Abstract:
A speckle readhead includes a light source that outputs light towards an optically rough surface. Light scattered from this surface contains speckles. The scattered light is imaged onto an image detector, captured and stored. Subsequently, a second image is captured and stored. The two images are repeatedly compared at different offsets in a displacement direction. The comparison having the highest value indicates the amount of displacement between the readhead and the surface that occurred between taking the two images. An optical system of the readhead includes a lens and an aperture. The aperture can be round, with a diameter chosen so that the average size of the speckles is approximately equal to, or larger than, the dimensions of the elements of the image detector. The dimension of the aperture in a direction perpendicular to the direction of displacement can be reduced. Thus, the imaged speckles in that direction will be greater than the dimension of the image detector elements in that direction. Such a readhead is relatively insensitive to lateral offsets. The lens can be a cylindrical lens that magnifies the relative motion along the direction of displacement but does not magnify relative motions in the direction perpendicular to the direction of displacement. The optical system can also be telecentric. Thus, the readhead is relatively insensitive to both separation and relative motions between the readhead and the surface. The light source can be modulated to prevent smearing the speckles across the image detector. The light source can be strobed to freeze the image.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     This invention is directed to transducing positional displacements using speckle-image-correlation. 
     2. Description of Related Art 
     Various known devices use speckle images and correlation between speckle images to determine deformations and/or displacements. A speckle image is generated by illuminating an optically rough surface with a light source. Generally, the light source is a coherent light source, and more particularly, is a laser-generating light source, such as a laser, a laser diode, and the like. After the optically rough surface is illuminated by the light source, the light scattered from the optically rough surface is imaged onto an optical sensor, such as a charge-coupled device (CCD), a semi-conductor image sensor array, such as a CMOS image sensor array, or the like. 
     Prior to displacement or deformation of the optically rough sensor, a first speckle image is captured and stored. Subsequently, after deformation or displacement of the optically rough surface, a second speckle image is captured and stored. The previous and subsequent speckle images are then compared on a pixel by pixel basis. In particular, a plurality of comparisons are performed. In each comparison, the previous and subsequent speckle images are offset relative to each other, and the amount of offset is increased by one image element, or pixel, between each comparison. In each comparison, the image value of a particular pixel in the previous image is multiplied by, or subtracted from, the corresponding subsequent image pixel (based on the amount of offset) and the result is accumulated. The offset having the greatest correlation between the subsequent and previous images will generate a peak or a trough when the offset is plotted against the total accumulated value. 
     For example, U.S. Pat. No. 4,794,384 discloses a mouse which uses speckle-image-correlation to determine two dimensional motion directions of a mouse. In particular, in the 384 patent, the speckle-image-correlation does not need to be performed at a high rate and the accuracy only needs to be on the millimeter range. 
     U.S. Pat. No. 4,967,093 discloses systems and methods for measuring deformation of an object using speckle-image-correlation. In particular, the 093 patent describes in detail various conventional methods for comparing two speckle images and for determining when to update a current reference speckle image with a new reference speckle image. Similarly, published Japanese Patent Application 8-271231, published October 1996, discloses additional methods for avoiding accumulating error in a speckle-image-based displacement gage. 
     Finally, published Japanese Patent Application 5-52517, published March 1993, discloses a speckled-image-based displacement meter that uses a rectangular or elliptically shaped slit  51  in a slit plate  5 . The light beam from the laser light source passes through the slit  51  before it illuminates the optically rough surface. Thus, the light beam is shaped by the slit  51 . The shaped light beam allows an amount of displacement in a main displacement direction to be measured with high sensitivity while displacement components in a perpendicular direction relative to the main displacement direction do not effect the sensitivity of the device. 
     SUMMARY OF THE INVENTION 
     However, the above-described conventional speckle-image-correlation systems either determine surface displacement of speckle images to analyze body deformations and strain, where it is desirable to maximize the speckle effect of all surface motions, for determining low-resolution motions generated by a computer mouse or other low-resolution measurement devices. In particular, in these conventional speckle-image-correlations systems, there is usually no need to determine, to a high degree of accuracy, the motion of the rigid body along one or more prescribed axes of motion. 
     In those prior art devices that use speckle-image-correlation in high-accuracy positioning encoders and the like, the practical problems that effectively prevent determining position to a high resolution in a commercially marketable form have not been adequately considered. In particular, these prior art high-accuracy positioning encoders and the like implicitly assume that highly stable structures and highly accurate bearing systems can be used in particular implementations of such speckle-image-correlation, high-accuracy positioning encoders and the like. However, such high-precision mechanical systems are expensive. Furthermore, at the high levels of resolution and accuracy that are commercially demanded in the art, even high-accuracy mechanical systems exhibit unwanted measurement errors, due to play the in bearings, non-planar surfaces, and the like. 
     This invention provides speckle-image-correlation-based position transducers that enable high-resolution determination of position or displacement. 
     This invention separately provides speckle-image-correlation-based position transducers that have reduced sensitivity to lateral offsets. 
     This invention further provides speckle-image-correlation-based position transducers that have reduced sensitivity to lateral offsets by having an aperture which is longer in the direction parallel to the direction of displacement than the aperture is in a direction perpendicular to the direction of displacement. 
     This invention further provides speckle-image-correlation-based position transducers that have reduced sensitivity to lateral offsets by placing a cylindrical lens between the optically rough surface and a detector. 
     This invention separately provides speckle-image-correlation-based position transducers that have reduced sensitivity to separations between the optically rough surface and the light source and/or a detector in a direction normal to the optically rough surface. 
     This invention further provides speckle-image-correlation-based position transducers that are relatively insensitive to relative motions between the optically rough surface and the light source and/or detector in the direction normal to the optically rough surface. 
     This invention separately provides speckle-image-correlation-based position transducers that are usable to determine displacement for optically rough objects moving at a relatively high velocity. 
     This invention further provides speckle-image-correlation-based position transducers that strobe the light source to freeze the image during the exposure time of the imaging device to determine displacement for optically rough objects moving at a relatively high velocity. 
     This invention separately provides speckle-image-correlation based position transducers that have an improved cost/performance ratio. 
     This invention separately provides speckle-image-correlation based position transducers that have improved robustness and economy. 
     In various exemplary embodiments of the speckle-image-correlation-based position transducers according to this invention, a light source outputs a light beam towards an optically rough surface. Due to diffraction, the light scattered from the optically rough surface contains a random pattern of bright spots, or speckles. The light scattered from the optically rough surface is imaged onto an image detector having a two-dimensional array of light-sensitive elements. The image captured on the image detector is input and stored. Subsequently, a second image is captured and stored. The two images are then compared on a pixel-by-pixel basis, first without any offsets between the two images in a particular displacement direction. The two images are then compared, each time at a different offset in the particular displacement direction. The comparison having the highest, or lowest, comparison value indicates the amount of displacement of the optically rough surface relative to the light source that occurred between taking the two images. 
