Patent Publication Number: US-2012027430-A1

Title: Measuring developer density in an electrophotographic system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Reference is made to commonly assigned, co-pending U.S. patent application Ser. No. ______/______,______ (Kodak docket 96469, filed concurrently herewith, entitled Resonant-Frequency Measurement of Electrophotographic Developer Density, by Brown, et al, U.S. patent application Ser. No. ______/______,______ (Kodak docket 96432), filed concurrently herewith, entitled Electrophotographic Developer Toner Concentration Measurement, by Brown, et al, and U.S. patent application Ser. No. ______/______,______ (Kodak docket 96433), filed concurrently herewith, entitled Electrophotographic Developer Flow Rate Measurement, by Brown, et al, the disclosures of which are incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     This invention pertains to the field of electrophotographic printing and more particularly to sensing characteristics of developer during printer operation. 
     BACKGROUND OF THE INVENTION 
     Electrophotography is a useful process for printing images on a receiver (or “imaging substrate”), such as a piece or sheet of paper or another planar medium, glass, fabric, metal, or other objects as will be described below. In this process, an electrostatic latent image is formed on a photoreceptor by uniformly charging the photoreceptor and then discharging selected areas of the uniform charge to yield an electrostatic charge pattern corresponding to the desired image (a “latent image”). 
     After the latent image is formed, charged toner particles are brought into the vicinity of the photoreceptor and are attracted to the latent image to develop the latent image into a visible image. Note that the visible image may not be visible to the naked eye depending on the composition of the toner particles (e.g. clear toner). 
     After the latent image is developed into a visible image on the photoreceptor, a suitable receiver is brought into juxtaposition with the visible image. A suitable electric field is applied to transfer the toner particles of the visible image to the receiver to form the desired print image on the receiver. The imaging process is typically repeated many times with reusable photoreceptors. 
     The receiver is then removed from its operative association with the photoreceptor and subjected to heat or pressure to permanently fix (“fuse”) the print image to the receiver. Plural print images, e.g. of separations of different colors, are overlaid on one receiver before fusing to form a multi-color print image on the receiver. 
     Electrophotographic (EP) printers typically transport the receiver past the photoreceptor to form the print image. The direction of travel of the receiver is referred to as the slow-scan, process, or in-track direction. This is typically the vertical (Y) direction of a portrait-oriented receiver. The direction perpendicular to the slow-scan direction is referred to as the fast-scan, cross-process, or cross-track direction, and is typically the horizontal (X) direction of a portrait-oriented receiver. “Scan” does not imply that any components are moving or scanning across the receiver; the terminology is conventional in the art. 
     Electrophotographic developer can include toner particles and magnetic carrier particles, and is transported past the photoreceptor by a development member. Developer is compressible, and the image quality of the print image is strongly correlated with developer density. However, existing methods for measuring developer density and other properties require off-line processing, so it cannot provide the data necessary to maintain image quality on-line and thereby improve throughput of a printer. 
     Commonly-assigned U.S. Publication No. 2002/0168200 (&#39;200) by Stelter et al., the disclosure of which is incorporated herein by reference, describes determining developer mass velocity by, among other things, measuring developer flow rate and developer mass area density (DMAD). Measuring flow rate requires collecting developer in a hopper from a bench-top toning station, and measuring DMAD requires abruptly stopping the toning station. Although these operations are useful, neither is suitable for an operating machine; both are invasive procedures that require the machine to be partially disassembled. 
     U.S. Pat. No. 6,498,908 to Phillips et al. describes a charge measurement device for measuring charge transfer between a high-voltage power supply and a developing device during an imaging operation. However, charge transfer can occur for various reasons, and it can be difficult to determine which reason affects a particular charge transfer. A single measurement is therefore not always enough information to fix a problem. 
     U.S. Pat. No. 4,519,696 to Bruyndonckx et al. describes inductive measurement of toner concentration in a developer mixer. However, toner concentration and developer flow rate both affect the percentage of carrier particles in the measurement volume of a sensor, and therefore the developer density measured by that sensor. 
     There is a continuing need, therefore, for a way of measuring developer density, separating out different effects from each other. 
     SUMMARY OF THE INVENTION 
     According to the present invention, there is provided an apparatus for measuring developer density in an electrophotographic system, comprising: 
     a) a first electrode and a second electrode disposed to define a working volume between them through which developer moves without contacting the first electrode, wherein the electrodes are electrically insulated from each other by the working volume; 
     b) a voltage source for selectively applying an AC bias across the electrodes; 
     c) a measuring device for measuring the current across the electrodes while the bias is applied; and 
     d) a processor adapted to automatically determine the density of the developer in the working volume based on the measured current and the applied bias. 
     An advantage of this invention is that it provides non-contact measurements. Measurements are taken quickly, in embodiments in real time. Various quantities can be measured in-situ, with no disassembly required. The measurements use inexpensive hardware, and work with any toner/carrier combination. Various embodiments provide individual measurements of specific quantities, deconfounded from other quantities. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features, and advantages of the present invention will become more apparent when taken in conjunction with the following description and drawings wherein identical reference numerals have been used, where possible, to designate identical features that are common to the figures, and wherein: 
         FIG. 1  is an elevational cross-section of an electrophotographic reproduction apparatus suitable for use with this invention; 
         FIG. 2  is an elevational cross-section of the reprographic image-producing portion of the apparatus of  FIG. 1 ; 
         FIG. 3  is an elevational cross-section of one printing module of the apparatus of  FIG. 1 ; 
         FIG. 4  shows an apparatus for measuring developer density in an electrophotographic system according to an embodiment of the present invention; 
         FIG. 5  shows details of the apparatus of  FIG. 4  according to an embodiment of the present invention; 
         FIG. 6A  shows experimental data relating developer flow rate to average peak-to-peak measured current; 
         FIG. 6B  shows a summary of experimental data relating developer flow rate to average peak-to-peak measured current under various conditions; 
         FIG. 6C  shows the conditions used in  FIG. 6B ; 
         FIG. 6D  shows experimental data relating developer flow rate to average peak-to-peak measured current; 
         FIG. 7  shows an apparatus for measuring developer density in an electrophotographic system according to another embodiment of the present invention; 
         FIG. 8  shows a method of measuring developer density in an electrophotographic system according to an embodiment of the present invention. 
         FIG. 9  shows an apparatus using a series-resonant tank circuit and a voltage source useful with the present invention; 
         FIG. 10  shows an apparatus using a parallel-resonant tank circuit and a current source useful with the present invention; 
         FIG. 11  shows an apparatus for measuring developer toner concentration useful with the present invention; 
         FIG. 12  shows a method of controlling toner concentration useful with the present invention; 
         FIG. 13  shows an apparatus for measuring developer flow rate useful with the present invention; and 
         FIG. 14  shows a method of controlling flow rate useful with the present invention. 
     
    
    
     The attached drawings are for purposes of illustration and are not necessarily to scale. 
     DETAILED DESCRIPTION OF THE INVENTION 
     In a two component development system, the ability to apply sufficient developer (toner+carrier, as discussed below) to develop the latent image on the photoconductor is important in creating images with high fidelity and image quality. In various embodiments, developer has a predetermined optimum ratio of toner to carrier (Toner Concentration) and a controlled ratio of the charge on a prescribed amount of toner to its mass (Charge/Mass, or qlm ratio μc/gm). “Developer flow” refers to the amount of developer delivered to the toning zone per unit time. Developer flow can be measured by lowering a gate into the developer stream (e.g., a gate 2″ wide) and collecting developer for a specified amount of time (e.g., 0.5 sec). The collected developer is then weighed and reported in units of gm/in/s. Developer flow is correlated to imaging properties of the developer, such as toning contrast, and background. Since the measurement of developer flow aggregates the effects of developer mass density (nap density ND, gm/in 3 ) and developer velocity (nap velocity NV, in/s), the flow measurement is also proportional to the product of independently-measured developer mass density and developer velocity. 
     As discussed above, this flow-measurement method, although useful, needs to be made with the developer station removed from the machine, requires a scale, and thus is not well suited for a real time application. However, it is desirable to measure flow in real time. Flat-field uniformity can be improved by increasing the product ND*NV of the developer mass density (ND) (gm/in 3 ) and the developer velocity (NV) (in/s). However, ND cannot be increased arbitrarily. There is a limit on maximum developer density since over-compression of the developer can lead to catastrophic release of the developer from the toning station, e.g., in fully-compressed sheets. This phenomenon is known as Developer Compression Limit Failure (DCL), or “plop-out.” Measuring ND and NV separately can reveal different aspects of the developer that can be varied (e.g., velocity) to improve developer ND*NV, and thus image quality, without the negative side effects of developer over-compression. 
