Patent Publication Number: US-11644800-B2

Title: Coherent mixing interference based sensors for characterizing movement of a watch crown

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 16/379,551, filed Apr. 9, 2019, which is a nonprovisional of, and claims the benefit under 35 U.S.C. § 119(e) of, U.S. Provisional Patent Application No. 62/657,531, filed Apr. 13, 2018, the contents of which are incorporated by reference as if fully disclosed herein. 
    
    
     FIELD 
     The described embodiments relate generally to an electronic watch or other wearable electronic device. More particularly, the described embodiments relate to an electronic watch having a crown, and to techniques for sensing or characterizing movement of the crown. 
     BACKGROUND 
     An electronic watch or other wearable electronic device may have a crown that can be manipulated to provide user input to the device. The user input may take the form of movement or non-movement of the crown, a direction of rotation of the crown, a speed of rotation of the crown, an acceleration of the crown, a direction of translation of the crown (e.g., whether the crown is being translated inward or outward with respect to the watch), or a position of the crown (e.g., an angle of rotation or state of translation of the crown). These inputs may be characterized by one or more sensors associated with the crown, and may be reported to a processor for use by system utilities or user applications. In some cases, a processor may update a state of the watch (e.g., a displayed time, displayed screen, or speaker volume), provide feedback to an application running locally on (or remotely from) the device, or provide haptic feedback to acknowledge receipt of the user input. Often the one or more sensors may include an optical encoder that senses rotational parameters of the crown, and a tactile switch that senses translational parameters of the crown. 
     SUMMARY 
     Embodiments of the systems, devices, methods, and apparatus described in the present disclosure are directed to an electronic watch (e.g., a smart watch) or other wearable electronic device having a crown, in which user input is provided to the device by moving the crown, and parameters characterizing movement of the crown are sensed by a sensor system including one or more at least partially coherent electromagnetic radiation sources (e.g., coherent or partially coherent electromagnetic radiation sources, such as edge-emitting laser diodes, vertical-cavity surface-emitting lasers (VCSELs), quantum-dot lasers (QDLs), or superluminescent diodes) that emit, receive, and self-mix electromagnetic radiation (e.g., visible or invisible light) at least partially coherently. An electromagnetic radiation source of the sensor system may emit a beam of electromagnetic radiation toward a crown surface (e.g., a watch crown surface). The beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source. The coherent mixing of electromagnetic radiation may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source and a second amount of electromagnetic radiation redirected (e.g., reflected or scattered) into the resonant cavity by the watch crown surface. A sensor of the sensor system may measure a first parameter of the beam of electromagnetic radiation. For example, the sensor may measure a modulated power of the beam of electromagnetic radiation. The sensor may use the first parameter of the beam of electromagnetic radiation to determine a value of a second parameter characterizing movement of the crown. The second parameter may include, for example, movement or non-movement of the crown, a direction of rotation of the crown, a speed of rotation of the crown, an acceleration of the crown, a direction of translation of the crown (e.g., whether the crown is being translated inward or outward with respect to the device), or a position of the crown (e.g., an angle of rotation or state of translation of the crown). 
     In a first aspect, the present disclosure describes an electronic watch. The electronic watch may include a housing, a user-operable watch crown mounted to the housing, an electromagnetic radiation source, and a sensor. The electromagnetic radiation source may emit a beam of electromagnetic radiation toward a watch crown surface. The beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source. The coherent mixing may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source and a second amount of electromagnetic radiation redirected into the resonant cavity by the watch crown surface. The sensor may measure a first parameter of the beam of electromagnetic radiation and determine, using the measurement of the first parameter, a value of a second parameter characterizing movement of the watch crown. 
     In another aspect, the present disclosure describes a watch crown sensor system. The watch crown sensor system may include a first electromagnetic radiation source emitting a first beam of electromagnetic radiation, a second electromagnetic radiation source emitting a second beam of electromagnetic radiation, and a set of one or more sensors. The second electromagnetic radiation source may have a known position and orientation with respect to the first electromagnetic radiation source. Each of the first beam of electromagnetic radiation and the second beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a first resonant cavity of the first electromagnetic radiation source or a second resonant cavity of the second electromagnetic radiation source. The coherent mixing of electromagnetic radiation within each of the first resonant cavity and the second resonant cavity may include a mixing of a first amount of electromagnetic radiation generated by the first electromagnetic radiation source or the second electromagnetic radiation source and a second amount of electromagnetic radiation redirected into the first resonant cavity or the second resonant cavity by the watch crown surface. The set of one or more sensors may measure a first parameter of each of the first beam of electromagnetic radiation and the second beam of electromagnetic radiation, and may determine, using the measurements of the first parameter, a value of a second parameter characterizing movement of a watch crown. 
     In still another aspect of the disclosure, a method of determining a value of a parameter characterizing movement of a watch crown is described. The method may include generating a first amount of coherent light in a resonant cavity of a laser; receiving into the resonant cavity a second amount of coherent light redirected from a watch crown surface; emitting from the resonant cavity a beam of coherent light dependent on a coherent mixing of the first amount of coherent light and the second amount of coherent light; measuring a junction voltage or a bias current of the laser, the junction voltage or the bias current dependent on the coherent mixing of the first amount of coherent light and the second amount of coherent light within the resonant cavity; and determining, from at least the measurement of the junction voltage or the bias current, the value of the parameter characterizing movement of the watch crown. 
     In addition to the 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: 
         FIG.  1    shows an example of an electronic watch having a crown; 
         FIG.  2    shows a portion of a watch body (e.g., a portion of the watch body shown in  FIG.  1   ) including a watch crown assembly; 
         FIG.  3    shows alternative or additional positions for components of a sensor system; 
         FIG.  4    shows a first embodiment of a sensor system such as the sensor system described with reference to  FIG.  2   ; 
         FIGS.  5 A- 5 C  is a block diagram showing examples of the voltage sensor described with reference to  FIG.  4   ; 
         FIG.  6    shows a second embodiment of a sensor system such as the sensor system described with reference to  FIG.  2   ; 
         FIG.  7    is a block diagram showing an example of an optoelectronic sensor including the photodetector described with reference to  FIG.  6   ; 
         FIG.  8    shows a third embodiment of a sensor system such as the sensor system described with reference to  FIG.  2   ; 
         FIG.  9    shows a fourth embodiment of a sensor system, such as the sensor system described with reference to  FIG.  2   , in which one or more optical components are positioned between an electromagnetic radiation source and a watch crown surface; 
         FIG.  10    shows intended and unintended alignments of a sensor system with respect to a watch crown surface (e.g., a circumference of a crown shaft); 
         FIG.  11    shows a fifth embodiment of a sensor system such as the sensor system described with reference to  FIG.  2   ; 
         FIG.  12    shows a sixth embodiment of a sensor system such as the sensor system described with reference to  FIG.  2   ; 
         FIG.  13    shows an embodiment of a sensor system positioned to illuminate a surface of a crown cap; 
         FIGS.  14 - 19    illustrate coherent mixing of electromagnetic radiation within an electromagnetic radiation source alters (modulates) the optical power of a beam of electromagnetic radiation emitted by the electromagnetic radiation source, providing an interference signal; 
         FIG.  20    shows an example of how a beam of electromagnetic radiation dependent on a coherent mixing of electromagnetic radiation within a resonant cavity of an electromagnetic radiation source may affect an amplified output current of a photodetector using a transimpedance amplifier, over time, to produce an interference signal; 
         FIG.  21    shows an example of how a beam of electromagnetic radiation dependent on a coherent mixing of electromagnetic radiation within a resonant cavity of an electromagnetic radiation source may affect a junction voltage of a laser, over time, to produce an interference signal; 
         FIGS.  22 - 25    show how a speed of rotation of a crown may be determined from an interference signal generated as the crown is rotated; 
         FIGS.  26 - 29    show how a direction of rotation of a crown may be determined from an interference signal generated as the crown is rotated; 
         FIG.  30    shows time correlated graphs of an electromagnetic radiation source&#39;s current, wavelength, and interference signal indicating movement of a target (e.g., a crown); 
         FIG.  31    shows a flowchart of a method for determining speed or direction of rotation of a crown; 
         FIG.  32    shows an example of a circuit that can be used when determining a speed or direction of rotation of a crown in the time domain; 
         FIG.  33    shows time correlated graphs for determining a speed or direction of rotation of a crown in the time domain; 
         FIG.  34    shows time correlated graphs of a target&#39;s speed of rotation (or speed of movement) and a sampled output of the circuit shown in  FIG.  32   ; 
         FIG.  35    shows an example of a microphone having a diaphragm; 
         FIG.  36    shows an example method of determining a value of a parameter characterizing movement of a watch crown; and 
         FIG.  37    shows a sample 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 disclosure relates to techniques for characterizing the movement of a watch crown (e.g., a digital crown). The techniques utilize a sensor system that includes one or more coherent or partially coherent electromagnetic radiation sources, such as edge-emitting laser diodes, VCSELs, QDLs, or superluminescent diodes. An electromagnetic radiation source of the sensor system may emit a beam of electromagnetic radiation (e.g., a beam of coherent or partially coherent light) toward a watch crown surface (e.g., a surface of a shaft of the crown, or a surface of a cap of the crown). In some embodiments, the watch crown surface may be optically flat (e.g., providing specular reflections) or rough (e.g., providing scattering/diffusive reflections). In some embodiments, the watch crown surface may be defined by a bidirectional reflectance distribution function (BRDF). The watch crown surface need not have a structured optical pattern (e.g., an encoder pattern) thereon, but works if it does have a structured optical pattern thereon. In some cases, feedback that varies based on changes in the structured optical pattern may provide an additional or secondary means for characterizing watch crown movement. The beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source. The coherent mixing of electromagnetic radiation may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source and a second amount of electromagnetic radiation redirected (e.g., reflected or scattered) into the resonant cavity by the watch crown surface. The coherent mixing of electromagnetic radiation modifies the electric field, carrier distribution, and lasing threshold of a resonant cavity, producing a measurable interference signal (or interferometric signal). Parameters of the interference signal may be measured by measuring a junction voltage of the electromagnetic radiation source (which junction voltage may modulate in response to the coherent mixing of electromagnetic radiation within the resonant cavity when the electromagnetic radiation source is biased at a constant bias current), by measuring a bias current of the electromagnetic radiation source (which bias current may modulate in response to coherent mixing of electromagnetic radiation within the resonant cavity when the electromagnetic radiation source is biased at a constant junction voltage), or by measuring a power (e.g., an optical power) of the beam of electromagnetic radiation (which power may also modulate in response to the coherent mixing). The junction voltage or bias current may be measured by an electrical sensor, and the power (e.g., optical power) may be measured by an optoelectronic sensor. 