     In particular, in the various exemplary embodiments of the speckle-image-correlation-based position transducers according to this invention, an optical system is placed between the optically rough surface and the image detector. In various exemplary embodiments, the optical system includes a lens and a pinhole aperture. In various exemplary embodiments of the optical system, the pinhole aperture is round and has a diameter chosen so that the average size of the speckles of the random speckle pattern is at least approximately equal to, and in various exemplary embodiment, larger than, the dimensions of the square light-sensitive elements of the image detector. 
     In other exemplary embodiments of the optical system, the dimension of the pinhole aperture in the direction perpendicular to the direction of displacement is reduced. As a result, the image of the speckles in the direction perpendicular to the direction of displacement is greater than the dimension of the light-sensitive elements of the image detector in that direction. Accordingly, speckle-image-correlation-based position transducers having such pinhole apertures become relatively insensitive to lateral offsets. 
     In yet other exemplary embodiments of the optical system, the lens is a cylindrical lens that magnifies the relative motions along the direction of displacement but does not magnify relative motions in the direction laterally perpendicular to the direction of displacement. In yet even other exemplary embodiments of the optical system, the optical system is telecentric. As a result, the speckle-image-correlation-based position transducers becomes relatively less sensitive to both separation between the optical system and the optically rough surface, as well as any relative motions between the optical system and the optically rough surface. 
     In various exemplary embodiments of the speckle-image-correlation-based position transducers according to this invention, the light source is modulated to prevent smearing of the speckle images across the array of light-sensitive elements of the image detector. In particular, in various exemplary embodiments, the light source is strobed for a short period of time to effectively freeze the image during the exposure time of the image detector, which is significantly longer than the strobe period of the light source. 
     In various exemplary embodiments of the speckle-image-correlation-based position transducer according to this invention, the light source, the optical system, and the image detector are incorporated into a readhead which is moving relative to the optically rough surface, along a one-dimensional displacement axis. In particular, in various exemplary embodiments of the light source, the light source is an optically coherent light source. In particular, in various exemplary embodiments of the coherent light source, the coherent light source is a laser. 
     In a first exemplary embodiment, the light beam emitted by the light source is emitted at an angle relative to an optical axis of the optical system. The optically rough surface scatters the speckle pattern towards the optical system, which images the speckle pattern on the image detector. In a second exemplary embodiment, the light beam emitted by the light source is emitted at an angle relative to the optical axis of the optical system onto a beamsplitter. That beamsplitter redirects the emitted light beam so that the beam is parallel to the optical axis before the light beam is scattered off the optically rough surface. The optically rough surface scatters the light beam back along the optical axis, through the optical system, including the beamsplitter, and onto the image detector. 
     In a third exemplary embodiment of the optical system, the light beam is emitted by the light source along the optical axis. In this third exemplary embodiment, the optical system is integrated into a block of material that is optically transparent at the wavelength of the light beam emitted by the light source. In particular, the lens of the optical system is either formed integrally with the block of material or is adhesively attached to block of material. Additionally, in this third exemplary embodiment, rather than a pinhole aperture formed in an otherwise opaque material, the integral optical system includes a semi-transparent thin film that is deposited onto one surface of the optically transparent material across the optical axis. 
     In particular, this semi-transparent thin film acts as a reverse pinhole, in that the semi-transparent thin film reflects only as much of the scattered light beam as normally is passed by the pinhole aperture. The reverse pinhole semi-transparent thin film redirects the scattered light beam within the block of optically transparent material, to a fully reflective thin-film formed on an opposite side of the block of optically transparent material. The fully reflective thin-film then reflects the speckle image pattern onto the image detector. 
     These and other features and advantages of this invention are described in or are apparent from the following detailed description of various exemplary embodiments of the systems and methods according to this invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various exemplary embodiments of this invention will be described in detail, with reference to the following figures, wherein: 
     FIG. 1 is a top plan view of a first exemplary embodiment of a position measuring device incorporating a speckle-image-correlation optical position transducer according to this invention; 
     FIG. 2 is a top plan view of an optically diffusing, or optically rough, surface usable with the various exemplary embodiments of the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 3 is an exploded perspective view of a second exemplary embodiment of a position measuring device incorporating the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 4 is a perspective view of a third exemplary embodiment of a position measuring device incorporating the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 5 is a perspective view of a fourth exemplary embodiment of a position measuring device incorporating the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 6 is a perspective view of a fifth exemplary embodiment of a position measuring device incorporating the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 7 illustrates the general operation and arrangement of various elements of various exemplary embodiments of the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 8 illustrates the arrangement and operation of a first exemplary embodiment of a readhead of the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 9 illustrates the arrangement and operation of a second exemplary embodiment of a readhead of the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 10 illustrates the arrangement and operation of a third exemplary embodiment of a readhead of the speckle-image-correlation optical position transducer according to this invention; 
     FIG. 11 is a graph illustrating the results of comparing first and second captured speckled images when offset at various pixel displacements; 
     FIG. 12 is a block diagram outlining one exemplary embodiment of the signal generating and processing circuitry of the speckle-image-based optical position transducer according to this invention; 
     FIG. 13 illustrates a first exemplary embodiment of a speckle pattern formed using the speckle-image-correlation optical position transducer according to this invention; and 
     FIG. 14 illustrates a second exemplary embodiment of a speckle pattern formed using the speckle-image-correlation optical position transducer according to this invention. 
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     FIG. 1 is a plan view of a first exemplary embodiment of a position measuring device  100  incorporating a speckle-image-based optical position transducer according to this invention. As shown in FIG. 1, the position measuring device  100  includes a scale member  102  and a readhead assembly  106 . In particular, an optically diffusing, or optical rough, surface  104  of the scale member  102  is positioned adjacent to an open, or illuminating, end of the readhead assembly  106 . Another surface of the readhead assembly  106  includes a plurality of control buttons  105  and a position or displacement value display device  107 . 
     In various exemplary embodiments, the display  107  is a liquid crystal display. However, the display  107  can be any known or later developed display device, including an LED display device or the like. The control buttons  105  include a millimeter/inch toggle button, and on/off button, and a set zero position button. The millimeter/inch toggle button  105  toggles the display between displaying the displacement or position in millimeter and in inches. The set zero position button  105  resets the current position of the readhead relative to the scale member as the zero position. Thus, any subsequent measurements made using the position measuring device  100  will be made relative to the reset zero position. 
     FIG. 2 shows a portion of the scale member  102  in greater detail. In particular, as shown in FIG. 2, the optically diffusing, or optically rough, surface  104  of the scale member  102  diffracts or otherwise scatters light used to illuminate the optically diffusing, or optically rough, surface  104 . Thus, when the optically diffusing, or optically rough, surface  104  is illuminated and scatters light towards a light detecting device, such as a camera, an electronic or digital camera, a CCD array, an array of CMOS light sensitive elements or the like, the scattered light has regions where the optically diffusing, or optically rough, surface  104  causes the diffracted light waves to positively or negatively superimpose in the image plane of the light detecting device. As a result, the image captured by the light detecting device will contain a pattern of relatively bright spots, or speckles, where the diffracted light waves positively combined to form a peak, and relatively dark spots where the diffracted light waves have negatively combined to cancel out. 
