frequency range to within the first frequency range to generate a shifted signal. In some embodiments, the method includes receiving the shifted signal to produce one or more points in a point set. 
     In another aspect, the present disclosure is directed to a system of array waveguide receivers and optical frequency shifting in a frequency-modulated continuous wave (FMCW) light detection and ranging (LIDAR) system to enhance detection of distant objects. In some embodiments, the system includes one or more waveguides, responsive to a transmission of a plurality of optical beams towards at least one target, to receive a first returned reflection to generate a first waveguide signal and receive a second returned reflection to generate a second waveguide signal. In some embodiments, the system includes one or more photodetectors to generate, based on the first waveguide signal and a first local oscillator (LO) signal, a first output signal within a first frequency range, and generate, based on the second waveguide signal and a second LO signal, a second output signal within a second frequency range. In some embodiments, the second frequency range is different from the first frequency range. In some embodiments, the system includes an optical frequency shifter (OFS) to shift a frequency of the second LO signal to cause the second output signal to shift from within the second frequency range to within the first frequency range to generate a shifted signal for receipt by a first analog-to-digital converter (ADC) from a plurality of different ADCs. In some embodiments, the first ADC is configured to process one or more signals within the first frequency range. 
     These and other features, aspects, and advantages of the present disclosure will be apparent from a reading of the following detailed description together with the accompanying figures, which are briefly described below. The present disclosure includes any combination of two, three, four or more features or elements set forth in this disclosure, regardless of whether such features or elements are expressly combined or otherwise recited in a specific example implementation described herein. This disclosure is intended to be read holistically such that any separable features or elements of the disclosure, in any of its aspects and example implementations, should be viewed as combinable unless the context of the disclosure clearly dictates otherwise. 
     It will therefore be appreciated that this summary is provided merely for purposes of summarizing some example implementations so as to provide a basic understanding of some aspects of the disclosure. Accordingly, it will be appreciated that the above described example implementations are merely examples and should not be construed to narrow the scope or spirit of the disclosure in any way. Other example implementations, aspects, and advantages will become apparent from the following detailed description taken in conjunction with the accompanying figures which illustrate, by way of example, the principles of some described example implementations. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURE(S) 
       Embodiments and implementations of the present disclosure will be understood more fully from the detailed description given below and from the accompanying drawings of various aspects and implementations of the disclosure, which, however, should not be taken to limit the disclosure to the specific embodiments or implementations, but are for explanation and understanding only. 
         FIG.  1    is a block diagram illustrating an example of a LIDAR system, according to some embodiments; 
         FIG.  2    is a time-frequency diagram illustrating an example of an FMCW scanning signal that can be used by a LIDAR system to scan a target environment, according to some embodiments; 
         FIG.  3    is a block diagram illustrating an example environment for using array waveguide receivers (AWRs) in the LIDAR system  100  in  FIG.  1    to enhance detection of distant objects, according to some embodiments; 
         FIG.  4    is a block diagram illustrating an example environment for using AWRs and optical frequency shifters (OFS) in the LIDAR system  100  in  FIG.  1    to enhance detection of distant objects, according to some embodiments; 
         FIG.  5    is a series of graphs illustrating the effect of frequency remapping/shifting of the LO using OFSs in the LIDAR system  100  in  FIG.  1    to enhance detection of distant objects, according to some embodiments; 
         FIG.  6    is a block diagram illustrating an example environment for using AWRs and OFSs, and additionally, polarization splitter-rotator (PSRs) and/or variable optical attenuators (VOAs) in the LIDAR system  100  to enhance detection of distant objects, according to some embodiments; and 
         FIG.  7    is a flow diagram illustrating an example method for using array waveguide receivers and optical frequency shifting in an FMCW LIDAR system to enhance detection of distant objects, according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     According to some embodiments, the described LIDAR system using an array waveguide receiver and optical frequency shifting (AWR/OFS) may be implemented in a variety of sensing and detection applications, such as, but not limited to, automotive, communications, consumer electronics, and healthcare markets. According to some embodiments, the described LIDAR system using AWR/OFS may be implemented as part of a front-end of frequency modulated continuous-wave (FMCW) device that assists with spatial awareness for automated driver assist systems, or self-driving vehicles. According to some embodiments, the AWR/OFS configuration may be agnostic to specific optical scanning architecture and can be tailored to enhance scanning LIDAR performance for a desired target range and/or to increase frame rate for a given range on the fly. 
     In a coherent LIDAR system, a frequency-modulated continuous wave (FMCW) transmitted light source (Tx) is used to determine the distance and velocity of objects in the scene by mixing a copy of the Tx source, known as the local oscillator (LO), with the received light (Rx) from the scene. The LO and Rx paths are combined on a fast photodiode (e.g., a photodetector), producing beat frequencies, proportional to object distance, which are processed electronically to reveal distance and velocity information of objects in the scene. To generate a point-cloud image, scanning optics are commonly used to deflect the Tx beam (e.g., signal) through the system field of view (FOV), comprising azimuth and zenith angles. In many applications, it is desirable to simultaneously achieve the highest possible scan rate and a large signal-to-noise ratio (SNR), as these two parameters directly affect the frame-rate of the LIDAR system, its maximum range (e.g., distance), range and velocity resolution, and the lateral spatial resolution. 
     However, increasing the scan rate produces a larger lag angle between the Rx light from a given object and the receive aperture (e.g., a lens) of the system. This lag angle effect creates a descan problem, where the Rx signals from distant objects are returned outside of the receive aperture, which reduces the SNR, as well as, limits the achievable scan/frame rate and maximum range of a scanning LIDAR systems. Furthermore, the detection of objects at large range produces large beat frequencies. Therefore, detecting distant objects with high fidelity requires the use of analog-to-digital convertors (ADCs) with very large sampling rates, approaching Giga-samples per second (Gsps), which consume a large amount of power. 
     Accordingly, the present disclosure addresses the above-noted and other deficiencies by disclosing systems and methods for using array waveguide receivers and optical frequency shifting in a frequency-modulated continuous wave (FMCW) light detection and ranging (LIDAR) system. As described in the below passages with respect to one or more embodiments, a LIDAR system may include an array waveguide receiver (AWR) and one or more optical frequency shifters (OFS) into a single device architecture, such as a photonic integrated circuit (PIC). The AWR includes a main optical axis waveguide and one or more displaced satellite waveguides for collecting Rx power from distant objects that would otherwise be lost due to the descan lag angle, which is proportional to scan rate and target distance. Frequency shifted local oscillator (LO) signals are combined with the Rx signals on the satellite waveguides to remap (e.g., down-convert, shift, adjust) the target beat frequencies to the radio frequency (RF) baseband. The combined effect is that the SNR (e.g., SNR ∝ P LO P Rx /BW ADC ) of the LIDAR system can be drastically improved while concurrently reducing the ADC bandwidth and/or sampling requirements, and thus reducing the electrical power dissipation in the system. 
     The present disclosure includes several powerful and distinct techniques into a single device architecture (e.g., a PIC), which provides significant potential enhancements to maximum LIDAR range, velocity resolution, and framerate. The AWR and/or OFS subcomponents of the LIDAR system can be optimized to tailor these performance enhancements to different applications (e.g., long-range versus short-range detection). 
     Furthermore, the present disclosure introduces a new approach to improving range by binning (e.g., shifting, remapping) target ranges into a desired detection bandwidth. Enabled by an OFS configuration, binning the scene along the optical axis is unique to the disclosed system compared to conventional LIDAR systems. 
