Patent Publication Number: US-7898725-B2

Title: Apparatuses with enhanced low range bit depth

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 12/345,551, filed Dec. 29, 2008, which is a continuation of U.S. patent application Ser. No. 11/454,162, filed Jun. 15, 2006, issued as U.S. Pat. No. 7,471,442 on Dec. 30, 2008, each of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The field of the invention relates to microelectromechanical systems (MEMS). 
     2. Description of the Related Art 
     Microelectromechanical systems (MEMS) include micro mechanical elements, actuators, and electronics. Micromechanical elements may be created using deposition, etching, 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. One type of MEMS device is called an interferometric modulator. As used herein, the term interferometric modulator or interferometric light modulator refers to a device that selectively absorbs and/or reflects light using the principles of optical interference. In certain embodiments, an interferometric modulator may comprise a pair of conductive plates, one or both of which may be transparent and/or reflective in whole or part and capable of relative motion upon application of an appropriate electrical signal. In a particular embodiment, one plate may comprise a stationary layer deposited on a substrate and the other plate may comprise a metallic membrane separated from the stationary layer by an air gap. As described herein in more detail, the position of one plate in relation to another can change the optical interference of light incident on the interferometric modulator. Such devices have a wide range of applications, and it would be beneficial in the art to utilize and/or modify the characteristics of these types of devices so that their features can be exploited in improving existing products and creating new products that have not yet been developed. 
     SUMMARY OF THE INVENTION 
     The system, method, and devices of the invention each have several aspects, no single one of which is solely responsible for its desirable attributes. Without limiting the scope of this invention, its more prominent features will now be discussed briefly. After considering this discussion, and particularly after reading the section entitled “Detailed Description of Certain Embodiments” one will understand how the features of this invention provide advantages over other display devices. 
     In certain embodiments, a light modulator device comprises a first electrical conduit, a second electrical conduit electrically isolated from the first conduit, a first display element configured to communicate with the first conduit and the second conduit, and a second display element configured to communicate with the first conduit and the second conduit. The first display element is in an actuated state when a voltage difference between the first conduit and the second conduit has a magnitude greater than a first actuation voltage. The first display element is in a released state when the voltage difference between the first conduit and the second conduit has a magnitude less than a first release voltage. The second display element is in an actuated state when a voltage difference between the first conduit and the second conduit has a magnitude greater than a second actuation voltage. The second display element is in a released state when the voltage difference between the first conduit and the second conduit has a magnitude less than a second release voltage. Either the first actuation voltage is substantially equal to the second actuation voltage and the first release voltage is different from the second release voltage or the first actuation voltage is different from the second actuation voltage and the first release voltage is substantially equal to the second release voltage. 
     In certain embodiments, a light modulator device comprises a first means for conducting electrical signals, a second means for conducting electrical signals, and a first means for modulating light configured to communicate with the first conducting means and the second conducting means. The second conducting means is electrically isolated from the first conducting means. The first modulating means is in an actuated state when a voltage difference between the first conducting means and the second conducting means has a magnitude greater than a first actuation voltage. The first modulating means is in a released state when the voltage difference between the first conducting means and the second conducting means has a magnitude less than a first release voltage. The second modulating means is configured to communicate with the first conducting means and the second conducing means. The second modulating means is in an actuated state when a voltage difference between the first conducting means and the second conducting means has a magnitude greater than a second actuation voltage. The second modulating means is in a released state when the voltage difference between the first conducting means and the second conducting means has a magnitude less than a second release voltage. Either the first actuation voltage is substantially equal to the second actuation voltage and the first release voltage is different from the second release voltage or the first actuation voltage is different from the second actuation voltage and the first release voltage is substantially equal to the second release voltage. 
     In certain embodiments, a method of modulating light comprises providing a first display element configured to communicate with a first conduit and a second conduit, providing a second display element configured to communicate with the first conduit and the second conduit, and selectively applying voltages to the first and second conduits to selectively actuate and release the first display element and the second display element. The first display element is in an actuated state when a voltage difference between the first conduit and the second conduit has a magnitude greater than a first actuation voltage. The first display element is in a released state when the voltage difference between the first conduit and the second conduit has a magnitude less than a first release voltage. The second display element is in an actuated state when a voltage difference between the first conduit and the second conduit has a magnitude greater than a second actuation voltage. The second display element is in a released state when the voltage difference between the first conduit and the second conduit has a magnitude less than a second release voltage. Either the first actuation voltage is substantially equal to the second actuation voltage and the first release voltage is different from the second release voltage or the first actuation voltage is different from the second actuation voltage and the first release voltage is substantially equal to the second release voltage. 
     In certain embodiments, a method of displaying images comprises providing a plurality of pixels, selectively actuating the display elements of a pixel to provide a first bit density for a first range of intensities of the pixel, and selectively actuating the display elements of the pixel to provide a second bit density for a second range of intensities of the pixel. Each pixel comprises a plurality of display elements. The second range of intensities is higher than the first range of intensities. The second bit density is less than the first bit density. 
     In certain embodiments, a method of manufacturing a light modulator device comprises forming a first electrical conduit, forming a second electrical conduit electrically isolated from the first conduit, forming a first display element configured to communicate with the first conduit and the second conduit, and forming a second display element configured to communicate with the first conduit and the second conduit. The first display element is in an actuated state when a voltage difference between the first conduit and the second conduit has a magnitude greater than a first actuation voltage. The first display element is in a released state when the voltage difference between the first conduit and the second conduit has a magnitude less than a first release voltage. The second display element is in an actuated state when a voltage difference between the first conduit and the second conduit has a magnitude greater than a second actuation voltage. The second display element is in a released state when the voltage difference between the first conduit and the second conduit has a magnitude less than a second release voltage. Either the first actuation voltage is substantially equal to the second actuation voltage and the first release voltage is different from the second release voltage or the first actuation voltage is different from the second actuation voltage and the first release voltage is substantially equal to the second release voltage. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an isometric view depicting a portion of one embodiment of an interferometric modulator display in which a movable reflective layer of a first interferometric modulator is in a relaxed position and a movable reflective layer of a second interferometric modulator is in an actuated position. 
         FIG. 2  is a system block diagram illustrating one embodiment of an electronic device incorporating a 3×3 interferometric modulator display. 
         FIG. 3  is a diagram of movable mirror position versus applied voltage for one exemplary embodiment of an interferometric modulator of  FIG. 1 . 
         FIG. 4  is an illustration of a set of row and column voltages that may be used to drive an interferometric modulator display. 
         FIG. 5A  illustrates one exemplary frame of display data in the 3×3 interferometric modulator display of  FIG. 2 . 
         FIG. 5B  illustrates one exemplary timing diagram for row and column signals that may be used to write the frame of  FIG. 5A . 
