PATENT DOCUMENT

Publication Number: US-11774342-B2
Application Number: US-202016833199-A
Country: US
Kind Code: B2

Title: Particulate matter sensors based on split beam self-mixing interferometry sensors

Abstract:
Various sensors, including particulate matter sensors, are described. One particulate matter sensor includes a self-mixing interferometry sensor and a set of one or more optical elements. The set of one or more optical elements is positioned to receive an optical emission of the self-mixing interferometry sensor, split the optical emission into multiple beams, and direct each beam of the multiple beams in a different direction. The self-mixing interferometry sensor is configured to generate particle speed information for particles passing through respective measurement regions of the multiple beams.

Claims:
What is claimed is: 
     
       1. A particulate matter sensor, comprising:
 a self-mixing interferometry sensor configured to generate a self-mixing interference signal; 
 a set of one or more optical elements positioned to receive an optical emission of the self-mixing interferometry sensor, split the optical emission into multiple beams, direct each beam of the multiple beams in a different direction towards a respective measurement region, and redirect received reflections or backscatters of the multiple beams from the respective measurement regions back into the self-mixing interferometry sensor to generate the self-mixing interference signal, wherein each of the multiple beams is separated from other beams of the multiple beams by 120 degrees in a plane perpendicular to an axis of the optical emission and each of the multiple beams has a secondary axis that diverges from the axis of the optical emission by a same angle θ; and 
 circuitry configured to:
 extract, from the self-mixing interference signal, particle speed information for particles passing through any of the multiple beams; 
 estimate a particle speed using the angle θ and using the particle speed information for particles passing through any of the multiple beams interchangeably; 
 estimate, using the particle speed, an air flow volume through respective measurement regions of the multiple beams; 
 count a number of time-domain disturbances in the self-mixing interference signal over a period of time, the number of time-domain disturbances corresponding to the number of particles passing through the respective measurement regions over the period of time; and 
 estimate a particulate matter concentration using the number of particles, and the air flow volume. 
 
 
     
     
       2. The particulate matter sensor of  claim 1 , wherein the particle speed information comprises Doppler frequency shifts. 
     
     
       3. The particulate matter sensor of  claim 2 , wherein the circuitry is further configured to:
 perform a frequency domain analysis to extract the Doppler frequency shifts from the self-mixing interference signal. 
 
     
     
       4. The particulate matter sensor of  claim 2 , wherein the circuitry is further configured to:
 perform a time-frequency domain analysis to extract the Doppler frequency shifts from the self-mixing interference signal. 
 
     
     
       5. The particulate matter sensor of  claim 2 , wherein the Doppler frequency shifts comprise unsigned Doppler frequency shifts. 
     
     
       6. The particulate matter sensor of  claim 1 , wherein the angle θ is selected such that cos 2 (θ)=⅓. 
     
     
       7. The particulate matter sensor of  claim 1 , wherein the circuitry is further configured to detect an existence of particulate matter using the particle speed. 
     
     
       8. The particulate matter sensor of  claim 1 , wherein the multiple beams consist of three beams. 
     
     
       9. The particulate matter sensor of  claim 1 , wherein the self-mixing interferometry sensor comprises an electromagnetic radiation source integrated with a photodetector. 
     
     
       10. The particulate matter sensor of  claim 1 , wherein:
 the self-mixing interferometry sensor comprises an electromagnetic radiation source and a photodetector; 
 the electromagnetic radiation source has a resonant optical cavity bounded by first and second mirrors, with each of the first mirror and the second mirror being at least partially transmissive to a wavelength of electromagnetic radiation; and 
 the electromagnetic radiation source is stacked on the photodetector. 
 
     
     
       11. The particulate matter sensor of  claim 1 , wherein:
 the set of one or more optical elements is a first set of one or more optical elements; and 
 the particulate matter sensor further comprises a second set of one or more optical elements configured to receive the set of multiple beams and redirect the set of multiple beams toward a set of overlapping or consonant measurement regions. 
 
     
     
       12. A method of sensing particulate matter, comprising:
 splitting an optical emission received from a self-mixing interferometry sensor into multiple beams; 
 directing each beam of the multiple beams in a different direction towards a respective measurement region, wherein each of the multiple beams is separated from other beams of the multiple beams by 120 degrees in a plane perpendicular to an axis of the optical emission and each of the multiple beams has a secondary axis that diverges from the axis of the optical emission by a same angle θ; 
 redirecting received reflections or backscatters of the multiple beams from the respective measurement regions back into the self-mixing interferometry sensor to generate the self-mixing interferometry signal;
 extracting, from the self-mixing interference signal, particle speed information for particles passing through any of the multiple beams; 
 
 estimating a particle speed using the angle θ, and the particle speed information for particles passing through any of the multiple beams interchangeably; 
 estimating, using the particle speed, an air flow volume through respective measurement regions of the multiple beams; 
 counting a number of time-domain disturbances in the self-mixing interference signal over a period of time, the number of time-domain disturbances corresponding to the number of particles passing through the respective measurement regions over a period of time; and 
 estimating a particulate matter concentration using the number of particles, and the air flow volume. 
 
     
     
       13. The method of  claim 12 , wherein the particle speed information comprises Doppler frequency shifts, and the method further comprises:
 performing a frequency domain analysis to extract the Doppler frequency shifts from the self-mixing interference signal. 
 
     
     
       14. The method of  claim 12 , wherein: the angle θ is selected such that cos 2 (θ)=⅓. 
     
     
       15. The method of  claim 12 , wherein the particle speed information comprises Doppler frequency shifts, and the method further comprises:
 performing a time-frequency domain analysis to extract the Doppler frequency shifts from the self-mixing interference signal. 
 
     
     
       16. The method of  claim 15 , wherein the Doppler frequency shifts comprise unsigned Doppler frequency shifts. 
     
     
       17. The method of  claim 12 , further comprising:
 receive the set of multiple beams and redirect the set of multiple beams toward a set of overlapping or consonant measurement regions.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a nonprovisional of and claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application No. 62/830,085, filed Apr. 5, 2019, the contents of which are incorporated herein by reference as if fully disclosed herein. 
    