     The measurement of the interference signal may be used to determine a value of a second parameter characterizing movement of the crown. For example, the interference signal may be measured over a particular time interval, and input to a fast Fourier transform (FFT) algorithm to determine a spectral density of the interference signal. The strongest frequency component of the interference signal can be interpreted as a Doppler shift between the electromagnetic radiation generated by an electromagnetic radiation source and electromagnetic radiation received back into a resonant cavity of the electromagnetic radiation source. Hence, the Doppler shift contains information about the speed of rotation (velocity) of the crown. Because of the nonlinear distortion that occurs in the coherent mixing process, the phase of the second harmonic of the interference signal contains information about the direction of rotation of the crown. Alternatively (or additionally), movement of a crown (e.g., speed of rotation, direction of movement, and so on) may be deduced in the time domain. 
     In some embodiments, a watch crown assembly may include a watch crown, an electromagnetic radiation source, and a sensor. The electromagnetic radiation source may emit a beam of electromagnetic radiation toward a watch crown surface. The beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source. The coherent mixing may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source and a second amount of electromagnetic radiation redirected into the resonant cavity by the watch crown surface. A sensor may measure a first parameter of the beam of electromagnetic radiation and determine, using the measurement of the first parameter, a value of a second parameter characterizing movement of the watch crown. 
     In some embodiments, a watch crown sensor system may include a first electromagnetic radiation source, a second electromagnetic radiation source, and a set or one or more sensors. The first electromagnetic radiation source may emit a first beam of electromagnetic radiation, and the second electromagnetic radiation source may emit a second beam of electromagnetic radiation. The second electromagnetic radiation source may have a known position and orientation with respect to the first electromagnetic radiation source. Each of the first beam of electromagnetic radiation and the second beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a first resonant cavity of the first electromagnetic radiation source or a second resonant cavity of the second electromagnetic radiation source. The coherent mixing of electromagnetic radiation within each of the first resonant cavity and the second resonant cavity may include a mixing of a first amount of electromagnetic radiation generated by the first electromagnetic radiation source or the second electromagnetic radiation source and a second amount of electromagnetic radiation redirected into the first resonant cavity or the second resonant cavity by the watch crown surface. The electromagnetic radiation that is redirected into the first or second resonant cavity may be redirected from different portions of the circumference of a shaft of the watch crown. The set of one or more sensors may measure a first parameter of each of the first beam of electromagnetic radiation and the second beam of electromagnetic radiation, and may determine, using the measurements of the first parameter, a value of a second parameter characterizing movement of the watch crown. The use of measurements associated with different electromagnetic radiation sources that emit electromagnetic radiation toward different portions of a surface can enable the watch crown sensor system to factor out (or account for) certain alignment tolerances between the watch crown sensor system and the watch crown. 
     These and other embodiments are discussed with reference to  FIGS.  1 - 37   . 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. 
       FIG.  1    shows an example of an electronic watch  100  having a crown (i.e., a watch crown). The electronic watch may include a watch body  102  and a watch band  104 . The watch body  102  may include a housing  106 . As an example, the housing  106  may define a perimeter (e.g., a set of edges or sidewalls) of the watch body  102 . The housing  106  may also define part or all of a watch face or a watch back. The housing  106  may be formed by one or more housing members, which housing member(s) may include metallic, plastic, ceramic, crystal, or other types of housing members. 
     In some embodiments, as shown, the housing  106  may define one or more of a watch face opening, a watch crown shaft opening, or a button opening. The housing  106  may also define a watch back opening (not shown). A cover  108  may be mounted to the housing  106  such that it covers the watch face opening. The cover  108  may be transparent, and may protect a display mounted within the housing  106 . The display may be viewable by a user through the cover  108 . In some cases, the cover  108  may be part of a display stack, which display stack may include a touch sensing or force sensing capability. The display may be configured to depict a graphical output of the electronic watch  100 , and a user may interact with the graphical output (e.g., using a finger or stylus). As one example, a user may interact with a graphic, icon, or the like by touching or pressing a corresponding location on the cover  108 . In some examples, the cover  108  may include a crystal, such as a sapphire crystal. In other examples, the cover  108  may be formed of glass, plastic, or other materials. A second cover may be mounted to the housing  106  such that it covers a watch back opening. In alternate embodiments, the housing  106  may not include the watch face opening or the watch back opening, and the front cover  108  or back cover may be provided by portions of the housing  106 . 
     The watch body  102  may include at least one input device or selection device, such as a crown, scroll wheel, knob, dial, button, or the like, which input device may be operated by a user of the electronic watch  100 . For example, the watch body  102  may include a crown  110 . The crown may include a shaft that extends through a crown shaft opening in the housing  106 . The crown  110  may be manipulated by a user to rotate or translate the shaft. The shaft may be mechanically, electrically, magnetically, optically, or otherwise coupled to components (e.g., one or more sensors) within the housing  106 . A user may manipulate the crown  110  to, in turn, manipulate or select various elements displayed on the display, to adjust a volume of a speaker, to turn the electronic watch  100  on or off, to provide input to a system utility or user application, and so on. In addition to the crown  110 , the watch body  102  may include a button  112 . The button  112  may extend through a button opening in the housing  106 . 
     The housing  106  may include structures for attaching the watch band  104  to the watch body  102 . In some cases, the structures may include elongate recesses or apertures through which ends of the watch band  104  may be inserted and attached to the watch body  102 . In other cases, the structures may include indents (e.g., dimples or depressions) in the housing  106 , which indents may receive ends of spring pins that are attached to or threaded through ends of the watch band  104  to attach the watch band  104  to the watch body  102 . 
     The watch band  104  may be used to secure the electronic watch  100  to a user, another device, a retaining mechanism, and so on. 
     Other electronic devices that may incorporate a crown include other wearable electronic devices, other timekeeping devices, other health monitoring or fitness devices, other portable computing devices, mobile phones (including smart phones), tablet computing devices, digital media players, or the like. 
       FIG.  2    shows a portion of a watch body (e.g., a portion of the watch body  102  shown in  FIG.  1   ) including a watch crown assembly  200 . The watch crown assembly  200  may include a crown  202  and a sensor system  204 . The crown  202  may include a shaft  206  that extends through and into the watch body (e.g., through a housing  210  of the watch body), and a cap  208  that is affixed to the shaft  206  and at least partially external to the watch body. The cap  208  may be touched, rotated, or translated by a user to operate the crown  202 . The sensor system  204  may detect movement of the crown  202 . The sensor system  204  may be mounted in or on the watch body, and in some cases may be mounted partially or wholly within the housing  210 . 
     In some embodiments, the sensor system  204  may include a set of one or more coherent or partially coherent electromagnetic radiation sources (e.g., one or more edge-emitting laser diodes, VCSELs, QDLs, or superluminescent diodes) and a sensor (e.g., one or more electronic or optoelectronic circuits). More electromagnetic radiation source/sensor pairs provide multiple measurements that may be averaged or otherwise combined to improve system performance or reliability. For example, more electromagnetic radiation source/sensor pairs may increase a system&#39;s signal-to-noise ratio (SNR). Each of the electromagnetic radiation sources may emit a beam of electromagnetic radiation (e.g., visible or invisible light) toward a surface of the watch crown (i.e., toward a watch crown surface), and may be operated in a continuous wave mode or a pulsed mode. In the case of multiple electromagnetic radiation sources being operated in a pulsed mode, the electromagnetic radiation sources may be operated to emit electromagnetic radiation at the same time or at different times (e.g., in a time-multiplexed manner that can minimize cross-talk between different electromagnetic radiation source/sensor pairs). A beam of electromagnetic radiation may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source. The coherent mixing of electromagnetic radiation may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source and a second amount of electromagnetic radiation redirected (e.g., reflected or scattered) into the resonant cavity by the watch crown surface. In some cases, an electromagnetic radiation source may be coupled to a temperature controller to stabilize its operating temperature. 
     In some cases, the sensor may include a radiation-sensitive element, such as an optoelectronic sensor (e.g., a photodetector) adjacent the electromagnetic radiation source or a photodetector stacked together with (e.g., under) or integrated with the electromagnetic radiation source. Such a sensor may monitor a power (e.g., an optical power) of the beam of electromagnetic radiation, which power may modulate in response to the coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source. In other cases, the sensor may include an electrical sensor, such as a circuit that monitors a junction voltage or bias current of the electromagnetic radiation source, which junction voltage or bias current may modulate due to the coherent mixing of electromagnetic radiation within the resonant cavity of the electromagnetic radiation source. In either case, the sensor may measure at least a first parameter of the beam of electromagnetic radiation by measuring the power, junction voltage, or bias current, and may determine, using at least the first parameter, a value of at least a second parameter characterizing movement of the crown  202 . The second parameter may indicate one or more of: movement or non-movement of the crown  202 , a direction of rotation  212  of the crown  202 , a speed of rotation of the crown  202 , an acceleration of the crown  202 , a direction of translation  214  of the crown  202  (e.g., whether the crown  202  is being translated inward or outward with respect to the watch body), or a position of the crown  202  (e.g., an angle of rotation or state of translation of the crown  202 ). 
     In some embodiments, the components of the sensor system  204  may be mounted on a common substrate, or be part of a common application-specific integrated circuit (ASIC), or be included in a common module. When mounted in a common module, the module may have one or more apertures or openings through which light may be emitted from or received into the module. Each aperture or opening may be covered (e.g., by a lens or cover that allows the coherent light to pass) or uncovered. 
     By way of example, the sensor system shown in  FIG.  2    is positioned to emit electromagnetic radiation toward, and receive redirected electromagnetic radiation from, one or more portions of a circumference  216  of the shaft  206 . As shown in  FIG.  3   , the sensor system  204  may alternatively or additionally be positioned to emit electromagnetic radiation toward, and receive redirected electromagnetic radiation from, a surface at an end of the shaft  206  (e.g., when the sensor system  204  includes components positioned at  204   a ), or a surface of the cap  208  facing the watch body (e.g., when the sensor system  204  includes components positioned at  204   b ). In some embodiments, the sensor system  204  may be distributed across two or more of the positions shown in  FIGS.  2  and  3   , or at other positions. 