         FIGS. 6A and 6B  are system block diagrams illustrating an embodiment of a visual display device comprising a plurality of interferometric modulators. 
         FIG. 7A  is a cross section of the device of  FIG. 1 . 
         FIG. 7B  is a cross section of an alternative embodiment of an interferometric modulator. 
         FIG. 7C  is a cross section of another alternative embodiment of an interferometric modulator. 
         FIG. 7D  is a cross section of yet another alternative embodiment of an interferometric modulator. 
         FIG. 7E  is a cross section of an additional alternative embodiment of an interferometric modulator. 
         FIG. 8  is a schematic diagram of an embodiment of a monochrome interferometric modulator. 
         FIG. 9  is a schematic diagram of an embodiment of a grayscale interferometric modulator. 
         FIG. 10  is a schematic diagram of an embodiment of a color interferometric modulator. 
         FIG. 11  is a schematic diagram of an embodiment of an interferometric modulator in which the rows have been subdivided into three subrows. 
         FIG. 12  is a schematic diagram of an embodiment of an interferometric modulator in which the rows have been subdivided into three subrows that are configured to communicate with a common row driver connection. 
         FIG. 13  is a diagram of movable mirror position versus applied positive and negative voltage illustrating one exemplary embodiment of three interferometric modulators that have nested stability windows. 
         FIG. 14  is a timing diagram that illustrates a series of row and column signals applied to the top row of the embodiment of the array of  FIG. 12  to produce the illustrated display arrangement. 
         FIG. 15  is a flowchart illustrating one embodiment of a method of driving an interferometric modulator array. 
         FIG. 16  is a schematic diagram of an embodiment of the interferometric modulator in which the rows have been subdivided into four subrows and in which two subrows are configured to communicate with a common row driver connection. 
         FIG. 17  is a diagram of movable mirror position versus applied positive voltage illustrating one exemplary embodiment of two interferometric modulators that have different stability windows in which the release voltages are about the same but the actuation voltages are different. 
         FIG. 18  is a diagram of movable mirror position versus applied positive voltage illustrating one exemplary embodiment of two interferometric modulators that have different stability windows in which the release voltages are different but the actuation voltages are about the same. 
         FIG. 19  schematically illustrates the quantization steps and quantization levels provided by the schematic of  FIG. 10 . 
         FIG. 20  is a chart illustrating the quantization steps and quantization levels provided by the schematic of  FIG. 10 . 
         FIG. 21  schematically illustrates the quantization steps and quantization levels provided by the schematic of  FIG. 16 . 
         FIG. 22  is a chart illustrating the quantization steps and quantization levels provided by the schematic of  FIG. 16 . 
         FIG. 23  is a schematic diagram of another embodiment of the interferometric modulator in which the rows have been subdivided into four subrows and in which two subrows are configure to communicate with a common row driver connection. 
         FIG. 24  schematically illustrates the quantization steps and quantization levels provided by the schematic of  FIG. 23 . 
         FIG. 25  is a chart illustrating the quantization steps and quantization levels provided by the schematic of  FIG. 23 . 
         FIG. 26  is a schematic diagram of an embodiment of the interferometric modulator in which the rows have been subdivided into five subrows, in which two subrows are configured to communicate with one common row driver connection, and in which two other subrows are configured to communicate with another common row driver connection. 
         FIG. 27  schematically illustrates the quantization steps and quantization levels provided by the schematic of  FIG. 26 . 
         FIG. 28  is a chart illustrating the quantization steps and quantization levels provided by the schematic of  FIG. 26 . 
         FIG. 29  is a partial schematic diagram of an embodiment of an interferometric modulator in which the rows have been subdivided into six subrows, in which two subrows are configured to communicate with one common row driver connection, in which two other subrows are configured to communicate with another common row driver connection, and in which the remaining two subrows are configured to communicate with yet another common row driver connection. 
         FIG. 30  schematically illustrates the quantization steps and quantization levels provided by the schematic of  FIG. 29 . 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following detailed description is directed to certain specific embodiments of the invention. However, the invention can be embodied in a multitude of different ways. In this description, reference is made to the drawings wherein like parts are designated with like numerals throughout. As will be apparent from the following description, the embodiments may be implemented in any device that is configured to display an image, whether in motion (e.g., video) or stationary (e.g., still image), and whether textual or pictorial. More particularly, it is contemplated that the embodiments may be implemented in or associated with a variety of electronic devices such as, but not limited to, mobile telephones, wireless devices, personal data assistants (PDAs), hand-held or portable computers, GPS receivers/navigators, cameras, MP3 players, camcorders, game consoles, wrist watches, clocks, calculators, television monitors, flat panel displays, computer monitors, auto displays (e.g., odometer display, etc.), cockpit controls and/or displays, display of camera views (e.g., display of a rear view camera in a vehicle), electronic photographs, electronic billboards or signs, projectors, architectural structures, packaging, and aesthetic structures (e.g., display of images on a piece of jewelry). MEMS devices of similar structure to those described herein can also be used in non-display applications such as in electronic switching devices. 
     A set of display elements is provided that either have actuation voltages that are substantially equal and release voltages that are different or have release voltages that are substantially equal and actuation voltages that are different. Operation using these hysteresis windows allows for a decrease in the number of electrical conduits because the display elements may share common row and column drivers. In some embodiments, the optical active areas of the display elements are weighted to provide enhanced low range bit depth. In some embodiments, the ratio of the optically active areas of the display elements is 3, 7, 15, 31, 127, or 255. 
     One interferometric modulator display embodiment comprising an interferometric MEMS display element is illustrated in  FIG. 1 . In these devices, the pixels are in either a bright or dark state. In the bright (“on” or “open”) state, the display element reflects a large portion of incident visible light to a user. When in the dark (“off” or “closed”) state, the display element reflects little incident visible light to the user. Depending on the embodiment, the light reflectance properties of the “on” and “off” states may be reversed. MEMS pixels can be configured to reflect predominantly at selected colors, allowing for a color display in addition to black and white. 
       FIG. 1  is an isometric view depicting two adjacent pixels in a series of pixels of a visual display, wherein each pixel comprises a MEMS interferometric modulator. In some embodiments, an interferometric modulator display comprises a row/column array of these interferometric modulators. Each interferometric modulator includes a pair of reflective layers positioned at a variable and controllable distance from each other to form a resonant optical cavity with at least one variable dimension. In one embodiment, one of the reflective layers may be moved between two positions. In the first position, referred to herein as the relaxed position, the movable reflective layer is positioned at a relatively large distance from a fixed partially reflective layer. In the second position, referred to herein as the actuated position, the movable reflective layer is positioned more closely adjacent to the partially reflective layer. Incident light that reflects from the two layers interferes constructively or destructively depending on the position of the movable reflective layer, producing either an overall reflective or non-reflective state for each pixel. 
