Patent Publication Number: US-9891516-B1

Title: Methods for calibrating a light field projection system

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application claims priority to U.S. Provisional patent application Ser. No. 62/378,319 filed on Aug. 23, 2016 and entitled “Methods for Calibrating a Light Field Projection System,” which is herein incorporated by reference as if fully set forth in this description. 
    
    
     BACKGROUND 
     Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section. 
     Three-dimensional (3D) displays/projections have become a topic of much interest in recent years. Many 3D displays require the cumbersome use of a headset (e.g., active or passive 3D glasses) by the viewer. Further, while glasses-less 3D display systems do exist, such systems may not allow for multiple viewers at different azimuthal viewing angles, elevations, and distances from the display. 
     A light field is a function (sometimes referred to as the “5D plenoptic function”) that describes the composite of the amount of light flowing in a given direction at a given location for every location in space. If all the light that comprises a light field is emanating from one plane, for example, the function can be reduced to four dimensions. An example basis set of those four dimensions may be an x-location on the plane, a y-location on the plane, an azimuthal angle (from 0°-360°) in the plane (sometimes called φ), and an elevation angle (from 0°-90°, 0° being in the plane, 90° being exactly normal to the plane) out of the plane (sometimes called θ). If an intensity, in Watts for example, is specified for each possible quadruple (x, y, φ, and θ) at the plane (assuming the plane to be infinite in x and y directions), then a light field can be defined for every point in 3D space (barring interference with objects outside of the plane). 
     A light field display can generate such a light field, subject to practical limitations (e.g., the display plane is not infinite in x and y directions). The more granular the selection of values for each of the four dimensions, the higher the resolution of the viewable light field that is displayed. Additionally, the intensity of the light field displayed may only be defined for a single wavelength. Therefore, a number of light fields may be separately displayed at different wavelengths. In the visible spectrum, each wavelength represents the color of the respective light field, thereby enabling color light field displays. 
     A viewer may view the light field generated by a light field display from various locations in space and from various azimuthal and elevation angles. Given that a viewer has two eyes (and therefore two perspectives) from which to observe the light field, a viewer can spectroscopically observe the scene coming from the light field display in 3D. 
     Such a light field display may be offset when installed in a home, for example. Additionally or alternatively, the light field display may have defects that arise during fabrication. Such offsets or defects may result in the system not producing high quality light fields at certain viewing angles/observation locations. To an observer, a lower quality light field could yield a degraded 3D image of the scene that is being reproduced (e.g., a low resolution 3D image). Therefore, accounting for potential offsets and defects via calibration can be desirable. 
     SUMMARY 
     The specification and drawings disclose embodiments that relate to systems and methods for calibrating a light field projection system. 
     In one aspect the disclosure describes a method for calibrating a light field projection system comprising a screen having a plurality of convex reflective elements. The method includes sequentially scanning the plurality of convex reflective elements, by a projection unit of the light field projection system, using light modulated according to a baseline intensity profile. The method also includes detecting, using a light detector located at a first perspective relative to the screen and the projection unit, a first measured intensity profile of light reflected from the plurality of convex reflective elements. Further, the method includes comparing the first measured intensity profile with a first expected intensity profile based on the baseline intensity profile and the first perspective of the light detector. In addition, the method includes modifying operation of a control system of the light field projection system to account for any differences between the first measured intensity profile and the first expected intensity profile. The control system is configured to determine a light field modulation scheme for projecting a light field using the light field projection system. Still further, the method includes moving the light detector to a second perspective relative to the screen and the projection unit. Additionally, the method includes sequentially scanning the plurality of convex reflective elements, by the projection unit of the light field projection system, using light modulated according to the baseline intensity profile. Even further, the method includes detecting, using the light detector located at a second perspective relative to the screen and the projection unit, a second measured intensity profile of light reflected from the plurality of convex reflective elements. Furthermore, the method includes comparing the second measured intensity profile with a second expected intensity profile based on the baseline intensity profile and the second perspective of the light detector. Further yet, the method includes modifying operation of the control system of the light field projection system to account for any differences between the second measured intensity profile and the second expected intensity profile. 
     In another aspect the disclosure describes a method for calibrating a light field projection system comprising a screen having a plurality of convex reflective elements. The method includes sequentially scanning the plurality of convex reflective elements, by a projection unit of the light field projection system, using light modulated according to a baseline intensity profile. The method also includes detecting, using a light detector located at a first perspective relative to the screen and the projection unit, a first measured intensity profile of light reflected from the plurality of convex reflective elements. The method further includes comparing the first measured intensity profile with a first expected intensity profile based on the baseline intensity profile and the first perspective of the light detector. Additionally, the method includes modifying operation of a control system of the light field projection system to account for any differences between the first measured intensity profile and the first expected intensity profile. The control system is configured to determine a light field modulation scheme for projecting a light field using the light field projection system. Still further, the method includes rotating the screen in a first angular direction relative to the light detector and the projection unit so the light detector is located at a second perspective relative to the screen and the projection unit. In addition, the method includes sequentially scanning the plurality of convex reflective elements, by the projection unit of the light field projection system, using light modulated according to the baseline intensity profile. Even further, the method includes detecting, using the light detector located at a second perspective relative to the screen and the projection unit, a second measured intensity profile of light reflected from the plurality of convex reflective elements. Furthermore, the method includes comparing the second measured intensity profile with a second expected intensity profile based on the baseline intensity profile and the second perspective of the light detector. Further yet, the method includes modifying operation of the control system of the light field projection system to account for any differences between the second measured intensity profile and the second expected intensity profile. 
     In a third aspect the disclosure describes a method for calibrating a light field projection system comprising a screen having a plurality of convex reflective elements. The method includes sequentially scanning the plurality of convex reflective elements, by a projection unit of the light field projection system, using light modulated according to a baseline intensity profile. The method also includes detecting, using a first light detector located at a first perspective relative to the screen and the projection unit, a first measured intensity profile of light reflected from the plurality of convex reflective elements. The method further includes detecting, using a second light detector located at a second perspective relative to the screen and the projection unit, a second measured intensity profile of light reflected from the plurality of convex reflective elements. Additionally, the method includes comparing the first measured intensity profile with a first expected intensity profile based on the baseline intensity profile and the first perspective of the first light detector. Still further, the method includes comparing the second measured intensity profile with a second expected intensity profile based on the baseline intensity profile and the second perspective of the second light detector. In addition, the method includes modifying operation of a control system of the light field projection system to account for any differences between the first measured intensity profile and the first expected intensity profile and any differences between the second measured intensity profile and the second expected intensity profile. The control system is configured to determine a light field modulation scheme for projecting a light field using the light field projection system. 
     The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the figures and the following detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is an illustration of a light field projection system, according to example embodiments. 
         FIGS. 2 a -2 d    are illustrations of a screen (angled view, side view, top view, and a coordinate system, respectively), according to example embodiments. 
         FIGS. 3 a -3 d    are illustrations of various convex reflective elements, according to example embodiments. 
         FIG. 4  is an illustration of a method of scanning convex reflective elements, according to example embodiments. 
         FIGS. 5 a  and 5 b    are illustrations of light rays occurring during a scanning of convex reflective elements (side view and top view, respectively), according to example embodiments. 
         FIG. 6  is an illustration of two perspective views of a light field, according to example embodiments. 
         FIG. 7  is an illustration of two perspective views of a light field, according to example embodiments. 
         FIG. 8  is an illustration of a light field projection system, according to example embodiments. 
         FIG. 9  is an illustration of a method of generating light fields of different colors, according to example embodiments. 
         FIG. 10  is an illustration of a method of generating light fields of different colors, according to example embodiments. 
         FIG. 11  is an illustration of a light field projection system, according to example embodiments. 
         FIG. 12  is an illustration of a light field projection system, according to example embodiments. 
         FIG. 13  is a flow chart illustration of a method, according to example embodiments. 
         FIGS. 14 a  and 14 b    are illustrations of a calibration method, according to example embodiments. 
         FIGS. 15 a  and 15 b    are illustrations of another calibration method, according to example embodiments. 
         FIG. 16  is an illustration of another calibration method, according to example embodiments. 
         FIG. 17  is a flow chart illustration of a method, according to example embodiments. 
         FIG. 18  is a flow chart illustration of a method, according to example embodiments. 
         FIG. 19  is a flow chart illustration of a method, according to example embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Example methods and systems are described herein. Any example embodiment or feature described herein is not necessarily to be construed as preferred or advantageous over other embodiments or features. The example embodiments described herein are not meant to be limiting. It will be readily understood that certain aspects of the disclosed systems and methods can be arranged and combined in a wide variety of different configurations, all of which are contemplated herein. 
     Furthermore, the particular arrangements shown in the figures should not be viewed as limiting. It should be understood that other embodiments might include more or less of each element shown in a given figure. In addition, some of the illustrated elements may be combined or omitted. Similarly, an example embodiment may include elements that are not illustrated in the figures. 
     I. OVERVIEW 
     Example embodiments include methods for calibrating a light field projection system. The light field projection system may include a screen having convex reflective elements, in some embodiments. In other embodiments, the screen may have concave refractive elements. 
     Methods of calibrating the light field projection system may include recording two, or more, differing light intensity profiles and comparing each to a corresponding expected light intensity profile. The methods may further include modifying an operation of a control system that determines modulation schemes used for projection by the light field projection system to reproduce light fields viewable from a plurality of perspectives. Modifying the operation of the control system that determines modulation schemes may include the control system inserting or removing time delays from the modulation schemes, increasing or decreasing light intensities at certain times during the modulation schemes, or increasing or decreasing a wavelength of light being projected at certain times during the modulation schemes. 
     The two, or more, differing light intensity profiles may be measured by one or more light detectors. In some embodiments, a light detector may be moved in between a measurement of a first measured light intensity profile and a measurement of a second measured light intensity profile. This movement may change the light detector from having a first perspective relative to the screen to having a second perspective relative to the screen. In alternate embodiments, the screen may rotate in between a measurement of the first measured light intensity profile and a measurement of the second measured light intensity profile. This rotation may change the perspective of the light detector from the first measurement to the second measurement. In still other embodiments, there may be separate light detectors, each at different perspectives relative to the screen, measuring the first and the second measured light intensity profiles. 
     The measured light intensity profiles may be measurements, by the one or more light detectors, of light that is reflected from the screen. The light that is reflected may have been scanned across the convex reflective elements by the light field projection system. Further, the light that was scanned across the convex reflective elements of the screen may have been modulated according to a light modulation scheme to produce a light field with a baseline intensity profile. The baseline intensity profile may correspond to a particular light field that is suitable for calibration. The expected light intensity profiles to which the measured light intensity profiles are compared may be based on the perspective(s) of the light detector(s) with respect to the screen and a projection unit of the light field projection system, as well as the baseline intensity profile. 
     In some applications, the calibration methods described herein may be used in a fabrication facility of the screens of the projection system. For example, the calibration may be done to perform quality assurance of the convex reflective elements and the screen of the light field projection system. Additionally or alternatively, the calibration methods may be used upon installation of the light field projection system prior to viewing a light field projected by the light field projection system. In still other applications, the calibration methods may be performed concurrently with projection of light fields by the light field projection system. This may be done to continually ensure optimized light field viewing quality. For example, locations of one or more viewers may be tracked by the light field projection system (e.g., using a camera), and the light field projected to the perspectives corresponding to those viewer locations may be calibrated. In such cases, the calibration methods may use light in non-visible portions of the electromagnetic spectrum (e.g., infrared wavelengths between 750 and 2,500 nm) to perform calibration, so as not to interfere with the concurrent viewing of the light field by the viewer(s). 
