Abstract:
Two dimensional position sensing system and sensors for use in such systems are disclosed. The sensors incorporate linear array sensors having sensor elements and an aperture plate. Some embodiments include a radiation source that directs radiation onto some of the sensor elements. Other embodiments including radiation blocking objects that block radiation from reaching some of sensor elements. The direction or position of the radiation source or radiation blocking object may be estimated from the radiation incident on the sensor elements.

Description:
FIELD 
       [0001]    The described embodiments relate to systems and methods for sensing the position of a radiation source or a radiation blocking object in two dimensions. The embodiments also relate to sensors for use in such systems and methods. 
       SUMMARY 
       [0002]    Some embodiments of the invention provide sensors for estimating the direction of an object relative to the sensor. A radiation source emits generated or reflected radiation towards a sensor. The sensor has a linear optical sensor array behind an aperture plate. The sensor array has a plurality of sensor elements arranged linearly. The aperture plate has an aperture to allow radiation from the radiation source to reach only some of the sensor elements when the system is in use. An intensity signal from the sensor is coupled to a processor which is configured to identify sensor elements upon which the radiation is incident. A center sensor element is chosen from among the illuminated sensor elements and is used to estimate the direction of the radiation source relative to the sensor. 
         [0003]    Other embodiments provide a sensor that has a linear array sensor. A plurality of radiation sources is provided to illuminate a range of sensor elements in a linear array sensor. The radiation from each radiation source passes through an aperture in an aperture plate and illuminates only some of the sensor elements. A radiation blocking element is used to block radiation from some of the radiation sources from reaching some of the sensor elements. The absence of radiation reaching the sensor elements is measured and is used to estimate the direction of the radiation blocking element relative to the sensor. 
         [0004]    In another aspect, a pair of sensors is provided. The sensors are positioned in a known spacing relative to one another. Each sensor determines the direction of a radiation source (in some embodiments) or a radiation blocking object (in other embodiments) relative to the sensor. The position of the radiation source or radiation blocking object is estimated based on the direction of the source or object from each sensor and the known relative positioning of the sensors. 
         [0005]    Another aspect provides a method of estimating the direction of a radiation source positioned in a sensing region, the method comprising: providing a radiation sensor, the radiation sensor comprising: a linear array sensor having a plurality of sensor elements, the sensor elements facing the sensing region; an aperture plate positioned between the linear array sensor and the sensing region to block radiation from the sensing region from reach the linear array sensor; and an aperture formed in the aperture plate to allow radiation from the radiation source to reach some of the sensor elements; receiving an intensity signal from the linear array sensor, wherein the intensity signal includes intensity values corresponding to radiation incident on the sensor elements through the aperture; and determining the direction based on the intensity signal. 
         [0006]    In some embodiments, the radiation intensity signal includes at least one high intensity value exceeding a threshold value, and wherein the direction is determined based on the at least one high intensity value. 
         [0007]    In some embodiments, the radiation intensity signal includes a range of high intensity values exceeding a threshold value, and wherein determining the direction includes: selecting a center sensor element based on the range of high intensity values; and determining a direction based on the center sensor element. 
         [0008]    In some embodiments, the radiation intensity signal includes at least one low intensity value below a threshold value, and wherein the direction is determined based on the at least one low intensity value. 
         [0009]    In some embodiments, the radiation intensity signal includes a range of low intensity values below a threshold value, and wherein determining the direction includes: selecting a center sensor element based on the range of low intensity values; and determining a direction based on the center sensor element. 
         [0010]    In some embodiments, the radiation intensity signal is an analog signal and wherein determining the direction includes: converting the analog radiation intensity signal into a corresponding final radiation intensity; and determining a direction based on the final radiation intensity signal. 
         [0011]    In some embodiments, the radiation intensity signal is a digital signal having either a high value or a low value corresponding to each of the sensor elements and wherein determining the direction includes: selecting a center sensor element based on a range of high intensity values; and determining a direction based on the center sensor element. 
