Patent Publication Number: US-8125549-B2

Title: Methods and apparatus to capture compressed images

Description:
FIELD OF THE DISCLOSURE 
     This disclosure relates generally to image capture and, more particularly, to methods and apparatus to capture compressed images. 
     BACKGROUND 
     Traditionally, an image is captured or acquired by projecting the image onto one or more photodetectors, which convert light into a current or voltage. The currents or voltages are subsequently converted to digital signals or values via, for example, one or more analog-to-digital converters. The digital values are stored together in a file, memory(-ies) and/or memory device(s) that represent the original image. In some examples, the digital values are quantized, compressed and/or encoded prior to storage. 
     BRIEF DESCRIPTION OF THE INVENTION 
     Example methods and apparatus to capture compressed images are disclosed. A disclosed example method includes capturing a first output of a photodetector representative of a first weighted sum of a first plurality of portions of an image, capturing a second output of the detector representative of a second weighted sum of a second plurality of portions of the image, and computing a first wavelet coefficient for the image using the first and second captured outputs. 
     A disclosed example apparatus includes a mirror array module, a mirror module controller to control the mirror array module to reflect a first plurality of portions of an image onto a detector at a first time and to reflect a second plurality of portions of the image onto the detector at a second time, a converter to form a first value representative of a first output of the detector at the first time and to form a second value representative of a second output of the detector at the second time, and a coefficient computation module to compute a first wavelet coefficient for the image using the first and second values. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustration of an example compressed-image capture device. 
         FIG. 2  illustrates an example manner of implementing the example digital micro-mirror device (DMD) module of  FIG. 1 . 
         FIG. 3  is a diagram illustrating example relationships between wavelet coefficients of an image. 
         FIGS. 4A and 4B  are a flowchart representative of an example process that may be carried out to implement the example compressed-image capture device of  FIG. 1 . 
         FIG. 5  is a schematic illustration of an example processor platform that may be used and/or programmed to carry out the example process of  FIGS. 4A and 4B , and/or to implement any or all of the example methods and apparatus described herein. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a schematic illustration of an example compressed-image capture device  100  constructed in accordance with the teachings of this disclosure. The example compressed-image capture device  100  of  FIG. 1  captures and/or acquires an image  105  directly in a compressed domain (e.g., directly as wavelet coefficients) obviating either: (a) the need to first capture all portions (e.g., pixels) of the image  105  and then compress the captured image or (b) the need to acquire the image using a representation that is incoherent with wavelets (e.g., using pseudo-random mask) and then compute wavelet coefficients using ‘sparsity’ minimization. Such traditional approaches require large amounts of memory to store the original or un-compressed image  105 , and significant computational resources to compress the captured image. During operation, the example compressed-image capture device  100  of  FIG. 1  uses previously captured, measured and/or acquired wavelet coefficients to adjust and/or determine whether and/or which additional wavelet coefficients should be captured, measured and/or acquired, which: (a) reduces the time and complexity to obtain or capture a compressed image, (b) allows the quality of a captured compressed image  135  to be adaptive adjusted or controlled, and (c) facilitates a low complexity decoding and/or reconstruction process. The example compressed-image capture device  100  of  FIG. 1  may be used to capture and/or acquire compressed images  135  for any type of imaging device such as, but not limited to, a medical imaging or diagnostic device. In some examples, the compressed-image capture device  100  is used to acquire and compress a video stream. In such examples, each frame of the video stream is represented by an image  105 , and wavelet coefficients for each video frame are captured, measured and/or acquired by the example compressed-image capture device  100 . By directly sampling wavelet coefficients, the example compressed-image capture device  100  of  FIG. 1  performs substantially less measurements than would be required to capture all of the pixels of the original image  105 . The original image  105  can be substantially reconstructed from the captured compressed data (i.e., wavelet coefficients)  125 . The quality of the reconstructed image depends on the number of captured wavelet coefficients  125 . 
