Patent Publication Number: US-2016223808-A1

Title: Systems and methods for selecting an operating voltage of a display apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application claims priority to U.S. Provisional Patent Application No. 62/109,944 entitled “SYSTEMS AND METHODS FOR SELECTING AN OPERATING VOLTAGE OF A DISPLAY APPARATUS,” filed Jan. 30, 2015, assigned to the assignee hereof and hereby expressly incorporated by reference herein. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to the field of imaging displays, and to light modulators incorporated into imaging displays. 
     DESCRIPTION OF THE RELATED TECHNOLOGY 
     Electromechanical systems (EMS) include devices having electrical and mechanical elements, actuators, transducers, sensors, optical components such as mirrors and optical films, and electronics. EMS devices or elements can be manufactured at a variety of scales including, but not limited to, microscales and nanoscales. For example, microelectromechanical systems (MEMS) devices can include structures having sizes ranging from about a micron to hundreds of microns or more. Nanoelectromechanical systems (NEMS) devices can include structures having sizes smaller than a micron including, for example, sizes smaller than several hundred nanometers. Electromechanical elements may be created using deposition, etching, lithography, and/or other micromachining processes that etch away parts of substrates and/or deposited material layers, or that add layers to form electrical and electromechanical devices. 
     EMS-based display apparatus have been proposed that include display elements that modulate light by selectively moving a light-blocking component into and out of an optical path through an aperture defined through a light-blocking layer. Some of the display elements may actuate at different voltage levels due to non-uniformity in the manufacturing process. Incorporating optically inactive test pixels can help in the selection of a lower operating voltage to save power. 
     SUMMARY 
     The systems, methods and devices of this disclosure each have several innovative aspects, no single one of which is solely responsible for the desirable attributes disclosed herein. 
     One innovative aspect of the subject matter described in this disclosure can be implemented in an apparatus. The apparatus can include a first substrate and an array of image-forming display elements positioned on the first substrate to form an image-forming region. Each image-forming display element can include a shutter. The apparatus also can include a plurality of optically inactive display elements positioned on the first substrate. Each optically inactive display element can include a shutter. Each image-forming display element and each optically inactive display element can have a common architecture. Each image-forming display element can be substantially identical to each other image-forming display element. Each optically inactive display element can have at least one design parameter that differs from a corresponding design parameter of the image-forming display elements. The at least one design parameter of a first optically inactive display element can differ from the at least one design parameter of a second optically inactive display element. 
     In some implementations, each image-forming display element and each optically inactive display element can include at least one actuator including a load beam attached to its respective shutter and a drive beam. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements is a separation distance between the respective load beam and a distal end of the respective drive beam. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements is an angle of the respective drive beam relative to the respective load beam. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements is a length of the respective drive beam. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements is a length of the respective load beam. 
     In some implementations, each image-forming display element and each optically inactive display element can include a respective transistor. For each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements can be a channel width of the respective transistor. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements is a width of the respective shutter. 
     In some implementations, the apparatus can include a second substrate opposed to the first substrate. For each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements can be a separation distance between a surface of the respective shutter and a surface of the second substrate. In some implementations, the apparatus can include at least one of a photodiode or a camera capable of measuring a response time to an applied voltage for the respective shutters of each optically inactive display element. 
     In some implementations, the apparatus can include a controller configured to select an operating voltage for the apparatus. The controller can be further configured to select the operating voltage for the apparatus based on a measured response to a single voltage applied to each optically inactive display element. The controller also can be further configured to select the operating voltage for the apparatus based on a measured response to a range of voltages applied to each optically inactive display element. In some implementations, the optically inactive display elements can be positioned outside of the image-forming region. In some implementations, the optically inactive display elements can be positioned within the image-forming region. 
     In some implementations, the apparatus can include a display and a processor capable of communicating with the display. The processor can be capable of processing image data. The apparatus also can include a memory device capable of communicating with the processor. In some implementations, the apparatus can include a driver circuit capable of sending at least one signal to the display and a controller capable of sending at least a portion of the image data to the driver circuit. In some implementations, the apparatus can include an image source module capable of sending the image data to the processor. The image source module can include at least one of a receiver, transceiver, and transmitter. In some implementations, the apparatus includes an input device capable of receiving input data and communicating the input data to the processor. 
     Another innovating aspect of the subject matter described in this disclosure can be implemented in a system for calibrating a display apparatus. The system can include a controller configured to transmit to each of a plurality of optically inactive display elements positioned over a display element substrate a signal causing a shutter associated with each of the plurality of optically inactive display elements to move into a closed position. The system can include a backlight positioned behind the display element substrate. The system can include an optical detection system configured to measure a response time for each of the optically inactive display elements. 
     In some implementations, the optical detection system can include at least one of a photodiode or a camera. In some implementations, the display element substrate can include an array of image-forming display elements positioned on the first substrate to form an image-forming region. The plurality of optically inactive display elements can be positioned outside of the image-forming region. 
     In some implementations, each image-forming display element and each optically inactive display element can have a common architecture. Each image-forming display element can be substantially identical to each other image-forming display element. Each optically inactive display element can have at least one design parameter that differs from a corresponding design parameter of the image-forming display elements. The at least one design parameter of a first optically inactive display element can differ from the at least one design parameter of a second optically inactive display element. 
     In some implementations, the controller can be configured to select an operating voltage for the apparatus. In some implementations, the controller can be configured to select the operating voltage for the apparatus based on a measured response to a range of voltages applied to each optically inactive display element. In some implementations, the apparatus can include a memory element configured to store a lookup table indicating operating voltages suitable for a range of measured response times of optically inactive display elements. 
     Another innovating aspect of the subject matter described in this disclosure can be implemented in a method for manufacturing a display apparatus. The method can include forming, according to a first set of design parameters, an array of image-forming display elements between a front substrate and a rear substrate to form an image-forming region, each image-forming display element including a shutter. The method can include forming a plurality of optically inactive display elements between the front substrate and the rear substrate. Each optically inactive display element can include a shutter and can be formed according to a respective set of design parameters that includes at least one design parameter that differs from a corresponding design parameter of the first set of design parameters. The method can include applying at least one voltage to each of the plurality of optically inactive display elements. The method can include evaluating a voltage response for each optically inactive display element, based on the at least one applied voltage. The method can include selecting an operating voltage for the display apparatus, based on the voltage response evaluation for each optically inactive display element. 
     Another innovating aspect of the subject matter described in this disclosure can be implemented in a method for calibrating a display apparatus. The method includes applying, by a controller, at least one voltage to each of a plurality of optically inactive display elements positioned on a first substrate of the display apparatus. The optically inactive display elements share a common architecture with a plurality of image-forming display elements positioned on the first substrate. Each image-forming display element is substantially identical to each other image-forming display element. Each optically inactive display element has at least one design parameter that differs from a corresponding design parameter of the image-forming display elements. The at least one design parameter of a first optically inactive display element differs from the at least one design parameter of a second optically inactive display element. The method includes evaluating a voltage response for each optically inactive display element, based on the at least one applied voltage. The method includes selecting an operating voltage for the display apparatus, based on the voltage response evaluation for each optically inactive display element. 
     In some implementations, the method can include applying, by the controller, a range of voltages to each of the plurality of optically inactive display elements positioned on a first substrate of the display apparatus. The method can include evaluating voltage responses for each optically inactive display element, based on the range of applied voltages. The method can include selecting the operating voltage for the display apparatus, based on the voltage responses evaluations for each optically inactive display element. In some implementations, the method also can include illuminating the first substrate. Evaluating the voltage response for each optically inactive display element can include measuring, by an optical detection system, a response time for each of the optically inactive display elements. 
     In some implementations each image-forming display element and each optically inactive display element can include at least one actuator including a load beam attached to its respective shutter and a drive beam. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements can be a separation distance between the respective load beam and a distal end of the respective drive beam. In some implementations, for each optically inactive display element, the at least one design parameter that differs from a design parameter of the image-forming display elements is an angle of the respective drive beam relative to the respective load beam. 
     Details of one or more implementations of the subject matter described in this disclosure are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages will become apparent from the description, the drawings and the claims. Note that the relative dimensions of the following figures may not be drawn to scale. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows a schematic diagram of an example direct-view microelectromechanical systems (MEMS)-based display apparatus. 
         FIG. 1B  shows a block diagram of an example host device. 
         FIGS. 2A and 2B  show views of an example dual actuator shutter assembly. 
         FIG. 3  shows an example display apparatus incorporating image-forming display elements and optically inactive display elements. 
         FIG. 4  shows a flow chart of an example process for manufacturing a display apparatus. 
         FIG. 5A  shows a first example lookup table for selecting an operating voltage of a display apparatus. 
         FIG. 5B  shows a second example lookup table for selecting an operating voltage of a display apparatus. 
         FIG. 6A  shows a block diagram of an example system for selecting an operating voltage for a display apparatus. 
         FIG. 6B  shows a perspective view of a portion of the system shown in  FIG. 6A . 
         FIGS. 7A-7C  show example optically inactive display elements having various tip gap separations. 
         FIGS. 8A-8C  show example optically inactive display elements having drive beams positioned at various angles. 
         FIGS. 9A-9C  show example optically inactive display elements having shutters of various widths. 
