Patent Publication Number: US-7710350-B2

Title: Method and apparatus for display

Description:
This application is a divisional of application Ser. No. 10/753,144, filed 7 Jan. 2004, now U.S. Pat. No. 7,173,601. 

   TECHNICAL FIELD OF THE INVENTION 
   This invention relates generally to optical dithering and more particularly to a method and apparatus for providing position feedback for an optical dithering element. 
   BACKGROUND OF THE INVENTION 
   Televisions and other types of displays are pervasive in today&#39;s society. Recent years have seen the introduction of higher definition displays. Engineers continue to try to increase the resolution of displays to provide better picture quality, but also face constraints associated with providing such increased resolution. 
   One approach for increasing the resolution of a display involves increasing a perceived resolution of a display by a user. Rather than providing more pixels, a first image is displayed including a set number of pixels corresponding to the same number of sample data points of the image to be displayed. Then at a time period very close to the display of the first image, a second image is displayed including the same number of pixels but with slightly different sample points of the image. This second image on the display is offset by a small amount from the display of the first image. The human eye perceives both images as being displayed at the same time, resulting in an effective doubling of the display resolution. This technique is referred to in the industry by many names including modulation, optical dithering, and SmoothPicture™. 
   In one technique for effecting the offset of the two images, a mirror is used as an optical dithering element to direct light corresponding to pixels to be displayed onto the display. The mirror is repeatedly switched from one position to another such that the first position of the mirror corresponds to a display of an unshifted image and the second position corresponds to a display of a shifted image. Thus rapid positioning of the mirror between the first and second positions allows an increase in the perceived resolution of the display. 
   In order to control the position of an optical dithering element, it is useful to measure the position of the optical dithering element. However, such a measurement can often be costly, adding undue expense to the underlying product. 
   SUMMARY OF THE INVENTION 
   According to one embodiment, a method for providing position feedback for a device includes providing a photointerrupter having a light-emitting diode, a phototransistor, and an aperture between the light-emitting diode and the phototransistor. For a given size aperture, a current through the phototransistor is a function of a current through the light-emitting diode. The method also includes controlling the current through the light-emitting diode such that a change in the aperture size results in a desired approximately proportional change in photocurrent through the phototransistor. While controlling the current through the light-emitting diode, a portion of the aperture is blocked by an arm that has a position indicative of the position of the device. The method also includes providing a signal indicative of the change in current through the photodiode as an indication of the change in position of the device. 
   Some embodiments of the invention provide numerous technical advantages. Some embodiments may benefit from some, none, or all of these advantages. For example, according to one embodiment, a low-cost position feedback signal is generated by using a photointerrupter that allows fine tuning the position of an optical dithering element. Thus, the position of an optical dithering element can be controlled without the use of expensive servo systems. Other technical advantages may be readily ascertainable by one of skill in the art. 

   
     BRIEF DESCRIPTION OF THE FIGURES 
     For a more complete understanding of the invention, and for further features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  is a schematic diagram illustrating a system for displaying light with increased perceived resolution according to the teachings of the invention; 
       FIG. 2A  is a graph illustrating a desirable transition of the mirror of  FIG. 1  from a first position to a second position; 
       FIG. 2B  is a graph illustrating a position versus response curve for the mirror of  FIG. 1  during transition without a control signal controlling the position response of the mirror; 
       FIG. 2C  is a graph illustrating the position of the mirror with respect to time for numerous transitions of the mirror between first and second positions without use of a control signal to control the response; 
       FIG. 3A  is a graph illustrating a desirable response, a control signal used to develop a desirable response, and an undesirable response of the system of  FIG. 1 ; 
       FIG. 3B  is a graph analogous to  FIG. 3A  but illustrates several periods of responses and associated control signals for the position of the mirror of  FIG. 1 ; 
       FIG. 3C  is a graph illustrating overshoot versus a plurality of parameters that may be used to determine a desirable control signal for the system of  FIG. 1 ; 
       FIG. 4A  is a block diagram of the dither control architecture according to one embodiment of the invention; 
       FIG. 4B  is a block diagram of the field programmable gate array controller of  FIG. 4A , according to one embodiment of the invention; 
       FIG. 4C  is a block diagram of the dither control architecture according to a second embodiment of the invention; 
       FIG. 4D  is a block diagram of an application specific integrated circuit controller of  FIG. 4C ; 
       FIG. 5  is a graph illustrating sampling of a plurality of data points for use in control of an optical dithering element according to the teachings of the invention; 
       FIG. 6  is a flowchart illustrating a method for controlling an optical dithering element according to the teachings of the invention; 
       FIG. 7A  is an error signature map corresponding to the drive waveform having a low amplitude; 
       FIG. 7B  is an error signature map having the drive waveform of a desired amplitude; 
       FIG. 7C  is an error signature map corresponding to the drive waveform having a high amplitude; 
       FIG. 8  is a table illustrating a plurality of error signatures and the corresponding adjustment to delay width and magnitude of the drive signal; 
       FIG. 9A  is a schematic diagram illustrating an optical dithering element and an associated position measurement system according to the teachings of the invention; 
       FIG. 9B  is a schematic diagram along the lines  9 B- 9 B of  FIG. 9A  showing additional detail of the aperture and the device arm of  FIG. 9A ; 
       FIG. 9C  is a graph illustrating the photocurrent versus distance for the photointerrupter of  FIG. 9A ; 
       FIG. 10  is a circuit diagram illustrating control circuitry and the associated photointerrupter of  FIG. 9A ; and 
       FIG. 11  is a flow chart illustrating a method for providing position feedback for an optical dithering element. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Embodiments of the invention and its advantages are best understood by referring to  FIGS. 1-11  of the drawings, like numerals being used for like and corresponding parts of the various drawings. 
