Patent Publication Number: US-2021165194-A1

Title: Wide Field of View Five Element Lens System

Description:
BACKGROUND 
     This application is a continuation of U.S. patent application Ser. No. 16/120,142, filed Aug. 31, 2018, which claims benefit of priority to U.S. Provisional Application Ser. No. 62/577,679, filed Oct. 26, 2017, and which are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     This disclosure relates generally to camera systems, and more specifically to small form factor camera and lens systems. 
     DESCRIPTION OF THE RELATED ART 
     The advent of small, mobile multipurpose devices such as smartphones and tablet or pad devices has resulted in a need for high-resolution, small form factor cameras that are lightweight, compact, and capable of capturing high resolution, high quality images at low F-numbers for integration in the devices. However, due to limitations of conventional camera technology, conventional small cameras used in such devices tend to capture images at lower resolutions and/or with lower image quality than can be achieved with larger, higher quality cameras. Achieving higher resolution with small package size cameras generally requires use of a photosensor with small pixel size and a good, compact imaging lens system. Advances in technology have achieved reduction of the pixel size in photosensors. However, as photosensors become more compact and powerful, demand for compact imaging lens systems with improved imaging quality performance has increased. In addition, there are increasing expectations for small form factor cameras to be equipped with higher pixel count and/or larger pixel size image sensors (one or both of which may require larger image sensors) while still maintaining a module height that is compact enough to fit into portable electronic devices. Thus, a challenge from an optical system design point of view is to provide an imaging lens system that is capable of capturing high brightness, high resolution images under the physical constraints imposed by small form factor cameras. 
     SUMMARY OF EMBODIMENTS 
     Embodiments of the present disclosure may provide an imaging lens system including a front aperture and five lens elements that may, for example, be used in a compact camera and that provide a low F-number (&lt;=2.4), wide field of view (&gt;=82 degrees), and short total track length (TTL) that allow the camera to be implemented in a small package size while still capturing sharp, high-resolution images, making embodiments of the camera suitable for use in small and/or mobile multipurpose devices. Embodiments of the lens system include five lens elements with refractive power arranged along an optical axis from a first lens element on the object side to a fifth lens on the image side. The lens system includes a front aperture stop located at the first lens element at or behind the front vertex of the lens system. 
     Lens system parameters and relationships including but not limited to lens shape, thickness, geometry, position, materials, spacing, and the surface shapes of certain lens elements may be selected at least in part to reduce, compensate, or correct for optical aberrations and lens artifacts and effects across the field of view. 
     In some embodiments, the lens system may include an infrared (IR) filter to reduce or eliminate interference of environmental noise on the photosensor. The IR filter may, for example, be located between the fifth lens element and a photosensor. In some embodiments, a cover glass may be located on the object side of the lens system. In some embodiments, the cover glass may have a small amount of refractive power. In some embodiments, the lens system is a fixed-focus lens. However, in some embodiments, the camera may include an optical actuator component located in front of the lens system that provides autofocus (AF) functionality for the camera. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional illustration of a lens system that includes five lens elements and a front aperture and that provide a low F-number (&lt;=2.4), wide field of view (&gt;=82 degrees), and short total track length (TTL), according to some embodiments. 
         FIG. 2  illustrates optical characteristics of the fourth and fifth lens elements of a lens system as illustrated in  FIG. 1 , according to some embodiments. 
         FIGS. 3A and 3B  illustrate local radius/curvature of a first surface of the fifth lens element of a lens system as illustrated in  FIG. 1 , according to some embodiments. 
         FIGS. 4A and 4B  illustrate local thickness delta of the fifth lens element of a lens system as illustrated in  FIG. 1 , according to some embodiments. 
         FIGS. 5 and 6  illustrate relationships of the fourth and fifth lens elements of a lens system as illustrated in  FIG. 1 , according to some embodiments. 
         FIG. 7A  is a cross-sectional illustration of a first embodiment of a lens system that includes five lens elements. 
         FIG. 7B  is a graph illustrating the modulation transfer function (MTF) for a lens system as illustrated in  FIG. 7A . 
         FIG. 8A  is a cross-sectional illustration of a second embodiment of a lens system that includes five lens elements. 
         FIG. 8B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 9A . 
         FIG. 9A  is a cross-sectional illustration of a third embodiment of a lens system that includes five lens elements. 
         FIG. 9B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 3A . 
         FIG. 10A  is a cross-sectional illustration of a fourth embodiment of a lens system that includes five lens elements. 
         FIG. 10B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 10A . 
         FIG. 11A  is a cross-sectional illustration of a fifth embodiment of a lens system that includes five lens elements. 
         FIG. 11B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 11A . 
         FIG. 12A  is a cross-sectional illustration of a sixth embodiment of a lens system that includes five lens elements. 
         FIG. 12B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 12A . 
         FIG. 13A  is a cross-sectional illustration of a seventh embodiment of a lens system that includes five lens elements. 
         FIG. 13B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 13A . 
         FIG. 14A  is a cross-sectional illustration of an eighth embodiment of a lens system that includes five lens elements. 
         FIG. 14B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 14A . 
         FIG. 15  is a flowchart of a method for capturing images using a camera as illustrated in  FIGS. 1A through 8C , according to some embodiments. 
         FIG. 16  illustrates an example computer system that may be used in embodiments. 
     