     Developer Mass Area Density (DMAD) is another measure of developer density, and is generally measured in terms of gm/in̂2. DMAD is measured by collecting the developer in a unit area. Ratio q/m is the toner charge to mass ratio and is generally expressed μC/gm. TC is toner concentration and is given in terms of weight percent of toner to developer. In an embodiment, TC is approximately 6 wt. pct. 
     As discussed above, image quality is related to developer density. This is discussed further in commonly-assigned co-pending application U.S. Ser. No. 12/333,355, filed Dec. 12, 2008 (Publication No. 2010/0150592), by Kenneth  3 . Brown, the disclosure of which is incorporated herein by reference. 
     As used herein, the terms “parallel” and “perpendicular” have a tolerance of ±10°. 
     As used herein, “sheet” is a discrete piece of media, such as receiver media for an electrophotographic printer (described below). Sheets have a length and a width. Sheets are folded along fold axes, e.g. positioned in the center of the sheet in the length dimension, and extending the full width of the sheet. The folded sheet contains two “leaves,” each leaf being that portion of the sheet on one side of the fold axis. The two sides of each leaf are referred to as “pages.” “Face” refers to one side of the sheet, whether before or after folding. 
     In the following description, some embodiments of the present invention will be described in terms that would ordinarily be implemented as software programs. Those skilled in the art will readily recognize that the equivalent of such software can also be constructed in hardware. Because image manipulation algorithms and systems are well known, the present description will be directed in particular to algorithms and systems forming part of, or cooperating more directly with, the method in accordance with the present invention. Other aspects of such algorithms and systems, and hardware or software for producing and otherwise processing the image signals involved therewith, not specifically shown or described herein, are selected from such systems, algorithms, components, and elements known in the art. Given the system as described according to the invention in the following, software not specifically shown, suggested, or described herein that is useful for implementation of the invention is conventional and within the ordinary skill in such arts. 
     A computer program product can include one or more storage media, for example; magnetic storage media such as magnetic disk (such as a floppy disk) or magnetic tape; optical storage media such as optical disk, optical tape, or machine readable bar code; solid-state electronic storage devices such as random access memory (RAM), or read-only memory (ROM); or any other physical device or media employed to store a computer program having instructions for controlling one or more computers to practice the method according to the present invention. 
     As used herein, “toner particles” are particles of one or more material(s) that are transferred by an EP printer to a receiver to produce a desired effect or structure (e.g. a print image, texture, pattern, or coating) on the receiver. Toner particles can be ground from larger solids, or chemically prepared (e.g. precipitated from a solution of a pigment and a dispersant using an organic solvent), as is known in the art. Toner particles can have a range of diameters, e.g. less than 8 μm, on the order of 10-15 μm, up to approximately 30 μm, or larger (“diameter” refers to the volume-weighted median diameter, as determined by a device such as a Coulter Multisizer). 
     “Toner” refers to a material or mixture that contains toner particles, and that can form an image, pattern, or coating when deposited on an imaging member including a photoreceptor, a photoconductor, or an electrostatically-charged or magnetic surface. Toner can be transferred from the imaging member to a receiver. Toner is also referred to in the art as marking particles, dry ink, or developer, but note that herein “developer” is used differently, as described below. Toner can be a dry mixture of particles or a suspension of particles in a liquid toner base. 
     Toner includes toner particles and can include other particles. Any of the particles in toner can be of various types and have various properties. Such properties can include absorption of incident electromagnetic radiation (e.g. particles containing colorants such as dyes or pigments), absorption of moisture or gasses (e.g. desiccants or getters), suppression of bacterial growth (e.g. biocides, particularly useful in liquid-toner systems), adhesion to the receiver (e.g. binders), electrical conductivity or low magnetic reluctance (e.g. metal particles), electrical resistivity, texture, gloss, magnetic remittance, florescence, resistance to etchants, and other properties of additives known in the art. 
     In single-component or monocomponent development systems, “developer” refers to toner alone. In these systems, none, some, or all of the particles in the toner can themselves be magnetic. However, developer in a monocomponent system does not include magnetic carrier particles. In dual-component, two-component, or multi-component development systems, “developer” refers to a mixture including toner particles and magnetic carrier particles, which can be electrically-conductive (useful in conventional two-component development systems) or -non-conductive (useful in small-particle, dry (SPD) development systems). Toner particles can be magnetic or non-magnetic. The carrier particles can be larger than the toner particles, e.g. 15-20 μm or 20-300 μm in diameter. A magnetic field is used to move the developer in these systems by exerting a force on the magnetic carrier particles. The developer is moved into proximity with an imaging member or transfer member by the magnetic field, and the toner or toner particles in the developer are transferred from the developer to the member by an electric field, as will be described further below. The magnetic carrier particles are not intentionally deposited on the member by action of the electric field; only the toner is intentionally deposited. However, magnetic carrier particles, and other particles in the toner or developer, can be unintentionally transferred to an imaging member. Developer can include other additives known in the art, such as those listed above for toner. Toner and carrier particles can be substantially spherical or non-spherical. 
     The electrophotographic process can be embodied in devices including printers, copiers, scanners, and facsimiles, and analog or digital devices, all of which are referred to herein as “printers.” Various aspects of the present invention are useful with electrostatographic printers such as electrophotographic printers that employ toner developed on an electrophotographic receiver, and ionographic printers and copiers that do not rely upon an electrophotographic receiver. Electrophotography and ionography are types of electrostatography (printing using electrostatic fields), which is a subset of electrography (printing using electric fields). 
     A digital reproduction printing system (“printer”) typically includes a digital front-end processor (DFE), a print engine (also referred to in the art as a “marking engine”) for applying toner to the receiver, and one or more post-printing finishing system(s) (e.g. a UV coating system, a glosser system, or a laminator system). A printer can reproduce pleasing black-and-white or color onto a receiver. A printer can also produce selected patterns of toner on a receiver, which patterns (e.g. surface textures) do not correspond directly to a visible image. The DFE receives input electronic files (such as Postscript command files) composed of images from other input devices (e.g., a scanner, a digital camera). The DFE can include various function processors, e.g. a raster image processor (RIP), image positioning processor, image manipulation processor, color processor, or image storage processor. The DFE rasterizes input electronic files into image bitmaps for the print engine to print. In some embodiments, the DFE permits a human operator to set up parameters such as layout, font, color, paper type, or post-finishing options. The print engine takes the rasterized image bitmap from the DFE and renders the bitmap into a form that can control the printing process from the exposure device to transferring the print image onto the receiver. The finishing system applies features such as protection, glossing, or binding to the prints. The finishing system can be implemented as an integral component of a printer, or as a separate machine through which prints are fed after they are printed. 
     The printer can also include a color management system which captures the characteristics of the image printing process implemented in the print engine (e.g. the electrophotographic process) to provide known, consistent color reproduction characteristics. The color management system can also provide known color reproduction for different inputs (e.g. digital camera images or film images). 
     In an embodiment of an electrophotographic modular printing machine useful with the present invention, e.g. the NEXPRESS 2100 printer manufactured by Eastman Kodak Company of Rochester, N.Y., color-toner print images are made in a plurality of color imaging modules arranged in tandem, and the print images are successively electrostatically transferred to a receiver adhered to a transport web moving through the modules. Colored toners include colorants, e.g. dyes or pigments, which absorb specific wavelengths of visible light. Commercial machines of this type typically employ intermediate transfer members in the respective modules for transferring visible images from the photoreceptor and transferring print images to the receiver. In other electrophotographic printers, each visible image is directly transferred to a receiver to form the corresponding print image. 
     Electrophotographic printers having the capability to also deposit clear toner using an additional imaging module are also known. The provision of a clear-toner overcoat to a color print is desirable for providing protection of the print from fingerprints and reducing certain visual artifacts. Clear toner uses particles that are similar to the toner particles of the color development stations but without colored material (e.g. dye or pigment) incorporated into the toner particles. However, a clear-toner overcoat can add cost and reduce color gamut of the print; thus, it is desirable to provide for operator/user selection to determine whether or not a clear-toner overcoat will be applied to the entire print. A uniform layer of clear toner can be provided. A layer that varies inversely according to heights of the toner stacks can also be used to establish level toner stack heights. The respective color toners are deposited one upon the other at respective locations on the receiver and the height of a respective color toner stack is the sum of the toner heights of each respective color. Uniform stack height provides the print with a more even or uniform gloss. 
       FIGS. 1-3  are elevational cross-sections showing portions of a typical electrophotographic printer  100  useful with the present invention. Printer  100  is adapted to produce images, such as single-color (monochrome), CMYK, or pentachrome (five-color) images, on a receiver (multicolor images are also known as “multi-component” images). Images can include text, graphics, photos, and other types of visual content. One embodiment of the invention involves printing using an electrophotographic print engine having five sets of single-color image-producing or -printing stations or modules arranged in tandem, but more or less than five colors can be combined on a single receiver. Other electrophotographic writers or printer apparatus can also be included. Various components of printer  100  are shown as rollers; other configurations are also possible, including belts. 