         [0012]    In some embodiments, the radiation intensity signal is a digital signal having either a high value or a low value corresponding to each of the sensor elements and wherein determining the direction includes: selecting a center sensor element based on a range of low intensity values; and determining a direction based on the center sensor element. 
         [0013]    In some embodiments, the radiation intensity signal may be filtered to remove spurious values before determining the direction. 
         [0014]    In some embodiments, determining the direction includes looking up an angle in a lookup table. 
         [0015]    In some embodiments, determining the direction includes calculating an angle. 
         [0016]    Another aspect provides a method of estimating the position of a radiation source relative to a sensing region, the method comprising: positioning a first position sensor in a first position relative to the sensing region; positioning a second position sensor in a second position relative to the plane, wherein the first and second position sensors are separated by a distance; determining a first ray relative to first position sensor; determining a second ray relative to the second position sensor; and estimating the position of the radiation source to be at the intersection of the first and second rays. 
         [0017]    In some embodiments, the sensing region is a surface of a display screen. 
         [0018]    In some embodiments, the sensing region is a surface of a writing surface. 
         [0019]    In some embodiments, the radiation source is an active radiation source that emits radiation detectable by the first and second position sensors. 
         [0020]    In some embodiments, the radiation source is a passive reflective radiation and further including providing one or more active radiation sources in a fixed position, and wherein the passive radiation source reflects radiation from the active radiation sources onto the first and second position sensors. 
         [0021]    In some embodiments, the sensing region is a surface of a display screen. 
         [0022]    In some embodiments, the sensing region is a surface of a writing surface. 
         [0023]    Another aspect provides a method of estimating the position of a radiation source relative to a sensing region, the method comprising: providing a plurality of active radiation sources adjacent the sensing region; positioning a first position sensor in a first position relative to the sensing region wherein radiation emitted by at least some of the radiation sources is incident upon the first radiation sensor; positioning a second position sensor in a second position relative to the plane wherein radiation emitted by at least some of the radiation sources is incident upon the second radiation sensor, and wherein the first and second position sensors are separated by a distance; determining a first ray relative to first position sensor; determining a second ray relative to the second position sensor; and estimating the position of the radiation source to be at the intersection of the first and second rays. 
         [0024]    In some embodiments, the radiation from a first group of active radiation sources is blocked from reaching the first position sensor and radiation from a second group of radiation sources is blocked from reaching the second radiation sensor and wherein the first ray corresponds to the first group and the second ray corresponds to the second group. 
         [0025]    Another aspect provides a position sensor comprising: a linear array sensor having a plurality of sensor elements arranged linearly, the sensor elements facing a sensing region; an aperture plate positioned between the linear array sensor and the sensing region to block radiation from the sensing region from reaching the linear array sensor; and an aperture formed in the aperture plate to allow radiation from the sensing region to reach some of the sensor elements. 
         [0026]    In some embodiments, the sensor includes a processor coupled to the linear array sensor to receive a radiation intensity signal from the linear array sensor, wherein the radiation intensity signal corresponds to the intensity of radiation incident on a range of sensor elements through the aperture. 
         [0027]    In some embodiments, the sensor includes an optical filter to filter radiation reaching the sensor elements. 
         [0028]    In some embodiments, the sensor elements are sensitive to radiation emitted by a radiation source in the sensing region and wherein the optical filter is selected to allow radiation emitted by the radiation source to reach the sensor elements. 
         [0029]    In some embodiments, the sensing region is generally planar and wherein the sensor elements are linearly arranged generally parallel to the sensing region. 
         [0030]    In some embodiments, the processor is configured to estimate a direction relative to the position sensor in response to the radiation intensity signal. 
