Patent Publication Number: US-9411431-B2

Title: Tracking a position in relation to a surface

Description:
RELATED APPLICATION 
     The present application claims the benefit of priority of U.S. Provisional Application No. 60/882,771, filed Dec. 29, 2007, entitled “Improving Dead Reckoning Through Use of Multiple Optical Sensors.” This provisional application is expressly incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This invention generally relates to tracking a position of an object in relation to a surface. 
     BACKGROUND 
     A position of an object may be tracked in relation to a surface for various applications. Relative to a known position of the object, a subsequent position of the object can be determined by sensing local features in the surface as the object is moved in relation to the surface. 
     In one example relating to a personal computer or other console, a tracking device is implemented in an optical mouse to enable a human user to input relative changes in position to a personal computer or other console by moving the mouse. The mouse is moved across a surface, such as a mousepad, that has local differences in color or texture. The tracking device may include a light-emitting diode (LED) to illuminate a predetermined area of the surface. An optical sensor may detect positions of the local differences within the illuminated area at a first point in time, and then again at a second point in time. The tracking device determines a relative shift of the local differences between the first and second time points to determine a two-dimensional movement of the mouse across the surface. 
     The optical sensor may be controlled to detect the surface at a sufficiently high frequency to determine typical two-dimensional movements of the object across a typical surface. However, the optical sensor may also have a characteristic maximum frequency of operation. Thus, the object may be moved sufficiently fast that a movement between periodic differences in the surface, or between two consecutive detection times, exceeds a dimension of the predetermined area of detection. Moreover, if the tracking device is not successful at detecting a movement at one time point, then it may have to wait until a subsequent time point to attempt to detect the movement. By waiting to detect the movement, the tracking device may lose information about the movement between consecutive, successful detection time points. These environmental factors can cause inaccuracies in the determination of the movement of the object. 
     In addition, the tracking device may not be able to detect rotations of the object in relation to the surface. For example, the optical sensor may output the detected magnitude of a movement along a first (“x”) axis and the detected magnitude of a movement along a second (“y”) axis that is orthogonal to the first axis. However, a rotation of the object may not cause any detectable movement of the optical sensor along the ‘x’ axis or the ‘y’ axis. Even if the rotation causes a detectable movement of the optical sensor, the tracking device may not be able to determine a magnitude or direction of the rotation based on the detectable movement. The tracking device may therefore be unable to determine a rotation of the object relative to the surface. 
     Thus, it is desirable to more accurately track a position of an object. It is further desirable to track the position of the object with improved robustness to environmental factors. Moreover, it is desirable to detect rotations of the object in relation to the surface. 
     SUMMARY 
     A tracking device is provided for tracking a position of the tracking device in relation to a surface. The tracking device comprises a first sensor to capture a primary image of a surface and a second sensor to capture a secondary image of the surface. One or more processors are provided to evaluate the primary and secondary images to determine a movement of the tracking device in relation to the surface. 
     In another aspect, a tracking device is provided for tracking a position of the tracking device in relation to a surface. The tracking device comprises a first optical sensor to capture a primary image of a surface at a first time and at a second time. The tracking device further comprises a second optical sensor to capture a secondary image of the surface at a third time and at a fourth time. In addition, the tracking device comprises one or more processors to perform the following to determine a movement of the tracking device in relation to the surface: (i) compare the primary image captured at the second time to the primary image captured at the first time to determine a displacement of the first optical sensor in a first dimension and a displacement of the first optical sensor in a second dimension that is different from the first dimension, and (ii) compare the secondary image captured at the fourth time to the secondary image captured at the third time to determine a displacement of the second optical sensor in the first dimension and a displacement of the second optical sensor in the second dimension. 
     In yet another aspect, a method is provided of tracking a position of an object in relation to a surface. The method comprises, at the object, capturing a primary image of a surface and capturing a secondary image of the surface. The method further comprises evaluating the primary and secondary images to determine a movement of the object in relation to the surface. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present invention and, together with the description, serve to explain advantages and principles of the invention. In the drawings: 
         FIG. 1  is a schematic diagram of an exemplary embodiment, consistent with the present invention, of a tracking device having first and second optical sensors; 
         FIG. 2  is a block diagram of an exemplary embodiment, consistent with the present invention, of electronic circuitry implementing a tracking device; 
         FIG. 3  is a schematic diagram of an exemplary embodiment, consistent with the present invention, of first and second optical sensors at a first set of positions and then at a second set of positions; 
         FIG. 4 a    is a schematic diagram of an exemplary embodiment, consistent with the present invention, of a tracking device during different phases of a sequence in which first and second optical sensors are alternately activated; and 
         FIG. 4 b    is a schematic diagram of an exemplary embodiment, consistent with the present invention, of a tracking device during different phases of a sequence in which first, second, third, and fourth optical sensors are alternately activated. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Reference will now be made in detail to embodiments consistent with the present invention, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. 