     To compute a value representative of a sum of one or more portions of the image  105 , the example compressed-image capture device  100  of  FIG. 1  includes a digital micro-mirror (DMD) module  110 . As shown in  FIG. 2 , the example DMD module  110  of  FIG. 2  includes an array  205  of electrostatically actuated micro-mirrors (one of which is designated at reference numeral  210 ) that are each suspended above a corresponding static random-access memory (SRAM) cell, and individually configurable and/or controllable to reflect a corresponding portion of the image  105  onto a detector  215 . An example detector  215  includes a photodetector such as a photodiode. Each mirror  210  of the example mirror array  205  is individually positionable, controllable and/or configurable to reflect a corresponding portion (e.g., pixel) of the image  105  either (a) onto the detector  210  or (b) such that the corresponding portion does not contribute to an output  220  of the detector  215 . By controlling all or a set of the mirrors  210  of the mirror array  205  to reflect corresponding portions of the image  105  onto the detector  215 , the output  220  of the detector  215  represents a sum of the reflected portions of the image  105 . When only a single mirror  210  reflects its corresponding portion onto the detector  215 , the output  220  only represents a single portion (e.g., pixel of the image  105 ). The positions of the mirrors  210  are controlled and/or configured by control signals  225  created and/or provided by a DMD controller  115  ( FIG. 1 ). An example mirror array  205  has mirrors  210  that are positionable at either +12 degrees or −12 degrees with respect to horizontal. When a mirror  210  is positioned at +12 degrees its corresponding portion of the image  105  is projected onto the detector  215 . 
     To convert the output  220  of the detector  215  into a digital representation  230 , the example DMD module  110  of  FIG. 2  includes any type of analog-to-digital converter (ADC)  235 . Using any number and/or type(s) of circuit(s), components and/or topologies, the example ADC  235  of  FIG. 2  converts detector outputs  220  into a digital form (e.g., a stream of digital samples or values  230 ) suitable for processing by remaining portions of the example compressed-image capture device  110  of  FIG. 1 . An example ADC  235  includes a 12-bit converter. The example DMD module  110  of  FIG. 2  may include one or more filters, one or more gain amplifiers, in addition to the ADC  235 , that operate on the detector output  220 . 
     To project and/or focus the image  105  onto the mirror array  205 , the example DMD module  110  of  FIG. 2  includes any number and/or type(s) of lenses, one of which is designated at reference numeral  240 . Likewise, to project and/or focus light reflected by the mirrors  210  onto the detector  215 , the example DMD module  110  of  FIG. 2  includes any number and/or type(s) of lenses, one of which is designated at reference numeral  245 . 
     While an example manner of implementing the example DMD module  110  of  FIG. 1  is illustrated in  FIG. 2 , one or more of the elements illustrated in  FIG. 2  may be combined, divided, re-arranged, omitted, eliminated and/or implemented in any other way. Further, a DMD module may include elements instead of, or in addition to, those illustrated in  FIG. 2  and/or may include more than one of any or all of the illustrated elements. For example, while a single mirror array  205  and detector  215  are shown in  FIG. 2 , a DMD module could implement more than one mirror array and detector. For example, by implementing more than one mirror array and detector, sums of different portions of the image  105  may be performed substantially in parallel (i.e., at substantially the same time). When more than one mirror array is implemented, the mirror arrays may be associated with disjoint and/or overlapping sections of the image  105 . Because the example methods and apparatus described herein adaptively and/or recursively navigate a wavelet tree, different sections of the image  105  can be processed in parallel with non-overlapping mirror arrays. 
     Returning to  FIG. 1 , the wavelet coefficient associated with a Haar wavelet of type 1 can be expressed mathematically as: 
                     ⁢               〈     f   ,     Ψ     j   ,   k     1       〉     =       ∫             ⁢       f   ⁡     (   x   )       ⁢       Ψ     j   ,   k     1     ⁡     (   x   )       ⁢           ⁢     ⅆ   x           ,           EQN   ⁢           ⁢     (   1   )                   
where   is the two-dimensional space of real numbers, f represents the image  105  at a two-dimensional location x, and Ψ 1   j,k  represents the univariate orthonormal Haar basis function of scale or resolution j and location k. Rewriting EQN (1) in discrete form, and substituting the univariate Haar scaling function φ and the Haar wavelet ψ for the Haar basis function Ψ j,k   1 ,the wavelet coefficient associated with a Haar wavelet of type 1 can be expressed as:
 
                       〈     f   ,     Ψ     j   ,   k     1       〉     =       2     -   j       ⁢     (         ∑       i   1     =     2     jk   1           2     f   ⁡     (       k   1     +   1     )           ⁢       ∑       i   2     =     2     jk   2           2     j   ⁡     (       k   2     +     1   /   2       )           ⁢     f   ⁡     (       i   1     ,     i   2       )           -       ∑       i   1     =     2     jk   1           2     j   ⁡     (       k   1     +   1     )           ⁢       ∑       i   2     =     2     j   ⁡     (       k   2     +     1   /   2       )             2     j   ⁡     (       k   2     +   1     )           ⁢     f   ⁡     (       i   1     ,     i   2       )             )         ,           EQN   ⁢           ⁢     (   2   )                 
where f(i 1 , i 2 ) represents a portion of the image  105  corresponding to particular mirror  210  ( FIG. 2 ). As shown in EQN (2), a wavelet coefficient of type 1 can be computed by computing two sums over appropriate portions of the image  105  (i.e., measuring two outputs of the detector  215 ), computing a difference of the sums, and multiplying the difference with a scale factor. In EQN (2), the indices for the summation operators define which portions of the image  105  are included in a particular sum. Ex Wavelet coefficients of types 2 and 3 can likewise be expressed in discrete mathematical forms, as shown in EQN (3) and EQN (4), respectively. The mathematical expressions of EQN (3) and EQN (4) indicate that wavelet coefficients of types 2 and 3 may also be computed using two outputs of the detector  215  (i.e., using two sums).
