Patent Publication Number: US-7586507-B2

Title: Printer for recording on a moving medium

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This is a divisional application of Ser. No. 10/872,614, filed Jun. 21, 2004 now U.S. Pat. No 7,221,383. 

   FIELD OF THE INVENTION 
   This invention generally relates to pixel recording apparatus and methods and more particularly relates to an apparatus and method for recording pixels onto a photosensitive medium that is moving at a variable rate. 
   BACKGROUND OF THE INVENTION 
   Various types of apparatus have been developed or proposed for recording a pattern of pixels onto a photosensitive medium, using various types of light sources including LEDs and lasers. In the conventional model, image content is recorded onto photosensitive media, such as photosensitive film or paper, a full frame at a time. A number of pixel-based digital imaging apparatus follow this traditional model by modulating a full frame of pixels at one time for exposure of the image content. For example, various types of two-dimensional spatial light modulators, such as liquid crystal devices (LCDs) or digital micromirror devices (DMDs) can be used to provide a complete frame of image data for exposure. 
   As just one example, commonly-assigned U.S. Pat. No. 6,215,547 (Ramanujan et al.) discloses a writing apparatus employing a reflective LCD spatial light modulator for providing modulated light for exposure of a photosensitive medium, one image frame at a time. 
   In applying this conventional frame-based imaging model, the photosensitive medium is moved or indexed into position within an exposure apparatus and is then maintained in a stationary position during exposure of the pixel pattern within the image frame. The job of exposing successive pixel image frames onto a length of photosensitive medium requires successive steps for moving and stopping the media to record each frame. 
   It can be appreciated that constant starting and stopping of media movement has a number of drawbacks, particularly with respect to throughput and to the overall mechanical complexity of the film transport system. In response to the need for improved efficiency, a number of alternatives have been proposed. For example:
         U.S. Pat. No. 6,163,363 (Nelson et al.) discloses a DMD spatial light modulator used to expose an image onto a continuously moving photosensitive medium, one or more lines of pixels at a time.   Similarly, U.S. Pat. No. 5,953,103 (Nakamura) discloses a color printer using an array of modulated light sources that records four lines of pixels at a time by progressively indexing the media past a stationary printhead.   U.S. Pat. No. 5,968,719 (Nakamura) discloses a side printer for printing bar codes and other information onto a section of filmstrip media during processing.       

   While the above-listed patents describe methods for writing one or more lines of pixels onto moving photosensitive media, these methods are limited to applications in which the photosensitive medium moves through the exposure region at a relatively constant speed. There is a need to print digital watermark images onto motion picture photosensitive medium while the photosensitive medium is in motion. Such would be the situation in the manufacturing process of the motion picture photosensitive medium where forming latent watermarks images on the photosensitive medium would be done while the photosensitive medium was moving at high speeds. The prior art methods listed above would not be readily suitable for applications in which the photosensitive medium moves at variable speeds. 
   Addressing the problem of writing pixels at variable media speed, commonly-assigned U.S. Pat. No. 5,294,942 (Loewenthal et al.) discloses an apparatus for forming a pixel pattern, one line of pixels at a time, onto a medium that is moving at a variable rate. The apparatus of U.S. Pat. No. 5,294,942 tracks the speed of the moving photosensitive medium and adapts its pixel exposure timing, based on speed tracking results, to obtain a uniform exposure. The method and apparatus of U.S. Pat. No. 5,294,942 thus provides a more flexible solution for obtaining uniform exposure levels for recording pixels. For example, a pattern of pixels can be recorded on the leading or trailing end of a film roll without requiring that the film be moving through an exposure region at a constant speed. 
   However, while methods described in U.S. Pat. No. 5,294,942 and in related prior art enable the recording of a pixel pattern onto a continuously moving medium in line-by-line fashion, high-speed manufacturing and film processing environments can impose even further requirements. One area of particular concern relates to forming a latent image watermark onto a photosensitive medium during manufacture of the medium. 
   For example, as is disclosed in U.S. Patent Application 2003/0012569 (Lowe et al.), a latent watermark image can be exposed onto the “raw” photosensitive medium itself, at the time of manufacture. Then, when the medium is exposed with image content, the image frame is effectively overlaid onto the watermark pattern. Such a method is also disclosed in U.S. Pat. No. 6,438,231 (Rhoads). The Rhoads &#39;231 patent discloses this type of pre-exposure of the watermark onto the film emulsion within the frame area of negative film, for example. 