    
     FIELD 
     The described embodiments relate generally to particulate matter sensors. More particularly, the described embodiments relate to particulate matter sensors based on split beam self-mixing interferometry sensors. 
     BACKGROUND 
     Self-mixing interferometry is an optical sensing technology that can be used for particulate matter detection and air quality monitoring. In self-mixing interferometry, coherent or partially coherent electromagnetic radiation emitted by a stimulated emission-based electromagnetic radiation source (e.g., a laser) may be re-coupled into the electromagnetic radiation source&#39;s resonant optical cavity through reflection/backscattering from particulate matter (e.g., small solid or liquid particles, such as particles contained in pollution (smog), ash, dust, pollen, water vapor, and so on). Such re-coupling induces a measurable phase-sensitive change (e.g., a Doppler frequency shift) in the electric field and carrier distribution of the optical resonant cavity. 
     SUMMARY 
     Embodiments of the systems, devices, methods, and apparatus described in the present disclosure are directed to particulate matter sensors, and more particularly, to particulate matter sensors based on split beam self-mixing interferometry sensors. A self-mixing interferometry sensor is defined herein as a sensor configured to generate electromagnetic radiation within an optical resonant cavity, emit the electromagnetic radiation from the optical resonant cavity, receive a reflection or backscatter of the electromagnetic radiation back into the optical resonant cavity, self-mix the generated and reflected/backscattered electromagnetic radiation within the optical resonant cavity, and generate an output indicative of the self-mixing. The generated, emitted, and received electromagnetic radiation may be coherent or partially coherent. In some examples, the electromagnetic radiation emitted by a self-mixing interferometry sensor may be generated by an electromagnetic radiation source such as a vertical-cavity surface-emitting laser (VCSEL), a vertical external-cavity surface-emitting laser (VECSEL), a quantum-dot laser (QDL), a quantum cascade laser (QCL), or a light-emitting diode (LED) (e.g., an organic LED (OLED), a resonant-cavity LED (RC-LED), a micro LED (mLED), a superluminescent LED (SLED), or an edge-emitting LED), and so on. The generated, emitted, and received electromagnetic radiation may include, for example, visible or invisible light (e.g., green light, infrared (IR) light, ultraviolet (UV) light, and so on). The output of a self-mixing interferometry sensor may include a photocurrent produced by a photodetector (e.g., a photodiode) that is integrated with, or positioned under, above, or next to, the sensor&#39;s electromagnetic radiation source. Alternatively or additionally, the output of a self-mixing interferometry sensor may include a measurement of a bias current or junction voltage of the self-mixing interferometry sensor. 
     As described herein, a single self-mixing interferometry sensor may be used to determine one or more of: the existence of particulate matter within a set of measurement regions, a speed of particles passing through the measurement regions, an air flow through the measurement regions, a particulate matter concentration within the measurement regions, an air quality within the measurement regions, and so on. 
     In a first aspect, the present disclosure describes a particulate matter sensor. The particulate matter sensor may include a self-mixing interferometry sensor and a set of one or more optical elements. The set of one or more optical elements may be positioned to receive an optical emission of the self-mixing interferometry sensor, split the optical emission into multiple beams, and direct each beam of the multiple beams in a different direction. The self-mixing interferometry sensor may be configured to generate particle speed information for particles passing through respective measurement regions of the multiple beams. 
     In another aspect, the present disclosure describes a sensor including an electromagnetic radiation source and a splitter. The electromagnetic radiation source may have a resonant optical cavity. The splitter may be configured to split an optical emission of the electromagnetic radiation source into a set of multiple beams, and to receive reflections or backscatters of the multiple beams and direct the received reflections or backscatters into the resonant optical cavity. 
     In still another aspect of the disclosure, a method of sensing particulate matter is described. The method may include splitting an optical emission received from a self-mixing interferometry sensor into multiple beams; directing each beam of the multiple beams in a different direction; and outputting, from the self-mixing interferometry sensor, particle speed information for particles passing through respective measurement regions of the multiple beams. 
     In addition to the exemplary aspects and embodiments described above, further aspects and embodiments will become apparent by reference to the drawings and by study of the following description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure will be readily understood by the following detailed description in conjunction with the accompanying drawings, wherein like reference numerals designate like structural elements, and in which: 
         FIGS.  1 A and  1 B  show a first example of a device that may include a particulate matter sensor; 
         FIGS.  2 A and  2 B  show a second example of a device that may include a particulate matter sensor; 
         FIG.  3    shows an example block diagram of a particulate matter sensor; 
         FIG.  4    shows an example elevation of a particulate matter sensor; 
         FIG.  5    shows a plan view of the particulate matter sensor; 
         FIGS.  6 A- 8 B  show respective plan views (“A” views) and elevations (“B” views) of the beams shown in  FIGS.  4  and  5   ; 
         FIG.  9    shows an example method of estimating particulate matter concentration, which method may be performed by circuitry associated with a self-mixing interferometry sensor; 
         FIG.  10    shows an example method of sensing particulate matter; and 
         FIG.  11    shows an example electrical block diagram of an electronic device. 
     
    
    