     A tracking device is provided for tracking a position in relation to a surface. The tracking device may detect changes in position that include displacements in location and rotations that result in a changed angular orientation relative to the surface. By detecting these movements, the tracking device can determine the approximate position of the tracking device relative to an earlier known position. 
       FIG. 1  is a schematic diagram of an exemplary embodiment of a tracking device  100 . Tracking device  100  is provided only to illustrate an exemplary embodiment consistent with the present invention, and should not be used to limit the scope of the invention or its equivalents to the exemplary embodiments provided herein. 
     Tracking device  100  may be implemented in an object  110  to track the position of object  110  in relation to a surface  120 . For example, tracking device  100  may be implemented in object  110  such that object  110  forms an input device (as shown in  FIG. 1 ), a distance-measuring device, or a device adapted for another purpose related to tracking a position. The input device may include, for example, a computer mouse, a trackball, a device for inputting drawing or writing by hand, or a monitoring device that can be attached to a target object to track the position of the target object. In an exemplary embodiment, the object  110  forms a handheld printer that includes an inkjet print head to print a pattern on a surface according to the tracked position of object  110  in relation to the surface. 
     The movement of tracking device  100  may be expressed as a present position of tracking device  100  in relation to a position of tracking device  100  at a time before the movement. If the position of tracking device  100  before the movement is known relative to an external reference frame, then the current position of tracking device  100  may also be determined relative to the external reference frame. For example, tracking device  100  may be adapted to be initialized at an initial position that is used as a reference position by tracking device  100 . If tracking device  100  is implemented in object  110 , or is otherwise disposed in a known positional relationship to object  110 , tracking device  100  may also track the position of object  110  in relation to surface  120 . 
     Surface  120  may have features  130  that can be detected by optical sensors. Features  130  may be located at substantially periodic intervals or substantially aperiodically, such as substantially randomly. Surface  120  may be shaped approximately two-dimensionally (i.e., approximately flat). For example, surface  120  may be an exposed surface of a mouse pad. Alternatively, surface  120  may be shaped substantially three-dimensionally (i.e., substantially non-flat). For example, surface  120  may be textured, curve smoothly, or bend at a kink. In yet another example, surface  120  may be an exposed surface of a perforated layer of material, such as for example one side of a mesh of material. 
     Tracking device  100  may include a plurality of optical sensors  140   a ,  140   b  to capture images of surface  120  at selected points in time. Upon activation, optical sensors  140   a ,  140   b  may generate the images based on electromagnetic radiation that optical sensors  140   a ,  140   b  detect from features  130  at one or more wavelengths. For example, optical sensors  140   a ,  140   b  may detect positions of features  130  based on emissions or reflections of light from features  130  at visible, infrared, or other wavelengths. Optical sensors  140   a ,  140   b  may capture images that are two-dimensional to represent features  130  across two orthogonal dimensions. The images may further include data in additional dimensions. Alternatively, optical sensors  140   a ,  140   b  may capture one-dimensional images that represent features  130  across one dimension. 
     One or more of optical sensors  140   a ,  140   b  may be disposed such that the dimensions of the images captured by optical sensors  140   a ,  140   b  are not parallel to predetermined dimensions along which tracking device  100  is commonly moved. Such placement of optical sensors  140   a ,  140   b  may enable positional changes along these dimensions of common movement to be registered along a plurality of the dimensions of the images captured by optical sensors  140   a ,  140   b . Tracking device  100  may thus be able to track its position with a higher degree of accuracy during typical use. For example, one or more of optical sensors  140   a ,  140   b  may be disposed such that the dimensions of the images captured by optical sensors  140   a ,  140   b  are at an angle of from about 30 to about 60 degrees in relation to a predetermined dimension along which tracking device  100  is often moved. In an exemplary embodiment, one or more of optical sensors  140   a ,  140   b  may be disposed such that its captured images have a dimension that is at an angle of about 45 degrees relative to a dimension of common movement of tracking device  100 . 