    
    
     This specification includes references to “one embodiment” or “an embodiment.” The appearances of the phrases “in one embodiment” or “in an embodiment” do not necessarily refer to the same embodiment. Particular features, structures, or characteristics may be combined in any suitable manner consistent with this disclosure. 
     “Comprising.” This term is open-ended. As used in the appended claims, this term does not foreclose additional structure or steps. Consider a claim that recites: “An apparatus comprising one or more processor units . . . ”. Such a claim does not foreclose the apparatus from including additional components (e.g., a network interface unit, graphics circuitry, etc.). 
     “Configured To.” Various units, circuits, or other components may be described or claimed as “configured to” perform a task or tasks. In such contexts, “configured to” is used to connote structure by indicating that the units/circuits/components include structure (e.g., circuitry) that performs those task or tasks during operation. As such, the unit/circuit/component can be said to be configured to perform the task even when the specified unit/circuit/component is not currently operational (e.g., is not on). The units/circuits/components used with the “configured to” language include hardware—for example, circuits, memory storing program instructions executable to implement the operation, etc. Reciting that a unit/circuit/component is “configured to” perform one or more tasks is expressly intended not to invoke 35 U.S.C. § 112, sixth paragraph, for that unit/circuit/component. Additionally, “configured to” can include generic structure (e.g., generic circuitry) that is manipulated by software and/or firmware (e.g., an FPGA or a general-purpose processor executing software) to operate in manner that is capable of performing the task(s) at issue. “Configure to” may also include adapting a manufacturing process (e.g., a semiconductor fabrication facility) to fabricate devices (e.g., integrated circuits) that are adapted to implement or perform one or more tasks. 
     “First,” “Second,” etc. As used herein, these terms are used as labels for nouns that they precede, and do not imply any type of ordering (e.g., spatial, temporal, logical, etc.). For example, a buffer circuit may be described herein as performing write operations for “first” and “second” values. The terms “first” and “second” do not necessarily imply that the first value must be written before the second value. 
     “Based On.” As used herein, this term is used to describe one or more factors that affect a determination. This term does not foreclose additional factors that may affect a determination. That is, a determination may be solely based on those factors or based, at least in part, on those factors. Consider the phrase “determine A based on B.” While in this case, B is a factor that affects the determination of A, such a phrase does not foreclose the determination of A from also being based on C. In other instances, A may be determined based solely on B. 
     DETAILED DESCRIPTION 
     Embodiments of a small form factor camera including a photosensor and a lens system are described. Embodiments of an imaging lens system including a front aperture and five lens elements that may be used in the camera and that provide a low F-number (&lt;=2.4), wide field of view (&gt;=82 degrees) and short total track length (TTL) that allow the camera to be implemented in a small package size while still capturing sharp, high-resolution images, making embodiments of the camera suitable for use in small and/or mobile multipurpose devices such as cell phones, smartphones, pad or tablet computing devices, laptop, netbook, notebook, subnotebook, and ultrabook computers, and so on. However, note that aspects of the camera (e.g., the lens system and photosensor) may be scaled up or down to provide cameras with larger or smaller package sizes than those described. In addition, embodiments of the camera system may be implemented as stand-alone digital cameras. In addition to still (single frame capture) camera applications, embodiments of the camera system may be adapted for use in video camera applications. Embodiments of the lens system may be used in small form factor cameras to capture high brightness, high resolution images with a low F-number and wide field of view. 
       FIG. 1  is a cross-sectional illustration of a lens system that includes five lens elements and a front aperture and that provide a low F-number (&lt;=2.4), wide field of view (&gt;=82 degrees), and short total track length (TTL), according to some embodiments. As shown in  FIG. 1 , an example camera  100  includes at least a lens system  110  and a photosensor  120 . Embodiments of the lens system  110  include five lens elements  101 - 105  (also referred to as L 1 -L 5 ) with refractive power arranged along an optical axis (AX) from a first lens element  101  on the object side to a fifth lens element  105  on the image side. The aperture stop  130  is located at the first lens element  101  at or behind the front vertex of the lens system  110 . Lens system parameters and relationships including but not limited to power distribution, lens shape, thickness, geometry, position, materials, spacing, and the surface shapes of certain lens elements may be selected at least in part to reduce, compensate, or correct for optical aberrations and lens artifacts and effects across the field of view including one or more of but not limited to vignetting, chromatic aberration, the field curvature or Petzval sum, and lens flare. 
     Referring again to  FIG. 1 , the refractive lens elements in embodiments of the lens system  110  may, for example, be composed of a plastic material. In some embodiments, the refractive lens elements may be composed of an injection molded plastic material. However, other transparent materials (e.g., glass) may be used. Also note that, in a given embodiment, different ones of the lens elements may be composed of materials with different optical characteristics, for example different Abbe numbers and/or different refractive indices. The Abbe number, V d , may be defined by the equation: 
         V   d =( N   d −1)/( N   F   −N   C )
 