     The use of cross-hatching or shading in the accompanying figures is generally provided to clarify the boundaries between adjacent elements and also to facilitate legibility of the figures. Accordingly, neither the presence nor the absence of cross-hatching or shading conveys or indicates any preference or requirement for particular materials, material properties, element proportions, element dimensions, commonalities of similarly illustrated elements, or any other characteristic, attribute, or property for any element illustrated in the accompanying figures. 
     Additionally, it should be understood that the proportions and dimensions (either relative or absolute) of the various features and elements (and collections and groupings thereof) and the boundaries, separations, and positional relationships presented therebetween, are provided in the accompanying figures merely to facilitate an understanding of the various embodiments described herein and, accordingly, may not necessarily be presented or illustrated to scale, and are not intended to indicate any preference or requirement for an illustrated embodiment to the exclusion of embodiments described with reference thereto. 
     DETAILED DESCRIPTION 
     Reference will now be made in detail to representative embodiments illustrated in the accompanying drawings. It should be understood that the following description is not intended to limit the embodiments to one preferred embodiment. To the contrary, it is intended to cover alternatives, modifications, and equivalents as can be included within the spirit and scope of the described embodiments as defined by the appended claims. 
     The following description relates to particulate matter sensing. When estimating particulate matter concentration using self-mixing interferometry, accurate particulate matter concentration estimation depends on an accurate three-dimensional (3D) reconstruction of particle speed (e.g., reconstruction of a particle speed vector). However, an intrinsic limit to self-mixing interferometry is that, when a particle passes through a beam of electromagnetic radiation close to the beam&#39;s focus, only the absolute particle speed of a particle in the direction of the beam can be measured, while the speed of the particle perpendicular to the beam is lost. Thus, the conventional approach to estimating particulate matter concentration using self-mixing interferometry is to use three self-mixing interferometry sensors oriented in three different directions. However, the use of multiple self-mixing interferometry sensors drives up the cost, complexity, and power consumption of a particulate matter sensor, as well as the size of the particulate matter sensor. 
     As described herein, a single self-mixing interferometry sensor may be used to determine one or more of: the existence of particulate matter within a set of measurement regions, a speed of particles passing through the measurement regions, an air flow through the measurement regions, a particulate matter concentration within the measurement regions, an air quality within the measurement regions, and so on. A single self-mixing interferometry sensor may be used to sense particulate matter by splitting an optical emission of the self-mixing interferometry sensor into multiple beams having different directions. The optical emission may be split into multiple beams using a set of one or more optical elements, which optical element(s) may include one or more diffractive optical elements (or holographic elements, or periodic sub-wavelength elements, or aperiodic sub-wavelength elements) and one or more beam-shaping optical elements (e.g., one or more focusing, tilting, and/or collimating optical elements). Particle speed information obtained from a self-mixing interference signal (also referred to, at times, as a self-mixing interferometry signal) generated by the self-mixing interferometry sensor, in combination with information regarding the beam geometry, may then be used to estimate particle speed, particulate matter concentration, and other parameters. In some cases, the detected particulate matter may include particulate matter on the order of PM10 (particulate matter less than 10 micrometers (μm) in diameter) or PM2.5 (particulate matter less than 2.5 μm in diameter). 
     These and other embodiments and advantages are discussed with reference to  FIGS.  1 A- 11   . However, those skilled in the art will readily appreciate that the detailed description given herein with respect to these figures is for explanatory purposes only and should not be construed as limiting. 
     Directional terminology, such as “top”, “bottom”, “upper”, “lower”, “front”, “back”, “over”, “under”, “above”, “below”, “left”, “right”, etc. is used with reference to the orientation of some of the components in some of the figures described below. Because components in various embodiments can be positioned in a number of different orientations, directional terminology is used for purposes of illustration only and is in no way limiting. The directional terminology is intended to be construed broadly, and therefore should not be interpreted to preclude components being oriented in different ways. The use of alternative terminology, such as “or”, is intended to indicate different combinations of the alternative elements. For example, A or B is intended to include A, or B, or A and B. 
       FIGS.  1 A and  1 B  show a first example of a device  100  that may include a particulate matter sensor. The device&#39;s dimensions and form factor, including the ratio of the length of its long sides to the length of its short sides, suggest that the device  100  is a mobile phone (e.g., a smartphone). However, the device&#39;s dimensions and form factor are arbitrarily chosen, and the device  100  could alternatively be any portable electronic device including, for example, a mobile phone, tablet computer, portable computer, portable music player, health monitor device, portable terminal, vehicle navigation system, robot navigation system, or other portable or mobile device. The device  100  could also be a device that is semi-permanently located (or installed) at a single location.  FIG.  1 A  shows a front isometric view of the device  100 , and  FIG.  1 B  shows a rear isometric view of the device  100 . The device  100  may include a housing  102  that at least partially surrounds a display  104 . The housing  102  may include or support a front cover  106  or a rear cover  108 . The front cover  106  may be positioned over the display  104 , and may provide a window through which the display  104  may be viewed. In some embodiments, the display  104  may be attached to (or abut) the housing  102  and/or the front cover  106 . In alternative embodiments of the device  100 , the display  104  may not be included and/or the housing  102  may have an alternative configuration. 
     The display  104  may include one or more light-emitting elements including, for example, an LED, OLED, liquid crystal display (LCD), electroluminescent (EL) display, or other type of display element. In some embodiments, the display  104  may include, or be associated with, one or more touch and/or force sensors that are configured to detect a touch and/or a force applied to a surface of the front cover  106 . 
     The various components of the housing  102  may be formed from the same or different materials. For example, the sidewall  118  may be formed using one or more metals (e.g., stainless steel), polymers (e.g., plastics), ceramics, or composites (e.g., carbon fiber). In some cases, the sidewall  118  may be a multi-segment sidewall including a set of antennas. The antennas may form structural components of the sidewall  118 . The antennas may be structurally coupled (to one another or to other components) and electrically isolated (from each other or from other components) by one or more non-conductive segments of the sidewall  118 . The front cover  106  may be formed, for example, using one or more of glass, a crystal (e.g., sapphire), or a transparent polymer (e.g., plastic) that enables a user to view the display  104  through the front cover  106 . In some cases, a portion of the front cover  106  (e.g., a perimeter portion of the front cover  106 ) may be coated with an opaque ink to obscure components included within the housing  102 . The rear cover  108  may be formed using the same material(s) that are used to form the sidewall  118  or the front cover  106 . In some cases, the rear cover  108  may be part of a monolithic element that also forms the sidewall  118  (or in cases where the sidewall  118  is a multi-segment sidewall, those portions of the sidewall  118  that are non-conductive). In still other embodiments, all of the exterior components of the housing  102  may be formed from a transparent material, and components within the device  100  may or may not be obscured by an opaque ink or opaque structure within the housing  102 . 
     The front cover  106  may be mounted to the sidewall  118  to cover an opening defined by the sidewall  118  (i.e., an opening into an interior volume in which various electronic components of the device  100 , including the display  104 , may be positioned). The front cover  106  may be mounted to the sidewall  118  using fasteners, adhesives, seals, gaskets, or other components. 
     A display stack or device stack (hereafter referred to as a “stack”) including the display  104  may be attached (or abutted) to an interior surface of the front cover  106  and extend into the interior volume of the device  100 . In some cases, the stack may include a touch sensor (e.g., a grid of capacitive, resistive, strain-based, ultrasonic, or other type of touch sensing elements), or other layers of optical, mechanical, electrical, or other types of components. In some cases, the touch sensor (or part of a touch sensor system) may be configured to detect a touch applied to an outer surface of the front cover  106  (e.g., to a display surface of the device  100 ). 