 
     
       
         
           
             
               
                 
                   
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     In the example mathematical expressions of EQN (2), EQN (3) and EQN (4), all portions of the image  105  are weighted equally. As such, the sums defined in EQN (2), EQN (3) and/or EQN (4) can be realized with a binary mirror array  205 . That is, a mirror  210  either reflects its corresponding image portion onto the detector  215  or not. The computation of other types of wavelet coefficients may require that different portions of the image be weighted differently. In such instances, a gray-scale mirror array may be used. Each mirror of a gray-scale mirror array is individually configurable to reflect or not reflect their corresponding portion onto the detector  215 . When a gray-scale mirror is reflecting its corresponding portion onto the detector  215 , the mirror is individually configurable to adjust how much of the corresponding portion is reflected onto the detector  215 . Additionally or alternatively, a binary mirror array  205  may be used. In such an example, image portions assigned a first weight are captured as a first output  220 , image portions assigned a second weight are captured as a second output  220 , etc., with the outputs  220  subsequently weighted in the digital domain to form a particular sum used to compute a wavelet coefficient. 
     To control the example DMD module  110 , the example compressed-image capture device  100  of  FIG. 1  includes the example DMD controller  115 . For a desired wavelet coefficient the example DMD controller  115  of  FIG. 1  determines and/or computes which sums of combinations of mirrors  210  of the DMD module  110  are needed to compute the desired wavelet coefficient. For a particular combination, the DMD controller  115  provides control inputs  225  to the DMD module  110  and directs the DMD module  110  to acquire, capture and/or measure a detector output  220 . For example, for a Haar wavelet coefficient of type 1, the example DMD controller  115  uses EQN (2) to determine which sums are to be acquired, captured and/or measured by the DMD module  110 . The example DMD controller  115  configures a first combination of the mirrors  210  so that a first digital value  230  represents the first term of EQN (2), and configures a set combination of the mirrors  210  so that a second digital value  230  represents the second term of EQN (2). The example DMD controller  115  can likewise configure combinations of the mirrors  210  to compute the first and second terms of EQN (3) and EQN (4). 
     To compute wavelet coefficients, the example compressed-image capture device  100  of  FIG. 1  includes a coefficient computation module  120 . Using sums of image portions  230  computed by the DMD module  110 , the example coefficient computation module  120  of  FIG. 1  computes a wavelet coefficient. For example, for a Haar wavelet coefficient of type 1, the example coefficient computation module  120  computes the wavelet coefficient by computing a difference of two sums  230  computed by the DMD module  110 , and multiplying the difference by a scale factor, as illustrated in EQN (2). The example coefficient computation module  120  of  FIG. 1  stores the computed wavelet coefficient in a coefficient database  125  using any number and/or type(s) of data structure(s). The example coefficient database  125  of  FIG. 1  may be implemented using any number and/or type(s) of memory(-ies), memory device(s) and/or storage device(s) such as a bard disk drive, a compact disc (CD), a digital versatile disc (DVD), a floppy drive, etc. 