     where N F  and N C  are the refractive index values of the material at the F and C lines of hydrogen, respectively. In some embodiments, lens elements 102 and  104  may be composed of a material with a relatively low Abbe number (15&lt;V d &lt;30), and lens elements 101, 103, and  105  may be composed of a material with a relatively high Abbe number (45&lt;V d &lt;70). 
     The photosensor  120  may be an integrated circuit (IC) technology chip or chips implemented according to any of various types of photosensor technology. Examples of photosensor technology that may be used are charge-coupled device (CCD) technology and complementary metal-oxide-semiconductor (CMOS) technology. In some embodiments, pixel size of the photosensor  120  may be 1.2 microns or less, although larger pixel sizes may be used. In a non-limiting example embodiment, the photosensor  120  may be manufactured according to a 1280×720 pixel image format to capture 1 megapixel images. However, other pixel formats may be used in embodiments, for example 5 megapixel, 10 megapixel, or larger or smaller formats. In the non-limiting example embodiments described herein, an example photosensor with a semi-diagonal image height within a range of 2.0 to 2.7 mm may be used; however, larger or smaller photosensors may be used with appropriate adjustment of the lens system dimensions. 
     The lens system  110  may also include a front aperture stop located at the first lens element at or behind the front vertex of the lens system. 
     The camera  100  may also, but does not necessarily, include an infrared (IR) filter, for example located between the last or fifth lens element  105  of the lens system  110  and the photosensor  120 . The IR filter may, for example, be composed of a glass material. However, other materials may be used. In at least some embodiments, the IR filter does not have refractive power, and does not affect the effective focal length f of the lens system. In some embodiments, instead of an IR filter as shown in the Figures, a coating may be used on one or more of the lens elements, or other methods may be used, to provide IR filtering. 
     In some embodiments, a cover glass may be located on the object side of the lens system  110  in the camera  100 , for example as shown in  FIG. 7A . In some embodiments, the cover glass may have a small amount of refractive power. The cover glass may, for example, be composed of a glass material. However, other materials may be used.  FIG. 13A  shows an example embodiment that does not include a cover glass. 
     In some embodiments, the lens system  110  is a fixed-focus lens. However, in some embodiments, the camera  100  may include an optical actuator component, for example an optical microelectromechanical system (MEMS), located in front of (i.e., on the object side of) the lens system  110  that provides autofocus (AF) functionality for the camera  100 . In some embodiments, the optical actuator may include, but is not limited to, a substrate (e.g., a clear glass or plastic substrate), a flexible optical element (e.g., a flexible lens), and an actuator component that is configured to change the shape of the flexible optical element to provide adaptive optical functionality for the camera without physically moving the camera lens  110 . The optical functionality provided by the optical actuator may include autofocus (AF) functionality. In some embodiments, the optical actuator may provide other optical functionality for the camera  100 , for example tilt and/or optical image stabilization (OIS) functionality. The optical actuator may also be referred to as an SSAF (Solid-State Auto-Focus) component or module. In some embodiments, the adaptive optical functionality for the camera  100  is provided by the optical actuator changing the shape of the flexible optical element to affect light rays passing from the object field through the flexible optical element to the camera lens, rather than by physically moving the camera lens  110 . 
     Further note that the camera  100  may also include other components than those illustrated and described herein. 
     In the camera  100 , the lens system  110  forms an image at an image plane (IP) at or near the surface of the photosensor  120 . The image size for a distant object is directly proportional to the effective focal length f of a lens system  110 . The total track length (TTL) of the lens system is the distance on the optical axis (AX) between the front vertex at the object side surface of the first (object side) lens element  101  and the image plane. The ratio of total track length to focal length (TTL/f) is referred to as the telephoto ratio. To be classified as a telephoto lens system, TTL/f is less than or equal to 1. For a non-telephoto lens system, the telephoto ratio is greater than 1. 
     In at least some embodiments, the lens system  110  may be configured such that the effective focal length f of the lens system is less than 3mm, and the F-number is 2.4 or less. The lens system  110  may be configured to satisfy specified optical, imaging, and/or packaging constraints for particular camera system applications. Note that the F-number, also referred to as the focal ratio or f/#, is defined by f/D, where D is the diameter of the entrance pupil, i.e. the effective aperture. As an example, in the embodiment illustrated in  FIG. 7A , at f=@2.4 mm, an F-number of 2.0 is achieved with an effective aperture of @1.2 mm. The example embodiments may be configured with a full field of view (FOV) of 82 degrees or more. For example, in the embodiment illustrated in  FIG. 7A , FOV=95 degrees. In some embodiments, a photosensor  120  with a semi-diagonal image height within a range of 2.0 to 2.7 mm may be used, and the lens system may have a total track length (TTL) of 4 mm or less. 