       FIG.  1    is a block diagram illustrating an example of a LIDAR system, according to some embodiments. The LIDAR system  100  includes one or more of each of a number of components, but may include fewer or additional components than shown in  FIG.  1   . One or more of the components depicted in  FIG.  1    can be implemented on a photonics chip, according to some embodiments. The optical circuits  101  may include a combination of active optical components and passive optical components. Active optical components may generate, amplify, and/or detect optical signals and the like. In some examples, the active optical component includes optical beams at different wavelengths, and includes one or more optical amplifiers, one or more optical detectors, or the like. In some embodiments, one or more LIDAR systems  100  may be mounted onto any area (e.g., front, back, side, top, bottom, and/or underneath) of a vehicle to facilitate the detection of an object in any free space relative to the vehicle. In some embodiments, the vehicle may include a steering system and a braking system, each of which may work in combination with one or more LIDAR systems  100  according to any information (e.g., distance/ranging information, Doppler information, etc.) acquired and/or available to the LIDAR system  100 . In some embodiments, the vehicle may include a vehicle controller that includes the one or more components and/or processors of the LIDAR system  100 . 
     Free space optics  115  may include one or more optical waveguides to carry optical signals, and route and manipulate optical signals to appropriate input / output ports of the active optical circuit. In embodiments, the one or more optical waveguides may include one or more graded index waveguides, as will be described in additional detail below at  FIGS.  3 - 6   . The free space optics  115  may also include one or more optical components such as taps, wavelength division multiplexers (WDM), splitters/combiners, polarization beam splitters (PBS), collimators, couplers or the like. In some examples, the free space optics  115  may include components to transform the polarization state and direct received polarized light to optical detectors using a PBS, for example. The free space optics  115  may further include a diffractive element to deflect optical beams having different frequencies at different angles along an axis (e.g., a fast-axis). 
     In some examples, the LIDAR system  100  includes an optical scanner  102  that includes one or more scanning mirrors that are rotatable along an axis (e.g., a slow-axis) that is orthogonal or substantially orthogonal to the fast-axis of the diffractive element to steer optical signals to scan an environment according to a scanning pattern. For instance, the scanning mirrors may be rotatable by one or more galvanometers. Objects in the target environment may scatter an incident light into a return optical beam or a target return signal. The optical scanner  102  also collects the return optical beam or the target return signal, which may be returned to the passive optical circuit component of the optical circuits  101 . For example, the return optical beam may be directed to an optical detector by a polarization beam splitter. In addition to the mirrors and galvanometers, the optical scanner  102  may include components such as a quarter-wave plate, lens, anti-reflective coated window or the like. 
     To control and support the optical circuits  101  and optical scanner  102 , the LIDAR system  100  includes LIDAR control systems  110 . The LIDAR control systems  110  may include a processing device for the LIDAR system  100 . In some examples, the processing device may be one or more general-purpose processing devices such as a microprocessor, central processing unit, or the like. More particularly, the processing device may be complex instruction set computing (CISC) microprocessor, reduced instruction set computer (RISC) microprocessor, very long instruction word (VLIW) microprocessor, or processor implementing other instruction sets, or processors implementing a combination of instruction sets. The processing device may also be one or more special-purpose processing devices such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), network processor, or the like. 
     In some examples, the LIDAR control system  110  may include a processing device that may be implemented with a DSP, such as signal processing unit  112 . The LIDAR control systems  110  are configured to output digital control signals to control optical drivers  103 . In some examples, the digital control signals may be converted to analog signals through signal conversion unit  106 . For example, the signal conversion unit  106  may include a digital-to-analog converter. The optical drivers  103  may then provide drive signals to active optical components of optical circuits  101  to drive optical sources such as lasers and amplifiers. In some examples, several optical drivers  103  and signal conversion units  106  may be provided to drive multiple optical sources. 
     The LIDAR control systems  110  are also configured to output digital control signals for the optical scanner  102 . A motion control system  105  may control the galvanometers of the optical scanner  102  based on control signals received from the LIDAR control systems  110 . For example, a digital-to-analog converter may convert coordinate routing information from the LIDAR control systems  110  to signals interpretable by the galvanometers in the optical scanner  102 . In some examples, a motion control system  105  may also return information to the LIDAR control systems  110  about the position or operation of components of the optical scanner  102 . For example, an analog-to-digital converter may in turn convert information about the galvanometers’ position to a signal interpretable by the LIDAR control systems  110 . 
     The LIDAR control systems  110  are further configured to analyze incoming digital signals. In this regard, the LIDAR system  100  includes optical receivers  104  to measure one or more beams received by optical circuits  101 . For example, a reference beam receiver may measure the amplitude of a reference beam from the active optical component, and an analog-to-digital converter converts signals from the reference receiver to signals interpretable by the LIDAR control systems  110 . Target receivers measure the optical signal that carries information about the range and velocity of a target in the form of a beat frequency, modulated optical signal. The reflected beam may be mixed with a second signal from a local oscillator. The optical receivers  104  may include a high-speed analog-to-digital converter to convert signals from the target receiver to signals interpretable by the LIDAR control systems  110 . In some examples, the signals from the optical receivers  104  may be subject to signal conditioning by signal conditioning unit  107  prior to receipt by the LIDAR control systems  110 . For example, the signals from the optical receivers  104  may be provided to an operational amplifier for amplification of the received signals and the amplified signals may be provided to the LIDAR control systems  110 . 
     In some applications, the LIDAR system  100  may additionally include one or more imaging devices  108  configured to capture images of the environment, a global positioning system  109  configured to provide a geographic location of the system, or other sensor inputs. The LIDAR system  100  may also include an image processing system  114 . The image processing system  114  can be configured to receive the images and geographic location, and send the images and location or information related thereto to the LIDAR control systems  110  or other systems connected to the LIDAR system  100 . 
     In operation according to some examples, the LIDAR system  100  is configured to use nondegenerate optical sources to simultaneously measure range and velocity across two dimensions. This capability allows for real-time, long range measurements of range, velocity, azimuth, and elevation of the surrounding environment. 
     In some examples, the scanning process begins with the optical drivers  103  and LIDAR control systems  110 . The LIDAR control systems  110  instruct, e.g., via signal processing unit  112 , the optical drivers  103  to independently modulate one or more optical beams, and these modulated signals propagate through the optical circuits  101  to the free space optics  115 . The free space optics  115  directs the light at the optical scanner  102  that scans a target environment over a preprogrammed pattern defined by the motion control system  105 . The optical circuits  101  may also include a polarization wave plate (PWP) to transform the polarization of the light as it leaves the optical circuits  101 . In some examples, the polarization wave plate may be a quarter-wave plate or a half-wave plate. A portion of the polarized light may also be reflected back to the optical circuits  101 . For example, lensing or collimating systems used in LIDAR system  100  may have natural reflective properties or a reflective coating to reflect a portion of the light back to the optical circuits  101 . 