     The image captured by the light detecting device has an intensity pattern that depends primarily on the portion of the optically diffusing, or optically rough, surface  104  that scatters the light captured by the light detecting device and the characteristics of the optical path. In particular, the intensity pattern generated by any illuminated portion of the optically diffusing, or optically rough, surface  104  is random. The randomness of the intensity pattern is due solely to the surface properties of the optically diffusing, or optically rough, surface  104 . In particular, the optically diffusing, or optically rough, surface  104  does not need to be ruled or intentionally patterned in any way to generate the intensity pattern. Thus, the random intensity pattern of any illuminated portion of the optically diffusing, or optically rough, surface  104  is not dependent upon any marks that need to be placed on the surface  104 . 
     FIG. 3 shows a second exemplary embodiment of the position measuring device  100 . As shown in FIG. 3, the position measuring device  100  includes the scale member  102  having the optically diffusing, or optically rough, surface  104 . In particular, as shown in FIG. 3, the scale member  102  has a channel  112  formed in it that receives a separate insert member  103  having the optically diffusing, or optically rough, surface  104 . Thus, the scale member  102  can have a variety of different types of optically rough inserts  103  usable with a speckle-image-correlation-type readhead, as disclosed below. The scale member  102  includes a pair of arms  108  and  120  that extend perpendicularly from the scale member  102  relative to a measurement axis  300  of the optically diffusing, or optically rough, surface  104 . 
     The readhead assembly  106  includes a base member  124  and a readhead  126 . In particular, the scale member  102  is positionable in a slot  125  of the base member  124 . When the scale member  102  is positioned in the slot  125 , the optically diffusing, or optically rough, surface  104  faces an open, or illuminating, end of the readhead  126 . The readhead  126  is then attached to the base member  124  to securely hold the scale member  102  in the slot  125  so that the optically diffusing, or optically rough, surface  104  is positioned at a generally stable distance from a light source and an optical system housed in the readhead  126  of the readhead assembly  106 . 
     Like the scale member  102 , the base member  124  includes a pair of arms  116  and  118  that extend perpendicularly to the base member  124  relative to the measurement axis  300 . In particular, the arms  108  and  116  oppose each other at their faces  114 . Thus, the arms  108  and  116  are particularly useful for measuring outside dimensions of an object to be measured. In contrast, the arms  118  and  120  have measurement surfaces  122  that face away from each other. Thus, the arms  118  and  120  are particularly useful for measuring inside diameters of objects, such as holes, voids, and the like. 
     FIGS. 1 and 3 show the readhead assembly  106  as a self-contained device with operating control buttons and displays. However, in other exemplary embodiments, the readhead  126  can be used independently of the guiding base member  124  and the base member  102 . 
     FIGS. 4-6 show third-fifth exemplary embodiments of the position measuring device  100 . FIGS. 4-6 illustrate that the optically diffusing, or optically rough, surface  104  may be provided as an integral surface of a separately existing mechanism, and that the functions of the readhead  126  can be operated and displayed via remote electronics. FIG. 5 illustrates that the readhead  126  may be used to measure the motion of a rotating surface along a tangential direction. Thus, the readhead  126  can be used to infer the rotational displacement of a rotating surface or disk. Similarly, FIG. 6 illustrates that the readhead  126  may be used to measure the motion of a rotating cylinder along a tangential direction. Thus, the readhead  126  can be used to infer the rotational displacement of a rotating cylinder or shaft. 
     Additionally, as shown in FIGS. 4-6, the readhead assembly  106  does not need to be physically combined with a specially designed or provided scale member  102 . Rather, the readhead  126  can be mounted on a first portion  410  of a machine or device  400 . In particular, the machine or device  400  includes the first portion  410  and a second portion  420  that can move relative to the first portion  410  along or about at least one rotational or translational axis. Of course, it should be appreciated that this means that one of the first and second portions  410  and  420  is stationary in some frame of reference, and that the other one of the first and second portions  410  and  420  moves along or about the at least one rotational or translational axis in that frame of reference. 
     In particular, in FIGS. 4-6, the second portion  420  has an optically diffusing, or optically rough, portion  422  that is positionable within the field of view of the optical system housed in the readhead  126 . That is, this optically diffusing, or optically rough, portion  422  of the second portion  420  forms the optically diffusing, or optically rough, surface  104  discussed above with respect to FIGS. 1-3 and below with respect to FIGS. 7-14. 
     As shown in FIG. 4, the second portion  420  can have a generally planar surface  421  that includes the optically diffusing, or optically rough, portion  422 . In the exemplary embodiment illustrated in FIG. 4, the machine or device  400  can be a machine tool, such as a vision system having a planar stage or a milling machine having a planar X-Y table on which a workpiece to be milled can be positioned. In this case, the second portion  420  is the generally planar stage or table. In general, such generally planar second portions  420  can translate relative to the readhead assembly  106  along either one or both of two orthogonal axes  401  and  403 . 
     In FIG. 4, the readhead  126  can be mounted to a surface  402  of the machine or device  400 . This surface  402  can be an integral part of the machine or device  400 , or an added mounting bracket. In the exemplary embodiment shown in FIG. 4, the surface  402  is aligned parallel to the expected axis of motion of the optically diffusing, or optically rough, portion  422 . The surface  402  may also include a ledge (not shown) or a mark that is aligned parallel to the optically diffusing, or optically rough, portion  422 . 
     An alignment surface  127  of the readhead  126 , which abuts the surface  402 , is constructed so that when the surface  402  is aligned parallel to the axis of relative motion of the optically diffusing, or optically rough, portion  422 , the intensity pattern created on the imaging array of elements in the image detector of the readhead  126  by the light scattered from the optically diffusing, or optically rough, portion  422  translates across the array in a direction corresponding to a known predetermined spacing of the imaging array elements, during relative motion. That is, the alignment surface  127  serves to externally establish the expected alignment of the internal components of the readhead  126 , relative to the expected relative motion to be measured. It should be noted that internal optical path may be bent or “twisted”. In this case, the imaging array itself does not need to be physically aligned parallel to the external alignment surface  128 . 
     The alignment surface  127 , positioned relative to the surface  402 , establishes the most critical alignment of the readhead  126 . However, the alignment surface  127  does not ensure that the readhead  126  observes precisely in a direction normal to the optically diffusing, or optically rough, portion  422 . However, when the readhead  126  observes precisely in a direction normal to the optically diffusing, or optically rough, portion  422 , the most robust and accurate alignment configuration for most embodiments of the readhead  126  is obtained. Therefore, as shown in FIG. 4, the readhead  126  can further include a second alignment surface  128 . An alignment feature  406  is arranged parallel to the optically diffusing, or optically rough, portion  422  and to the expected axis of travel of the optically diffusing, or optically rough, portion  422 . When the second alignment surface  128  is aligned parallel to the alignment feature  406 , the alignment of the readhead  126  so that it observes in a direction normal to the optically diffusing, or optically rough, portion  422  is obtained. 