   It can be appreciated that watermark pre-exposure would have advantages for marking motion picture film at the time of manufacture or prior to exposure with image content. A length of motion picture film could be pre-exposed with unique identifying information, encoded in latent fashion, that could be used for forensic tracking of an illegal copy made from this same length of film. However, prior art watermarking techniques proposed for photosensitive media in general fall short of what is needed for motion picture watermarking, particularly watermarking during high-speed film manufacture. Problems that make it difficult or impractical to use conventional watermark application techniques for pre-exposure of film in manufacture relate to both throughput requirements and image quality. Among the problems with watermark application in high-speed manufacturing environments are the difficulty of exposure control, not only for maintaining a uniform exposure, but for modulating exposure to produce a watermark pixel pattern having a selectable number of grayscale levels. Another problem, not a factor during pixel-wise exposure at lower speeds, relates to pixel shape. That is, with the photosensitive medium moving at high speeds during pixel recording, there can be a significant amount of pixel elongation in the travel direction, visible as “smear.” Unfortunately, the amount of pixel smear varies with the speed of media travel, effectively changing the dimensions of the pixel depending on the specific rate of speed of the media past the exposure source. 
   Referring to  FIG. 1A , there is represented how a pixel  10  is recorded onto a photosensitive medium  12  by a pixel exposure source  14  when photosensitive medium  12  is stationary. ( FIG. 1A  elements are not to scale, but are represented to show the overall concept.) The exposure light beam from pixel exposure source  14  has a uniform power output density W (typically expressed in Watts/cm 2 ). This exposure level is enabled for a period of time (t), or exposure time, to create a density (D) where D=log H. As is well known in the imaging arts, exposure (H) is a function expressed in general terms as H=W−t. The overall shape of pixel  10  resembles the output shape of pixel exposure source  14 ; a circular output aperture of pixel exposure source  14  yields a substantially circular pixel  10 . In  FIG. 1A , pixel exposure source  14  has an output diameter of some arbitrary pixel size, depending on the application. Since pixel dimensions can vary over a range, the pixel diameter is simply considered as a normalized “pixel unit” in the description that follows. With reference to  FIG. 1A , latent image pixel  10  formed by exposure is 1 pixel unit in diameter and has a density level, D. As shown in  FIG. 1B , a density profile  32  in the direction along the length of the medium through the center of the pixel has a uniform density profile  32 , so that density D is fairly consistent across pixel  10 . 
   In contrast with  FIG. 1A ,  FIG. 2A  shows how an elongated pixel  20  is formed when photosensitive medium  12  is moving, in the direction of the arrow. Again,  FIG. 2A  is not to scale, but is sized for comparison with  FIG. 1A . For example, photosensitive medium  12  is transported in a length direction, termed its travel direction, at a velocity of V mm/t, during exposure time t. The resulting exposure on photosensitive medium  12  forms an elliptical pixel  20  with a dimension that is a factor of 1 pixel unit times V velocity. The elongated or elliptical shape of pixel  20 , also termed “smearing,” is caused by the movement of photosensitive medium  12  while pixel  20  is exposed. A density profile  32   a  through the center of pixel  20  shows non-uniform density, as is shown in  FIG. 2B . This non-uniformity of density occurs since the middle third of the mid section receives light for the full exposure time t while leading and trailing portions of pixel  20  receive light for a shorter time, which can be considered as the integrated time t/2. 
     FIGS. 3A and 3B  show a representative portion of a pixel pattern where photosensitive medium  12  is held stationary and where moving, respectively. Different shading is used to indicate that each individual pixel  10 ,  20  is also assigned a density level D. By comparing  FIGS. 3A and 3B , it is readily seen that different pixel  10 ,  20  shapes result, depending on whether or not photosensitive medium  12  is moving. Pixels  20  also exhibit a different density profile  32   a  depending on speed. Moreover, both the shape of pixel  20  in the travel direction and its density profile  32   a  will vary depending on the transport speed of photosensitive medium  12 . Thus, the change in pixel  20  shape and density profile  32   a  with transport speed complicates the task of forming latent indicia of any type onto photosensitive medium  12 . In addition, variation in pixel  20  shape and density profile  32   a  also make it difficult to modulate the relative density of pixel  20  to allow encoding of information corresponding to pixel  20  density. 
   Where the speed of photosensitive medium  12  is fairly slow, the actual effect of pixel  20  smearing, as represented in  FIG. 2A , is negligible. That is, the exposure time is so short that the basic response represented in  FIG. 1A  occurs for slow moving photosensitive medium  12 . On the other hand, the faster the speed of photosensitive medium  12 , the more pronounced is the elongation of pixel  20 . It can be appreciated by those skilled in the imaging arts that forming pixels  20  at very high film speeds can result in considerable distortion of pixel  20 . It can be difficult to control both the shape and the effective density of pixel  20 , particularly if the rate of photosensitive medium  12  speed changes. For instance, at the beginning or near the end of a spool of a film medium, the necessary acceleration or deceleration of the film medium would cause pixels  20  to have different dimensions relative to their dimensions at portions of the film medium when printed at full speed. Moreover, any attempt to control the density level of pixels  20  recorded at various media transport speeds would be particularly difficult using existing exposure timing techniques. Thus, it would be very difficult to record, in high-speed film manufacture or processing, a pattern of pixels  20  having consistent shape and having controllable effective density over all portions of a length of photosensitive medium  12 . 