       FIG.  4    shows a first embodiment of a sensor system such as the sensor system  204  described with reference to  FIG.  2   . The embodiment is illustrated with respect to a cross-section of the shaft  206  of the crown  202 . The sensor system  400  may include an electromagnetic radiation source  402  positioned to emit a beam of electromagnetic radiation  404  (e.g., a beam of coherent or partially coherent light) toward the circumference  216  of the shaft  206 . The beam of electromagnetic radiation  404  may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source  402 . The coherent mixing of electromagnetic radiation may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source  402 , and a second amount of electromagnetic radiation redirected (e.g., reflected or scattered) from the circumference  216  of the shaft  206  into the electromagnetic radiation source  402  (e.g., into a resonant cavity of the electromagnetic radiation source  402 ). The axis  406  of the beam of electromagnetic radiation  404  may intersect the circumference  216  of the shaft  206 , but may not intersect the longitudinal axis  408  of the shaft  206 . In some embodiments, the axis  406  of the beam of electromagnetic radiation  404  may be neither perpendicular nor parallel to tangents of the circumference of the shaft  206  (e.g., the axis  406  may intersect the shaft  206  at an acute angle). 
     The electromagnetic radiation source  402  may include a first (or bottom) mirror  410  and a second (or top) mirror  412  stacked on (e.g., formed on) a semiconductor substrate  414 . The first and second mirrors  410 ,  412  may have reflective surfaces that face one another to form a resonant cavity  416  therebetween. The second mirror  412  may be partially transmissive, and may  1 ) allow a portion of the electromagnetic radiation generated by the electromagnetic radiation source  402  to escape the VCSEL  402 , and 2) allow a portion of the electromagnetic radiation redirected (e.g., reflected or scattered) from the circumference  216  of the shaft  206  to re-enter the resonant cavity of the electromagnetic radiation source  402 . In some embodiments, the second mirror&#39;s transmissivity to the wavelength of electromagnetic radiation generated/received by the electromagnetic radiation source  402  may be about 1%, although higher or lower transmissivities may be used. The first mirror  410  may also be partially transmissive to the wavelength of electromagnetic radiation generated/received by the electromagnetic radiation source  402 , but in some embodiments may be less transmissive than the second mirror  412 . 
     By way of example, the electromagnetic radiation source  402  may be a VCSEL having a top-emitting configuration. In other embodiments, the electromagnetic radiation source  402  may be a VCSEL having a bottom-emitting configuration. In a bottom-emitting configuration, a VCSEL may have optical elements etched to its bottom substrate to change the light emitted by the VCSEL. In some cases, the optical elements may be used to adjust the divergence of light emitted by the VCSEL. 
     The resonant cavity  416  may be electrically or optically pumped to generate electromagnetic radiation (e.g., light), and a gain material within the resonant cavity  416  may amplify the electromagnetic radiation that reflects within the resonant cavity  416  (e.g., the gain material may receive x photons and emit y photons, with y≥x). When pumped to generate electromagnetic radiation, a current (I) may flow through the electromagnetic radiation source  402 . The portion of the emitted electromagnetic radiation that is redirected from the circumference  216  of the shaft  206 , and that re-enters the electromagnetic radiation source  402 , is coherent with the electromagnetic radiation that is generated by the electromagnetic radiation source  402 , and interacts (mixes) with the generated electromagnetic radiation coherently. However, the electromagnetic radiation that re-enters the electromagnetic radiation source  402  may have a phase delay with respect to the electromagnetic radiation that is generated by the electromagnetic radiation source  402 . The coherent mixing of generated and redirected electromagnetic radiation within the resonant cavity therefore produces an interference signal that modulates the beam of electromagnetic radiation  404  emitted by the electromagnetic radiation source  402 . For example, if the nominal power of the beam of electromagnetic radiation  404  is one Watt (1 W), the actual power of the beam of electromagnetic radiation  404  may vary between 0.999 W and 1.001 W due to the coherent mixing of generated and redirected electromagnetic radiation within the electromagnetic radiation source  402 . The modulation in power (or interference signal) carries information about the movement and/or position of the crown  202 . 
     The afore-mentioned change in power happens as the threshold power of the electromagnetic radiation source  402  is modulated. For the same reason, the junction voltage of the electromagnetic radiation source  402  changes when it is driven with a constant bias current, or the current passing through the electromagnetic radiation source  402  changes when the electromagnetic radiation source  402  is driven with a constant voltage. 
     The interference signal created by the coherent mixing of generated and redirected light may be measured by a sensor, such as an electrical sensor or an optoelectronic sensor. As an example,  FIG.  4    shows an electrical sensor (e.g., a voltage sensor  418 ) coupled to the electromagnetic radiation source  402  (e.g., a VCSEL) to monitor a junction voltage (V) of the electromagnetic radiation source  402 . Measurement of the junction voltage provides an indirect measurement of the power of the beam of electromagnetic radiation  404 , because the junction voltage modulates in response to the coherent mixing of electromagnetic radiation within the electromagnetic radiation source  402 . 
     In some embodiments, the sensor system  400  may be mounted within a module  420  having an open or covered aperture  422 . 
       FIG.  5 A  is a block diagram  500  showing an example of the voltage sensor  418  described with reference to  FIG.  4   . As shown, the voltage sensor  418  may be capacitively coupled (e.g., AC-coupled, as illustrated by capacitor  504 ) to a junction  502  between the electromagnetic radiation source  402  and a constant current driver circuit  506 , and may sense the modulated voltage (V) of the junction  502  while removing the DC component of the junction voltage. Alternatively, the voltage sensor  418  may be DC-coupled to the junction  502 . The voltage sensor  418  may include, for example, a voltage amplifier  508 , a bandpass filter  510 , digitization and processing circuitry  512  (e.g., an analog-to-digital converter (ADC) and processor), and/or other components. By way of example, the voltage amplifier  508  may include a single-stage low-noise amplifier or a multi-stage low-noise amplifier. In some cases, the bandpass filter  510  may be replaced with a low-pass filter or a high-pass filter. The digitization and processing circuitry  512  may compute an FFT of an interference signal obtained from the junction voltage, and may determine a velocity from the FFT (e.g., from a Doppler frequency). Alternatively, the digitization and processing circuitry  512  (or voltage sensor  418  as a whole) may characterize watch crown movement using time-domain processing. 
       FIG.  5 B  is a block diagram  550  showing another example of the voltage sensor  418  described with reference to  FIG.  4   . As shown, the voltage sensor  418  may be capacitively coupled (e.g., AC-coupled, as illustrated by capacitor  504 ) to a junction  502  between the electromagnetic radiation source  402  and a resistor (R). The electromagnetic radiation source  402  may be driven by a constant voltage driver circuit  552 , and the voltage sensor  418  may sense a modulated voltage (V) across the resistor R, which modulated voltage corresponds to the current (I) flowing through the electromagnetic radiation source  402 . Alternatively, the voltage sensor  418  may be DC-coupled to the junction  502 . The voltage sensor  418  may include components that are the same as (or similar to) those described with reference to  FIG.  5 A . 
       FIG.  5 C  is a block diagram  580  showing another example of the voltage sensor  418  described with reference to  FIG.  4   . As shown, the voltage sensor  418  may be capacitively coupled (e.g., AC-coupled, as illustrated by capacitor  504 ) to one terminal of a resistor (R) coupled between the voltage sensor  418  and the electromagnetic radiation source  402 . The electromagnetic radiation source  402  may be driven by a constant voltage driver circuit  582 , and the voltage sensor  418  may sense a modulated voltage (V) across the resistor R, which modulated voltage corresponds to the current (I) flowing through the electromagnetic radiation source  402 . Alternatively, the voltage sensor  418  may be DC-coupled to the resistor R. The voltage sensor  418  may include, for example, a transimpedance amplifier (TIA)  584 , a bandpass filter  586 , digitization and processing circuitry  588  (e.g., an ADC and processor), and/or other components. In some cases, the bandpass filter  586  may be replaced with a low-pass filter or a high-pass filter. The digitization and processing circuitry  588  may compute an FFT of an interference signal obtained from the current flowing through the electromagnetic radiation source  402 , and may determine a velocity from the FFT (e.g., from a Doppler frequency). Alternatively, the digitization and processing circuitry  588  (or voltage sensor  418  as a whole) may characterize watch crown movement using time-domain processing. 
       FIG.  6    shows a second embodiment of a sensor system such as the sensor system  204  described with reference to  FIG.  2   . The embodiment is illustrated with respect to a cross-section of the shaft  206  of the crown  202 . The sensor system  600  may include an electromagnetic radiation source  602  positioned to emit a beam of electromagnetic radiation  604  toward the circumference  216  of the shaft  206 . The beam of electromagnetic radiation  604  may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source  602 . The coherent mixing of electromagnetic radiation may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source  602 , and a second amount of electromagnetic radiation redirected (e.g., reflected or scattered) from the circumference  216  of the shaft  206  into the electromagnetic radiation source  602  (e.g., into a resonant cavity of the electromagnetic radiation source  602 ). The electromagnetic radiation source  602  may be configured similarly to the electromagnetic radiation source  402  described with reference to  FIG.  4   , and the beam of electromagnetic radiation  604  emitted by the electromagnetic radiation source  602  may have an axis  606  oriented similar to the axis  406  of the beam of electromagnetic radiation  404  described with reference to  FIG.  4   . However, the electromagnetic radiation source  602  may be stacked together or integrated with (e.g., stacked on, or formed during a wafer process flow with) a photodetector  608  (e.g., the photodetector  608  may be formed on a semiconductor substrate  610 , and the electromagnetic radiation source  602  may be formed above the photodetector  608 , or the photodetector  608  may be formed in a first set of layers, and the electromagnetic radiation source  602  may be formed in a second set of layers, during a same wafer process flow). When the photodetector  608  and electromagnetic radiation source  602  are formed during the same wafer process flow, the wafer-level processing steps to form the photodetector  608  may occur before, after, or intermingled with the wafer-level processing steps to form the electromagnetic radiation source  602 . 
     The photodetector  608  may generate an interference signal (e.g., a current, I 2 ) that modulates based on parameters of the beam of electromagnetic radiation  604 . The interference signal (current I 2 ) may be sensed, for example, by sensing a voltage (V 2 ) across a resistance (R) through which the current I 2  flows. Alternatively, I 2  can be input to a transimpedance amplifier (TIA) and converted to a sensing voltage, as described with reference to  FIG.  7   . 
     In some embodiments, the sensor system  600  may be mounted within a module  612  having an open or covered aperture  614 . 
       FIG.  7    is a block diagram  700  showing an example of an optoelectronic sensor  702  including the photodetector  608  described with reference to  FIG.  6   . As shown, a TIA  704  may be capacitively coupled (illustrated by capacitor  706 ) to the photodetector  608 , and may sense the modulated voltage (V 2 ) while removing the DC component of the voltage V 2 . Alternatively, the photodetector  608  may be DC-coupled to the TIA  704 . The optoelectronic sensor  702  may further include, for example, a bandpass filter  708 , digitization and processing circuitry  710  (e.g., an ADC and processor), and/or other components. In some cases, the bandpass filter  708  may be replaced with a low-pass filter or a high-pass filter. The digitization and processing circuitry  710  may compute an FFT of an interference signal obtained from the photodetector  608 , and may determine a velocity from the FFT (e.g., from a Doppler frequency). Alternatively, the digitization and processing circuitry  710  (or optoelectronic sensor  702  as a whole) may characterize watch crown movement using time-domain processing. 
