Abstract:
An apparatus is disclosed for capturing image information. The apparatus includes a waveguide having opposed planar input and output faces. A diffractive optical element (DOE) is formed across the waveguide. The DOE is configured to couple a portion of the light passing through the waveguide into the waveguide. The light coupled into the waveguide is directed via total internal reflection to an exit location on the waveguide. The apparatus further includes a light sensor having an input positioned adjacent the exit location of the waveguide to capture light exiting therefrom and generate output signals corresponding thereto. A processor determines the angle and position of the coupled light with respect to the input face of the waveguide based on the output signals.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to U.S. Provisional Patent Application No. 62/163,733, filed on May 19, 2015, entitled “DUAL COMPOSITE LIGHT FIELD DEVICE”, which is hereby incorporated by reference in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The subject invention relates to an optical device that is used in an augmented reality system. The augmented reality system is of the type that includes a planar waveguide for transmitting a view of the world while also generating and delivering computer generated images to the user. In the subject invention, one or more additional waveguides are provided to capture images from the world. 
       BACKGROUND OF THE INVENTION 
       [0003]    There is considerable interest in developing systems that create an augmented reality for a user. In one example of such a system, the user would be provided with a head mounted device that includes a window for viewing the outside world. The window would have the capability to generate image information and project that image information into the eyes of the user. In such a system, images of an imaginary object could be generated and added to the real world scene. 
         [0004]    A description of a device for creating an augmented reality can be found in U.S. Patent Publication No. 2015/0016777, published Jan. 15, 2015, the disclosure of which is incorporated herein by reference. 
         [0005]    As described in the latter publication and illustrated in  FIG. 1  herein, the optical system  100  can include a primary waveguide apparatus  102  that includes a planar waveguide  1 . The planar waveguide is provided with one or more diffractive optical elements (DOEs)  2  for controlling the total internal reflection of the light within the planar waveguide. The optical system further includes an optical coupler system  104  and a control system  106 . 
         [0006]    As best illustrated in  FIG. 2 , the primary planar waveguide  1  has a first end  108   a  and a second end  108   b , the second end  108   b  opposed to the first end  108   a  along a length  110  of the primary planar waveguide  1 . The primary planar waveguide  1  has a first face  112   a  and a second face  112   b , at least the first and the second faces  112   a ,  112   b  (collectively,  112 ) forming a partially internally reflective optical path (illustrated by arrow  114   a  and broken line arrow  114   b , collectively,  114 ) along at least a portion of the length  110  of the primary planar waveguide  1 . The primary planar waveguide  1  may take a variety of forms which provide for substantially total internal reflection (TIR) for light striking the faces  112  at less than a defined critical angle. The planar waveguides  1  may, for example, take the form of a pane or plane of glass, fused silica, acrylic, or polycarbonate. 
         [0007]    The DOE  2  (illustrated in  FIGS. 1 and 2  by dash-dot double line) may take a large variety of forms which interrupt the TIR optical path  114 , providing a plurality of optical paths (illustrated by arrows  116   a  and broken line arrows  116   b , collectively,  116 ) between an interior  118  and an exterior  120  of the planar waveguide  1  extending along at least a portion of the length  110  of the planar waveguide  1 . The DOE  2  may advantageously combine the phase functions of a linear diffraction grating with that of a circular or radial symmetric zone plate, allowing positioning of apparent objects and a focus plane for apparent objects. The DOE may be formed on the surface of the waveguide or in the interior thereof. 
         [0008]    With reference to  FIG. 1 , the optical coupler subsystem  104  optically couples light to the waveguide apparatus  102 . As illustrated in  FIG. 1 , the optical coupler subsystem may include an optical element  5 , for instance a reflective surface, mirror, dichroic mirror or prism to optically couple light into an edge  122  of the primary planar waveguide  1 . The light can also be coupled into the waveguide apparatus through either the front or back faces  112 . The optical coupler subsystem  104  may additionally or alternatively include a collimation element  6  that collimates light. 
         [0009]    The control subsystem  106  includes one or more light sources and drive electronics that generate image data that is encoded in the form of light that is spatially and/or temporally varying. As noted above, a collimation element  6  may collimate the light, and the collimated light is optically coupled into one or more primary planar waveguides  1  (only one primary waveguide is illustrated in  FIGS. 1 and 2 ). 