     In the following accompanying figures and description,  FIGS. 1-13  illustrate example embodiments relating to a light field projection system, and  FIGS. 14-19  illustrate example embodiments relating to a method of calibrating a light field projection system. 
     II. EXAMPLE LIGHT FIELD PROJECTION SYSTEMS 
       FIG. 1  is an illustration of a light field projection system  100 , according to example embodiments. The light field projection system  100  includes a screen  102  and a projection unit  110 . The screen has a plurality of convex reflective elements  104  arranged in a two-dimensional array thereon. The projection unit  110  projects a plurality of light rays  106  toward the screen  102 . The light rays  106  may be reflected off the screen toward an observer  108  In addition, the projection unit  110  comprises a light source  112 , a modulator  114 , a control system  116 , a horizontally rotating movable mirrored element  118 , and a vertical rotating movable mirrored element  120 . 
     The screen  102  has a surface on which the convex reflective elements  104  are disposed. In some embodiments, the convex reflective elements  104  will be molded into the screen  102  or stamped into the screen  102  by a machining process. Alternatively, the convex reflective elements  104  may be independently fabricated and adhered to the surface of the screen  102 . The screen  102  may loosely resemble rigid bubble-wrap. 
     The screen  102  may be made of a non-rigid material, such as a polymer or a plastic. This may allow the screen  102  to be rolled or folded when not in use, for example. In other embodiments, the screen  102  may be made of a substantially rigid material, such as glass. The screen  102  is further illustrated in  FIGS. 2 a -2 c    and further described in the accompanying description. 
     The convex reflective elements  104  are disposed on or embedded in the surface of the screen  102 . The convex reflective elements  104  serve to reflect light rays projected toward the screen  102  by the projection unit  110 . The plurality of convex reflective elements  104  may have mirrored surfaces. For example, each convex reflective element  104  may be a glass substrate coated with silver or aluminum. In addition, the plurality of convex reflective elements  104  may be substantially hemispherical, having a diameter greater than the width of the light rays projected by the projection unit  110  (e.g., greater than the beam waist of the respective laser if the light source  112  is a laser). In some example embodiments, the diameter of each of the convex reflective elements  104  may be roughly equivalent to ten wavelengths of the light projected by the projection unit (e.g., 5 μm). 
     In alternate embodiments, the convex reflective elements  104  may resemble squashed hemispheres. Because it is unnecessary for the convex reflective elements  104  to reflect light horizontally toward other convex reflective elements  104 , it is unnecessary to have the regions of the convex reflective elements closest to the surface of the screen  102  (i.e., the “edges” of the convex reflective elements  104 ) be perfectly vertical. 
     In some embodiments, the plurality of convex reflective elements  104  may be more or less identical in shape regardless of their position in the two-dimensional array. Alternatively, the shape of each of the plurality of convex reflective elements  104  may depend on its location within the two-dimensional array. For example, the convex reflective elements  104  that are located nearer to the edges of the array may be more peaked, allowing for the reflection angle to be greater over a wider facial area of the convex reflective elements  104 , thereby having the ability to reflect light toward the center of a viewing region in front of the screen  102  from a larger range of locations on its face. Likewise, the vertical dimension and the horizontal dimension of the plurality of convex reflective elements  104  may not be equal for an individual convex reflective element  104 . Furthermore, the vertical and/or the horizontal dimensions may vary for different convex reflective elements  104  at different locations within the two-dimensional array. 
     The plurality of convex reflective elements  104  may additionally be faceted, rather than have a uniformly smooth surface. Potential designs and shapes of the convex reflective elements  104  are illustrated and discussed further with regard to  FIGS. 3 a   - 3   d.    
     The observer  108 /the light path  106  are illustrated in  FIG. 1  to show one potential location relative to the light field projection system  100  in which they may reside. The projection unit  110  projects light toward the screen  102  to sequentially scan the two-dimensional array of convex reflective elements  104 . The light projected toward the screen is then reflected by the plurality of convex reflective elements  104  to generate a light field viewable at a plurality of perspectives. The observer  108  may be located at one of the perspective locations. Thus, the observer  108  is able to observe the light field generated by the light field projection system  100  at the observer&#39;s respective quadruple within the light field (i.e., at a given x-location, y-location, φ-angle, and θ-angle relative to the screen  102 ). 
     The projection unit  110  comprises sub-units that project light toward the screen  102 . In some embodiments, the projection unit  110  may be packaged within a singular housing. Alternatively, the projection unit  110  may utilize free space optics to link the various components comprising the projection unit  110 . For example, the light source  112  may output light that is reflected by a mirror or focused by a lens prior to entering the modulator  114 . Additionally, multiple components of the projection unit  110  could be located inside or behind the screen  102  with respect to the observer, in various embodiments. 
     The light source  112  may include a white light source, for example. The light source  112  may also include a lens for focusing the light generated by the light source  112  prior to the light being transmitted to the modulator  114 . Furthermore, the light source  112  may include an optical filter to select specific wavelengths of light from the original source. For example, if the light source  112  includes a white light source, there may be an optical filter that only passes light in the range of red wavelengths in the optical spectrum so the light source  112  performs as a red light source. 
     In other embodiments, the light source  112  may be a laser, such as a fiber laser or a diode laser. This may permit specific colors to be projected by the projection unit  110  without a need for additional optics. Also, in embodiments where the light source  112  is a laser, the light could be tightly spatially focused before leaving the projection system  110 , allowing for high resolution light fields reflected from the screen  102 . 
     The modulator  114  alters the light generated by the light source  112 . In some embodiments, the modulator  114  may alter the intensity of the light generated by the light source  112 . The modulator  114  may do so, for example, according to a modulation scheme determined by the control system  116 . The modulator  114  may be an electro-optic modulator in various embodiments (e.g., a Kerr cell, a Pockels cell, or a Mach-Zehnder interferometer). The modulator  114  may, in alternate embodiments, utilize multiple modulation schemes that are multiplexed with one another in time or combined in amplitude to allow for a greater variation in the intensity of the light output by the modulator  114  or to permit a greater dynamic range in that light. Alternatively or additionally, the light source  112  may modulate the light output by the light source  112 . 
     The control system  116  determines the modulation scheme for use by the modulator  114 . The control system  116  may determine the modulation scheme in order to produce a light field viewable at the perspective of the observer  108 , for example. The control system  116  may be integrated into the projection unit  110 , as illustrated in  FIG. 1 . Alternatively, the control system  116  may be integrated into the screen  102  or a separate device that is communicatively coupled to the projection unit  110 . In some embodiments, the control system  116  may include one or more processing units, such one or more central processing units (CPUs). Additionally or alternatively, the control system  116  may include one or more special purpose processing units, such as application specific integrated circuits (ASICs) or GPUs. The control system  116  may also include a non-volatile memory that stores instructions executable by one or more processing units and/or a volatile memory (e.g., random access memory—RAM) that aids one or more processing units in determining the modulation scheme. 
     In some embodiments, the control system  116 , itself, may modulate the modulator  114  using the modulation scheme. In alternate embodiments, the modulation scheme determined by the control system  116  may be transmitted to the modulator  114  and carried out by the modulator  114 . The modulation scheme may be rendered by the control system  116  based on an input scene. Furthermore, the modulation scheme may include renderings of different perspectives of the light field from different processing units. The separate rendered perspectives may then be multiplexed or super-imposed by the control system  116  to form the modulation scheme that ultimately drives the modulator  114 . 
     The horizontally rotating movable mirrored element  118  may define the horizontal location on the screen  102  at which the light from the light source  112  is aimed. In some embodiments, the horizontally rotating movable mirrored element  118  may be a thin cylinder with facets around the circumference (e.g., one facet for each horizontal location along the screen  102  to which the light will be directed). Each facet may have a planar mirror mounted on its exterior to reflect the light leaving the modulator  114 . Furthermore, each facet may be oriented at a slightly different angle with respect to the horizontal axis of the screen  102  so as to reflect the light toward a slightly different horizontal location. In some embodiments, the horizontally rotating movable mirrored element  118  may rotate about magnetic bearings, which enable a high rotational velocity with low friction, and thus without the concern of heat generation and/or mechanical wear to the horizontally rotating movable mirrored element  118 . 
     In some embodiments, the horizontally rotating movable mirrored element  118  may be driven by the control system  116 . Alternatively, the horizontally rotating movable mirrored element  118  may independently rotate and a modulation scheme determined by the control system  116  and utilized by the modulator  114  may be synchronized to the rotation of the horizontally rotating movable mirrored element  118 . 
     The vertically rotating movable mirrored element  120  may define the vertical location on the screen  102  at which the light from the light source  112  is aimed. In some embodiments, the vertically rotating movable mirrored element  120  may be a thin cylinder with facets around the circumference (e.g., one facet for each vertical location along the screen  102  to which the light will be directed). Each facet may have a planar mirror mounted on its exterior to reflect the light leaving the modulator  114 . Furthermore, each facet may be oriented at a slightly different angle with respect to the vertical axis of the screen  102  so as to reflect the light toward a slightly different vertical location. In some embodiments, the vertically rotating movable mirrored element  120  may rotate about magnetic bearings, which enable a high rotational velocity with low friction, and thus without the concern of heat generation and/or mechanical wear to the vertically rotating movable mirrored element  120 . 
     In some embodiments, the vertically rotating movable mirrored element  120  may be driven by the control system  116 . Alternatively, the vertically rotating movable mirrored element  120  may independently rotate and a modulation scheme determined by the control system  116  and utilized by the modulator  114  may be synchronized to the rotation of the vertically rotating movable mirrored element  120 . 
     As illustrated in  FIG. 1 , the superposition of a first respective facet on the horizontally rotating movable mirrored element  118  and a second respective facet on the vertically rotating movable mirrored element  120  off of which a light ray is reflected may determine a specific location on the screen  102  toward which the light ray is reflected. Such a light ray may contribute to generating a portion of a light field, for example. 
     The horizontally rotating movable mirrored element  118  and the vertically rotating movable mirrored element  120  may rotate about axes that are perpendicular to one another (as shown in  FIG. 1 ). Alternatively, the horizontally rotating movable mirrored element  118  and the vertically rotating movable mirrored element  120  may rotate about parallel axes and have facets angled in such a way as to account for the parallel axially rotation (e.g., the facets on the horizontally rotating movable mirrored element  118  are angled in a planar fashion from left to right and the facets on the vertically rotating movable mirrored element  120  are angled in a planar fashion from top to bottom). 
     In some embodiments, a single movable mirrored element may be used rather than a composition of a horizontally rotating movable mirrored element  118  and a vertically rotating movable mirrored element  120 . For example, a cylinder with facets around the circumference may be used, each facet having a planar mirror that has a slightly different angle with respect to the horizontal axis of the screen  104  and a slightly different angle with respect to the vertical axis of the screen  102 . In this way, an array of locations on the screen  102  may have light reflected toward them from the projection unit  110  using a single movable mirrored element. In alternate embodiments, alternate means of sequentially scanning the convex reflective elements  104  by reflection of light from the light source  112  may be used in place of the movable mirrored elements  118 / 120 . 