       FIG.  8    shows a third embodiment of a sensor system such as the sensor system  204  described with reference to  FIG.  2   . The embodiment is illustrated with respect to a cross-section of the shaft  206  of the crown  202 . The sensor system  800  may include an electromagnetic radiation source  802  positioned to emit a beam of electromagnetic radiation  804  toward the circumference  216  of the shaft  206 . The beam of electromagnetic radiation  804  may depend on a coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source  802 . The coherent mixing of electromagnetic radiation may include a mixing of a first amount of electromagnetic radiation generated by the electromagnetic radiation source  802 , and a second amount of electromagnetic radiation redirected (e.g., reflected or scattered) from the circumference  216  of the shaft  206  into the electromagnetic radiation source  802  (e.g., into a resonant cavity of the electromagnetic radiation source  802 ). The electromagnetic radiation source  802  may be configured similarly to the electromagnetic radiation source  402  described with reference to  FIG.  4   , and the beam of electromagnetic radiation  804  emitted by the electromagnetic radiation source  802  may have an axis  806  oriented similar to the axis  406  of the beam of electromagnetic radiation  404  described with reference to  FIG.  4   . However, the electromagnetic radiation source  802  may be positioned adjacent a photodetector  808  (e.g., the photodetector  808  and the electromagnetic radiation source  802  may be formed adjacent one another on a semiconductor substrate  810 ). 
     The photodetector  808  may generate an interference signal (e.g., a current, I 2 ) that modulates based on parameters of the beam of electromagnetic radiation  804 . The interference signal (current I 2 ) may be sensed as described with reference to  FIGS.  6  and  7   . In some embodiments, the photodetector  808  may monitor the output power of the beam of electromagnetic radiation  804  and generate the interference signal in response to specular reflection, of the generated beam of electromagnetic radiation  804 , from an optical element positioned within the aperture  814 . 
     In some embodiments, the sensor system  800  may be mounted within a module  812  having an open or covered aperture  814 . 
     In some embodiments, and as shown in  FIG.  9    (which in some cases may be a fourth embodiment of the sensor system  204  described with reference to  FIG.  2   ), one or more optical components (e.g., a lens  906  or other optical element having one or more reflective, refractive, or diffractive optical surfaces) may be positioned between an electromagnetic radiation source  902  and a watch crown surface  904 . For example, a lens  906  may be positioned on or over a light-emitting aperture of the electromagnetic radiation source  902 . Alternatively or additionally, in embodiments in which an adjacent photodetector  908  is used to sense parameters of a beam of electromagnetic radiation  910  emitted by the electromagnetic radiation source  902  and redirected (e.g., reflected or scattered) by the watch crown surface  904 , one or more optical components (e.g., a lens  912  or other optical element having one or more reflective, refractive, or diffractive optical surfaces) may be positioned between the watch crown surface  904  and the photodetector  908 . For example, a lens  912  may be positioned on or over a light-receiving surface of the photodetector  908 . The lens  906  and/or other optical components positioned between the electromagnetic radiation source  902  and the watch crown surface  904  may change the direction of the beam of electromagnetic radiation  910  emitted by the electromagnetic radiation source  902 , or change the direction of electromagnetic radiation redirected by the watch crown surface  904  and re-entering the electromagnetic radiation source  902 . The lens  906  and/or other optical components may also help to collimate or focus electromagnetic radiation (e.g., light), or filter out wavelengths of electromagnetic radiation other than a particular wavelength of electromagnetic radiation emitted by the electromagnetic radiation source  902 . In some cases, a lens  906  or other optical component may be formed directly on the electromagnetic radiation source  902  using semiconductor processing or die encapsulation techniques. 
     In embodiments including the photodetector  908 , the photodetector  908  may sense electromagnetic radiation redirected from the lens  906 , or electromagnetic radiation redirected from the watch crown surface  904  through the lens  912 , or a combination of both to monitor the output power of the beam of electromagnetic radiation  910  emitted by the electromagnetic radiation source  902  and generate an interference signal. 
     The lens  912  and/or other optical components positioned between the watch crown surface  904  and the photodetector  908  may change the direction of, collimate, or focus electromagnetic radiation redirected (e.g., reflected or scattered) by the watch crown surface  904 , to increase the amount of electromagnetic radiation received by the photodetector  908  (e.g., to improve electromagnetic radiation (e.g., light) collection efficiency). The lens  912  and/or other optical components may also filter out wavelengths of electromagnetic radiation other than a particular wavelength of electromagnetic radiation emitted by the electromagnetic radiation source  902 . In some cases, a lens  912  or other optical component may be formed directly on the photodetector  908  using semiconductor processing or die encapsulation techniques. 
     The lens  906  or  912  may also be used to control the spectral spread of a particular wavelength or wavelengths of electromagnetic radiation in the frequency domain. The Doppler frequency of the electromagnetic radiation is proportional to the cosine of an angle between the beam of electromagnetic radiation and the surface tangent of the watch crown surface  904 . The lens  906  or  912  may therefore be configured to stabilize this angle over the area of illumination and, therefore, the width of the Doppler frequency peak may be minimized, improving the SNR. 
     The lens  906  or  912  may be positioned on-axis or off-axis with respect to the electromagnetic radiation source  902  or photodetector  908 . 
     In some embodiments, the sensor system  900  may be mounted within a module  914  having one or more apertures  916 ,  918  in which the lenses  906 ,  912  are mounted. 
     When an electromagnetic radiation source is used to illuminate a watch crown surface and perform coherent mixing of generated/received electromagnetic radiation, the parameters of the beam of electromagnetic radiation measured by a sensor may vary based on the position or orientation of a sensor system with respect to the watch crown surface. For example, the Doppler frequency shift is a function of the cosine of an angle between the beam of electromagnetic radiation and a surface tangent of a watch crown surface.  FIG.  10    shows an intended alignment  1000  (or nominal alignment) of a sensor system  1002  with respect to a watch crown surface (e.g., a circumference  1004  of a shaft  1006 ) in solid lines, and shows an unintended alignment  1008  of the sensor system  1002  with respect to the circumference  1004  of the shaft  1006  in broken lines. 
     A beam of electromagnetic radiation  1010  emitted by the sensor system  1002  when the sensor system  1002  has the intended alignment  1000  may intersect a first portion of the circumference  1004  at a first distance and a first angle of incidence. A beam of electromagnetic radiation  1012  emitted by the sensor system  1002  when the sensor system  1002  has the unintended alignment  1008  may intersect a second portion of the circumference  1004  at a second distance and a second angle of incidence (different from the first distance and/or second angle of incidence). The unintended alignment  1008  of the sensor system  1002  may therefore change the phase shift, frequency shift, or other parameters of redirected electromagnetic radiation, and may introduce errors (e.g., angle errors or gain errors) that cause a processor to identify an incorrect speed of rotation of the crown or shaft  1006 . 
     Although not specifically shown in  FIG.  10   , an unintended alignment of the sensor system  1002  with respect to the watch crown surface may also result from an unintended alignment of a module  1014  that includes the sensor system  1002 , resulting in a module-to-crown misalignment, or from a tilt of the crown or its shaft  1006  (e.g., a tilt of the shaft  1006  along an axis that is out-of-plane with respect to the two-dimensional view shown in  FIG.  10   ). 
     In the next set of embodiments, a sensor system includes multiple electromagnetic radiation sources having a predetermined relationship (e.g., two electromagnetic radiation sources that are formed or mounted on a substrate with a predetermined spacing and orientation therebetween), and signals generated by the multiple electromagnetic radiation sources may be used in combination to factor out assembly tolerances (e.g., particular misalignments of the sensor system with respect to the watch crown surface). 
       FIG.  11    shows a fifth embodiment of a sensor system such as the sensor system  204  described with reference to  FIG.  2   . The embodiment is illustrated with respect to a cross-section of the shaft  206  of the crown  202 . The sensor system  1100  may include a first electromagnetic radiation source  1102  configured to emit a first beam of electromagnetic radiation  1104  toward the circumference  216  of the shaft  206 , and a second electromagnetic radiation source  1106 ) configured to emit a second beam of electromagnetic radiation  1108  toward the circumference  216  of the shaft  206 . Each beam of electromagnetic radiation  1104 ,  1108  may depend on a coherent mixing of electromagnetic radiation within a first resonant cavity of the first electromagnetic radiation source  1102  or a second resonant cavity of the second electromagnetic radiation source  1106 . The coherent mixing of electromagnetic radiation within each of the first resonant cavity and the second resonant cavity may include a mixing of a first amount of electromagnetic radiation generated by the first electromagnetic radiation source  1102  or the second electromagnetic radiation source  1106  and a second amount of electromagnetic radiation redirected into the first resonant cavity or the second resonant cavity from the circumference  216  of the shaft  206 . Each of the first electromagnetic radiation source  1102  and the second electromagnetic radiation source  1106  may be configured similarly to any of the electromagnetic radiation sources described with reference to  FIG.  4 ,  6 ,  8   , or  9 . A set of one or more sensors  1110  may be associated with each electromagnetic radiation source  1102  or  1106  (e.g., as a circuit that monitors a junction voltage or bias current of the electromagnetic radiation source  1102  or  1106 , or as a photodetector stacked together or monolithically integrated with the electromagnetic radiation source  1102  or  1106 ), or be configured as a photodetector positioned adjacent each electromagnetic radiation source  1102  or  1106 . In  FIG.  11   , and by way of example, the set of one or more sensors  1110  is presumed to include a circuit (e.g., a voltage sensor) that monitors a junction voltage of each electromagnetic radiation source  1102 ,  1106 . 
     The electromagnetic radiation sources  1102 ,  1106  may be formed on a common substrate  1112 , with a predetermined spacing and orientation therebetween. In operation, the electromagnetic radiation sources  1102 ,  1106  may emit electromagnetic radiation toward (e.g., illuminate) different portions of the shaft  206  having different slopes (e.g., slopes M 1  and M 2 ). However, a change in the illuminated portions of the shaft  206  due to misalignment of the sensor system  1100  with respect to the shaft  206  may be compensated for using 1) the known spacing and orientation between the electromagnetic radiation sources  1102 ,  1106 , in combination with  2 ) parameters of the beams of electromagnetic radiation  1104 ,  1108  (which beams of electromagnetic radiation  1104 ,  1108  modulate as a result of coherent mixing of electromagnetic radiation within the resonant cavities of the electromagnetic radiation sources  1102 ,  1106 , and modulate differently based on which portions of the shaft  206  are illuminated by the electromagnetic radiation sources  1102 ,  1106 ). The electromagnetic radiation sources  1102  and  1106  may emit beams of electromagnetic radiation at the same time or at different times (e.g., in a time-multiplexed manner that can mitigate or prevent cross-talk). 
     In some cases, a change in the illuminated portions of the shaft  206 , due to misalignment of the sensor system  1100  with respect to the shaft  206 , may also or alternatively be compensated for by combining the interference signals generated by the first and second electromagnetic radiation sources  1102 ,  1106  or combining computations based thereon. For example, a speed of rotation ( v ) of the shaft  206  may be computed by averaging a first speed of rotation ( v   A ) computed using measurements of the first beam of electromagnetic radiation  1104  and a second speed of rotation ( v   B ) computed using measurements of the second beam of electromagnetic radiation  1108 : 
     