         [0031]    These and other aspects of the invention are described below in a description of the some example embodiments of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]    Various embodiments of the invention will now be described with reference to the drawings, in which: 
           [0033]      FIG. 1  illustrates a sensor according to the present invention; 
           [0034]      FIG. 2  is a partial cut-away front view of the sensor of  FIG. 1 ; 
           [0035]      FIG. 3  is a cross-sectional top-view of the sensor of  FIG. 1 ; 
           [0036]      FIG. 4  illustrates an intensity signal from the sensor of  FIG. 1 ; 
           [0037]      FIGS. 5 and 6  illustrate other example intensity signals; 
           [0038]      FIG. 7  illustrates a final intensity signal based on the signal of  FIG. 4 ; 
           [0039]      FIG. 8  illustrates a system for estimating the position of a radiation source; 
           [0040]      FIG. 9  illustrates a first whiteboard system according to the present invention; 
           [0041]      FIG. 10  illustrates a radiation source for use with the whiteboard system of  FIG. 9 ; 
           [0042]      FIG. 11  illustrates a second whiteboard system according to the present invention; 
           [0043]      FIG. 12  illustrates a reflective radiation source for use with the present invention; 
           [0044]      FIG. 13  illustrates a third whiteboard system according to the present invention; 
           [0045]      FIG. 14  illustrates an intensity signal from a sensor of the whiteboard system of  FIG. 13 ; 
           [0046]      FIG. 15  illustrates a final intensity signal based on the signal of  FIG. 14 ; and 
           [0047]      FIG. 16  illustrates intensity signals in another embodiment of the present invention. 
       
    
    
       [0048]    The drawings are illustrative only and are not drawn to scale. 
       DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0049]    Exemplary embodiments described herein provide details relating to optical sensor systems and methods for determining the position of a radiation source or radiation blocking object. Other exemplary embodiments describe details of whiteboard systems for tracking the movement of a pen or other object on a whiteboard surface. The radiating source may radiate radiation generated by the radiation source or may reflect radiation from other sources. The radiation may be in the visible light spectrum or in other radiation spectrums, such as the ultraviolet or infrared spectrums. The embodiments described herein are exemplary only and other implementations and configurations of optical sensors are also possible. 
         [0050]    Reference is first made to  FIGS. 1 ,  2  and  3 , which illustrate a position sensor  100  and a radiation source  110 . Radiation source  110  emits radiation  112  that is incident on the sensor  100 . A radiation source is described herein as emitting radiation regardless of whether the radiation source simply reflects radiation produced by another radiation source or the radiation source generates radiation which then propagates away from the radiation source. In some embodiments, radiation source  110  may be a passive source which reflects radiation initially produce by another radiation source. For example, radiation source may be a reflective source that simply reflects radiation towards sensor  100 . In some embodiments, radiation source  110  may be an active radiation source such as a LED, a light bulb or other source. 
         [0051]    Sensor  100  includes a linear sensor array  114 , an aperture plate  118  and a processor  120 . Linear sensor array  114  is mounted on a sensor support  128 , which is in turn mounted on a base plate  126 . The aperture plate  118  is also mounted on base plate  126 . 
         [0052]    Sensor array  114  has a plurality of sensor elements  116  that are arranged linearly. Each of the sensor elements  116  is sensitive to radiation emitted by radiation source  110 . For example, sensor array  114  may be a linear CMOS sensor that is sensitive to visible or infra-red radiation emitted by radiation source  110 . Sensor array  114  is coupled to processor  120 . Sensor array  114  provides a intensity signal  122  to the processor  120 . 
         [0053]    Aperture plate  118  has an aperture  124  formed in it such that radiation emitted by radiation source  110  is incident on only some of the sensor elements  116 . In this embodiment, aperture  124  is a slit, allowing the radiation source  110  to be moved in the z dimension and still emit radiation onto sensor  100  through aperture  124 . In other embodiments, the aperture may be a hole or may have another shape. In some embodiments, the shape (including the size) of the aperture may be selected based on the sensitivity, shape and spacing of the sensor elements  116 . 
         [0054]    The sensing region  111  is the range of space in which a radiation source  110  can emit radiation that will be incident on a sensing element  116  through the aperture  124 . The sensor elements  116  are arranged generally parallel to the plane of the sensing region  111 . As radiation source  110  moves in the x or y dimensions relative to sensor  100 , radiation emitted by the radiation source  110  passes through aperture  124  and is incident on different sensor elements  116 . 