     The components of the light field projection system  100  are configured to produce a light field viewable from one or more perspectives of the observer  108 . The light field, if viewed stereoscopically from two perspectives of the observer  108 , may create a 3D view of a scene. Further, the light field projection system  100  may produce a light field viewable from perspectives of additional observers. Additionally, the light field produced by the light field projection system  100  may allow the observer  108  to move to various locations to view the scene recreated by the light field from various perspectives. 
       FIG. 2 a    is an angled view of the screen  102  and the plurality of convex reflective elements  104  thereon. The dotted lines on the plurality of convex reflective elements  104  serve to depict the three-dimensionality of the convex reflective elements  104  (i.e., the convex reflective elements  104  may have a substantially hemispherical shape, and therefore have a depth). The screen  102  may have many more rows and/or columns than depicted in  FIG. 2 a   .  FIG. 2 a    is provided as an example. Furthermore, adjacent rows of convex reflective elements may be off-set from one another, and similarly for adjacent columns. There may additionally be black/dark space (i.e., portions of the screen  102  that do not reflect light) between adjacent convex reflective elements. Such black/dark space may ensure that, if the screen is sequentially scanned by a projection unit  110  (as illustrated in  FIG. 1 ), any extraneous light rays that do not contribute to the generation of a light field are not reflected from the screen. Therefore, such extraneous light rays will not interfere with or obscure the light field for an observer. In some embodiments, the spacing between adjacent convex reflective elements  104  may be different in the horizontal direction than in the vertical direction. 
     One method of fabricating the screen  102  and the convex reflective elements  104  thereon may include injection molding. The entire screen  102 , including the convex reflective elements  104 , may be injection molded as one piece. Alternatively, the convex reflective elements  104  may be fabricated individually using injection molding and then adhered to the face of the screen  102  to form the array. 
       FIG. 2 b    is a partial side view illustration of the screen  102 . Four of the rows of the plurality of convex reflective elements  104  in the two-dimensional array are shown. 
       FIG. 2 c    is a partial top view illustration of the screen  102 . Four of the columns of the plurality of convex reflective elements  104  in the two-dimensional array are shown. 
     As can be seen from the example embodiments of  FIGS. 2 b  and 2 c   , the convex reflective elements  104  may not be exactly hemispherical. The shape illustrated in  FIGS. 2 b  and 2 c    may prevent light from being reflected amongst one or more of the convex reflective elements. Such reflections may be unnecessary or even degrade the quality of the light field output by the light field projection system. Additional shapes are possible, in various embodiments; some of which are depicted in  FIGS. 3 a   - 3   d.    
       FIG. 2 d    illustrates a possible coordinate system with respect to the screen  102  that defines light field quadruples (x, y, φ, and θ). For instance, the 4 coordinates of the quadruple may represent one light ray  202  reflected from one of the convex reflective elements  104  to produce the light field. The horizontal axis, in the plane of the screen, may represent the x-coordinate along the screen (with positive x being toward the right). Similarly, the vertical axis, in the plane of the screen, may represent the y-coordinate along the screen (with positive y being toward the top). The angle in the plane of the screen  102  (i.e., the azimuthal angle) may range from 0 to 360 degrees counterclockwise, beginning in the first quadrant of the x-y plane. The angle of the quadruple normal to the screen  102  (i.e., the elevation angle) may range from 90 degrees (exactly normal to the plane of the screen  102 ) to 0 degrees (exactly parallel to the plane of the screen  102 ). 
       FIG. 3 a    is a side view illustration of a first possible shape  311  for the convex reflective elements  104 . The first possible shape  311  is substantially hemispherical. The first possible shape  311  may be similar to the shape of the convex reflective elements  104  as illustrated in the embodiment of  FIGS. 1 and 2 . The first possible shape  311  illustrated in  FIG. 3 a    may represent a substantially smooth, domed surface. The surface of the first possible shape  311  may allow for a continuous (as opposed to a discrete) distribution of azimuthal angles and elevation angles (within a defined range) at which light can be reflected from the convex reflective element  104 . 
       FIG. 3 b    is an isometric illustration of a second possible shape  321  for the convex reflective elements  104 . The second possible shape  321  is pyramidal. The dotted lines depict the back, bottom corners of the convex reflective element  104  that are hidden from view. The surface of the second possible shape  321  may provide a defined, discrete distribution of azimuthal angles (e.g., four different azimuthal angles at 0 degrees, 90 degrees, 180 degrees, and 270 degrees) with a single elevation angle (e.g., 45 degrees) at which light can be reflected from the convex reflective element  104 . 
       FIG. 3 c    is a side view illustration of a third possible shape  331  for the convex reflective elements  104 . The third possible shape  331  is faceted in an orderly fashion. The surface of the third possible shape  331  may allow for a discrete, evenly spaced distribution of azimuthal angles (e.g., 0 to 360 degrees spaced in 3 degree increments) with a discrete, evenly spaced distribution of elevation angles (e.g., 5 degrees to 90 degrees spaced in 1 degree increments) at which light can be reflected from the convex reflective element  104 . 
       FIG. 3 d    is a side view illustration of a fourth possible shape  341  for the convex reflective elements  104 . The fourth possible shape  341  is faceted in an irregular fashion. The surface of the fourth possible shape  341  may allow for a discrete, unevenly spaced distribution of azimuthal angles (e.g., one-hundred different select angles from 0 to 360 degrees) with a discrete, unevenly spaced distribution of elevation angles (e.g., fifty different select angles from 1 to 90 degrees) at which light can be reflected from the convex reflective element  104 . 
       FIG. 4  is an illustration of a method  400  of sequentially scanning the convex reflective elements  104  on the screen  102  using the projection unit  110 . The number of convex reflective elements  104  on the screen  102  illustrated in  FIG. 4  is provided as an example, and may not reflect the preferred number of convex reflective elements  104  in an actual system. The convex reflective elements  104  on the screen  102  may be sequentially scanned, as illustrated in  FIG. 4 , by reflecting light emitted from the light source  112  within the projection unit  110  off of the horizontally rotating movable mirrored element  118  and off of the vertically rotating movable mirrored element  120  toward the screen  102 . The sequential scanning method  400  of  FIG. 4  may provide a light field that is concurrently viewable from a plurality of perspectives. 
     In the example embodiment illustrated in  FIG. 4 , the method  400  includes sweeping the light emitted from the light source  112  from left to right, horizontally, across the screen  102 . Next, the method  400  includes moving down to a second vertical location on the screen  102  and sweeping that horizontal path using light emitted from the light source  112  from right to left. After, the method  400  includes moving down to a third vertical location on the screen  102 . These steps may repeat until light has been reflected from the bottom-rightmost location on the screen  102  from which light is reflected to generate a light field. To achieve a scanning pattern as depicted in  FIG. 4 , the horizontally rotating movable mirrored element  118  may be rotating at a higher rate than the vertically rotating movable mirrored element  120 , in some embodiments. 
     In various embodiments, the light from the light source  112  may be swept across the convex reflective elements  104  in a continuous manner or at discrete points, depending on the design of the horizontally rotating movable mirrored element  118  and the vertically rotating movable mirrored element  120 . For example, if the horizontally rotating movable mirrored element  118  includes a mirror wrapped around a rotating cylinder, and the mirror has a continuously varying angle, the horizontal portion of the scan may be continuous from left to right and right to left, as illustrated in  FIG. 4 . Further, to generate the scanning pattern illustrated in  FIG. 4 , the vertically rotating movable mirrored element  120  may be faceted such that only specific vertical locations on the screen  102  are scanned. In alternate embodiments, the horizontal scanning lines may be segmented due to a discrete horizontal scan occurring, as opposed to a continuous scan. Further, in alternate embodiments, the vertical locations of the horizontal scans may be more densely or less densely packed than in  FIG. 4 . Furthermore, the horizontal density and/or vertical density with which the light ray projection locations on the screen  102  occur may serve to define an effective “resolution” of the generated light field. 
     Additionally, alternate scanning patterns are possible, in various embodiments. For example, each horizontal scan may occur from left to right, and be reset after every horizontal line back to the left end of the screen  102 . Alternatively, each horizontal scan may occur from right to left, and be reset after every horizontal line back to the right end of the screen  102 . As an additional alternative, a sequential scan of the screen  102  may occur from the bottom of the screen  102  upward rather than from the top of the screen downward. Still further, the scan could be wholly irregular, appearing to jump from one random location on a given convex reflective element  104  to another, based on the design of the one or more movable mirrored elements  118 / 120  (e.g., facets covered with mirrors on the movable mirrored elements  118 / 120  are not placed angularly sequentially around the perimeter of the movable mirrored elements  118 / 120 , thus the light ray emitted from the projection unit  110  may appear to illuminate the screen  102  in an irregular pattern). In addition, rather than tracing out the scanned pattern from top to bottom, line by line (i.e., performing a progressive scan), the projection unit  110  could skip every other line and then come back and fill in the skipped lines (i.e., perform an interlaced scan, similar to the way in which cathode ray tubes, CRTs, perform interlaced scans). 
     Still further, the rate at which the method  400  scans the entirety of the screen  102  may vary based on a modulation scheme determined by a control system  116  within the projection unit  110 . The rate may also depend on the rotational speed of one or more movable mirrored elements  118 / 120 , for example. The rate at which the scan occurs determines the rate at which a generated light field is refreshed when viewed from a plurality of perspectives. Due to the phenomenon referred to as “the persistence of vision”, the light field projection system  100  may be used to generate light fields that represent a moving scene to an observer. In such embodiments, the light field refresh rate may be at least 24 Hz to ensure a “persistence of vision” by observers of the light fields. In some embodiments, the scan refresh rate may be higher than 24 Hz. For example, in embodiments where an additional scan of the screen  102  occurs for each of three primary colors (red, green, and blue, for example) to generate multiple light fields of different colors, and thereby recreate a color scene for an observer, the refresh rate may be at least 72 Hz (24 Hz times 3 for each color). 
       FIG. 5 a    is a side view illustration of light rays  510 ,  520 ,  530 ,  540 ,  550  occurring during a horizontal scan of five different latitudinal positions on the convex reflective elements  104 , similar to five of the horizontal scan lines occurring in  FIG. 4 . Different from  FIG. 4 , however, is the fact that there are five horizontal scans occurring across each convex reflective element  104 , rather than three horizontal scans. 
     Each light ray  510 ,  520 ,  530 ,  540 ,  550  represents multiple light rays projected at various horizontal positions along the screen  102  (or longitudinal position along the individual convex reflective element  104 ) but at the same respective vertical position along the screen  102  (or latitudinal position along the individual convex reflective element  104 ). 