     The depicted portion of the pixel array in  FIG. 1  includes two adjacent interferometric modulators  12   a  and  12   b . In the interferometric modulator  12   a  on the left, a movable reflective layer  14   a  is illustrated in a relaxed position at a predetermined distance from an optical stack  16   a , which includes a partially reflective layer. In the interferometric modulator  12   b  on the right, the movable reflective layer  14   b  is illustrated in an actuated position adjacent to the optical stack  16   b.    
     The optical stacks  16   a  and  16   b  (collectively referred to as optical stack  16 ), as referenced herein, typically comprise several fused layers, which can include an electrode layer, such as indium tin oxide (ITO), a partially reflective layer, such as chromium, and a transparent dielectric. The optical stack  16  is thus electrically conductive, partially transparent, and partially reflective, and may be fabricated, for example, by depositing one or more of the above layers onto a transparent substrate  20 . The partially reflective layer can be formed from a variety of materials that are partially reflective such as various metals, semiconductors, and dielectrics. The partially reflective layer can be formed of one or more layers of materials, and each of the layers can be formed of a single material or a combination of materials. 
     In some embodiments, the layers of the optical stack  16  are patterned into parallel strips, and may form row electrodes in a display device as described further below. The movable reflective layers  14   a ,  14   b  may be formed as a series of parallel strips of a deposited metal layer or layers (orthogonal to the row electrodes of  16   a ,  16   b ) deposited on top of posts  18  and an intervening sacrificial material deposited between the posts  18 . When the sacrificial material is etched away, the movable reflective layers  14   a ,  14   b  are separated from the optical stacks  16   a ,  16   b  by a defined gap  19 . A highly conductive and reflective material such as aluminum may be used for the reflective layers  14 , and these strips may form column electrodes in a display device. 
     With no applied voltage, the cavity  19  remains between the movable reflective layer  14   a  and optical stack  16   a , with the movable reflective layer  14   a  in a mechanically relaxed state, as illustrated by the pixel  12   a  in  FIG. 1 . However, when a potential difference is applied to a selected row and column, the capacitor formed at the intersection of the row and column electrodes at the corresponding pixel becomes charged, and electrostatic forces pull the electrodes together. If the voltage is high enough, the movable reflective layer  14  is deformed and is forced against the optical stack  16 . A dielectric layer (not illustrated in this Figure) within the optical stack  16  may prevent shorting and control the separation distance between layers  14  and  16 , as illustrated by pixel  12   b  on the right in  FIG. 1 . The behavior is the same regardless of the polarity of the applied potential difference. In this way, row/column actuation that can control the reflective vs. non-reflective pixel states is analogous in many ways to that used in conventional LCD and other display technologies. 
       FIGS. 2 through 5B  illustrate one exemplary process and system for using an array of interferometric modulators in a display application. 
       FIG. 2  is a system block diagram illustrating one embodiment of an electronic device that may incorporate aspects of the invention. In the exemplary embodiment, the electronic device includes a processor  21  which may be any general purpose single- or multi-chip microprocessor such as an ARM, Pentium®, Pentium II®, Pentium III®, Pentium IV®, Pentium® Pro, an 8051, a MIPS®, a Power PC®, an ALPHA®, or any special purpose microprocessor such as a digital signal processor, microcontroller, or a programmable gate array. As is conventional in the art, the processor  21  may be configured to execute one or more software modules. In addition to executing an operating system, the processor may be configured to execute one or more software applications, including a web browser, a telephone application, an email program, or any other software application. 
     In one embodiment, the processor  21  is also configured to communicate with an array driver  22 . In one embodiment, the array driver  22  includes a row driver circuit  24  and a column driver circuit  26  that provide signals to a display array or panel  30 . The cross section of the array illustrated in  FIG. 1  is shown by the lines  1 - 1  in  FIG. 2 . For MEMS interferometric modulators, the row/column actuation protocol may take advantage of a hysteresis property of these devices illustrated in  FIG. 3 . It may require, for example, a 10 volt potential difference to cause a movable layer to deform from the relaxed state to the actuated state. However, when the voltage is reduced from that value, the movable layer maintains its state as the voltage drops back below 10 volts. In the exemplary embodiment of  FIG. 3 , the movable layer does not relax completely until the voltage drops below 2 volts. Thus, there exists a window of applied voltage, about 3 to 7 V in the example illustrated in  FIG. 3 , within which the device is stable in either the relaxed or actuated state. This is referred to herein as the “hysteresis window” or “stability window.” For a display array having the hysteresis characteristics of  FIG. 3 , the row/column actuation protocol can be designed such that during row strobing, pixels in the strobed row that are to be actuated are exposed to a voltage difference of about 10 volts, and pixels that are to be relaxed are exposed to a voltage difference of close to zero volts. After the strobe, the pixels are exposed to a steady state voltage difference of about 5 volts such that they remain in whatever state the row strobe put them in. After being written, each pixel sees a potential difference within the “stability window” of 3-7 volts in this example. This feature makes the pixel design illustrated in  FIG. 1  stable under the same applied voltage conditions in either an actuated or relaxed pre-existing state. Since each pixel of the interferometric modulator, whether in the actuated or relaxed state, is essentially a capacitor formed by the fixed and moving reflective layers, this stable state can be held at a voltage within the hysteresis window with almost no power dissipation. Essentially no current flows into the pixel if the applied potential is fixed. 
     In typical applications, a display frame may be created by asserting the set of column electrodes in accordance with the desired set of actuated pixels in the first row. A row pulse is then applied to the row  1  electrode, actuating the pixels corresponding to the asserted column lines. The asserted set of column electrodes is then changed to correspond to the desired set of actuated pixels in the second row. A pulse is then applied to the row  2  electrode, actuating the appropriate pixels in row  2  in accordance with the asserted column electrodes. The row  1  pixels are unaffected by the row  2  pulse, and remain in the state they were set to during the row  1  pulse. This may be repeated for the entire series of rows in a sequential fashion to produce the frame. Generally, the frames are refreshed and/or updated with new display data by continually repeating this process at some desired number of frames per second. A wide variety of protocols for driving row and column electrodes of pixel arrays to produce display frames are also well known and may be used in conjunction with the present invention. 
       FIGS. 4 ,  5 A, and  5 B illustrate one possible actuation protocol for creating a display frame on the 3×3 array of  FIG. 2 .  FIG. 4  illustrates a possible set of column and row voltage levels that may be used for pixels exhibiting the hysteresis curves of  FIG. 3 . In the  FIG. 4  embodiment, actuating a pixel involves setting the appropriate column to −V bias , and the appropriate row to +ΔV, which may correspond to −5 volts and +5 volts, respectively Relaxing the pixel is accomplished by setting the appropriate column to +V bias , and the appropriate row to the same +ΔV, producing a zero volt potential difference across the pixel. In those rows where the row voltage is held at zero volts, the pixels are stable in whatever state they were originally in, regardless of whether the column is at +V bias , or −V bias . As is also illustrated in  FIG. 4 , it will be appreciated that voltages of opposite polarity than those described above can be used, e.g., actuating a pixel can involve setting the appropriate column to +V bias , and the appropriate row to +ΔV. In this embodiment, releasing the pixel is accomplished by setting the appropriate column to −V bias , and the appropriate row to the same −ΔV, producing a zero volt potential difference across the pixel. 