     FIGS. 3B and 3C  show the elongated nature of pixels  20  and show how some amount of overlap can occur between adjacent pixels  20  in the length direction.  FIG. 3B  shows the spatial outlines of pixels  20  in dotted line form, with only two pixels  20  represented to show non-uniform density profiles  32   a , corresponding to two pixels  10  in  FIG. 3A . The overlap area between pixels  20  may effectively receive exposure for two pixels  20 ; however, the effect on density in this overlap area has been shown to be minimal, due to response characteristics of the media.  FIG. 3C  shows the inter-pixel timing in more detail, with a preferred timing of encoder pulses  28 , as described subsequently, and resulting density profiles  32   a  for each successive pixel  20  in the length direction. The combined effect of the applied exposure is shown as a pixel-to-pixel additive density profile  44 . Again, the additive density profile  44  shown in  FIG. 3C  is a first approximation; response characteristics of the media are a key factor in determining the effects of successive applications of exposure energy from different exposure sources in the overlap area of pixels  20 . 
   From an imaging perspective, properties of a watermark image or other indicia may need to meet high levels of quality. For example, complex watermark extraction methods may require that certain properties of watermark pixels be maintained in order to allow successful extraction of the encoded information. Pixel size and density are among key properties for this purpose. Thus, there is a need for methods of forming pixel patterns for watermarks and other latent indicia on photosensitive media, where the method compensates for acceleration/deceleration of the moving medium. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide an apparatus and method for recording a pattern of pixels onto a medium where pixel dimensions and densities are well controlled, regardless of the speed of the photosensitive medium during pixel exposure. With this object in mind, the present invention provides a method for forming a pixel having a predetermined density onto a sensitized recording medium moving in a length direction comprising:
         (a) energizing a pixel exposure source to begin exposure at the leading edge of a pixel and for a first predetermined time interval;   (b) de-energizing the pixel exposure source for a period depending on the predetermined density and on media transport speed;   (c) re-energizing the pixel exposure source at the termination of the period;   (d) de-energizing the pixel exposure source at the end of a second predetermined time interval to terminate exposure substantially at the trailing edge of the pixel; and   such that steps (a)-(d) are executed in sequence over the length of a single pixel.       

   From another aspect, the present invention provides a method for forming a pixel of a predetermined density by applying an exposure energy onto a photosensitive medium moving in a length direction comprising:
         (a) determining the pixel length from a leading edge of the pixel to a trailing edge of the pixel according to exposure, over an exposure interval, at maximum speed;   (b) defining a leading edge initiation time by associating the leading edge of the pixel to the timing of a positional signal from a feedback apparatus that is coupled with a media transport system;   (c) calculating an anticipated trailing edge termination time by associating a trailing edge of the pixel to the timing of the positional signal from the feedback apparatus coupled with the media transport system;   (d) initiating a first exposure pulse at the leading edge initiation time and applying the first exposure pulse for a first time period according to the predetermined density; and   (e) initiating a second exposure pulse after a delay period following termination of the first exposure pulse, such that the second exposure pulse terminates at the anticipated trailing edge termination time.       

   It is a feature of the present invention that it provides an apparatus capable of adapting pixel exposure to the transport speed of a photosensitive medium for maintaining dimensional and density control. 
   It is an advantage of the present invention that it controls the timing, rather than the overall intensity level, of the exposure sources used for pixel recording. 
   It is a further advantage of the present invention that it provides a consistent pixel recording apparatus and method, providing a robust image or other pixel pattern that is consistent within any portion of a length of media. 