     Referring to  FIG. 1 , printer  100  is an electrophotographic printing apparatus having a number of tandemly-arranged electrophotographic image-forming printing modules  31 ,  32 ,  33 ,  34 ,  35 , also known as electrophotographic imaging subsystems. Each printing module produces a single-color toner image for transfer using a respective transfer subsystem  50  (for clarity, only one is labeled) to a receiver  42  successively moved through the modules. Receiver  42  is transported from supply unit  40 , which can include active feeding subsystems as known in the art, into printer  100 . In various embodiments, the visible image can be transferred directly from an imaging roller to a receiver, or from an imaging roller to one or more transfer roller(s) or belt(s) in sequence in transfer subsystem  50 , and thence to receiver  42 . Receiver  42  is, for example, a selected section of a web of, or a cut sheet of, planar media such as paper or transparency film. 
     Each receiver, during a single pass through the five modules, can have transferred in registration thereto up to five single-color toner images to form a pentachrome image. As used herein, the term “pentachrome” implies that in a print image, combinations of various of the five colors are combined to form other colors on the receiver at various locations on the receiver, and that all five colors participate to form process colors in at least some of the subsets. That is, each of the five colors of toner can be combined with toner of one or more of the other colors at a particular location on the receiver to form a color different than the colors of the toners combined at that location. In an embodiment, printing module  31  forms black (K) print images,  32  forms yellow (Y) print images,  33  forms magenta (M) print images, and  34  forms cyan (C) print images. 
     Printing module  35  can form a red, blue, green, or other fifth print image, including an image formed from a clear toner (i.e. one lacking pigment). The four subtractive primary colors, cyan, magenta, yellow, and black, can be combined in various combinations of subsets thereof to form a representative spectrum of colors. The color gamut or range of a printer is dependent upon the materials used and process used for forming the colors. The fifth color can therefore be added to improve the color gamut. In addition to adding to the color gamut, the fifth color can also be a specialty color toner or spot color, such as for making proprietary logos or colors that cannot be produced with only CMYK colors (e.g. metallic, fluorescent, or pearlescent colors), or a clear toner. 
     Receiver  42 A is shown after passing through printing module  35 . Print image  38  on receiver  42 A includes unfused toner particles. 
     Subsequent to transfer of the respective print images, overlaid in registration, one from each of the respective printing modules  31 ,  32 ,  33 ,  34 ,  35 , receiver  42 A is advanced to a fuser  60 , i.e. a fusing or fixing assembly, to fuse print image  38  to receiver  42 A. Transport web  81  transports the print-image-carrying receivers to fuser  60 , which fixes the toner particles to the respective receivers by the application of heat and pressure. The receivers are serially de-tacked from transport web  81  to permit them to feed cleanly into fuser  60 . Transport web  81  is then reconditioned for reuse at cleaning station  86  by cleaning and neutralizing the charges on the opposed surfaces of the transport web  81 . A mechanical cleaning station (not shown) for scraping or vacuuming toner off transport web  81  can also be used independently or with cleaning station  86 . The mechanical cleaning station can be disposed along transport web  81  before or after cleaning station  86  in the direction of rotation of transport web  81 . 
     Fuser  60  includes a heated fusing roller  62  and an opposing pressure roller  64  that form a fusing nip  66  therebetween. In an embodiment, fuser  60  also includes a release fluid application substation  68  that applies release fluid, e.g. silicone oil, to fusing roller  62 . Alternatively, wax-containing toner can be used without applying release fluid to fusing roller  62 . Other embodiments of fusers, both contact and non-contact, can be employed with the present invention. For example, solvent fixing uses solvents to soften the toner particles so they bond with the receiver. Photoflash fusing uses short bursts of high-frequency electromagnetic radiation (e.g. ultraviolet light) to melt the toner. Radiant fixing uses lower-frequency electromagnetic radiation (e.g. infrared light) to more slowly melt the toner. Microwave fixing uses electromagnetic radiation in the microwave range to heat the receivers (primarily), thereby causing the toner particles to melt by heat conduction, so that the toner is fixed to the receiver. 
     The receivers (e.g. receiver  42 B) carrying the fused image (e.g. fused image  39 ) are transported in a series from the fuser  60  along a path either to a remote output tray  69 , or back to printing modules  31 ,  32 ,  33 ,  34 ,  35  to create an image on the backside of the receiver, i.e. to form a duplex print. Receivers can also be transported to any suitable output accessory. For example, an auxiliary fuser or glossing assembly can provide a clear-toner overcoat. Printer  100  can also include multiple fusers  60  to support applications such as overprinting, as known in the art. 
     In various embodiments, between fuser  60  and output tray  69 , receiver  42 B passes through finisher  70 . Finisher  70  performs various paper-handling operations, such as folding, stapling, saddle-stitching, collating, and binding. 
     Printer  100  includes main printer apparatus logic and control unit (LCU)  99 , which receives input signals from the various sensors associated with printer  100  and sends control signals to the components of printer  100 . LCU  99  can include a microprocessor incorporating suitable look-up tables and control software executable by the LCU  99 . It can also include a field-programmable gate array (FPGA), programmable logic device (PLD), microcontroller, or other digital control system. LCU  99  can include memory for storing control software and data. Sensors associated with the fusing assembly provide appropriate signals to the LCU  99 . In response to the sensors, the LCU  99  issues command and control signals that adjust the heat or pressure within fusing nip  66  and other operating parameters of fuser  60  for receivers. This permits printer  100  to print on receivers of various thicknesses and surface finishes, such as glossy or matte. 
     Image data for writing by printer  100  can be processed by a raster image processor (RIP; not shown), which can include a color separation screen generator or generators. The output of the RIP can be stored in frame or line buffers for transmission of the color separation print data to each of the respective LED writers, e.g. for black (K), yellow (Y), magenta (M), cyan (C), and red (R), respectively. The RIP or color separation screen generator can be a part of printer  100  or remote therefrom. Image data processed by the RIP can be obtained from a color document scanner or a digital camera or produced by a computer or from a memory or network which typically includes image data representing a continuous image that needs to be reprocessed into halftone image data in order to be adequately represented by the printer. The RIP can perform image processing processes, e.g. color correction, in order to obtain the desired color print. Color image data is separated into the respective colors and converted by the RIP to halftone dot image data in the respective color using matrices, which comprise desired screen angles (measured counterclockwise from rightward, the +X direction) and screen rulings. The RIP can be a suitably-programmed computer or logic device and is adapted to employ stored or computed matrices and templates for processing separated color image data into rendered image data in the form of halftone information suitable for printing. These matrices can include a screen pattern memory (SPM). 
     Further details regarding printer  100  are provided in U.S. Pat. No. 6,608,641, issued on Aug. 19, 2003, to Peter S. Alexandrovich et al., and in U.S. Publication No. 2006/0133870, published on Jun. 22, 2006, by Yee S. Ng et al., the disclosures of which are incorporated herein by reference. 
     Referring to  FIG. 2 , receivers R n -R (n-6)  are delivered from supply unit  40  ( FIG. 1 ) and transported through the printing modules  31 ,  32 ,  33 ,  34 ,  35 . The receivers are adhered (e.g., electrostatically using coupled corona tack-down chargers  124 ,  125 ) to an endless transport web  81  entrained and driven about rollers  102 ,  103 . Each of the printing modules  31 ,  32 ,  33 ,  34 ,  35  includes a respective imaging member ( 111 ,  121 ,  131 ,  141 ,  151 ), e.g. a roller or belt, an intermediate transfer member ( 112 ,  122 ,  132 ,  142 ,  152 ), e.g. a blanket roller, and transfer backup member ( 113 ,  123 ,  133 ,  143 ,  153 ), e.g. a roller, belt or rod. Thus in printing module  31 , a print image (e.g. a black separation image) is created on imaging member PC 1  ( 111 ), transferred to intermediate transfer member ITM 1  ( 112 ), and transferred again to receiver R (n-1)  moving through transfer subsystem  50  ( FIG. 1 ) that includes transfer member ITM 1  ( 112 ) forming a pressure nip with a transfer backup member TR 1  ( 113 ). Similarly, printing modules  32 ,  33 ,  34 , and  35  include, respectively: PC 2 , ITM 2 , TR 2  ( 121 ,  122 ,  123 ); PC 3 , ITM 3 , TR 3  ( 131 ,  132 ,  133 ); PC 4 , ITM 4 , TR 4  ( 141 ,  142 ,  143 ); and PC 5 , ITM 5 , TR 5  ( 151 ,  152 ,  153 ). The direction of transport of the receivers is the slow-scan direction; the perpendicular direction, parallel to the axes of the intermediate transfer members ( 112 ,  122 ,  132 ,  142 ,  152 ), is the fast-scan direction. 