     Optical signals reflected back from an environment pass through the optical circuits  101  to the optical receivers  104 . Because the polarization of the light has been transformed, it may be reflected by a polarization beam splitter along with the portion of polarized light that was reflected back to the optical circuits  101 . In such scenarios, rather than returning to the same fiber or waveguide serving as an optical source, the reflected signals can be reflected to separate optical receivers  104 . These signals interfere with one another and generate a combined signal. The combined signal can then be reflected to the optical receivers  104 . Also, each beam signal that returns from the target environment may produce a time-shifted waveform. The temporal phase difference between the two waveforms generates a beat frequency measured on the optical receivers  104  (e.g., photodetectors). 
     The analog signals from the optical receivers  104  are converted to digital signals by the signal conditioning unit  107 . These digital signals are then sent to the LIDAR control systems  110 . A signal processing unit  112  may then receive the digital signals to further process and interpret them. In some embodiments, the signal processing unit  112  also receives position data from the motion control system  105  and galvanometers (not shown) as well as image data from the image processing system  114 . The signal processing unit  112  can then generate 3D point cloud data (sometimes referred to as, “a LIDAR point cloud”) that includes information about range and/or velocity points in the target environment as the optical scanner  102  scans additional points. In some embodiments, a LIDAR point cloud may correspond to any other type of ranging sensor that is capable of Doppler measurements, such as Radio Detection and Ranging (RADAR). The signal processing unit  112  can also overlay 3D point cloud data with image data to determine velocity and/or distance of objects in the surrounding area. The signal processing unit  112  also processes the satellite-based navigation location data to provide data related to a specific global location. 
       FIG.  2    is a time-frequency diagram illustrating an example of an FMCW scanning signal that can be used by a LIDAR system to scan a target environment, according to some embodiments. In one example, the scanning waveform  201 , labeled as f FM (t), is a sawtooth waveform (sawtooth “chirp”) with a chirp bandwidth Δfc and a chirp period Tc. The slope of the sawtooth is given as k = Δfc/Tc).  FIG.  2    also depicts target return signal  202  according to some embodiments. Target return signal  202 , labeled as f FM (t-Δt), is a time-delayed version of the scanning waveform  201 , where Δt is the round trip time to and from a target illuminated by scanning waveform  201 . The round trip time is given as Δt = 2R/v, where R is the target range and v is the velocity of the optical beam, which is the speed of light c. The target range, R, can therefore be calculated as R = c(Δt/2). When the return signal  202  is optically mixed with the scanning signal, a range-dependent difference frequency (“beat frequency”) Δf R (t) is generated. The beat frequency Δf R (t) is linearly related to the time delay Δt by the slope of the sawtooth k. That is, Δf R (t) = kΔt. Since the target range R is proportional to Δt, the target range R can be calculated as R = (c/2)(Δf R (t)/k). That is, the range R is linearly related to the beat frequency Δf R (t). The beat frequency Δf R (t) can be generated, for example, as an analog signal in optical receivers  104  of system  100 . The beat frequency can then be digitized by an analog-to-digital converter (ADC), for example, in a signal conditioning unit such as signal conditioning unit  107  in LIDAR system  100 . The digitized beat frequency signal can then be digitally processed, for example, in a signal processing unit, such as signal processing unit  112  in system  100 . It should be noted that the target return signal  202  will, in general, also includes a frequency offset (Doppler shift) if the target has a velocity relative to the LIDAR system  100 . The Doppler shift can be determined separately, and used to correct (e.g., adjust, modify) the frequency of the return signal, so the Doppler shift is not shown in  FIG.  2    for simplicity and ease of explanation. For example, LIDAR system  100  may correct the frequency of the return signal by removing (e.g., subtracting, filtering) the Doppler shift from the frequency of the returned signal to generate a corrected return signal. The LIDAR system  100  may then use the corrected return signal to calculate a distance and/or range between the LIDAR system  100  and the object. In some embodiments, the Doppler frequency shift of target return signal  202  that is associated with an object may be indicative of a velocity and/or movement direction of the object relative to the LIDAR system  100 . 
     It should also be noted that the sampling frequency of the ADC will determine the highest beat frequency that can be processed by the system without aliasing. In general, the highest frequency that can be processed is one-half of the sampling frequency (i.e., the “Nyquist limit”). In one example, and without limitation, if the sampling frequency of the ADC is 1 gigahertz, then the highest beat frequency that can be processed without aliasing (Δf Rmax ) is 500 megahertz. This limit in turn determines the maximum range of the system as R max  = (c/2)(Δf Rmax /k) which can be adjusted by changing the chirp slope k. In one example, while the data samples from the ADC may be continuous, the subsequent digital processing described below may be partitioned into “time segments” that can be associated with some periodicity in the LIDAR system  100 . In one example, and without limitation, a time segment might correspond to a predetermined number of chirp periods T, or a number of full rotations in azimuth by the optical scanner. 
       FIG.  3    is a block diagram illustrating an example environment for using AWRs in the LIDAR system  100  in  FIG.  1    to enhance detection of distant objects, according to some embodiments. The environment  300  includes the optical scanner  102  (e.g., a prism, a mirror), a lens (sometimes referred to as, “optical element”), and an array waveguide receiver (AWR) that is fabricated on a photonic integrated circuit (PIC)  350 . In some embodiments, any of the components (e.g., lens  320 , PIC  350  with AWRs, etc.) in the environment  300  may be added as a component of the LIDAR system  100  in  FIG.  1   , or be used to replace or modify any of the one or more components (e.g., free space optics  115 , optical circuits, optical receivers  104 , etc.) of the LIDAR system  100 . 
     The environment  300  includes one or more objects, such as object  308   a  (e.g., a street sign), object  308   b  (e.g., a tree), and object  308   c  (e.g., a pedestrian); each collectively referred to as objects  308 . Although  FIG.  3    shows only a select number of objects  308 , the environment  300  may include any number of objects  308  of any type (e.g., pedestrians, vehicles, street signs, raindrops, snow, street surface) that are within a short distance (e.g., 30 meters) or a long distance (e.g., 300 meters, 500 meters and beyond) from the optical scanner  102 . In some embodiments, an object  308  may be stationary or moving with respect to the optical scanner  102 . 
     In some embodiments, the optical scanner  102  is configured to receive one or more optical beams  304  from an optical beam source (not shown in  FIG.  3   ). In some embodiments, the optical scanner  102  is configured to redirect (e.g., steer, transmit, scatter) the one or more optical beams  304  into free space toward the one or more objects  308 , which causes the one or more optical beams to scatter into returned optical beams  306   a ,  306   b ,  306   c  (collectively referred to as, “returned optical beams  306 ”). For example, the one or more optical beams  304  scatter against the object  308   a  to create a returned optical beam  306   a , which is returned to the LIDAR system  100 . As another example, the one or more optical beams  304  scatter against the object  308   b  to create a returned optical beam  306   b , which is returned to the LIDAR system  100 . As another example, the one or more optical beams  304  scatter against the object  308   c  to create a returned optical beam  306   c , which is returned to the LIDAR system  100 . 
     The environment  300  includes a lens  320  (sometimes referred to as, “an optical element”) for collecting (e.g., receiving, acquiring, aggregating) the returned optical beams  306  that scatter from the one or more objects  308  in response to the optical scanner  102  redirecting the one or more optical beams  304  into free space. In some embodiments, the lens  320  may be a symmetric lens having a diameter. In some embodiments, the lens  320  may be an asymmetric lens. 
     As shown in  FIG.  3   , the lag angle between a respective returned optical beam  306  and the lens  320  is indicated by θ DS,n , where n is an integer. For example, the lag angle between the returned optical beam  306   a  and the lens  320  is indicated by θ DS,0  (not shown in  FIG.  3   ), the lag angle between the returned optical beam  306   b  and the lens  320  is indicated by θ DS,1 , and the lag angle between the returned optical beam  306   c  and the lens  320  is indicated by θ DS,2  (shown in  FIG.  3    as, θ DS,n )- In some embodiments, increasing the scan rate of the optical scanner  102  produces a larger lag angle between one or more of the returned optical beams  306 . 
     As shown in  FIG.  3   , the PIC  350  includes a set (e.g., one or more) of waveguides. The set of waveguides may include a primary on-axis waveguide (shown in  FIG.  3    as, WG 0 ) and off-axis satellite waveguides (shown in  FIG.  3    as, WG S,n ), which are positioned at a location in the PIC  350 , for example, as expressed by the following Equation: 
     