         FIG. 10  shows a cross-sectional view of an example display apparatus including three optically inactive display elements having various cell gaps. 
         FIGS. 11A and 11B  show system block diagrams of an example display apparatus that includes a plurality of display elements. 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     The following description is directed to certain implementations for the purposes of describing the innovative aspects of this disclosure. However, a person having ordinary skill in the art will readily recognize that the teachings herein can be applied in a multitude of different ways. The described implementations may be implemented in any device, apparatus, or system that is capable of displaying an image, whether in motion (such as video) or stationary (such as still images), and whether textual, graphical or pictorial. The concepts and examples provided in this disclosure may be applicable to a variety of displays, such as liquid crystal displays (LCDs), organic light-emitting diode (OLED) displays, field emission displays, and electromechanical systems (EMS) and microelectromechanical (MEMS)-based displays, in addition to displays incorporating features from one or more display technologies. 
     The described implementations may be included in or associated with a variety of electronic devices such as, but not limited to: mobile telephones, multimedia Internet enabled cellular telephones, mobile television receivers, wireless devices, smartphones, Bluetooth® devices, personal data assistants (PDAs), wireless electronic mail receivers, hand-held or portable computers, netbooks, notebooks, smartbooks, tablets, printers, copiers, scanners, facsimile devices, global positioning system (GPS) receivers/navigators, cameras, digital media players (such as MP3 players), camcorders, game consoles, wrist watches, wearable devices, clocks, calculators, television monitors, flat panel displays, electronic reading devices (such as e-readers), computer monitors, auto displays (such as odometer and speedometer displays), cockpit controls and/or displays, camera view displays (such as the display of a rear view camera in a vehicle), electronic photographs, electronic billboards or signs, projectors, architectural structures, microwaves, refrigerators, stereo systems, cassette recorders or players, DVD players, CD players, VCRs, radios, portable memory chips, washers, dryers, washer/dryers, parking meters, packaging (such as in electromechanical systems (EMS) applications including microelectromechanical systems (MEMS) applications, in addition to non-EMS applications), aesthetic structures (such as display of images on a piece of jewelry or clothing) and a variety of EMS devices. 
     The teachings herein also can be used in non-display applications such as, but not limited to, electronic switching devices, radio frequency filters, sensors, accelerometers, gyroscopes, motion-sensing devices, magnetometers, inertial components for consumer electronics, parts of consumer electronics products, varactors, liquid crystal devices, electrophoretic devices, drive schemes, manufacturing processes and electronic test equipment. Thus, the teachings are not intended to be limited to the implementations depicted solely in the Figures, but instead have wide applicability as will be readily apparent to one having ordinary skill in the art. 
     The dimensions of display elements in a display apparatus impact the voltages required to drive the display. Generally, higher drive voltages result in higher power consumption by the display apparatus. Typically, each display element in a display apparatus is fabricated according to a common set of design parameters. Ideally therefore, each display element would be identical to each other display element. However, due to imprecisions in the manufacturing process, some variation in the actual dimensions of the display elements can be expected. These dimensional variations lead to variations in the voltage required to drive each display element. The operating voltage of the display apparatus should be sufficient to drive every display element, or at least the vast majority of display elements. To account for the potential of the variation described above, display apparatus are often driven at higher voltages than are required. Determining appropriate operating voltages for a specific display apparatus based on a characterization of the voltage response of that display apparatus can result in lower power consumption. 
     To facilitate such a characterization, a display apparatus can include image-forming display elements positioned within an image-forming region of the display apparatus and optically inactive display elements positioned outside of the image-forming region. The optically inactive display elements can share a common architecture with the image-forming display elements, but can include design parameters that differ slightly from those of the image-forming display elements and from each other. Test voltages can be applied to the optically inactive display elements to cause the optically inactive display elements to move into a closed or open position. The voltage responses of the optically inactive display elements can be measured. These measurements can be used to select an operating voltage for the display that will provide a high degree of likelihood that a sufficient number of the image-forming display elements within the display apparatus will function properly, without using excess power. 
     Particular implementations of the subject matter described in this disclosure can be implemented to realize one or more of the following potential advantages. By incorporating optically inactive display elements into a display apparatus and testing their voltage responses, an appropriate operating voltage for the display apparatus can be selected. As such, some display apparatus may use lower operating voltages than other display apparatus whose nominal design parameters are the same. This can help to save power in some of the display apparatus without sacrificing image quality. In some implementations, the optically inactive display elements may be used to calibrate the operating voltage of the display apparatus over time to account for changes in the characteristics of the display elements that may occur over the lifetime of the display apparatus. In some implementations, the variation in design parameters of the optically inactive display elements can be selected to approximate the variation expected to occur within the image-forming display elements. Thus, the variation across all of the image-forming display elements may be estimated based on a significantly smaller number of optically inactive display elements. 
       FIG. 1A  shows a schematic diagram of an example direct-view MEMS-based display apparatus  100 . The display apparatus  100  includes a plurality of light modulators  102   a - 102   d  (generally light modulators  102 ) arranged in rows and columns. In the display apparatus  100 , the light modulators  102   a  and  102   d  are in the open state, allowing light to pass. The light modulators  102   b  and  102   c  are in the closed state, obstructing the passage of light. By selectively setting the states of the light modulators  102   a - 102   d , the display apparatus  100  can be utilized to form an image  104  for a backlit display, if illuminated by a lamp or lamps  105 . In another implementation, the apparatus  100  may form an image by reflection of ambient light originating from the front of the apparatus. In another implementation, the apparatus  100  may form an image by reflection of light from a lamp or lamps positioned in the front of the display, i.e., by use of a front light. 
     In some implementations, each light modulator  102  corresponds to a pixel  106  in the image  104 . In some other implementations, the display apparatus  100  may utilize a plurality of light modulators to form a pixel  106  in the image  104 . For example, the display apparatus  100  may include three color-specific light modulators  102 . By selectively opening one or more of the color-specific light modulators  102  corresponding to a particular pixel  106 , the display apparatus  100  can generate a color pixel  106  in the image  104 . In another example, the display apparatus  100  includes two or more light modulators  102  per pixel  106  to provide a luminance level in an image  104 . With respect to an image, a pixel corresponds to the smallest picture element defined by the resolution of image. With respect to structural components of the display apparatus  100 , the term pixel refers to the combined mechanical and electrical components utilized to modulate the light that forms a single pixel of the image. 
     The display apparatus  100  is a direct-view display in that it may not include imaging optics typically found in projection applications. In a projection display, the image formed on the surface of the display apparatus is projected onto a screen or onto a wall. The display apparatus is substantially smaller than the projected image. In a direct view display, the image can be seen by looking directly at the display apparatus, which contains the light modulators and optionally a backlight or front light for enhancing brightness and/or contrast seen on the display. 
     Direct-view displays may operate in either a transmissive or reflective mode. In a transmissive display, the light modulators filter or selectively block light which originates from a lamp or lamps positioned behind the display. The light from the lamps is optionally injected into a lightguide or backlight so that each pixel can be uniformly illuminated. Transmissive direct-view displays are often built onto transparent substrates to facilitate a sandwich assembly arrangement where one substrate, containing the light modulators, is positioned over the backlight. In some implementations, the transparent substrate can be a glass substrate (sometimes referred to as a glass plate or panel), or a plastic substrate. The glass substrate may be or include, for example, a borosilicate glass, wine glass, fused silica, a soda lime glass, quartz, artificial quartz, Pyrex, or other suitable glass material. 
     Each light modulator  102  can include a shutter  108  and an aperture  109 . To illuminate a pixel  106  in the image  104 , the shutter  108  is positioned such that it allows light to pass through the aperture  109 . To keep a pixel  106  unlit, the shutter  108  is positioned such that it obstructs the passage of light through the aperture  109 . The aperture  109  is defined by an opening patterned through a reflective or light-absorbing material in each light modulator  102 . 
     The display apparatus also includes a control matrix coupled to the substrate and to the light modulators for controlling the movement of the shutters. The control matrix includes a series of electrical interconnects (such as interconnects  110 ,  112  and  114 ), including at least one write-enable interconnect  110  (also referred to as a scan line interconnect) per row of pixels, one data interconnect  112  for each column of pixels, and one common interconnect  114  providing a common voltage to all pixels, or at least to pixels from both multiple columns and multiples rows in the display apparatus  100 . In response to the application of an appropriate voltage (the write-enabling voltage, V WE ), the write-enable interconnect  110  for a given row of pixels prepares the pixels in the row to accept new shutter movement instructions. The data interconnects  112  communicate the new movement instructions in the form of data voltage pulses. The data voltage pulses applied to the data interconnects  112 , in some implementations, directly contribute to an electrostatic movement of the shutters. In some other implementations, the data voltage pulses control switches, such as transistors or other non-linear circuit elements that control the application of separate drive voltages, which are typically higher in magnitude than the data voltages, to the light modulators  102 . The application of these drive voltages results in the electrostatic driven movement of the shutters  108 . 