     In various exemplary embodiments of the speckle-correlation-based readhead  126  shown in FIG. 4, the optically diffusing, or optically rough, surface  104  is formed as an integral portion of a guided member of an existing machine. For instance, the guided member of the machine can be the moving table of a machine tool that moves in one direction. Alternatively, the guided member of the machine can be the moving x-y table of a microscope that moves parallel to the plane defined by the surface  104 . It should be appreciated that the displacement determining methods described herein for using a single direction in an imaging detector to measure displacement of a surface along a first axis can also be applied along a second orthogonal direction in an imaging detector, to measure displacement of the same surface along a second axis orthogonal to the first axis. This may be done using two separate and orthogonal 1-dimensional imaging detector arrays, using the two orthogonal directions of a 2-dimensional imaging detector array, or using two separate 2-dimensional detector arrays, where each detector array is used to measure displacement in one of the two orthogonal dimensions. 
     In contrast, as shown in FIG. 5, the second portion  420  can have a more or less generally circular shape and a generally planar surface that includes the optically diffusing, or optically rough, portion  422 . In the exemplary embodiment illustrated in FIG. 5, the machine or device  400  can be a rotor of a motor, a rotary encoder or any other known or later developed element that rotates about the rotational axis  403  relative to the readhead  126 . It should also be appreciated that, in various other exemplary embodiments, the readhead  126  and the first portion  410  are the devices that rotate about the axis  403  in the particular frame of reference. In this case, the second portion  420  and the optically diffusing, or optically rough, portion  422  can have any desired shape and in particular do not need to be circular in any way, so long as the annular field of view swept out by the optical system of the readhead assembly  106  remains substantially within the bounds of the optically diffusing, or optically rough, portion  422  as the readhead  126  rotates about the rotational axis  403 . 
     As shown in FIG. 6, in contrast to both the third and fourth exemplary embodiments, in the fifth exemplary embodiment, the second portion  420  can have a more or less cylindrical shape and a generally cylindrical surface that includes the optically diffusing, or optically rough, portion  422 . In the exemplary embodiment illustrated in FIG. 6, the machine or device  400  can be a rotor of a motor, a rotary encoder, a pulley or a belt on a pulley, or any other known or later developed element that rotates about the rotational axis  403  relative to the readhead  126 . It should also be appreciated that, in various other exemplary embodiments, the readhead  126  and the first portion  410  are the devices that rotate about the axis  403  in the particular frame of reference. In this case, the second portion  420 , outside of the region occupied by the optically diffusing, or optically rough, portion  422 , can have any desired shape and in particular does not need to be cylindrical in any way, so long as the optically diffusing, or optically rough, portion  422  is cylindrical so that the readhead assembly  106  will remain at a substantially constant distance from the optically diffusing, or optically rough, portion  422  as the readhead  126  rotates about the rotational axis  403 . 
     FIG. 7 generally illustrates the operation and general arrangement of various optical elements of the speckle-image-based optical position transducer according to this invention. As shown in FIG. 7, a light beam  134  emitted by a light source (not shown) is directed onto the optically diffusing, or optically rough, surface  104  and illuminates a portion of the optically diffusing, or optically rough, surface  104 . As a result, the illuminated portion of the optically diffusing, or optically rough, surface  104  both scatters and diffracts light about an optical axis  144 . 
     It should be appreciated that, when the optical axis or direction of scattered light is discussed herein, the optical axis or direction of scattered light is defined by the central ray of the scattered light, where the central ray is that ray that passes through the centers of the lens  140  and the pinhole aperture  152 . 
     The light scattered and/or diffracted from the illuminated portion of the optically diffusing, or optically rough, surface  104  about the optical axis  144  passes through a lens  140 . In various exemplary embodiments, the lens  140  collects the light  136  scattered from the illuminated portion of the optically diffusing, or collects the scattered light  136  from optically rough, surface  104 . In general, when the lens  140  collects the light  136  gathered from the illuminated portion of the optically diffusing, or optically rough, surface  104 , and the limiting aperture  152  is located at the back focal plane of the lens  140 , the optical system becomes telecentric. 
     The lens  140  then projects the collected light  142  from the illuminated portion of the optically diffusing, or optically rough, surface  104  onto a pinhole plate  150  having a pinhole aperture  152 . In particular, the lens  140  is spaced from the plate  150  having the pinhole aperture by a distance f, which is equal to the focal length of the lens  140 . Moreover, it should be appreciated that the pinhole plate  150  having the pinhole aperture  152  is spaced from the illuminated portion of the optically diffusing, or optically rough, surface  104  by a distance h. 
     In particular, by locating the plate  150  at the focal distance of the lens  140 , the optical system of the speckle-image-based optical position transducer according to this invention becomes telecentric. In particular, in telecentric systems, the optical system, and thus the speckle-image-based optical position transducer according to this invention, becomes relatively less sensitive to changes in the gap distance h. Moreover, by using a pinhole  152  in the pinhole plate  150 , the speckle size and the dilation of the speckle pattern depends solely on the dimensions of the pinhole  152  and, more particularly, becomes independent of any lens parameters of the lens  140 . 
     The collected light  142  from the lens  140  passes through the pinhole  152 . In particular, the light  154  passed by the pinhole  152  is projected along the optical axis  144  and onto an array  166  of image elements  162  of a light detector  160 . In particular, the light detector  160  can be a charge-coupled device (CCD), an array of CMOS light sensitive elements, or any other known or later developed type of light sensitive material or device that can be organized into an array of independent and individual light sensing elements. In particular, the surface of the array  166  of the light sensitive elements  162  onto which the passed portion  154  of the collected light  142  from the lens  140  is separated from the plate  150  by distance d. More particularly, the speckle size depends only on the angle α subtended by the dimensions of the pinhole  152  and a distance d between the pinhole plate  150  and the surface formed by the array  166  of image elements  162  of the light detector  160 . 
     The approximate size D of the speckles within the detected portion of the light received from the illuminated portion of the optically diffusing, or optically rough, surface  104  onto the array  166  of image elements  162  is: 
     
       
           D ≈λ/tan(α)=(λ* d )/ w   (1) 
       
     
     where: 
     λ is the wavelength of the light beam  134 ; and 
     w is the diameter of a round pinhole. 
     In various exemplary embodiments, typical values for Eq. 1 include: λ=0.6 μm, d=10 cm (100,000 μm), and w=1 mm (1,000 μm). As a result, the approximate speckle size D is 60 μm. 
     FIG. 8 shows a first exemplary embodiment of the readhead assembly  106  useable with the speckle-image-based optical position transducer according to this invention. As shown in FIG. 8, the readhead assembly  106  includes the light source  130 , the lens  140 , the pinhole plate  150  having the pinhole  152  and the light detector  160  having the array  166  of the image elements  162 . The readhead assembly  106  also includes signal generating and processing circuitry  200 . One exemplary embodiment of the signal generating and processing circuitry  200  is described below with respect to FIG.  12 . 
     As shown in FIG. 8, a signal line  132  from the signal generating and processing circuitry  200  is connected to the light source  130  and provides a drive signal to drive the light source  130 . In response to the drive signal on the signal line  132 , the light source  130  outputs the beam of light  134  to illuminate a portion of the optically diffusing, or optically rough, surface  104 . In various exemplary embodiments, the light source  130  can be a white-light source. In this case, the light will generate an image of the illuminated portion, which can be projected onto the array  166  of the image elements  162 . However, while this image can be correlated in the same way that a speckle image can be correlated, this image will not include speckles formed by scattering from the optically diffusing, or optically rough, surface  104 . 