     FIG. 1  is a schematic diagram illustrating a system  10  for displaying an image with increased perceived resolution. System  10  includes an image source  12 , an optical dithering system  14 , and a display  16 . Image source  12  is operable to general light  18  representative of an image for eventual display on display  16 . According to one embodiment, image source  12  comprises a digital micro-mirror device (DMD), available from Texas instruments, for selectively modulating light to represent an image. In one embodiment, image source  12  may sequentially generate light of different colors and provide those different colors in sequence for display on display  16 . Image source  12  may provide these different colors for appropriate time periods such that a user&#39;s eye viewing the light on display  16  will integrate the various colors to result in a desired color to be displayed. According to one embodiment in which image source  12  is a DMD, the number of mirrors in the DMD is equal to the unenhanced resolution of the display of display  16 . Thus image source  12  may provide an array of light signals  18  for eventual display on display  16 . 
   Optical dithering system  14  receives light signals  18  and reflects them onto display  16 . Optical dithering system  14  includes an optical dithering element  20 , which may be a lens, mirror, or other device operable to selectively direct light to a desired location. In the present example, optical dithering element  20  is a mirror. Mirror  20  rotates about an angle  22  between first and second positions to selectively reflect light  18  from image source  12  to display  16  into one of two positions. In one embodiment, angle  22  is very small and on the order of 0.015 degrees. This corresponds to approximately four microns of vertical movement of the end of mirror  20 . Thus, mirror  20  produces an offset light beam  24  and an unoffset light beam  26  for display on display  16 . If mirror  20  is rotated sufficiently rapidly between these two positions, display  16  appears to have a resolution equal to twice the unenhanced resolution. It should be noted that the perceived resolution of display  16  could be increased by a factor of four, rather than two, if mirror  20  is rotated about two axes rather than just one axis. The teachings of the invention may be incorporated into such a system as well. 
   Mirror  20  rotates about a pivot point  28 . An actuator  30 , which in one embodiment is a voice coil, either pushes or pulls mirror  20  up or down to effect movement between the first and second positions. Actuator  30  may take other forms that are operable to effect movement of mirror  20 . A spring  32  is coupled to mirror  20  such that the resulting movement of mirror  20  is approximately proportional to the force applied by actuator  30 . By utilizing spring  32 , which provides an approximately proportional response between a force applied and position of the spring, control of the position of mirror  20  is facilitated. 
   A controller  34  is provided to control actuator  30  such that mirror  20  is rotated between first and second positions in a desirable manner. Controller  34  communicates with actuator  30  over line  38 . Controller  34  may take any suitable form, such as an ASIC or an FPGA, and may be programmed according to the teachings of the invention as described in greater detail below. 
   A position sensor  40  provides an indication of the position of mirror  20 . Feedback from position sensor  40  may be provided to controller  34 ; however, as described in greater detail below, feedback of the position of mirror  20  has a limited role in one embodiment. Any suitable position sensor may be used that provides an indication of the position of mirror  20 ; however, according to one embodiment, the position sensor described in  FIGS. 9A through 11  is utilized. 
   One challenge recognized by the invention with transitioning mirror  20  from a first position to a second position involves overshoot and ringing of the position of mirror  20 . Actuator  30  may apply a force to mirror  20  to cause it to start moving from a first position to a second position (or between multiple positions in other embodiments), but causing mirror  20  to stop at the second position requires some control. One approach for solving this problem would be to provide a position feedback signal such that a servo control loop could precisely control the position of mirror  20  and it could transition from a first position to a second position with minimal overshoot. However, such a control system would require a high bandwidth feedback and a very rapid control system, both of which would significantly increase costs associated with mirror system  14 . 
   According to the teachings of the invention, rather than providing a control feedback loop and precisely controlling the position of mirror  20  during its transition from a first position to a second position, a predetermined control waveform is transmitted from controller  34  to actuator  30  over line  38  that effects a desirable position versus time response of mirror  20  during transition from its first position to its second position and then back to its first position. By utilizing a predetermined waveform, lower cost components may be used and expensive and high bandwidth feedback control systems are not required. Additional details of such a control signal are described in greater detail below in conjunction with  FIGS. 2A through 3C . 