         [0055]    In some embodiments, an optical filter may be used to limit the frequency band of radiation incident on the sensor array  114 . Referring to  FIGS. 2 and 3 , an optical filter may be positioned in front of aperture  124  (as shown in  FIG. 2 ), or between aperture  124  and the sensor array  114  to reduce the amount of extraneous radiation reaching sensor element  116 . For example, a filter may allow only radiation in a frequency range corresponding to radiation emitted by the radiation source  110  to reach the sensor elements  116 . In some embodiments, an optical notch filter may be used to block undesirable radiation from reaching the sensor elements  116 . Using an optical filter can improve the operation of sensor  100 , for example, by increasing the signal-to-noise ratio in an intensity signal. 
         [0056]      FIG. 4  illustrates an example intensity signal  122 . Intensity signal  122  is an analog signal provided by sensor array  114 . Intensity signal  122  generally has a low intensity level corresponding to most sensor elements  116  on which little or no radiation from radiation source  110  is incident. Intensity signal  122  has a relatively high intensity level corresponding to sensor elements  116  upon which radiation from radiation source  110  is incident. 
         [0057]    In various embodiments, the dimensions and spacing of the sensor elements  116  and the aperture  124  may be such that only one or a few sensor elements  116  may have radiation from radiation source  110  incident upon them. In other embodiments, the aperture  124  may be shaped to allow radiation from radiation source  110  to be incident on a larger number of sensor elements. 
         [0058]    In various embodiments, the intensity signal  122  may be an analog signal or a digital signal (or a combination of both). In embodiments in which the intensity signal is a digital signal, intensity levels corresponding to specific array elements may have two or more values. For example,  FIG. 5  illustrates an intensity signal  122  in which intensity levels are at either a high level or a low level depending on whether the radiation incident on each sensor element is below or above a threshold. In other embodiments, the intensity of the radiation incident on each sensor element may be reported as an intensity level within a range of values. For example,  FIG. 6  illustrates an intensity signal in which an intensity level between a low value and a high value is provided for each sensor element. The low value may be 0 and the high value may be 255, if eight bits are provided for reporting the intensity level for each sensor element. 
         [0059]    Referring again to  FIG. 4 , in this embodiment, intensity signal  122  is a raw intensity signal that is converted into a final intensity signal  136  by processor  120 . In this embodiment, processor  120  is configured to do so in the following manner. Processor  120  first estimates a threshold value for distinguishing between background levels of radiation and higher levels of radiation emitted by radiation source  110 . This may be done for example, by identifying the most common intensity level (a modal value) and setting the threshold at a level between than the modal intensity level and the peak levels of the raw intensity signal. The raw intensity signal  122  may be a bi-modal signal and the threshold may be set at a level between the two modal values. In other embodiments, this may be done by calculating the average intensity level (a mean value, which will typically be between the background radiation level and the level of radiation emitted by the radiation source  110 . In other embodiments, the threshold level may be selected in another manner. A threshold level  134  is calculated in this example as follows: 
         [0000]      Threshold Level 134=(Peak Intensity Level−Average Intensity Level)*30%+Average Intensity Level
 
         [0060]    Referring to  FIGS. 4 and 7 , the final intensity signal  136  has a high intensity for sensor elements that had an intensity level exceeding the threshold  134  in the raw intensity signal and a low intensity level for sensor element that had an intensity level at or below the threshold in the raw intensity signal. 
         [0061]    Typically, the final intensity signal  136  will have a range of intensity levels at the high level corresponding to sensor elements on which radiation from radiation source  110  is incident through aperture plate  118 . In this embodiment, the processor then identifies a center sensor element in the middle of the range of sensor elements for which the final intensity signal  136  has a high level. In the example of  FIGS. 4 and 7 , sensor array has 4096 sensor elements and the intensity levels for sensor elements  2883  to  2905  are high in the final intensity signal  136 . Sensor element  2894  is the center element, as is shown in  FIG. 3 . 