     A receiver, R n , arriving from supply unit  40  ( FIG. 1 ), is shown passing over roller  102  for subsequent entry into the transfer subsystem  50   
     ( FIG. 1 ) of the first printing module,  31 , in which the preceding receiver R (n-1)  is shown. Similarly, receivers R (n-2) , R (n-3) , R (n-4) , and R (n-5)  are shown moving respectively through the transfer subsystems (for clarity, not labeled) of printing modules  32 ,  33 ,  34 , and  35 . An unfused print image formed on receiver R (n-6)  is moving as shown towards fuser  60  ( FIG. 1 ). 
     A power supply  105  provides individual transfer currents to the transfer backup members  113 ,  123 ,  133 ,  143 , and  153 . LCU  99  ( FIG. 1 ) provides timing and control signals to the components of printer  100  in response to signals from sensors in printer  100  to control the components and process control parameters of the printer  100 . A cleaning station  86  for transport web  81  permits continued reuse of transport web  81 . A densitometer array includes a transmission densitometer  104  using a light beam  110 . The densitometer array measures optical densities of five toner control patches transferred to an interframe area  109  located on transport web  81 , such that one or more signals are transmitted from the densitometer array to a computer or other controller (not shown) with corresponding signals sent from the computer to power supply  105 . Densitometer  104  is preferably located between printing module  35  and roller  103 . Reflection densitometers, and more or fewer test patches, can also be used. 
       FIG. 3  shows more details of printing module  31 , which is representative of printing modules  32 ,  33 ,  34 , and  35 . Primary charging subsystem  210  uniformly electrostatically charges photoreceptor  206  of imaging member  111 , shown in the form of an imaging cylinder. Charging subsystem  210  includes a grid  213  having a selected voltage. Additional necessary components provided for control can be assembled about the various process elements of the respective printing modules. Measuring device  211  measures the uniform electrostatic charge provided by charging subsystem  210 , and measuring device  212  measures the post-exposure surface potential within a patch area of a latent image formed from time to time in a non-image area on photoreceptor  206 . Other meters and components can be included. 
     LCU  99  sends control signals to the charging subsystem  210 , the exposure subsystem  220  (e.g. laser or LED writers), and the respective development station  225  of each printing module  31 ,  32 ,  33 ,  34 ,  35 , among other components. Each printing module can also have its own respective controller (not shown) coupled to LCU  99 . 
     Imaging member  111  includes photoreceptor  206 . Photoreceptor  206  includes a photoconductive layer formed on an electrically conductive substrate. The photoconductive layer is an insulator in the substantial absence of light so that electric charges are retained on its surface. Upon exposure to light, the charge is dissipated. In various embodiments, photoreceptor  206  is part of, or disposed over, the surface of imaging member  111 , which can be a plate, drum, or belt. Photoreceptors can include a homogeneous layer of a single material such as vitreous selenium or a composite layer containing a photoconductor and another material. Photoreceptors can also contain multiple layers. 
     An exposure subsystem  220  is provided for image-wise modulating the uniform electrostatic charge on photoreceptor  206  by exposing photoreceptor  206  to electromagnetic radiation to form a latent electrostatic image (e.g. of a separation corresponding to the color of toner deposited at this printing module). The uniformly-charged photoreceptor  206  is typically exposed to actinic radiation provided by selectively activating particular light sources in an LED array or a laser device outputting light directed at photoreceptor  206 . In embodiments using laser devices, a rotating polygon (not shown) is used to scan one or more laser beam(s) across the photoreceptor in the fast-scan direction. One dot site is exposed at a time, and the intensity or duty cycle of the laser beam is varied at each dot site. In embodiments using an LED array, the array can include a plurality of LEDs arranged next to each other in a line, all dot sites in one row of dot sites on the photoreceptor can be selectively exposed simultaneously, and the intensity or duty cycle of each LED can be varied within a line exposure time to expose each dot site in the row during that line exposure time. 
     As used herein, an “engine pixel” is the smallest addressable unit on photoreceptor  206  or receiver  42  ( FIG. 1 ) which the light source (e.g. laser or LED) can expose with a selected exposure different from the exposure of another engine pixel. Engine pixels can overlap, e.g. to increase addressability in the slow-scan direction (S). Each engine pixel has a corresponding engine pixel location, and the exposure applied to the engine pixel location is described by an engine pixel level. 
     The exposure subsystem  220  can be a write-white or write-black system. In a write-white or charged-area-development (CAD) system, the exposure dissipates charge on areas of photoreceptor  206  to which toner should not adhere. Toner particles are charged to be attracted to the charge remaining on photoreceptor  206 . The exposed areas therefore correspond to white areas of a printed page. In a write-black or discharged-area development (DAD) system, the toner is charged to be attracted to a bias voltage applied to photoreceptor  206  and repelled from the charge on photoreceptor  206 . Therefore, toner adheres to areas where the charge on photoreceptor  206  has been dissipated by exposure. The exposed areas therefore correspond to black areas of a printed page. 
     A development station  225  includes toning shell  226 , which can be rotating or stationary, for applying toner of a selected color to the latent image on photoreceptor  206  to produce a visible image on photoreceptor  206 . Development station  225  is electrically biased by a suitable respective voltage to develop the respective latent image, which voltage can be supplied by a power supply (not shown). Developer is provided to toning shell  226  by a supply system (not shown), e.g. a supply roller, auger, or belt. Toner is transferred by electrostatic forces from development station  225  to photoreceptor  206 . These forces can include Coulombic forces between charged toner particles and the charged electrostatic latent image, and Lorentz forces on the charged toner particles due to the electric field produced by the bias voltages. 
     In an embodiment, development station  225  employs a two-component developer that includes toner particles and magnetic carrier particles. Development station  225  includes a magnetic core  227  to cause the magnetic carrier particles near toning shell  226  to form a “magnetic brush,” as known in the electrophotographic art. Magnetic core  227  can be stationary or rotating, and can rotate with a speed and direction the same as or different than the speed and direction of toning shell  226 . Magnetic core  227  can be cylindrical or non-cylindrical, and can include a single magnet or a plurality of magnets or magnetic poles disposed around the circumference of magnetic core  227 . Alternatively, magnetic core  227  can include an array of solenoids driven to provide a magnetic field of alternating direction. Magnetic core  227  preferably provides a magnetic field of varying magnitude and direction around the outer circumference of toning shell  226 . Further details of magnetic core  227  can be found in U.S. Pat. No. 7,120,379 to Eck et al., issued Oct. 10, 2006, and in U.S. Publication No. 2002/0168200 to Stelter et al., published Nov. 14, 2002, the disclosures of which are incorporated herein by reference. Development station  225  can also employ a mono-component developer comprising toner, either magnetic or non-magnetic, without separate magnetic carrier particles. 
     Transfer subsystem  50  ( FIG. 1 ) includes transfer backup member  113 , and intermediate transfer member  112  for transferring the respective print image from photoreceptor  206  of imaging member  111  through a first transfer nip  201  to surface  216  of intermediate transfer member  112 , and thence to a receiver (e.g.  42 B) which receives the respective toned print images  38  from each printing module in superposition to form a composite image thereon. Print image  38  is e.g. a separation of one color, such as cyan. Receivers are transported by transport web  81 . Transfer to a receiver is effected by an electrical field provided to transfer backup member  113  by power source  240 , which is controlled by LCU  99 . Receivers can be any objects or surfaces onto which toner can be transferred from imaging member  111  by application of the electric field. In this example, receiver  42 B is shown prior to entry into second transfer nip  202 , and receiver  42 A is shown subsequent to transfer of the print image  38  onto receiver  42 A. 
       FIG. 4  shows apparatus for measuring developer density in an electrophotographic system according to an embodiment of the present invention. In some monocomponent systems, developer density and toner density are equal. In some dual-component systems, developer density is the net density of toner particles and carrier particles. 
     First electrode  410  and second electrode  415  are disposed to define working volume  420  between them. The shape shown for working volume  420  is merely illustrative; the actual shape of the working volume is defined by the electric field pattern between electrodes  410  and  415 , or between electrode  415  and development member  710  ( FIG. 7 ). Developer can move through working volume  420  without contacting first electrode  410 . First electrode  410  and second electrode  415  are electrically insulated from each other by the working volume  420 . In an embodiment, the working volume  420  is filled with air. The working volume  420  can also be filled with nitrogen or vacuum. 
     First electrode  410  and second electrode  415  are two terminals of a capacitor having capacitance  425 ; working volume  420  and anything in working volume  420  serve as the dielectric of the capacitor. This will be discussed further below with respect to  FIG. 5 . In an embodiment, first electrode  410  is grounded. 