     FIG. 2A  is a series of graphs illustrating the transition of mirror  20  from a first position to a second position. The top graph of  FIG. 2A  illustrates the position of mirror  20  as mirror  20  transitions from a first position to a second position, and includes curves  50  and  52 . The bottom graph is an indication of a particular color of light  18  provided by image source  12  for a given pixel that is being displayed at a particular time. It should be noted that image source  12  generates such a signal for a large number of pixels. According to one aspect of the invention, it has been determined that transitioning mirror  20  from a first position to a second position is desirable to be performed in a time period in which only blue light, if any, is displayed. As described above, in one embodiment, light  18  is provided sequentially in various colors and the user&#39;s eye integrates these colors to generate a desired color to be displayed. The proportion of the time frame in which any particular color may be transmitted determines the resulting color. Light  18  includes, in this embodiment, white light  56 , blue light  58 , red light  60 , and green light  62 . Thus, in the time period in which blue light  58  may be displayed the teachings of the invention recognize that mirror  20  should be transitioned during this time period. This is because transitioning while blue light is displayed is less perceptible to a viewer&#39;s eye than transitioning while other colors are displayed because the human eye has its lowest spatial response in blue light and blue light produces the fewest lumens. It should be noted that although transitioning normally occurs during this time period it is not necessarily the case that blue light is displayed. Rather, this time period is the time period in which no color other than blue may be displayed. Transitioning may also occur during the time period dedicated to transmitting other colors of light, if any, that are determined to result in a desirable lack of perception by a viewer of the transition. 
   Curves  50  and  52  indicate that, according to one embodiment, a range of transition profiles may take place such that transitioning from a first position to a second position of mirror  20  occurs within the time period associated with blue light transmission.  FIG. 2A  also illustrates that transitioning back from a second position to a first position also occurs during the time period in which the blue light may be displayed. As illustrated, a generally trapezoidal response in which the position of mirror  20  rises quickly from a first position to a second position is desirable. In one embodiment, the transition from a first position to a second position occurs in about 1.3 milliseconds. 
     FIG. 2B  is a graph illustrating a position versus time graph of mirror  20  resulting from a step control signal  38  provided by controller  34 . Because optical dithering system  14  is a spring mass system, a step response for control signal  38  such as that illustrated in  FIG. 2B  result in transitioning from a first position to a second position with a time versus response curve  42  illustrated in  FIG. 2B . Thus, mirror  20  overshoots its desired position, swings back, and continues to oscillate for some time period before it comes to a generally resting position at the desired second position. This type of response is undesirable, and would result in a fuzzy image on display  16 . 
     FIG. 2C  is analogous to  FIG. 2B  but illustrates the response of mirror  20  in moving from a first position to a second position and then back to the first position repeatedly over time in response to control signal  38 . As illustrated, mirror  20  overshoots its desired position and begins to oscillate until the next period of control signal  38  is provided, in which case mirror  20  again overshoots in the opposite direction, resulting in an undesirable response. As described above, controlling this undesirable response through use of a feedback control system would be prohibitively expensive. Thus, according to the teachings of the invention, a predetermined control signal is provided that addresses the undesirable response curves for position signal  42  of  FIGS. 2B and 2C . 
     FIG. 3A  illustrates a desirable response curve  142  of mirror  20  in moving from a first position to a second position as well as the associated control signal  138 . Control signal  138  is determined, as described in greater detail below, based upon modeling of the spring mass system of optical dithering system  14  and its characteristics are predetermined independent of the operation of mirror  20 . Thus, the position of mirror  20  at any given time is not utilized to determine the characteristics of control signal  138 . However, as described in greater detail below, the characteristics of predetermined control signal  138  may be tuned based upon the position response of mirror  20  in previous transitions. 
   As illustrated, desirable response curve  142  quickly rises from a first position to a second position with little overshoot and ringing. This is in contrast to undesirable response curve  42  with significant overshoot and ringing. Predetermined control signal  138  comprises, in this example, an initial step  144  having a pulse width  146  and a magnitude  148 . Predetermined control signal  138  also includes a quench pulse  150  having a width  152  and a magnitude  154  that is equal in magnitude but the opposite polarity of magnitude  148 , in this embodiment. Step width  146  of initial step  144  is also referred to herein as quench pulse delay  146  because it indicates the delay of quench pulse  152 . System modeling has determined that, according to one embodiment, step width  146  of the initial step pulse  144  would last for about twenty percent of the resonant response period. The resonant response period herein refers to the period associated with the natural frequency of the spring mass system. It has further been determined that the width of quench pulse  152  would be about fourteen percent of the resonant response period, in one embodiment. Thus for a 250 Hz system, the quench pulse  150  would have an offset of about 0.8 milliseconds and a hold time of 0.55 milliseconds. The ratio between the offset and hold times is dependent of the mechanical Q of the system. 