       FIG. 5B  is a timing diagram showing a series of row and column signals applied to the 3×3 array of  FIG. 2  which will result in the display arrangement illustrated in  FIG. 5A , where actuated pixels are non-reflective. Prior to writing the frame illustrated in  FIG. 5A , the pixels can be in any state, and in this example, all the rows are at 0 volts, and all the columns are at +5 volts. With these applied voltages, all pixels are stable in their existing actuated or relaxed states. 
     In the  FIG. 5A  frame, pixels ( 1 , 1 ), ( 1 , 2 ), ( 2 , 2 ), ( 3 , 2 ) and ( 3 , 3 ) are actuated. To accomplish this, during a “line time” for row  1 , columns  1  and  2  are set to −5 volts, and column  3  is set to +5 volts. This does not change the state of any pixels, because all the pixels remain in the 3-7 volt stability window. Row  1  is then strobed with a pulse that goes from 0, up to 5 volts, and back to zero. This actuates the ( 1 , 1 ) and ( 1 , 2 ) pixels and relaxes the ( 1 , 3 ) pixel. No other pixels in the array are affected. To set row  2  as desired, column  2  is set to −5 volts, and columns  1  and  3  are set to +5 volts. The same strobe applied to row  2  will then actuate pixel ( 2 , 2 ) and relax pixels ( 2 , 1 ) and ( 2 , 3 ). Again, no other pixels of the array are affected. Row  3  is similarly set by setting columns  2  and  3  to −5 volts, and column  1  to +5 volts. The row  3  strobe sets the row  3  pixels as shown in  FIG. 5A . After writing the frame, the row potentials are zero, and the column potentials can remain at either +5 or −5 volts, and the display is then stable in the arrangement of  FIG. 5A . It will be appreciated that the same procedure can be employed for arrays of dozens or hundreds of rows and columns. It will also be appreciated that the timing, sequence, and levels of voltages used to perform row and column actuation can be varied widely within the general principles outlined above, and the above example is exemplary only, and any actuation voltage method can be used with the systems and methods described herein. 
       FIGS. 6A and 6B  are system block diagrams illustrating an embodiment of a display device  40 . The display device  40  can be, for example, a cellular or mobile telephone. However, the same components of display device  40  or slight variations thereof are also illustrative of various types of display devices such as televisions and portable media players. 
     The display device  40  includes a housing  41 , a display  30 , an antenna  43 , a speaker  44 , an input device  48 , and a microphone  46 . The housing  41  is generally formed from any of a variety of manufacturing processes as are well known to those of skill in the art, 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. In one embodiment, the housing  41  includes 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  of exemplary display device  40  may be any of a variety of displays, including a bi-stable display, as described herein. In other embodiments, the display  30  includes a flat-panel display, such as plasma, EL, OLED, STN LCD, or TFT LCD as described above, or a non-flat-panel display, such as a CRT or other tube device, as is well known to those of skill in the art. However, for purposes of describing the present embodiment, the display  30  includes an interferometric modulator display, as described herein. 
     The components of one embodiment of exemplary display device  40  are schematically illustrated in  FIG. 6B . The illustrated exemplary display device  40  includes a housing  41  and can include additional components at least partially enclosed therein. For example, in one embodiment, the exemplary display device  40  includes a network interface  27  that includes an antenna  43 , which is coupled to a transceiver  47 . 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 (e.g., filter a signal). The conditioning hardware  52  is connected to a speaker  45  and a microphone  46 . The processor  21  is also connected to an input device  48  and a driver controller  29 . The driver controller  29  is coupled to a frame buffer  28  and to an array driver  22 , which in turn is coupled to a display array  30 . A power supply  50  provides power to all components as required by the particular exemplary display device  40  design. 
     The network interface  27  includes the antenna  43  and the transceiver  47  so that the exemplary display device  40  can communicate with one or more devices over a network. In one embodiment, the network interface  27  may also have some processing capabilities to relieve requirements of the processor  21 . The antenna  43  is any antenna known to those of skill in the art for transmitting and receiving signals. In one embodiment, the antenna transmits and receives RF signals according to the IEEE 802.11 standard, including IEEE 802.11(a), (b), or (g). In another embodiment, the antenna transmits and receives RF signals according to the BLUETOOTH standard. In the case of a cellular telephone, the antenna is designed to receive CDMA, GSM, AMPS, or other known signals that are used to communicate within a wireless cell phone network. The transceiver  47  pre-processes 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 processes signals received from the processor  21  so that they may be transmitted from the exemplary display device  40  via the antenna  43 . 
     In an alternative embodiment, the transceiver  47  can be replaced by a receiver. In yet another alternative embodiment, network interface  27  can be replaced by an image source, which can store or generate image data to be sent to the processor  21 . For example, the image source can be a digital video disc (DVD) or a hard-disk drive that contains image data, or a software module that generates image data. 
     Processor  21  generally controls the overall operation of the exemplary 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 is readily processed into raw image data. The processor  21  then sends the processed data to the driver controller  29  or to 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. 
     In one embodiment, the processor  21  includes a microcontroller, CPU, or logic unit to control operation of the exemplary display device  40 . Conditioning hardware  52  generally includes amplifiers and filters for transmitting signals to the speaker  45 , and for receiving signals from the microphone  46 . Conditioning hardware  52  may be discrete components within the exemplary display device  40 , or may be incorporated within the processor  21  or other components. 
     The driver controller  29  takes the raw image data generated by the processor  21  either directly from the processor  21  or from the frame buffer  28  and reformats the raw image data appropriately for high speed transmission to the array driver  22 . Specifically, the driver controller  29  reformats 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 , such as a LCD controller, is often associated with the system processor  21  as a stand-alone Integrated Circuit (IC), such controllers may be implemented in many ways. They 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 . 
     Typically, the array driver  22  receives the formatted information from the driver controller  29  and reformats the video data into a parallel set of waveforms that are applied many times per second to the hundreds and sometimes thousands of leads coming from the display&#39;s x-y matrix of pixels. 