     In some cases, a force sensor (or part of a force sensor system) may be positioned within the interior volume below and/or to the side of the display  104  (and in some cases within the device stack). The force sensor (or force sensor system) may be triggered in response to the touch sensor detecting one or more touches on the front cover  106  (or a location or locations of one or more touches on the front cover  106 ), and may determine an amount of force associated with each touch, or an amount of force associated with the collection of touches as a whole. 
     As shown primarily in  FIG.  1 A , the device  100  may include various other components. For example, the front of the device  100  may include one or more front-facing cameras  110 , speakers  112 , microphones, or other components  114  (e.g., audio, imaging, and/or sensing components) that are configured to transmit or receive signals to/from the device  100 . In some cases, a front-facing camera  110 , alone or in combination with other sensors, may be configured to operate as a bio-authentication or facial recognition sensor. The device  100  may also include various input devices, including a mechanical or virtual button  116 , which may be accessible from the front surface (or display surface) of the device  100 . In some cases, the front-facing camera  110 , virtual button  116 , and/or other sensors of the device  100  may be integrated with a display stack of the display  104  and moved under the display  104 . 
     The device  100  may also include buttons or other input devices positioned along the sidewall  118  and/or on a rear surface of the device  100 . For example, a volume button or multipurpose button  120  may be positioned along the sidewall  118 , and in some cases may extend through an aperture in the sidewall  118 . The sidewall  118  may include one or more ports  122  that allow air, but not liquids, to flow into and out of the device  100 . In some embodiments, one or more sensors may be positioned in or near the port(s)  122 . For example, an ambient pressure sensor, ambient temperature sensor, internal/external differential pressure sensor, gas sensor, particulate matter sensor, or air quality sensor may be positioned in or near a port  122 . 
     In some embodiments, the rear surface of the device  100  may include a rear-facing camera  124  or other optical sensor (see  FIG.  1 B ). A flash or light source  126  may also be positioned along the rear of the device  100  (e.g., near the rear-facing camera). In some cases, the rear surface of the device  100  may include multiple rear-facing cameras. 
     The camera(s), microphone(s), pressure sensor(s), temperature sensor(s), biometric sensor(s), button(s), proximity sensor(s), touch sensor(s), force sensor(s), particulate matter or air quality sensor(s), and so on of the device  100  may form parts of various sensor systems. 
       FIGS.  2 A and  2 B  show a second example of a device  200  that may include a particulate matter sensor. The device&#39;s dimensions and form factor, and inclusion of a band  204 , suggest that the device  200  is an electronic watch. However, the device  200  could alternatively be any wearable electronic device.  FIG.  2 A  shows a front isometric view of the device  200 , and  FIG.  2 B  shows a rear isometric view of the device  200 . The device  200  may include a body  202  (e.g., a watch body) and a band  204 . The watch body  202  may include an input or selection device, such as a crown  214  or a button  216 . The band  204  may be used to attach the body  202  to a body part (e.g., an arm, wrist, leg, ankle, or waist) of a user. The body  202  may include a housing  206  that at least partially surrounds a display  208 . The housing  206  may include or support a front cover  210  ( FIG.  2 A ) or a rear cover  212  ( FIG.  2 B ). The front cover  210  may be positioned over the display  208 , and may provide a window through which the display  208  may be viewed. In some embodiments, the display  208  may be attached to (or abut) the housing  206  and/or the front cover  210 . In alternative embodiments of the device  200 , the display  208  may not be included and/or the housing  206  may have an alternative configuration. 
     The housing  206  may in some cases be similar to the housing  102  described with reference to  FIGS.  1 A- 1 B , and the display  208  may in some cases be similar to the display  104  described with reference to  FIGS.  1 A- 1 B . 
     The device  200  may include various sensor systems, and in some embodiments may include some or all of the sensor systems included in the device  100  described with reference to  FIGS.  1 A- 1 B . In some embodiments, the device  200  may have a port  218  (or set of ports) on a side of the housing  206  (or elsewhere), and an ambient pressure sensor, ambient temperature sensor, internal/external differential pressure sensor, gas sensor, particulate matter sensor, or air quality sensor may be positioned in or near the port(s)  218 . 
     In some cases, the rear surface (or skin-facing surface) of the device  200  may include a flat or raised area  220  that includes one or more skin-facing sensors. For example, the area  220  may include a heart-rate monitor, a respiration-rate monitor, or a blood pressure monitor. The area  220  may also include an off-wrist detector or other sensor. 
       FIG.  3    shows an example block diagram of a particulate matter sensor  300 . The particulate matter sensor  300  may include a self-mixing interferometry sensor  302  and a set of one or more optical elements  304  (hereafter referred to as a set of optical elements  304 ). The set of optical elements  304  may be positioned to receive an optical emission  306  of the self-mixing interferometry sensor  302 . The set of optical elements  304  may split the optical emission  306  into a set of multiple beams  308 - 1 ,  308 - 2 ,  308 - 3  and direct each beam of the multiple beams  308 - 1 ,  308 - 2 ,  308 - 3  in a different direction. The self-mixing interferometry sensor  302  may be configured to generate particle speed information  310  for particles  312  passing through respective measurement regions  314 - 1 ,  314 - 2 ,  314 - 3  of the multiple beams  308 - 1 ,  308 - 2 ,  308 - 3 . 
     The self-mixing interferometry sensor  302  may include an electromagnetic radiation source that emits the optical emission  306 . The optical emission  306  may include a beam of coherent or partially coherent electromagnetic radiation. In some embodiments, the electromagnetic radiation source may include a VCSEL, a VECSEL, a QDL, a QCL, or an LED (e.g., an OLED, an RC-LED, an mLED, a SLED, or an edge-emitting LED). 
     In some embodiments, the self-mixing interferometry sensor  302  may include an electromagnetic radiation source integrated with a photodetector. In some embodiments, the self-mixing interferometry sensor  302  may include an electromagnetic radiation source that is stacked on, below, or near (e.g., adjacent), a photodetector. In embodiments in which a photodetector is positioned near an electromagnetic radiation source, the set of optical elements  304  may redirect received reflections or backscatters of the multiple beams  308 - 1 ,  308 - 2 ,  308 - 3  toward the photodetector. An output current of the photodetector (e.g., a photocurrent, I PD ) may provide the particle speed information  310 . Alternatively, the particle speed information  310  may be obtained by monitoring a junction voltage of the electromagnetic radiation source when the electromagnetic radiation source is driven by a constant current, or by monitoring a current of the electromagnetic radiation source when the electromagnetic radiation source is driven by a constant voltage. 
     The output current of the photodetector, or junction voltage of the electromagnetic radiation source, or current of the electromagnetic radiation source may vary in response to coherent self-mixing of 1) electromagnetic radiation generated by the electromagnetic radiation source and 2) reflected or backscattered electromagnetic radiation that is received into a resonant optical cavity of the electromagnetic radiation source and coherently mixed with the electromagnetic radiation generated by the electromagnetic radiation source. 
     The set of optical elements  304  may include, for example, one or more diffractive optical elements (and in some cases a holographic element, a periodic sub-wavelength element, and/or an aperiodic sub-wavelength element) and one or more beam-shaping optical elements (e.g., one or more focusing, tilting, and/or collimating optical elements). The set of optical elements  304  may split the optical emission of the self-mixing interferometry sensor  302  into two, three, four, or more beams. Splitting the optical emission into more beams may improve the accuracy of the particle speed information  310  generated by the self-mixing interferometry sensor  302  (e.g., when the beams are non-orthogonal to each other), but at the expense of reducing the optical power per beam  308 - 1 ,  308 - 2 ,  308 - 3  and decreasing the sensitivity of the particulate matter sensor  300  (e.g., as a result of increasing the minimum particle size that can be detected by the particulate matter sensor  300 ). Conversely, splitting the optical emission  306  into fewer beams may increase the sensitivity of the particulate matter sensor  300  (e.g., as a result of decreasing the minimum particle size that can be detected by the particulate matter sensor  300 ), but at the expense of decreasing the accuracy of the particle speed information  310  generated by the self-mixing interferometry sensor  302 . As described herein, computations to estimate particle speed, air flow volume, and particulate matter concentration may be simplified by splitting the optical emission  306  of the self-mixing interferometry sensor  302  into three beams, and in particular, three beams that form an orthogonal basis. 