     However, note that the focal length f, F-number, TTL, photosensor size, and/or other lens system and camera parameters may vary in different embodiments, and may be scaled or adjusted to meet various specifications of optical, imaging, and/or packaging constraints for other camera system applications. Constraints for a camera system that may be specified as requirements for particular camera system applications and/or that may be varied for different camera system applications include but are not limited to the focal length f, effective aperture, TTL, aperture stop location, F-number, field of view (FOV), telephoto ratio, photosensor size, imaging performance requirements, and packaging volume or size constraints. 
     In some embodiments, the lens system  110  may be adjustable. For example, in some embodiments, a lens system  110  as described herein may be equipped with an adjustable iris (entrance pupil) or aperture stop  130 . Using an adjustable aperture stop, the F-number (focal ratio, or f/#) may be dynamically varied within a range. In some embodiments, the lens system may be used at faster focal ratios by adjusting the aperture stop at the same FOV, possibly with degraded imaging quality performance, or with reasonably good performance at a smaller FOV. 
     Lens System Parameters and Relationships 
     As previously noted, the lens system  110  is a front-aperture lens system with a wide FOV (&gt;=82 degrees) and a TTL of 4 mm or less, with a semi-diagonal image height within a range of 2.0 to 2.7 mm. Designing a wide FOV lens system using a front aperture while maintaining good image quality is challenging. Front aperture lens systems are more compact than mid-aperture lens systems, but generally provide a modest FOV that is less than 82 degrees because a FOV region of &gt;=82 degrees is an extreme region for achieving good image quality in lens systems with a front-aperture configuration. With such a wide FOV, optical aberrations that deteriorate the image quality, for example field-curvature, lateral chromatic aberration and distortion, become extremely difficult to correct without the introduction of stop symmetry. Mid-aperture configurations are thus typically used to provide lens systems with a wide FOV. However, mid-aperture lens systems are longer than front-aperture lens systems, and thus may not be suitable for applications where z-axis space is limited such as the front-facing cameras of thin mobile multipurpose devices such as smartphones. 
     Thus, in embodiments of a lens system  110  as illustrated in  FIG. 1 , lens system parameters and relationships including but not limited to power distribution, lens shape, thickness, geometry, position, materials, spacing, and the surface shapes of certain lens elements may be selected at least in part to reduce, compensate, or correct for optical aberrations and lens artifacts and effects across the field of view of a wide FOV front aperture lens system including one or more of, but not limited to, field-curvature, lateral chromatic aberration, and distortion. 
     The design parameters and relationships of the aspheric lens pair comprising the fourth and fifth lens elements (lenses  104  and  105 ) are of primary importance in correcting for optical aberrations and lens artifacts and effects across the field of view of the wide FOV front aperture lens system  110 .  FIGS. 2 through 6  illustrate several parameters and relationships for the fourth and fifth lens element of a lens system  110  as illustrated in  FIG. 1 . However, to correct the optical aberrations and achieve good image quality, the entire lens stack needs to be considered together. Thus, relationships for the first through third lens elements (lenses  101  through  103 ) are defined as well as relationships for lenses four and five. 
       FIG. 2  illustrates optical characteristics of the fourth and fifth lens elements of a lens system as illustrated in  FIG. 1 , according to some embodiments. Lenses  104  and  105  are aspheric lenses. In some embodiments, lens element  104  may be formed of a material with a relatively low Abbe number (15&lt;V d &lt;30), and lens  105  may be formed of a material with a relatively high Abbe number (45&lt;V d &lt;70). 
     In the high-FOV (peripheral) region (region  150 A), field curvature aberration dominates. A corresponding portion of lens element  104  diverges light; a substantial change from light diverging to converging happens at lens element  105 . Thus, lens element  105  is paired with lens element  104  to balance the field curvature at high FOV. 
     In the mid-FOV region (region  150 B), coma balances with field curvature and astigmatism. In this region, both lens element  104  and lens element  105  effectively diverge the ray bundle. 
     In the central region (region  150 C), the optical power of lens element  105  is modest. Spherical aberration dominates the central region, and is mainly corrected by lenses  101  through  104 . Lens element  105  may only provide small adjustments for aberration. 
       FIGS. 3A and 3B  illustrate local radius/curvature of a first surface of the fifth lens element of a lens system as illustrated in  FIG. 1 , according to some embodiments. The local radius/curvature formula is given by: 
     