         [0010]    As illustrated in  FIG. 2 , the light propagates along the primary planar waveguide with at least some reflections or “bounces” resulting from the TIR propagation. It is noted that some implementations may employ one or more reflectors in the internal optical path, for instance thin-films, dielectric coatings, metalized coatings, etc., which may facilitate reflection. Light that propagates along the length  110  of the waveguide  1  intersects with the DOE  2  at various positions along the length  110 . The DOE  2  may be incorporated within the primary planar waveguide  1  or abutting or adjacent one or more of the faces  112  of the primary planar waveguide  1 . The DOE  2  accomplishes at least two functions. The DOE  2  shifts an angle of the light, causing a portion of the light to escape TIR, and emerge from the interior  118  to the exterior  120  via one or more faces  112  of the primary planar waveguide  1 . The DOE  2  can also be configured to direct the out-coupled light rays to control the virtual location of an object at the desired apparent viewing distance. Thus, someone looking through a face  112   a  of the primary planar waveguide  1  can see digital imagery at one or more viewing distances. 
         [0011]    In some implementations, a scanning light display is used to couple light into one or more primary planar waveguides. The scanning light display can comprise a single light source that forms a single beam that is scanned over time to form an image. This scanned beam of light may be intensity-modulated to form pixels of different brightness levels. Alternatively, multiple light sources may be used to generate multiple beams of light, which are scanned either with a shared scanning element or with separate scanning elements to form imagery. These light sources may comprise different wavelengths, visible and/or non-visible, they may comprise different geometric points of origin (X, Y, or Z), they may enter the scanner(s) at different angles of incidence, and may create light that corresponds to different portions of one or more images (flat or volumetric, moving or static). 
         [0012]    The light may, for example, be scanned to form an image with a vibrating optical fiber, for example as discussed in U.S. patent application Ser. No. 13/915,530, International Patent Application Serial No. PCT/US2013/045267, and U.S. provisional patent application Ser. No. 61/658,355. The optical fiber may be scanned biaxially by a piezoelectric actuator. Alternatively, the optical fiber may be scanned uniaxially or triaxially. As a further alternative, one or more optical components (e.g., rotating polygonal reflector or mirror, oscillating reflector or mirror) may be employed to scan an output of the optical fiber. 
         [0013]    In other embodiments, the image can be generated using a LCOS (liquid crystal on silicon) mirrors formed in an array. 
         [0014]      FIG. 3  shows an optical system  300  including a waveguide apparatus, an optical coupler subsystem to optically couple light to or from the waveguide apparatus, and a control subsystem, according to one illustrated embodiment. 
         [0015]    Many of the structures of the optical system  300  of  FIG. 3  are similar or even identical to those of the optical system  100  of  FIG. 1 . In the interest of conciseness, in many instances only significant differences are discussed below. 
         [0016]    The optical system  300  may employ a distribution waveguide apparatus to relay light along a first axis (vertical or Y-axis in view of  FIG. 3 ), and expand the light&#39;s effective exit pupil along the first axis (e.g., Y-axis). The distribution waveguide apparatus may, for example include a distribution planar waveguide  3  and at least one DOE  4  (illustrated by double dash-dot line) associated with the distribution planar waveguide  3 . The distribution planar waveguide  3  may be similar or identical in at least some respects to the primary planar waveguide  1 , having a different orientation therefrom. Likewise, the DOE  4  may be similar or identical in at least some respects to the DOE  2 . For example, the distribution planar waveguide  3  and/or DOE  4  may be comprised of the same materials as the primary planar waveguide  1  and/or DOE  2 , respectively. 
         [0017]    The relayed and exit pupil expanded light is optically coupled from the distribution waveguide apparatus into one or more primary planar waveguide  1 . The primary planar waveguide  1  relays light along a second axis, preferably orthogonal to first axis, (e.g., horizontal or X-axis in view of  FIG. 3 ). Notably, the second axis can be a non-orthogonal axis to the first axis. The primary planar waveguide  1  expands the light&#39;s effective exit pupil along that second axis (e.g., X-axis). For example, a distribution planar waveguide  3  can relay and expand light along the vertical or Y-axis, and pass that light to the primary planar waveguide  1  which relays and expands light along the horizontal or X-axis. The remainder of the elements of system  300  shown in  FIG. 3  will be discussed below with respect to  FIG. 4 . 
         [0018]      FIG. 4  shows the optical system  300 , illustrating generation thereby of a single focus plane that is capable of being positioned closer than optical infinity. 