   It should be noted that the predetermined control signal  138  is one example of a predetermined waveform that provides a desirable response. Other waveform shapes, magnitudes, and frequencies may be utilized based on modeling of the system to be controlled. As another example, a control signal may be provided that is analogous to control signal  138  illustrated in  FIG. 3A , but in which the magnitude of the control signal after the quench pulse has a reduced value; however, many other types of control signals may be used. A narrower quench pulse may be used with more highly-damped or lower Q systems because less energy is required to damp out the overshoot and ringing in such systems. 
     FIG. 3B  is analogous to  FIG. 3A  but shows the response over time characteristics of control signal  138 , response curve  142 , and undesirable position signal  42 . 
     FIG. 3C  is a three-dimensional graph illustrating the overshoot amplitudes that occur for signal  142  for various combinations of width  152  of quench pulse  150  and width  146  of step pulse  144  (or quench pulse delay). As illustrated, the minimum overshoot occurs at a combination corresponding to the time periods described above. Although the particular combination of pulse widths may vary according to the characteristics of mirror  20 , spring  32 , and other associated components, the teachings of the invention recognize that such characteristics may be modeled and a desirable control signal  138  may be determined a priori and thus a high bandwidth feedback control system is not required. However, the teachings of the invention also recognize that there may be some disparity between the modeled parameters and the actual parameters for any given mirror system  14 . Thus a feedback signal  42  is provided to controller  34  to allow fine tuning of widths  146  and  152  based on actual system parameters to fine tune the predetermined control signal. This fine tuning is described in conjunction with  FIGS. 4A through 8  below. 
     FIG. 4A  is a block diagram of a system for controlling the positioning of an optical dithering element, such as mirror  20 . System  200  includes, in this embodiment, an application specific integrated circuit (ASIC)  202 , a field programmable gate array (FPGA)  204 , a bridge driver  206 , a torque motor and mirror  208 , and a setpoint position feedback block  210 . FPGA  204  may correspond to controller  34  of  FIG. 1  and torque motor and mirror block  208  may correspond to voice coil  30  and mirror  20  of  FIG. 1 . 
   ASIC  202  has a primary purpose of controlling modulation of image source  12  to produce light  18 . However, field programmable gate array  204  receives from ASIC  202  a sub-frame sink signal over line  212  such that field programmable gate array  204  may control movement of optical dithering element  20  such that movements of optical dithering element  20  are aligned at an appropriate point in time with respect to the transmission of light  18 , such as is shown in  FIG. 2A . A serial bus  214  is provided between FPGA  204  and ASIC  202  for writing initial delay and hold time, sample period, and amplitude data to the FPGA and for reading back operational status data from the FPGA. FPGA controller  204 &#39;s primary purpose is to control movement of optical dithering element  20 . FPGA controller  204  produces a differential drive signal over lines  216  and  218  and provides this signal to bridge driver  206 . FPGA controller  204  receives feedback over line  222  as described in greater detail below. Bridge driver  206  provides the drive signal that drives the torque motor associated with optical dithering element  20 , which in one example is voice coil motor  30 . Setpoint position feedback block  210  represents the measurement of the position of optical dithering element  20  and determination of whether the position is higher or lower than a desired setpoint. This indication is provided to FPGA controller  204  over line  222 . In one embodiment, the sampling rate of the position of optical dithering element  20  is about 1000 Hz or four times the natural resonant frequency of the system. 
   In operation, FPGA controller  204  provides a predetermined waveform over differential pair  216  and  218  to bridge driver  206 . Bridge driver  206  in turn drives the torque motor associated with optical dithering element with an associated waveform. The resulting position versus time of the optical dithering element is compared at a plurality of sample points to the desired setpoint and an error indication of whether the actual position exceeded or fell below the desired setpoint is provided over line  222  to FPGA controller  204 . In response to this feedback, FPGA controller  204  modifies the waveform transmitted over lines  216  and  218  to compensate for differences between the of the optical dithering element at the sample points and the desired setpoint. Additional details of this modification are described below in conjunction with  FIG. 4B . 
     FIG. 4B  is a block diagram illustrating portions of FPGA controller  204  according to one embodiment of the invention. FPGA controller  204  includes a registers and modifiers block  230 , a pulse width modulator  232 , a torque motor waveform generator  234 , a sampler  236 , and a look-up table  238 . 