     The control matrix also may include, without limitation, circuitry, such as a transistor and a capacitor associated with each shutter assembly. In some implementations, the gate of each transistor can be electrically connected to a scan line interconnect. In some implementations, the source of each transistor can be electrically connected to a corresponding data interconnect. In some implementations, the drain of each transistor may be electrically connected in parallel to an electrode of a corresponding capacitor and to an electrode of a corresponding actuator. In some implementations, the other electrode of the capacitor and the actuator associated with each shutter assembly may be connected to a common or ground potential. In some other implementations, the transistor can be replaced with a semiconducting diode, or a metal-insulator-metal switching element. 
       FIG. 1B  shows a block diagram of an example host device  120  (i.e., cell phone, smart phone, PDA, MP3 player, tablet, e-reader, netbook, notebook, watch, wearable device, laptop, television, or other electronic device). The host device  120  includes a display apparatus  128  (such as the display apparatus  100  shown in  FIG. 1A ), a host processor  122 , environmental sensors  124 , a user input module  126 , and a power source. 
     The display apparatus  128  includes a plurality of scan drivers  130  (also referred to as write enabling voltage sources), a plurality of data drivers  132  (also referred to as data voltage sources), a controller  134 , common drivers  138 , lamps  140 - 146 , lamp drivers  148  and an array of display elements  150 , such as the light modulators  102  shown in  FIG. 1A . The scan drivers  130  apply write enabling voltages to scan line interconnects  131 . The data drivers  132  apply data voltages to the data interconnects  133 . 
     In some implementations of the display apparatus, the data drivers  132  are capable of providing analog data voltages to the array of display elements  150 , especially where the luminance level of the image is to be derived in analog fashion. In analog operation, the display elements are designed such that when a range of intermediate voltages is applied through the data interconnects  133 , there results a range of intermediate illumination states or luminance levels in the resulting image. In some other implementations, the data drivers  132  are capable of applying only a reduced set, such as 2, 3 or 4, of digital voltage levels to the data interconnects  133 . In implementations in which the display elements are shutter-based light modulators, such as the light modulators  102  shown in  FIG. 1A , these voltage levels are designed to set, in digital fashion, an open state, a closed state, or other discrete state to each of the shutters  108 . In some implementations, the drivers are capable of switching between analog and digital modes. 
     The scan drivers  130  and the data drivers  132  are connected to a digital controller circuit  134  (also referred to as the controller  134 ). The controller  134  sends data to the data drivers  132  in a mostly serial fashion, organized in sequences, which in some implementations may be predetermined, grouped by rows and by image frames. The data drivers  132  can include series-to-parallel data converters, level-shifting, and for some applications digital-to-analog voltage converters. 
     The display apparatus optionally includes a set of common drivers  138 , also referred to as common voltage sources. In some implementations, the common drivers  138  provide a DC common potential to all display elements within the array  150  of display elements, for instance by supplying voltage to a series of common interconnects  139 . In some other implementations, the common drivers  138 , following commands from the controller  134 , issue voltage pulses or signals to the array of display elements  150 , for instance global actuation pulses which are capable of driving and/or initiating simultaneous actuation of all display elements in multiple rows and columns of the array. 
     Each of the drivers (such as scan drivers  130 , data drivers  132  and common drivers  138 ) for different display functions can be time-synchronized by the controller  134 . Timing commands from the controller  134  coordinate the illumination of red, green, blue and white lamps ( 140 ,  142 ,  144  and  146  respectively) via lamp drivers  148 , the write-enabling and sequencing of specific rows within the array of display elements  150 , the output of voltages from the data drivers  132 , and the output of voltages that provide for display element actuation. In some implementations, the lamps are light emitting diodes (LEDs). 
     The controller  134  determines the sequencing or addressing scheme by which each of the display elements can be re-set to the illumination levels appropriate to a new image  104 . New images  104  can be set at periodic intervals. For instance, for video displays, color images or frames of video are refreshed at frequencies ranging from 10 to 300 Hertz (Hz). In some implementations, the setting of an image frame to the array of display elements  150  is synchronized with the illumination of the lamps  140 ,  142 ,  144  and  146  such that alternate image frames are illuminated with an alternating series of colors, such as red, green, blue and white. The image frames for each respective color are referred to as color subframes. In this method, referred to as the field sequential color method, if the color subframes are alternated at frequencies in excess of 20 Hz, the human visual system (HVS) will average the alternating frame images into the perception of an image having a broad and continuous range of colors. In some other implementations, the lamps can employ primary colors other than red, green, blue and white. In some implementations, fewer than four, or more than four lamps with primary colors can be employed in the display apparatus  128 . 
     In some implementations, where the display apparatus  128  is designed for the digital switching of shutters, such as the shutters  108  shown in  FIG. 1A , between open and closed states, the controller  134  forms an image by the method of time division gray scale. In some other implementations, the display apparatus  128  can provide gray scale through the use of multiple display elements per pixel. 
     In some implementations, the data for an image state is loaded by the controller  134  to the array of display elements  150  by a sequential addressing of individual rows, also referred to as scan lines. For each row or scan line in the sequence, the scan driver  130  applies a write-enable voltage to the write enable interconnect  131  for that row of the array of display elements  150 , and subsequently the data driver  132  supplies data voltages, corresponding to desired shutter states, for each column in the selected row of the array. This addressing process can repeat until data has been loaded for all rows in the array of display elements  150 . In some implementations, the sequence of selected rows for data loading is linear, proceeding from top to bottom in the array of display elements  150 . In some other implementations, the sequence of selected rows is pseudo-randomized, in order to mitigate potential visual artifacts. And in some other implementations, the sequencing is organized by blocks, where, for a block, the data for only a certain fraction of the image is loaded to the array of display elements  150 . For example, the sequence can be implemented to address only every fifth row of the array of the display elements  150  in sequence. 
     In some implementations, the addressing process for loading image data to the array of display elements  150  is separated in time from the process of actuating the display elements. In such an implementation, the array of display elements  150  may include data memory elements for each display element, and the control matrix may include a global actuation interconnect for carrying trigger signals, from the common driver  138 , to initiate simultaneous actuation of the display elements according to data stored in the memory elements. 
     In some implementations, the array of display elements  150  and the control matrix that controls the display elements may be arranged in configurations other than rectangular rows and columns. For example, the display elements can be arranged in hexagonal arrays or curvilinear rows and columns. 
     The host processor  122  generally controls the operations of the host device  120 . For example, the host processor  122  may be a general or special purpose processor for controlling a portable electronic device. With respect to the display apparatus  128 , included within the host device  120 , the host processor  122  outputs image data as well as additional data about the host device  120 . Such information may include data from environmental sensors  124 , such as ambient light or temperature; information about the host device  120 , including, for example, an operating mode of the host or the amount of power remaining in the host device&#39;s power source; information about the content of the image data; information about the type of image data; and/or instructions for the display apparatus  128  for use in selecting an imaging mode. 
     In some implementations, the user input module  126  enables the conveyance of personal preferences of a user to the controller  134 , either directly, or via the host processor  122 . In some implementations, the user input module  126  is controlled by software in which a user inputs personal preferences, for example, color, contrast, power, brightness, content, and other display settings and parameters preferences. In some other implementations, the user input module  126  is controlled by hardware in which a user inputs personal preferences. In some implementations, the user may input these preferences via voice commands, one or more buttons, switches or dials, or with touch-capability. The plurality of data inputs to the controller  134  direct the controller to provide data to the various drivers  130 ,  132 ,  138  and  148  which correspond to optimal imaging characteristics. 
     The environmental sensor module  124  also can be included as part of the host device  120 . The environmental sensor module  124  can be capable of receiving data about the ambient environment, such as temperature and or ambient lighting conditions. The sensor module  124  can be programmed, for example, to distinguish whether the device is operating in an indoor or office environment versus an outdoor environment in bright daylight versus an outdoor environment at nighttime. The sensor module  124  communicates this information to the display controller  134 , so that the controller  134  can optimize the viewing conditions in response to the ambient environment. 
       FIGS. 2A and 2B  show views of an example dual actuator shutter assembly  200 . The dual actuator shutter assembly  200 , as depicted in  FIG. 2A , is in an open state.  FIG. 2B  shows the dual actuator shutter assembly  200  in a closed state. The shutter assembly  200  includes actuators  202  and  204  on either side of a shutter  206 . Each actuator  202  and  204  is independently controlled. A first actuator, a shutter-open actuator  202 , serves to open the shutter  206 . A second opposing actuator, the shutter-close actuator  204 , serves to close the shutter  206 . Each of the actuators  202  and  204  can be implemented as compliant beam electrode actuators. The actuators  202  and  204  open and close the shutter  206  by driving the shutter  206  substantially in a plane parallel to an aperture layer  207  over which the shutter is suspended. The shutter  206  is suspended a short distance over the aperture layer  207  by anchors  208  attached to the actuators  202  and  204 . Having the actuators  202  and  204  attach to opposing ends of the shutter  206  along its axis of movement reduces out of plane motion of the shutter  206  and confines the motion substantially to a plane parallel to the substrate (not depicted). 
     In the depicted implementation, the shutter  206  includes two shutter apertures  212  through which light can pass. The aperture layer  207  includes a set of three apertures  209 . In  FIG. 2A , the shutter assembly  200  is in the open state and, as such, the shutter-open actuator  202  has been actuated, the shutter-close actuator  204  is in its relaxed position, and the centerlines of the shutter apertures  212  coincide with the centerlines of two of the aperture layer apertures  209 . In  FIG. 2B , the shutter assembly  200  has been moved to the closed state and, as such, the shutter-open actuator  202  is in its relaxed position, the shutter-close actuator  204  has been actuated, and the light-blocking portions of the shutter  206  are now in position to block transmission of light through the apertures  209  (depicted as dotted lines). 