   These and other objects, features, and advantages of the present invention will become apparent to those skilled in the art upon a reading of the following detailed description when taken in conjunction with the drawings wherein there is shown and described an illustrative embodiment of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter of the present invention, it is believed that the invention will be better understood from the following description when taken in conjunction with the accompanying drawings, wherein: 
       FIG. 1A  is a perspective view showing the conventional method of forming a pixel onto a stationary photosensitive medium; 
       FIG. 1B  is a graph showing a density profile for the conventional pixel formed onto a stationary medium; 
       FIG. 2A  is a perspective view showing how a pixel is formed onto a moving photosensitive medium; 
       FIG. 2B  is a graph showing a density profile for the pixel formed on a moving medium; 
       FIG. 3A  is a top view of an array of pixels formed in the conventional manner; 
       FIG. 3B  is a top view of an array of pixels formed onto moving medium; 
       FIG. 3C  is a graphical representation of pixel exposure area relative to timing and additive density due to pixel overlap; 
       FIG. 4  is a block diagram showing the basic components of a pixel forming apparatus; 
       FIG. 5  is a timing chart showing the relationship of encoder pulses to clock pulses; 
       FIG. 6  is a graph showing the relationship of the exposure drive pulse to density for one encoder pulse; 
       FIG. 7  is a graph showing a timing sequence used and the resultant exposure densities for each pulse of the dual-pulse modulation according to the present invention; 
       FIG. 8  is a graph showing relative relationship of the individual dual-pulse modulation exposure densities and their combination; 
       FIG. 9  is graph showing relative relationships of positioning, timing, and exposure signals for obtaining a desired density profile at one speed; 
       FIGS. 10A and 10B  are graphs showing the relative timing of encoder and driver signals for different media transport speeds; 
       FIG. 11  is graph showing relative relationships of positioning, timing, and exposure signals for obtaining a desired density profile at an alternate speed; 
       FIG. 12  is a graph showing driver timing for achieving a different density level according to the present invention; and 
       FIG. 13  is a functional block diagram of the logic and timing components for a pixel forming apparatus according to one embodiment. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present description is directed in particular to elements forming part of, or cooperating more directly with, apparatus in accordance with the invention. It is to be understood that elements not specifically shown or described may take various forms well known to those skilled in the art. 
   The term “indicia” (singular: indicium) as used in the present application comprises any type of discriminating mark, including the full range of pixel patterns that can be recorded onto photosensitive media. In broadest terms, the pixel recording apparatus and method of the present invention could be applied for recording image scene content, in pixel form, as latent indicia. Other types of latent indicia include watermarks, time stamps, batch identifiers, and other types of pixel patterns that would be useful to the manufacturer, processor, or end user of film and other sensitized media. These latent pixel patterns are typically within the image area of the sensitized media; however, latent indicia could alternately be formed along borders or edges of the media, wholly or partially outside the image area. 
   Apparatus 
   Referring to  FIG. 4 , there is shown, in block diagram form, the basic arrangement of components used in a pixel recording apparatus  30  of the present invention. A media transport apparatus  16  transports photosensitive medium  12 , which is typically fed from a roll  26 , past pixel exposure sources  14 . Pixel exposure sources  14  are typically arranged as a linear array of light sources, such as LEDs, and include any necessary lenses or other supporting optical components. An encoder  18  is coupled to media transport apparatus  16  for determining speed and position of photosensitive medium  12 . Encoder  18  provides this feedback to a control logic processor  22  that controls a driver  24  for each pixel exposure source  14 . Control logic processor  22  is some type of logic processor that provides driver  24  timing logic and other functions. In one embodiment, control logic processor  22  uses a dedicated microprocessor; other embodiments could include a computer workstation or other computing platform with appropriate software for modulating pixel exposure sources  14  according to timing and positional feedback signals and to image data for the pixel pattern to be recorded. 
   Encoder  18  provides information about the angular displacement of a rotating device such as a spool or drum. As is well known in the film handling arts, the diameter of the rotating device and the linear distance traversed at the surface of the device is proportional to its angular displacement. A sufficiently high-resolution encoder  18  would be used such that the placement of the pixel pattern can be aligned to perforations, notches, or other film features if required. Encoder  18  provides linear distance information used to dynamically adjust the effective exposure level and exposure time for pixel  20  formation, as described subsequently. 
   Determining Media Transport Speed 
   Referring to  FIG. 5 , there is shown a relationship of encoder pulses (ENC)  28  to clock cycles (CLK)  40 . CLK cycles  40 , typically generated from a crystal oscillator or other accurate frequency-generating componentry, provide a timing reference. ENC pulses  28  provide information on position of photosensitive medium  12 . Thus, as is well known to those skilled in positioning mechanisms, dividing the distance information provided from ENC pulses  28  by the timing information provided from CLK cycles  40  gives the travel speed of photosensitive medium  12  along travel direction D. 