     Voltage source  430  selectively applies an AC bias across first electrode  410  and second electrode  415 . Voltage source  430  can be a commutated generator, sine-wave generator, arbitrary-waveform generator, programmable power supply, or other voltage sources known in the art capable of generating AC power. The AC bias is preferably sinusoidal. The magnitude and frequency of the AC bias are selected so that current can pass through the capacitor formed by first electrode  410 , working volume  420 , and second electrode  415 . These magnitudes and frequencies can be selected by those skilled in the art. In various embodiments, first electrode  410  and second electrode  415  are arranged parallel to each other, are spaced apart 0.1″, or are spaced apart by the expected maximum height of a developer blanket on one of the electrodes plus 0.03″. In various embodiments, the AC bias is 3 kV pk-pk  at 3 kHz. In various embodiments, first electrode  410  or second electrode  415  has a surface area facing the other electrode of 4 in 2 . In various embodiments, the AC bias has a magnitude between 2.5 kV and 3.5 kV peak-to-peak, or a frequency between 2.5 kHz and 3.5 kHz. 
     Measuring device  440  measures the current across the electrodes while the AC bias is applied. Measuring device  440  can be a high-side or low-side current sensor, a Hall-effect sensor, a loop current meter (such as the FLUKE 902 TRUE-RMS HVAC CLAMP METER, which has a range of 0-600A AC), or another current measurement unit known in the art. Measuring device  440  can measure the voltage drop across a known impedance and convert that measurement into current. Measuring device  440  can be connected in series with voltage source  430 , as shown here, or in parallel with it. Measuring device  440  can include an analog-to-digital converter, an analog or digital low-pass filter, an instrumentation amplifier, a sample-and-hold unit, or other conditioning and conversion circuitry known in the art. 
     In another embodiment, voltage source  430  includes a switcher or other DC-to-AC power source, optionally followed by a step-up transformer. Measuring device  440  measures the DC input current to voltage source  430 . Any of the current-sensing techniques discussed above can be used to measure this input current. For example, the voltage drop across a resistor in series with the DC input to voltage source  430  can be measured. 
     Processor  450  automatically determines the density of developer in working volume  420  based on the measured current and the applied bias. Processor  450  can be a CPU, GPU, FPGA, PAL, PLD, or other processor known in the art. Processor  450  can include a look-up table (LUT) preloaded with characterization data relating current and bias to density. Alternatively, the sensed current can be used as the feedback signal in a control system to adjust density by maintaining the sensed current within a target range. The target range can be determined by one skilled in the art, or can be automatically calculated by processor  450  using a calibration routine to measure the currents corresponding to a selected set of development hardware conditions. Instead of a LUT, a linear, polynomial, exponential, logarithmic, or other function, or piecewise combination of functions, can be used to relate current and bias to density. Throughout this disclosure, any LUT can be implemented in this way. 
     In various embodiments, the capacitance of the working volume is automatically determined. In steady-state AC, V=ZI by Ohm&#39;s Law, so Z=V/I. The applied V is known, and I is measured, so Z is readily calculated. Capacitor  500  has complex impedance Z=−j/ωC, so C=−j/ωZ. The frequency w of the applied bias is known, so C is readily calculated. The equivalent computation can be performed for an applied alternating current I and a measured voltage V to determine C. 
       FIG. 5  shows details of the apparatus of  FIG. 4  according to an embodiment of the present invention. As discussed above, first electrode  410  and second electrode  415  are two terminals of capacitor  500 ; working volume  420  and anything in working volume  420  serve as the dielectric of capacitor  500 . When working volume  420  is empty of solids, the capacitor is a simple parallel-plate capacitor having the dielectric constant (relative permittivity) of the material in working volume  420  (vacuum=1, pure nitrogen gas at 20° C.=1.0005480, typical air=1.0006). Therefore the capacitance C=∈ r ∈ 0  A/d for dielectric constant ∈ r , permittivity of free space ∈ 0 =8.85×10 −12  Fm −1 , common area between the plates A, and distance d between the plates. This is true when there are no free charges between the plates of the capacitor (first electrode  410  and second electrode  415 ). 
     When no free charges are present, and developer is present in working volume  420 , the capacitance between the plates increases. The dielectric constant increases when insulating materials such as toner particles or non-conductive carrier particles are added to the working volume, and the geometry of the capacitor changes by splitting capacitors and reducing spacings when electrically-conductive carrier particles are added to the working volume. 
     When electrically-insulating materials are added to working volume  420 , the average dielectric constant of working volume  420  increases. For example, insulating toner particle  512  can have a dielectric constant on its own of 1.7, as discussed in commonly-assigned U.S. Pat. No. 5,655,183 to Tombs, the disclosure of which is incorporated herein by reference. In other embodiments, insulating toner particle  512  has a dielectric constant of 3±0.5, or 3±1. This increase in dielectric constant increases the capacitance of capacitor  500 . Another example of an electrically-insulating material is a permanently-magnetized strontium ferrite carrier particle, which is not highly electrically conductive. In various embodiments, carrier particles are coated with polymers or other materials that are triboelectrically complementary to the toner, that is, materials that will charge when rubbed against toner particles. The material can be selected or doped by one skilled in the art to obtain a desired charge polarity and magnitude on the carrier and toner particles. Coated carrier particles can be electrically insulating even if they have an electrically-conductive core, since the outer surface of the particle is coated with an insulator. 
     When electrically-conductive materials are added to working volume  420 , the geometry of capacitor  500  changes. For example, carrier particle  514 , made of, e.g., manganese oxide, ferric oxide and titanium dioxide, is a conductor. Such a carrier particle is described in U.S. Pat. No. 6,294,304 to Sukovich et al., the disclosure of which is incorporated herein by reference. As a result, when carrier particle  514  is inserted in working volume  420 , electric field line  520  in area  551  is changed to electric field lines  524   a ,  524   b . Electric field lines  524   a ,  524   b  are shown offset horizontally from electric field line  520  for clarity only. As a result, capacitor  504   a  is formed between first electrode  410  and carrier particle  514 , and capacitor  504   b  is formed between carrier particle  514  and second electrode  415 . Each capacitor  504   a ,  504   b  has slightly more than twice the capacitance of the original capacitance between first electrode  410  and second electrode  415  in area  551 , since the distance d for each (the lengths of electric field lines  504   a ,  504   b  respectively) has been reduced to less than one-half its former value (here, one-half of the length of electric field line  520  minus one-half of the diameter of carrier particle  514 ). Capacitors  504   a ,  504   b  add in series to total capacitance C T =[1/C 504a +1/C 504b ] −1 , so C T &gt;C 520 . The more conductive particles are present, the more significant this effect is. Furthermore, conductive particles form additional capacitances between themselves. 
     Furthermore, as electrically-conductive material in contact with either first electrode  410  or second electrode  415 , but not both, extends over more of the distance between first electrode  410  and second electrode  415 , the capacitance between the free end of the conductive material and the non-contacted electrode increases. For example, chain  534  includes electrically-conductive carrier particles  514   a ,  514   b , and  514   c , which are in electrical contact with each other. Carrier particle  514   c  is in electrical contact with first electrode  410 . Capacitor  503  has distance d approximately half its value before chain  534  is formed, so the capacitance in area  531  has approximately doubled. 
     The result of these effects is that the capacitance of capacitor  500  increases as the density of developer in working volume  420  increases, as long as there are substantially no free charges in working volume  420 . The increase in capacitance decreases impedance, increasing current flow. That is, there is a positive correlation between developer density and current flow. An example of this effect is shown in  FIG. 6D , below. 
     When free charges are present in working volume  420 , the capacitance C of capacitor  500  cannot be calculated using the parallel-plate formulas. C is a function of capacitor geometry and the distribution of charge in working volume  420 . This will now be discussed, with respect to  The Feynman Lectures on Physics, The Definitive Edition Volume  2 (2nd Edition) by Richard P. Feynman, Robert B. Leighton, and Matthew Sands, San Francisco: Pearson/Addison-Wesley, 2005, ISBN 0-8053-9047-2, the disclosure of which is incorporated herein by reference, and particularly with respect to chapters 4, 6, 13, 15, and 17 thereof. 
     The voltage across a capacitor is by definition the work done in moving a unit charge between the plates against the electric field E between them=Es. The effect of E on the momentum p of a particle with charge q in the field is qE=dp/dt, which is proportional to the acceleration a on the charge when mass is constant (i.e., at velocities ν&lt;&lt;c.). Charges between the plates of the capacitor can be arranged in a way that will increase or decrease E at any point between the plates. When E is decreased by adding charge to working volume  420 , electrons are decelerated between the plates, decreasing the current between the plates. Moreover, when positive charge is present in working volume  420 , it will deflect electrons, increasing the mean path length between the plates of the capacitor and decreasing current (and likewise for negative charge with positive ions as charge carriers). These effects can cause a negative correlation between developer density and capacitor current. An example of a negative correlation is shown in  FIG. 6A . 