   Registers and modifiers block  230  comprise a plurality of registers for storing appropriate data signals and associated logic for modifying the data stored in the registers in response to received feedback. Pulse width modular  232  produces a waveform for controlling the magnitude of the drive waveform generated by torque motor waveform generator  234 . Sampler  236  samples the output of the analog comparator of setpoint position feedback block at predetermined sample intervals. In addition, sampler  236  generates an error signature based upon the sampled signals as described in detail below and provides the error signature to look-up table  238 . Look-up table  238  determines, based upon the received error signal, modifications to the quench pulse delay, the quench pulse width, and the PWM count to produce a more desirable position versus time curve of optical dithering element  20  for subsequent transitions. These modifications are provided as increments and decrements to the predetermined values corresponding to the predetermined waveform (such as control signal  138 ), which are stored in registers and modifiers block  230 . Based on these modifications, revised values are provided by registers and modifiers block  230  to the pulse width modulator  232  and torque motor waveform generator  234 , as described in greater detail below. 
   Registers and modifiers block  230  produces five signals: a base count  240 , a pulse width modulation count  242 , a quench pulse width  244 , a quench pulse delay  246 , and a sample period  248 . Together base count  240  and pulse width modulation count  242  control pulse width modulator  232  such that the magnitude of the drive signals on  216  and  218  is appropriate. Quench pulse width signal  244  controls the width of the quench pulse produced at lines  216  and  218 . Quench pulse delay signal  246  controls the delay of the quench pulse of a drive waveform at lines  216  and  218 . The output of pulse width modulator  232  is provided over line  250  to torque motor waveform generator  234 . The rising edges of the H-bridge drive waveforms on lines  216  and  218  are synchronized to the rising edge of PWM signal on line  250 . This output is also provided to sampler  236  over line  258 , as is a sub-frame sink signal over line  260 . At line  222  an indication of whether the position of optical dithering element exceeds or falls below a desired setpoint is provided to sampler  236 . 
   Sampler  236  takes samples of this high or low signal at appropriate time periods. According to one embodiment of the invention, appropriate time periods correspond to quadrature points based on the natural frequency of the inertia/torsion spring system of optical dithering system  14 . Thus, according to one embodiment, samples are taken every 90 degrees of the natural resonant frequency of optical dithering system  14 . Quadrature sampling allows characterization of both the magnitude and phase of position errors. Further, in one embodiment, samples begin at the end of the quench pulse as indicated by the sample start signal on line  262  and the sample interval is set by the sample period on line  248 . However, sample points may be taken at different times and may begin at different time periods. According to one embodiment, five quadrature sample points are taken; however, any suitable number of samples may be taken, including two samples. Sampler  236  may incorporate a shift register to store a plurality of sample points and then provide a word over line  264  representing an error signature. The word is comprised of a number of bits equal to the number of sample points desired. In one example, in which five quadrature point samples are taken, a five-bit word is provided over line  264  that is the error signature. 
   Look-up table  238  is indexed by the error signature word  264 . Thus, in the example where five samples are utilized, look-up table  238  comprises 32 entries indexed by 32 different possible five-bit words. An example of such a table is described in greater detail in connection with  FIG. 8 . Based upon look-up table  238 , increments or decrements are provided over lines  266 ,  268 , and  270  corresponding to increments or decrements in the stored values associated with quench pulse delay, quench pulse width, PWM count. The PWM count determines the magnitude of the quench pulse. Additional details of the control of optical dithering element  20  and look-up table  238  are described in greater detail below in conjunction with  FIGS. 5 through 8 . 
     FIG. 4C  is a block diagram of an alternative embodiment of a system  300  for controlling the dithering of optical element  20 . System  300  is analogous to system  200  except that the functions of FPGA controller  204  have been incorporated within application-specific integrated circuit  302 . Therefore, many of the functions that are executed in firmware of the FPGA controller  204  may be executed in the software as described in greater detail below in conjunction with  FIG. 4D . 
     FIG. 4D  illustrates portions of ASIC  302  applicable to the control of optical dithering element  20 .  FIG. 4D  is analogous to  FIG. 4B  except that a software code block  306  is provided. Software code block  306  performs similar functions to that of look-up table  238  of  FIG. 4B . Software code block  306  receives initial values over line  308  and modifies these values based upon the error signature  264  in an analogous manner to that described above in conjunction with FPGA controller  204  of  FIG. 4B . 
     FIG. 5  is a graph illustrating a plurality of waveforms associated with control of optical dithering element  20 . Waveform  320  is the drive waveform produced at line  220  for driving the motor that positions optical dithering element  20 . Waveform  322  represents a setpoint for the desired position of optical dithering element  20 . Note that in this embodiment, because the position of the mirror of interest occurs only in the first period of drive waveform  320 , a setpoint is a constant value. However, it will be understood that the desired setpoint for optical dithering element  20  varies between two different positions. Waveform  324  corresponds to the desired position versus time response of optical dithering element  20 . Waveform  326  corresponds to the undamped, uncontrolled response that would occur for optical dithering element in response to a simple step drive waveform for waveform  320  (without the quench pulse). Quadrature sample points  328  illustrate the location at which a plurality of quadrature samples of the actual position versus time waveform of optical dithering element  20 . Thus, if the sampled value falls above setpoint waveform  322  at one of the sample points, an error indicator is generated indicating a high value at that sample point. In one example, a one indicates a high value and a zero indicates a lower value. It should be understood that if the actual position is equal to the setpoint that either a one or a zero could be provided; however, in one embodiment of the invention if the actual position is equal to the setpoint then a zero is generated. 