   Determining Pixel  20  Dimensions 
   The goal of the apparatus and method of the present invention is to provide a mechanism for forming latent indicia onto a moving medium, wherein pixels  20  formed in the pixel pattern have consistent shape and density profile  32   a  characteristics, regardless of media transport speed. As was shown in the examples of  FIGS. 2A and 3B , pixels  20  formed during movement of photosensitive medium  12  are elongated, having a leading edge  34  and a trailing edge  36 , which bound the central area having concentrated density and a portion of smear area. Since the goal of the present invention is to provide pixels  20  of equal dimension regardless of the speed of photosensitive medium  12 , it is necessary to use, as a baseline condition, the worst-case dimensions for pixel  20 , that is, the length dimension L′ of pixel  20  when formed at the highest transport speed. This dimension then dictates the exposure timing for all transport speeds less than the maximum. (Note that in  FIG. 3B , pixels  20  are exaggerated in dimension, for the sake of description and to contrast the shape and density profile of elongated pixels  20 , exposed onto a moving medium, from conventional pixels  10  exposed onto a stationary medium as in  FIG. 3A . In practice, center-to-center spacing for elongated pixels  20  would be the same as center-to-center pixel spacing for conventional pixels  10 .) 
   Referring back to  FIG. 5 , it can be observed that length L′ of pixel  20  is related proportionally to some distance measurement obtained from encoder pulse  28 . That is, the time interval for exposure of a certain length of moving photosensitive medium  12  can be related to some number of encoder pulses  28 . To simplify the discussion that follows, pixel  20  length L′ is written during one half-cycle of encoder pulse  28 . (In actual practice, pixel  20  length L′ may be written during some multiple or fraction of encoder pulse  28 ; what is important is to observe that there is some synchronization between ENC pulses  28  and pixel-forming pulses.) 
     FIG. 6  shows the relationship of exposure timing to density, where an exposure pulse  42  has the duration of one half of one encoder pulse  28 , as shown. For this example, normalized density for a maximum media transport speed is expressed as 1.0. At this maximum speed, pixels  20  are formed with a 50% smear condition, as was represented in  FIG. 3C . Density profile  32   a  shows the maximum speed condition. Exposure begins when ENC pulse  28  goes high. The exposure source remains energized until encoder ENC pulse  28  goes low. The resulting exposure yields a smeared pixel  20  with non-uniform density profile  32   a , over the 1.5 pixel length shown. This profile then sets a baseline for the desired density to be obtained at any speed. 
   Decreasing media transport speed results in an increase in density above the normalized 1.0 value, as shown by a second density profile  32   b  in the graph of  FIG. 6 . Thus, in order to provide an equivalent 1.0 density exposure at lower speed, the applied exposure energy must be reduced. 
   One possible tactic for control of density is to dynamically vary the exposure level using amplitude modulation. However, as can be well appreciated, this requires dynamic modulation of the exposure intensity of pixel exposure source  14  in order to adapt to changing media transport speeds. It is readily recognized that dynamic control of this analog value would be difficult to achieve in practice. 
   An alternate approach is to adjust exposure pulse  42  timing using pulse-width modulation, PWM. With this method, the duration of exposure pulses  42  would be adjusted to provide a suitable amount of exposure energy based on media transport speed. PWM techniques could be employed to control pixel  20  density. However, this solves only part of the problem. With reference to  FIG. 6 , it has been shown that density profile  32   a  adds an amount of smear to the shape of pixel  20 . Thus, any solution for writing onto a moving medium must provide both control of pixel  20  density and control of pixel  20  shape. This added requirement for maintaining pixel  20  dimensions along with exposure control calls for an innovative approach to PWM timing. 
   Control of PWM Timing 
   Given that exposure is a factor of intensity multiplied by time, base-case conditions for exposure onto moving media occur where media transport speed is highest. Referring to  FIGS. 7 and 8 , there is given a first example showing the use of pulse width modulation for controlling both exposure energy level and duration. A first exposure pulse  42   a , initiated at time 0 and ending approximately at time 0.25, generates a density profile  32   c . Exposure pulse  42   a  provides sufficient exposure for obtaining a density level of 0.5 over a pixel length of about 1.25 pixel units dimension. A second exposure pulse  42   b , initiated at time 0.25 and ending approximately at time 0.5, generates a density profile  32   d . Exposure pulse  42   b  similarly provides sufficient exposure for obtaining a density level of 0.5 over a pixel length of about 1.25 pixel units dimension. As is shown along the length axes in  FIG. 7 , density profile  32   d  spatially trails density profile  32   c .  FIG. 8  shows the combined temporal pulses  42   a  and  42   b  and their resultant effect on density profiles  32   c  and  32   d  whose densities overlap over an area of travel from 0.25 to 1.25 pixel units. On the photosensitive medium, density profiles  32   c  and  32   d , timed differently as shown in  FIG. 7 , are additive, providing the 1.0 density profile indicated in combined density profile  32   d  of  FIG. 8 . In this way, the baseline density profile  32   a  of  FIG. 6 , obtained at the maximum media transport speed, can be achieved using a timed pair of exposure pulses  42   a  and  42   b.    