     In some cases, the set of optical elements  304  may focus each beam of the multiple beams  308 - 1 ,  308 - 2 ,  308 - 3  at one of the respective measurement regions  314 - 1 ,  314 - 2 ,  314 - 3 . In some cases, the set of optical elements  304  may include one or more of free-form optics, a micro-lens, a micro-lens per beam, a tilted total internal reflection (TIR) lens per beam, and so on. 
     In addition to splitting an optical emission of the self-mixing interferometry sensor  302  into multiple beams, the set of optical elements  304  may receive reflections or backscatters of the multiple beams  308 - 1 ,  308 - 2 ,  308 - 3  and direct the received reflections or backscatters into a resonant optical cavity of the self-mixing interferometry sensor&#39;s electromagnetic radiation source. The set of optical elements  304  may therefore function as a transmitter and splitter when optical transmissions pass through the splitter in a first general direction, and operate as a receiver when optical transmissions pass through the splitter in a second general direction, opposite the first general direction). 
       FIG.  4    shows an example elevation of a particulate matter sensor  400 . The particulate matter sensor  400  is an example of the particulate matter sensor described with reference to  FIG.  3   , and may include a self-mixing interferometry sensor  402  and set of one or more optical elements  404  (hereafter referred to as a set of optical elements  404 ). The set of optical elements  404  may be positioned to receive an optical emission  406  of the self-mixing interferometry sensor  402 . The set of optical elements  404  may split the optical emission  406  into a set of multiple beams  408 - 1 ,  408 - 2 ,  408 - 3  and direct each beam of the multiple beams  408 - 1 ,  408 - 2 ,  408 - 3  in a different direction. The self-mixing interferometry sensor  402  may be configured to generate particle speed information  410  for particles  412  passing through respective measurement regions  414 - 1 ,  414 - 2 ,  414 - 3  of the multiple beams  408 - 1 ,  408 - 2 ,  408 - 3 . 
     The self-mixing interferometry sensor  402  may include an electromagnetic radiation source  416 , which in some cases may take the form of any of the electromagnetic radiation sources described with reference to  FIG.  3   . In some embodiments, the electromagnetic radiation source  416  may include a first (or bottom) mirror  418 - 1  and a second (or top) mirror  418 - 2  that are stacked on (e.g., formed on) a semiconductor substrate. The first and second mirrors  418 - 1 ,  418 - 2  may have reflective surfaces that face one another to form (e.g., bound) a resonant optical cavity  420  therebetween. The second mirror  418 - 2  may be partially transmissive, and may 1) allow a portion of the electromagnetic radiation generated by the electromagnetic radiation source  416  to escape the resonant optical cavity  420  as the optical transmission  406 , and 2) allow a portion of the electromagnetic radiation redirected (e.g., reflected or scattered) from a particle  412  passing through one of the measurement regions  414 - 1 ,  414 - 2 ,  414 - 3  to re-enter the electromagnetic radiation source  416  and coherently mix with electromagnetic radiation generated by the electromagnetic radiation source  416 . In some embodiments, the second (or top) mirror&#39;s transmissivity to the wavelength of electromagnetic radiation generated/received by the electromagnetic radiation source  416  may be about 0.5%, although higher or lower transmissivities may be used. The first (or bottom) mirror  418 - 1  may also be partially transmissive to the wavelength of electromagnetic radiation generated/received by the self-mixing interferometry sensor  402 , but in some embodiments may be less transmissive than the second mirror  418 - 2 . 
     In some cases, the self-mixing interferometry sensor  402  may also include a photodetector  422 , which in some cases may be integrated with the electromagnetic radiation source  416 . The electromagnetic radiation source  416  may emit the optical emission  406 , and an output current of the photodetector  422 , or a junction voltage or current of the electromagnetic radiation source  416 , may provide the particle speed information  410  (e.g., a self-mixing interference signal containing the particle speed information  410 ). 
     In some cases, the self-mixing interferometry sensor  402  may include an electromagnetic radiation source that is stacked on or under a photodetector. In these examples, the first mirror  418 - 1  may be at least partially transmissive, and electromagnetic radiation passing through the first mirror  418 - 1  may be detected by the photodetector. 
     In some embodiments, the set of optical elements  404  may include a diffractive optical element  424  that receives the optical emission  406  and splits it into the multiple beams (e.g., three beams  408 - 1 ,  408 - 2 , and  408 - 3 ). The diffractive optical element  424  may in some cases be an element having three optical or physical apertures that pass portions of the electromagnetic radiation emitted by the self-mixing interferometry sensor  402 . The set of optical elements  404  may also include a set of one or more beam-shaping elements  426  that receives the three beams  408 - 1 ,  408 - 2 ,  408 - 3  and focuses each of the beams at one of the respective measurement regions  414 - 1 ,  414 - 2 ,  414 - 3 . In some embodiments, the set of beam-shaping elements  426  may include a plano-concave lens having its concave surface facing a surface of the diffractive optical element  424 . In some embodiments, the set of beam-shaping elements  426  may focus the multiple beams  408 - 1 ,  408 - 2 ,  408 - 3  at overlapping or consonant measurement regions  414 - 1 ,  414 - 2 ,  414 - 3  (instead of in disjoint measurement regions  414 - 1 ,  414 - 2 ,  414 - 3 , as shown). 
     In addition to splitting an optical emission of the self-mixing interferometry sensor  402  into multiple beams, the set of optical elements  404  may receive reflections or backscatters of the multiple beams  408 - 1 ,  408 - 2 ,  408 - 3 , and direct the received reflections or backscatters into a resonant optical cavity of the self-mixing interferometry sensor&#39;s electromagnetic radiation source. The set of optical elements  404  shown in  FIG.  4   , as a whole, functions as a splitter. 
     As shown in  FIG.  4   , particles  412  passing through the measurement regions  414 - 1 ,  414 - 2 ,  414 - 3  may have a particle speed including an x-direction particle speed component ({right arrow over (v x )}) and a z-direction particle speed component ({right arrow over (v z )}). The particles  412  may also have a y-direction particle speed component ({right arrow over (v y )}). 
       FIG.  5    shows a plan view of the particulate matter sensor  400 . Although the beams  408 - 1 ,  408 - 2 ,  408 - 3  may have various relationships to one another, computations made by a processor to estimate particle speed and/or other parameters may be simplified if the beams  408 - 1 ,  408 - 2 ,  408 - 3  form an orthogonal basis. The beams  408 - 1 ,  408 - 2 ,  408 - 3  may form an orthogonal basis, in some embodiments, when each beam  408 - 1 ,  408 - 2 ,  408 - 3  is separated from other beams  408 - 1 ,  408 - 2 ,  408 - 3  by 120 degrees (120°), in a plane perpendicular to an axis  500  of the optical emission  406  described with reference to  FIG.  4   , and when each beam has a secondary axis  502 - 1 ,  502 - 2 , or  502 - 3  that diverges from the axis  500  of the optical emission by an angle, θ, where cos 2 (θ)=⅓. The angle θ may be configured as part of the optical design of the particulate matter sensor  400 . 
     In  FIG.  5    and later figures, the beams  408 - 1 ,  408 - 2 ,  408 - 3  are respectively designated Beam 1  408 - 1 , Beam 2  408 - 2 , and Beam 3  408 - 3 . 
       FIGS.  6 A- 8 B  show respective plan views and elevations of each of Beam 1, Beam 2, and Beam 3. Turning first to  FIGS.  6 A and  6 B ,  FIG.  6 A  shows a plan view of Beam 1 in relation to Beam 2 and Beam 3, and  FIG.  6 B  shows an elevation of Beam 1. In a plane perpendicular to the axis  500  of the optical emission  406 , Beam 1 is separated from each of Beam 2 and Beam 3 by 120°. Beam 1 has a secondary axis  502 - 1  that diverges from the axis  500  of the optical emission by an angle, θ. In some cases, θ may satisfy the condition: cos 2 (θ)=⅓. 
     A particle traveling through the measurement region  414 - 1  may have a particle speed vector: {right arrow over (v p )}=v x {circumflex over (x)}+v y ŷ+v z {circumflex over (z)}, where {circumflex over (x)}, ŷ, and {circumflex over (z)} are unit vectors in orthogonal x, y, and z directions. However, the self-mixing interferometry sensor  402  may only measure a component of the particle&#39;s speed, which component is in the direction of a unit vector, û 1 . The unit vector û 1  shares an axis with Beam 1, and may be defined with respect to an x/y/z orthogonal basis as:
 