   According to the invention, the sign of the difference between the actual position of mirror  20  and the setpoint  322  at each of the sample points  328  is utilized to adjust control signal  320  to reduce overshoot and ringing and produce desired waveform  324 . 
     FIG. 6  is a flowchart illustrating one example of a method for controlling optical dithering element  20 . The method begins at step  402 . At step  404  the output of a comparator is sampled at specified intervals. In one embodiment, such output could correspond to the output provided over line  222  by an analog comparator within setpoint position feedback block  210 . As described above, the specified intervals may occur at the quadrature points corresponding to the natural frequency of optical dithering system  14 . In one embodiment, the sampling occurs after the end of quench pulse  150  but could also be coincident with the end of the quench pulse  150 . At step  406 , two or more of the samples collected at step  404  are combined to form an error signature word. According to one embodiment of the invention five samples are collected; however, two or more samples would also work. At step  408  the binary word that is created from the two or more samples of step  406  create an error signal. At step  410 , the error signature value is used as a pointer to a look-up table, in an embodiment in which a look-up table is used. Further, the value of the error signature may also be used as the argument in a case statement, for example where a software program is utilized for the control function. 
   At step  412 , a quench pulse delay timer, a quench pulse width timer, and a pulse width modulation amplitude control register are incremented, decremented, or held based upon the error signature and the sample period is adjusted. According to one embodiment, the sample period is set to 75 percent of the sum of quench pulse delay and quench pulse width. The resulting control signals having the new values are utilized at step  410  to produce a new control signal. The above procedure may be repeated for each transition of optical dithering element  20 , as indicated by reference number  416 , or may be repeated as desired to result in a control signal that generates a desired position versus time signal of optical dithering element  20 . It should be noted that feedback processing and waveform parameter modification can be prioritized to have a low priority and does not need to occur on each cycle because the control waveform will repeat until the next modification. The method concludes at step  418 . 
   According to one embodiment of the invention the increment and decrement values are modified as a function of time from turn on of the system. This allows larger step sizes at start up for faster convergence and then going to smaller step sizes for finer convergence. For example, a series of timer step sizes of 10, 5, 2 and then 1 and pulse width modulation step sizes of 2 and then 1 may be used over the first three seconds of operation. It should also be noted that the initial quadrature-sampling interval is calculated as a percentage of the sum of the initial quench pulse delay and the initial quench pulse width. Modeling systems over a wide range of natural frequencies has shown a 75 percent ratio to be optimum. Thus, the time at which sampling points occur is modified as the quench pulse delay and pulse width change to optimize the drive waveform. If the quadrature-sampling interval is determined based upon a percentage of the quench pulse delay and the quench pulse width, this aspect is taken into account and modifications to the drive waveform produce modifications to the time period for sampling. The incrementing, decrementing or holding of the appropriate values to effect modification of the drive waveform may be determined as described in greater detail below in connection with  FIGS. 7A through 7C . 
     FIGS. 7A through 7C  are graphs illustrating error signatures as a function of the pulse delay error and pulse width error for drive waveforms having amplitudes that are low, correct, and high, respectively. Such graphs may be utilized to determine appropriate corrections to the increment, decrement, or hold rules described above. These graphs were generated by introducing known error in the various parameters, determining the resulting error signature, and placing these on these graphs. The error signature maps covered the range of expected errors. Modification rules for each error signature determined by examining its occurrence in each error map and deciding the best course of action to reduce error values and coverage to a trapezoidal waveform response. These three graphs show error maps for a five-bit sampling. 
   With reference to  FIG. 7A , an error signature having a value of 25 indicates that the pulse width is too low and should be incremented, whereas an error signature of 6 indicates that the pulse width is too high and should be decremented. An error signature of 25 also indicates that the pulse delay is too high and should be decremented. In contrast, an error signature of 6 does not inform whether a pulse delay is correct or incorrect. Thus by mapping the various error signatures and visually determining an appropriate correction, a look-up table, such as that described below in conjunction with  FIG. 8  may be generated.  FIGS. 7B and 7C  show additional maps for various values of the amplitude parameters. These three graphs as well as others may be combined to generate the modification rules illustrated in Table  461  of  FIG. 8 . 
     FIG. 8  is a table showing modification rules for a five-bit error signature for a particular implementation. It should be noted that these rules may differ from system to system, but may be determined based upon the teachings described above of modeling a system and determining appropriate responses due to detected errors. Table  461  comprises a signature error column  462 , a delay column  464 , a pulse width column  466  and a pulse width modulation count  468 . As indicated, any given signature results in a hold, an increment, or a decrement value for each of the relevant parameters. 