         [0019]    The optical system  300  may include one or more sources of red, green, and blue light  11 , which may be optically coupled into a proximal end of a single mode optical fiber  9 . A distal end of the optical fiber  9  may be threaded or received through a hollow tube  8  of piezoelectric material. The distal end protrudes from the tube  8  as fixed-free flexible cantilever  7 . The piezoelectric tube  8  is associated with four quadrant electrodes (not illustrated). The electrodes may, for example, be plated on the outside, outer surface or outer periphery or diameter of the tube  8 . A core electrode (not illustrated) is also located in a core, center, inner periphery or inner diameter of the tube  8 . 
         [0020]    Drive electronics  12 , for example electrically coupled via wires  10 , drive opposing pairs of electrodes to bend the piezoelectric tube  8  in two axes independently. The protruding distal tip of the optical fiber  7  has mechanical modes of resonance. The frequencies of resonance depend upon a diameter, length, and material properties of the optical fiber  7 . By vibrating the piezoelectric tube  8  near a first mode of mechanical resonance of the fiber cantilever  7 , the fiber cantilever  7  is caused to vibrate, and can sweep through large deflections. By stimulating resonant vibration in two axes, the tip of the fiber cantilever  7  is scanned biaxially in an area filling 2D scan. By modulating an intensity of light source(s)  11  in synchrony with the scan of the fiber cantilever  7 , light emerging from the fiber cantilever  7  forms an image. 
         [0021]    Collimator  6  collimates the light emerging from the scanning fiber cantilever  7 . The collimated light may be reflected by mirrored surface  5  into a narrow distribution planar waveguide  3  which contains at least one diffractive optical element (DOE)  4 . The collimated light propagates vertically (i.e., relative to view of  FIG. 4 ) along the distribution planar waveguide  3  by total internal reflection, and in doing so repeatedly intersects with the DOE  4 . The DOE  4  preferably has a low diffraction efficiency. This causes a fraction (e.g., 10%) of the light to be diffracted toward an edge of the larger primary planar waveguide  1  at each point of intersection with the DOE  4 , and a fraction of the light to continue on its original trajectory down the length of the distribution planar waveguide  3  via TIR. At each point of intersection with the DOE  4 , additional light is diffracted toward the entrance of the primary waveguide  1 . By dividing the incoming light into multiple outcoupled sets, the exit pupil of the light is expanded vertically by the DOE  4  in the distribution planar waveguide  3 . This vertically expanded light coupled out of distribution planar waveguide  3  enters the edge of the primary planar waveguide  1 . 
         [0022]    Light entering primary waveguide  1  propagates horizontally (i.e., relative to view of  FIG. 4 ) along the primary waveguide  1  via TIR. As the light intersects with DOE  2  at multiple points as it propagates horizontally along at least a portion of the length of the primary waveguide  1  via TIR. The DOE  2  may advantageously be designed or configured to have a phase profile that is a summation of a linear diffraction grating and a radially symmetric diffractive lens. The DOE  2  may advantageously have a low diffraction efficiency. At each point of intersection between the propagating light and the DOE  2 , a fraction of the light is diffracted toward the adjacent face of the primary waveguide  1  allowing the light to escape the TIR, and emerge from the face of the primary waveguide  1 . The radially symmetric lens aspect of the DOE  2  additionally steers the beam at an angle that matches the designed focus level.  FIG. 4  illustrates four beams  18 ,  19 ,  20 ,  21  extending geometrically to a focus point  13 , and each beam is advantageously imparted with a convex wavefront profile with a center of radius at focus point  13  to produce an image or virtual object at a given focal plane. 
         [0023]      FIG. 5  shows the optical system  300  illustrating generation thereby of a multi-focal volumetric display, image or light field. As in  FIG. 4 , a first set of four beams  18 ,  19 ,  20 ,  21  extends geometrically to a focus point  13 , and each beam  18 ,  19 ,  20 ,  21  is advantageously imparted with a convex wavefront profile with a center of radius at focus point  13  to produce another portion of the image or virtual object at a respective focal plane to be viewed by the eye  22 .  FIG. 5  further illustrates a second set of four beams  24 ,  25 ,  26 ,  27  extending geometrically to a focus point  23 , and each beam  24 ,  25 ,  26 ,  27  is advantageously imparted with a convex wavefront profile with a center of radius at focus point  23  to produce another portion of the image or virtual object  22  at a respective focal plane. 