     Furthermore, one or more of optical sensors  140   a ,  140   b  may be implemented as an integrated circuit (IC). The IC may incorporate very large scale integration (VLSI) or ultra large scale integration (ULSI), indicating the degree of spatial density of transistors in a single IC. Typically, the IC is incorporated into a monolithic structure, such as a semiconductor “chip.” For example, one or more of optical sensors  140   a ,  140   b  may include an ADNS-3080 optical mouse sensor, available from Avago Technologies Limited, San Jose, Calif. 
     In an exemplary embodiment, tracking device  100  may have a first optical sensor  140   a  to capture a first image of surface  120  and a second optical sensor  140   b  to capture a second image of surface  120 . In  FIG. 1 , first optical sensor  140   a  and second optical sensor  140   b  are disposed such that a center point of first optical sensor  140   a  is separated by a distance ‘d’ from a center point of second optical sensor  140   b . For example, the first and second optical sensors  140   a ,  140   b  may be disposed to have a distance ‘d’ between their respective center points of at least about 5 cm to obtain information about surface  120  from sufficiently distant locations. Tracking device  100  may include additional optical sensors (not shown) such that more than two sensors in total are provided. 
     First and second optical sensors  140   a ,  140   b  may be adapted to repeatedly capture the images of surface  120  at sequential points in time. For example, a clock may be provided to supply a periodic clock signal that activates one or more of optical sensors  140   a ,  140   b  to capture an image at each of multiple periodic time points. In an exemplary embodiment, the clock and optical sensors  140   a ,  140   b  may be adapted to capture the images at a periodic rate of from about 4000 to about 10,000 frames per second (fps). For example, the clock and optical sensors  140   a ,  140   b  may be adapted to capture the images at a rate of about 6400 fps. 
     One or more illuminators  150   a ,  150   b  may be provided to illuminate one or more areas of surface  120  that may be at predetermined positions relative to illuminators  150   a ,  150   b  illuminators  150   a ,  150   b  may be provided to illuminate surface  120  at one or more wavelengths selected to be detected by optical sensors  140   a ,  140   b . In an exemplary embodiment, illuminators  150   a ,  150   b  may be adapted to provide light at a wavelength range that includes the visible wavelength of 639 nm such that reflections be detected by optical sensors  140   a ,  140   b  at substantially the same wavelength. Illuminators  150   a ,  150   b  may include electromagnetic radiation sources, such as for example light-emitting diodes (LEDs), laser sources, incandescent bulbs, reflectors, optically-transmissive conduits, or other suitable components for delivering a field of electromagnetic radiation onto the predetermined areas of surface  120  in relation to tracking device  100  illuminators  150   a ,  150   b  may also have one or more light-shaping or light-directing components, such as for example lenses, mirrors, or optically-transmissive conduits, to further shape or direct the radiation field onto the predetermined areas of surface  120 . In an exemplary embodiment, one or more of Illuminators  150   a ,  150   b  may include an HLMP-ED80 LED illumination source and an ADNS-2120 lens, both available from Avago Technologies Limited, San Jose, Calif. 
     In another exemplary embodiment, one or more of illuminators  150   a ,  150   b  may include laser sources in addition to one or more light-shaping or light-directing components to deliver a laser beam at a predetermined wavelength. Optical sensors  140   a ,  140   b  may be laser sensors that are adapted to detect the laser beam after the laser beam has reflected from surface  120 . Implementing optical sensors  140   a ,  140   b  and illuminators  150   a ,  150   b  to use a laser beam may enable the images of surface  120  to be captured at one or more of a higher resolution and a higher capture rate than with non-laser electromagnetic radiation sources. 
     One or more processors may be provided to evaluate the first and second images from optical sensors  140   a ,  140   b  to determine a movement of tracking device  100  in relation to surface  120 . “Determining a movement” refers to determining a value of a property of the movement of tracking device  100  in relation to surface  120 . For example, determining the value of the property may include determining a magnitude of a displacement of tracking device  100 , a magnitude of a rotation of tracking device  100 , or a point of rotation of tracking device  100 . 