       FIG. 3  is a recursive tree diagram illustrating example relationships between wavelet coefficients. Wavelet coefficients can be regarded as multi-scale edge detectors, where the absolute value of a wavelet coefficient corresponds to the local strength of the edge, that is, the amount of discontinuity present in the image at a particular location and scale. In the illustrated example of  FIG. 3 , low-frequency edges are depicted in the upper left-band corner with progressively higher-frequency edges occurring downward and/or rightward in the example diagram. Each (parent) wavelet coefficient of  FIG. 3  is associated with four children coefficients that represent higher-frequency edge information related to the parent coefficient. For example, a parent coefficient  305  is associated with four children coefficients  310 . If a particular wavelet coefficient is insignificant (e.g., has an absolute value less than a threshold), then with high probability its four children coefficients are also insignificant. Thus, by comparing each wavelet coefficient as it is computed with a threshold, a determination can be made whether to acquire, capture and/or sample its children wavelet coefficients. In this way, which and how many wavelet coefficients that are computed is adjusted and/or adapted while the compressed image is being captured. Detection of an edge at a particular resolution results in higher-resolution sampling of the detected edge. In this way, the example compressed-image capture device  100  of  FIG. 1  implements an adaptive edge acquisition and/or detection device where acquisition resolution is adaptively increased in the vicinity of edges. In some examples, the threshold used to determine whether a computed wavelet coefficient is significant depends on the scale of the wavelet coefficient. 
     Additionally or alternatively, other methods, algorithms and/or criteria may be used to determine which wavelet coefficients are to be computed. For example, wavelet coefficients associated with a significant ancestor (e.g., having a different type) rather than just a significant direct parent may be captured. That is, a wavelet coefficient may be captured even though its direct parent is insignificant. For example, a wavelet coefficient may be identified for capture when a dot-product of the image  105  and a local shift of a previously computed wavelet are significant. While such approaches may increase the number of captured wavelet coefficients, they may improve the robustness of the resulting compressed image and/or decrease the probability of missing high-resolution details of some features of the image  105 . 
     Returning to  FIG. 1 , the example coefficient computation module  120  of  FIG. 1  compares the absolute value of computed wavelet coefficients with a threshold. If the absolute value of a computed wavelet coefficient is greater than the threshold, the coefficient computation module  120  adds indices to a sample queue  130  that represent and/or specify the children coefficients of the computed wavelet coefficient that are to be capture and/or sampled. The number of wavelet coefficients measured by the example compressed-image capture device  100  of  FIG. 1  depends on the value of the threshold and the amount of visual activity in the image  105  (e.g., the number of edges). For the same image  105 , a larger threshold results in fewer wavelet coefficients being captured. For the same threshold, a more visually active image  105  results in more wavelet coefficients being captured. 
     Indices of wavelet coefficients to be acquired, captured and/or measured may be stored in the sample queue  130  using any number and/or type(s) of data structures. In some examples, the index of a wavelet coefficient is represented as (e, j, k), where e represents wavelet sub-band and/or type, j represents scale (or resolution), and k represents location of the wavelet coefficient. The example sample queue  130  of  FIG. 1  may be implemented using any number and/or type(s) of memory(-ies), memory device(s) and/or storage device(s) such as a hard disk drive, a CD, a DVD, a floppy drive, etc. 
     During operation, the example DMD controller  115  of  FIG. 1  queries the example sample queue  130  to determine whether the sample queue  130  contains one or more indices of wavelet coefficients to be acquired, captured and/or measured. If the sample queue  130  is not empty, the example DMD controller  115  removes the next wavelet coefficient index from the sample queue  130 , and configures the example DMD module  110  to compute the one or more sums needed by the coefficient computation module  120  to compute the corresponding wavelet coefficient. 
     To further reduce the amount of data needed to represent a compressed representation  135  of the image  105 , the example compressed-image capture device  100  of  FIG. 1  includes an image compression module  140 . Using any number and/or type(s) of algorithm(s), method(s) and/or logic, the example image compression module  140  processes the wavelet coefficients  125  for the image  105  to further reduce redundancy and/or to reduce the amount of data needed to store and/or represent the wavelet coefficients  125 . For example, the wavelet coefficients  125  may be quantized, and/or entropy encoded according to their tree-structure using, for example, a so-called “zero-tree” compression algorithm. In some examples, local groups of wavelet coefficients  125  at given scales are compressed into different data blocks. By grouping wavelet coefficients in different data blocks, only a portion of the compressed image  135  needs to be extracted to begin reconstructing the original image  105 . Such groupings of wavelet coefficients facilitate the rendering of only a particular region-of-interest of the image  105 , and/or facilitate the progressive reconstruction of the image  105  with increasing resolution as the remainder of the compressed image  135  is extracted and/or received. The example compressed image  135  may be stored using any number and/or type(s) of data structures in any number and/or type(s) of memory(-ies), memory device(s) and/or storage device(s) such as a hard disk drive, a CD, a DVD, a floppy drive, etc. 