       
         
           
             
               v 
               _ 
             
             = 
             
               
                 
                   
                     v 
                     _ 
                   
                   A 
                 
                 - 
                 
                   
                     v 
                     _ 
                   
                   B 
                 
               
               2 
             
           
         
       
     
     In the above equation, the first and second beams of electromagnetic radiation  1104 ,  1108  are presumed to intersect the circumference  216  of the shaft  206  at positive and negative angles of incidence, such that  v   A  and  v   B  have opposite signs. 
     More complicated compensation equations can also be derived and used by calculating the change in M 1  and M 2  (and therefore the change in speed/velocity estimations  v   A  and  v   B ) as a function of the misalignment of the electromagnetic radiation sources  1102 ,  1106  from nominal. Such equations generally depend on the nominal values of M 1  and M 2 . 
       FIG.  12    shows a sixth embodiment of a sensor system such as the sensor system  204  described with reference to  FIG.  2   . The embodiment is illustrated with respect to a cross-section of the shaft  206  of the crown  202 . The sensor system  1200  is similar to the sensor system  1100  described with reference to  FIG.  11    and may include a first electromagnetic radiation source  1202  configured to emit a first beam of electromagnetic radiation  1204  toward the circumference  216  of the shaft  206 , and a second electromagnetic radiation source  1206  configured to emit a second beam of electromagnetic radiation  1208  toward the circumference  216  of the shaft  206 . However, a lens  1210  or other optical element(s) may be mounted between the first electromagnetic radiation source  1202  and the shaft  206 , and/or a lens  1212  or other optical element(s) may be mounted between the second electromagnetic radiation source  1206  and the shaft  206 . In some cases, a lens or other optical element (e.g., the lens  1210  or  1212 ) may redirect the beam of electromagnetic radiation  1204  or  1208  emitted by the electromagnetic radiation source  1202  or  1206 , or redirect, collimate, or focus light reflected or scattered by the circumference  216  of the shaft  206  for reception back into the electromagnetic radiation source  1202  or  1206 . As an example, the lenses  1210 ,  1212  shown in  FIG.  12    redirect the beams of electromagnetic radiation  1204 ,  1208  emitted by the first and second electromagnetic radiation sources  1202 ,  1206  and cause the beams to cross before they illuminate different portions of the circumference  216  of the shaft  206 . In other embodiments, the beams of electromagnetic radiation  1204 ,  1208  may be redirected but not cross. 
     In some embodiments, the lens  1210  or  1212  may filter electromagnetic radiation (e.g., light) and allow only the wavelength of electromagnetic radiation emitted by the electromagnetic radiation source  1202  or  1206  (or a small range of wavelengths) to pass. 
     The sensor system  1100  or  1200  may be relatively wide in a direction transverse to the axis  408  of the shaft  206 , but relatively thin in a direction parallel to the axis  408  of the shaft  206 . In some embodiments, the sensor system  1100  or  1200  may be mounted within a module housing  1114  or  1214 . In some embodiments, the module housing  1114  or  1214  may be substantially non-reflective (or less reflective than the circumference  216  of the shaft  206 ). The module housing  1114  may have a pair of openings or windows through which the beams of electromagnetic radiation  1104 ,  1108  pass. The module housing  1214  may have the lenses  1210  and  1212  mounted within openings therein. 
       FIG.  13    shows an embodiment of a sensor system  1300  positioned to illuminate a surface  1302  of a crown cap  1304 . The crown cap  1304  may or may not be attached to a shaft that extends through a housing  1306  of a watch body (e.g., in some embodiments, an entirety of a watch crown may be positioned external to the housing  1306 , and in some embodiments, the watch crown may only include the crown cap  1304 ). By way of example, the crown cap  1304  is not attached to a shaft, but is coupled to the housing  1306  by a circumferential groove  1308  on the crown cap  1304  that receives a circumferential ridge  1310  within a crown cap retainer  1312  affixed to the housing  1306 . In alternate embodiments, the ridge may be formed on the crown cap  1304  and the groove may be formed in the crown cap retainer  1312 , or the crown cap  1304  may be retained by a crown cap retainer in other ways. The crown cap retainer  1312  may be an integral part of the housing  1306 , or may be permanently or semi-permanently mounted to the housing  1306 . 
     The sensor system  1300  may be mounted within the housing  1306 . The sensor system  1300  may include an electromagnetic radiation source that emits a beam of electromagnetic radiation  1314  toward a surface  1302  of the crown cap  1304  facing the housing  1306 . The beam of electromagnetic radiation  1314  may pass through an opening  1316  in the housing  1306 . The opening  1316  may be covered by a cover, lens, or other optical component that is transparent to at least a wavelength of electromagnetic radiation emitted by the electromagnetic radiation source. In some embodiments, the housing  1306  may not include the opening, but may be formed of a material that is transparent to at least a wavelength of electromagnetic radiation emitted by the electromagnetic radiation source. In some embodiments, the housing  1306  or optical component through which the beam of electromagnetic radiation  1314  passes may be coated with an ink or film that matches or coordinates with a color of the watch body and passes at least a wavelength of electromagnetic radiation emitted by the electromagnetic radiation source. 
     In some embodiments, the axis of the beam of electromagnetic radiation  1314  may intersect the surface  1302  of the crown cap  1304  at an angle other than 90 degrees (e.g., at an acute angle). In alternatives to the embodiment shown in  FIG.  13   , a shaft may be attached to the crown cap  1304 , and a sensor system may emit electromagnetic radiation toward an end of the shaft (as discussed with reference to  FIG.  3   ), or the shaft may include a disc or larger diameter portion having a surface that extends radially from the shaft, and a sensor system may emit electromagnetic radiation toward a surface of the disc or larger diameter portion. 
       FIGS.  14 - 19    illustrate coherent mixing of electromagnetic radiation within a resonant cavity of an electromagnetic radiation source alters (modulates) the power of a beam of electromagnetic radiation emitted by the electromagnetic radiation source, thereby providing an interference signal. 
     As shown in  FIG.  14   , an electromagnetic radiation source  1400  may include a first mirror  1402  and a second mirror  1404  defining opposite ends of a resonant cavity  1406 . Each mirror may include a plurality of layers of material defining a distributed Bragg reflector (e.g., a set of layers having alternating high and low refractive indices). Electromagnetic radiation generated by the electromagnetic radiation source  1400  reflects between the mirrors  1402 ,  1404  and is amplified as it passes through an optical gain material  1408  (a quantum well) between the mirrors  1402 ,  1404 . The gain material may include multiple doped layers of III-V semiconductors (i.e., layers from the third row of the periodic table, and layers from the fifth row of the periodic table). In one example, the gain material may include aluminum-gallium-arsenide (AlGaAs), indium-gallium-arsenide (InGaAs), or gallium-arsenide (GaAs). 
     The electromagnetic radiation within the resonant cavity  1406  is: coherent (i.e., all photons in the light have a same frequency (i.e., same wavelength, λ) and phase), has an electric field E 0 (r), and has a carrier profile n 0 (r). The electrical field at any point within the resonant cavity  1406  is a function (cosine function) of the distance between the mirrors  1402 ,  1404 . The electrical field at each mirror  1402 ,  1404  is zero. The resonant cavity  1406  may be pumped electrically, by applying a voltage across the resonant cavity  1406  (e.g., to electrodes formed on each mirror, outside the resonant cavity  1406 ), or optically, by receiving electromagnetic radiation into the resonant cavity  1406 . The second mirror  1404  may have a reflectivity of less than 100% (e.g., 99%), such that a portion of the electromagnetic radiation amplified by the optical gain material  1408  may escape the resonant cavity  1406  through the second mirror  1404  (e.g., into free space). The escaping electromagnetic radiation has an emission power (i.e., an optical power) of P 0 . 