     Each aperture has at least one edge around its periphery. For example, the rectangular apertures  209  have four edges. In some implementations, in which circular, elliptical, oval, or other curved apertures are formed in the aperture layer  207 , each aperture may have only a single edge. In some other implementations, the apertures need not be separated or disjointed in the mathematical sense, but instead can be connected. That is to say, while portions or shaped sections of the aperture may maintain a correspondence to each shutter, several of these sections may be connected such that a single continuous perimeter of the aperture is shared by multiple shutters. 
     In order to allow light with a variety of exit angles to pass through the apertures  212  and  209  in the open state, the width or size of the shutter apertures  212  can be designed to be larger than a corresponding width or size of apertures  209  in the aperture layer  207 . In order to effectively block light from escaping in the closed state, the light-blocking portions of the shutter  206  can be designed to overlap the edges of the apertures  209 .  FIG. 2B  shows an overlap  216 , which in some implementations can be predefined, between the edge of light-blocking portions in the shutter  206  and one edge of the aperture  209  formed in the aperture layer  207 . 
     The electrostatic actuators  202  and  204  are designed so that their voltage-displacement behavior provides a bi-stable characteristic to the shutter assembly  200 . For each of the shutter-open and shutter-close actuators, there exists a range of voltages below the actuation voltage, which if applied while that actuator is in the closed state (with the shutter being either open or closed), will hold the actuator closed and the shutter in position, even after a drive voltage is applied to the opposing actuator. The minimum voltage needed to maintain a shutter&#39;s position against such an opposing force is referred to as a maintenance voltage V m . 
     In some implementations, the actuators  202  and  204  and the shutter  206  can all be fabricated in an integrated process from the same materials. For example, in some implementations, a multi-level mold made of sacrificial material, such as a photodefinable resin, is formed using photolithography. The mold includes surfaces that are parallel to the primary plane of the mold, and sidewalls that are normal to the primary plane of the mold. After the mold is defined, one or more layers of structural material, such as metals or semiconductors, are deposited over the mold in one or more conformal deposition processes, including, e.g., sputtering, physical vapor deposition (PVD), electroplating, chemical vapor deposition (CVD), plasma-enhanced chemical vapor deposition (PECVD), or atomic level deposition (ALD). Specific examples of suitable materials include, without limitation, amorphous silicon (a-Si), titanium (Ti), and aluminum (Al). The structural materials are then etched using one or more etch processes. In some implementations, an anisotropic etch is used to remove undesired portions of the structural material deposited on surfaces of the mold that are parallel to the primary plane of the mold, while leaving structural material on the sidewalls. This material on the sidewalls forms the beams of the actuators  202  and  204 . It also forms the vertical surfaces of the anchors  208 . The mold is then removed through a release process, freeing the remaining components to move. 
       FIG. 3  shows an example display apparatus  300  incorporating image-forming display elements  302  and optically inactive display elements  304 . The optically inactive display elements  304  do not contribute to the formation of an image, but can be used for other purposes, such as testing and calibration, for example, selecting an appropriate operating voltage for the display apparatus  300 . For illustrative purposes, the image-forming display elements  302  are arranged in a grid pattern having fourteen columns and ten rows. In an actual display, the array  300  could have hundreds or thousands of rows and/or columns. The image-forming display elements  302  define an image-forming region  306  of a display. In some implementations, each image-forming display element  302  can be implemented as a shutter-based light modulator capable of outputting various intensities of light, as described above in connection with  FIGS. 2A and 2B . A controller can determine whether each shutter of the image-forming display elements  302  should be in a light-transmissive or light-obstructing state based on the content of an image to be displayed within the image-forming region  306 . The optically inactive display elements  304  are positioned outside of the image forming region  306  so that their presence does not interfere with the formation of images within the image-forming region  306 . 
     In some implementations, the optically inactive display elements  304  can include display elements that have the same general architecture as the image-forming display elements  302 . That is, the optically inactive display elements  304  can have substantially the same mechanical structure and control circuitry as the image forming display elements  302 . For example, the optically inactive display elements  304  can include components such as shutters, drive beams, load beams, anchors, and electronic circuitry which are similar in shape, function, and arrangement to corresponding components of the image-forming display elements  302 . However, each optically inactive display element  304  may have at least one design parameter that differs from a corresponding design parameter of the image-forming display elements  302 . For example, the optically inactive display elements  304  may include display elements having, without limitation, differing separation distances between a front portion of their drive beams and load beams (i.e., differing tip gaps), differing drive beam angles, differing shutter widths, differing shutter heights, or differing transistor characteristics. 
     In some implementations, the optically inactive display elements  304  may include other design parameters that differ from corresponding parameters of the image-forming display elements  302 . For example, in some implementations, each optically inactive display element  304  and each image-forming display element  302  may include at least one transistor. The image-forming display elements  302  may have transistors whose feature sizes (e.g., channel widths) are all substantially identical, while the optically inactive display elements  304  may include transistors having a range of sizes for their channels or other features. 
     As discussed further below in relation to  FIG. 4 , the voltage response of the optically inactive display elements can be evaluated to determine appropriate operating voltages for the display apparatus as a whole. In some implementations, positioning the optically inactive display elements  304  on either side of the image-forming region  306  can help to evaluate display element voltage response variations that may be spatially dependent. For example, some voltage response variations may be correlated with the position of a particular display element within the display  300 . By including optically inactive display elements  304  on both sides of the image-forming region  306 , rather than on only one side, such spatially dependent variations have a higher probability of being present in the optically inactive display elements  304 . Therefore, a process that makes use of the optically inactive display elements  304  to select an operating voltage, such as the process described below in connection with  FIG. 4 , is more likely to compensate for these spatially dependent variations. 
     In some other implementations, optically inactive display elements  304  can be included within the image forming region  306 . For example, if the display element density of the display apparatus  300  is sufficiently high, a viewer may not be able to discern the presence of optically inactive display elements  304  within the image-forming region  306 . As a result, positioning some of the optically inactive display elements  304  within the image-forming region may not negatively impact the quality of images produced by the display apparatus  300 . 
       FIG. 4  shows a flow chart of an example process  400  for manufacturing a display apparatus. In brief overview, the process  400  includes forming image-forming display elements according to a first set of design parameters (stage  402 ). Optically inactive display elements having at least one modified design parameter are formed (stage  404 ). A voltage is applied to each optically inactive display element (stage  406 ). The voltage response of the optically inactive display elements is evaluated (stage  408 ). An operating voltage for the display is selected based on the voltage response evaluation (stage  410 ). 
     The process  400  includes forming a plurality of image-forming display elements according to a first set of design parameters (stage  402 ). The image-forming display elements can be formed within an image-forming region, such as the image-forming region  306  shown in  FIG. 3 . All of the design parameters can be identical for each image forming display element. Ideally, the resulting image-forming display elements will be substantially identical. However, due to imperfections that result from the manufacturing process, some variation in the image-forming display elements is generally expected. These variations can impact the operating voltage required to actuate the shutter of each image-forming display element. Because the distribution and/or degree of display element variations may differ in each display apparatus, it can be difficult to select appropriate operating voltages for each display apparatus on an individual basis. 
     The process  400  includes forming optically inactive display elements (stage  404 ). At least some of the optically inactive display elements have at least one design parameter that differs from a corresponding design parameter of the image-forming display elements. For example, the optically inactive display elements can include variations in the tip gap, drive beam angle, drive beam length, load beam length, shutter height, or transistor channel width. In some implementations, the optically inactive display elements can be formed outside of the image-forming region of the display, such that they will not interfere with the formation of images within the image-forming region. In other implementations, some of the optically inactive display elements can be formed within the image-forming region, although they will not contribute to the formation of an image. 
     In some implementations, the optically inactive display elements may be formed simultaneously with the image-forming display elements. For example, the image-forming display elements and the optically inactive display elements may both be formed by depositing one or more layers of material over a mold formed over a substrate. The optically inactive display elements can be formed from the same layers of material used to form the image-forming display elements. The design parameters of the optically inactive display elements can be varied, for example, by altering the dimensions of the mold in the regions where the optically inactive display elements are to be formed accordingly. In some other implementations, the process used to fabricate the optically inactive display elements may be separate from the process used to fabricate the image-forming display elements. For example, the optically inactive display elements may be formed before or after the formation of the image-forming display elements. 
     In some implementations, other circuitry associated with the display elements may also be formed. For example, each display element can include at least one transistor configured to apply an actuation voltage to its respective display element. The transistors associated with the optically inactive display elements can be formed using different design parameters, such as channel widths, than those used to form the transistors associated with the image-forming display elements. In some implementations, the design parameters of the components of each display element can be altered by altering the feature sizes of a photoresist mask used in the manufacturing process. For example, a photoresist mask can be deposited over one or more layers of structural, semiconductive, and/or conductive material. The mask can then be patterned to serve as an etch mask for the structural, semiconductive, and/or conductive material. Altering the feature sizes of the mask in the regions where the optically inactive display elements are formed can allow a subsequent etching step to result in optically inactive display elements whose design parameters are different from the design parameters of the image-forming display elements. 