       
         
           
             
               x 
               n 
             
               
             = 
             n 
             ⋅ 
             
               p 
               
                 W 
                 G 
                 s 
               
             
           
         
       
     
      where: n is the waveguide number; and p WGs  is the designed pitch. In some embodiments, other than being positioned at unique locations in the PIC  350 , a primary waveguide and a satellite waveguide may be the same type of waveguide. 
     As shown in  FIG.  3   , PIC  350  includes waveguide (WG)  352   a  that is configured as the primary on-axis waveguide for receiving the return optical beam  306   a  via the lens  320  responsive to the optical scanner  102  transmitting the one or more optical beams  304  into free space. The PIC  350  (sometimes referred to as, “an optical receiver”) includes waveguide (WG)  352   b  that is configured as an off-axis satellite waveguide for receiving the return optical beam  306   b  via the lens  320  responsive to the optical scanner  102  transmitting the one or more optical beams  304  into free space. The PIC  350  includes waveguide (WG)  352   c  that is configured as an off-axis satellite waveguide for receiving the return optical beam  306   c  via the lens  320  responsive to the optical scanner  102  transmitting the one or more optical beams  304  into free space. 
     Thus, a satellite waveguide may be configured (e.g., positioned, arranged, constructed) to serve as an additional Rx channel to collect a returned optical beam  306  (e.g., scattered light) that is received at a particular lag angle, for example, as expressed in the following Equation: 
     