         [0062]    In some embodiments, the center element may be calculated directly from the raw intensity signal. The process for selecting the center element from the final intensity signal  136  may also be used to calculate a center element directly from digital intensity signal that has only two values, as illustrated in  FIG. 5 . In other embodiments, the center element may be calculated in other ways. For example, if the sensor provides a range of intensity level, as shown in  FIGS. 4 and 6 , the processor may be configured to select the sensor element with the highest sensor intensity level. In some embodiments, the processor may filter the raw or final intensity signal to remove spurious values. For example, an intensity signal may be filtered to remove high intensity levels for one or a small number of sensor elements that are surrounded by low intensity levels. The aperture plate and the geometry of the sensor array  118  may be arranged such that radiation from the radiation source  110  will illuminate a group of sensor elements. If a small group of elements, fewer than should be illuminated by the radiation source, have a high intensity level and are surrounded by sensor elements with a low intensity level, the group of elements may be treated as having a low intensity level. 
         [0063]    Referring again to  FIG. 1 , sensor  100  is positioned at a predetermined angle relative to the x-y plane. In this embodiment, sensor  100  is positioned at a 45° angle to the x and y dimensions. Processor  120  receives the intensity signal  122  and determines an angle  8  ( FIG. 1 ) at which radiation from radiation source  110  is incident on the sensor  100 . 
         [0064]    Processor  120  determines angle θ based on the center sensor element. This may be done using a variety of geometric or computing techniques or a combination of techniques. 
         [0065]    A geometric technique is illustrated on  FIG. 3 . Processor  120  determines angle θ relative to a reference point, which will typically be within the dimensions of sensor  100 . In some embodiments, the reference point may be outside the dimensions of sensor  100 . In the present embodiment, angle θ is determine relative to reference point  130 , which is at the centre of aperture  124 . The sensor array is positioned a distance h from the aperture plate with the centre  140  of the sensor array directly behind reference point  130 . Center sensor element  2894  is spaced a distance d from the centre  140  of the sensor array. Angle θ may be calculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
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         [0066]    In some embodiments, a lookup table may be used to determine angle θ. Angle θ may be calculated in advance for every sensor element  116  in the sensor array  114  and the result may be stored in a lookup table that is accessible to processor  120 . Processor  120  may then lookup angle θ after the center element has been identified. 
         [0067]    Collectively reference point  130  and angle θ define a ray  132  along which radiation source  110  is located relative to sensor  100 . 
         [0068]    Reference is next made to  FIG. 8 , which illustrates a system  200  for estimating the position of a radiation source  210  relative to an x-y plane. System  200  includes a pair of sensors  202  and  204 , which are similar to sensor  100 . Sensor  202  has a reference point  230 . Ray  232  passes through reference point  230  and is at an angle θ from the y-dimension. Sensor  204  has a reference point  236 . Ray  246  passes through reference point  236  and is at an angle φ relative to the y dimension. Radiation source  210  lies at the intersection of rays  232  and  246 . Sensors  202  and  204  may share a processor  220  such that their respective sensor arrays  214  and  248  provide an intensity signal to the processor  220 . Processor  220  calculates rays  232  and  246  in the manner described above in relation to ray  132  and  FIG. 3 . Processor  220  may calculate the rays in any manner, including the lookup table technique described above. 
         [0069]    Rays  232  and  246  lies on the x-y plane. Processor  220  calculates the intersection point  250  at which rays  232  and  246  intersect. The intersection point  250  is an estimate of the position of the radiation source  210 . 
         [0070]    Reference is next made to  FIG. 9 , which illustrates a whiteboard system  300 . Whiteboard system  300  includes a whiteboard  352  with a pair of sensors  302  and  304 . Sensors  302  and  304  are similar to sensors  202  and  204  of system  200  and operate in the same manner. Sensor  302  is mounted behind a radiation shield  354  which reduces the amount of ambient radiation that is incident on sensor  302 . Similarly, sensor  304  is mounted behind a radiation shield  356 . Sensing region  311  is on the surface of the whiteboard  352 . Radiation source  310  is positioned in the sensing region  311 . The embodiment of  FIG. 9  may equally be used with a display screen to form a touchscreen or an electronic whiteboard. The sensing region  311  would be on the surface of the display screen with the sensors  302  and  304  mounted adjacent corners of the display screen. In other embodiments, the sensing region may be on the surface of another writing or display surface. 