     In one embodiment, the driver controller  29 , array driver  22 , and display array  30  are appropriate for any of the types of displays described herein. For example, in one embodiment, driver controller  29  is a conventional display controller or a bi-stable display controller (e.g., an interferometric modulator controller). In another embodiment, array driver  22  is a conventional driver or a bi-stable display driver (e.g., an interferometric modulator display). In one embodiment, a driver controller  29  is integrated with the array driver  22 . Such an embodiment is common in highly integrated systems such as cellular phones, watches, and other small area displays. In yet another embodiment, display array  30  is a typical display array or a bi-stable display array (e.g., a display including an array of interferometric modulators). 
     The input device  48  allows a user to control the operation of the exemplary display device  40 . In one embodiment, input device  48  includes a keypad, such as a QWERTY keyboard or a telephone keypad, a button, a switch, a touch-sensitive screen, or a pressure- or heat-sensitive membrane. In one embodiment, the microphone  46  is an input device for the exemplary display device  40 . When the microphone  46  is used to input data to the device, voice commands may be provided by a user for controlling operations of the exemplary display device  40 . 
     Power supply  50  can include a variety of energy storage devices as are well known in the art. For example, in one embodiment, power supply  50  is a rechargeable battery, such as a nickel-cadmium battery or a lithium ion battery. In another embodiment, power supply  50  is a renewable energy source, a capacitor, or a solar cell, including a plastic solar cell and solar-cell paint. In another embodiment, power supply  50  is configured to receive power from a wall outlet. 
     In some embodiments, control programmability resides, as described above, in a driver controller which can be located in several places in the electronic display system. In some embodiments, control programmability resides in the array driver  22 . Those of skill in the art will recognize that the above-described optimizations may be implemented in any number of hardware and/or software components and in various configurations. 
     The details of the structure of interferometric modulators that operate in accordance with the principles set forth above may vary widely. For example,  FIGS. 7A-7E  illustrate five different embodiments of the movable reflective layer  14  and its supporting structures.  FIG. 7A  is a cross section of the embodiment of  FIG. 1 , where a strip of metal material  14  is deposited on orthogonally extending supports  18 . In  FIG. 7B , the moveable reflective layer  14  is attached to supports at the corners only, on tethers  32 . In  FIG. 7C , the moveable reflective layer  14  is suspended from a deformable layer  34 , which may comprise a flexible metal. The deformable layer  34  connects, directly or indirectly, to the substrate  20  around the perimeter of the deformable layer  34 . These connections are herein referred to as support posts. The embodiment illustrated in  FIG. 7D  has support post plugs  42  upon which the deformable layer  34  rests. The movable reflective layer  14  remains suspended over the cavity, as in  FIGS. 7A-7C , but the deformable layer  34  does not form the support posts by filling holes between the deformable layer  34  and the optical stack  16 . Rather, the support posts are formed of a planarization material, which is used to form support post plugs  42 . The embodiment illustrated in  FIG. 7E  is based on the embodiment shown in  FIG. 7D , but may also be adapted to work with any of the embodiments illustrated in  FIGS. 7A-7C , as well as additional embodiments not shown. In the embodiment shown in  FIG. 7E , an extra layer of metal or other conductive material has been used to form a bus structure  44 . This allows signal routing along the back of the interferometric modulators, eliminating a number of electrodes that may otherwise have had to be formed on the substrate  20 . 
     In embodiments such as those shown in  FIG. 7 , the interferometric modulators function as direct-view devices, in which images are viewed from the front side of the transparent substrate  20 , the side opposite to that upon which the modulator is arranged. In these embodiments, the reflective layer  14  optically shields the portions of the interferometric modulator on the side of the reflective layer opposite the substrate  20 , including the deformable layer  34 . This allows the shielded areas to be configured and operated upon without negatively affecting the image quality. Such shielding allows the bus structure  44  in  FIG. 7E , which provides the ability to separate the optical properties of the modulator from the electromechanical properties of the modulator, such as addressing and the movements that result from that addressing. This separable modulator architecture allows the structural design and materials used for the electromechanical aspects and the optical aspects of the modulator to be selected and to function independently of each other. Moreover, the embodiments shown in  FIGS. 7C-7E  have additional benefits deriving from the decoupling of the optical properties of the reflective layer  14  from its mechanical properties, which are carried out by the deformable layer  34 . This allows the structural design and materials used for the reflective layer  14  to be optimized with respect to the optical properties, and the structural design and materials used for the deformable layer  34  to be optimized with respect to desired mechanical properties. 
       FIG. 8  illustrates one embodiment of a monochrome display including one interferometric modulator per pixel, the “on” or “off” state of the modulator being set based on the value of the one bit of data per pixel. The pixel is configured to communicate with one column conduit and one row conduit. A grayscale image may include several bits of data per pixel. For example, a “3-bit” grayscale display includes three bits of data per pixel that correspond to one of eight (2 3 ) shades of gray that may be assigned to each pixel. The pixel is configured to communicate with one column conduit and three row conduits.  FIG. 9  illustrates an exemplary embodiment of a display for displaying a 3-bit grayscale image including three interferometric modulators  91 ,  92 ,  93  for each pixel  90 . To obtain the eight shades, the three modulators  91 ,  92 ,  93  reflect light according to a varying size ratio. In one such embodiment, each of the interferometric modulators  91 ,  92 ,  93  includes mirrors having a reflective surface area that varies according to the ratio of 4:2:1. The reflective portion of one mirror or modulator may be referred to as “subtending” a portion of the pixel. For example, the mirror with a surface area of one in the 4:2:1 embodiment subtends about 1/7 of the pixel. A particular shade in a pixel is obtained by setting each modulator to an “on” or “off” state based on the binary value of a corresponding bit of the three bits of data. 
       FIG. 10  illustrates one embodiment of a color display having pixel  100  that works similarly to the grayscale pixel  90  of  FIG. 9 , except that the pixel  100  includes a group of red interferometric modulators  101 ,  102 ,  103 , green interferometric modulators  104 ,  105 ,  106 , and blue interferometric modulators  107 ,  108 ,  109 . For example, the pixel  100  is responsive to a 9-bit signal in which three groups of 3 bits each correspond to the three colors. As another example, in a 12-bit color display, four of the twelve bits correspond to each of sixteen intensities of red, green, and blue that are produced by red, green, or blue interferometric modulators. 
     Such grayscale or color displays have more display elements to address than does a monochrome display. In order to address these display elements for such embodiments of gray or color displays, the number of conduits (or “driver connections” or “addressing lines” or “leads”) to the display control typically increases. For example,  FIG. 11  illustrates one embodiment of a 3-bit grayscale display in which the pixels are in a 3×3 configuration with each of the three rows subdivided into three subrows of modulators. Such an embodiment has nine row driver connections and three column driver connections for a total of twelve driver connections rather than the six driver connections used for a 3×3 monochrome display. One way of reducing the number of driver connections is to configure a group of modulators to communicate with a single row conduit, for example (as depicted in  FIG. 12 ), the three subrows in the 3-bit grayscale embodiment discussed above, and drive the group with a signal that changes the state of a selected subset of the group. 