       
         
           
             
               θ 
               
                 D 
                 S 
               
             
             = 
             
               
                 2 
                 R 
               
               / 
               
                 c 
                 ⋅ 
                   
                 
                   θ 
                   ˙ 
                 
               
             
           
         
       
     
      where: R is the target distance, c is the speed of light, and  
     
       
         
           
             θ 
             ˙ 
           
         
       
     
      is the azimuthal scan rate. In other words, one or more satellite waveguides may be positioned throughout the PIC  350  to allow a LIDAR system (e.g., LIDAR system  100 ) to receive returned optical beams  306  at increasing (e.g., large) values of lag angle. 
     In some embodiments, the returned optical beams  306  may have large lag angles that would otherwise be lost from the primary on-axis waveguide (WG 0 ) channel due to the finite size of the diameter of the lens  320  and/or the focal spot and de-scanned position of the returned optical beams  306 , for example, as expressed in the following Equation: 
     
       
         
           
             
               x 
               
                 D 
                 S 
               
             
             = 
             
               θ 
               
                 D 
                 S 
               
             
             ⋅ 
             
               f 
               
                 R 
                 x 
               
             
           
         
       
     
      where f Rx  is the focal length of the lens  320 . 
     Although not shown in  FIG.  3   , the PIC  350  couples to the LIDAR control system  110  in  FIG.  1    such to be able to pass any of the optical beams that are received by any of the WGs  352  to the LIDAR control system  110  for processing by the signal processing unit  112 . 
       FIG.  4    is a block diagram illustrating an example environment for using AWRs and optical frequency shifters (OFS) in the LIDAR system  100  in  FIG.  1    to enhance detection of distant objects, according to some embodiments. The environment  400  includes the optical scanner  102 , a polarizing beam splitter (PBS)  414 , a quarter-wave plate (QWP)  416 , a lens  420 , an FMCW laser  440 , a fiber splitter  442  (e.g., a 1x2 fiber splitter), a polarization controller  444 , a collimator  446 , an optical fiber array  446 , and a PIC  450 . The environment  400  includes transimpedance amplifiers  470   a ,  470   b ,  470   c  (collectively referred to as, “TIAs 470”). The environment  400  includes ADCs  480   a ,  480   b ,  480   c  (collectively referred to as, ADCs  480 ) and a multiplexer (shown in  FIG.  4    as, “MUX 490”). 
     The PIC  450  (sometimes referred to as, “an optical receiver”) includes waveguide (WG)  452   a  that is configured as the primary on-axis waveguide for receiving the return optical beam  406   a  from the PBS  414  via the lens  420  responsive to the optical scanner  102  transmitting the one or more collimated optical beams  404  into free space. The PIC  450  includes waveguide (WG)  452   b  that is configured as an off-axis satellite waveguide for receiving the return optical beam  406   b  from the PBS  414  via the lens  420  responsive to the optical scanner  102  transmitting the one or more collimated optical beams  404  into free space. The PIC  450  includes waveguide (WG)  452   c  that is configured as an off-axis satellite waveguide for receiving the return optical beam  406   c  from the PBS  414  via the lens  420  responsive to the optical scanner  102  transmitting the one or more collimated optical beams  404  into free space. Although  FIG.  4    shows that the PIC  450  includes only a select number of satellite waveguides (e.g., WG  452   a , WG  452   b , WG  452   a ), the PIC  450  may include any number of satellite waveguides to depending on desired performance and application. 
     The PIC  450  includes optical frequency shifters (OFS)  452 ,  454 . The PIC  450  includes balanced photodiodes (PD)  460   a ,  460   b ,  460   c  (collectively referred to as, “PDs  460 ”). In some embodiments, the OFSs  453 ,  454  may be implemented using a variety of PIC architectures including a serrodyne Mach-Zehnder interferometer, a single-sideband modulator, an in-phase/quadrature (I/Q) optical modulator, or adaptations thereof. 
     In some embodiments, any of the components (e.g., PIC  450 , fiber splitter  442 , etc.) in the environment  400  may be added as a component of the LIDAR system  100  in  FIG.  1   , or be used to replace or modify any of the one or more components (e.g., free space optics  115 , optical circuits, optical receivers  104 , etc.) of the LIDAR system  100 . 
     The environment  400  includes one or more objects, such as object  408   a  (e.g., a street sign), object  408   b  (e.g., a tree), and object  408   c  (e.g., a pedestrian); each collectively referred to as objects  408 . Although  FIG.  4    shows only a select number of objects  408 , the environment  400  may include any number of objects  408  of any type that are within a short distance (e.g., 30 meters) or a long distance (e.g., 300 meters, 500 meters and beyond) from the optical scanner  102 . In some embodiments, an object  408  may be stationary or moving with respect to the optical scanner  102 . 
     An output terminal of the FMCW laser  440  is coupled to an input terminal of the fiber splitter  442 . A first output terminal of the fiber splitter  442  is coupled to an input terminal of the collimator  446  and a second output terminal of the fiber splitter  442  is coupled to an input terminal of the polarization controller  444 . The output terminal of the polarization controller  444  is coupled to an input terminal of the optical fiber array  446 . A first output terminal of the optical fiber array  446  is coupled to an input terminal of the OFS  453 , whose output terminal is coupled to a second input terminal of the PD  460   c . A second output terminal of the optical fiber array  446  is coupled to an input terminal of the OFS  454 , whose output terminal is coupled to a second input terminal of the PD  460   b . A third output terminal of the optical fiber array  446  is coupled to a second input terminal of the PD  460   a . 
     An output terminal of the WG  452   c  is coupled to a first input terminal of the PD  460   c . An output terminal of the WG  452   b  is coupled to a first input terminal of the PD  460   b . An output terminal of the WG  452   a  is coupled to a first input terminal of the PD  460   a . 