       FIG. 6A  shows experimental data relating developer flow rate on the abscissa to average peak-to-peak measured current I pk-pk,avg  through electrodes  410 ,  415  ( FIG. 4 ) on the ordinate. The plotted points are measured data; curve  610  is a polynomial fit with equation y=−0.1209x 2 +0.2299x+7.7805 and R 2 =0.9772. Developer flow rate was used since developer density is difficult to directly control. In the configuration used in this experiment, developer density is negatively correlated with developer flow rate. A 3 kV pk-pk  AC bias at 3 kHz was used, with A≈4 in 2  and s≈0.1″. Curve  610  shows that as developer flow (thus developer density) rises, I pk-pk,avg  falls. 
       FIG. 6B  shows a summary of experimental data relating developer flow rate to average peak-to-peak measured current. Various experimental configurations were employed, covering variations in capacitor plate area (A), capacitor thickness (s), and frequency of the AC bias. In each configuration, data were collected relating average peak-to-peak measured current (dependent) to flow rate (independent). A linear fit of the collected data was performed for each configuration. The slopes of the linear fits are shown in  FIG. 6B , with one bar per configuration. Most of the slopes were positive, indicating that current increased with flow rate as described above (positive correlation). However, configuration  620  has a negative slope (negative correlation), as do the data shown in  FIG. 6A . Therefore, average peak-to-peak measured current can be positively or negatively correlated with developer flow rate. 
       FIG. 6C  shows the conditions used in  FIG. 6B . Measurements were taken using various plate areas, voltage amplitudes, frequencies, and electrode spacings. Measurements were taken as described above with respect to  FIG. 6B . The slope, intercept, and R 2  of the linear fit for each condition are shown in the table. Each condition was measured at three different feed conditions (low/medium/high). The linear fits relate current (dependent) to flow rate (independent). In these tests, the three feed conditions were three voltages of the motor driving the feed roller to feed developer onto the development member. The speed of the development member was constant. 
     Negative slopes can be due to resonant effects due to parasitics in the measurement system. In practice, the circuit shown in  FIG. 4  has parasitic resistances, inductances, and capacitances in addition to capacitance  425 , shown. These parasitics can affect the behaviour of the circuit at the frequency of the AC bias, e.g., by adding poles or zeros. 
     In embodiments with significant parasitics, the DC input currents to voltage source  430  ( FIG. 4 ) are preferably measured instead of the actual AC currents across working volume  420  ( FIG. 4 ). When performing high-voltage, low-current measurements, parasitics can starve overload the power supply if care is not taken. Measuring the low-voltage, high-current input to voltage supply  430  reduces the chance of overload. 
       FIG. 6D  shows an example of positive correlation. The axes are the same as  FIG. 6A . As developer flow (abscissa, Win/s) rises, current (ordinate, μA) rises as shown by curve  690 . Fit  695  is a linear fit of current, with equation y=0.1837x+6.132, and R 2 =0.9918. Linear, quadratic, or other fits can be made to measured data for ease of computation. 
       FIG. 7  shows apparatus for measuring developer density in an electrophotographic system according to an embodiment of the present invention. Rotatable development member  710  (e.g. toning shell  226 ) transports developer. Moreover, development member  710  performs the functions of first electrode  410  ( FIG. 4 ). In an embodiment, development member  710  is grounded. Electrode  415  performs the functions of second electrode  415  shown in  FIG. 4 . Electrode  415  is displaced with respect to development member  710  to define working volume  420  between them. The shape shown for working volume  420  is merely illustrative; the actual shape of the working volume is defined by the electric field pattern between electrode  415  and development member  710 . Developer can move through working volume  420 , preferably without contacting the electrode. Electrode  415  is electrically insulated from development member  710  by working volume  420 , so that capacitance  425  is formed between the electrode and the development member. Voltage source  430  is electrically connected to electrode  415  and development member  710  for selectively applying an AC bias, as described above, across working volume  420 . 
     Measurement device  740  is electrically connected to electrode  415  and development member  710  for measuring the capacitance  425  of working volume  420  while development member  710  rotates. Measurement device  740  can include a meter (e.g. measuring device  440 , shown in  FIG. 4 ), an ammeter, a voltmeter, a capacitance meter based on resonant-frequency measurements, or another type of capacitance measurement device known in the art. Measurement device  740  can be connected in series with voltage source  430 , as shown here, or in parallel with it. 
     Processor  450  automatically determines the density of the developer in the working volume based on the measured capacitance and the applied bias. Processor  450  can include a characterization LUT or function (as described above) mapping measured capacitance and bias to developer density. 
       FIG. 8  shows a method of measuring developer (i.e., toner, or toner and carrier, as described above) density in an electrophotographic system according to an embodiment of the present invention. 
     Processing begins with step  810 . In step  810 , a first electrode and a second electrode are provided, e.g., as shown in  FIG. 4 . The electrodes are disposed to define a working volume between them through which developer passes without contacting the first electrode, and the electrodes are electrically insulated from each other by the working volume. Step  810  is followed by step  815 . 
     In step  815 , one terminal of a power source is connected to one of the electrodes. The power source can be a voltage source or a current source. In embodiments providing a voltage source, the voltage source is adapted to selectively provide an AC bias having a selected magnitude and frequency to the connected electrode. In embodiments providing a current source, the current source is adapted to selectively provide an alternating current having a selected magnitude and frequency to the connected electrode. Step  815  is followed by step  820 . 
     In step  820 , an inductor is provided. In embodiments providing a voltage source, the inductor is provided electrically connected in series with the voltage source and is connected to the other of the electrodes, i.e., to the electrode to which the voltage source is not connected. In this way, the voltage source provides the AC bias across the electrodes through the inductor. The voltage source therefore provides the AC bias across a series-resonant tank circuit including the inductor and the capacitance between the electrodes. 
     In embodiments providing a current source, the inductor is provided electrically connected in parallel with the current source. The current source and inductor are both connected to both of the electrodes, so that the current source provides the alternating current across the electrodes. The current source therefore provides the alternating current into a parallel-resonant tank circuit including the inductor and the capacitance between the electrodes. Step  820  is followed by step  825 . 
     In step  825 , a bias is applied using the voltage source, or a current is applied using the voltage source. Step  825  is followed by step  830 , or, optionally, step  850 . In optional step  850 , a plurality of biases or currents having different frequencies is applied. Step  850  is followed by step  830 . 
     In step  830 , the current is measured for an applied bias, or the voltage across the current source is measured for an applied current. In embodiments applying a plurality of biases or currents, respective currents or voltages are measured. Step  830  is followed by step  835 . 
     In step  835 , the density is automatically determined using a processor (e.g., processor  450 , as described above). In embodiments using a single current, density is determined as described above and as shown in  FIGS. 4 and 6 . The processor is responsive to the measured current and the applied bias. 
     In embodiments using a single applied alternating current, the processor determines the capacitance of the working volume based on the relationship between applied current and measured voltage, as described above. The processor then automatically determines the density of the developer in the working volume based on the measured capacitance. Processor  450  can include a characterization LUT or function (as described above) mapping measured capacitance and current to developer density. 
     In embodiments using a plurality of applied biases or currents, the density of the developer can be automatically determined by determining a density for each measurement individually. The measurements are then combined, e.g., by arithmetic or geometric averaging or taking the RMS value (quadratic mean), to produce a single measured density. 
     In other embodiments using a plurality of applied biases or currents, the density is determined using the processor based on the plurality of biases and the measured respective currents. Specifically, the capacitance of the working volume is automatically determined from the resonant properties of the tank circuit, and the density is determined from the capacitance as described above. In steady-state AC, V=ZI by Ohm&#39;s Law, so Z=V/I. 
       FIG. 9  shows an apparatus using a series-resonant tank circuit and a voltage source. First electrode  410 , second electrode  415 , working volume  420 , capacitance  425 , voltage source  430 , measuring device  440 , and processor  450  are as shown in  FIG. 4 . Inductor  919  is connected in series with voltage source  430 . 
     V is known, I is measured, and Z is calculated. Each applied bias has a different frequency, and a different Z. At the resonant frequency of the tank, Z=0, neglecting non-idealities such as wire resistance. The resonant frequency f r  is determined by selecting the lowest impedance (highest current for a given applied bias) from the measured current data or by interpolation between measured currents or between calculated impedance values. f r =[2π(LC) 1/2 ] −1 , and L is known, so C is calculated from L and f r : 
     
       
         
           
             
               
                 
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     The calculated capacitance C is then used to determine density, as discussed above. 