         [0024]      FIG. 6  shows an optical system  600  according to one illustrated embodiment. The optical system  600  is similar in some respects to the optical systems  100  and  300 . In the interest of conciseness, only some of the differences are discussed. 
         [0025]    The optical system  600  includes a waveguide apparatus  102 , which as described above may comprise one or more primary planar waveguides  1  and associated DOE(s)  2  (not illustrated in  FIG. 6 ). In contrast to the optical system  300  of  FIGS. 3 to 5 , the optical system  600  employs a plurality of microdisplays or projectors  602   a - 602   e  (only five shown, collectively,  602 ) to provide respective image data to the primary planar waveguide(s)  1 . The microdisplays or projectors  602  can be arrayed or arranged along a face or along an edge  122  of the primary planar waveguide  1 . There may, for example, be a one to one (1:1) ratio or correlation between the number of planar waveguides  1  and the number of microdisplays or projectors  602 . The microdisplays or projectors  602  may take any of a variety of forms capable of providing images to the primary planar waveguide  1 . For example, the microdisplays or projectors  602  may take the form of light scanners or other display elements, for instance the cantilevered fiber  7  previously described or a LCOS mirror set. The optical system  600  may additionally or alternatively include a collimation element  6  that collimates light provided from microdisplay or projectors  602  prior to entering the primary planar waveguide(s)  1 . 
         [0026]    The optical system  600  can enable the use of a single primary planar waveguide  1 , rather than using two or more primary planar waveguides  1  (e.g., arranged in a stacked configuration along the Z-axis of  FIG. 6 ). The multiple microdisplays or projectors  602  can be disposed, for example, in a linear array along the edge  122  of a primary planar waveguide that is closest to a temple of a viewer&#39;s head. Each microdisplay or projector  602  injects modulated light encoding sub-image data into the primary planar waveguide  1  from a different respective position, thus generating different pathways of light. These different pathways can cause the light to be coupled out of the primary planar waveguide  1  by a multiplicity of DOEs  2  at different angles, focus levels, and/or yielding different fill patterns at the exit pupil. Different fill patterns at the exit pupil can be beneficially used to create a light field display. Each layer in the stack or in a set of layers (e.g., 3 layers) in the stack may be employed to generate a respective color (e.g., red, blue, green). Thus, for example, a first set of three adjacent layers may be employed to respectively produce red, blue and green light at a first focal depth. A second set of three adjacent layers may be employed to respectively produce red, blue and green light at a second focal depth. 
       BRIEF SUMMARY OF THE INVENTION 
       [0027]    In each of the embodiments discussed above, a light source is provided for injecting image information into the waveguide and using the DOE to distribute the light to the wearer. As discussed below, in the subject invention, a similar combination including a planar waveguide and a diffractive optical element is used to capture light entering one of the planar faces of the waveguide and then measuring the captured light with a sensor. The collection waveguide can be used alone or in combination with an output waveguide. 
         [0028]    In a preferred embodiment, the apparatus includes a waveguide having opposed planar input and output faces. A diffractive optical element (DOE) is formed across the waveguide. The DOE is configured to couple a portion of the light passing through the waveguide into the waveguide. The light coupled into the waveguide is directed via total internal reflection to an exit location on the waveguide. The apparatus further includes a light sensor having an input positioned adjacent the exit location of the waveguide to capture light exiting therefrom and generate output signals corresponding thereto. A processor determines the angle and position of the coupled light with respect to the input face of the waveguide based on the output signals. The apparatus may include a narrow band wavelength filter aligned with the waveguide. 
         [0029]    The apparatus may further include a second waveguide having opposed planar input and output faces, where the second waveguide may be aligned with and parallel to the first waveguide. A DOE may be formed across the second waveguide. The DOE may be configured to control the level of reflectivity at locations across faces of the second waveguide. The apparatus may further include a light generator having an output positioned adjacent the second waveguide to inject light into the second waveguide. A processor may control the light being injected into the second waveguide to guide light entering the second waveguide via total internal reflection to exit the waveguide at particular locations across the output face of the second waveguide. 
         [0030]    The apparatus may further include a third waveguide extending along an edge of the first waveguide. The third waveguide may capture light exiting the exit location of the first waveguide and delivering the light to the sensor. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]      FIG. 1  is a schematic diagram showing an optical system including a waveguide apparatus, a subsystem to couple light to or from the waveguide apparatus, and a control subsystem, according to one illustrated embodiment. 