     As shown in  FIG.  15   , the electromagnetic radiation emitted by the electromagnetic radiation source  1400  may reflect from a target  1502  (e.g., a watch crown surface) positioned at a nominal distance, L, from the second mirror  1404 . Some of the reflected electromagnetic radiation may re-enter the resonant cavity  1406  as feedback. The feedback carries information about the target  1502 . The electromagnetic radiation that re-enters the resonant cavity  1406  mixes with the electromagnetic radiation generated by the electromagnetic radiation source  1400  coherently, to modify both the electromagnetic radiation within the resonant cavity  1406  and the electromagnetic radiation emitted by the electromagnetic radiation source  1400 . The modified electromagnetic radiation within the resonant cavity  1406  has an electric field, E 0 (r)+E f     B    (r, L), and a carrier profile, n 0 (r)+Δn(r, L). A portion of the electromagnetic radiation that mixes within the resonant cavity  1406  may escape the resonant cavity  1406  through the second mirror  1404 , into free space, and has an emission power of P 0 −ΔP(L). The nominal distance to the target, L, can be considered a length of a feedback cavity, such that the resonant cavity  1406  and the feedback cavity represent arms (or branches) of an interferometer, and the power of the beam of electromagnetic radiation emitted by the electromagnetic radiation source  1400  is an interference signal. 
     Electromagnetic radiation feedback also changes the emission frequency (or wavelength) of the electromagnetic radiation source  1400 , due to a modification of the resonant cavity resonance condition in the presence of the feedback cavity. In some embodiments, this wavelength change can be used to detect the interference signal. 
       FIG.  16    is a plot showing the distance traveled by a beam of electromagnetic radiation (e.g., a beam of electromagnetic radiation (e.g., light) emitted by an electromagnetic radiation source), in free space (e.g., in the scenario illustrated in  FIG.  14   ), over time.  FIG.  16    characterizes the distance traveled by the electromagnetic radiation in terms of a potential feedback cavity length, L, and a number of wavelengths of coherent electromagnetic radiation, λ, that define the length of the feedback cavity. Assuming that a feedback cavity has a fixed length, L,  FIG.  17    shows a plot of P 0 −ΔP(L) over time. The target always reflects or scatters the same power, but the phase of the reflected or scattered electromagnetic radiation varies. Depending on this phase, ΔP(L) takes a cosine form with ΔP(L) ∝ cos (4πL/λ). In the presence of a strongly varying target movement, this cosine signal can become distorted in a way that indicates the direction of movement of the target. The target may be configured to always redirect the same power of electromagnetic radiation, such that the phase of the redirected electromagnetic radiation that couples into the resonant cavity of the electromagnetic radiation source depends on (or varies with) the feedback cavity length, L. 
       FIG.  18    shows a plot indicating effective changes in feedback cavity length, L, over time, as might occur when a user rotates a crown such that a surface of the crown effectively moves toward (forward, or in one direction) or away (backward, or in an opposite direction) with respect to a laser. By way of example, the feedback cavity length, L, is shown to have a nominal length equal to 2.35λ.  FIG.  19    shows the power associated with a beam of electromagnetic radiation reflected by a rotating crown as the crown is rotated in one direction (e.g., forward, or clockwise) then another direction (e.g., backward, or counter-clockwise). When the crown is rotating in the forward direction (e.g., away from the beam of electromagnetic radiation), the power of the reflected beam of electromagnetic radiation has a cosine profile with fringes (peaks) leaning to the left. When the crown is rotating in the backward direction (e.g., toward the beam of electromagnetic radiation), the power of the reflected beam of electromagnetic radiation has a cosine profile with fringes leaning to the right. How pronounced the leaning is depends on the crown surface roughness, the reflectivity of the crown surface, and the distance between the electromagnetic radiation source and the crown surface. 
       FIG.  20    shows an example of how a beam of electromagnetic radiation dependent on a coherent mixing of electromagnetic radiation within a resonant cavity of an electromagnetic radiation source may affect an amplified output current of a photodetector using a TIA (e.g., the photodetector described with reference to  FIG.  6  or  8   ), over time, to produce an interference signal  2002 .  FIG.  21    shows an example of how the same beam of electromagnetic radiation may affect a junction voltage of an electromagnetic radiation source (e.g., the junction voltage of the electromagnetic radiation source described with reference to  FIG.  4   ), over time, to produce an interference signal  2102 . In each of  FIGS.  20  and  21   , the time lapse between two fringes in the illustrated waveform is associated with a length (or distance) of λ/2, and thus, a distance to a target or a speed of movement of a target may be determined from the interference signal shown in  FIG.  20  or  21    in the time domain. 
       FIGS.  22 - 25    show how a speed of rotation of a crown may be determined from an interference signal generated as the crown is rotated.  FIG.  22    shows the resonant cavity  1406  and feedback cavity described with reference to  FIG.  15   , but shows the target  1502  moving at a speed,  v , along the axis of the beam of electromagnetic radiation emitted/received by the resonant cavity. In the case of a crown, the crown may be rotating at a speed of rotation having a component parallel to the propagation direction of the electromagnetic radiation. 
     A beam of electromagnetic radiation emitted by the electromagnetic radiation source  1400  may be emitted at a wavelength, λ, but reflected at a wavelength of λ+Δλ due to movement of the target  1502 . A Doppler shift between the electromagnetic radiation generated by the electromagnetic radiation source  1400  and the electromagnetic radiation redirected by the target  1502  therefore exists within the resonant cavity  1406  and affects the beam of electromagnetic radiation emitted by the electromagnetic radiation source  1400 . This Doppler shift is also present in the junction voltage of the electromagnetic radiation source  1400 , and in a current or voltage generated by a photodetector that detects the beam of coherent light. In addition, the Doppler shift is also present in the bias current of the electromagnetic radiation source  1400  when the electromagnetic radiation source  1400  is driven at a constant voltage. The Doppler shift includes information about the velocity of the target  1502  (e.g., the velocity of a crown), whereas the phase of the second harmonic of the beam of electromagnetic radiation indicates a direction of rotation of the crown. 
     The junction voltage of the electromagnetic radiation source  1400  (e.g., an interference signal) may be monitored as a crown is rotated, and amplified by a voltage sensor. The amplified junction voltage may have a waveform  2300  as shown in  FIG.  23   . Upon visual inspection, the interference signal appears to have a distorted cosine function with a slight lean to the right (implying movement of the crown in a first direction). An FFT  2400  of the interference signal may appear as shown in  FIG.  24   , and may include a number of frequency components, including a DC component  2402  at frequency 0, a fundamental beat  2404  at frequency f B , a second harmonic  2406  at frequency 2f B , and a third harmonic  2408  at frequency 3f B . The following equations may be used, for example, to determine the speed of movement (e.g., speed of rotation) of the target  1502  shown in  FIG.  15  or  22   , or the speed of a watch crown: 
     
       
         
           
             
               f 
               B 
             
             = 
             
               c 
               × 
               
                 Δλ 
                 
                   λ 
                   2 
                 
               
             
           
         
       
       
         
           
             Δλ 
             = 
             
               
                 
                   2 
                   ⁢ 
                   λ 
                 
                 c 
               
               ⁢ 
               
                 v 
                 _ 
               
             
           
         
       