     In certain embodiments, the interferometric modulators of each of the subrows may have varying actuation and release voltages so as to enable a group of subrows that are configured to communicate with a single row conduit to be individually addressed.  FIG. 13  is a diagram of movable mirror position versus applied positive and negative voltage illustrating one exemplary embodiment of three interferometric modulators that have nested stability windows. As used herein, the term “nested” is to mean with exploitable differences in both actuation voltages and release voltages. The innermost nested hysteresis window, indicated by the traces  802 , has actuation and release voltages having magnitudes of 8 volts and 4 volts, respectively. This hysteresis window is nested in the hysteresis window indicated by traces  804  and is nested in the hysteresis window indicated by traces  806 . The next nested hysteresis window, indicated by the traces  804 , has actuation and release voltages having magnitudes of 10 volts and 2 volts, respectively. This hysteresis window is nested in the hysteresis window indicated by traces  806 . The outermost hysteresis window, indicated by the traces  806 , has actuation and release voltages having magnitudes of 12 volts and 0 volts, respectively. 
     The hysteresis window of the modulators associated with each subrow may be selected by varying the geometry and/or materials of the modulators. In particular, the width (difference between the actuation and release voltages), the location (the absolute values of the actuation and release voltages), and the relative values of the actuation and release voltages may be selected by varying geometric and material properties of the modulators. The varied properties may include, for example, the distance between movable mirror supports, the mass associated with the movable mirror relative to the spring constant, the thickness, tensile stress, or stiffness of the mirror and/or the layers or mechanism that moves the mirror, and the dielectric constant and/or thickness of a dielectric layer between the stationary electrode and the movable electrode. More details of the selection of the hysteresis properties of the interferometric modulators are disclosed in U.S. patent application Ser. No. 11/193,012, entitled “Method and Device for Selective Adjustment of Hysteresis Window,” filed on Sep. 27, 2004, incorporated herein by reference in its entirety. 
     In one embodiment in which the modulators of each of the subrows have hysteresis stability windows that are nested within each other, the interferometric modulators are arranged as in  FIG. 12 . In the illustrated embodiment, the stability windows are nested from outer to inner, such as the windows depicted in  FIG. 13 , from the top subrow to the bottom subrow.  FIG. 14  is an exemplary timing diagram that illustrates a series of row and column signals applied to the top row (Row  1 ) of such an embodiment to produce the display arrangement illustrated in Row  1  of  FIG. 12 . In general, the positive voltage regime and the negative voltage regime are substantially equivalent to one another, as shown in  FIG. 13 . Although described and illustrated herein in terms of the positive voltage regime, in certain embodiments, the interferometric modulators can be similarly operated in the negative voltage regime. The row pulses decrease in magnitude from left to right, corresponding to the subrows from top to bottom. This decreasing magnitude of the pulses is selected to address only those modulators in subrows that have smaller actuation and greater release voltages. For example, in the illustrated embodiment, potentials of +6 and −6 volts are applied to the columns and row pulses of +6, +4, and +2 volts are applied to the rows. 
     The pulses of  FIG. 14  set the state of Row  1  of the display to that depicted in  FIG. 12  as follows. For the first line time for Row  1 , Column  1 , a Column  1  potential of −6 volts is applied along with a row pulse of +6 volts, producing a 12-volt difference across the modulators of Row  1 , Column  1 , to set the state of the modulators of each of the Row  1 , Column  1  subrows in the actuated position as illustrated along the bottom of  FIG. 14 . The Column  1  potential remains at −6 for the remaining Row  1  line times to continue to set the state of each of the elements in the Row  1 , Column  1  subrows to the actuated position. In Column  2 , a Column  2  potential of +6 volts is applied in conjunction with the row pulse at +6 volts in the first line time, producing a zero-volt difference across the modulators of Row  1 , Column  2 , to release all modulators in the subrows in Row  1 , Column  2 . During the second line time for Row  1 , a Column  2  potential of −6 volts is applied in conjunction with a row pulse of +4 volts, producing a 10-volt difference across the modulators of Row  1 , Column  2 , to actuate the bottom two subrows of Row  1 , Column  2 . During the third row time for Row  1 , a Column  2  potential is applied at +6 volts in conjunction with a row pulse of +2 volts, producing a 4-volt difference across the modulators of Row  1 , Column  2 , to release the modulator in the bottom subrow of Row  1 , Column  2 . In Column  3 , a Column  3  potential of −6 volts is applied in conjunction with the row pulse at +6 volts in the first line time, producing a 12-volt difference across the modulators of Row  1 , Column  3 , to actuate all modulators in the subrows in Row  1 , Column  3 . During the second line time for Row  1 , a Column  3  potential of +6 volts is applied in conjunction with a row pulse of +4 volts, producing a 2-volt difference across the modulators of Row  1 , Column  3 , to release the bottom two subrows of Row  1 , Column  3 . During the third row time for Row  1 , a Column  3  potential is applied at −6 volts in conjunction with the row pulse of +2 volts, producing an 8-volt difference across the modulators of Row  1 , Column  3 , to actuate the modulator in the bottom subrow of Row  1 , Column  3 . 
       FIG. 15  is a flowchart illustrating one embodiment of a method  850  of updating an embodiment of a display such as depicted in  FIG. 12 . The method  850  begins at a block  852  in which the driver  22  of  FIG. 2  receives image data value for a subrow. In one embodiment, the driver  22  receives the data value from a frame buffer. Next, at a block  854 , the driver  22  applies a row strobe to all subrows of interferometric modulators along with a column potential that corresponds to the image data value. Moving to block  856 , the driver  22  receives the data for the next subrow. Next, at block  860 , the acts of blocks  854  and  856  are repeated for each of the subrows. In one embodiment, the acts of the blocks  854  and  856  occur at least partially concurrently. 
     At least one aspect of the present invention is the realization that quantization artifacts are more visible to the user in low-intensity regions than in high-intensity regions because the percentage change between quantization levels is greater at lower intensities. For example, in a 7-bit (2 7 =128 quantization levels) system, the intensity change from level 100 to level 101 is 1%. Most users cannot discern intensity changes below about 4%, so transitions at or below this quantization level appear smooth. However, the change from level 10 to level 11 is 10%, an intensity change that is easily seen by most users. Therefore, at low intensity quantization levels, the quantization of analog data into discrete digitized quantization steps is clearly seen as an artifact. The most straightforward approach to this problem is to digitize at higher bit densities. For example, instead of being digitized to 7 bits across the intensity range, the given signal is digitized to 10 bits (2 10 =1,024 quantization levels) across the intensity range so that the analog quantization levels that would have fallen around level 10 in the 128-level configuration fall around level 80 in the 1,024 level configuration. The transition from level 80 to level 81 is about 1.2%, and would then be indiscernible to the user. However, such increases in system bit density can lead to greater system complexity and cost (e.g., the number of driver connections would increase by about 38% from 24 in a 3×3 7-bit grayscale display to 33 in a 3×3 10-bit grayscale display). 