     In various other exemplary embodiments, the light source  130  is a coherent light source. In general, the coherent light source  130  will be a laser beam emitting light source. However, any other known or later developed coherent light source that is capable of emitting a coherent beam of light can be used in place of a laser. 
     When the coherent light source  130  is driven by the drive signal on the signal line  132  and outputs the coherent light beam  134 , the coherent light beam  134  illuminates a portion of the optically diffusing, or optically rough, surface  104  that lies along the optical axis of the optical system of the readhead assembly  106 . In particular, the light  136  scattered from the illuminated portion of the optically diffusing, or optically rough, surface  104  is gathered by the lens  140 . The collected light  142  from the lens  140  is projected along the optical axis  144  onto the pinhole plate  150  and passes through the pinhole  152 . The portion of the light  154  passing through the pinhole  152  is projected along the optical axis  144  onto the array  166  of the image elements  162  of the light detector  160 . A signal line  164  connects the light detector  160  and the signal generating and processing circuitry  200 . In particular, each of the image elements  162  of the array  160  can be individually addressed to output a value representing the light intensity on that image element  162  over the signal line  164  to the signal generating and processing circuitry  200 . 
     In the first exemplary embodiment of the readhead assembly  106  shown in FIG. 8, the coherent light beam  134  emitted by the coherent light source  130  is emitted at a non-normal angle to the optical axis  144 . Because the light beam  134  is at a non-normal angle to the optical axis  144 , if the light beam  134  underfills the effective field of view of the optically diffusing, or optically rough, surface  104 , changes in the gap distance h between the pinhole  152  and the illuminated portion of the optically diffusing, or optically rough, surface  104  effectively changes the portion of the optically diffusing, or optically rough, surface  104  that actually contributes to the speckle pattern projected onto the light detector  160 . This change is independent of any relative movement along the measurement axis  300  between the readhead assembly  106  and the optically diffusing, or optically rough, surface  104 . As a result, if the light beam  134  underfills the effective field of view of the optically diffusing, or optically rough, surface  104 , the positions of speckles in the light  136  scattered from the optically diffusing, or optically rough, surface  104  will be imaged onto the array  166  of the image elements  162  at positions that depend upon the gap distance or separation h. Thus, if the light beam  134  underfills the effective field of view of the optically diffusing, or optically rough, surface  104 , such displacements of the speckle pattern onto the array  166  of the image elements  162  due solely to undesirable changes in the gap separation or distance h will be incorrectly converted into apparent translations between the readhead assembly  106  and the optically diffusing, or optically rough, surface  104 . 
     FIG. 9 illustrates the arrangement and operation of a second exemplary embodiment of the readhead assembly  106  of the speckle-image-based optical position transducer according to this invention. As shown in FIG. 9, the readhead assembly  106  includes the coherent light source  130 , the lens  140 , the pinhole plate  150  having the pinhole  152 , the light detector  160  having the array  166  of the image elements  162 , and the signal generating and processing circuitry  200 , as shown in the first exemplary embodiment shown in FIG.  8 . However, the second exemplary embodiment of the readhead assembly  106  also includes a beam splitter  138  positioned between the pinhole plate  150  and the light detector  160 . 
     In particular, the coherent light beam  134  emitted by the coherent light source  130  no longer directly illuminates the illuminated portion of the optically diffusing, or optically rough, surface  104 , as in the first exemplary embodiment of the readhead assembly  106  shown in FIG.  8 . Rather, the coherent light beam  134  is directed onto the beam splitter  138 , which redirects the coherent light beam  134  along the optical axis  144 , and through the pinhole  152  and the lens  140 , before the coherent light beam  134  illuminates the illuminated portion of the optically diffusing, or optically rough, surface  104 . 
     As in the first exemplary embodiment of the readhead assembly  106  shown in FIG. 8, the illuminated portion of the optically diffusing, or optically rough, surface  104  scatters light  136  onto the lens  140 . The lens  140  directs the collected light  142  passing through the lens  140  onto the pinhole plate  150 . The pinhole  152  passes the portion of light  154  and directs it onto the array  166  of the image elements  162 . 
     In particular, in this second exemplary embodiment of the readhead assembly  106 , the readhead assembly  106  is generally more compact than the first exemplary embodiment of the readhead assembly  106  shown in FIG.  8 . Additionally, in various exemplary embodiments, the second exemplary embodiment of the readhead assembly  106  delivers better characteristics for the speckles, because it is able to produce speckles having a higher contrast than the speckles in the first exemplary embodiment of the readhead assembly  106  shown in FIG.  8 . 
     Likewise, because the coherent light beam  134  is projected along the image axis  144  before the redirected coherent light beam  134  illuminates the illuminated portion of the optically diffusing, or optically rough, surface  104 , changes in the gap separation or distance h between the illuminated portion of the optically diffusing, or optically rough, surface  104  and the pinhole plate  150  does not cause the portion of the optically diffusing, or optically rough, surface  104  actually illuminated by the coherent light beam  134  to be displaced, as in the first exemplary embodiment of the readhead assembly  106  shown in FIG.  8 . Thus, the second exemplary embodiment of the readhead assembly  106  shown in FIG. 9 is easier to operate over a large range of gaps h, and is more independent of the gap h and any changes in the gap separation or distance h that may occur between image capture operations. 
     Finally, because the coherent light beam  134  is redirected along the optical axis by the beam splitter  138 , it is easier to align the optical elements of the readhead assembly  106  and to obtain the collected light  142  from the lens  140 . However, because of the additional elements and the need to precisely align the light beam  134  with the optical axis  144  after it is redirected by the beam splitter  138 , the second exemplary embodiment of the readhead assembly  106  is more complicated to assemble and more costly to manufacture than the first exemplary embodiment of the readhead assembly  106  shown in FIG.  8 . 
     FIG. 10 shows a third exemplary embodiment of the readhead assembly  106  sable with the speckle-image-based optical position transducer according to this invention. As shown in FIG. 10, the optical system comprising the physically independent lens  140  and the physically independent pinhole plate  150  and, optionally, the physically independent beam splitter  138 , as discussed above, is replaced by an integral or combined optical system  170 . 
     In particular, the readhead assembly  106  includes the coherent light source  130 , the optical system  170 , which includes a integrally formed or otherwise attached lens  140 , a reverse pinhole metal film  172 , and a reflective metal film  174  all integrally formed with, formed on, or otherwise attached to a block of material  176  that is optically transparent to the particular wavelength of the coherent light beam  134  emitted by the coherent light source  130 . The third exemplary embodiment of the readhead assembly  106  shown in FIG. 10 also includes the light detector  160  having the array  166  of the image elements  162  and the signal generating and processing circuitry  200 . 
     In operation, in the third exemplary embodiment of the readhead assembly  106  shown in FIG. 10, the coherent light beam  134  emitted by the coherent light source  130  is aligned with the optical axis  144  when emitted. The coherent light beam  134  passes through the semi-transparent metal film  172  deposited on one surface of the block of optically transparent material  176  and passes through the semi-transparent metal film  172  and the lens  140  and illuminates an illuminated portion of the optically diffusing, or optically rough, surface  104 . In various other exemplary embodiments, the metal film can be fully reflective, and include a small opening or hole through which the light beam  134  can pass. 