   Thus, by determining whether the desired waveform exceeds or falls below a setpoint at a plurality of sample points, the associated control signal (or drive waveform may be modified for future transitions of optical dithering element  20  to reduce such error. This modification may occur without examining the magnitude of the error of the position of the optical dithering element  20 , but rather merely examining whether it is too high or too low. Such a system may be implemented in a much less costly fashion than a complicated server servo control system. 
     FIG. 9A  is a schematic diagram illustrating measurement of the position of an optical dithering element  500  according to the teachings of the invention. As described above, an optical dithering element  500  (such as optical dithering element  20 ) may pivot about a point  502  causing rotational movement of optical dithering element  500 , as indicated by arrows  504 . Rotational movement  504  has an associated translational movement  506 . For small angles of rotational movement  504 , a translational movement  506  of optical dithering element  500  is essentially in one direction. It is a movement in this direction for which feedback is desired for controlling positioning of optical dithering element  500 , as described above. In one embodiment, these movements are very small and may be on the order of 0.015 degrees of rotation and four microns of translation at end  505  of optical dithering element  500 . 
   To effect measurement of end  505  of optical dithering element  500  a photointerrupter  508  is utilized. Photointerrupter  508  includes a light-emitting diode  510 , a phototransistor  512 , and a slot  513  separating light-emitting diode  510  from phototransistor  512 . The light transmission bundle across slot  513  from the light-emitting diode  510  to the phototransistor  512  is physically constrained by apertures  514  and  515 . Disposed within slot  513  is an optical dithering element arm  516 , which is also coupled to end  505  of optical dithering element  500 . Optical dithering element arm  516  may be formed from any suitable substance that may block light transmitted across slot  514 . In one embodiment, optical dithering element arm  516  is a vane made of metal. 
   According to the teachings of the invention, optical dithering element arm  516  is positioned slot  513  such that movement  506  of end  505  of optical dithering element  500  changes the effective size of apertures  514  and  515  by blocking a portion of the light bundle, which results in a change in current through phototransistor  512 . The teachings of the invention recognize that current through phototransistor  512  varies approximately linearly with respect to the size of the apertures  514  and  515  if the current of light-emitting diode  510  is appropriately controlled. Thus, the position of end  505  of optical dithering element  500  may be determined as a function of the current through phototransistor  512 . Components illustrated in  FIG. 9A  for measuring the position of end  505  of optical dithering element  500  may correspond, in one embodiment, to setpoint position feedback block  210  of  FIG. 4A . 
   Associated control circuitry  518  is provided to appropriately control the light-emitting diode current and to generate feedback signals indicative of the position of end  505  of optical dithering element  500 . In one example, these feedback signals include a feedback signal  520 , which is an indication of whether the position of end  50  is greater or less than a desired setpoint. In this regard, signal  520  is analogous to signal  222  of  FIG. 4B . Additionally, in one embodiment, a position signal indicative of the peak-to-peak swing of the position of end  505  may be provided at signal  522 . Additional details of control circuitry  518  and the operation of photointerrupter  508  are described in greater detail below in conjunction with  FIGS. 9B through 11 . 
     FIG. 9B  is a schematic diagram along lines  9 B- 9 B of  FIG. 9A , showing additional details of apertures  514  and  515 . As illustrated in this view, optical dithering element arm  516  is positioned about halfway down the height of apertures  514  and  515 . Movement along arrows  506  results in a small change in the effective size of apertures  514  and  515 , as indicated by lines  517 . According to one embodiment, the approximate distance moved by end  505  is about four microns. Thus, according to the teachings of the invention, a fairly small distance change may be measured by converting the distance change into current through a phototransistor. This is accomplished by recognizing that the photocurrent varies approximately linearly with respect to the size of apertures  514  and  515  if the current through light-emitting diode  510  is appropriately controlled. 
     FIG. 9C  is a graph illustrating current through phototransistor  512  versus a height of aperture  514 . As illustrated, no current flows when apertures  514  and  515  are completely blocked and maximum current flows when apertures  514  and  515  are completely un-blocked. Three curves are illustrated in  FIG. 9C  corresponding to three different tested photointerrupters. These three cases correspond to a high gain unit, a middle gain unit, and a low gain unit. The high gain unit corresponds to an LED current of approximately 7.04 milliamps required to produce a photocurrent of 5 amps at maximum aperture. The middle gain unit corresponds to an LED current of 10.29 milliamps to obtain 5 milliamps of photocurrent at maximum aperture. The low gain unit corresponds to an LED current of 14.7 milliamps in order to reach a photocurrent of 5 milliamps at maximum aperture. As illustrated in  FIG. 9C , photocurrent varies linearly with the size of aperture  460  over a range of aperture sizes. In particular, near the middle of the aperture size, photocurrent varies very linearly with aperture size. Thus, disposing optical dithering element arm  516  such that it blocks approximately half of apertures  514  and  515  can result in a linear change in photocurrent in response to small changes in the position of optical dithering element arm  516  from its setpoint. 