     An output terminal of the PD  460   c  is coupled to an input terminal of the TIA  470   c , whose output terminal is coupled to an input terminal of the ADC  480   c , whose output terminal is coupled to a first input terminal of the MUX  490 . An output terminal of the PD  460   b  is coupled to an input terminal of the TIA  470   b , whose output terminal is coupled to an input terminal of the ADC  480   b , whose output terminal is coupled to a first input terminal of the MUX  490 . An output terminal of the PD  460   a  is coupled to an input terminal of the TIA  470   a , whose output terminal is coupled to an input terminal of the ADC  480   a , whose output terminal is coupled to a first input terminal of the MUX  490 . 
     In some embodiments, the FMCW laser  440  is configured to generate and transmit an optical beam (e.g., light) to the fiber splitter  442 , which is configured to split (e.g., divide, duplicate) the optical beam into a split optical beam to propagate along a Tx path and an LO signal (sometimes referred to as, “an LO beam”) to propagate along an LO path. In some embodiments, the collimator  446  is configured to generate a collimated optical beam  404  using the split optical beam and the PBS  414  is configured to redirect the collimated optical beam  404  onto a main Tx/Rx path. In some embodiments, the QWP  416  is configured to convert the collimated optical beam  404  - which is linearly polarized light - into circularly polarized light, which is then directed to free space (e.g., the scene) via the optical scanner  102 . 
     In some embodiments, Rx signals (e.g., return optical beam  406   a , return optical beam  406   b , return optical beam  406   c ) are generated by the objects (e.g., objects  408   a ,  408   b ,  408   c ) in the scene and returned to the LIDAR system  100  with opposite circular polarization and an inherent θ DS  according to Equation. (2). In some embodiments, the QWP  416  is configured to convert each of the Rx beams to a linear polarization which passes through the PBS  414  and is focused onto a respective waveguide (e.g., WG  452   a , WG  452   b , WG  452   c ) using the lens  420 . In some embodiments, light from the LO path of the fiber splitter  442  passes through a polarization controller  444  and is coupled onto separate LO paths on the PIC  450  using the optical fiber array  446 . 
     In some embodiments, each satellite LO channel (e.g., the channels associated with WG  452   b  and WG  452   c ) is frequency shifted by a unique (e.g., different) amount, whereas the main channel (e.g., the channel associated with WG  452   a ) remains unshifted. For example, the OFS  453  is configured to frequency shift (and/or phase shift) the light that it receives from the polarization controller  444  by a first offset to generate an LO signal (shown in  FIG.  4    as, “LO 2 ”). As another example, the OFS  454  is configured to frequency shift (and/or phase shift) the light that it receives from the polarization controller  444  by a second offset to generate a LO signal (shown in  FIG.  4    as, “LO 1 ”). As another example, the light / LO signal (shown in  FIG.  4    as, “LO 0 ”) that is transmitted from the third terminal of the optical fiber array  446  is not shifted. 
     In some embodiments, some or all of the LO signals are mixed with an Rx signal on a waveguide (e.g., WG  452   a , WG  452   b , WG  452   c ), and passed onto a balanced photodiode (e.g., PD  460 , PD  462 , PD  464 ). In this approach, having a dedicated PD-TIA-ADC path for each waveguide channel allows a pristine signal to be produced without interference from other channels. 
     Although not shown in  FIG.  4   , the output of the MUX  490  couples to the LIDAR control system  110  in  FIG.  1    such to be able to pass any of the optical beams that are received by any of the WGs  452  to the LIDAR control system  110  for processing by the signal processing unit  112 . 
       FIG.  5    is a series of graphs illustrating the effect of frequency remapping/shifting of the LO using OFSs in the LIDAR system  100  in  FIG.  1    to enhance detection of distant objects, according to some embodiments. The graph  502   a  shows an example FMCW signal that includes multiple objects with beat frequencies f beat,i  = γ(Δτ i ), where γ is the FMCW chirp rate and Δτ i  ≈ 2R/c is the target time delay. The full FMCW scan displays a characteristic reduction of the Rx power of target objects with increasing distance/beat frequency. As shown in graphs  502   b ,  504   b ,  506   b , the detection range includes frequencies up to f max,ADC , which for large distances can necessitate sampling rates of Giga-samples per second (Gsps). Such high sampling rates may result in high electrical power dissipation in an ADC (e.g., ADCs  480 , ADCs  580 ) and increase system cost. As shown in graphs  504   a  and  506   a , applying a frequency shift Δf LO,n  to the LOs (e.g., LO 1  and LO 2 ) may have the effect of mapping target frequencies to f beat,i  = f beat,i  - Δf LO,n . In some embodiments, for a given choice of Δf LO,n , a desired target range may be mapped to the RF baseband (e.g., zero frequency), thereby allowing distant targets to be captured at low frequency. 
     This remapping/shifting scheme has the advantage of reducing the required bandwidth of the ADCs (BW ADC ) in a LIDAR system using the optical frequency shifters (OFS) in environment  400  in  FIG.  4    and the environment  500  in  FIG.  5   . Combined with the increased Rx power (P Rx ), a descan-tolerant AWR+OFS LIDAR architecture (as depicted in environment  400  in  FIG.  4    and environment  500  in  FIG.  5   ) can significantly enhance the SNR of distant objects via SNR ∝ P LO P RX /BW ADC , reduce power consumption and cost, enable large scan/frame rates, and provide a unique distance binning approach that is inaccessible in the conventional LIDAR system. 
       FIG.  6    is a block diagram illustrating an example environment for using AWRs and OFSs, and additionally, polarization splitter-rotator (PSRs) and/or variable optical attenuators (VOAs) in the LIDAR system  100  to enhance detection of distant objects, according to some embodiments. The environment  600  includes the optical scanner  102 , a quarter-wave plate (QWP)  616 , a lens  620 , an FMCW laser  640 , and a photonic integrated circuit (PIC)  450 . The environment  400  includes transimpedance amplifiers  670   a ,  670   b ,  670   c  (collectively referred to as, “TIAs  670 ”). The environment  600  includes ADCs  680   a ,  680   b ,  680   c  (collectively referred to as, ADCs  680 ) and a multiplexer (shown in  FIG.  4    as, “MUX  690 ”). 