     For example, as shown in  FIG. 5 b    (a top view illustration), the light ray  530  represented in  FIG. 5 a    is projected along the corresponding row of convex reflective elements  104  at longitudinal positions  531 ,  532 ,  533 ,  534 ,  535 . The longitudinal positions  531 ,  532 ,  533 ,  534 ,  535  may be based on the angle of projection of light emitted from the projection unit  110 . The five consecutive angles of projection used to emit light to the five longitudinal positions  531 ,  532 ,  533 ,  534 ,  535 , for example, may be defined by five consecutive faceted reflectors at different angles along the perimeter of the horizontally rotating movable mirrored element  118 . Because, in the embodiments illustrated in  FIGS. 5 a  and 5 b   , the convex reflective elements  104  are substantially hemispherical, each pair of latitudinal position and longitudinal position on a single convex reflective element  104  produces a reflection at a different pair of azimuthal and elevation angles. The use of five latitudinal positions and five longitudinal positions is by way of example, and may not reflect the preferred number of positions in an actual system for an individual convex reflective element  104 . 
       FIG. 6  is an illustration of two perspective views  612 ,  622  of a scene (e.g., one block on top of another) recreated by a light field. The orientation of the two observers  610 ,  620  viewing the reflections with respect to the screen  102  is displayed from above. The two observers  610 ,  620  are at different x-locations (i.e., horizontal locations) with respect to the screen coordinates. Each observer  610 ,  620  may receive one or more reflections from each of the convex reflective elements  104  on the screen  102 . Because the screen  102  may include a 2D array of convex reflective elements  104 , the number of convex reflective elements  104  providing reflections may be more than is shown in  FIG. 6 , as  FIG. 6  is a top-view. The more densely packed and the smaller the convex reflective elements  104 , the more the light field generated by the light field projection system may appear to represent a full, continuous light field to the observers  610 ,  620 . The light field responsible for the two perspective views  612 ,  622  in  FIG. 6  may be projected by a light field projection unit  110 . 
     The perspective view from the left  612  illustrates how the observer  610  on the left may perceive the light field. Similarly, the perspective view from the right  622  illustrates how the observer  620  on the right may perceive the light field. If the two observers  610 / 620  were close enough to one another (e.g., if the two observers  610 / 620  were two eyes of a person), a binocular view of the scene may be created. Such a binocular view may create a stereoscopic 3D image for the union of the two observers  610 / 620 . 
     The reason that the perspective view from the left  612  and the perspective view from the right  622  produce different views of the scene is because the two perspective views  612 / 622  are receiving different light rays from different angles reflected off of the screen  102 . Each of the two observers  610 / 620  is located at a different set of quadruples (sets of x, y, φ, and θ) within the light field that is reflected from the screen  102 . The light field may be projected by a projection unit  110 , for example, such that each respective quadruple correctly recreates a perception of the scene from that quadruple. For example, a control system  116  within a projection unit  110  may determine a modulation scheme for a modulator  104  such that the light rays modulated according to the modulation scheme properly reconstruct the scene for each of the two observers  610 / 620 . 
     If the location of one or both of the observers  610 / 620  changed, the respective observer may be located at a new set of quadruples (sets of x′, y′, φ′, and θ′) within the light field. Thus, the perception of the scene from the new quadruples may be different than the perception of the scene from the original quadruples. This is similar to the way the perspective view from the left  612  of the scene is different from the perspective view from the right  622  of the scene. Alternatively, the observers  610 / 620  could be located at different y-locations (i.e., vertical locations) with respect to the screen  102 . An example of such an orientation of observers is illustrated and described with respect to  FIG. 7 . 
       FIG. 7  is an illustration of two perspective views  712 ,  722  of a scene (e.g., one block on top of another) recreated by a light field. The orientation of the two observers  710 ,  720  viewing the reflections from the screen  102  is displayed from the right side. The two observers  710 ,  720  are at different y-locations with respect to the screen coordinates. Each observer  710 ,  720  may receive a reflection from each of the convex reflective elements  104  on the screen  102 . The more densely packed and the smaller the convex reflective elements  104 , the more the light field generated by the light field projection system may appear to represent a full, continuous light field to the observers  710 ,  720   
     The light field generating the two perspective views  712 ,  722  in  FIG. 7  may be projected by a light field projection unit  110 . 
     The perspective view from the top  712  illustrates how the observer  710  on the top may perceive the light field. Similarly, the perspective view from the bottom  722  illustrates how the observer  720  on the bottom may perceive the light field. If the two observers  610 / 620  were close enough to one another (e.g., if the two observers  710 / 720  were two eyes of a person), a binocular view of the scene may be created. Such a binocular view may create a stereoscopic 3D image for the union of the two observers  710 / 720 . 
     The reason that the perspective view from the top  712  and the perspective view from the bottom  722  produce different views of the scene is because the two perspective views  712 / 722  are receiving different light rays from different angles reflected off of the screen  102 . Each of the two observers  710 / 720  is located at a different set of quadruples (sets of x, y, φ, and θ) within the light field that is reflected from the screen  102 . The light field may be projected by a projection unit  110 , for example, such that each respective quadruple correctly recreates a perception of the scene from that quadruple. For example, a control system  116  within a projection unit  110  may determine a modulation scheme for a modulator  104  such that the light rays modulated according to the modulation scheme properly reconstruct the scene for each of the two observers  710 / 720 . 
     If the location of one or both of the observers  710 / 720  changed, the respective observer may be located at a new set of quadruples (sets of x′, y′, φ′, and θ′) within the light field. Thus, the perception of the scene from the new quadruples may be different than the perception of the scene from the original quadruples. This is similar to the way the perspective view from the top  712  of the scene is different from the perspective view from the bottom  722  of the scene. Alternatively, the observers  710 / 720  could be located at different x-locations (i.e., horizontal locations) with respect to the screen  102 . An example of such an orientation of observers is illustrated and described with respect to  FIG. 6 . 
     Furthermore, the observers  710 / 720  could be located at both different x-locations and different y-locations with respect to one another. In this case, the differences between the perspective views of the scenes shown in  FIGS. 6 and 7  may be superposed. 
     In some embodiments, certain quadruples of the light field may be generating different scenes, entirely. For example, the light field may be projected by the projection unit  110  such that any quadruples with an azimuthal angle (φ) of 0 to 180 degrees will reproduce a mountain scene when viewed by an observer, whereas any quadruples that have an azimuthal angle (φ) of 180 to 360 degrees will reproduce an ocean scene. This would allow observers above a certain vertical location with respect to the screen  102  to perceive one scene (e.g., the mountain scene) and would allow observers below a certain vertical location with respect to the screen  102  to perceive a separate scene (e.g., the ocean scene). This could alternately be done base on the horizontal location of the observer by instead varying the azimuthal angle (φ) range of the mountain scene from 0 to 90 degrees and 270 to 360 degrees and the azimuthal angle (φ) range of the ocean scene from 90 to 270 degrees. 
       FIG. 8  is an illustration of a light field projection system  800 . The light field projection system  800  is similar to that illustrated in  FIG. 1 . Please consult  FIG. 1  and accompanying description for more information regarding the screen  102 , the convex reflective elements  104 , and the projection unit  110  (including the control system  116 ). However, in the light field projection system  800  of  FIG. 8 , a location of an observer  806  may be tracked by a location tracking device  810 . The dashed line in  FIG. 8  represents a communicative coupling between the location tracking device  810  and the control system  116 . 
     The location tracking device  810  may be an infrared sensor, a low-power laser system, or a camera, in various embodiments. The location tracking device  810  may identify, relative to the screen  102 , the location of the observer  806 . This may include the location tracking device  810  determining one or more quadruples of a generated light field that the observer  806  could perceive at its given location. Upon identifying the location of the observer  806 , the location tracking device  810  may transmit a notification to the control system  116  indicating the location of the observer  806 . This may be done by a wireline communication (e.g., over an Ethernet or universal serial bus—USB cable) or wireless communication (e.g., using Bluetooth® or WiFi-IEEE 802.11 standards), for example. In some embodiments, the location tracking device  810  may be a part of the screen  102 . In alternate embodiments, the location tracking device  810  may be part of the projection unit  110 . In still further embodiments, the location tracking device  810  may operate independently and transmit the results to the control system  116 , as illustrated in  FIG. 8 . 
     Upon receiving the location of the observer  806 , the control system  116  may modify a modulation scheme for use by the modulator  114  to generate the light field. For example, if the observer  806  constitutes all of the potential quadruples of the light field at which the light field will be viewed (e.g., the observer  806  is the only one perceiving the light field), the modulator  114  need not modulate light to generate other regions of the light field. This may reduce the calculation time (i.e., rendering time) for the control system  116  to determine a modulation scheme to reproduce the scene as a light field for different perspectives, because many possible perspectives need not be rendered. Furthermore, certain portions of the screen  102  and certain portions of each convex reflective element  104  may not need to be illuminated. This could conserve energy usage by the projection unit  110 . 
     In some embodiments, the location tracking device  810  may be configured to track the locations multiple observers. The location tracking device  810  may then transmit multiple locations to the control system  116 , thereby permitting the control system to determine a modulation scheme that would produce a light field viewable from a plurality, but not all possible, perspectives. Further, the location tracking device  810  may track two observer locations where each observer location corresponds to a person&#39;s left or right eye. Upon transmitting these two locations to the control system  116 , the control system  116  could determine a modulation scheme that would project a light field viewable from the perspective (i.e., collection of one or more quadruples with respect to the light field) of both eyes. This may permit the projection unit  110  to project a light field that appears stereoscopically 3D to a viewer while only modulating the light field so that it is viewable in two, rather than all possible, viewing locations. 
     Similarly, the location of multiple separate observers could be tracked by the location tracking device  810  to permit a scene change within the light field. For example, the location tracking device  810  may transmit the location of two users to the control system  110 . The control system  110  may then determine a modulation scheme to generate a light field that creates a different scene for each observer (e.g., one observer perceives a mountain scene and one perceives an ocean scene). As an additional application, if the projection system  100  were used to play a game, one observer could be shown her poker hand while the second observer was shown his poker hand, without each being able to see the other&#39;s poker hand. Furthermore, this may allow the control system  116  to determine a modulation scheme that produces a light field with a variation in intensity or produces multiple light fields that vary in color at different observing locations. Such variations could accommodate viewers who are partially blind and/or are color blind while not altering the viewing experience of viewers who do not have such visual impairments. 
       FIG. 9  is an illustration of a method of generating light fields of different colors with a projection unit  910 . The projection unit  910  is analogous to the projection unit  110  illustrated in  FIG. 1 , please consult  FIG. 1  and the accompanying description for more detail regarding the projection unit  910 . Similar to the projection unit  110  illustrated in  FIG. 1 , the projection unit  910  has a light source  912 , a modulator  914 , a control system  916 , and two movable mirrored elements  918 / 920 . Unlike the projection unit  110  illustrated in  FIG. 1 , though, the projection unit  910  illustrated in  FIG. 910  is configured to produce light fields of different frequencies. 
     One method of producing light fields of different colors may include multiplexing the light fields in time, as illustrated in  FIG. 9 . More specifically, a red light ray may be emitted toward the horizontally rotating movable mirrored element  918 , and then reflect off the horizontally rotating movable mirrored element  918  and the vertically rotating movable mirrored element  920 . This red light ray is then reflected off the screen  102  at a later time. Before one or both of the mirrored elements  918 / 920  rotate to display their next facet, however, a green light ray may follow the same path the red light ray followed and reflect off the same location on the screen  102 . Similarly for a blue light ray. These three colors (red, green, and blue—RGB, or, in alternate embodiments, cyan, magenta, and yellow—CMY) may then be perceived by an observer as overlapping, given that they are reflected off of the screen  102  at the same quadruple and at roughly the same time. Hence, the three quadruples of disparate light fields may appear to the observer as a single quadruple of one “colored light field”. Given the weighted light intensity of each of the red, green, and blue rays, multiple other colors can be generated that are perceivable by an observer. 