     The process  400  includes applying a voltage to each optically inactive display element (stage  406 ). In some implementations, the voltage can be selected to be equal to a nominal operating voltage of the display. In other implementations, a different voltage may be applied. In some implementations, a range of voltages, rather than a single voltage, can be applied to the optically inactive display elements. The voltage can be applied to the optically inactive display elements by drivers included within the display apparatus. For example, instructions may be sent to the drivers  130 ,  132 , and  138  shown in  FIG. 1B  to cause an actuation voltage to be applied to the optically inactive display elements. 
     The process  400  includes evaluating a voltage response of the optically inactive display elements (stage  408 ). In some implementations, the voltage response can be measured by an optical detection system, such as a photodiode array or a high-speed camera. 
     In some implementations, the evaluation of the voltage response is a shutter response time. The shutter response time can be calculated as the time it takes for an optically inactive display element to reduce its light output below a threshold (or increase its light output over a threshold) value after the actuation voltage is applied. In implementations in which a range of actuation voltages are applied to the optically inactive display elements, the shutter response time for each optically inactive display element can be measured separately for each test voltage. The shutter response times can then be stored in a memory. In some implementations, the test voltage may be applied (stage  406 ) to all of the optically inactive display elements simultaneously. This can allow for the shutter response times for each of the optically inactive display elements to be measured (stage  408 ) at the same time, thereby reducing the amount of time required to complete the process  400 . 
     In some implementations, the voltage response can be measured in terms of the number or percentage of optically inactive display elements that change state in less than a threshold amount of time. In some implementations, this can be determined by comparing the individual shutter response times of the display elements to the threshold. In some implementations, the number is determined by obtaining an instantaneous count at the threshold time of the number of optically inactive display elements that have fully actuated. The threshold time can be the minimum acceptable actuation time for the display apparatus. In this example, it is not necessary to determine the specific actuation time for each optically inactive display element. A binary value corresponding to whether each optically inactive display element is able to actuate within the threshold amount of time can then be stored in a memory. Alternatively, a total amount of actuating display elements is stored. 
     The process  400  includes selecting an operating voltage for the display based on the voltage response evaluation (stage  410 ). In some implementations, the voltage response evaluation results may be compared to values stored in a lookup table. 
       FIG. 5A  shows a first example lookup table  500  for selecting an operating voltage of a display apparatus. The table  500  includes n rows and two columns, where n is the number of optically inactive display elements included in the display apparatus. 
     Using the table  500 , the operating voltage is selected based on the number of optically inactive display elements that actuate sufficiently fast in response to a test voltage. For example, if it is determined that four of the optically inactive display elements actuated within the threshold amount of time, then V 4  can be selected as the operating voltage of the display. In some implementations, the values stored in the operating voltage column (such as V 4 ) can be dimensionless weighting factors that can be multiplied by the applied test voltage to determine the operating voltage for the display. In some implementations, the stored values may be specific operating voltages. In other implementations, the lookup table may be implemented in other forms. 
       FIG. 5B  shows a second example lookup table  501  for selecting an operating voltage of a display apparatus. The table  501  includes nine rows and three columns. The leftmost column represents the number of optically inactive display elements actuated at a first test voltage, and the center column represents the number of optically inactive display elements actuated at a second test voltage. For illustrative purposes, the table  501  only includes entries for a display having zero, one, or two optically inactive display elements that fully actuate in response to the test voltages. In practice, a display apparatus may have tens, hundreds, or thousands of optically inactive display elements, and the lookup table  501  may have thousands or millions of rows. In some implementations, the table  501  can be stored in a computer memory as a data structure such as an array. 
     Using table  501 , the operating voltage can be selected as the value in the rightmost column corresponding to the row whose entries match that of the display apparatus under test. For example, if two optically inactive display elements actuate in response to the first test voltage and one optically inactive display element actuates in response to the second test voltage, then the operating voltage for the display apparatus can be selected as V 6 . In some implementations, the table  501  may have additional columns corresponding to additional test voltages. 
     Tables  500  and  501  can be populated based on historical data collected from one or more display apparatus that have been manufactured in the past. For example, in some implementations, display apparatus may be tested at a regular frequency during the course of manufacturing many display apparatus (e.g., one out of every thousand display apparatus may be tested to generate the lookup tables  500  and  501 ). Such a scheme can be used to update the lookup tables  500  and  501  over time, which can help to account for variations in display elements caused by imperfections in the manufacturing process that may also change over time. 
     Image quality can be impacted by the percentage of image-forming display elements that are able to actuate within the threshold time. In general, a display apparatus incorporating a larger percentage of image-forming display elements that are able to actuate within the threshold time can produce higher quality images than a display apparatus having a smaller percentage of image-forming display elements that can actuate within the threshold time. However, in some implementations, sufficient image quality may be obtained with less than 100% of the image-forming display elements actuating fully within the threshold time. For example, it may only be necessary for at least 95% of the image-forming display elements to fully actuate within the threshold time. In other implementations, it may be necessary for more than 96%, more than 97%, more than 98% or more than 99% of the image-forming display elements to actuate within the threshold time. 
     In some implementations, a lookup table, such as the lookup table  500  or the lookup table  501 , may be generated by determining a correlation between the number of optically inactive display elements that actuate fully within a threshold time and the operating voltage sufficient to achieve a predetermined image quality from the image-forming display elements. For example, a display apparatus may be tested at a range of voltages to determine the minimum operating voltage at which a desired percentage of the image-forming display elements actuate within the threshold amount of time. The optically inactive display elements of the display apparatus can then be tested to determine the number of optically inactive display elements that actuate fully within the threshold time for a given test voltage level. 
     In some implementations, many display apparatus may be tested in this way, such that a correlation between the minimum operating voltage and the number of optically inactive display elements that actuate in response to a test voltage can be determined. In some implementations, the correlation can be determined using statistical analysis techniques, such as linear or polynomial regression. In other implementations, a computer model of the test data may be used to determine the correlation between minimum operating voltages and voltage response of optically inactive display elements to a test voltage. This information can then be stored in the form of a lookup table. The minimum operating voltage of a display apparatus can then be estimated based on the voltage response of its optically inactive display elements by referring to the lookup table, as discussed above. This can allow each display apparatus to have an operating voltage that is selected individually, so that each display apparatus operates at the lowest voltage likely to produce images of a sufficient quality. 
       FIG. 6A  shows a block diagram of an example system  600  for selecting an operating voltage for a display apparatus.  FIG. 6B  shows a perspective view of a portion of the system  600  shown in  FIG. 6A . The system  600  includes a voltage selection apparatus  602  which includes a processor  606 , a backlight  608 , an optical detection system  610 , and memory  612 . The voltage selection apparatus  600  communicates with a display apparatus  611 . 
     The voltage selection apparatus  602  can be used to select an operating voltage for the display apparatus based on the voltage responses of a plurality of optically inactive display elements. For example, the system  600  can carry out steps  406 - 410  of the process  400  shown in  FIG. 4 . In some implementations, the voltage selection apparatus  602  can receive a partially formed display apparatus  611 . The partially formed display apparatus  611  may include a substrate on which a plurality of display elements have been fabricated. The display elements can include image-forming display elements within an image-forming region, as well as optically inactive display elements positioned outside of the image-forming region. Other components, such as the drivers  130 ,  132 , and  138 , and the controller  134  shown in  FIG. 1B , may also be included in the partially formed display apparatus  611 . 
     As shown in  FIG. 6B , the display apparatus  611  can include a light blocking layer  618  positioned over a plurality of optically inactive display elements  601   a - 601   f  (generally referred to as optically inactive display elements  601 ). The optically inactive display elements  601  are shown in  FIG. 6B  with broken lines because they are obstructed by the optically inactive light blocking layer  618 . Each of the optically inactive display elements  601  is associated with a respective pair of the apertures  607   a - 607   l  formed through the light blocking layer  618 . Also shown in  FIG. 6B  is a light source  660  and a light guide  661 , which together form the backlight  608 . The backlight is positioned below the display elements  601  and is substantially parallel with the light blocking layer  618 . For illustrative purposes, the optical detection system  610 , memory  612 , and processor  606  are not shown in  FIG. 6B . In practice, the optical detection system  610  can be positioned on the side of the light blocking layer opposite the backlight  608 . This arrangement can allow the optical detection system  610  to detect a presence or absence of light passing through the apertures  607   a - 607   l  formed through the light blocking layer  618 . 
     The processor  606  can control the backlight  608  of the voltage selection apparatus to turn on. The backlight can be positioned behind the light blocking layer  618  of the partially formed display apparatus  611 , such that the partially formed display apparatus  611  is illuminated from behind the light blocking layer  618  when the backlight  608  is turned on. Light emitted from the backlight  608  can pass through the apertures  607   a - 607   l  when the shutters of the respective optically inactive display elements  601  are in an open position, and will be blocked when the respective shutters are in a closed position. When the display apparatus  611  is fully formed, an additional light blocking layer (not shown in  FIG. 6B ) can be positioned over or beneath the optically inactive display elements  601  to ensure that light does not escape from the display through any of the optically inactive display elements  601 , regardless of the state of their shutters. 