     The PIC  650  (sometimes referred to as, “an optical receiver”) includes a polarization splitter-rotator (PSR)  664   a  that is configured to receive the return optical beam  606   a  from the QWP  616  via the lens  620  responsive to the optical scanner  102  transmitting the one or more optical beams  604  into free space. The PIC  650  includes a PSR  664   b  that is configured to receive the return optical beam  606   b  from the QWP  616  via the lens  620  responsive to the optical scanner  102  transmitting the one or more optical beams  604  into free space. The PIC  650  includes a PSR  664   c  that is configured to receive the return optical beam  606   c  from the QWP  616  via the lens  620  responsive to the optical scanner  102  transmitting the one or more optical beams  604  into free space. 
     The PIC  650  includes waveguide (WG)  652   a  that is configured as the primary on-axis waveguide for receiving the return optical beam  606   a  from the PSR  664   a . The PIC  650  includes waveguide (WG)  652   b  that is configured as an off-axis satellite waveguide for receiving the return optical beam  606   b  from the PSR  664   b . The PIC  650  includes waveguide (WG)  652   c  that is configured as an off-axis satellite waveguide for receiving the return optical beam  606   c  from the PSR  664   c . Although  FIG.  6    shows that the PIC  650  includes only a select number of satellite waveguides (e.g., WG  652   a , WG  652   b , WG  652   a ), the PIC  650  may include any number of satellite waveguides to depending on desired performance and application. 
     The PIC  650  includes a directional coupler  645  and a splitter  642 . The PIC  650  includes optical frequency shifters (OFSs)  652 ,  654 . The PIC  650  includes variable optical attenuators (VOAs)  656 ,  658 . The PIC  650  includes balanced photodiodes (PD)  660   a ,  660   b ,  660   c  (collectively referred to as, “PDs  660 ”). In some embodiments, the OFSs  653 ,  654  may be implemented using a variety of PIC architectures including a serrodyne Mach-Zehnder interferometer, a single-sideband modulator, an in-phase/quadrature (I/Q) optical modulator, or adaptations thereof. 
     In some embodiments, any of the components (e.g., PIC  650  or any of the components of PIC  650 , etc.) in the environment  600  may be added as a component of the LIDAR system  100  in  FIG.  1   , or be used to replace or modify any of the one or more components (e.g., free space optics  115 , optical circuits, optical receivers  104 , etc.) of the LIDAR system  100 . As shown in  FIG.  6   , the Tx and Rx paths are contained within the same PIC architecture. 
     The environment  600  includes one or more objects, such as object  608   a  (e.g., a street sign), object  608   b  (e.g., a tree), and object  608   c  (e.g., a pedestrian); each collectively referred to as objects  608 . Although  FIG.  4    shows only a select number of objects  608 , the environment  600  may include any number of objects  608  of any type that are within a short distance (e.g., 30 meters) or a long distance (e.g., 300 meters, 500 meters and beyond) from the optical scanner  102 . In some embodiments, an object  608  may be stationary or moving with respect to the optical scanner  102 . 
     An output terminal of the FMCW laser  640  is coupled to an input terminal of the directional coupler  645 . A first output terminal of the directional coupler  645  is coupled to a second input terminal of the PSR  664   a  and a second output terminal of the directional coupler  645  is coupled to an input terminal of the fiber splitter  642 . 
     A first output terminal of the fiber splitter  642  is coupled to an input terminal of the OFS  653 , whose output terminal is coupled to an input terminal of the VOA  656 , whose output terminal is coupled to a second terminal of the PD  660   c . A second output terminal of the fiber splitter  642  is coupled to an input terminal of the OFS  654 , whose output terminal is coupled to an input terminal of the VOA  658 , whose output terminal is coupled to a second terminal of the PD  660   b . A third output terminal of the fiber splitter  642  is coupled to a second terminal of the PD  660   a . 
     An input terminal of the WG  652   c  is coupled to an output terminal of the PSR  664   c  and an output terminal of the WG  652   c  is coupled to a first input terminal of the PD  660   c . An output terminal of the PD  660   c  is coupled to an input terminal of the TIA  670   c , whose output terminal is coupled to an input terminal of the ADC  680   c , whose output terminal is coupled to a first input terminal of the MUX  690 . 
     An input terminal of the WG  652   b  is coupled to an output terminal of the PSR  664   b  and an output terminal of the WG  652   b  is coupled to a first input terminal of the PD  660   b . An output terminal of the PD  660   b  is coupled to an input terminal of the TIA  670   b , whose output terminal is coupled to an input terminal of the ADC  680   b , whose output terminal is coupled to a second input terminal of the MUX  690 . 
     An input terminal of the WG  652   a  is coupled to an output terminal of the PSR  664   a  and an output terminal of the WG  652   a  is coupled to a first input terminal of the PD  660   a . An output terminal of the PD  660   a  is coupled to an input terminal of the TIA  670   a , whose output terminal is coupled to an input terminal of the ADC  680   a , whose output terminal is coupled to a third input terminal of the MUX  690 . 
     In some embodiments, the FMCW laser  640  is configured to generate and transmit an optical beam (e.g., light) to the directional coupler  645 , which is configured to separate (e.g., split, divide, duplicate) the optical beam into an optical beam (e.g., Tx path)  604  and an LO signal (sometimes referred to as, “an LO beam”). 
     As discussed herein, each channel of the AWR in PIC  650  may have a respective PSR (e.g., PSR  664   a , PSR  664   b , PSR  664   c ). For the primary on-axis waveguide (e.g., WG  652   a ), the PSR  664   a  passes the Tx light onto the lens  620  and the QWP  616 . The PSRs  664  on each channel are configured to receive oppositely polarized light from objects and convert the received light to the same polarization as Tx for mixing on the balanced PDs  660 . In some embodiments, the same LO branch and procedure may be used with the addition of the VOAs  656 ,  658  that are placed on the satellite channels. In some embodiments, the VOAs  656 ,  658  are configured to balance the LO and Rx power to maximize fringe visibility on the PDs  660 . The embodiment depicted in environment  600  is more compact and requires fewer optical alignments compared to external Tx paths, while generating the same performance benefits. 