     The method for multiplexing the three, or more, colored light rays in time may include three consecutive light rays of different colors being generated by the light source  912 . Alternatively, the light source  912  may generate white light and then have a selective filter for the three, or more, different colors that is modulated at a 33% duty cycle for each color (using the three color example of  FIG. 9 ) and offset in time, one from the next, by 33%. In other embodiments, the modulator  914  may instead have a frequency filter. Further, the modulator  914  may have other means of modulating the frequency of the light emitted by the light source  912 . Additionally, a modulation scheme encoded by the control system  916  may include frequency modulation of the light emitted by the light source  912  in addition to intensity modulation. The frequency selected by such a modulation scheme may be capable of selecting the requisite frequency for the light field within a range of frequencies, rather than selecting one of three colors (e.g., RGB) and attempting to use combinations of those three colors to create alternate colors. 
     An alternative means of multiplexing multiple light fields of differing frequencies (colors) may involve a different design of the movable mirrored elements  918 / 920 . Rather than the movable mirrored elements  918 / 920  solely determining the location on the screen  102  at which the light emitted from the light source  912  is directed, the movable mirrored elements  918 / 920  may also select the frequency of the light they reflect. For example, three consecutive facets on the horizontally rotating movable mirrored element  918  may be angled with respect to the screen  102  at the same angle. However, each of the three consecutive facets may be coated with a different material, each materially selectively reflecting light of a different color (RGB, in an example embodiment analogous to the embodiment illustrated in  FIG. 9 ). 
       FIG. 10  is an illustration of another method of generating light fields of different colors. The components illustrated in  FIG. 10  may be part of a larger projection unit. The components include a light combining fiber  1002 , a first light source  1022  and a corresponding first modulator  1024 , a second light source  1032  and a corresponding second modulator  1034 , a third light source  1042  and a corresponding third modulator  1044 , and a control system  1016 . Similar to the projection units  110 ,  910  illustrated in  FIGS. 1 and 9 , respectively, the light output at the end of the light combining fiber  1002  could next be directed to a horizontally rotating movable mirrored element. 
     The light combining fiber  1002  may be formed of multiple input fibers (e.g., one for each light source  1022 ,  1032 ,  1042 ) spliced together at a fusion splice with a single output fiber. The lengths of the multiple input fibers may be the same, such that the optical path length for light emitted from each of the light sources  1022 ,  1032 ,  1042  is the same. In some embodiments, the light combining fiber  1002  may be made of silicon dioxide, for example. In alternate embodiments, free space optics, such as one or more mirrors or one or more lenses, may be used in addition to or in place of the light combining fiber  1002 . 
     The light sources  1022 ,  1032 ,  1042  may emit light of differing wavelengths. In the example embodiment illustrated in  FIG. 10 , the first light source  1022  emits light of a wavelength corresponding to the color red in the visible spectrum. Similarly, the second light source  1032  emits light of a wavelength corresponding to the color green in the visible spectrum and the third light source  1042  emits light of a wavelength corresponding to the color blue in the visible spectrum. The light sources  1022 ,  1032 ,  1042  may be lasers, in various embodiments. In some embodiments, there may be more than three light sources  1022 ,  1032 ,  1042 . For example, there may be six light sources, in some embodiments; one that emits red light, one that emits orange light, one that emits yellow light, one that emits green light, one that emits blue light, and one that emits violet light. 
     In the example embodiment illustrated in  FIG. 10 , each of the light sources  1022 ,  1032 ,  1042  is modulated by a corresponding modulator  1024 ,  1034 ,  1044 . Each of the modulators  1024 ,  1034 ,  1044  may modulate light according to a modulation scheme determined by the control system  1016 . The light may be modulated by each modulator  1024 ,  1034 ,  1044  such that a light field is projected off a screen (e.g., the screen  102  illustrated in  FIG. 1 ) corresponding to each of the three colors. These three light fields may be superimposed when perceived by an observer to form one scene with a continuum of colors based on the intensity of each of the base colors (e.g., red, green, and blue). In alternate embodiments, each of the modulators  1024 ,  1034 ,  1044  may be independently controlled by a respective control system, rather than jointly by a single control system  1016 , as illustrated in  FIG. 10 . 
       FIG. 11  is an illustration of a light field projection system  1100 . The light field projection system  1100  may comprise multiple subsystems that are similar to the light field projection system  110  illustrated in  FIG. 1  tiled together such that the corresponding screens are adjacent. The light field projection system  1100  includes a first screen  1112  and a corresponding first projection unit  1110 , a second screen  1122  and a corresponding second projection unit  1120 , a third screen  1132  and a corresponding third projection unit  1130 , and a fourth screen  1142  and a corresponding fourth projection unit  1140 . The embodiment illustrated in  FIG. 11  may permit borderless tiling of multiple screens to widen an area of permitted perspectives for viewing. In some embodiments, the projection units  1110 ,  1120 ,  1130 ,  1140  may sequentially scan the respective screens  1112 ,  1122 ,  1132 ,  1142  in different fashions (e.g., the projection unit  1110  may scan the corresponding screen  1112  from left-to-right, top-to-bottom and the projection unit  1120  may scan the corresponding screen  1122  from right-to-left, bottom-to-top). 
     The individual screens  1112 ,  1122 ,  1132 ,  1142  and the individual projection units  1110 ,  1120 ,  1130 ,  1140  may be analogous to the screen  102  and the projection unit  110  illustrated in  FIG. 1 , for example. However, in some embodiments of the light field projection system  1100  of  FIG. 11 , the screens  1112 ,  1122 ,  1132 ,  1142  and the projection units  1110 ,  1120 ,  1130 ,  1140  may work in tandem to produce a single light field (i.e., the range of x-coordinates and y-coordinates possible is increased given the increased size of the super-screen formed by the four individual screens  1112 ,  1122 ,  1132 ,  1142  disposed adjacent to one another). Such a single light field may reproduce one or more scenes concurrently viewable from various observer perspectives (analogous to the embodiment illustrated in  FIG. 1 ). In order to accomplish this, control systems of the projection units  1110 ,  1120 ,  1130 ,  1140  may communicate with one another to determine a modulation scheme for each of the modulators within the respective projection units  1110 ,  1120 ,  1130 ,  1140 . Additionally, because each of the projection units  1110 ,  1120 ,  1130 ,  1140  may only be rendering one-quarter of a given scene, the computational burden placed on each of the control systems within the respective projection units  1110 ,  1120 ,  1130 ,  1140  may be reduced compared to an embodiment in which each respective projection unit  1110 ,  1120 ,  1130 ,  1140  reproduced the entire given scene. Furthermore, in some embodiments, there may be an additional control system that is configured to divvy up a scene into smaller sub-scenes that are projected by each projection unit  1110 ,  1120 ,  1130 ,  1140 . In alternate embodiments, there may be a single control system that determines the modulation scheme for use by the modulator within each of the projection units  1110 ,  1120 ,  1130 ,  1140 , thereby replacing the respective control system within each respective projection unit  1110 ,  1120 ,  1130 ,  1140 . 
       FIG. 12  is an illustration of a light field projection system  1200 . The light field projection system  1200  includes a screen  1202 , with a plurality of concave refractive elements  1204  arranged into a two-dimensional array thereon, an observer  1206 , and a projection unit  1210 . The projection unit  1210  includes a light source  1212 , a modulator  1214 , a control system  1216 , and movable mirrored elements  1218 / 1220 . The light field projection system  1200  has a projection unit  1210  analogous to the projection unit  110  illustrated in  FIG. 1 . Please consult  FIG. 1  and the accompanying description for more details regarding the light source  1212 , the modulator  1214 , the control system  1216 , or the movable mirrored elements  1218 / 1220 . The primary difference of the embodiment of the light field projection system  1200  illustrated in  FIG. 12 , however, is that the screen  1202 , has concave refractive elements  1204  thereon, and lies between the projection unit  1210  and the observer  1206 . The light field projection system  1200  illustrated in  FIG. 12  may be spatially more compact, than the embodiment  100  illustrated in  FIG. 1 . 
     The concave refractive elements  1204  refract light projected by the projection unit  1210  to produce a light field. Analogous to the convex reflective elements  104 , the concave refractive elements  1204  may be sequentially scanned by the projection unit  1210  and disperse light to project a light field (e.g., a light field that represents a scene when viewed from the respective perspective of the observer  1206 , for example). The concave refractive elements  1204  may be, for example, substantially hemispherical lenses. The concave refractive elements  1204  may be fabricated of fused quartz, fluorite, or acrylic, in example embodiments. 
     III. EXAMPLE LIGHT FIELD PROJECTION METHODS 
       FIG. 13  is a flow chart illustration of a method of generating a light field  1300 , according to example embodiments. The method of generating the light field  1300  may be used to recreate one or more scenes that are viewable from a plurality of perspectives. Furthermore, the method of generating the light field  1300  may be performed by a projection unit of a light field projection system. 
     At step  1302 , the method  1300  includes receiving light field image data for projecting. The light field image data may be retrieved by a processor in a control system  116  from a non-transitory computer-readable medium within the control system  116 , for example. Alternatively, the light field image data may be transmitted to the control system  116  of the projection unit  110  by another device (e.g., over the public Internet). In some embodiments, the light field image data will be a single light field frame of a larger light field video data stream. 
     At step  1304 , the method  1300  includes decomposing the light field image data into one or more perspective images based on a number of perspectives. The number of perspectives may be defined by the location of observers (e.g., as tracked by a location tracking device  810  illustrated in  FIG. 8 ). Alternatively, the perspectives may be predefined locations (i.e., sets of quadruples) from which the light field is viewable. The control system  116  may use the perspectives to determine the modulation scheme. Therefore, a reduced number of perspectives may reduce the computation time required by the processor in the control system  116  to determine the modulation scheme. 
     At step  1306 , the method  1300  includes rendering perspective images into the modulation scheme that forms a light field when used to modulate light from a light source. Based on the number of perspectives, certain portions of the light field may be neglected to be projected, as those portions of the light field may not be displayed (e.g., there may be no observer located at the location where the perspective corresponding to that portion of the light field is viewable, therefore it is not displayed). Because they may be neglected to be projected, the modulation scheme may include skipping over those perspectives (i.e., those perspectives are not rendered into the modulation scheme). Rendering perspective images into the modulation scheme that forms the light field may include calculating intensity values at each location (i.e., each light field quadruple) of the perspective image. Furthermore, calculating intensity values may include calculating intensity values for multiple wavelengths corresponding to multiple light fields when a color perspective light field image is to be displayed. 
     At step  1308 , the method  1300  includes beginning rotation of the movable mirrored elements (e.g., the horizontally rotating movable mirrored element  118  and the vertically rotating movable mirrored element  120  illustrated in  FIG. 1 ). This may involve engaging a motor or a set of electromagnets to begin the motion of the movable mirrored elements  118 / 120 . In alternate embodiments in which alternate means of reflecting light from the light source  112  toward the screen  102  are used, step  1308  may by altered or neglected. 