     The processor  606  can then control all of the optically inactive display elements to move into their fully closed positions. In some implementations, the processor  606  can control the optically inactive display elements  601  by communicating with the controller  134  shown in  FIG. 1A . For example, in some implementations, the controller  134  may already be coupled to the display apparatus  611 . The processor  606  can pass instructions to the controller  134  to cause the controller  134  to cause the drivers  130 ,  132 , and  138  to command each of the optically inactive display elements  601  to move into a fully closed position. 
     By monitoring the amount of light passing through each optically inactive display element  601 , the optical detection system  610  can be used to measure a response time for each optically inactive display element  601 . For example, the optical detection system  610  can be a high speed camera or a photodiode array configured to determine the duration of time between the application of an actuation voltage and the time at which a light level falls below a threshold level for each optically inactive display element  601 . In some implementations, the optical detection system  610  can determine whether each optically inactive display element  601  actuates fully within a threshold amount of time, rather than determining a particular actuation time for each optically inactive display element  601 . For example, the optical detection system  610  can be configured to capture an image after a threshold time has passed since the application of the actuation voltage. The optical detection system  610  can then analyze the captured image to determine whether each optically inactive display element  601  has been actuated within the threshold time. In some implementations, this information can be stored in the memory  612 . 
       FIG. 6B  shows the system  600  after the threshold time has elapsed. As shown, the shutters associated with the optically inactive display elements  601   b - 601   f  have actuated fully, as indicated by the dark appearance of their respective apertures  607   c - 607   l . However, the shutter associated with the optically inactive display element  601   a  is only partially actuated, and therefore light is able to pass through the apertures  607   a  and  607   b . In some implementations, the optical detection system  610  can determine which optically inactive display elements  601  have actuated within the threshold time by measuring the light output of the respective apertures  607   a - 607   l  after the threshold time has passed. While the example of  FIG. 6B  has been described with respect to the application of an actuation voltage tending to cause the optically inactive display elements  601  to move into a closed position, in some implementations the applied voltage can tend to cause the optically inactive display elements  601  to move into an open position from a closed position, and the optical detection system  610  can be used to determine the voltage response in a similar manner. In some implementations, the optical detection system  610  can be used to determine the voltage response of the optically inactive display elements  601  by commanding them to move into both closed and open positions. Data for both voltage responses can be stored in the memory  612 . For a given optically inactive display element  601 , the voltage response observed when the optically inactive display element  601  is commanded to move from an open position into a closed position may differ from the voltage response observed when the optically inactive display element  601  is commanded to move from a closed position into an open position. 
     The processor  606  can then use the voltage response for the optically inactive display elements to calculate an operating voltage for the display apparatus. In some implementations, the processor  606  can select an operating voltage based on a comparison of the response times to historical data for display apparatus having similar nominal characteristics (e.g., display architecture and resolution). In some implementations, the processor  606  can determine the number of optically inactive display elements  601  that have fully actuated, and can select the operating voltage associated with that number from a lookup table. 
     The processor  606  can be implemented in a variety of ways. For example, in some implementations, the processor  606  can be defined by computer instructions executing on a general purpose processor. In other implementations, the processor  606  can be implemented by special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). For example, the processor  606  can include a collection of circuitry and logic instructions within an FPGA or ASIC. The processor  606  can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, an operating system, or a cross-platform runtime environment. 
     In some implementations, the system  600  can be included within the display apparatus  611 . For example, the backlight  608  can be the backlight used by the display apparatus  611  and the optical detection system can be a photodiode array included within the housing of the display apparatus  611 . The system  600  can then be used any time during the life of the display to adjust the operating voltage of the display apparatus  611 . This can help to ensure that the display apparatus  611  operates at a sufficient operating voltage even if some of the design parameters change over time. 
       FIGS. 7A-7C  show example optically inactive display elements  700   a - 700   c  having various tip gap separations  719   a - 719   c . The optically inactive display elements  700   a - 700   c  are formed according to a common architecture. For example, the optically inactive display element  700   a  includes a shutter  702   a  and an actuator  704   a . The actuator  704   a  is an electrostatic actuator including a load beam  706   a  that is fixed at one end to an edge of the shutter  702   a  and at another end to a load anchor  716   a . The actuator  704   a  also includes a drive beam  708   a . The drive beam  708   a  is shaped as a loop arranged at an angle with respect to the shutter  702   a . A front end  710   a  (sometimes also referred to as the tip  710   a ) of the drive beam  708   a  is positioned closer to the load beam  706   a  than a rear end  712   a  of the drive beam  708   a . A drive anchor  714   a  is positioned on a back portion of the looped drive beam  708   a  (i.e., the side facing away from the load beam  706   a ). The drive anchor  714   a  mechanically couples the drive beam  708   a  to an underlying substrate over which the shutter  702  and the actuators  704  are suspended. A load anchor  716   a  couples the load beam  706   a  to the underlying substrate. The load beam  706   a  extends along substantially the entire length of the drive beam  708   a.    
     The optically inactive display elements  700   b  and  700   c  include components similar to those included in the optically inactive display element  700   a , and like reference numerals refer to like components. The primary differences between the three optically inactive display elements  700   a - 700   c  are the separation distances between the front ends  710  of their respective drive electrodes  708  and their respective load beams  706 . This separation distance is referred to as the tip gap. For example, the tip gap  719   a  of the optically inactive display element  700   a  is smaller than the tip gap  719   b  of the optically inactive display element  700   b . The tip gap  719   b  of the optically inactive display element  700   b  is smaller than the tip gap  719   c  of the optically inactive display element  700   c . For illustrative purposes, reference is made primarily to the optically inactive display element  700   a  in describing its functionality below, but the principles discussed apply equally to the optically inactive display elements  700   b  and  700   c  as well. 
     The position of the shutter  702   a  is controlled by the actuator  704   a . For example, an actuation voltage can be applied across the drive beam  708   a  and the load beam  706   a  of the actuator  704   a . The actuation voltage creates an electrostatic force that tends to draw the drive beam  708   a  and the load beam  706   a  together. Because the drive beam  708   a  is fixed to the substrate by the drive anchor  714   a , the electrostatic force causes the load beam  706   a  to move towards the drive beam  708   a . As the load beam  706   a  moves, the shutter  702   a  also moves toward the drive beam  708   a  while remaining substantially parallel to the underlying substrate, because the load beam  706   a  is fixed to the edge of the shutter  702 . When the actuation voltage is removed, the load beam  706   a  can move back to its relaxed position. Therefore, by selectively applying actuation voltages to actuator  704   a , the position of the shutter  702   a  can be controlled. 
     The shutter  702   a  includes an aperture  718   a  through which light can pass when the aperture  718   a  is aligned with an aperture formed in the underlying substrate. To ensure that the optically inactive display element  700   a  does not permit light to escape from the display apparatus in which it is formed, a light blocking layer may be formed directly over the optically inactive display element  700   a . Thus, by modulating the position of the shutter  702   a  using the actuators  704 , the amount of light that is permitted to pass through the shutter  702   a  can be controlled, but the optically inactive display element  700   a  can remain optically dark regardless of the position of the shutter  702   a.    
     The actuation voltage required to move the shutter  702   a  towards the actuator  704   a  can be partially based on the separation distance  719   a  between the load beam  706   a  and the drive beam  708   a . In particular, the separation distance  719   a  between the tip of the load beam  706   a  and the drive beam  708   a  can impact the actuation voltage, with a larger separation distance typically resulting in a larger actuation voltage. Therefore, an optically inactive display element having a larger tip gap, such as the optically inactive display element  700   c , may require a higher actuation voltage than an optically inactive display element having a smaller tip gap, such as the optically inactive display element  700   a . As such, the optically inactive display elements  700   a - 700   c  having different tip gaps  719   a - 719   c  should exhibit varying voltage responses. By manufacturing the optically inactive display elements  700   a - 700   c  with differing tip gaps  719   a - 719   c  and measuring the voltage responses for a given operating voltage or range of operating voltages, a required operating voltage for a display in which the optically inactive display elements  700   a - 700   c  are incorporated can be determined. 
     In some implementations, the variation of the tip gaps  719   a - 719   c  can be selected to approximate the variation expected to occur within a set of image-forming display elements that are manufactured to have nominally identical tip gaps. For example, the tip gap  719   b  of the optically inactive display element  700   b  may be selected to be the same as the nominal tip gap for the image-forming display elements. The tip gap  719   a  of the optically inactive display element  700   a  may be selected to be slightly smaller, and the tip gap  719   c  of the optically inactive display element  700   c  may be selected to be slightly larger, such that the optically inactive display elements  700   a - 700   c  incorporate tip gaps  719   a - 719   c  that span the range of tips gaps expected to occur within the image-forming display elements due to imperfections in the deposition and etching processes discussed above. 
     In some implementations, a display apparatus may include more than three optically inactive display elements having different tip gaps, in order to generate a larger data set of the actuation responses for display elements incorporating different tip gaps. Other optically inactive display elements can be formed with variations in other design parameters, as discussed further below. 