     In interferometric modulator-based systems, these complexity issues tend to impact the cost and complexity of driver integrated circuits and the cost and complexity of the systems themselves. Several drive scheme methods for complex interferometric modulator displays have been disclosed that reduced driver complexity and cost at the expense of imposing even further operational limitations and tighter manufacturing tolerances on the interferometric modulator systems. Many of these drive schemes also involve adding additional addressing cycles to the interferometric modulator. These additional cycles tend to reduce the maximum frame height and rate capability of the interferometric modulator or require further technology development of the interferometric modulator in order to maintain the frame rate of previous levels. Many of these solutions and improvements are overkill in the sense that they decrease the quantization step size throughout the entire range of the digitized signal, even though there is no need to decrease the step size at the high-intensity end of the signal range (e.g., at least above the quantization steps from about 30 to 31, which is only 3.3%). 
       FIG. 16  is a schematic diagram of an embodiment of a color interferometric modulator pixel  160 . In the embodiment illustrated in  FIG. 16 , the interferometric modulator  101  of  FIG. 10  has been partitioned or replaced by two interferometric modulators  161 ,  162  (or “display elements”) arranged in two subrows that are configured to communicate with a common row conduit. In  FIG. 10 , the modulator  101  subtends about 4/7 of the area of the first column. When partitioned as in  FIG. 16 , the modulator  161  subtends about half ( 7/14) of the first column and the modulator  162  subtends about 1/14 of the first column. The first display element  161  has a first optically active area and the second display element  162  has a second optically active area. In certain embodiments, the ratio of the first optically active area to the second optically active area is approximately equal to an integer to one (e.g., 7 to 1, 7:1, 7/1). In some embodiments, the integer is 2, 3, 4, 5, 6, 7, 8, 9, or 10. In some embodiments, the integer is 3, 7, 15, 31, 63, 127, 255, or any number 2 n −1 where n is an integer greater than or equal to 2. 
     When both of the modulators  161 ,  162  are driven together, the function of the pixel  160  is unchanged from the pixel  100  schematically depicted in  FIG. 10 . Although  FIG. 16  represents an embodiment partitioning the modulators  101 ,  104 , and  107  in  FIG. 10 , such partitioning may also be appropriate for grayscale displays (e.g., by partitioning the modulator  91  depicted in  FIG. 9 ). 
     As used herein, the terms “divided,” “partitioned,” and “replaced” in relation to the plurality of interferometric modulators or mirrors of various embodiments does not require that a larger interferometric modulator or mirror actually be created and then partitioned into smaller interferometric modulators or mirrors. Instead, the terms are used to compare the relative structures from previously described configurations. For example, the modulators  161  and  162  in  FIG. 16  are typically formed independently from one another, as opposed to having been formed as a single modulator  101  as depicted in  FIG. 10  and then partitioned into smaller modulators. Moreover, independent creation is preferable in some embodiments to allow for individual adjustment of the hysteresis curves for the modulators  161 ,  162  as described above. 
       FIG. 17  is a diagram of modulator position versus applied positive voltage illustrating one exemplary embodiment of two interferometric modulators (e.g., the two modulators  161 ,  162  illustrated in  FIG. 16 ) that have hysteresis curve stability windows in which the actuation voltages are different, but the release voltages are about the same. The traces  810  represent the hysteresis loop of the modulator  161  and the traces  808  represent the hysteresis loop of the modulator  162 . In certain embodiments, the release voltages of the two modulators  161 ,  162  are considered to be substantially equal to one another when any differences between the respective release voltages are not used to selectively release one of the modulators and not the other. The hysteresis loop depicted by the traces  808  has an actuation voltage of about 9 volts and a release voltage of about 1 volt. The hysteresis loop represented by the traces  810  has an actuation voltage of about 15 volts and has a release voltage of about 1 volt. Because the release voltages of the hysteresis loops of  FIG. 17  are not exploitably different from each other (i.e., there are no voltages that can be applied to reliably release one modulator and not the other modulator), the hysteresis loops of  FIG. 17  cannot be said to be “nested” as defined herein. 
       FIG. 18  is a diagram of modulator position versus applied positive voltage illustrating another exemplary embodiment of two interferometric modulators (e.g., the two modulators  161 ,  162  illustrated in  FIG. 16 ) that have different stability windows in which the release voltages are different, but the actuation voltages are about the same. The traces  814  represent the hysteresis loop of the modulator  161  and the traces  812  represent the hysteresis loop of the modulator  162 . In certain embodiments, the actuation voltages of the two modulators  161 ,  162  are considered to be substantially equal to one another when any differences between the respective actuation voltages are not used to selectively actuate one of the modulators and not the other modulator. The hysteresis loop depicted by the traces  812  has an actuation voltage of about 15 volts and a release voltage of about 6 volts. The hysteresis loop represented by the traces  814  has an actuation voltage of about 15 volts, but has a release voltage of about 1 volt. Because the actuation voltages of the hysteresis loops of  FIG. 18  are not exploitably different from each other (i.e., there are no voltages that can be applied to reliably actuate one modulator and not the other modulator), these hysteresis loops cannot be said to be “nested” as defined herein. 
     Unlike the embodiment described above in which nested hysteresis windows are intended to be used to both selectively actuate and selectively release the modulators at different voltages, the exemplary embodiments depicted in  FIGS. 16-18  provide additional manufacturing advantages. The actuation voltages and release voltages of each of the nested hysteresis loops of  FIG. 13  are proximate to each other. For example, the release voltage for the loop  804  is about 2 volts and the release voltage for the loop  802  is about 4 volts. Thus, in order to selectively release the modulator represented by loop  802 , but to selectively not release the modulator represented by loop  804 , the voltage applied would be between 2 and 4 volts, preferably around 3 volts. This voltage accuracy can present problems if the manufacturing tolerances of the modulators that release at 2 volts and 4 volts are not sufficiently precise. For example, if the modulator represented by loop  802  was manufactured such that its release voltage was 3.5 volts and the modulator represented by loop  804  was manufactured such that its release voltage was 2.5 volts, the tolerance window for the applied voltage would shrink considerably. The applied voltage may also vary with manufacturing tolerances such that an application of 3 volts to the modulator may actually result in a voltage difference across the modulator closer to 2.5 volts. Thus, a voltage applied to the modulators to release the modulator represented by loop  802  may inadvertently also release the modulator represented by loop  804 . The manufacturing tolerances for each of the three subrows represented in  FIG. 13  would need to be highly accurate as there are six precise actuation and release voltages that would need to be achieved in order to accurately differentially actuate and release each of the three modulators. By contrast, the two modulators represented by the hysteresis loops in  FIG. 17  or  FIG. 18  require only three voltages, represented by lines A, B, and C, to differentially actuate and release the two modulators. Additionally, because the size differential between the modulator  161  and the modulator  162  is large, the voltages for actuation and/or release can advantageously be less precise than the voltages for the configuration depicted in  FIG. 13 . 