     At step  1310 , the method  1300  includes emitting light from the light source  112 . Step  1310  may include the light source  112  being powered on and/or set to emission mode. Furthermore, step  1310 , in some embodiments, may be performed by a control system within or connected to the light source  112 . Additionally, step  1310  may include emitting light from multiple light sources. For example, if a light field projection unit being used to carry out method  1300  is analogous to the light field projection unit illustrated in  FIG. 10 , there may be multiple light sources  1022 ,  1032 ,  1042  for multiple wavelengths of light (i.e., colors in the visible spectrum). 
     At step  1312 , the method  1300  includes modulating light from the light source using the modulation scheme. The modulation scheme may be stored within a memory of a modulator  114 . Alternatively, the modulation scheme may be used by the control system  116  to repeatedly alter the conformation of the modulator  114  to modulate the light. Modulating the light may include electro-optic modulation methods of altering the intensity of the light received from the light source  112 . Additionally or alternatively, modulating the light may include altering the wavelength of the light from the light source. 
     At step  1314 , the method  1300  includes reflecting the modulated light toward a screen using the rotating movable mirrored elements  118 / 120  (or alternate elements, in various embodiments). In many embodiments, the modulation scheme created by the control system  116  has accounted for the timing of the rotation of the movable mirrored elements  118 / 120  such that the light is modulated in intensity for the specific, corresponding spot on the movable mirrored elements  118 / 120 , and thus, ultimately, the corresponding location on the screen  102 , to which that light will be directed. Also, in many embodiments, steps  1310 ,  1312 , and  1314  may occur repeatedly and/or concurrently when carrying out the method  1300 . 
     In some embodiments, one or more of the steps of method  1300  may be repeated multiple times for different scenes. For example, a sequence of light fields representing a moving scene (e.g., a live baseball game) may be projected by the projection unit. If the steps of method  1300  are repeated with sufficient rapidity (e.g., more than 24 times a second), motion in the moving scene may appear continuous to an observer due to the “persistence of vision” phenomenon. As an example calculation, if there are 1000 perspectives (e.g.,  10  vertical locations of perspectives, each with  100  corresponding horizontal perspective locations), and the two-dimensional resolution of the scene at each of those perspectives is equivalent to 1080p technology (i.e., a resolution of 1920 quadruples by 1080 quadruples), with a refresh rate of 24 Hz, the projection unit  110  may need to output light rays at a rate of about 50 GHz (1000×1920×1080×24 Hz). If distributed among four projection units  1110 ,  1120 ,  1130 ,  1140  (as illustrated in  FIG. 11 ), for example, this rate could be reduced by a factor of four for each respective projection unit  1110 ,  1120 ,  1130 ,  1140 . 
     Additionally, the light fields generated by repeating one or more of the steps of method  1300  may be concurrently viewable from a plurality of perspectives. This may permit a binocular viewer to stereoscopically observe the progressing light fields, thereby being provided with a continuous-motion, 3D image of the moving scene. 
     IV. EXAMPLE CALIBRATION METHODS 
     The calibration methods presented with regard to the following figures ( FIGS. 14-19 ) may be capable of accounting for any errors in the fabrication of a screen (e.g., the screen  102  illustrated in the previous figures), damage caused to the screen, misalignment of the screen relative to a given viewer, and/or misalignment of the screen relative to a projection unit (e.g., the projection unit  110  illustrated in the previous figures). A screen having convex reflective elements thereon that can be used to project light fields can be calibrated using the following methods, for example. Additionally, screens having concave refractive elements thereon that can be used to project light fields could also be calibrated in analogous methods as those described herein. 
     The calibration methods presented herein can be used to account for surface, macro-orientation alignment errors of the entire screen or errors in distribution of the convex reflective elements (or concave refractive elements) within an array on the screen (e.g., if the sizes of the non-reflective interstitial regions between adjacent convex reflective elements is not consistent across the array). For example, if the convex reflective elements (or concave refractive elements) are spaced unevenly, rather than in consistent horizontal and vertical increments across the screen, time delays could be added or removed from a modulation scheme used to project a light field that generates a plurality of concurrently viewable perspectives to account for the inconsistency in spacing. 
     In the following example methods, one or more perspectives relative to the screen may undergo calibration. The following methods could be used to calibrate a single perspective (e.g., a specific intended viewing perspective designated by a user). The following methods could also be used to calibrate two perspectives (e.g., two perspectives corresponding to the perspective locations of two eyes of a viewer who location is being tracked by the projection system). Further, the following methods could be repeated for any number of perspectives relative to the screen, up to and including the maximum number of viewable perspectives relative to the screen. In other words, the calibration methods that follow can be used to calibrate one section of the surface of one of the convex reflective elements, multiple sections of the surface of one of the convex reflective elements, multiple sections of the surfaces of multiple convex reflective elements, multiple sections of the surfaces of all of the convex reflective elements, the entire surface of one of the convex reflective elements, the entire surface of multiple convex reflective elements, or the entire surface of all of the convex reflective elements (similarly for concave refractive elements). 
     In addition, the calibration methods that follow can be executed at various points in the lifetime of the screen/projection system. For example, any of the following methods could be performed while the screen and/or projection system are being fabricated, or immediately after the screen and/or projection system are fabricated, to ensure that the fabrication process produced a reliable screen/projection system. The calibration methods could also be performed upon installation of the projection system (e.g., in a user&#39;s home), upon powering on the projection system (e.g., an initialization occurs each time the projection system is powered on), or while the projection system is in use (e.g., the projection system performs calibration using infrared light so as not to interfere with the viewing experience of users of the projection system). The following calibration methods could also be performed at various other times in the lifetime of the screen/projection system. 
       FIGS. 14 a  and 14 b    are illustrations of a calibration method, according to example embodiments. 
       FIG. 14 a    depicts a light field projection unit  110  of a light field projection system scanning a screen  102 . The light used to scan the screen  102  may be infrared (e.g., having an electromagnetic wavelength between 750 and 2,500 nm), for example, so as not to be visible by a viewer of the light field projection system. A light detector  1402  (e.g., an avalanche photodiode, a photoresistor, or a photovoltaic cell) is positioned at a first perspective relative to the screen  102  and the projection unit  110 , as well. In addition to or alternative to being configured to detect light intensity, the light detector  1402  may be configured to detect a wavelength of light reflected from the screen  102 . The first perspective may be defined by a set of a horizontal position, a vertical position, an azimuthal angle (φ), and an elevation angle (θ), all relative to the screen. The first perspective corresponds to one set of azimuthal and elevation angles on one of the convex reflective elements on the screen  102  (as indicated by the one reflected ray illustrated). Additionally or alternatively, the light detector  1402  may include multiple light-sensitive elements (e.g., in a sensor array of a charge-coupled device—CCD). The multiple light-sensitive elements may be spread out horizontally or vertically. 
     The scan of the screen  102  by the projection unit  110  may include a modulator within the projection unit  110  modulating light according to a baseline light intensity profile. The baseline intensity profile may correspond to a specific light field used for calibration (e.g., a light field that is similar to a Quick Response code—QR Code®), in some embodiments. This baseline light intensity profile may be used in conjunction with a location of the first perspective of the light detector  1402  to determine a first expected light intensity profile for measurement by the light detector  1402 . The first expected light intensity profile may be compared with a first measured light intensity profile, measured by the light detector  1402 , to determine if the light field projection system should be adjusted (i.e., calibrated) to account for any differences between the first measured light intensity profile and the first expected light intensity profile. Measuring the first measured light intensity profile using the light detector  1402  may include outputting a voltage and/or a current signal to a control system that corresponds to a light intensity value. The voltage and/or current signal may vary with respect to time as the light intensity incident on the light detector  1402  changes. For example, if the light detector  1402  is an avalanche photodiode, light incident on the light detector  1402  may excite charge within the light detector  1402 . The excited charge may be separated between two terminals of the light detector  1402 , thus manifesting the light intensity incident on the light detector  1402  as a voltage differential across the two terminals. 
     Accounting for any differences may include modifying the operation of a control system of the projection unit  110 . Modifying the operation of the control system may include altering a modulation scheme, for use by a modulator in the projection unit  110 , that is determined by the control system to produce a light field that is concurrently viewable from a plurality of perspectives relative to the screen  102  (e.g., by inserting or removing time delays or altering an intensity output by the modulator at a certain time point in the modulation scheme). For example, if the first expected light intensity profile has a spike of light intensity at 100 ps into the scan of the screen  110 , but the first measured light intensity profile has a spike of light intensity at 98 ps into the scan of the screen  110 , a time delay of 2 ps may be added to modulation schemes determined by the control system. Altering the modulation scheme may additionally or alternatively include increasing or decreasing the intensity output by the projection unit  110  at various times of the modulation scheme. Further, altering the modulation scheme may include increasing or decreasing the wavelength of light emitted by the projection unit  110  at various times of the modulation scheme. 
     In  FIG. 14 b   , the light detector  1402  has been translated horizontally to the left (as illustrated in reference diagram  1450 ). In alternate embodiments, the light detector  1402  could be translated horizontally to the right. Additionally or alternatively, the light detector  1402  could be translated vertically. The new location of the light detector  1402  corresponds to a second perspective (x′, y′, φ′, and θ′) relative to the screen  102 . In some embodiments, the distance translated between  FIGS. 14 a  and 14 b    will correspond to a distance between two human eyes at a given distance from the screen  102 ; namely, the distance at which the light detector  1402  is located. This may allow the method to calibrate for a stereoscopic set of perspectives for use by a viewer at one possible viewing location, for example. Additionally or alternatively, the distance translated between  FIGS. 14 a  and 14 b    may be defined by a step size of a motor or a stage configured to translate the light detector  1402  (e.g. a piezoelectric stage or a stepper motor). The step size may correspond to a predefined resolution of the calibration method. Even further, the distance translated could correspond to the width of a typical human pupil under specific lighting conditions at the distance at which the light detector  1402  is from the screen  102 , or at the farthest distance from the screen  102  at which the screen  102  is ostensibly viewable. After the light detector  1402  translates to the left, the projection unit  110  scans the screen  102 . As with the first perspective, the second perspective of the light detector  1402  corresponds to a second set of azimuthal and elevation angles on one of the convex reflective elements. The distance between the first and the second perspectives may correspond to a resolution between discrete viewing perspectives of the light field projection system. 
     As with  FIG. 14 a   , the scan of the screen  102  by the projection unit  110  may include the modulator within the projection unit  110  modulating light according to the baseline light intensity profile. The baseline light intensity profile may similarly be used in conjunction with a location of the second perspective of the light detector to determine a second expected light intensity profile for measurement by the light detector. The second expected light intensity profile may be compared with a second measured light intensity profile, measured by the light detector, to determine if the light field projection system should be adjusted (i.e., calibrated) to account for any differences between the second measured light intensity profile and the second expected light intensity profile. Accounting for any differences may include modifying the operation of a control system of the projection unit  110 . Modifying the operation of the control system may include altering a modulation scheme, for use by a modulator in the projection unit  110 , that is determined by the control system to produce a light field that is concurrently viewable from a plurality of perspectives relative to the screen  102  (e.g., by inserting or removing time delays or altering an intensity output by the modulator at a certain time point in the modulation scheme). For example, if the second expected light intensity profile has a spike of light intensity at 100 ps into the scan of the screen  110 , but the second measured light intensity profile has a spike of light intensity at 98 ps into the scan of the screen  110 , a time delay of 2 ps may be added to modulation schemes determined by the control system. Altering the modulation scheme may additionally or alternatively include increasing or decreasing the intensity output by the projection unit  110  at various times of the modulation scheme. Further, altering the modulation scheme may include increasing or decreasing the wavelength of light emitted by the projection unit  110  at various times of the modulation scheme. 