           [0032]      FIG. 2  is an elevational view showing a waveguide apparatus including a planar waveguide and at least one diffractive optical element positioned within the planar waveguide, illustrating a number of optical paths including totally internally reflective optical paths and optical paths between an exterior and an interior of the planar waveguide, according to one illustrated embodiment. 
           [0033]      FIG. 3  is a schematic diagram showing an optical system including a waveguide apparatus, an optical coupler subsystem to optically couple light to or from the waveguide apparatus, and a control subsystem, according to one illustrated embodiment. 
           [0034]      FIG. 4  is a schematic diagram of the optical system of  FIG. 3  illustrating generation of a single focus plane that is capable of being positioned closer than optical infinity, according to one illustrated embodiment. 
           [0035]      FIG. 5  is a schematic diagram of the optical system of  FIG. 3  illustrating generation of a multi-focal volumetric display, image or light field, according to one illustrated embodiment. 
           [0036]      FIG. 6  is a schematic diagram showing an optical system including a waveguide apparatus, an optical coupler subsystem including a plurality of projectors to optically couple light to a primary planar waveguide, according to one illustrated embodiment. 
           [0037]      FIG. 7  is a schematic diagram showing an optical system with a planar waveguide and sensor in accordance with a basic embodiment of the subject invention. 
           [0038]      FIG. 8  is a schematic diagram of the system of the subject invention that includes three planar waveguides and associated color filters. 
           [0039]      FIG. 9  is a schematic diagram of a preferred embodiment of the subject invention that includes two planar waveguides, one of the waveguides is used as in the prior art to deliver images to the eye and the other waveguide is used to capture images from the real world. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0040]      FIG. 7  is a schematic diagram of a first embodiment of a system  700  of the subject invention. The system  700  includes a planar waveguide  702  having at least one diffractive optical element  704  formed therein. It is envisioned that the waveguide  702  could be constructed in a manner similar to any of the output type waveguides discussed above. In use, light rays from the real world will be partially transmitted through the waveguide to the eye  706  of the user. 
         [0041]    In accordance with the subject invention, a portion of the rays entering waveguide  702  will be trapped by the waveguide and directed via total internal reflection along the length of the waveguide to an exit location shown at  710 . The light exit location  710  can be on either the front or back of the waveguide or at a side edge thereof. Light exiting the waveguide can be captured by a sensor  712 . Signals generated by the sensor are coupled to a processor  714  for analysis. 
         [0042]    Various types of sensors could be used. For example, the sensor can include a movable fiber optic as discussed above with the output device. Similarly, an array of sensors could be provided. In addition, the sensor could include a LCOS system selectively directing light to additional, fixed position sensors such as CMOS or CCD imagers. 
         [0043]    The processor  714  would analyze the input signals to determine the input position and angle of the rays that were captured by the waveguide and channeled to the exit location  710 . In practice, this analysis could be complicated if only a single waveguide were used. For example, the single waveguide embodiment would produce signals that combine more than one wavelength of light reaching the waveguide. 
         [0044]    Accordingly, in one preferred embodiment, three similar waveguides would be used, each waveguide arranged to capture either red, blue or green light.  FIG. 8  illustrates one example of such an arrangement. In  FIG. 8 , three aligned waveguides are provided,  702   a ,  702   b  and  702   c . Diffractive filters  716  are provided in front of each waveguide to control the light entering the waveguides. The order of the filters could be selected to optimize the distribution of the light into the waveguides. For example, filter  716   a  could diffract a portion of the red light into waveguide  702   a  but allow the blue and green light to pass through the waveguide  702   a . Filter  716   b  could diffract a portion of the green light into waveguide  702   b . Filter  716   c  could diffract a portion of the blue light into waveguide  702   c . Separate sensors  712   a ,  712   b  and  712   c  would collect light from waveguides  702   a ,  702   b  and  702   c , respectively. The signals generated by the sensors would be analyzed by the processor. 
         [0045]    It should be noted that the light rays which enter from any particular point on the waveguide will effectively be summed with light of the same color which enters at certain other points but on the same TIR path back to the sensor. In effect, one would get a superposition of light from many sources. The processor would need to be arranged to unravel this superposition of information via digital analysis. In practice, the algorithms could include various statistical analyses in conjunction with a learning system. The specific data analysis approach is not the subject of this application. 
         [0046]    It should be noted that if the device is capturing an image of a flat object (e.g. a photograph), the deconvolution problem is much simpler. For a flat object, the deconvolution will have N displaced images, where N is the number of entry pupils on the edge element. 