     The light  136  scattered from the illuminated portion of the optically diffusing, or optically rough, surface  104  passes through the lens  140  and is projected onto the semi-transparent metal film  172 . In particular, the lens  140  can be formed integrally with the block of optically transparent material  176 . Alternately, the lens  140  can be a separately formed element that is later attached to the block of optically transparent material  176 . In various exemplary embodiments, the lens  140  is adhesively attached to the block of optically transparent material  176 . However, it should be appreciated that any other known or later developed method for attaching the separately formed lens  140  to the block of optically transparent material  176  can be used. 
     The semi-transparent metal film  172  acts as a reverse pinhole, in that the semi-transparent metal film  172  reflects only as much of the light  142  from the lens  140  onto the reflective metal film  174  as would be passed by the pinhole  152  in the pinhole plate  150  in the first and second exemplary embodiments of the readhead assembly  106  shown in FIGS. 8 and 9. That is, in the first and second exemplary embodiments of the readhead assembly  106  shown in FIGS. 8 and 9, the pinhole plate  150  blocks most of the light  142  projected onto the pinhole plate  150  by the lens  140 . The pinhole  152  passes only a portion  154  of the collected light  142  projected onto the pinhole plate  150 . 
     Similarly, the semi-transparent metal film  172  effectively reflects only a portion of the light  142  from the lens  140  onto the reflective metal film  174 . In particular, the portions of the collected light  142  which are not reflected by the semi-transparent metal film  172  onto the reflective metal film  174  exit the block of optically transparent material  176 . These portions of the light  142  are thus removed in the same way that the portions of the collected light  142  blocked by the pinhole plate  150  in the first and second exemplary embodiments of the readhead assembly  106  are removed. Thus, the semi-transparent film  172  acts as a “reverse” pinhole. 
     The portion of the light  173  reflected by the semi-transparent metal film  172  is directed onto the reflective metal layer  174 . The reflective metal layer  174  redirects the portion of the light  173  out of the block of optically transparent material  176  and onto the array  166  of the image elements  162  of the light detector  160 . 
     In particular, in the third exemplary embodiment of the readhead assembly  106 , the portion of light  136  scattered from the illumination portion of the optically diffusing, or optically rough, surface  104  is folded to reduce the dimensions of the readhead assembly  106 . Not only is this configuration of the readhead assembly  106  more compact, it is also more robust, as it is less sensitive to temperature variations than either the first or second exemplary embodiments of the readhead assembly  106  shown in FIGS. 8 and 9. 
     Regardless of which exemplary embodiment of the readhead assembly  106  is implemented in a particular speckle-image-based optical position transducer according to this invention, the signal generating and processing circuitry  200  operates essentially the same. In particular, the signal generating and processing circuitry  200  outputs a drive signal on the signal line  132  to drive the coherent light source  130  to emit the coherent light beam  134 . The light beam  134  illuminates a portion of the optically diffusing, or optically rough, surface  104 . The light scattered and diffracted from the illuminated portion of the optically diffusing, or optically rough, surface  104  is imaged onto the array  166  of the image elements  162  of the light detector  160 . The signal generating and processing circuitry  200  then inputs a plurality of signal portions over the signal line  164 , where each signal portion corresponds to the image value detected by one of the individual image elements  162 . The signal portions received from the light detector  160  by the signal generating and processing circuitry  200  for a particular image are then stored in memory. 
     A short time later, the signal generating and processing circuitry  200  again drives the coherent light source  130  and inputs an image signal from the light detector  106  over the signal line  164 . In various exemplary embodiments, the subsequent image is generated and captured within approximately  100  Us of the previous image. However, it should be appreciated that any appropriate time period between capturing the previous and subsequent images can be used. In particular, an appropriate time period will depend upon the dimensions of the array  166 , especially the dimensions of the array  166  in the direction along the measurement axis  300 , the magnification of the image projected onto the array  166  by the optical system of the readhead assembly  106  and the velocity of relative displacement between the readhead assembly  106  and the optically diffusing, or optically rough, surface  104 . In particular, the second image must be generated and acquired within a sufficiently short time period that the previous and subsequent images are sufficiently overlapped that a correlation between the two images can be determined. 
     In particular, the subsequent and previous images are processed to generate a correlation function. In practice, the subsequent image is shifted digitally relative to the previous image over a range of offsets that includes an offset that causes the two images to align. The correlation function is simply a measure of the amount of offset required to get the two images to align as the images are digitally shifted. It should be appreciated that any known or later developed algorithm can be used to determine the correlation function between the subsequent and previous images. 
     Referring back briefly to FIGS. 4-6, position signals from the readhead assembly  106  can be transmitted to remotely located signal processing electronic over a cable  430 . It should be appreciated that, in various exemplary embodiments corresponding to the third-fifth exemplary embodiments shown in FIGS. 4-6, the readhead assembly  106  can include the signal generating and processing circuitry  200 . In this case, the position value signals are output over the cable  430  to the remotely located signal processing electronics. In contrast, in various other exemplary embodiments corresponding to the third-fifth exemplary embodiments shown in FIGS. 4-6, the readhead assembly  106  can exclude, except for the light detector interface  230  discussed below, the signal generating and processing circuitry  200 . In this case, the image signals from the light detector  160  are output over the cable  430  to the remotely located signal processing electronics. The remotely located signal processing electronics will include, in this case, those portions of the signal generating and processing circuitry  200  excluded from the readhead assembly  106 . 
     Alternatively, in various other exemplary embodiments, the remotely located signal processing electronics can input the image signals from the light detector interface  230  or position signals from the signal generating and processing circuitry  200  and output signals compatible with servo systems, such as numerically controlled machine tools and the like. 
     For those exemplary embodiments where the readhead assembly  106  rotates relative to a stationary second portion  420 , the cable  430  can be replaced with a wireless link to allow the readhead assembly to communicate with the remotely located signal processing electronics. In various exemplary embodiments, the wireless link can be an infrared transmitter, a radio-frequency transmitter, such as a digital or analog cellular telephone transmitter, or any other known or later developed wireless link. In this case, the wireless receiver can be connected directly to the remotely located signal processing electronics or can be connected to the remotely located signal processing electronics over a distributed network and/or a switched telephone network. 
     FIG. 11 shows one exemplary embodiment of a correlation function. In particular, the correlation function includes a plurality of discrete data points that are separated by a predetermined distance. This distance depends upon the effective center-to-center spacing between the individual image elements  162  in the direction along the measurement axis  300  and the amount of magnification of the displacement of the optically diffusing, or optically rough, surface  104  by the optical system of the readhead assembly  106 . 
     For example, if the effective center-to-center spacing of the image elements  162  in the direction along the measurement axis is 10 μm, and the optical system of the readhead assembly  106  magnifies the surface displacement by 10×, then a 1 μm displacement of the illuminated portion of the optically diffusing, or optically rough, surface  104  will be magnified into a 10 μm displacement of the speckle pattern on the image elements  162 . 