   From the example of  FIGS. 7 and 8 , it can clearly be seen that lesser densities than 1.0 can be obtained by applying exposure pulses  42   a ,  42   b  of shorter duration. However, it must again be emphasized that the same pixel  20  length dimensions must be maintained for any density. Thus, the timing of exposure pulses  42   a  and  42   b , and the duration of the variable interval between them, must be closely controlled for generating pixel  20  having suitable density and length dimensions. 
   Referring now to  FIG. 9 , the timing of exposure pulses  42   a  and  42   b  is represented relative to encoder pulse  28  and CLK cycle  40 . Notably, first exposure pulse  42   a  begins at the beginning of an encoder cycle, where the encoder  18  half-cycle is synchronous with the spatial location of pixel  20  placement. Second exposure pulse  42   b  ends at the half-cycle of encoder pulse  28 .  FIG. 9  represents the base-case, that is, the highest density (normalized to 1.0 as in the previous example of  FIGS. 6-8 ) at the maximum media transport speed. Thus, second exposure pulse  42   b  follows first exposure pulse  42   a  almost immediately, substantially providing exposure energy during the complete half-cycle of encoder pulse  28 . 
     FIGS. 10A and 10B  show, for comparison, the relative timing of first and second exposure pulses  42   a  and  42   b  for different media transport speeds.  FIG. 10A  shows timing for somewhat less than the full speed timing of  FIG. 9 . The duration of the encoder pulse  28  half-cycle is seven CLK cycles  40 ; this additional time compared to the six CLK cycles  40  of  FIG. 9  indicates a slightly slower speed. The duration of first exposure pulse  42   a , three CLK cycles  40  as shown, is given as a time t 3 . The duration of second exposure pulse  42   b , also three CLK cycles  40  as shown, is given as a time t 4 . In the example given here, exposure pulses  42   a  and  42   b  are of the same duration as shown in  FIG. 9  where the media in indicated to be at its highest speed. 
   Time intervals t 3  and t 4  are calculated based on the level of exposure energy needed to obtain the desired density for pixel  20 , when limited to an acceptable amount of smear. In one embodiment, time intervals t 3  and t 4  are equal. As shown in  FIGS. 10A and 10B , equal time intervals t 3  and t 4  provide the equivalent maximum density exposure, as was shown in  FIG. 9 . The resultant density profile  32  is similar to that shown subsequently in  FIG. 11 . 
   A first encoder pulse  28  begins at time t 0 ; the second encoder pulse  28  begins at time t 1 . A time t 5 , four CLK cycles  40  as shown, is defined as the interval from the beginning of encoder pulse  28  for the pixel to the beginning of second exposure pulse  42   b . Time t 5  can be computed as follows:
 
 t 5=(( t 1− t 0)/2)− t 4
 
     FIG. 10B  shows first and second exposure pulses  42   a  and  42   b  of equivalent duration to  FIG. 10A ; however, the number of CLK cycles  40  compared to encoder pulse  28  indicates relatively slow media transport speed in comparison with the  FIG. 10A  example. Corresponding encoder pulse timing t 0 ′ and t 1 ′ and timing intervals t 3 ′, t 4 ′, and t 5 ′ are indicated in  FIG. 10B . It is significant to note that interval t 3 ′ is equal to t 3 , interval t 4 ′ is equal to t 4 . In addition, the leading edge position of t 3 ′ corresponds to that of t 3 , and the tailing edge position of t 4 ′ corresponds to that of t 4 . Here, time t 5 ′ can be computed similarly:
   t 5′=(( t 1′− t 0′)/2)− t 4′ 
   The use of two exposure pulses  42   a ,  42   b  is significant for obtaining the proper dimensions of pixel  20 . Referring back to  FIG. 3B , in the two-pulse modulation scheme of the present invention, the first exposure pulse  42   a  begins at leading edge  34  of pixel  20  and the second exposure pulse  42   b  ends at trailing edge  36 . 
   It is worthwhile to observe that the calculation of time t 5  gives an accurate estimate for coordinating the timing of exposure pulse  42   b  with the location of trailing edge  36  of pixel  20 , as shown in  FIG. 3B . This estimate, used to anticipate the time corresponding to trailing edge  36 , is based on the latest available data on media transport speed, measured from preceding encoder pulses  28 . As is well known to those skilled in the motion control arts, the media transport speed does not change instantaneously; even while accelerating, the estimate from recent data is sufficiently close for computing time t 5  for accurate pixel  20  placement. 