       FIGS. 8A-8C  show example optically inactive display elements  800   a - 800   c  having drive beams  808   a - 808   c  positioned at various angles. The optically inactive display elements  800   a - 800   c  have a general architecture that is similar to that of the optically inactive display element  700   a  shown in  FIG. 7A . For example, the optically inactive display element  800   a  includes a shutter  802   a  having an aperture  818   a . The shutter  802   a  is coupled to an electrostatic actuator  804   a . The actuator  804   a  includes a load beam  806   a  coupled to a respective edge of the shutter  802   a  at one end and to a load anchor  816   a  at the other end. The actuator  804   a  also includes a drive beam  808   a . The optically inactive display elements  800   b  and  800   c  include similar features, with like reference numerals referring to like elements. 
     In contrast to the optically inactive display elements  700   a - 700   c  shown in  FIGS. 7A-7C , the optically inactive display elements  800   a - 800   c  all have substantially the same tip gap. However, the optically inactive display elements  800   a - 800   c  have differing angles for their corresponding drive beams  808   a - 808   c . As shown, the angle of the drive beam  808   a  relative to the load beam  806   a  is smaller than the angle of the drive beam  808   b  relative to the load beam  806   b , and the angle of the drive beam  808   b  relative to the load beam  806   b  is smaller than the angle of the drive beam  808   c  relative to the load beam  806   c . The other design parameters of the optically inactive display elements  800   a - 800   c  are substantially the same. 
     In some implementations, the angle of the drive beams  808   a - 808   c  relative to the respective load beams  806   a - 806   c  can impact the actuation voltage for each optically inactive display element  800   a - 800   c . For example, the differing angles result in differing separation distances between the drive beams  808   a - 808   c  and the respective load beams  806   a - 806   c  along the lengths of the drive beams  808   a - 808   c  and the load beams  806   a - 806   c . Larger separation distances typically require higher voltages for actuation. Therefore, a drive beam arranged at a larger angle, such as the drive beam  808   c  of the optically inactive display element  800   c , may lead to a higher required actuation voltage than a drive beam arranged at a smaller angle, such as the drive beam  808   a  of the optically inactive display element  800   a . As such, the optically inactive display elements  800   a - 800   c  whose drive beams  808   a - 808   c  are arranged at different angles should exhibit varying voltage responses. 
       FIGS. 9A-9C  show example optically inactive display elements having shutters of various widths. The optically inactive display elements  900   a - 900   c  have a general architecture that is similar to that of the optically inactive display element  700   a  shown in  FIG. 7A . For example, the optically inactive display element  900   a  includes a shutter  902   a  having an aperture  918   a . The shutter  902   a  is coupled to an electrostatic actuator  904   a . The actuator  904   a  includes a load beam  906   a  coupled to a respective edge of the shutter  902   a  at one end and to a load anchor  916   a  at the other end. The actuator  904   a  also includes a drive beam  908   a . The optically inactive display elements  900   b  and  900   c  include similar features, with like reference numerals referring to like elements. 
     Rather than differing tip gaps or drive beam angles, the optically inactive display elements  900   a - 900   c  have differing widths for their respective shutters  902   a - 902   b . As shown, the width of the shutter  902   a  is smaller than the width of the shutter  902   b , and the width of the shutter  902   b  is smaller than the width of the shutter  902   c . The other design parameters of the optically inactive display elements  900   a - 900   c  are substantially the same. 
     In some implementations, a display apparatus incorporating the optically inactive display elements  900   a - 900   c  can be filled with a substantially incompressible fluid, such as an oil, that surrounds the shutters  902   a - 902   c  of the optically inactive display elements  900   a - 900   c . As the shutters  902   a - 902   c  move in response to an actuation voltage, they can experience resistance exerted by the fluid. This resistance can vary according to the size of the shutters  902   a - 902   c . Therefore, a shutter having a larger size, such as the shutter  902   c  of the optically inactive display element  900   c , may experience greater fluid resistance than a shutter having a smaller size, such as the shutter  900   a  of the optically inactive display element  900   a . As such, the optically inactive display elements  900   a - 900   c  having different sized shutters  902   a - 902   c  should exhibit varying voltage responses. 
       FIG. 10  shows a cross-sectional view of an example display apparatus  1001  including three optically inactive display elements  1000   a - 1000   c  having various cell gaps. The cell gap for a display element is defined as the distance between a front substrate positioned in front of the display element and a rear substrate positioned behind the display element. The optically inactive display elements  1000   a - 1000   c  are substantially similar to the optically inactive display elements  700   a  shown in  FIG. 7A , and like reference numerals refer to like elements. For illustrative purposes, not all of the components of the optically inactive display elements  1000   a - 1000   c  are shown. 
     The optically inactive display elements are formed over the rear substrate  1003 . A light blocking layer  1005  covers the rear substrate  1003 . First apertures  1007   a - 1007   c  and second apertures  1080   a - 1080   c , each associated with a respective one of the optically inactive display elements  1000   a - 1000   c , are formed in the light blocking layer  1005 . A front substrate  1009  is positioned in front of the optically inactive display elements  1000   a - 1000   c  and the rear substrate  1003 . A light source  1011  and a light guide  1013 , together forming a backlight, are positioned behind the rear substrate  1003 . To ensure that the optically inactive display elements  1000   a - 1000   c  do not emit light, a light-blocking layer  1015  is formed on the rear surface of the front substrate  1009 . 
     To achieve differing cell gaps, a first layer of material  1039  is deposited over the light blocking layer  1015  in the region above the shutters  1002   b  and  1002   c , and a second layer of material  1041  is deposited over the first layer of material  1039  in the region above the shutter  1002   c . The optically inactive display elements  1000   a - 1000   c  therefore have different cell gaps  1021   a - 1021   c . As shown, the cell gap  1021   a  of the shutter  1002   a  is greater than the cell gap  1021   b  of the shutter  1002   b , and the cell gap  1021   b  of the shutter  1002   b  is greater than the cell gap  1021   c  of the shutter  1002   c . The other design parameters of the optically inactive display elements  1000   a - 1000   c  are substantially the same. 
     As discussed above, a display incorporating the optically inactive display elements  1000   a - 1000   c  can be filled with a substantially incompressible fluid. The cell gap can impact the actuation speed and actuation time in the presence of such a fluid. For example, the fluid is more easily displaced by an actuating shutter when the cell gap is larger, because there is more space into which the fluid can be moved by the shutter. Therefore, the shutter  1002   a  will likely actuate at a lower voltage than the shutter  1002   b , and the shutter  1002   b  will likely actuate at a lower voltage than the shutter  1006   c . As such, the optically inactive display elements  1000   a - 1000   c  having different cell gaps should exhibit varying voltage responses. 
     In some implementations, an optical detection system such as the optical detection system  610  shown in  FIG. 6A  may be positioned on the front side of the front substrate  1009 . The optical detection system and the materials used for the various components of the optically inactive display elements  1000   a - 1000   c  may be selected to allow the optical detection system to measure the voltage responses of the optically inactive display elements  1000   a - 1000   c  while still preventing visible light from escaping from the display apparatus  1001 . For example, the backlight  1011  may be configured to emit a broad spectrum of light, including wavelengths that are outside the visible range of the human visual system. The shutters  1002   a - 1002   c  of the optically inactive display elements  1000   a - 1000   c  can be formed from a material that blocks substantially all light (i.e., visible and invisible wavelengths), while the light blocking layer  1015  can be formed from a material that blocks visible light but is transparent to certain light wavelengths that are not visible to humans (e.g., infrared light). The optical detection system can then be configured to detect the invisible light that passes through the light blocking layer  1015 . For example, the shutters  1002   a - 1002   c  can be formed from aluminum, which is substantially opaque to visible light and infrared light, while the light blocking layer  1015  can be formed from silicon, which blocks visible light but is substantially transparent to infrared light. An infrared optical detection system could then be used to determine the voltage responses of the optically inactive display elements  1000   a - 1000   c.    
     In some other implementations, the voltage responses of the optically inactive display elements  1000   a - 1000   c  can be measured before the light blocking layer  1015  is formed. Alternatively, the optical detection system may be positioned behind the rear substrate  1005  and configured to measure the voltage responses of the optically inactive display elements  1000   a - 1000   c  by detecting the reflection of light off of the shutters  1002   a - 1002   c.    
       FIGS. 11A and 11B  show system block diagrams of an example display device  40  that includes a plurality of display elements. The display device  40  can be, for example, a smart phone, a cellular or mobile telephone. However, the same components of the display device  40  or slight variations thereof are also illustrative of various types of display apparatus such as televisions, computers, tablets, e-readers, hand-held devices and portable media devices. 
     The display device  40  includes a housing  41 , a display  30 , an antenna  43 , a speaker  45 , an input device  48  and a microphone  46 . The housing  41  can be formed from any of a variety of manufacturing processes, including injection molding, and vacuum forming. In addition, the housing  41  may be made from any of a variety of materials, including, but not limited to: plastic, metal, glass, rubber and ceramic, or a combination thereof. The housing  41  can include removable portions (not shown) that may be interchanged with other removable portions of different color, or containing different logos, pictures, or symbols. 
     The display  30  may be any of a variety of displays, including a bi-stable or analog display, as described herein. The display  30  also can be capable of including a flat-panel display, such as plasma, electroluminescent (EL) displays, OLED, super twisted nematic (STN) display, LCD, or thin-film transistor (TFT) LCD, or a non-flat-panel display, such as a cathode ray tube (CRT) or other tube device. In addition, the display  30  can include a mechanical light modulator-based display, as described herein. 