     While an example compressed-image capture device  100  has been illustrated in  FIG. 1 , one or more of the interfaces, data structures, elements, processes and/or devices illustrated in  FIG. 1  may be combined, divided, re-arranged, omitted, eliminated and/or implemented in any other way. Further, the example DMD controller  115 , the example coefficient computation module  120 , the example image compression module  140  and/or, more generally, the example compressed-image capture device  100  of  FIG. 1  may be implemented by hardware, software, firmware and/or any combination of hardware, software and/or firmware. Thus, for example, any of the example DMD controller  115 , the example coefficient computation module  120 , the example image compression module  140  and/or, more generally, the example compressed-image capture device  100  may be implemented by one or more circuit(s), programmable processors, application specific integrated circuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or field programmable logic device(s) (FPLD(s)), etc. When any of the appended claims are read to cover a purely software and/or firmware implementation, at least one of the example DMD controller  115 , the example coefficient computation module  120 , the example image compression module  140  and/or, more generally, the example compressed-image capture device  100  are hereby expressly defined to include a tangible computer-readable medium such as a memory, a DVD, a CD, etc. storing the firmware and/or software. Further still, a compressed-image capture device may include interfaces, data structures, elements, processes and/or devices instead of, or in addition to, those illustrated in  FIG. 1  and/or may include more than one of any or all of the illustrated interfaces, data structures, elements, processes and/or devices. 
       FIGS. 4A and 4B  illustrate an example process that may be carried out to implement the example compressed-image capture device  100  of  FIG. 1 . The example process of  FIGS. 4A and 4B  may be carried out by a processor, a controller and/or any other suitable processing device. For example, the example process of  FIGS. 4A and 4B  may be embodied in coded instructions stored on a tangible computer-readable medium such as a flash memory, a CD, a DVD, a floppy disk, a read-only memory (ROM), a random-access memory (RAM), a programmable ROM (PROM), an electronically-programmable ROM (EPROM), and/or an electronically-erasable PROM (EEPROM), an optical storage disk, an optical storage device, magnetic storage disk, a magnetic storage device, and/or any other medium which can be used to carry or store program code and/or instructions in the form of machine-readable instructions or data structures, and which can be accessed by a processor, a general purpose or special purpose computer or other machine with a processor (e.g., the example processor platform P 100  discussed below in connection with  FIG. 5 ). Combinations of the above are also included within the scope of computer-readable media. Machine-readable instructions comprise, for example, instructions and data that cause a processor, a general-purpose computer, special purpose computer, or a special-purpose processing machine to perform one or more particular processes. Alternatively, some or all of the example process of  FIGS. 4A and 4B  may be implemented using any combination(s) of ASIC(s), PLD(s), FPLD(s), discrete logic, hardware, firmware, etc. Also, some or all of the example process of  FIGS. 4A and 4B  may be implemented manually or as any combination of any of the foregoing techniques, for example, any combination of firmware, software, discrete logic and/or hardware. Further, many other methods of implementing the example operations of  FIGS. 4A and 4B  may be employed. For example, the order of execution of the blocks may be changed, and/or one or more of the blocks described may be changed, eliminated, sub-divided, or combined. Additionally, any or all of the example process of  FIGS. 4A and 4B  may be carried out sequentially and/or carried out in parallel by, for example, separate processing threads, processors, devices, discrete logic, circuits, etc. 
     The example process of  FIGS. 4A and 4B  begins the example coefficient computation DMD controller  115  ( FIG. 1 ) setting a value J equal to 1 (block  405 ), and configuring the DMD module  110  to compute the sums for a first wavelet coefficient of resolution j=J (block  410 ). Using the sums computed by the example DMD module  110 , the example coefficient computation module  120  computes the first wavelet coefficient of resolution j=J (block  415 ). If the computed wavelet coefficient is significant (e.g., its absolute value exceeds a threshold) (block  420 ), the coefficient computation module  120  adds indices representative of the child coefficient of the computed coefficient to the sample queue  130  (block  425 ). If the computed wavelet coefficient is not significant (block  420 ), control proceeds to block  430  without adding any indices to the sample queue  130 . 