         [0071]    Reference is made to  FIG. 10 . Radiation source  310  generates and emits radiation in all directions from the radiation source. Radiation source  310  is a ring  370  mounted to a dry erase pen  358  that is used to write on whiteboard  352 . Ring  370  includes a plurality of LEDs  372  that are powered by a battery (not shown). Ring  370  may optionally be removable for mounting on a different dry erase pen. LEDs  372  emit radiation that is detected by sensors  302  and  304 . 
         [0072]    Referring again to  FIG. 9 , sensors  302  and  304  have reference points  330  and  336 . Sensors  302  and  304  are separate by a distance d in the x-dimension. Reference point  336  is located at the origin of the x-y plane (that is at point (0,0)). Reference point  330  is located at point (d,0). Radiation source  310  is located at point (x p , y p ). 
         [0073]    A processor  320  is coupled to sensors  302  and  304 . Processor  320  calculates angles θ and φ as described above. The position of the radiation source  310  is calculated as follows: 
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         [0074]    Processor  320  is configured to estimate to the position of radiation source  310  repetitively. As a user writes on whiteboard  352  with pen  358 , the radiation source  310  moves in conjunction with the pen. Processor  320  tracks the movement of the radiation source in the x-y plane. Each calculated position is recorded, providing a record of the information written by the user on the whiteboard. 
         [0075]    Radiation source  310  is an active radiation source, which generates and emits its own radiation. The emitted radiation may be visible light or it may be outside of the visible spectrum, so long as the sensors  302  and  304  are sensitive to the emitted radiation. 
         [0076]    Reference is next made to  FIG. 11 , which illustrates a whiteboard system  400 , which is similar to whiteboard system  300  in structure and operation. Corresponding components are identified by similar reference numerals. Whiteboard system  400  differs from whiteboard system  300  in the nature of the radiation source  410 . Radiation source  410  is a passive reflective radiation source. A pair of active fixed position radiation sources  462  and  464  are mounted in a bezel  466  of the whiteboard  452 . Each radiation source emits radiation across all or most of the writing surface  468  of the whiteboard. 
         [0077]    Reference is made to  FIG. 12 . Radiation source  410  is a reflective ring  470  mounted on a dry erase pen  458 . Reflective ring  470  may be removable for mounting on a different dry-erase pen. In some embodiments, reflective ring  470  may have an outer surface covered with a reflective tape. In other embodiments, the outer surface may be a polished metal surface. 
         [0078]    Referring again to  FIG. 10 , radiation emitted by active radiation source  462  is incident on radiation source  410  along line  474  and is reflected to sensor  402  along line  432 . Radiation emitted by active radiation source  464  is incident on radiation source  410  along line  478  and is reflected to sensor  404  along line  446 . Processor  420  is coupled to sensors  402  and  404  and estimates the position of radiation source  410  as described above in relation to whiteboard system  300 . Whiteboard system  400  is able to track the movement of pen  458  without providing an active radiation source mounted to the pen. Optionally, the bezel  466  may be colored to reduce reflection of radiation from the active radiation sources  462  and  464  onto sensors  402  and  404 , thereby reducing the base level of radiation that is measured by sensor elements in the sensors, and increasing the difference in intensity of radiation reflected by the radiation source  410  onto the sensors compared to background or base level radiation from other sources. 
         [0079]    Reference is next made to  FIG. 13 , which illustrates another whiteboard system  500 . Whiteboard system  500  is similar in structure and operation to whiteboard systems  300  and  400  and corresponding components are identified by corresponding reference numerals. 