     The components of the display device  40  are schematically illustrated in  FIG. 11B . The display device  40  includes a housing  41  and can include additional components at least partially enclosed therein. For example, the display device  40  includes a network interface  27  that includes an antenna  43  which can be coupled to a transceiver  47 . The network interface  27  may be a source for image data that could be displayed on the display device  40 . Accordingly, the network interface  27  is one example of an image source module, but the processor  21  and the input device  48  also may serve as an image source module. The transceiver  47  is connected to a processor  21 , which is connected to conditioning hardware  52 . The conditioning hardware  52  may be configured to condition a signal (such as filter or otherwise manipulate a signal). The conditioning hardware  52  can be connected to a speaker  45  and a microphone  46 . The processor  21  also can be connected to an input device  48  and a driver controller  29 . The driver controller  29  can be coupled to a frame buffer  28 , and to an array driver  22 , which in turn can be coupled to a display array  30 . One or more elements in the display device  40 , including elements not specifically depicted in  FIG. 11A , can be capable of functioning as a memory device and be capable of communicating with the processor  21 . In some implementations, a power supply  50  can provide power to substantially all components in the particular display device  40  design. 
     The network interface  27  includes the antenna  43  and the transceiver  47  so that the display device  40  can communicate with one or more devices over a network. The network interface  27  also may have some processing capabilities to relieve, for example, data processing requirements of the processor  21 . The antenna  43  can transmit and receive signals. In some implementations, the antenna  43  transmits and receives RF signals according to any of the IEEE 16.11 standards, or any of the IEEE 802.11 standards. In some other implementations, the antenna  43  transmits and receives RF signals according to the Bluetooth® standard. In the case of a cellular telephone, the antenna  43  can be designed to receive code division multiple access (CDMA), frequency division multiple access (FDMA), time division multiple access (TDMA), Global System for Mobile communications (GSM), GSM/General Packet Radio Service (GPRS), Enhanced Data GSM Environment (EDGE), Terrestrial Trunked Radio (TETRA), Wideband-CDMA (W-CDMA), Evolution Data Optimized (EV-DO), 1×EV-DO, EV-DO Rev A, EV-DO Rev B, High Speed Packet Access (HSPA), High Speed Downlink Packet Access (HSDPA), High Speed Uplink Packet Access (HSUPA), Evolved High Speed Packet Access (HSPA+), Long Term Evolution (LTE), AMPS, or other known signals that are used to communicate within a wireless network, such as a system utilizing 3G, 4G or 5G, or further implementations thereof, technology. The transceiver  47  can pre-process the signals received from the antenna  43  so that they may be received by and further manipulated by the processor  21 . The transceiver  47  also can process signals received from the processor  21  so that they may be transmitted from the display device  40  via the antenna  43 . 
     In some implementations, the transceiver  47  can be replaced by a receiver. In addition, in some implementations, the network interface  27  can be replaced by an image source, which can store or generate image data to be sent to the processor  21 . The processor  21  can control the overall operation of the display device  40 . The processor  21  receives data, such as compressed image data from the network interface  27  or an image source, and processes the data into raw image data or into a format that can be readily processed into raw image data. The processor  21  can send the processed data to the driver controller  29  or to the frame buffer  28  for storage. Raw data typically refers to the information that identifies the image characteristics at each location within an image. For example, such image characteristics can include color, saturation and gray-scale level. 
     The processor  21  can include a microcontroller, CPU, or logic unit to control operation of the display device  40 . The conditioning hardware  52  may include amplifiers and filters for transmitting signals to the speaker  45 , and for receiving signals from the microphone  46 . The conditioning hardware  52  may be discrete components within the display device  40 , or may be incorporated within the processor  21  or other components. 
     The driver controller  29  can take the raw image data generated by the processor  21  either directly from the processor  21  or from the frame buffer  28  and can re-format the raw image data appropriately for high speed transmission to the array driver  22 . In some implementations, the driver controller  29  can re-format the raw image data into a data flow having a raster-like format, such that it has a time order suitable for scanning across the display array  30 . Then the driver controller  29  sends the formatted information to the array driver  22 . Although a driver controller  29  is often associated with the system processor  21  as a stand-alone Integrated Circuit (IC), such controllers may be implemented in many ways. For example, controllers may be embedded in the processor  21  as hardware, embedded in the processor  21  as software, or fully integrated in hardware with the array driver  22 . 
     The array driver  22  can receive the formatted information from the driver controller  29  and can re-format the video data into a parallel set of waveforms that are applied many times per second to the hundreds, and sometimes thousands (or more), of leads coming from the display&#39;s x-y matrix of display elements. In some implementations, the array driver  22  and the display array  30  are a part of a display module. In some implementations, the driver controller  29 , the array driver  22 , and the display array  30  are a part of the display module. 
     In some implementations, the driver controller  29 , the array driver  22 , and the display array  30  are appropriate for any of the types of displays described herein. For example, the driver controller  29  can be a conventional display controller or a bi-stable display controller (such as a mechanical light modulator display element controller). Additionally, the array driver  22  can be a conventional driver or a bi-stable display driver (such as a mechanical light modulator display element controller). Moreover, the display array  30  can be a conventional display array or a bi-stable display array (such as a display including an array of mechanical light modulator display elements). In some implementations, the driver controller  29  can be integrated with the array driver  22 . Such an implementation can be useful in highly integrated systems, for example, mobile phones, portable-electronic devices, watches or small-area displays. 
     In some implementations, the input device  48  can be configured to allow, for example, a user to control the operation of the display device  40 . The input device  48  can include a keypad, such as a QWERTY keyboard or a telephone keypad, a button, a switch, a rocker, a touch-sensitive screen, a touch-sensitive screen integrated with the display array  30 , or a pressure- or heat-sensitive membrane. The microphone  46  can be configured as an input device for the display device  40 . In some implementations, voice commands through the microphone  46  can be used for controlling operations of the display device  40 . Additionally, in some implementations, voice commands can be used for controlling display parameters and settings. 
     The power supply  50  can include a variety of energy storage devices. For example, the power supply  50  can be a rechargeable battery, such as a nickel-cadmium battery or a lithium-ion battery. In implementations using a rechargeable battery, the rechargeable battery may be chargeable using power coming from, for example, a wall socket or a photovoltaic device or array. Alternatively, the rechargeable battery can be wirelessly chargeable. The power supply  50  also can be a renewable energy source, a capacitor, or a solar cell, including a plastic solar cell or solar-cell paint. The power supply  50  also can be configured to receive power from a wall outlet. 
     In some implementations, control programmability resides in the driver controller  29  which can be located in several places in the electronic display system. In some other implementations, control programmability resides in the array driver  22 . The above-described optimization may be implemented in any number of hardware and/or software components and in various configurations. 
     As used herein, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover: a, b, c, a-b, a-c, b-c, and a-b-c. 
     The various illustrative logics, logical blocks, modules, circuits and algorithm processes described in connection with the implementations disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. The interchangeability of hardware and software has been described generally, in terms of functionality, and illustrated in the various illustrative components, blocks, modules, circuits and processes described above. Whether such functionality is implemented in hardware or software depends upon the particular application and design constraints imposed on the overall system. 
     The hardware and data processing apparatus used to implement the various illustrative logics, logical blocks, modules and circuits described in connection with the aspects disclosed herein may be implemented or performed with a general purpose single- or multi-chip processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, or, any conventional processor, controller, microcontroller, or state machine. A processor also may be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some implementations, particular processes and methods may be performed by circuitry that is specific to a given function. 
     In one or more aspects, the functions described may be implemented in hardware, digital electronic circuitry, computer software, firmware, including the structures disclosed in this specification and their structural equivalents thereof, or in any combination thereof. Implementations of the subject matter described in this specification also can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on a computer storage media for execution by, or to control the operation of, data processing apparatus. 
     If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. The processes of a method or algorithm disclosed herein may be implemented in a processor-executable software module which may reside on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that can be enabled to transfer a computer program from one place to another. A storage media may be any available media that may be accessed by a computer. By way of example, and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that may be used to store desired program code in the form of instructions or data structures and that may be accessed by a computer. Also, any connection can be properly termed a computer-readable medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. Additionally, the operations of a method or algorithm may reside as one or any combination or set of codes and instructions on a machine readable medium and computer-readable medium, which may be incorporated into a computer program product. 
     Various modifications to the implementations described in this disclosure may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other implementations without departing from the spirit or scope of this disclosure. Thus, the claims are not intended to be limited to the implementations shown herein, but are to be accorded the widest scope consistent with this disclosure, the principles and the novel features disclosed herein. 
     Additionally, a person having ordinary skill in the art will readily appreciate, the terms “upper” and “lower” are sometimes used for ease of describing the figures, and indicate relative positions corresponding to the orientation of the figure on a properly oriented page, and may not reflect the proper orientation of any device as implemented. 
     Certain features that are described in this specification in the context of separate implementations also can be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation also can be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Further, the drawings may schematically depict one more example processes in the form of a flow diagram. However, other operations that are not depicted can be incorporated in the example processes that are schematically illustrated. For example, one or more additional operations can be performed before, after, simultaneously, or between any of the illustrated operations. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.