     Although not shown in  FIG.  6   , the output of the MUX  690  couples to the LIDAR control system  110  in  FIG.  1    such to be able to pass any of the optical beams that are received by any of the WGs  652  to the LIDAR control system  110  for processing by the signal processing unit  112 . 
     In some embodiments, the described LIDAR system using an array waveguide receiver and optical frequency shifting (AWR/OFS) is agnostic to the optical scanning architecture, and thus the scheme is applicable to any mechanical approaches (e.g., galvanometer or hexagon systems). In some embodiments, the distance binning approach using AWR/OFS may be implemented in electrically driven optical phased arrays (e.g., distinct from wavelength-scan OPAs), whereby the exit/entrance aperture is defined by an array of emitters (e.g., grating couplers). In some embodiments, the frequency shift may be applied to a Tx signal (e.g., optical beam  304 , optical beam  404 , beams  504 ) rather than the LO paths to achieve the same effect. In some embodiments, a continuous wave (CW) laser maybe coupled onto the PIC (e.g., PIC  350 , PIC  450 , PIC  650 ) and the optical frequency shifters in a more complex manner, such as generating both the FMCW scan (e.g., triangle wave, sawtooth wave, etc.) and the single-frequency LO shifts on chip. 
       FIG.  7    is a flow diagram illustrating an example method for using array waveguide receivers and optical frequency shifting in an FMCW LIDAR system to enhance detection of distant objects. Additional, fewer, or different operations may be performed in the method depending on the particular arrangement. In some embodiments, some or all operations of method  700  may be performed by one or more processors executing on one or more computing devices, systems, or servers (e.g., remote/networked servers or local servers). In some embodiments, method  700  may be performed by a signal processing unit, such as signal processing unit  112  in  FIG.  1   . In some embodiments, method  700  may be performed by any of the components (e.g., scanner  102 , PIC  350 , etc.) in environment  300  in  FIG.  3   . In some embodiments, method  700  may be performed by any of the components (e.g., scanner  102 , PIC  450 , etc.) in environment  400  in  FIG.  4   . In some embodiments, method  700  may be performed by any of the components (e.g., scanner  102 , PIC  650 , etc.) in environment  600  in  FIG.  6   . Each operation may be re-ordered, added, removed, or repeated. 
     In some embodiments, the method  700  may include the operation  702  of receiving, responsive to a transmission of a plurality of optical beams into an environment, a first returned optical beam having a first lag angle. In some embodiments, the method  700  may include the operation  704  of generating a first waveguide signal based on the first returned optical beam. In some embodiments, the method  700  may include the operation  706  of receiving, responsive to the transmission of a plurality of optical beams into an environment, a second returned optical beam having a second lag angle. 
     In some embodiments, the method  700  may include the operation  708  of generating a second waveguide signal based on the second returned optical beam. In some embodiments, the method  700  may include the operation  710  of generating, based on the first waveguide signal and a first local oscillator (LO) signal, a first output signal within a first frequency range. 
     In some embodiments, the method  700  may include the operation  712  of shifting a frequency of the second LO signal to cause the second output signal to shift from within the second frequency range to within the first frequency range to generate a shifted signal. In some embodiments, the method  700  may include the operation  712  of receiving the shifted signal to produce one or more points in a point set. 
     The preceding description sets forth numerous specific details such as examples of specific systems, components, methods, and so forth, in order to provide a good understanding of several embodiments of the present disclosure. It will be apparent to one skilled in the art, however, that at least some embodiments of the present disclosure may be practiced without these specific details. In other instances, well-known components or methods are not described in detail or are presented in simple block diagram format in order to avoid unnecessarily obscuring the present disclosure. Thus, the specific details set forth are merely exemplary. While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. Particular embodiments may vary from these exemplary details and still be contemplated to be within the scope of the present disclosure. 
     Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiments included in at least one embodiment. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. In addition, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or.” 
     Although the operations of the methods herein are shown and described in a particular order, the order of the operations of each method may be altered so that certain operations may be performed in an inverse order or so that certain operations may be performed, at least in part, concurrently with other operations. In another embodiment, instructions or sub-operations of distinct operations may be in an intermittent or alternating manner. 
     The above description of illustrated implementations of the invention, including what is described in the Abstract, is not intended to be exhaustive or to limit the invention to the precise forms disclosed. While specific implementations of, and examples for, the invention are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the invention, as those skilled in the relevant art will recognize. The words “example” or “exemplary” are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “example” or “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the words “example” or “exemplary” is intended to present concepts in a concrete fashion. As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context, “X includes A or B” is intended to mean any of the natural inclusive permutations. That is, if X includes A; X includes B; or X includes both A and B, then “X includes A or B” is satisfied under any of the foregoing instances. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form. Moreover, use of the term “an embodiment” or “one embodiment” or “an implementation” or “one implementation” throughout is not intended to mean the same embodiment or implementation unless described as such. Furthermore, the terms “first,” “second,” “third,” “fourth,” etc. as used herein are meant as labels to distinguish among different elements and may not necessarily have an ordinal meaning according to their numerical designation.