       FIG. 10  shows an apparatus using a parallel-resonant tank circuit and a current source. First electrode  410 , second electrode  415 , working volume  420 , capacitance  425 , and processor  450  are as shown in  FIG. 4 . Current source  1030  provides a known alternating current I across capacitance  425  and inductor  919 . Measuring device  1040  (e.g., a voltmeter) measures the voltage across current source  1030 , inductor  919 , and capacitance  425  (the three voltages are the same since they are connected in parallel). I is known, V is measured, and Z is calculated. Each applied bias has a different frequency, and a different Z. At the resonant frequency of the tank, Z=∞, neglecting non-idealities such as series resistance of the inductor. The resonant frequency f r  is determined by selecting the highest impedance (highest voltage for a given applied current) from the measured current data or by interpolation between measured currents or between calculated impedance values. C is calculated from L and f r  using Eq. 1, above. The calculated capacitance C is then used to determine density, as discussed above. 
     Developer density is related to toner concentration and developer flow rate. In various embodiments, these factors can be determined individually. 
       FIG. 11  shows an embodiment of an apparatus for measuring developer toner concentration in an electrophotographic system. Rotatable development member  710  is as shown in  FIG. 7 . A drum, belt, foam roller, or other type of development member known in the art can be used. Movable photoreceptor  206  is arranged so that toning zone  1110  is defined between development member  710  and photoreceptor  206 , and development member  710  selectively supplies developer to photoreceptor  206  in toning zone  1110  while development member  710  or photoreceptor  206  rotates. In various embodiments, the developer includes toner particles and carrier particles. 
     Patterning unit  1160  is adapted to produce an electrostatic latent image on the photoreceptor. Patterning unit  1160  can include an exposure subsystem  220  as shown in  FIG. 3 , e.g., a laser or a bank of LEDs to expose photoreceptor  206  to actinic radiation. 
     Sensors  1120  and  1130  are disposed over the surface of development member  710 , one before and one after toning zone  1110  in direction of rotation  1171  of development member  710 . Each sensor includes a respective electrode  1125 ,  1135  arranged with respect to development member  710  to form a respective capacitance (as shown in  FIG. 4 ) between the respective electrode  1125 ,  1135  and development member  710 . The respective electrodes  1125 ,  1135  define respective working volumes  1122 ,  1132  between the respective electrodes  1125 ,  1135  and development member  710 . Developer passes through the respective working volumes  1122 ,  1132  without contacting the respective electrodes  1125 ,  1135 , and the respective electrodes  1125 ,  1135  are electrically insulated from development member  710  by the respective working volumes  1122 ,  1132 . 
     Voltage source  430  is as shown in  FIG. 4 , and can include one supply or two independent supplies. Voltage source  430  selectively applies respective AC biases across the respective working volumes  1122 ,  1132  of the sensors  1120 ,  1130 . The biases can be the same or different. Voltage source  430  can drive the electrodes  1125 ,  1135 , or it can drive the development member. Lines carrying the AC bias are shown dashed in this figure for clarity; lines carrying control signals are shown solid. 
     Measuring device  740  is as shown in  FIG. 7 . It is connected in series with voltage source  430  for measuring respective currents across the respective working volumes  1122 ,  1132  while the respective biases are applied. 
     In an alternative embodiment, a series- or parallel-resonant configuration, as shown in  FIGS. 9-10 , is used for each sensor. In a parallel-resonant configuration, a current source is used in place of voltage source  430 , and a voltmeter is used in place of measuring device  740 . 
     Controller  1170  controls the operation of the apparatus, and can include or communicate with a processor  450 , described above. Processor  1170  can be a CPU, GPU, FPGA, PAL, PLD, or other processor known in the art. 
     Controller  1170  receives pixel data corresponding to toner to be applied to the photoreceptor. Controller  1170  then causes patterning unit  1160  to produce an electrostatic latent image corresponding to the received pixel data on photoreceptor  206 . In an embodiment, the pixel data is a pre-selected test or calibration pattern. 
     After the electrostatic latent image is patterned, controller  1170  causes development member  710  to rotate and photoreceptor  206  to move. This can be accomplished using motors and drives known in the art, such as servomotors with optical quadrature encoders for closed-loop control. 
     While development member  710  is rotating, developer is moving through toning zone  1110 . Toner in the developer is being attracted to the latent image on photoreceptor  206 . Therefore, the toner concentration of developer in working volume  1132  is less than the toner concentration of developer in working volume  1122 . Controller  1170  receives respective currents measured by measuring device  740  for each sensor  1120 ,  1130 . Two meters and two sources can be used, one per sensor, or the bias can be provided to, and current measured from, one sensor ( 1120  or  1130 ) at a time. 
     Controller  1170  (or processor  450 , as described above) then computes toner concentration using the respective received currents and the pixel data. The respective density of developer in each working volume  1122 ,  1132  is determined as described above. If no carrier particles have been lost by pick-up onto photoconductor  206 , and if the magnetic field strength in working volume  1132  is the same as that in working volume  1122 , sensors  1120 ,  1130  will report results that differ only as a result of the removal of toner from the developer and its deposition on photoreceptor  206 . Specifically, developer flow rate is the same in working volumes  1122  and  1132 . Adjustments for lost carrier particles and varying magnetic field strengths can be made by those skilled in the electrophotographic art. Lost carrier particles reduce density, so the measured density in working volume  1132  can be increased to compensate. A difference of magnetic field strength can be used to compute the difference in nap height, or the respective nap heights in working volumes  1122 ,  1132  can be measured. The measured densities can then be normalized using the differences in nap height. 
     Controller  1170  computes the expected amount of toner removed in toning zone  1110  using the received pixel data. For example, the controller can receive, e.g., from a characterization file, the mass laydown per unit area for a 100% laydown of developer, and the mass and volume of toner particles. The controller can therefore calculate the amount of mass and volume deposited on a 100% patch of a given area (which area is computed from the pixel data and the size of each pixel). 
     Toner concentration (TC) is the mass percentage of toner particles in a given mass of developer. If TC is low, removing a certain amount of toner will have a small effect on developer density, because not that much toner is present to begin with. If TC is high, removing that amount of toner will have a large effect on developer density. These effects can be characterized before shipping a printer, and controller  1170  can use a lookup table or function (as described above) of the characterization data to map the respective currents from sensors  1120  and  1130 , and the received pixel data, to toner concentration. 
     In various embodiments, controller  1170  maintains toner concentration at a desired level. Sump  1180  (represented graphically here) holds developer to be applied to development member  710  for transfer to photoreceptor  206 . Toner bottle  1182  holds additional toner to be added to carrier particles in sump  1180  to provide replenished toner. Toner bottle  1182  includes gate  1184  operated by controller  1170 . This is discussed further with reference to  FIG. 12 . 
       FIG. 12  shows a method of controlling developer toner concentration in an electrophotographic system. Processing begins with step  1210 . An example of apparatus useful in the practice of various embodiments of this method is shown in  FIG. 11 , from which part numbers are given in parentheses to aid the understanding of this method. Other apparatus can also be used in the practice of this method. 
     Referring to  FIG. 12  and also to  FIG. 11 , in step  1210 , a rotatable development member ( 710 ) and a movable photoreceptor ( 206 ) are arranged so that a toning zone ( 1110 ) is defined between them. In this way the development member selectively supplies developer to the photoreceptor in the toning zone while it rotates. In this embodiment, the developer includes toner and carrier particles. Step  1210  is followed by step  1215 . 
     In step  1215 , two sensors ( 1120 ,  1130 ) are provided. One sensor ( 1120 ) is disposed before the toning zone in the direction of rotation of the development member, and one after ( 1130 ). Each sensor includes a respective electrode ( 1125 ,  1135 ) arranged with respect to the development member to form a respective capacitance between the respective electrode and development member. Each respective electrode defines a respective working volume ( 1122 ,  1132 ) between the respective electrode and the development member, wherein developer passes through the respective working volume without contacting the electrode, and the respective electrode is electrically insulated from the development member by the respective working volume. Step  1215  is followed by step  1220 . 
     In step  1220 , a voltage source ( 430 ) is provided. The voltage source selectively applies respective AC biases across the respective working volumes of the sensors. The biases can be the same or different, and can differ in phase, amplitude, or frequency content (e.g., number of superimposed waveforms). The voltage source can drive the electrode in each sensor or the development member. The voltage source can include one supply or two independent supplies for its two terminals. Step  1220  is followed by step  1225 . 
     In step  1225 , a measuring device ( 740 ) is provided. The measuring device measures respective currents across the respective working volumes while the respective biases are applied Step  1225  is followed by step  1230 . 
     In step  1230 , pixel data are received (by controller  1170 ) that correspond to toner to be applied to the photoreceptor. Step  1230  is followed by step  1235 . 
     In step  1235 , a patterning unit ( 1160 ) is caused to produce an electrostatic latent image corresponding to the received pixel data on the photoreceptor. Step  1235  is followed by step  1240 . 