     
     In the above equations, c is the speed of light. The table  2500  shown in  FIG.  25    shows an example set of relationships between the speed ( v ), Δζ, and the fundamental beat (f B ). 
       FIGS.  26 - 29    show how a direction of rotation of a crown may be determined from an interference signal generated as the crown is rotated.  FIG.  26    shows an example of an interference signal  2600  (e.g., a voltage signal) that may be generated over time as a crown is rotated. Upon visual inspection, the interference signal appears to be defined by a cosine function, but with a distortion that causes the fringes of the cosine waveform to lean to the right (implying movement of the crown in a first rotational direction).  FIG.  27    shows an FFT  2700  of the interference signal  2600  (e.g., an amplitude  2702  of the signal&#39;s frequency components, and a phase  2704  of the signal&#39;s frequency components). The phases of the first and second harmonics is indicative of the direction of rotation. For example, by solving the equation 2×(phase at f B )−(phase at 2f B ), rotated value of 103.3° may be obtained, which is greater than zero. Thus the crown has been rotated in the first direction (e.g., clockwise, or away from the sensor system). 
       FIG.  28    shows another example of an interference signal  2800  (e.g., a voltage signal) that may be generated over time as the crown is rotated. Upon visual inspection, the interference signal appears to be defined by a cosine function, but with a distortion that causes fringes of the cosine waveform to lean to the left (implying movement of the crown in a second rotational direction).  FIG.  29    shows an FFT  2900  of the interference signal  2800  (e.g., an amplitude  2902  of the signal&#39;s frequency components, and a phase  2904  of the signal&#39;s frequency components). The phases of the first and second harmonics is indicative of the direction of rotation. For example, by solving the equation 2×(phase at f B )−(phase at 2f B ), a value of −103.3° may be obtained, which is less than zero. Thus, the crown has been rotated in the second direction (e.g., counter-clockwise, or toward the sensor system). 
       FIG.  30    shows time correlated graphs  3000  of an electromagnetic radiation source&#39;s current  3002  (also called a modulated current), wavelength  3004 , and interference signal  3006  indicating movement of a target (e.g., a crown). The interference signal  3006  is shown superimposed on the current  3002 . The interference signal  3006  may be generated in response to a user moving a crown (e.g., in response to user input), and may be detected in by monitoring a current or voltage of an adjacent or integrated photodetector, or by monitoring a junction voltage (when the electromagnetic radiation source is at a constant current) or a bias current (when the electromagnetic radiation source is at a constant voltage). By driving an electromagnetic radiation source with a modulated input, such as the current  3002  having a triangular waveform, the electromagnetic radiation produced by the electromagnetic radiation source may have a wavelength  3004  that modulates similarly. As a result of movement of a crown (or other surface illuminated by a beam of electromagnetic radiation emitted by the electromagnetic radiation source), the coherent mixing of electromagnetic radiation within a resonant cavity of the electromagnetic radiation source causes the interference signal  3006  to appear as a waveform having a distorted cosine function superimposed on the modulated waveform  3002 . The triangular-shaped modulated current  3002  can enable spectrum analyses (e.g., FFTs, as explained with respect to  FIG.  31   ) of samples taken during the time intervals corresponding to ascending edges and/or descending edges of the triangular-shaped modulated current  3002 . While the graphs  3000  are shown for a triangular-shaped modulated current  3002 , the current could alternatively be modulated according to waveforms having other shapes. Also, while the current  3002  is shown to have equal time ascending and descending time intervals, these time intervals may have different durations in some embodiments. 
       FIG.  31    shows a flowchart  3100  of a method for determining speed or direction of rotation of a crown. The flowchart  3100  is predicated on driving an electromagnetic radiation source with a modulated current (e.g., current  3002 ) or voltage, and obtaining an interference signal (e.g., the signal  3006 ). At blocks  3102  and  3104 , the interference signal  3006  and modulated current  3002  are received at a processor. Various blocks of the method may be performed by the same or different processors. 
     At blocks  3106   a  and  3106   b , the direct current (DC) component of the two signals may be optionally computed removed from the signals  3002  and  3006 . At block  3108 , the signals  3002  and  3006  may be equalized, as necessary; the modulated signal  3002  may be subtracted from the signal  3006 , and information (e.g., digital samples) associated with the ascending and descending edges (sides) of the interference signal  3006  may be separated. 
     At block  3110 , a separate FFT may be performed for the information associated with the ascending edges and the information associated with the descending edges, and at block  3112 , the separate FFT spectra may be averaged. 
     At block  3114 , further processing of the averaged FFT spectra may be undertaken (e.g., to remove artifacts and reduce noise). Such further processing may include windowing, peak detection, and Gaussian fitting. 
     From the processed FFT spectra, information regarding user input to a crown, such as a speed or direction of rotation, can be obtained. 
     The method just described, and variations thereof, involve applying a spectrum analysis to an interference signal (e.g., a waveform having a distorted cosine function). Alternative methods for characterizing movement of a watch crown may be performed in the time domain, and may not require performing a spectrum analysis. 
       FIG.  32    shows an example of a circuit  3200  that can be used when determining a speed or direction of rotation of a crown in the time domain. A time domain analysis can be used to obtain properties of a user input directly from an interference signal, without the need to perform a spectrum analysis. The configuration of the circuit  3200  is one example of an embodiment, and in some cases the circuit may be otherwise embodied. 
     The circuit  3200  includes two sections. The first section  3202  includes an electromagnetic radiation source, such as a VCSEL  3204 , and other biasing circuitry. The circuitry includes an amplifier  3206  that accepts a bias voltage input and produces an output that drives a gate of transistor  3208  positioned at the cathode of the VCSEL  3204 . This input circuitry can be used to apply the modulated current  3002  to the VCSEL  3204 . Included in section  3202  is a sensing resistor (R SENSE ). 
     The second section  3220  of the circuit  3200  may receive and analyze an interference signal included a beam of electromagnetic radiation emitted by the VCSEL  3204 . In the particular embodiment shown, coherent light is received from the VCSEL  3204  at a photodiode  3210 . In other embodiments, such as those that do not use a photodiode, the interference signal may be obtained as a junction voltage, bias current, power, or other electrical property measured in section  3202 . For example, the current across the sensing resistor in section  3202 , rather than the photodiode current or voltage shown, may be the input to the amplifier  3212 . The amplifier  3212  can be used to buffer and/or amplify the interference signal. 
     The output of amplifier  3212  may be input to a pair of comparators  3214   a  and  3214   b . The comparators  3214   a  and  3214   b  may be configured to trigger at different threshold voltages, VTH 1  and VTH 2 , and may respectively detect rising and falling edges of the interference signal. The threshold voltages of the comparators  3214   a  and  3214   b  can be controlled by a microcontroller  3216  or other processor. In embodiments in which the microcontroller  3216  has digital outputs, the digital outputs thereof can adjust the trigger threshold voltages of the comparators  3214   a  and  3214   b  by first being converted to analog threshold voltages by the digital-to-analog (DAC) converters  3218   a  and  3218   b.    
       FIG.  33    shows time correlated graphs  3300  for determining a speed or direction of rotation of a crown in the time domain. The graphs  3300  show an interference signal  3302 , together with the outputs  3304  and  3306  of the comparators  3214   a  and  3214   b  described with reference to  FIG.  32   . The interference signal  3302 , in the example shown, traces a distorted cosine function. The comparator  3214   a  is configured (by the trigger threshold voltage, VTH 1 ) to detect when the signal  3302  crosses a high threshold, T 1 , and the comparator  3214   b  is configured (by the trigger threshold voltage, VTH 2 ) to detect when the signal  3302  crosses a lower threshold, T 2 . 
     Because the lower threshold T 2  is set lower than the upper threshold T 1 , the interference signal  3302  exceeds the lower threshold T 2  during a longer time period than it exceeds the upper threshold T 1 . The time period during which the signal  3302  exceeds the upper threshold T 1  is a sub-period of the time period during which the signal  3302  exceeds the lower threshold T 2 . As a consequence, there is a first time interval  3308  between when the comparator  3214   b  triggers ‘on’ until when the comparator  3214   a  triggers ‘on.’ This is the time difference between rising edges. Similarly, there is a second time interval  3310  between when the comparator  3214   a  triggers ‘off’ until when the comparator  3214   b  triggers ‘off.’ This is the time difference between falling edges. 
     The difference in lengths of time of the first time interval  3308  and the second time interval  3310  can be used to characterize watch crown movement. In the example shown, a watch crown is moving in a first direction (e.g., clockwise, or toward an electromagnetic radiation source), such that the signal  3302  has a distorted cosine shape with fringes leaning to the right. As result, the first time interval  3308  exceeds the second time interval  3310 . This excess implies the first direction of crown rotation. An opposite direction of movement would be implied by the opposite condition. The durations of the time periods during which the signal  3302  exceeds the lower threshold T 1  and the upper threshold T 2  may also be used to determine the speed of rotation of a crown. 
       FIG.  34    shows time correlated graphs  3400  of a target&#39;s speed of rotation (or speed of movement) and a sampled output of the circuit shown in  FIG.  32   . In this embodiment, the interference signal  3404  may in some cases be a sampling of the output of the amplifier  3212  shown in  FIG.  32   . The sampling period can be chosen to detect rapid changes in the target velocity due to user input. The interference signal  3404  shown may, for example, represent samples of the continuous time signal  3402 . 
     In the correlated graphs  3400 , the velocity  3402  is initially zero (or approximately so), such as may occur when a crown is not moved. When a user begins moving the crown, the velocity  3402  shows an initial increase before stabilizing at the user&#39;s desired scroll speed. As a result, the sampled interference signal  3404  may alternately exceed the upper threshold T 1  and then fall back below the lower threshold T 2 . The time interval  3406  from exceeding the upper threshold T 1  till falling below the lower threshold T 2  can be related to the target velocity. Similarly, the time interval between a sample being below the lower threshold T 2  until a sample exceeds the upper threshold T 1  may be used to determine the speed of rotation or other characteristics of watch crown movement. 
     To detect translation of a crown, a sensor system including an electromagnetic radiation source (as described herein) may be positioned at  204   a  or  204   b  in  FIG.  3   , for example, and may emit a beam of electromagnetic radiation having an axis that has a vectorial component parallel to the longitudinal axis of the shaft  206  shown in  FIG.  3   .  FIG.  35    shows another application in which a sensor system including an electromagnetic radiation source may be positioned to detect movement of a surface (or target) toward or away from the sensor system. In particular,  FIG.  35    shows an example of a microphone  3500  having a diaphragm  3502 . The diaphragm  3502  may be generally planar and have a circular circumference. In other embodiments, the diaphragm  3502  may be cupped, or have an oval or square perimeter, or have other shapes or forms. In some embodiments, the bottom (or inner) surface  3504  of the diaphragm  3502  may be optically flat (e.g., providing specular reflections) or rough (e.g., providing scattering/diffusive reflections). In some embodiments, the surface  3504  may be defined by a BRDF. 