         [0080]    Whiteboard system  500  has a plurality of active radiation emitters  562  mounted in fixed positions in the bezel  566  of the whiteboard  552 . The radiation emitters  562  emit radiation that is incident on sensors  502  and  504 . Sensor  502  has a plurality of sensor elements, like sensor ( FIG. 3 ), and an aperture plate such that radiation from each of radiation emitters  562  is incident on only one or some of the sensor elements. In this embodiment, (i) the shape of an aperture  524  (not shown) in the aperture plate  518  and (ii) the spacing and intensity of the active radiation sources  562  and the divergence (or collimation) of radiation emitted by the active radiation sources may be selected such that the radiation incident upon the sensor elements is approximately equal. The spacing, intensity and divergence or collimation of the radiation sources may differ around the bezel  566 . In other embodiments, the spacing, intensity or divergence or collimation, or some of these aspects may be the same for some or all of the radiation sources. 
         [0081]    A pen (or other radiation blocking object)  510  is moved about on the writing surface  568  of the whiteboard  552 . The pen blocks radiation from some of the radiation sources  562  from reaching some of the sensor elements. Radiation blocking object  510  blocks radiation from active radiation source  562   a  from reaching sensor  502  and radiation from active radiation source  562   b  from reaching sensor  504 . 
         [0082]    Reference is made to  FIG. 14 , which illustrates a raw intensity signal  522  from the sensor array  514  (not shown) of the sensor  502 . Raw intensity signal  522  has a relatively high intensity level for sensor elements upon which radiation from the radiation sources  562  and has a relatively low intensity level for sensor elements upon which radiation from the radiation is blocked by pen  558 . Sensors  502  and  504  are coupled to a processor  520 . Referring to  FIG. 15 , sensor  502  determines a threshold level  534  and generates a final intensity signal  536  by comparing the raw intensity signal  522  to the threshold level  534 . In  FIG. 15 , sensor elements that received less radiation than the threshold level have a high intensity value in the final intensity signal. The processor  520  then identifies a center sensor element based on the range of sensor elements for which final intensity signal has a high value, in the manner described above in relation to final intensity signal  136  and  FIG. 7 . The processor  520  then determines angle θ based on the center sensor element. Similarly, processor  520  determines angle φ and estimates the location of pen  558  based on the distance d between the sensors  502 ,  504 , and the angles θ and φ. 
         [0083]    Referring to  FIGS. 1 to 3 , sensor  100  relies on transitions from high to low radiation levels falling on different sensor elements  116 . Similarly, sensors  502  and  504  ( FIG. 13 ) rely on transitions from high to low radiation levels falling on different sensor elements  516  (not shown). The baseline or background radiation intensity level in sensor  100  is low, while in sensor  502  it is high, but both sensors operate using similar principles to determine a ray along which a radiation source or radiation blocker is located. 
         [0084]    Whiteboard system  500  can be used with a pen or other device that blocks radiation from radiation sources  562  from reaching sensors  502  and  504 , allowing the position and movement of a standard pen, a finger or other object on the whiteboard surface  568  to be estimated and tracked. 
         [0085]    Referring again to  FIGS. 13 and 14 , whiteboard system  500  is configured such that the radiation intensity on each of the sensor elements in sensors  502  and  504  is approximately equal in the absence of any radiation blocking device. 
         [0086]    In other embodiments, the intensity of radiation reaching the sensor elements  516  from radiation sources  562  may vary more significantly.  FIG. 16  illustrates several raw intensity signals from a sensor in an embodiment where the radiation intensity level across the sensor elements has not been balanced. Intensity signal  622   a  illustrates the relatively high variability of radiation that is incident on different sensor elements in the absence of any radiation blocking object such as a pen. Intensity signal  622   b  illustrates the effect of using a radiation block object to block radiation from radiation sources  562  from reaching some of the sensor elements. In this embodiment, the processor records the intensity signal  622   a  during a start-up phase of the whiteboard system and uses the recorded intensity signal as a baseline. During ongoing operation, the intensity signal, such as intensity signal  622   b , received from the sensor array is compared to the recorded baseline intensity signal to identify changes in the intensity signal. The difference between the baseline intensity signal  622   a  and intensity signal  622   b  is shown as differential intensity signal  622   c . Differential intensity signal  622   c  is used as a raw intensity signal to determine a threshold level and to identify a center sensor element. 
         [0087]    The present invention has been described here by way of example only. Various modification and variations may be made to these exemplary embodiments without departing from the spirit and scope of the invention.