     The steps of the method illustrated in  FIGS. 14 a  and 14 b    may be repeated for multiple perspectives relative to the screen  102 . For example, a user may have predetermined perspectives relative to the screen  102  for intended viewing. Similar to an audiophile listener who tweaks the transfer function of a sound system to obtain increased fidelity at specific listening locations within a space, the method of calibration described above with respect to  FIGS. 14 a  and 14 b    could be repeated for each of those predetermined perspectives. Further, in some embodiments, the steps of moving the detector  1402 , scanning the screen  102  using the projection unit  110 , measuring the corresponding light intensity profile, comparing the measured light intensity profile to the expected light intensity profile, and modifying the operation of a control system to account for any differences between the measured light field intensity profile and the expected light intensity profile may be repeated for each possible viewable perspective to calibrate each possible viewing perspective. In this way, the entirety of the screen  102  may be calibrated. 
     In other embodiments, the detector  1402  may not be moved at all (i.e., the steps illustrated in  FIG. 14 b    are not performed). This may be the case, for example, if the screen  102  is sufficiently rigid and resistant to damage so as to negate a possibility of bending or scratching of the screen  102 . Thus, from a single calibration measurement for a single perspective (e.g., the first perspective illustrated in  FIG. 14 a   ), the location of each, and any rotational offset of each, of the convex reflective elements relative to the projection unit  110  can be deduced. This may be accomplished by comparing the first measured intensity profile with an expected intensity profile that is based on a calibration previously performed for the screen  102 . For example, the screen  102  may have been calibrated at a factory after fabrication. Upon a viewer installing the screen  102 , the calibration step illustrated in  FIG. 14 a    may determine the first measured intensity profile. Assuming the screen is sufficiently rigid and resistant to damage, the first measured intensity profile could be compared to the expected intensity profile that is based on a previous calibration to determine and angular offsets or directional offsets of the installed screen  102  that have occurred on the macro-scale. This could then be accounted for by a control system of the projection unit  110 . 
       FIGS. 15 a  and 15 b    are illustrations of a calibration method, according to example embodiments. 
       FIG. 15 a    depicts a light field projection unit  110  of a light field projection system scanning a screen  102 . The light used to scan the screen  102  may be infrared (e.g., having an electromagnetic wavelength between 750 and 2,500 nm), for example, so as not to be visible by a viewer of the light field projection system. The measurement illustrated in  FIG. 15 a    can be the same as the measurement described with respect to and illustrated in  FIG. 14 a   . As illustrated in  FIG. 14 a   , a light detector  1402  (e.g., an avalanche photodiode, a photoresistor, or a photovoltaic cell) is positioned at a first perspective relative to the screen  102  and the projection unit  110 . In addition to or alternative to being configured to detect light intensity, the light detector  1402  may be configured to detect a wavelength of light reflected from the screen  102 . The first perspective may be defined by a set of a horizontal position, a vertical position, an azimuthal angle (φ), and an elevation angle (θ), all relative to the screen. The first perspective corresponds to one set of azimuthal and elevation angles on one of the convex reflective elements on the screen  102  (as indicated by the one reflected ray illustrated). 
     The scan of the screen  102  by the projection unit  110  may include a modulator within the projection unit  110  modulating light according to a baseline light intensity profile. The baseline intensity profile may correspond to a specific light field used for calibration (e.g., a light field that is similar to a Quick Response code—QR Code®), in some embodiments. This baseline light intensity profile may be used in conjunction with a location of the first perspective of the light detector  1402  to determine a first expected light intensity profile for measurement by the light detector  1402 . The first expected light intensity profile may be compared with a first measured light intensity profile, measured by the light detector  1402 , to determine if the light field projection system should be adjusted (i.e., calibrated) to account for any differences between the first measured light intensity profile and the first expected light intensity profile. Measuring the first measured light intensity profile using the light detector  1402  may include outputting a voltage and/or a current signal to a control system that corresponds to a light intensity value. The voltage and/or current signal may vary with respect to time as the light intensity incident on the light detector  1402  changes. For example, if the light detector  1402  is an avalanche photodiode, light incident on the light detector  1402  may excite charge within the light detector  1402 . The excited charge may be separated between two terminals of the light detector  1402 , thus manifesting the light intensity incident on the light detector  1402  as a voltage differential across the two terminals. 
     Accounting for any differences may include modifying the operation of a control system of the projection unit  110 . Modifying the operation of the control system may include altering a modulation scheme, for use by a modulator in the projection unit  110 , that is determined by the control system to produce a light field that is concurrently viewable from a plurality of perspectives relative to the screen  102  (e.g., by inserting or removing time delays or altering an intensity output by the modulator at a certain time point in the modulation scheme). For example, if the first expected light intensity profile has a spike of light intensity at 100 ps into the scan of the screen  110 , but the first measured light intensity profile has a spike of light intensity at 98 ps into the scan of the screen  110 , a time delay of 2 ps may be added to modulation schemes determined by the control system. Altering the modulation scheme may additionally or alternatively include increasing or decreasing the intensity output by the projection unit  110  at various times of the modulation scheme. Further, altering the modulation scheme may include increasing or decreasing the wavelength of light emitted by the projection unit  110  at various times of the modulation scheme. 
     The measurement performed in  FIG. 15 b    is analogous to the measurement described with respect to and illustrated in  FIG. 14 b   . However, rather than translating the light detector  1402  between measurements in  FIGS. 15 a  and 15 b   , the screen  102  has instead been rotated, when viewed from above, in a counterclockwise direction (as illustrated in reference diagram  1550 ). Thus, even though the light detector  1402  may not have moved, the light detector  1402  is in a new location relative to the screen  102 . In alternate embodiments, the screen  102  could be rotated in a clockwise direction. Additionally or alternatively, the screen  102  could rotate about a horizontal axis, as opposed to a vertical one. 
     The new location of the light detector  1402  corresponds to a second perspective (x′, y′, φ′, and θ′) relative to the screen  102 . This second perspective may be the same or a different perspective from the perspective illustrated in  FIG. 14 b   . In some embodiments, the angular rotation of the screen  102  between  FIGS. 15 a  and 15 b    will correspond to an angular width between two human eyes at a given distance from the screen  102 ; namely, the distance at which the light detector  1402  is located. This may allow the method to calibrate for a stereoscopic set of perspectives for use by a viewer at one possible viewing location, for example. Additionally or alternatively, the distance rotated between  FIGS. 15 a  and 15 b    may be defined by a step size of a motor or a stage configured to rotate the screen  102  (e.g. a piezoelectric stage or a stepper motor). The step size may correspond to a predefined resolution of the calibration method. After the screen  102  rotates in a counterclockwise direction, the projection unit  110  again scans the screen  102 . Even further, the angular rotation could correspond to the angular width of a typical human pupil under specific lighting conditions at the distance at which the light detector  1402  is from the screen  102  or at the farthest distance from the screen  102  at which the screen  102  is ostensibly viewable. As with the first perspective, the second perspective of the light detector  1402  corresponds to a second set of azimuthal and elevation angles on one of the convex reflective elements. The distance between the first and the second perspectives may correspond to a resolution between discrete viewing perspectives of the light field projection system. 
     As with  FIGS. 14 a , 14 b , and 15 a   , the scan of the screen  102  by the projection unit  110  may include the modulator within the projection unit  110  modulating light according to the baseline light intensity profile. The baseline light intensity profile may similarly be used in conjunction with a location of the second perspective of the light detector to determine a second expected light intensity profile for measurement by the light detector. The second expected light intensity profile may be compared with a second measured light intensity profile, measured by the light detector, to determine if the light field projection system should be adjusted (i.e., calibrated) to account for any differences between the second measured light intensity profile and the second expected light intensity profile. Accounting for any differences may include modifying the operation of a control system of the projection unit  110 . Modifying the operation of the control system may include altering a modulation scheme, for use by a modulator in the projection unit  110 , that is determined by the control system to produce a light field that is concurrently viewable from a plurality of perspectives relative to the screen  102  (e.g., by inserting or removing time delays or altering an intensity output by the modulator at a certain time point in the modulation scheme). For example, if the second expected light intensity profile has a spike of light intensity at 100 ps into the scan of the screen  110 , but the second measured light intensity profile has a spike of light intensity at 98 ps into the scan of the screen  110 , a time delay of 2 ps may be added to modulation schemes determined by the control system. Altering the modulation scheme may additionally or alternatively include increasing or decreasing the intensity output by the projection unit  110  at various times of the modulation scheme. Further, altering the modulation scheme may include increasing or decreasing the wavelength of light emitted by the projection unit  110  at various times of the modulation scheme. 
     The steps of the method illustrated in  FIGS. 15 a  and 15 b    may be repeated for multiple perspectives relative to the screen  102 . In some embodiments, for example, the steps of rotating the screen  102 , scanning the screen  102  using the projection unit  110 , measuring the corresponding light intensity profile, comparing the measured light intensity profile to the expected light intensity profile, and modifying the operation of a control system to account for any differences between the measured light field intensity profile and the expected light intensity profile may be repeated for each possible viewable perspective to calibrate each possible viewing perspective. In this way, the entirety of the screen  102  may be calibrated. 
       FIG. 16  is an illustration of a calibration method, according to example embodiments. 
       FIG. 16  depicts a light field projection unit  110  of a light field projection system scanning a screen  102 . The light used to scan the screen  102  may be infrared (e.g., having an electromagnetic wavelength between 750 and 2,500 nm), for example, so as not to be visible by a viewer of the light field projection system. The measurements illustrated in  FIG. 16  can be analogous to the measurements described with respect to and illustrated in  FIGS. 14 a  and 14 b    or  FIGS. 15 a  and 15 b   . As illustrated, a first light detector  1602  (e.g., an avalanche photodiode, a photoresistor, or a photovoltaic cell) and a second light detector  1604  (e.g., an avalanche photodiode, a photoresistor, or a photovoltaic cell) are positioned at a first perspective and a second perspective relative to the screen  102  and the projection unit  110 , respectively. In addition to or alternative to being configured to detect light intensity, the light detectors  1602 / 1604  may be configured to detect wavelengths of light reflected from the screen  102 . The first and second perspectives may each be defined by a set of a horizontal position, a vertical position, an azimuthal angle (φ), and an elevation angle (θ), all relative to the screen (e.g., x 1 , y 1 , φ 1 , θ 1  and x 2 , y 2 , φ 2 , θ 2 , respectively). The first and second perspectives correspond to two sets of azimuthal and elevation angles on two of the convex reflective elements on the screen  102  (as indicated by the reflected rays illustrated). The distance between the first and the second perspectives may correspond to a resolution between discrete viewing perspectives of the light field projection system. 