   Varying the Density Level of Pixel  20   
   Referring to  FIGS. 11 and 12 , there are shown key timing and spatial relationships for exposure energy effects of each exposure pulse  42   a ,  42   b  in forming density profile  32   a  where different media transport speeds are shown and different density levels are needed. As was shown with reference to  FIG. 8 , exposure pulses  42   a  and  42   b  are additive. Again, although exposure pulses  42   a  and  42   b  are separated in time, there is some overlap over part of the area of pixel  20 . This overlap area receives twice the exposure energy, increasing the density obtained, to provide the required density profile  32   a , such as is shown for a 1.0 density in  FIG. 11  and for a 0.5 density in  FIG. 12 . 
   The example of  FIG. 11  provides the same density as in  FIGS. 8 through 10 . Similar to  FIG. 10A , with seven CLK cycle  40  pulses, or  FIG. 10B , with nineteen CLK cycle  40  pulses,  FIG. 11  has ten CLK cycle  40  pulses during the exposure period. Exposure pulses  42   a ,  42   b  are of the same duration and are separated appropriately for a speed that is less than the maximum. The 1.0 density maximum matches that achieved in  FIGS. 8 and 9 , but has a slightly different profile due to the slower media transport speed in  FIG. 11 . (Recall that both  FIGS. 8 and 9  show behavior at maximum speed.) It is important to observe that density profile  32   a  in  FIG. 11  extends over the same 1.5 pixel length as for the examples of  FIGS. 8 and 9 . 
     FIG. 12  shows how the practice of the present invention achieves a lesser density value at lower speeds. The media transport speed for  FIG. 12  matches that of  FIG. 11 . In  FIG. 12  the desired density needed is 50% or 0.5 normalized. In this case, first exposure pulse  42   a  begins at the time corresponding to leading edge  34  of pixel  20 , as in previous examples, but is half of the duration of a full density pulse at full speed. Thus, here, the duration of each exposure pulse  42   a  and  42   b  is approximately 1.5 CLK cycle pulses  40 . The stepped characteristic of density profile  32   a  in  FIG. 12  approximates that of a full density profile at any speed, scaled to a lower density value. The length dimension of pixel  20  is maintained at 1.5 units, as used in the examples of  FIGS. 8 through 11 . As media transport speed decreases to near zero, the stepped characteristic of density profile  32   a  for pixel  20  having less than full density is less pronounced than for full density. 
   As  FIGS. 11 and 12  show, changing the duration of exposure pulses  42   a  and  42   b  results in a different output density level. For the same density level at any speed, the duration of exposure pulses  42   a  and  42   b  is the same. The timing of exposure pulses  42   a  and  42   b  follows the same pattern, with first exposure pulse  42   a  beginning at the time corresponding to leading edge  34  of pixel  20  and with second exposure pulse  42   b  ending at the anticipated time calculated for trailing edge  36 . 
   By coordinating the timing of first and second exposure pulses  42   a  and  42   b  with the timing of encoder pulses  28 , the method of the present invention adapts the delivery of exposure energy to a variable transport speed for photosensitive medium  12 . Further, by fitting both exposure pulses  42   a  and  42   b  appropriately within the time period available for forming pixel  20 , the method of the present invention maintains the dimensional profile of pixel  20  over the range of possible transport speeds. In addition to providing the same density and general shape at varying transport speeds, the method of the present invention also allows the density itself to be varied over a range of discrete levels. For example, it can be advantageous to provide a watermark or other latent indicium having a density at one of 4 or 8 or 256 discrete values. For providing an image as the indicium, for example, it may be a requirement to provide at least 128 discrete density levels, preferably more. 
   Timing Control Circuitry 
   Referring to  FIG. 13 , there is shown a functional schematic block diagram of the components used for timing control of pixel exposure source  14  in one embodiment. This same component arrangement would be used for each individual pixel driver circuit, timing both first exposure pulse  42   a  of duration t 3  and second exposure pulse  42   b  of duration t 4  for each pixel  20 . 
   A counter  50  maintains a count of fixed frequency high-speed reference clock CLK cycles  40  that are gated by encoder pulse  28 , using, as a reset, a rising edge detection circuit  52  for each pixel  20 . At reset, a comparator  72  signals that a constant  68  has been satisfied and a timing control  74  circuit uses CLK cycles  40  to generate exposure pulse  42   a  for a duration appropriate for a density constant  76  corresponding to time interval t 3 . The specific duration is determined by processing indicia pattern data using a look up table (LUT)  60 . LUT  60  yields a predetermined value of counts of CLK cycles  40  needed to provide the necessary exposure interval for obtaining the desired density for pixel  20 . This first pulse is directed to gate  78  for controlling driver  24  for pixel exposure source  14 . 