     FIG. 10  is a circuit diagram illustrating additional details of photointerrupter  508  and control circuitry  518 . As illustrated, photointerrupter  508  includes a light-emitting diode  510  and a phototransistor  512  separated by a slot  513 . Disposed within slot  513  is an optical dithering element control arm  516  coupled to optical dithering element  500 . In one embodiment, optical dithering element  500  is a mirror. According to one embodiment of the invention, a setpoint current through phototransistor  512  is set to be 2.5 milliamps, which corresponds to a particularly linear region of the photocurrent versus aperture size graph of  FIG. 9C . It is changes in current about the setpoint that are indicative of the position of end  505  of mirror  500 . 
   Setting of the phototransistor current setpoint may be achieved through use of a voltage source  521  and associated resistor  518 . According to one embodiment, voltage source  521  is 10 volts and resistor  518  is 2 kilo-ohms, and thus a current of 2.5 milliamps through phototransistor  512  produces a voltage of 5 volts at node  523 . 
   A voltage at node  523  is provided to one input of an operational amplifier  517  and compared to a second input, which receives an operating point bias. In this example, the operating point bias is 5 volts. Thus, when the current through phototransistor  512  is 2.5 milliamps, the output of operational amplifier  517  is also at 5 volts corresponding to no position change of end  505  of mirror  500 . 
   Operational amplifier  517  produces an output at node  525 . The output of node  525  is provided to an input of comparator  524 . Comparator  524  compares a voltage indicative of the position of end  505  of mirror  500  to a setpoint for a desired position of end  505  of mirror  500 . In one example, the setpoint bias provided to the other input of comparator  524  is set to 5.5 volts. The value of resistor  527  is selected such that the voltage at node  525  varies from the setpoint of 5 volts by approximately plus or minus 0.5 volts. In one example, the resistance of resistor  527  is 27 kiloohms. 
   Thus, according to the teachings of the invention, linear movement of end  505  of mirror  500  may be detected by converting this linear movement into a change in the effective size of apertures  514  and  515  of the associated photointerrupter  508  and then translating the resulting change in photocurrent into a voltage indicative of the position change of end  505  of mirror  500 . The teachings of the invention recognize that the characteristics of the photocurrent versus aperture size curve, such as  FIG. 9C , may vary depending on the LED current through LED  510 . Thus, the current through LED  510  must be controlled such that the photocurrent versus aperture size maintains a known linear relationship such as that illustrated in  FIG. 9C . This figure corresponds to a particular example in which 5 milliamps of current is achieved with maximum aperture size. But as described above, such photocurrent corresponds to varying levels of LED current based upon the gain of the photointerrupter. Thus, a controlled system is provided that maintains the LED current at a level that corresponds to 5 milliamps at the maximum aperture. This roughly corresponds, in this example, to achieving an average voltage level of 5 volts at node  525 . Thus, an integrator  519 , which receives the operating point bias of 5 volts, has as one input the voltage at node  525 . The voltage at node  525  is integrated over time to provide a feedback signal to LED  510 . Thus, if the setpoint is off, for example, case in which the setpoint photocurrent is 3 milliamps, then the voltage at node  525  is too high. This causes integrator  519  to integrate down such that it lowers LED current through LED  510 . This lowering of the current brings the photocurrent back to its setpoint of 2.5 milliamps. 
     FIG. 10  illustrates additional circuitry that may be utilized, if desired, for additional reasons. A synchronous rectifier and low pass filter  528  is coupled at node  525  to provide an indication of the average peak-to-peak amplitude at node  525 . This output is provided to one input of the comparator  530  and compared to the other input, which is a second setpoint bias. The resulting output of comparator  530  indicates whether the voltage representing the average peak-to-peak mirror movement at  505  is above or below the second setpoint bias. 
     FIG. 11  is a flow chart illustrating a method  600  for providing a position indication of an optical dithering element. The method begins at step  602 . At step  604  a photointerrupter having associated phototransistor and light-emitting diodes separated by an slot is provided. At a step  606  an optical dithering element arm coupled to an optical dithering element is disposed at a setpoint within the aperture of the photointerrupter. The setpoint is approximately mid way between a fully open and a fully closed aperture, such that a change in aperture size at the setpoint results in an approximate linear change in the current through the phototransistor. At step  508 , the current resulting in a change of position of the optical dithering element arm in response the optical dithering element is measured. During this process, the current through the LED is controlled to maintain a desired setpoint of the phototransistor, and thus, the phototransistor has a relatively constant proportional gain with respect to changes in effective aperture size, and therefore position of the optical dithering element. At step  12  the signal is generated that is indicative of the position of the optical dithering element. The method concludes at step  614 . 
   Although the present invention has been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention as defined by the appended claim.