     In step  1240 , the members are moved. Specifically, after the electrostatic latent image is patterned, the development member is caused to rotate and the photoreceptor to move. Step  1240  is followed by step  1245 . 
     In step  1245 , while the development member is rotating, the measuring device measures respective currents across the respective working volumes due to the respective applied AC biases. Step  1245  is followed by step  1250 . 
     In step  1250 , the toner concentration is automatically computed using a processor ( 450 ). The processor, which can be an FPGA, CPU, PLD, or other logic device, is responsive to the respective received currents and the pixel data. 
     Step  1250  is followed by step  1253  or step  1256 . Steps  1253  and  1256  adjust printer operational parameters in response to the determined toner concentration. In step  1253 , the developer flow rate is adjusted, e.g., by adjusting the speed of rotation of the development member, the metering skive gap, the feed roller speed, or the toning roller magnetic field strength. In step  1256 , toner is added to the developer, e.g., by opening the gate ( 1184 ) on the toner bottle ( 1182 ). These adjustments maintain laydown in a desired range. Toner concentration changes gradually, and the adjustments listed above take effect quickly. Therefore, toner concentration can be accurately maintained. Moreover, flow control provides a fine adjustment useful within a print or a small number of prints, while adding toner provides a coarser adjustment useful over large numbers of prints. Flow control can be adjusted between prints. 
       FIG. 13  shows an apparatus for measuring developer flow rate in an electrophotographic system. Rotatable development member  710 , electrode  1125 , working volume  1122 , voltage source  430 , and measuring device  740  are as shown in  FIG. 11 . Electrode  1125  can be located before or after toning zone  1110  in the direction of rotation of development member  710 . 
     In an alternative embodiment, a series- or parallel-resonant configuration, as shown in  FIGS. 9-10 , is used for each sensor. In a parallel-resonant configuration, a current source is used in place of voltage source  430 , and a voltmeter is used in lace of measuring device  740 . 
     Controller  1370  controls the operation of the apparatus, and can include or communicate with a processor  450 , described above. Processor  1370  can be a CPU, GPU, FPGA, PAL, PLD, or other processor known in the art. 
     Processor  1370  causes development member  710  to stop supplying toner to the photoreceptor. By “stop supplying” it is meant that the intentional flow of toner stops. Some toner can move to the photoreceptor because of residual charges and electric fields. Processor  1370  then causes development member  710  to rotate. While development member  710  is rotating, controller  1370  records the current measured by measuring device  740 . Controller  1370  then automatically computes developer flow rate using the measured current from measuring device  740 . A characterization LUT or function, as described above, can be used to convert the measured current into flow rate. 
       FIG. 14  shows a method of controlling developer flow rate in an electrophotographic system. Processing begins with step  1410 . An example of apparatus useful in the practice of various embodiments of this method is shown in  FIG. 13 , from which part numbers are given in parentheses to aid the understanding of this method. Other apparatus can also be used in the practice of this method. 
     Referring to  FIG. 14  and also to  FIG. 13 , in step  1410 , a rotatable development member ( 710 ) and a movable photoreceptor ( 206 ) are arranged so that a toning zone ( 1110 ) is defined between them, and the development member selectively supplies developer to the photoreceptor in the toning zone while it rotates. The developer includes toner and carrier particles. Step  1410  is followed by step  1415 . 
     In step  1415 , an electrode ( 1125 ) is provided. The electrode is arranged with respect to the development member to form a capacitance between the electrode and development member, and to define a working volume ( 1122 ) between the electrode and the development member. Developer passes through the working volume without contacting the electrode, and the electrode is electrically insulated from the development member by the working volume. Step  1415  is followed by step  1420 . 
     In step  1420 , a voltage source for selectively applying an AC bias across the working volume is provided. Step  1420  is followed by step  1425 . 
     In step  1425 , a measuring device for measuring a current across the working volume while the bias is applied is provided. Step  1425  is followed by step  1430 . 
     In step  1430 , the supply of developer to the photoreceptor is stopped. Specifically, the development member is caused to stop supplying toner to the photoreceptor. This is accomplished by adjusting the voltages on the development member and photoreceptor, by interposing a mechanical gate in part or all of the toning zone, or by moving the development member and photoreceptor away from each other. Step  1430  is followed by step  1440 . 
     In step  1440 , the development member is rotated, e.g., by driving it with a servomotor or stepper motor. Developer therefore moves with the development member at a certain developer flow rate. Step  1440  is followed by step  1445 . 
     In step  1445 , while the development member is rotating, the AC bias is applied using the voltage source and the current is measured using the measuring device. Step  1445  is followed by step  1450 . 
     In step  1450 , the developer flow rate is automatically computed using a processor ( 450 ) responsive to the measured current. Step  1450  is followed by step  1453 . 
     In step  1453 , the flow rate is adjusted, e.g., by changing the speed of rotation of the development member, the metering skive gap, the feed roller speed, or the toning roller magnetic field strength. These adjustments can maintain the flow at a desired rate. These adjustments are described above with reference to  FIG. 13 . 
     In various embodiments of sensors and measurement circuits described above, other configurations of tank circuits are used, including using current or voltage sources with series or parallel tank circuits, as will be obvious to those skilled in the art. In all circuit configurations discussed herein, negative and positive terminals can be interchanged as will be obvious to those skilled in the art. 
     The invention is inclusive of combinations of the embodiments described herein. References to “a particular embodiment” and the like refer to features that are present in at least one embodiment of the invention. Separate references to “an embodiment” or “particular embodiments” or the like do not necessarily refer to the same embodiment or embodiments; however, such embodiments are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to the “method” or “methods” and the like is not limiting. The word “or” is used in this disclosure in a non-exclusive sense, unless otherwise explicitly noted. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations, combinations, and modifications can be effected by a person of ordinary skill in the art within the spirit and scope of the invention. 
     PARTS LIST 
     
         
           31 ,  32 ,  33 ,  34 ,  35  printing module 
           38  print image 
           39  fused image 
           40  supply unit 
           42 ,  42 A,  42 B receiver 
           50  transfer subsystem 
           60  fuser 
           62  fusing roller 
           64  pressure roller 
           66  fusing nip 
           68  release fluid application substation 
           69  output tray 
           70  finisher 
           81  transport web 
           86  cleaning station 
           99  logic and control unit (LCU) 
           100  printer 
           102 ,  103  roller 
           104  transmission densitometer 
           105  power supply 
           109  interframe area 
           110  light beam 
           111 ,  121 ,  131 ,  141 ,  151  imaging member 
           112 ,  122 ,  132 ,  142 ,  152  transfer member 
           113 ,  123 ,  133 ,  143 ,  153  transfer backup member 
           124 ,  125  corona tack-down chargers 
           201  transfer nip 
           202  second transfer nip 
           206  photoreceptor 
           210  charging subsystem 
           211  measuring device 
           212  measuring device 
           213  grid 
           216  surface 
           220  exposure subsystem 
           225  development station 
           226  toning shell 
           227  magnetic core 
           240  power source 
           410  first electrode 
           415  second electrode 
           420  working volume 
           425  capacitance 
           430  voltage source 
           440  measuring device 
           450  processor 
           500  capacitor 
           503 ,  504   a ,  504   b  capacitor 
           512  toner particle 
           514 ,  514   a ,  514   b ,  514   c  carrier particle 
           520 ,  524   a ,  524   b  electric field line 
           531  area 
           534  chain 
           551  area 
           610  curve 
           620  configuration 
           690  curve 
           695  fit 
           710  development member 
           740  measurement device 
           810  provide electrodes step 
           815  connect source step 
           820  provide inductor step 
           825  apply bias or current step 
           830  measure current or voltage step 
           835  determine density step 
           850  apply biases or currents step 
           919  inductor 
           1030  current source 
           1040  voltmeter 
           1110  toning zone 
           1120 ,  1130  sensor 
           1122 ,  1132  working volume 
           1125 ,  1135  electrode 
           1160  patterning unit 
           1170  controller 
           1171  direction of rotation 
           1180  sump 
           1182  toner bottle 
           1184  gate 
           1210  arrange members step 
           1215  provide sensors step 
           1220  provide voltage source step 
           1225  provide measuring device step 
           1230  receive pixel data step 
           1235  produce latent image step 
           1240  move members step 
           1245  measure currents step 
           1250  compute to step 
           1253  adjust flow rate step 
           1256  add toner step 
           1370  controller 
           1410  arrange members step 
           1415  provide electrode step 
           1420  provide voltage source step 
           1425  provide measuring device step 
           1430  stop supply to photoreceptor step 
           1440  rotate member step 
           1445  measure currents step 
           1450  compute flow rate step 
           1453  adjust flow rate step 
         R n -R (n-6)  receiver 
         PC 1 -PC 5  imaging member 
         ITM 1 -ITM 5  transfer member 
         TR 1 -TR 5  transfer back up member 
         S slow scan direction