       FIG. 19  schematically illustrates the quantization levels provided by the schematic of  FIG. 10 . None of the modulators are in the “on” state in level 0 and all of the modulators are in the “on” state in level 7. Some of the modulators are in the “on” state in levels 1 through 6, providing varying amounts of intensity. The bit density at low intensity ranges is the same as the bit density at high intensity ranges. For example, as shown in  FIG. 20  for the pixel  100  of  FIG. 10 , the intensity difference between sequential quantization steps for intensities below level 4 (e.g., intensity difference of one) is the same as the intensity difference between sequential quantization steps for intensities above level 4 (e.g., intensity difference of one). 
     The two modulators  161 ,  162  of  FIG. 16  having the hysteresis curves  810 ,  808  of  FIG. 17  are used in certain embodiments to provide a higher bit density at lower intensity ranges than at higher intensity ranges. For example, in the sequence of levels 0 through 7 that can be provided by each column (e.g., as depicted in  FIG. 20 ), the modulator  161  is actuated or placed in an “on” state only for levels 4 and above. Thus, for all quantization steps below level 4, the actuation drive voltage on the modulators  161 ,  162  can be reduced so that only the modulator  162  is selectively actuated. Since this modulator  162  has a mirror with preferably about one-half the optical weight of the mirror of the modulator  164 , the modulators  162 ,  164 , and  163  have weights in the ratio 1:2:4, respectively, and can be used to generate eight quantization steps below quantization level 4, as illustrated in  FIG. 21 . The quantization steps below level 4 are illustrated in  FIG. 22 . Similarly, the two modulators  161 ,  162  of  FIG. 16  having the hysteresis curves  814 ,  812  of  FIG. 18  are used in certain other embodiments to provide a higher bit density at lower intensity ranges than at higher intensity ranges. 
     Referring again to  FIG. 16 , when the mirrors  164 ,  163 ,  162 ,  161  subtend the pixel in a ratio of 2:4:1:7, respectively, the number of sequential quantization steps are more than doubled in the lower portion of the display intensity range, which is the portion of the quantization range most in need of finer quantization. For example, comparing  FIGS. 20 and 22 , the number of sequential quantization steps for intensities below level 4 (i.e., eight) in  FIG. 22  is more than double the number of sequential quantization steps for intensities above level 4 (i.e., three) in either  FIG. 20  or  FIG. 22 . That is, rather than actuating and releasing three modulators to achieve seven quantization steps, four of which are below the fourth quantization level, as depicted in  FIGS. 19 and 20 , four modulators are actuated and released to provide eleven quantization steps, eight of which are below the fourth quantization level, as depicted in  FIGS. 21 and 22 . As used herein, the term “quantization step” refers to the change from one amount of intensity to the next amount of intensity and the term “quantization level” refers to the change from one bit depth to the next bit depth. For example, the change in intensity from one modulator to the next in the top row of  FIG. 21  is a quantization step, but not a quantization level, while the change in intensity from one modulator to the next modulator in the bottom row of  FIG. 21  is both a quantization step and a quantization level. It will be appreciated that the effect is much more pronounced at bit depths greater than 3-bit. 
       FIG. 23  is a schematic diagram of an embodiment of a color interferometric modulator pixel  230 . Although  FIG. 23  represents an embodiment partitioning the modulators  102 ,  105 , and  108  in  FIG. 10 , such partitioning may also be appropriate for grayscale displays (e.g., by partitioning the modulator  92  depicted in  FIG. 9 ). In the embodiment illustrated in  FIG. 23 , the modulator  104  has been divided into two modulators  232 ,  233  (or “display elements”) arranged in subrows that are configured to communicate with a common row conduit. In  FIG. 10 , the modulator  102  subtends about 2/7 of the area of the first column. When partitioned as in  FIG. 23 , the modulator  232  subtends about 3/14 of the first column and the modulator  233  subtends about 1/14 of the first column. When both of the modulators  232 ,  233  are driven together, the function of the pixel  200  is unchanged from the pixel  100  schematically depicted in  FIG. 10 . The hysteresis loops for the modulators  232 ,  233  may share a common actuation voltage or a common release voltage as displayed in  FIGS. 17 and 18 . 
     When the modulators  234 ,  233 ,  232 ,  231  subtend the pixel in a ratio of 2:1:3:8, respectively, the number of sequential quantization steps (i.e., two) are doubled below level 2 of the display quantization range, which is part of the portion of the quantization range most in need of finer quantization. Rather than actuating and releasing four modulators to provide eleven quantization steps, eight of which are below the fourth quantization level, as depicted in  FIGS. 21 and 22 , four modulators are actuated and released to provide eleven quantization steps, six of which are below the fourth quantization level, as depicted in  FIGS. 24 and 25 . Because the schematic illustrated in  FIG. 16  provides finer quantization steps between level 2 and level 4, partitioning the mirror  101  of  FIG. 10  is preferred to partitioning the mirror  104  of  FIG. 10 . 
     Even finer quantization may be created by partitioning both the mirror  101  and the mirror  104  depicted in  FIG. 10 , as illustrated by the schematic diagram in  FIG. 26 . As shown by  FIGS. 27 and 28 , such a schematic results in 17 quantization steps,  12  of which are below the fourth quantization level. For another example of the difference between a “quantization step” and a “quantization level, the change in intensity from the second modulator from the left in the top row of  FIG. 27  to the third modulator from the left in the top row of  FIG. 27  is a quantization step, while the change in intensity from the first modulator from the left in the top row of  FIG. 27  to the fifth modulator from the left in the top row of  FIG. 27  is a quantization level. 
     Still finer quantization may be achieved by partitioning all three mirrors  101 ,  104 , and  107  in  FIG. 10 , as illustrated by the schematic diagram in  FIG. 29 . As shown by  FIG. 30 , such a configuration results in 26 quantization steps,  18  of which are below the fourth quantization level. Thus, while maintaining only six total leads to a color pixel, the number of quantization steps advantageously increases from 7 to 26, most of which are in the region of low intensity most in need of finer quantization. This configuration dramatically reduces quantization level spacing at low intensities, the display range where it is most needed, without increasing the number of address lines from the driver IC. 
     Various specific embodiments have been described above. Although the invention has been described with reference to these specific embodiments, the descriptions are intended to be illustrative of the invention and are not intended to be limiting. Various modifications and applications may occur to those skilled in the art without departing from the true scope of the invention as defined in the appended claims.