 û   1 =sin(θ) {circumflex over (x)} +cos(θ) {circumflex over (z)} 
 
     When a particle passes through the measurement region  414 - 1 , the particle may generate a self-mixing interference signal (at the self-mixing interferometry sensor  402 ) oscillating at the frequency of the Doppler frequency shift induced by the particle on the reflected or back-scattered electromagnetic radiation. The Doppler frequency shift may be associated with a Doppler frequency, f 1 , which Doppler frequency may be proportionate to the particle&#39;s speed in the direction of Beam 1 and defined as follows: 
     
       
         
           
             
               f 
               1 
             
             = 
             
               
                 
                   2 
                   λ 
                 
                 ⁢ 
                 
                   
                     
                       v 
                       p 
                     
                     → 
                   
                   · 
                   
                     
                       u 
                       ^ 
                     
                     1 
                   
                 
               
               = 
               
                 
                   
                     
                       2 
                       λ 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             v 
                             x 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               θ 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             v 
                             z 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               θ 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     
                       
                         v 
                         x 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         v 
                         z 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                   
                 
                 = 
                 
                   
                     
                       f 
                       1 
                     
                     ⁢ 
                     λ 
                   
                   2 
                 
               
             
           
         
       
     
       FIG.  7 A  shows a plan view of Beam 2 in relation to Beam 1 and Beam 3, and  FIG.  7 B  shows an elevation of Beam 2. In a plane perpendicular to the axis  500  of the optical emission  406  described with reference to  FIG.  4   , Beam 2 is separated from each of Beam 1 and Beam 3 by 120°. Beam 2 has a secondary axis  502 - 2  that diverges from the axis  500  of the optical emission by an angle, θ. In some cases, θ may satisfy the condition: cos 2 (θ)=⅓. 
     A particle traveling through the measurement region  414 - 2  may also have the particle speed vector: {right arrow over (v p )}|=v x {circumflex over (x)}+v y ŷ+v z {circumflex over (z)}, but the self-mixing interferometry sensor  402  may only measure a component of the particle&#39;s speed, which component is in the direction of a unit vector, û 2 . The unit vector û 2  shares an axis with Beam 2, and may be defined with respect to an x/y/z orthogonal basis as: 
     
       
         
           
             
               
                 u 
                 ^ 
               
               2 
             
             = 
             
               
                 
                   
                     - 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   2 
                 
                 ⁢ 
                 
                   x 
                   ^ 
                 
               
               - 
               
                 
                   
                     
                       3 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   2 
                 
                 ⁢ 
                 
                   y 
                   ^ 
                 
               
               + 
               
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     θ 
                     ) 
                   
                 
                 ⁢ 
                 
                   z 
                   ^ 
                 
               
             
           
         
       
     
     When a particle passes through the measurement region  414 - 2 , the particle may generate a self-mixing interference signal (at the self-mixing interferometry sensor  402 ) oscillating at the frequency of the Doppler frequency shift induced by the particle on the reflected or back-scattered electromagnetic radiation. The Doppler frequency shift may be associated with a Doppler frequency, f 2 , which Doppler frequency may be proportionate to the particle&#39;s speed in the direction of Beam 2 and defined as follows: 
     
       
         
           
             
               f 
               2 
             
             = 
             
               
                 
                   2 
                   λ 
                 
                 ⁢ 
                 
                   
                     
                       v 
                       p 
                     
                     → 
                   
                   · 
                   
                     
                       u 
                       ^ 
                     
                     2 
                   
                 
               
               = 
               
                 
                   
                     
                       2 
                       λ 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               - 
                               
                                 v 
                                 x 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                           
                           2 
                         
                         - 
                         
                           
                             
                               3 
                             
                             ⁢ 
                             
                               v 
                               y 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                           
                           2 
                         
                         + 
                         
                           
                             v 
                             z 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               θ 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     
                       
                         v 
                         x 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         3 
                       
                       ⁢ 
                       
                         v 
                         y 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                     - 
                     
                       2 
                       ⁢ 
                       
                         v 
                         z 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                   
                 
                 = 
                 
                   
                     - 
                     
                       f 
                       2 
                     
                   
                   ⁢ 
                   λ 
                 
               
             
           
         
       
     
       FIG.  8 A  shows a plan view of Beam 3 in relation to Beam 1 and Beam 2, and  FIG.  8 B  shows an elevation of Beam 3. In a plane perpendicular to the axis  500  of the optical emission  406  described with reference to  FIG.  4   , Beam 3 is separated from each of Beam 1 and Beam 2 by 120°. Beam 3 has a secondary axis  502 - 3  that diverges from the axis  500  of the optical emission by an angle, θ. In some cases, θ may satisfy the condition: cos 2 (θ)=⅓. 
     A particle traveling through the measurement region  414 - 3  may have a particle speed vector: {right arrow over (v p )}=v x {circumflex over (x)}+v y ŷ+v z {circumflex over (z)}, where {circumflex over (x)}, ŷ, and {circumflex over (z)} are unit vectors in orthogonal x, y, and z directions. However, the self-mixing interferometry sensor  402  may only measure a component of the particle&#39;s speed, which component is in the direction of a unit vector, û 3 . The unit vector û 3  shares an axis with Beam 3, and may be defined with respect to an x/y/z orthogonal basis as: 
     
       
         
           
             
               
                 u 
                 ^ 
               
               3 
             
             = 
             
               
                 
                   
                     - 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   2 
                 
                 ⁢ 
                 
                   x 
                   ^ 
                 
               
               + 
               
                 
                   
                     
                       3 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   2 
                 
                 ⁢ 
                 
                   y 
                   ^ 
                 
               
               + 
               
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     θ 
                     ) 
                   
                 
                 ⁢ 
                 
                   z 
                   ^ 
                 
               
             
           
         
       
     
     When a particle passes through the measurement region  414 - 3 , the particle may generate a self-mixing interference signal (at the self-mixing interferometry sensor  402 ) oscillating at the frequency of the Doppler frequency shift induced by the particle on the reflected or backscattered electromagnetic radiation. The Doppler frequency shift may be associated with a Doppler frequency, f 3 , which Doppler frequency may be proportionate to the particle&#39;s speed in the direction of Beam 3 and defined as follows: 
     
       
         
           
             
               f 
               3 
             
             = 
             
               
                 
                   2 
                   λ 
                 
                 ⁢ 
                 
                   
                     
                       v 
                       p 
                     
                     → 
                   
                   · 
                   
                     
                       u 
                       ^ 
                     
                     3 
                   
                 
               
               = 
               
                 
                   
                     
                       2 
                       λ 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               - 
                               
                                 v 
                                 x 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                           
                           2 
                         
                         + 
                         
                           
                             
                               3 
                             
                             ⁢ 
                             
                               v 
                               y 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                           
                           2 
                         
                         + 
                         
                           
                             v 
                             z 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               θ 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                   → 
                   
                     
                       
                         v 
                         x 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                     - 
                     
                       
                         3 
                       
                       ⁢ 
                       
                         v 
                         y 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                     - 
                     
                       2 
                       ⁢ 
                       
                         v 
                         z 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                   
                 
                 = 
                 
                   
                     - 
                     
                       f 
                       3 
                     
                   
                   ⁢ 
                   λ 
                 
               
             
           
         
       
     
     Different particles may pass through the different measurement regions  414 - 1 ,  414 - 2 ,  414 - 3  described with reference to  FIGS.  4 - 8 B . However, the self-mixing interference signal provided by the self-mixing interferometry sensor  402  may include particle speed information for particles passing through each of the measurement regions  414 - 1 ,  414 - 2 ,  414 - 3 . In most cases, particles will pass through the different measurement regions  414 - 1 ,  414 - 2 ,  414 - 3  at different times, and thus the particle speed information for different particles will be distinguishable in time (even though the particular beam and measurement region through which a particle passed to generate the particle speed information may not be identifiable). The particle speed information may take the form of unsigned Doppler frequency shifts (e.g., If |f 1 |, |f 2 |, and |f 3 |) included in the self-mixing interference signal. Thus, only particle speed information (i.e., particle speed magnitude), and not particle speed information (i.e., a speed and direction of motion), may be extracted from the self-mixing interference signal. 
     As discussed with reference to  FIGS.  6 A- 8 B , the particle velocities (v x , v y , and v z ) of particles  412  passing through the measurement regions  414 - 1 ,  414 - 2 , and  414 - 3  are related to the angle θ, the wavelength, λ, of the optical emission  406 , and the Doppler frequencies f 1 , f 2 , and f 3  as follows:
 
 v   x  sin(θ)+ v   z  cos(θ)= f   1 λ/2
 
 v   x  sin(θ)+√{square root over (3)} v   y  sin(θ)−2 v   z  cos(θ)=− f   2 λ
 
 v   x  sin(θ)−√{square root over (3)} v   y  sin(θ)−2 v   z  cos(θ)=− f   3 λ
 
     Solving the above equations for the particle velocities v x , v y , and v z  yields the equations: 
     