   Similarly, counter  50  uses the count of the fixed frequency high-speed reference clock cycles  40  CLK to generate second exposure pulse  42   b . With this parallel arrangement, the output of counter  50  effectively yields the (t 1 −t 0 ) value described above with reference to  FIG. 10A . A divider  54  performs division by 2 and provides the resulting signal to a latch  56 . Latch  56  is gated off the rising edge of encoder pulse  28 , thereby storing the time duration of half of the preceding cycle as a predictive value for timing second exposure pulse  42   b  in this cycle. A subtractor  58  obtains a density constant  66  for interval t 4 . Subtractor  58  provides a stable value to comparator  62  for determining the timing interval t 5  for delay of second exposure pulse  42   b . A comparator  62  receives the present counter  50  value giving the amount of time since the beginning of the encoder cycle  28 . When comparator  62  indicates equivalency, the time t 5  has been reached. Comparator  62  output goes to a timing control component  64  which utilizes the t 4  count of CLK cycles to send second exposure pulse  42   b  through the same gated path to controlling driver  24  for pixel exposure source  14 . 
   The apparatus and method of the present invention thus provide a way to maintain the length dimension as well as overall density of each pixel  20  on photosensitive media  12  over the range of possible media transport speeds. Thus, for example, pixel  20  size and overall appearance are similar for pixels  20  written during ramp-up, during ramp-down, or during full speed operation. This means that the method and apparatus of the present invention are particularly well-suited for forming latent indicia on the media during manufacture. This method would have advantages in a manufacturing environment for film and other types of photographic media, for example, with possible application to other types of recording media, such as thermal and magnetic recording media, for example. In the most general case, pixel exposure source  14  applies some type of pixel-forming energy onto a sensitized medium, where the energy may be in the form of light, heat, or magnetic flux density, for example. 
   The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the scope of the invention as described above, and as noted in the appended claims, by a person of ordinary skill in the art without departing from the scope of the invention. For example, the control circuitry used could be embodied using a number of different designs, including the use of a programmable gate array or similar encoded device. While the embodiments described above use a pair of exposure pulses  42   a  and  42   b , the use of more than two pulses is possible, provided that the first pulse for a pixel begins at the leading edge position for the pixel and that the last pulse for the pixel end at the trailing edge position, so that pixel  20  has the desired dimensions. The use of more than two exposure pulses  42   a ,  42   b  could have a beneficial smoothing effect at the highest densities in some applications. However, at high media transport speeds, response characteristics of a sensitized medium may exhibit “reciprocity failure” familiar to those skilled in the photographic sciences, so that a photosensitive film would not have a linear, additive response to short pulses of exposure. Thus, for most media and transport speeds, the use of two exposure pulses  42   a  and  42   b  proves to be more advantageous than the use of more than two pulses. Exposure pulses  42   a ,  42   b  need not have equal duration as shown in the embodiments given above; however, it can be appreciated that this arrangement may simplify calculation and processing. 
   Pixel recording apparatus  30  as shown in  FIG. 4  can take a variety of forms. The timing sequence for pulse-width modulation of two or more exposure pulses  42   a  and  42   b  admits a number of options and variations from that described with reference to  FIGS. 7-12 . For example, the energy of the first pulse may be different from the energy of the second pulse. 
   As was noted with reference to  FIGS. 9 through 12 , the timing pattern used for the described embodiment employs a convenient synchronization arrangement in which a half-cycle of a single encoder pulse  28  corresponds to the spatial position of a single pixel  20 . Alternately, a different synchronization scheme could be used, with the spatial position of a single pixel  20  corresponding to some multiple or fraction of encoder pulse  28  cycles. 
   Thus, what is provided is an apparatus and method for recording pixels onto a sensitized recording medium that is moving at a variable rate, wherein pixel dimensions are maintained regardless of media transport speed. 
   PARTS LIST 
   
       
         10  pixel 
         12  photosensitive medium 
         14  pixel exposure source 
         16  media transport apparatus 
         18  encoder 
         20  pixel 
         22  control logic processor 
         24  driver 
         26  roll 
         28  encoder pulse 
         30  pixel recording apparatus 
         32  density profile 
         32   a  density profile 
         32   c  density profile 
         32   d  density profile 
         34  leading edge 
         36  trailing edge 
         40  clock cycle 
         42  exposure pulse 
         42   b  exposure pulse 
         42   b  exposure pulse 
         44  additive density profile 
         50  counter 
         52  rising edge detection circuit 
         54  divider 
         56  latch 
         58  subtractor 
         60  look up table (LUT) 
         62  comparator 
         64  timing control component 
         66  density constant 
         68  constant 
         72  comparator 
         74  timing control component 
         76  density constant 
         78  gate