     In an exemplary embodiment, the processors may be adapted to compare a frame of an image captured at one time point by first optical sensor  140   a  to a frame of the image captured at a subsequent time point by first optical sensor  140   a . Based on this first comparison, the processors may determine a displacement of first optical sensor  140   a  in a first dimension and a displacement of the first optical sensor in a second dimension that is orthogonal to the first dimension. The processors may also be adapted to compare a frame of an image captured at one time point by second optical sensor  140   a  to a frame of the image captured at a subsequent time point by second optical sensor  140   b . Based on this second comparison, the processors may determine a displacement of second optical sensor  140   b  in the first dimension and a displacement of second optical sensor  140   b  in the second dimension. The processors may further evaluate these determined displacement values corresponding to optical sensors  140   a ,  140   b  to determine one or more movements of tracking device  100 . 
     Tracking device  100  may further include one or more of an accelerometer and a gyroscope to determine movement in one or more dimensions. For example, the accelerometers and gyroscopes may be implemented in dimensions in which movement is not tracked by optical sensors  140   a ,  140   b , or the accelerometers and gyroscopes may be implemented to provide additional information about movement in the same dimensions as optical sensors  140   a ,  140   b . The processors may be adapted to process data from the accelerometers and gyroscopes to determine information about movement of tracking device  100 . 
     In addition, tracking device  100  may include one or more mechanical input components. For example, if tracking device  100  is implemented in a computer mouse or trackball, then tracking device  100  may include one or more buttons or scroll wheels. In  FIG. 1 , tracking device  100  is shown as having a first button  160   a  and a second button  160   b . First and second buttons  160   a ,  160   b  may be coupled to one or more of the processors. Tracking device  100  may further include one or more mechanical output components, such as for example a vibration-generating component or sound-producing component. 
     Tracking device  100  may transmit one or more signals to an external device  170  over a signal coupler  180 . The signals may describe the movement of tracking device  100  in one or more dimensions. External component  170  may include, for example, a personal computer, a game console, or a display. Signal coupler  180  may transmit signals as digital signals or as analog signals. Signal coupler  180  may include an electrical conductor, optical transmitter and receiver, radio frequency (RF) transmitter and receiver, or any other suitable coupling for transmitting information from one location to another location. For example, signal coupler  180  may include an electrical RS-232 interface, Universal Serial Bus (USB) interface, PS/2 interface, or Bluetooth® interface. 
       FIG. 2  is a block diagram of electronic circuitry that may implement tracking device  100 . Each of the lines connecting electronic components in  FIG. 2  represents one or more electrical couplings between those electronic components. Additional electronic components or electrical couplings that are not shown in  FIG. 2  may be used in the electronic circuitry to implement tracking device  100 , as would be understood by one of ordinary skill in the art. For example, the electronic circuitry may incorporate one or more oscillators, diodes, capacitors, resistors, field-effect transistors (FETs), jumpers, and sockets or other connectors to implement tracking device  100 . The electronic components and electrical couplings shown in  FIG. 2  are provided only to illustrate the invention, and should not be used to limit the scope of the invention or its equivalents to the exemplary embodiments provided herein. 
     Optical sensors  140   a ,  140   b  are provided to capture images of predetermined areas of surface  120 . Illuminators  150   a ,  150   b  may be coupled to respective optical sensors  140   a ,  140   b . For example, first illuminator  150   a  may be coupled to first optical sensor  140   a  while second illuminator  150   b  may be coupled to second optical sensor  140   b . Each of optical sensors  140   a ,  140   b  may activate its respective illuminator  150   a ,  150   b  while the optical sensor is capturing an image of the area of surface  120  illuminated by the activated illuminator. 
     In an exemplary embodiment, one of the processors described above may be implemented in each of optical sensors  140   a ,  140   b  as image processors  190   a ,  190   b , respectively. Each of image processors  190   a ,  190   b  may compare subsequent images captured by its respective optical sensor. Image processors  190   a ,  190   b  may be digital signal processors (DSPs) embedded in optical sensors  140   a ,  140   b . Image processors  190   a ,  190   b  may use these image comparisons to determine one or more movements of the respective optical sensors in relation to surface  120 . In an exemplary embodiment, image processor  190   a ,  190   b  at each of optical sensors  140   a ,  140   b  determines a first displacement magnitude in a first dimension and a second displacement magnitude in a second dimension that is orthogonal to the first dimension. For example, the first dimension may be a left-right dimension across a surface while the second dimension is a back-and-forth dimension across the same surface. 