       
         
           
             
               
                 v 
                 x 
               
               = 
               
                 
                   λ 
                   
                     6 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       2 
                       ⁢ 
                       
                         f 
                         1 
                       
                     
                     - 
                     
                       f 
                       2 
                     
                     - 
                     
                       f 
                       3 
                     
                   
                   ) 
                 
               
             
             ⁢ 
             
               
 
             
             ⁢ 
             
               
                 v 
                 y 
               
               = 
               
                 
                   λ 
                   
                     2 
                     ⁢ 
                     
                       3 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       f 
                       3 
                     
                     - 
                     
                       f 
                       2 
                     
                   
                   ) 
                 
               
             
             ⁢ 
             
               
 
             
             ⁢ 
             
               
                 v 
                 z 
               
               = 
               
                 
                   λ 
                   
                     6 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       f 
                       1 
                     
                     + 
                     
                       f 
                       2 
                     
                     + 
                     
                       f 
                       3 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Substituting the above equations into the particle speed equation 
     
       
         
           
             
                 
             
             ⁢ 
             
               
                  
                 
                   
                     v 
                     p 
                   
                   → 
                 
                  
               
               = 
               
                 
                   
                     
                       v 
                       x 
                       2 
                     
                     + 
                     
                       v 
                       y 
                       2 
                     
                     + 
                     
                       v 
                       z 
                       2 
                     
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 yields 
                 ⁢ 
                 
                   : 
                 
               
             
           
         
       
       
         
           
             
                
               
                 
                   v 
                   p 
                 
                 → 
               
                
             
             = 
             
               
                 λ 
                 
                   6 
                   ⁢ 
                   
                      
                     
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                      
                   
                 
               
               ⁢ 
               
                 
                   
                     
                       ( 
                       
                         1 
                         + 
                         
                           3 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             cos 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           f 
                           1 
                           2 
                         
                         + 
                         
                           f 
                           2 
                           2 
                         
                         + 
                         
                           f 
                           3 
                           2 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       ( 
                       
                         2 
                         - 
                         
                           6 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             cos 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             f 
                             1 
                           
                           ⁢ 
                           
                             f 
                             2 
                           
                         
                         + 
                         
                           
                             f 
                             1 
                           
                           ⁢ 
                           
                             f 
                             3 
                           
                         
                         + 
                         
                           
                             f 
                             2 
                           
                           ⁢ 
                           
                             f 
                             3 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     If θ is selected such that cos 2 (θ)=⅓, the above equation simplifies to: 
                      v   p     →          =       λ     6   ⁢            cos   ⁡     (   θ   )       ⁢           ⁢     sin   ⁡     (   θ   )                  ⁢       2   ⁢     (       f   1   2     +     f   2   2     +     f   3   2       )                 
and the particle speed, |{right arrow over (v p )}|, can be estimated using the unsigned Doppler frequency shifts |f 1 |, |f 2 |, and |f 3 |, without knowing the signs of the Doppler frequency shifts, and without knowing which Doppler frequency shift is experienced by which of the multiple beams  408 - 1 ,  408 - 2 ,  408 - 3  (i.e., |f 1 |, |f 2 |, and |f 3 | are interchangeable in the above equation, as are f 1 , f 2 , and f 3 ).
 