     If there are more wavelet coefficients of resolution j=J to compute (block  430 ), control returns to block  410  to compute the next wavelet coefficient of resolution j=J. If all wavelet coefficients of resolution j=J have been computed (block  430 ), the coefficient computation module  120  determines whether wavelet coefficients up to a particular resolution have been computed (block  435 ). If not all wavelet coefficients up to the particular resolution have been computed (block  435 ), J is incremented (block  440 ), and control returns to block  410  to compute the next wavelet coefficient. 
     If all wavelet coefficients up to the particular resolution have been computed (block  435 ), control proceeds to block  445  of  FIG. 4B . The example DMD controller  115  ( FIG. 1 ) determines whether the sample queue  130  is empty (block  445 ). If the sample queue  130  is not empty (block  445 ), the DMD controller  115  removes the next entry from the queue  130  (block  450 ) and configures the DMD module  110  to compute the sums for the wavelet coefficient represented by the removed entry (block  455 ). Using the sums computed by the example DMD module  110 , the example coefficient computation module  120  computes the wavelet coefficient (block  460 ). If the computed wavelet coefficient is significant (e.g., its absolute value exceeds a threshold) (block  465 ), the coefficient computation module  120  adds indices representative of the child coefficient of the computed coefficient to the sample queue  130  (block  470 ). If the computed wavelet coefficient is not significant (block  465 ), control returns to block  445  without adding any indices to the sample queue  130 . 
     Returning to block  445 , if the sample queue  130  is empty (block  445 ), the example image compression module  140  quantizes and/or encodes the computed wavelet coefficients (block  475 ). Control then exits from the example process of  FIGS. 4A and 4B . 
       FIG. 5  is a schematic diagram of an example processor platform P 100  that may be used and/or programmed to implement any or all of the example compressed-image capture device  100  of  FIG. 1 . For example, the processor platform P 100  can be implemented by one or more general-purpose processors, processor cores, microcontrollers, etc. 
     The processor platform P 100  of the example of  FIG. 5  includes at least one general-purpose programmable processor P 105 . The processor P 105  executes coded instructions P 110  and/or P 112  present in main memory of the processor P 105  (e.g., within a RAM P 115  and/or a ROM P 120 ). The processor P 105  may be any type of processing unit, such as a processor core, a processor and/or a microcontroller. The processor P 105  may execute, among other things, the example process of  FIGS. 4A and 4B  to implement the example compressed-image capture methods and apparatus described herein. 
     The processor P 105  is in communication with the main memory (including a ROM P 120  and/or the RAM P 115 ) via a bus P 125 . The RAM P 115  may be implemented by dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), and/or any other type of RAM device, and ROM may be implemented by flash memory and/or any other desired type of memory device. Access to the memory P 115  and the memory P 120  may be controlled by a memory controller (not shown). The example memory P 115  may be used to implement the example sample queue  130 , the example coefficient database  125  and/or the example compressed image  135  of  FIG. 1 . 
     The processor platform P 100  also includes an interface circuit P 130 . The interface circuit P 130  may be implemented by any type of interface standard, such as an external memory interface, serial port, general-purpose input/output, etc. One or more input devices P 135  and one or more output devices P 140  are connected to the interface circuit P 130 . The input devices P 135  may be used to, for example, implement the example detector  215  and/or the example ADC  235  of  FIG. 2 . The example output devices P 140  may be used to, for example, control the example mirror array  205 . 
     Generally, computer-executable instructions include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing the processes to implement the example methods and systems disclosed herein. The particular sequence of such executable instructions and/or associated data structures represent examples of corresponding acts for implementing the examples described herein. 
     The example methods and apparatus described herein may be practiced in a networked environment using logical connections to one or more remote computers having processors. Logical connections may include a local area network (LAN) and a wide area network (WAN) that are presented here by way of example and not limitation. Such networking environments are commonplace in office-wide or enterprise-wide computer networks, intranets and the Internet and may use a wide variety of different communication protocols. Such network computing environments may encompass many types of computer system configurations, including personal computers, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. The example methods and apparatus described herein may, additionally or alternatively, be practiced in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination of hardwired or wireless links) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices. 
     Although certain example methods, apparatus and articles of manufacture have been described herein, the scope of coverage of this patent is not limited thereto. On the contrary, this patent covers all methods, apparatus and articles of manufacture fairly falling within the scope of the appended claims either literally or under the doctrine of equivalents.