     The scan of the screen  102  by the projection unit  110  may include a modulator within the projection unit  110  modulating light according to a baseline light intensity profile. The baseline intensity profile may correspond to a specific light field used for calibration (e.g., a light field that is similar to a Quick Response code—QR Code®), in some embodiments. This baseline light intensity profile may be used in conjunction with a location of the first perspective and a location of the second perspective of the light detectors  1602 / 1604 , respectively, to determine a first expected light intensity profile and a second expected light intensity profile for measurement by the light detectors  1602 / 1604 . The first expected light intensity profile may be compared with a first measured light intensity profile, measured by the first light detector  1602 , and the second expected light intensity profile may be compared with a second measured light intensity profile, measured by the second light detector  1604 , to determine if the light field projection system should be adjusted (i.e., calibrated) to account for any differences between the measured light intensity profiles and the expected light intensity profiles. Measuring the first and second measured light intensity profiles using the light detectors  1602 / 1604  may include outputting voltage and/or current signals to one or more control systems that correspond to measured light intensity values. The voltage and/or current signals may vary with respect to time as the light intensity incident on the light detectors  1602 / 1604  changes. For example, if the light detectors  1602 / 1604  are avalanche photodiodes, light incident on the light detectors  1602 / 1604  may excite charge within the light detectors  1602 / 1604 . The excited charge may be separated between two terminals of the respective light detectors  1602 / 1604 , thus manifesting the light intensity incident on the light detectors  1602 / 1604  as a voltage differential across the two terminals of the respective light detector  1602 / 1604 . 
     Accounting for any differences may include modifying the operation of a control system of the projection unit  110 . Modifying the operation of the control system may include altering a modulation scheme, for use by a modulator in the projection unit  110 , that is determined by the control system to produce a light field that is concurrently viewable from a plurality of perspectives relative to the screen  102  (e.g., by inserting or removing time delays or altering an intensity output by the modulator at a certain time point in the modulation scheme). For example, if one of the expected light intensity profiles has a spike of light intensity at 100 ps into the scan of the screen  110 , but the corresponding measured light intensity profile has a spike of light intensity at 98 ps into the scan of the screen  110 , a time delay of 2 ps may be added to modulation schemes determined by the control system. Altering the modulation scheme may additionally or alternatively include increasing or decreasing the intensity output by the projection unit  110  at various times of the modulation scheme. Further, altering the modulation scheme may include increasing or decreasing the wavelength of light emitted by the projection unit  110  at various times of the modulation scheme. 
     In some embodiments, the two perspectives of the two light detectors  1602 / 1604  may be analogous to the two perspectives measured in  FIGS. 14 a  and 14 b    or in  FIGS. 15 a  and 15 b   . Alternatively, one or both of the perspectives could be different from those illustrated in previous figures. Further, the two perspectives of the two light detectors  1602 / 1604  could be located at binocular perspectives from an intended viewing location of the screen  102 . This may allow the method to calibrate for a stereoscopic set of perspectives for use by a viewer using two eyes to observe the screen  102 , for example. 
     A primary difference between the measurements made in  FIGS. 14 a  and 14 b    and  FIGS. 15 a  and 15 b    and the measurement made in  FIG. 16  is that in  FIG. 16 , only one scan of the screen  102  may be performed to do both measurements. This can occur because there are multiple light detectors  1602 / 1604 , as opposed to one light detector, performing simultaneous light intensity measurements. 
     In addition, the calibration model illustrated in  FIG. 16  is extensible for various numbers of light detectors. For example, three light detectors, as opposed to two, could be used to calibrate three perspectives of the screen using a single scan of the screen with the light projection unit. Additional light detectors could be added to calibrate additional perspectives relative to the screen (e.g., five light detectors, twenty light detectors, one hundred light detectors, one thousand light detectors, etc.). Further, rather than using discrete/individual light detectors, an array of light detectors could be used. For example, a screen of light detectors could be arranged in an array. The screen of light detectors could then be positioned relative to the screen of convex reflective elements such that each of the potential viewable perspectives relative to the screen of convex reflective elements would correspond to at least one of the light detectors in the array of light detectors on the screen of light detectors. This screen could then be used to calibrate each of the viewable perspectives relative to the screen using a single scan of the screen of convex reflective elements from the light projection unit according to a given baseline light intensity profile. Such a technique of calibration using an array of light detectors (e.g., a CCD) could be used in a fabrication facility to ensure a proper fabrication of the screen of convex reflective elements, for example. Alternatively, such a technique could be used by a service technician to correct defects noticed by a user. Other uses for such an embodiment are possible. 
       FIG. 17  is a flow chart illustration of a calibration method  1700  for calibrating a light field projection system comprising a screen having a plurality of convex reflective elements, according to example embodiments. The calibration method  1700  may be carried out by a control system  116  of the light field projection system  100 , in some embodiments. The calibration method  1700  may be executed each time the light field projection system  100  is powered on, for example. In other embodiments, the calibration method  1700  may take place in a screen production/fabrication facility after the screen  102  is fabricated. Steps of the calibration method  1700  may resemble the method illustrated in  FIGS. 14 a    and  14   b.    
     At step  1702 , the calibration method  1700  includes sequentially scanning the plurality of convex reflective elements, by a projection unit of the light field projection system, using light modulated according to a baseline intensity profile. 
     At step  1704 , the calibration method  1700  includes detecting, using a light detector located at a first perspective relative to the screen and the projection unit, a first measured intensity profile of light reflected from the plurality of convex reflective elements. 
     At step  1706 , the calibration method  1700  includes comparing the first measured intensity profile with a first expected intensity profile based on the baseline intensity profile and the first perspective of the light detector. 
     At step  1708 , the calibration method  1700  includes modifying operation of a control system of the light field projection system to account for any differences between the first measured intensity profile and the first expected intensity profile. The control system is configured to determine a light field modulation scheme for projecting a light field using the light field projection system. 
     At step  1710 , the calibration method  1700  includes moving the light detector to a second perspective relative to the screen and the projection unit. 
     At step  1712 , the calibration method  1700  includes sequentially scanning the plurality of convex reflective elements, by the projection unit of the light field projection system, using light modulated according to the baseline intensity profile. 
     At step  1714 , the calibration method  1700  includes detecting, using the light detector located at a second perspective relative to the screen and the projection unit, a second measured intensity profile of light reflected from the plurality of convex reflective elements. 
     At step  1716 , the calibration method  1700  includes comparing the second measured intensity profile with a second expected intensity profile based on the baseline intensity profile and the second perspective of the light detector. 
     At step  1718 , the calibration method  1700  includes modifying operation of the control system of the light field projection system to account for any differences between the second measured intensity profile and the second expected intensity profile. 
       FIG. 18  is a flow chart illustration of a calibration method  1800  calibrating a light field projection system comprising a screen having a plurality of convex reflective elements, according to example embodiments. The calibration method  1800  may be carried out by a control system  116  of the light field projection system  100 , in some embodiments. The calibration method  1800  may be executed each time the light field projection system  100  is powered on, for example. In other embodiments, the calibration method  1800  may take place in a screen production/fabrication facility after the screen  102  is fabricated. Steps of the calibration method  1800  may resemble the method illustrated in  FIGS. 15 a    and  15   b.    
     At step  1802 , the calibration method  1800  includes sequentially scanning the plurality of convex reflective elements, by a projection unit of the light field projection system, using light modulated according to a baseline intensity profile. 
     At step  1804 , the calibration method  1800  includes detecting, using a light detector located at a first perspective relative to the screen and the projection unit, a first measured intensity profile of light reflected from the plurality of convex reflective elements. 
     At step  1806 , the calibration method  1800  includes comparing the first measured intensity profile with a first expected intensity profile based on the baseline intensity profile and the first perspective of the light detector. 
     At step  1808 , the calibration method  1800  includes modifying operation of a control system of the light field projection system to account for any differences between the first measured intensity profile and the first expected intensity profile. The control system is configured to determine a light field modulation scheme for projecting a light field using the light field projection system. 
     At step  1810 , the calibration method  1800  includes rotating the screen in a first angular direction relative to the light detector and the projection unit so the light detector is located at a second perspective relative to the screen and the projection unit. Rotating the screen in the first angular direction may include rotating the screen through a first angle in the first angular direction. The first angle may correspond to an angular resolution between the first perspective and the second perspective. The angular resolution may also correspond to an angular separation between two eyes of a viewer at a set distance from the screen. The first angular direction may be an azimuthal angular direction relative to the screen, an elevation angular direction relative to the screen, or a superposition of the azimuthal angular direction and the elevation angular direction relative to the screen. 
     At step  1812 , the calibration method  1800  includes sequentially scanning the plurality of convex reflective elements, by the projection unit of the light field projection system, using light modulated according to the baseline intensity profile. 
     At step  1814 , the calibration method  1800  includes detecting, using the light detector located at a second perspective relative to the screen and the projection unit, a second measured intensity profile of light reflected from the plurality of convex reflective elements. 
     At step  1816 , the calibration method  1800  includes comparing the second measured intensity profile with a second expected intensity profile based on the baseline intensity profile and the second perspective of the light detector. 
     At step  1818 , the calibration method  1800  includes modifying operation of the control system of the light field projection system to account for any differences between the second measured intensity profile and the second expected intensity profile. 
       FIG. 19  is a flow chart illustration of a calibration method calibrating a light field projection system comprising a screen having a plurality of convex reflective elements, according to example embodiments. The calibration method  1900  may be carried out by a control system  116  of the light field projection system  100 , in some embodiments. The calibration method  1900  may be executed each time the light field projection system  100  is powered on, for example. In other embodiments, the calibration method  1900  may take place in a screen production/fabrication facility after the screen  102  is fabricated. A setup used for the calibration method  1900  may resemble the setup illustrated in  FIG. 16 . 
     At step  1902 , the calibration method  1900  includes sequentially scanning the plurality of convex reflective elements, by a projection unit of the light field projection system, using light modulated according to a baseline intensity profile. 
     At step  1904 , the calibration method  1900  includes detecting, using a first light detector located at a first perspective relative to the screen and the projection unit, a first measured intensity profile of light reflected from the plurality of convex reflective elements. 
     At step  1906 , the calibration method  1900  includes detecting, using a second light detector located at a second perspective relative to the screen and the projection unit, a second measured intensity profile of light reflected from the plurality of convex reflective elements. 
     At step  1908 , the calibration method  1900  includes comparing the first measured intensity profile with a first expected intensity profile based on the baseline intensity profile and the first perspective of the first light detector. 
     At step  1910 , the calibration method  1900  includes comparing the second measured intensity profile with a second expected intensity profile based on the baseline intensity profile and the second perspective of the second light detector. 
     At step  1912 , the calibration method  1900  includes modifying operation of a control system of the light field projection system to account for any differences between the first measured intensity profile and the first expected intensity profile and any differences between the second measured intensity profile and the second expected intensity profile. The control system is configured to determine a light field modulation scheme for projecting a light field using the light field projection system. 
     V. CONCLUSION 
     The above detailed description describes various features and functions of the disclosed systems, devices, and methods with reference to the accompanying figures. While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent. The various aspects and embodiments disclosed herein are for purposes of illustration only and are not intended to be limiting, with the true scope being indicated by the following claims.