     The particle speed |{right arrow over (v p )}| may be estimated even when cos 2 (θ)≠⅓, but the accuracy of the estimation improves (and error decreases) as cos 2 (θ) approaches ⅓. When cos 2 (θ)≠⅓, particle speed may still be estimated with sufficient accuracy by placing limits on particle flow direction. 
       FIG.  9    shows an example method  900  of estimating particulate matter concentration, which method  900  may be performed by circuitry (e.g., an ASIC or processor) associated with a self-mixing interferometry sensor. The circuitry may receive, as input, digitized samples of a self-mixing interference signal generated by the self-mixing interferometry sensor, or in some cases may receive, sample, and digitize the self-mixing interference signal. The self-mixing interferometry sensor may, in some embodiments, include any of the self-mixing interferometry sensors described with reference to  FIGS.  3 - 8 B . Alternatively, the self-mixing interferometry sensor may be another type of self-mixing interferometry sensor. 
     At block  902 , the method  900  may include performing a frequency domain analysis (e.g., a fast Fourier transform (FFT)) or a time-frequency domain analysis (e.g., a continuous wavelet transform) to extract, from the self-mixing interference signal, a set of unsigned Doppler frequency shifts (e.g., |f 1 |, |f 2 |, and |f 3 |). 
     At block  904 , the method  900  may include estimating a particle speed using relative orientations of the multiple beams and the unsigned Doppler frequency shifts. Of note, the estimated particle speed is actually the speed of a hypothetical particle, which hypothetical particle is assumed to behave similarly to the particles passing through different measurement regions associated with respective different beams split from an optical emission of the self-mixing interferometry sensor. 
     At block  906 , the method  900  may include estimating, using the particle speed, an air flow volume through the measurement regions (e.g., how much air passed through a collective volume of the three measurement regions within a given time (e.g., 100 microliter (μL) of air in one second (s))). 
     At block  908 , the method  900  may include counting a number of particles passing through the measurement regions over a period of time (e.g., 30 particles in one second). Particles may be counted by counting the number of time-domain disturbances (or Doppler frequency shifts) in the self-mixing interference signal over a period of time. 
     At block  910 , the method  900  may include estimating a particulate matter concentration (e.g., a particulate matter concentration in air) using the number of particles counted at block  908  and the air flow volume estimated at block  906 . In some embodiments, the circuitry may assume a fixed particle size and fixed mass density to convert from a number of particles within a volume to a particle mass or particle density within a volume. 
     In some cases, the circuitry that performs the method  900 , or other circuitry, may be configured to detect an existence of particulate matter (instead of, or in addition to, a particulate matter concentration). In some cases, the existence (or non-existence) of particulate matter may be detected using particle speed information (e.g., the Doppler frequency shifts) extracted from the self-mixing interference signal. 
       FIG.  10    shows an example method  1000  of sensing particulate matter. The method  1000  may be performed by a self-mixing interferometry sensor and circuitry (e.g., an ASIC or processor) associated with the self-mixing interferometry sensor. The self-mixing interferometry sensor may provide, as an input to the circuitry, digitized samples of a self-mixing interference signal generated by the self-mixing interferometry sensor. Alternatively, the circuitry may receive the self-mixing interference signal, and sample and digitize the self-mixing interference signal. The self-mixing interferometry sensor may, in some embodiments, include any of the self-mixing interferometry sensors described with reference to  FIGS.  3 - 8 B . Alternatively, the self-mixing interferometry sensor may be another type of self-mixing interferometry sensor. The circuitry may in some cases be or include some or all of the circuitry that performs the method  900  described with reference to  FIG.  9   . 
     At block  1002 , the method  1000  may include splitting an optical emission received from a self-mixing interferometry sensor into multiple beams. In some embodiments, the operation(s) at block  1002  may be performed by the set of optical elements described with reference to any of  FIGS.  3 - 8 B . 
     At block  1004 , the method  1000  may include directing each beam of the multiple beams in a different direction. Optionally, the operation(s) at block  1004  may include focusing each beam of the multiple beams at one of the respective measurement regions. In some embodiments, the operation(s) at block  1004  may be performed by the set of optical elements described with reference to any of  FIGS.  3 - 8 B . 
     At block  1006 , the method  1000  may include outputting, from the self-mixing interferometry sensor, particle speed information for particles passing through the multiple beams (e.g., through respective measurement regions of the multiple beams). In some embodiments, the particle speed information may include a set of unsigned Doppler frequency shifts (e.g., |f 1 |, |f 2 |, and |f 3 |) contained in a self-mixing interference signal. 
     At block  1008 , the method  1000  may optionally include estimating a particulate matter concentration using the particle speed information. The estimate may be made by the circuitry associated the self-mixing interferometry sensor. 
     Optionally, the method  1000  may include the operations of the method  900  described with reference to  FIG.  9   . 
       FIG.  11    shows a sample electrical block diagram of an electronic device  1100 , which electronic device may in some cases take the form of the device described with reference to  FIGS.  1 A- 1 B  or  FIGS.  2 A- 2 B  and/or include a particulate matter sensor as described with reference to any of  FIGS.  3 - 8 B . The electronic device  1100  may include a display  1102  (e.g., a light-emitting display), a processor  1104 , a power source  1106 , a memory  1108  or storage device, a sensor system  1110 , or an input/output (I/O) mechanism  1112  (e.g., an input/output device, input/output port, or haptic input/output interface). The processor  1104  may control some or all of the operations of the electronic device  1100 . The processor  1104  may communicate, either directly or indirectly, with some or all of the other components of the electronic device  1100 . For example, a system bus or other communication mechanism  1114  can provide communication between the display  1102 , the processor  1104 , the power source  1106 , the memory  1108 , the sensor system  1110 , and the I/O mechanism  1112 . 
     The processor  1104  may be implemented as any electronic device capable of processing, receiving, or transmitting data or instructions, whether such data or instructions is in the form of software or firmware or otherwise encoded. For example, the processor  1104  may include a microprocessor, a central processing unit (CPU), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a controller, or a combination of such devices. As described herein, the term “processor” is meant to encompass a single processor or processing unit, multiple processors, multiple processing units, or other suitably configured computing element or elements. 
     It should be noted that the components of the electronic device  1100  can be controlled by multiple processors. For example, select components of the electronic device  1100  (e.g., the sensor system  1110 ) may be controlled by a first processor and other components of the electronic device  1100  (e.g., the display  1102 ) may be controlled by a second processor, where the first and second processors may or may not be in communication with each other. 
     The power source  1106  can be implemented with any device capable of providing energy to the electronic device  1100 . For example, the power source  1106  may include one or more batteries or rechargeable batteries. Additionally or alternatively, the power source  1106  may include a power connector or power cord that connects the electronic device  1100  to another power source, such as a wall outlet. 
     The memory  1108  may store electronic data that can be used by the electronic device  1100 . For example, the memory  1108  may store electrical data or content such as, for example, audio and video files, documents and applications, device settings and user preferences, timing signals, control signals, and data structures or databases. The memory  1108  may include any type of memory. By way of example only, the memory  1108  may include random access memory, read-only memory, Flash memory, removable memory, other types of storage elements, or combinations of such memory types. 
     The electronic device  1100  may also include one or more sensor systems  1110  positioned almost anywhere on the electronic device  1100 . In some cases, sensor systems  1110  may be positioned as described with reference to  FIGS.  1 A- 1 B , or  FIGS.  2 A- 2 B . The sensor system(s)  1110  may be configured to sense one or more type of parameters, such as but not limited to, light; touch; force; heat; movement; relative motion; biometric data (e.g., biological parameters) of a user; particulate matter concentration; air quality; proximity; position; connectedness; and so on. By way of example, the sensor system(s)  1110  may include a heat sensor, a position sensor, a light or optical sensor, an accelerometer, a pressure transducer, a gyroscope, a magnetometer, a health monitoring sensor, a particulate matter sensor, an air quality sensor, and so on. Additionally, the one or more sensor systems  1110  may utilize any suitable sensing technology, including, but not limited to, magnetic, capacitive, ultrasonic, resistive, optical, acoustic, piezoelectric, or thermal technologies. 
     The I/O mechanism  1112  may transmit or receive data from a user or another electronic device. The I/O mechanism  1112  may include the display  1102 , a touch sensing input surface, a crown, one or more buttons (e.g., a graphical user interface “home” button), one or more cameras (including an under-display camera), one or more microphones or speakers, one or more ports such as a microphone port, and/or a keyboard. Additionally or alternatively, the I/O mechanism  1112  may transmit electronic signals via a communications interface, such as a wireless, wired, and/or optical communications interface. Examples of wireless and wired communications interfaces include, but are not limited to, cellular and Wi-Fi communications interfaces. 
     The foregoing description, for purposes of explanation, uses specific nomenclature to provide a thorough understanding of the described embodiments. However, it will be apparent to one skilled in the art, after reading this description, that the specific details are not required in order to practice the described embodiments. Thus, the foregoing descriptions of the specific embodiments described herein are presented for purposes of illustration and description. They are not targeted to be exhaustive or to limit the embodiments to the precise forms disclosed. It will be apparent to one of ordinary skill in the art, after reading this description, that many modifications and variations are possible in view of the above teachings.

Metadata:
Filing Date: 20200327
Publication Date: 20231003
Grant Date: 20231003
Priority Date: 20190405
Inventors: Mutlu, Mehmet
YAN, MIAOLEI
BROWN, MICHAEL K.
YEH, RICHARD
Assignee: APPLE INC
CPC Classifications: [{"code": "G01N15/1434", "inventive": true, "first": true, "tree": "[]"}, {"code": "G01N15/06", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/001", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/20", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/26", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S7/4916", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01N2015/0693", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01N2015/1454", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01P5/26", "inventive": true, "first": true, "tree": "[]"}, {"code": "G01N15/06", "inventive": true, "first": true, "tree": "[]"}, {"code": "G01N15/1434", "inventive": true, "first": true, "tree": "[]"}, {"code": "G01S17/58", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01N15/06", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01N2015/0003", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01N2015/0046", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01P5/001", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/20", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/26", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S7/4916", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01S17/58", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01N15/06", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01N2015/1454", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01S7/4916", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/26", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/001", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01P5/20", "inventive": true, "first": false, "tree": "[]"}, {"code": "G01N15/075", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01N15/075", "inventive": false, "first": false, "tree": "[]"}, {"code": "G01N15/075", "inventive": false, "first": false, "tree": "[]"}]
Family ID: 72662202