     Each data point is generated by digitally shifting the subsequent image relative to the previous image by the effective center-to-center spacing of the image elements  162  in the direction along the measurement axis  300 . Because, in this case, the effective center-to-center spacing of the image elements  162  corresponds to a 1 μm displacement of the optically diffusing, or optically rough, surface  104 , the discrete data points will be separated in this case by a distance of about 1 μm. In particular, the correlation function of FIG. 11, which is displayed in arbitrary units, will have a peak, or a trough, at the displacement value where the image, or intensity, pattern in each of the previous and subsequent images align. In the exemplary embodiment shown in FIG. 11, this peak occurs at a displacement of approximately 20 pixels or image elements  162 . 
     A true peak finding algorithm is then used to determine the location of the actual peak at a sub-pixel accuracy. In particular, this peak finding algorithm is an interpolation routine that fits a second order, or higher order, curve to the correlation function. In general, only the discrete data points that are substantially higher than the background noise level are used in this peak finding algorithm. 
     In various exemplary embodiments of the signal generating and processing circuitry  200 , the subsequent image is stored as the previous image and a third, new subsequent image is acquired and compared to the stored previous image and the displacement is determined. This process is then continuously repeated. In contrast, in various other exemplary embodiments of the signal generating and processing circuitry  200 , the subsequent image is stored in place of a previous image only when the displacement between the two images rises above a predetermined threshold amount of displacement. 
     FIG. 12 is a block diagram outlining one exemplary embodiment of the signal generating and processing circuitry  200 . As shown in FIG. 12, the signal generating and processing circuitry  200  includes a controller  210 , a light source driver  220 , a light detector interface  230 , a memory  240 , a comparing circuit  250 , a comparison result accumulator  260 , an interpolation circuit  270 , a position accumulator  280 , a display driver  290  and an optional input interface  295 . 
     The controller  210  is connected to the light source driver  220  by a control line  211 , to the image detector interface  230  by a signal line  212 , and to the memory  240  by a signal line  213 . Similarly, the controller  210  is connected by signal lines  214 - 217  to the comparing circuit  250 , the comparison result accumulator  260 , the interpolation circuit  270  and the position accumulator  280 , respectively. Finally, the controller  210  is connected to the display driver  290  by a control line  218  and, if provided, to the input interface  295  by a input signal line  219 . The memory  240  includes a previous image portion  242 , a current, or subsequent, image portion  244  and a correlation portion  246 . 
     In operation, the controller  210  outputs a control signal over the signal line  211  to the light source driver  220 . In response, the light source driver  220  outputs a drive signal to the coherent light source  130  over the signal line  132 . Subsequently, the controller  210  outputs a control signal to the image detector interface  230  and to the memory  240  over the signal lines  212  and  213  to store the signal portions received over the signal line  164  from the light detector  160  corresponding to each of the image elements  162  into the previous image portion  242  or the current image portion  244 . In particular, the image values from the individual image elements  162  are stored in a two-dimensional array in the previous image portion  242  and the current image portion  244  corresponding to the positions of the individual image elements  162  in the array  166 . 
     Once a first image is stored in the previous image portion  242 , the controller  210  waits the predetermined short time period to again output the control signal on the signal line  211  to the light source driver  220  to again drive the coherent light source  130 . The image detector interface  230  and the memory  240  are then controlled using signals on the signal lines  212  and  213  to store the resulting image in the current image portion  244 . 
     Then, the controller  210  outputs a signal on the signal line  214  to the comparing circuit  250 . In response, the comparing circuit  250  inputs an image value for a particular pixel from the previous image portion  242  over a signal line  252  and inputs the image value for the corresponding pixel, based on the current offset, from the current image portion  244  over the signal line  252 . The comparing circuit  250  then applies the particular correlation algorithm to determine a comparison result. The comparing circuit  250  outputs the comparison result on a signal line  254  to the comparison result accumulator  260  for the current correlation offset. Once the comparing circuit  250  has extracted and compared the image value for each of the image elements  162  from the previous image portion  242  and compared them to the corresponding image value stored in the current image portion  244 , applied the correlation algorithm and output the comparison result to the comparison result accumulator  260 , the value stored in the comparison result accumulator  260  defines the correlation value in absolute units, as shown in FIG.  11 . The controller  210  then outputs a signal over the signal line  215  to the comparison result accumulator  260  and to the memory  240  over the signal line  213 . As a result, the correlation algorithm result stored in the comparison result accumulator  260  is output and stored in the correlation portion  246  of the memory  240  at a location corresponding to the current offset. 
     The controller  210  then outputs a signal on the signal line  215  to clear the result accumulator  260 . Once all of the comparisons for all of the desired offsets between the previous image stored in the previous image portion  242  and the current image stored in the current image portion  244  have been performed by the comparing circuit  250 , and the results accumulated by the comparison result accumulator  260  over a signal line  262  and stored in the correlation portion  246  under control of the controller  210 , the controller  210  outputs a control signal over the signal line  216  to the interpolation circuit  270 . 
     In response, the interpolation circuit  270  inputs the correlation results stored in the correlation portion  246  over the signal line  252  and determines the location of a peak or trough of the correlation function and interpolates the data points around and including the peak/trough of the correlation function to fit a curve to the peak/trough of the correlation function to determine the actual sub-pixel displacement. The interpolation circuit  270  then outputs, under control of the signal from the signal controller  210  over the signal line  216 , the determined actual sub-pixel displacement value on the signal line  272  to the position accumulator  280 . The position accumulator  280 , under control of the signal from the signal controller  210  over the signal line  217 , adds the displacement value on the signal line  272  to an accumulated displacement stored in the position accumulator  280 . The position accumulator  280  then outputs the updated position displacement to the controller  210  over the signal line  282 . In response, the controller outputs the updated displacement value to the display driver  290  over the signal line  218 . The display driver  290  then outputs drive signals over the signal line  292  to the display device  107  to display the current displacement value. 
     The input interface  295 , if provided, provides an interface between the millimeter/inch button  105  over a signal line  296 , the on/off button  105  over a signal line  297  and the set zero position button  105  over a signal line  298 . The input interface  295  provides an interface between these buttons  105  and the controller  210  and outputs the control signals from the buttons  105  over one or more signal lines  219  to the controller  210 . However, it should be appreciated that the input interface  295  can be omitted, along with the signal lines  219 . In this case, the signal lines  296 - 298  from the various buttons  105  on the readhead assembly  106  are connected directly to the controller  210 . 
     As indicated above, any convenient or appropriate known or later developed correlation algorithm can be used by the comparing circuit  250  to compare the previous image stored in the previous image portion  242  with the current image stored in the current image portion  244  on a pixel-by-pixel basis based on the current offset. In particular, each of the previous and current or subsequent images comprises M×N pixels arranged in a two dimensional array of M rows of pixels and N columns of pixels. One convenient correlation algorithm is:                R        (   p   )       =       [       ∑     q   =   1     M          (       ∑     m   =   1     N              I   1          (   m   )       *       I   2          (     p   +   m     )           )       ]     /   M             (   2   )                                
     where: 
     is the current displacement or offset value, in pixels; 
     R(p) is the correlation value for the current displacement value; 
     q is the current row counter; 
     m is the current pixel counter for the current row; 
     I 1  is the image value for the current pixel in the previous image; and 
     I 2  is the image value for the subsequent or second image. 