     The processors of tracking device  100  may also include a multi-sensor processor  200  to receive signals from first and second optical sensors  140   a ,  140   b  and further evaluate these signals to determine a movement of tracking device  100  in relation to surface  120 . Optical sensors  140   a ,  140   b  may be communicatively coupled to multi-sensor processor  200  to transmit information related to the captured images to multi-sensor processor  200 . For example, optical sensors  140   a ,  140   b  may transmit the magnitudes of movements of respective optical sensors  140   a ,  140   b  in relation to surface  120 , as determined by image processors  190   a ,  190   b , to multi-sensor processor  200 . In an exemplary embodiment, multi-sensor processor  200  may include an 8-bit PIC family microcontroller, available from Microchip Technology, Inc., Chandler, Ariz. In an exemplary embodiment, multi-sensor processor  200  includes a PIC18F2620 microcontroller, available from Microchip Technology, Inc. 
     In an exemplary embodiment, each of first and second optical sensors  140   a ,  140   b  may output a magnitude of a displacement in the first dimension and a magnitude of a displacement in the second dimension. Multi-sensor processor  200  may receive signals indicating these magnitudes for each of first and second optical sensors  140   a ,  140   b . Multi-sensor processor  200  may process these magnitudes to determine one or more movements of tracking device  100  in one or more dimensions. 
     Multi-sensor processor  200  may be adapted to determine whether information related to an image captured by one of first and second optical sensors  140   a ,  140   b  is sufficiently reliable to determine the movement of tracking device  100 . If the information is not sufficiently reliable, multi-sensor processor  200  may evaluate information related to the other one of first and second optical sensors  140   a ,  140   b  to determine the movement of the tracking device absent further evaluation of the information related to the presently-unreliable optical sensor. If information is not available for the other one of optical sensors  140   a ,  140   b  at a current time point, multi-sensor processor  200  may wait to receive information for that optical sensor at a future time point. By redundantly using information from multiple optical sensors  140   a ,  140   b , tracking device  100  may be capable of tracking its relative position with substantial accuracy despite unreliable information from one or more of individual optical sensors  140   a ,  140   b . Thus, tracking device  100  may be substantially robust to environmental factors that can cause information related to the image from one of optical sensors  140   a ,  140   b  to be unreliable. These environmental factors may include, for example, a problematic speed with which the mouse may be moved, a periodicity of features of surface  120  or a substantial absence of features  130  of surface, or dust or other impurities that may degrade the accuracy of an image that is captured of surface  120 . 
     Processors  190   a ,  190   b , and  150  may be implemented in tracking device  100 , or one or more of processors  190   a ,  190   b , and  150  may alternatively be implemented external to tracking device  100 , such as in a remote processing center. The functions of processors  190   a ,  190   b , and  150  may be implemented together or separately, and as part of one or more physical components, as would be suitable for the desired application. For example, tasks described herein as performed by image processors  190 ,  190   b  may alternatively be performed by multi-sensor processor  200 , or vice versa. The functions of processors  190   a ,  190   b , and  150  may also be implemented in hardware, software, firmware, or a suitable combination thereof. 
     A transceiver  210  may be provided to communicatively couple tracking device  100  to external device  170  to enable communication between tracking device  100  and external device  170 . For example, transceiver  210  may communicatively couple multi-sensor processor  200  to external device  170 . Transceiver  210  may output a signal that indicates the movement of tracking device  100  as determined by processors  190   a ,  190   b , and  150 . Transceiver  210  may adapt electrical voltage or current levels of signals received from multi-sensor processor  200  to be compatible with a receiver at external device  170 , such as a transceiver at external device  170 . In an exemplary embodiment, transceiver  210  may include a MAX3233EEWP transceiver, available from Maxim Integrated Products, Inc., Sunnyvale, Calif. 
     A power regulator  220  may be provided to receive and regulate power from a power supply  230  to deliver regulated power to one or more electrical components that implement tracking device  100 . For example, power regulator  220  may be coupled to one or more of optical sensors  140   a ,  140   b , illuminators  150   a ,  150   b , multi-sensor processor  200 , and transceiver  210  to provide a regulated voltage to these components. Power regulator  220  may be incorporated into object  110  together with the rest of tracking device  100 . Alternatively, power regulator  220  may be disposed external to object  110 . Power regulator  220  may include a low-dropout (LDO) linear regulator. In an exemplary embodiment, power regulator  220  may include a LT® 1763 series regulator, available from Linear Technology, Milpitas, Calif. 