         [0047]    One way of addressing the deconvolution problem when imaging a three dimensional scene would be to utilize a plurality of DOEs across the waveguide that are actively switchable. Using electronic controls to vary the diffractive power of the DOEs, one could selectively allow individual entry pupils to be selectively turned on or shut off. Under this system, the processor would know in advance the entry location of light channeled by the waveguide and measured by the sensor. 
         [0048]    It should be noted that if an active DOE system were used to image a flat image, each pupil would capture the entire undistorted image of the object. 
         [0049]      FIG. 9  is a diagram of an embodiment  900  that includes one output waveguide  910  and one collection waveguide  920 . The output waveguide  910  would be of the type discussed above in the background of the specification and would include a light image source  924  and an optical fiber  929  for delivering the image information to the waveguide  910 . The collection waveguide  920  would be similar to the embodiment of  FIG. 7  wherein light captured by the waveguide  920  would be channeled by total internal reflection to an output location  930  and measured by sensor  932 . The output from sensor  932  is supplied to processor  934 . As discussed above, in a preferred embodiment, there would be three output waveguides and three input waveguides, each waveguide associated with a particular color spectrum (red, green, and blue). Only one of each type of waveguide is shown in  FIG. 9  for convenience of illustration. 
         [0050]    In the basic operation of the system  900 , some of the light rays from the real world will pass through both waveguides  910  and  920  and into the eye of the user. Waveguide  910  can be used to deliver additional visual images to the eye to achieve an augmented reality. Waveguide  920  can be used to capture and measure light rays from the real world. This information can be used in a variety of ways. 
         [0051]    For example, information captured from the real world can be used to modify the images generated for the output waveguide  910 . In particular, the light output from waveguide  910  can be some specific function of the input measured at the same coordinate on the waveguide  920  surface. This function could include linear scaling, nonlinear scaling, and clipped scaling, as well as any other specific function of the intensity as computed on a per pixel basis or computed locally with respect to a pixel location. 
         [0052]    The image information captured by waveguide  920  can also be used to help register virtual images generated by waveguide  910 . In many currently envisioned augmented reality implementations, virtual objects are located in three dimensions and complex projections are made to compute their location on the waveguide  910 . Information collected by waveguide  920  permits objects to be specifically registered with respect to the two dimensional image, thus guaranteeing their correct location relative to other landmarks in the image (i.e. no “jitter”). 
         [0053]    In another example, the image information collected by waveguide  920  can be used to recognize a specific image element in the real world and then compute a substitute element for presentation to the user via waveguide  910 . For example, the system could recognize a person&#39;s face and then render a modified image (e.g., face with a beard) to the user. In another example, the color of a building could be changed. In still another example, signage in the real world written in one language could be rendered in a different language. This concept extends not only to “filters” which use image recognition or modeling, but also to simpler filters such as blur, or combinations of the above. 
         [0054]    In an alternative embodiment, a controllable darkening layer (e.g., LCD, not shown) can be provided between the waveguides  910  and  920  for blocking the light from the real world from reaching the user&#39;s eye. Instead, this incoming light can be “substituted” with light generated by waveguide  910 . 
         [0055]    Algorithms for decoding the light captured by waveguide  920  and converted into a time sequential signal are context dependent. 
         [0056]    For example, in a system wherein the sensor is a scanning fiber, the signals can be converted into a two dimensional rectilinear array of the kind expected by many image processing algorithms. In some cases, it may be easier to process the pixels in their natural polar form and output them in the same polar form. 
         [0057]    In one implementation, there can be a direct assignment of the incoming polar coordinate pixel (IPCP) values to the rectangular coordinate pixels (RCP) found by direct computation. In another implementation, one can assign all rectangular coordinate pixels to the nearest rectangular coordinate pixel for which a corresponding incoming polar coordinate pixel can be found. In another approach, one can interpolate the assignment of rectangular coordinate pixels to the value of the nearest rectangular coordinate pixels for which a corresponding incoming polar coordinate pixel can be found. The latter approach includes linear, quadratic, or any other such interpolation. Finally, it is possible to pre-compute and store the relationship between the rectangular coordinate pixels and the associated incoming polar coordinate pixel projections. 
         [0058]    While the subject invention has been described with reference to some preferred embodiments, various changes and modifications could be made therein, by one skilled in the art, without varying from the scope and spirit of the subject invention as defined by the appended claims.