     The diaphragm  3502  may be supported at its perimeter by a housing or mechanical support member  3506  having an opening therein. The microphone  3500  need not have a backplate forming a cavity under the diaphragm  3502 . Elimination of any cavity or backplate under the diaphragm  3502  tends to reduce thermal noise and increase the SNR of the microphone  3500 . 
     A sensor system  3508  may be positioned under the diaphragm  3502 . The sensor system  3508  may include an electromagnetic radiation source  3510  (e.g., a VCSEL or other source) and a sensor  3512 . The sensor  3512  may include an electrical sensor (e.g., a voltage or current detector) or optoelectronic sensor (e.g., a photodetector), and may be configured similarly to one or more of the sensors described with reference to  FIG.  4 ,  6   , or  8 . By way of example,  FIG.  35    shows the sensor  3512  to be a photodetector positioned adjacent the electromagnetic radiation source  3510 . 
     In some embodiments of the microphone  3500 , one or more optical components (e.g., a lens  3514 ) may be positioned between the electromagnetic radiation source  3510  and the diaphragm  3502 . Alternatively or additionally, in embodiments in which the sensor  3512  includes a photodetector positioned adjacent the electromagnetic radiation source  3510 , one or more optical components (e.g., a lens  3516 ) may be positioned between the diaphragm and the photodetector. A lens and/or other optical components positioned between the laser and the diaphragm may, for example, collimate or focus electromagnetic radiation (e.g., light), or filter out wavelengths of electromagnetic radiation other than a particular wavelength or wavelengths of electromagnetic radiation emitted by the electromagnetic radiation source. In some cases, a lens or other optical component may be formed directly on the electromagnetic radiation source  3510  using semiconductor processing or die encapsulation techniques. 
     A lens  3516  and/or other optical components positioned between the diaphragm  3502  and a photodetector may focus electromagnetic radiation redirected (e.g., reflected or scattered) by the diaphragm  3502  to increase the amount of electromagnetic radiation received by the photodetector (e.g., to improve electromagnetic radiation collection efficiency). The lens  3516  and/or other optical components may also filter out wavelengths of electromagnetic radiation other than a particular wavelength of electromagnetic radiation emitted by the electromagnetic radiation source  3510 . In some cases, a lens  3516  or other optical component may be formed directly on a photodetector using semiconductor processing or die encapsulation techniques. 
     The lens  3514  or  3516  may be positioned on-axis or off-axis with respect to the electromagnetic radiation source  3510  or sensor  3512 . In some embodiments, reflective or diffractive optical elements can be used instead of or in addition to the lens  3514  or  3516 . 
     In operation, the electromagnetic radiation source  3510  may emit a beam of electromagnetic radiation toward the bottom or inner surface  3504  of the diaphragm  3502 . The beam of electromagnetic radiation may be redirected (e.g., reflected or scattered) by the diaphragm  3502  at an approximate right angle (e.g., perpendicular or substantially perpendicular to the diaphragm), and a portion of the redirected electromagnetic radiation may re-enter the electromagnetic radiation source  3510 . Electromagnetic radiation generated by the electromagnetic radiation source  3510  may coherently mix with the redirected electromagnetic radiation that re-enters the electromagnetic radiation source  3510 . The redirected electromagnetic radiation may have a phase difference compared to the generated electromagnetic radiation, resulting in an interference signal being produced when the generated and redirected electromagnetic radiation are coherently mixed. The phase difference may modulate (e.g., as sound or pressure waves cause the diaphragm to move). 
     Similarly to the detection of crown parameters, a sensor  3512  may be used to determine diaphragm parameters, such as a displacement of the diaphragm  3502 , a speed at which the diaphragm is moving toward or away from the sensor  3512 , or an acceleration of the diaphragm  3502 . From these parameters, a processor may reconstruct a stimulus (e.g., sound wave) received by the diaphragm  3502 . 
     In some embodiments, the bias current of the electromagnetic radiation source  3510  may be dynamically changed (e.g., in real-time) using a feedback circuit. In this manner, active phase nulling may be performed, owing to a change of an electromagnetic radiation wavelength with respect to the bias current. When using active phase nulling, diaphragm displacements much larger than the wavelength of the beam of electromagnetic radiation emitted by the electromagnetic radiation source  3510  may be unambiguously detected. 
     The structures and principles employed in the microphone  3500  may alternatively be used to detect movement characteristics of a squeezable exterior of an electronic device, or to detect movement of a physical or virtual button. 
       FIG.  36    shows an example method  3600  of determining a value of a parameter characterizing movement of a watch crown. 
     At block  3602 , a first amount of coherent light (or at least partially coherent electromagnetic radiation) may be generated in a resonant cavity of a laser (or other electromagnetic radiation source). The coherent light generated by the laser may be emitted from the resonant cavity toward a watch crown surface, and may be redirected (e.g., reflected or scattered) by the watch crown surface. The operation(s) at  3602  may be performed, for example, by the sensor system, electromagnetic radiation source, or laser described with reference to any of  FIG.  2 - 15 ,  22   , or  35 . 
     At block  3604 , a second amount of coherent light, redirected from the watch crown surface, may be received into (or re-enter) the resonant cavity. The operation(s) at  3604  may be performed, for example, by the sensor system, electromagnetic radiation source, or laser described with reference to any of  FIG.  2 - 15 ,  22   , or  35 . 
     At block  3606 , the resonant cavity may emit a beam of coherent light dependent on a coherent mixing of the first amount of coherent light and the second amount of coherent. The beam of coherent light may be emitted toward the watch crown surface, and may be redirected by the watch crown surface. The operations in blocks  3602 ,  3604 , and  3606  may be repeated. The operation(s) at  3606  may be performed, for example, by the sensor system, electromagnetic radiation source, or laser described with reference to any of  FIG.  2 - 15 ,  22   , or  35 . 
     At block  3608 , a junction voltage or a bias current of the laser may be measured. The junction voltage or the bias current may depend on the coherent mixing of the first amount of coherent light and the second amount of coherent light within the resonant cavity. Alternatively or additionally, the operation(s) at block  3608  may include measuring an optical power of the beam of coherent light. The operation(s) at  3608  may be performed, for example, by the sensor system or sensor described with reference to any of  FIG.  2 - 13  or  35   . 
     At block  3610 , a value of a parameter characterizing movement of the watch crown may be determined from at least the measurement of the junction voltage or the bias current. The operation(s) at  3610  may be performed, for example, by the sensor system or sensor described with reference to any of  FIG.  2 - 13  or  35   , or by the processor described with reference to  FIG.  37   . 
       FIG.  37    shows a sample electrical block diagram of an electronic device  3700 , which electronic device may in some cases take the form of an electronic watch or other wearable electronic devices described herein. The electronic device  3700  can include a display  3702  (e.g., a light-emitting display), a processor  3704 , a power source  3706 , a memory  3708  or storage device, a sensor system  3710 , and an input/output (I/O) mechanism  3712  (e.g., an input/output device, input/output port, or haptic input/output interface). The processor  3704  can control some or all of the operations of the electronic device  3700 . The processor  3704  can communicate, either directly or indirectly, with some or all of the components of the electronic device  3700 . For example, a system bus or other communication mechanism  3714  can provide communication between the processor  3704 , the power source  3706 , the memory  3708 , the sensor system  3710 , and the I/O mechanism  3712 . 
     The processor  3704  can be implemented as any electronic device capable of processing, receiving, or transmitting data or instructions. For example, the processor  3704  can be a microprocessor, a central processing unit (CPU), an application-specific integrated circuit (ASIC), a digital signal processor (DSP), or combinations 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  3700  can be controlled by multiple processors. For example, select components of the electronic device  3700  (e.g., a sensor system  3710 ) may be controlled by a first processor and other components of the electronic device  3700  (e.g., the display  3702 ) may be controlled by a second processor, where the first and second processors may or may not be in communication with each other. In some cases, the processor  3704  may determine a biological parameter of a user of the electronic device, such as an ECG for the user. 
     The power source  3706  can be implemented with any device capable of providing energy to the electronic device  3700 . For example, the power source  3706  may be one or more batteries or rechargeable batteries. Additionally or alternatively, the power source  3706  can be a power connector or power cord that connects the electronic device  3700  to another power source, such as a wall outlet. 
     The memory  3708  can store electronic data that can be used by the electronic device  3700 . For example, the memory  3708  can 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  3708  can be configured as any type of memory. By way of example only, the memory  3708  can be implemented as random access memory, read-only memory, Flash memory, removable memory, other types of storage elements, or combinations of such devices. 
     The electronic device  3700  may also include one or more sensor systems  3710  positioned almost anywhere on the electronic device  3700 . The sensor system(s)  3710  can be configured to sense one or more type of parameters, such as but not limited to, crown movement (rotation or translation); pressure on the display  3702 , a crown, a button, or a housing of the electronic device  3700 ; light; touch; heat; movement; relative motion; biometric data (e.g., biological parameters) of a user; and so on. For example, the sensor system(s)  3710  may include a watch crown sensor system, a heat sensor, a position sensor, a light or optical sensor, an accelerometer, a pressure transducer, a gyroscope, a magnetometer, a health monitoring sensor, and so on. Additionally, the one or more sensor systems  3710  can utilize any suitable sensing technology, including, but not limited to, capacitive, ultrasonic, resistive, optical, ultrasound, piezoelectric, and thermal sensing technology. In some examples, the sensor system(s)  3710  may include one or more of the watch crown sensor systems described herein (e.g., a sensor system including one or more electromagnetic radiation sources or lasers, voltage detectors or current detectors, photodetectors, and so on). 
     The I/O mechanism  3712  can transmit and/or receive data from a user or another electronic device. An I/O mechanism can include a display, a touch sensing input surface, a crown, one or more buttons (e.g., a graphical user interface “home” button), one or more cameras, one or more microphones or speakers, one or more ports such as a microphone port, and/or a keyboard. Additionally or alternatively, an I/O mechanism  3712  can transmit electronic signals via a communications network, such as a wireless and/or wired network connection. Examples of wireless and wired network connections include, but are not limited to, cellular, Wi-Fi, Bluetooth, IR, and Ethernet connections. 
     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 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.