       FIG. 3  is a schematic diagram of first and second optical sensors  140   a ,  140   b  of tracking device  100  at first respective positions (shown as p 1  and p 2 ) and subsequently at second respective positions (shown as p 1 ′ and p 2 ′). At the first respective positions, first and second optical sensors  140   a ,  140   b  are indicated by solid lines. At the later, second, respective positions, first and second optical sensors  140   a ,  140   b  are indicated by dashed lines. Tracking device  100 , as a unit, has been moved in a first dimension (shown in  FIG. 3  as the horizontal direction) by a magnitude labeled as ‘Δx’, and in a second dimension (shown as the vertical direction) that is orthogonal to the first dimension by a magnitude labeled as ‘Δy’.  FIG. 3  shows tracking device  100  as having been displaced to the right by an amount ‘Δx’, and upward by an amount ‘Δy’. 
     In an exemplary embodiment, first and second optical sensors  140   a ,  140   b  may determine displacement magnitudes ‘Δx 1 , Δx 2 ’ of first and second optical sensors  140   a ,  140   b , respectively, in the first dimension. First and second optical sensors  140   a ,  140   b  may also determine the displacement magnitudes ‘Δy 1 , Δy 2 ’ of first and second optical sensors  140   a ,  140   b , respectively, in the second dimension. First and second optical sensors  140   a ,  140   b  may transmit these magnitudes to multi-sensor processor  200 . Based on these displacement magnitudes, multi-sensor processor  200  may use predefined mathematical relationships to determine properties of the movement of tracking device  100 . 
     The displacement amount ‘Δx’ may be calculated by averaging the displacement magnitudes ‘Δx 1 , Δx 2 ’ of first and second optical sensors  140   a ,  140   b , respectively, in the first dimension. The displacement amount ‘Δy’ may be calculated by averaging the displacement magnitudes ‘Δy 1 , Δy 2 ’ of first and second optical sensors  140   a ,  140   b , respectively, in the second dimension. For example, multi-sensor processor  200  may calculate the displacement amounts ‘Δx’ and ‘Δy’ based on the received information according to Equations 1 and 2: 
     
       
         
           
             
               
                 
                   
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     In addition to displacements in the first and second dimensions, tracking device  100  may exhibit rotations about one or more axes. Optical sensors  140   a ,  140   b  of tracking device  100  are shown in  FIG. 3  as having been rotated clockwise by an amount ‘θ’, about an axis orthogonal to the first and second dimensions (horizontal and vertical dimensions in  FIG. 3 ), between the first respective positions (p 1  and p 2 ) and the second respective positions (p 1 ′ and p 2 ′). Multi-sensor processor  200  ( FIG. 2 ) may use predefined mathematical relationships to determine a magnitude of rotation between the first respective positions (p 1  and p 2 ) and the second respective positions (p 1 ′ and p 2 ′) of tracking device  100  based on the information received from first and second optical sensors  140   a ,  140   b . Multi-sensor processor  200  may use trigonometric rules pertaining to right triangles to calculate the magnitude of rotation. For example, multi-sensor processor  200  may calculate a magnitude of clockwise rotation ‘θ’ of tracking device  100  according to Equation 3, where the value of ‘a’ is defined by Equation 4: 
                   θ   =       sin     -   1       ⁡     (     a   d     )               (   3   )               a   =       Δ   ⁢           ⁢     y   1       -     Δ   ⁢           ⁢     y   2                 (   4   )               
Increasing the distance ‘d’ between the center points of first and second optical sensors  140   a ,  140   b  may provide a proportionately larger value of ‘a’ for the same actual value of the rotation magnitude ‘θ’. Thus, increasing the distance ‘d’ may increase the accuracy with which the rotation magnitude ‘θ’ can be determined.
 
     In addition, multi-sensor processor  200  may determine a point about which the tracking device  100  has been rotated, based on the information received from first and second optical sensors  140   a ,  140   b . In  FIG. 3 , a point of rotation is shown as ‘p r ’. The point of rotation ‘p r ’ and the first position ‘p 2 ’ of second optical sensor  140   b  are shown in  FIG. 3  as separated by a distance ‘b’. Using trigonometric rules, the distance ‘b’ may be calculated according to Equation 5:
 
 b=Δy   2 ·cot −1 θ  (5)
 
     The point of rotation ‘p r ’ may therefore be calculated relative to the first position ‘p 2 ’ of second optical sensor  140   b . Since the location of first optical sensor  140   a  may be known relative to the location of second optical sensor  140   b , the point of rotation ‘p r ’ may also be calculated relative to the first position ‘p 1 ’ of first optical sensor  140   a . Tracking device  100  may be rotated about one or more axes. For example, tracking device  100  may be rotated about two or three orthogonal axes. Tracking device  100  may also be adapted to determine a magnitude of rotation and point of rotation corresponding to each of these axes. 