     It should be appreciated that cyclical boundary conditions are assumed. 
     As indicated in Eq. 2, the correlation for each row is obtained and summed. The sum is then averaged over the M rows to obtain an average, and noise-reduced, correlation function. This average correlation function is desirable to ensure that the data points will be stable to roughly the resolution to be obtained by interpolating the correlation function peak. Thus, to obtain roughly nanometer resolution by interpolating the correlation peak when each data point represents approximately 1μ the data points need to be stable roughly to the desired nanometer resolution value. 
     To achieve this subpixel resolution and accuracy, a function f(x) is numerically fit to the peak data point and the data points, surrounding the peak data point, that are well above the noise level  310  . Subsequently, to find the actual displacement peak for the numerically fit function f(x), i.e., to find the absolute maximum or minimum of the numerically fit function f(x), the numerically fit function f(x) is differentiated to determine the displacement value x when the slope of f(x) is equal to zero. 
     In various exemplary embodiments, the numerically fit function f(x) is a quadratic function. However, it should be appreciated that other functions can be used. It should also be appreciated that this method is applicable not only to the correlation method shown in Eq. 2, but also to other methods. For example, it is possible to determine the displacement by subtracting shifted images and finding the minimum in the resulting correlation function. 
     As indicated above, in speckle correlation, the previous and subsequent speckle images are acquired before and after displacement. The previous and subsequent speckle images are then correlated to determine the displacement. To achieve high resolution, it is important that the average speckle size be approximately equal to, or larger than, the pixel size of the image elements  162  of the light detector  160 . Moreover, in various exemplary embodiments of the readhead  126  according to this invention, the average speckle size is greater than, and in other exemplary embodiments is up to three to four times, the pixel size of the image elements  162 . For linear encoders, which have a motion only along a single measurement axis  300 , a linear correlation is determined for each row. Then, the correlation functions for all rows are averaged, as outline above with respect to Eq. 2. 
     Since the speckle size is approximately equal to, or larger than, the pixel size, lateral displacements in directions perpendicular to the measurement direction  300  that occur between acquiring the subsequent and previous images result in a significant de-correlation in the compared speckle patterns. This thus causes substantial positional errors to be generated. The speckle size at the object plane, the plane of optically diffusing, or optically rough, surface  104 , in the direction perpendicular to the measurement direction is approximately equal to the size of the individual elements  162  in the direction perpendicular to the measurement axis  300  divided by the magnification in the direction perpendicular to the measurement axis  300 . Accordingly, any lateral motion greater than this speckle size results in effectively a complete de-correlation between the previous and subsequent images. 
     In various exemplary embodiments of the readhead assembly  106  of the speckle-image-based optical position transducer according to this invention, the pinhole  152  of the pinhole plate  150  is modified to shape the speckles such that the speckles are substantially elongated in the direction perpendicular to the measurement axis  300  relative to the size of the image elements  162  in the direction perpendicular to the measurement axis  160  divided by the corresponding magnification value. Consequently, the same speckle distribution will be sampled by a given row as the optically diffusing, or optically rough, surface  104  is displaced laterally in the direction perpendicular to the measurement axis. 
     In particular, both the size and the shape of the speckles is determined by the shape and size of the pinhole aperture  152 . Conventionally, only circular pinholes have been used. Such circular pinholes generate the speckle pattern shown in FIG.  13 . Such circular pinholes produce speckles that have approximately equal lengths and widths, statistically, in the directions along and perpendicular to the measurement axis  300 . In contrast, by shaping the pinhole  152  so that it is no longer circular, the speckles are shaped as shown in FIG.  14 . In particular, FIG. 14 was generated using a rectangular pinhole  152 , with the long leg of the rectangular pinhole  152  extending along the measurement axis  300 . In particular, this rectangular pinhole  152  has a large aspect ratio. As FIG. 14 clearly shows, the speckles are elongated in the direction perpendicular to the measurement axis  300 . Therefore, the same speckle distribution will sampled by a given row even if the optically diffusing, or optically rough, surface  104  is laterally displaced one or more pixels in the direction perpendicular to the measurement axis  300 . Thus, the correlation and the accuracy will be unaffected by such lateral displacements. 
     In the various exemplary embodiments described above, and especially in the exemplary embodiments of the position measuring device  100  shown in FIGS. 1 and 3, it is possible to move the readhead assembly  106  relative to the scale member  102  along the measurement axis  300  at relative high speeds. However, such high speed relative motion between the readhead assembly  106  and the scale member  102  are problematic, because the speckle images captured by the light detector  160  are effectively smeared across the array  166  of individual image elements  162 . This is analogous to an effect that occurs in cameras, when the image is smeared across the film when objects within the field of view move a substantial distance while the camera shutter is open. 
     As indicated above, in the speckle-image-based optical position transducers according to this invention, the optic system of the readhead assembly  106  is designed so that the speckles have a size in the image projected onto the array  166  of the image elements  162  that is approximately equal to, or larger than, the size of the image elements  162 . In contrast, the speckles in the plane of the optically diffusing, or optically rough, surface  104  have a size that is smaller by the magnification value of the optic system of the readhead assembly  106 . 
     If the image array is operated to have an exposure time τ and the readhead moves relative to the optically diffusing, or optically rough, surface  104  along the measurement axis  300  at a velocity v, the speckles will thus move a distance Δ=v*τ during the exposure τ. For example, for many uses of the position measuring devices  100 , the readhead assembly  106  will move at a velocity relative to the optically diffusing, or optically rough, surface  104  along the measurement axis  300  at a velocity v of 1 m/s. Additionally, in various exemplary embodiments, the light detector  160  will have an exposure time τ of approximately 100 μs. In this case, the distance Δx will be approximately 100 μm, which is much larger than the effective pixel size at the object plane, which is approximately equal to, or larger than, the speckle size at the object plane. As a result, at these speeds, the speckle-image-based optical position transducer according to this invention will not function. 
     To avoid this difficulty, in various exemplary embodiments of the speckle-image-based optical position transducers according to this invention, the coherent light source  130  may be strobed for a short period of time τ′ that is much less than the exposure time τ for the light detector  160 . This effectively freezes the image of the illuminated portion of the optically diffusing, or optically rough, surface  104  during the longer exposure time τ of the light detector  160 . For example, if the velocity v is 1 m/s and the strobe time τ′ is 0.1 μs, then the distance Ax is 0.1 μm. Because this is much smaller than the speckle and pixel size on the object plane, minimal smearing occurs. 
     Additionally, by strobing the light source  130  for the short strobe period τ′, it is possible to obtain much higher peak power from the light source  130 , by biasing it at much high power levels. 
     While this invention has been described in conjunction with the exemplary embodiments outlined above, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, the exemplary embodiments of the invention, as set forth above, are intended to be illustrative, not limiting. Various changes may be made without departing from the spirit and scope of the invention.