       FIG. 4 a    is a schematic diagram of an exemplary embodiment of a tracking device  100   a  during different phases of a sequence in which first and second optical sensors  140   a ,  140   b  are alternately activated to track a position in relation to a surface. Active sensors are shown as cross-hatched, while inactive sensors are shown without hatching. Arrows point in the time order of the phases for this exemplary embodiment. As shown in  FIG. 4 a   , first optical sensor  140   a  may be activated to capture an image while second optical sensor  140   b  is deactivated at a first point in time. At a second, subsequent point in time, first optical sensor  140   a  may be deactivated and second optical sensor  140   b  may be activated. At a third point in time, subsequent to the second time, second optical sensor  140   b  may again be deactivated and first optical sensor  140   a  may again be activated, just as in the first time point. This cycle may be repeated at a predetermined rate to continuously determine movements of tracking device  100   a.    
     In the exemplary embodiment of  FIG. 4 a   , first and second optical sensors  140   a ,  140   b  are activated at substantially the same rates to capture respective images at this rate. However, first optical sensor  140   a  is activated while second optical sensor  140   b  is deactivated, and vice versa, such that first optical sensor  140   a  captures frames of a primary image in a phase-shifted relationship to second optical sensor  140   b  capturing frames of a secondary image. In this example, the times at which frames of the primary image are captured are interlaced with the times at which the frames of the secondary image are captured. 
       FIG. 4 b    is a schematic diagram of an exemplary embodiment of a tracking device  100   b  in a sequence of activating first, second, third, and fourth optical sensors  140   a - 140   d  to track a position in relation to a surface. As shown in  FIG. 4 b   , first optical sensor  140   a  may be activated while second, third, and fourth optical sensors  140   b - 140   d  are inactive at a first point in time. At a second, subsequent point in time, first optical sensor  140   a  may be deactivated and fourth optical sensor  140   d  may be activated. At a third point in time, subsequent to the second time point, fourth optical sensor  140   d  may be deactivated and second optical sensor  140   b  may be activated. At a fourth point in time, subsequent to the third time point, second optical sensor  140   b  may be deactivated and third optical sensor  140   c  may be activated. At a fifth point in time, subsequent to the fourth time point, third optical sensor  140   c  may be deactivated and first optical sensor  140   a  may again be activated, just as in the first time point. This cycle may be repeated at a predetermined rate to continuously determine movements of tracking device  100   b.    
     Examples are described in which optical sensors  140   a - 140   d  are alternately activated such that one of optical sensors  140   a - 140   d  is activated while the remaining optical sensors are deactivated. In these examples, the times during which the different optical sensors  140   a - 140   d  are activated may be interlaced. Alternating activation times may be used to increase an effective frame rate of tracking device  100 , and thereby improve the robustness of positional tracking to environmental conditions, without necessitating an increase in the frequency of a clock signal provided to optical sensors  140   a - 140   d . In an exemplary embodiment, the effective frame rate is approximately proportionate to the number of optical sensors  140   a - 140   d  implemented in tracking device  100 . Thus, using multiple optical sensors may enable multi-sensor processor  200  to determine the position of tracking device  100  at a rate that is at least about twice a rate at which one of the optical sensors is activated. 
     However, other embodiments may be implemented to suit particular applications. For example, two or more of optical sensors  140   a - 140   d  may be activated during times that substantially coincide. Selecting activation times that substantially coincide may improve the accuracy of determining a magnitude of rotation of tracking device  100   b.    
     As explained above, a tracking device consistent with the present invention may improve the accuracy of tracking a position of the tracking device in relation to a surface. The tracking device may also track its position with increased robustness to environmental circumstances. Moreover, the tracking device may be adapted to detect rotations in relation to the surface. 
     Although embodiments consistent with the present invention have been described in considerable detail with regard to embodiments thereof, other versions are possible. For example, the tracking device may comprise other electronic structures equivalent in function to the illustrative structures herein. Furthermore, relative or positional terms, such as “first,” “second,” “third,” and “fourth,” are used with respect to the exemplary embodiments and are interchangeable. Therefore, the appended claims should not be limited to the description of the versions contained herein.