       
         
           
             R 
             = 
             
               
                 
                   ( 
                   
                     1 
                     + 
                     
                       
                         
                           d 
                           2 
                         
                          
                         z 
                       
                       
                         dy 
                         2 
                       
                     
                   
                   ) 
                 
                 1.5 
               
               
                 dz 
                 dy 
               
             
           
         
       
     
     where z is aspheric sag.  FIG. 3A  shows lens element  105  with a first (object side) surface ( 51 ). Region  160 A is a central region of lens element  105  that has a positive radius of curvature, region  160 B is a paraxial region of lens element  105  that has a negative radius of curvature, and region  160 C is a peripheral region of lens element  105  that has a positive radius of curvature.  FIG. 3B  is a graph of the change in sign (from positive to negative to positive) of local curvature for S 1  from the center (optical axis) of the lens element  105  to the peripheral region/edge of the lens. Referring to  FIG. 3B , in embodiments of the lens system  110 , the local curvature of lens  105 , S 1  crosses zero at least twice from the lens center to the lens edge. Thus, embodiments of the lens system  110  may satisfy the relationship: 
     L 5 , S 1  crosses zero at least twice from the lens center to the lens edge. 
       FIGS. 4A and 4B  illustrate local thickness delta of the fifth lens element (L 5 ) of a lens system as illustrated in  FIG. 1 , according to some embodiments. Referring to  FIG. 4A , the gray arrows indicate local thickness at example distances on the Y axis from the optical (Z) axis for lens element 105. Referring to  FIG. 4B , “0” is at the center of the lens. The Y axis indicates change (delta) in lens thickness progressing to the edge of the lens. Local thickness delta is defined as: 
     ΔLT(y)=lens thickness @ y—center thickness.
     ΔT1 is the maximum local thickness delta. ΔT2 is local thickness delta regression. Embodiments of L 5  in the lens system  110  may satisfy the relationship:   

     ΔT2/ΔT1&gt;0.3, where ΔT1 is max local thickness delta along the lens, and ΔT2 is max regression in local thickness delta within the lens section defined in the range from the point where max local thickness delta is reached to the max clear aperture of the lens. 
       FIGS. 5 and 6  illustrate relationships of the fourth and fifth lens elements of a lens system as illustrated in  FIG. 1 , according to some embodiments. Referring to  FIG. 5 , L 5  of lens system  110  may satisfy the relationship: 
       0.3&lt;Ym/SD&lt;0.7 
     where Ym is the height of the point where maximum local thickness occurs, and SD is the semi-diagonal image height. Referring to  FIGS. 6 , L 4  and L 5  of lens system  110  may satisfy the relationships: 
       0.1&lt;Y4/SD&lt;0.6 
       Y4&lt;Ym 
     where Y 4  is the height of the point where the aspheric inflection point of L 4 , S 2  occurs. 
     In embodiments, the lens system  110  may have an F-number of 2.4 or less, an effective focal length f of less than 3mm, and may provide a wide (&gt;=82 degrees) full field of view (FFOV). The lens system  110  may satisfy the relationship: 
         TTL/ 2SD&lt;0.85 
     where TTL is the total track length of the lens system  110 , and SD is the semi-diagonal image height. 
     The lens system  110  may include five lens elements with refractive power and effective focal length f, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element L 1  ( 101 ); 
     a second lens element L 2  ( 102 ); 
     a third lens element L 3  ( 103 ); 
     a fourth lens element L 4  ( 104 ); and 
     a fifth lens element L 5  ( 105 ). 
     In some embodiments, L 1  has positive refractive power. In some embodiments, the object side surface of L 1  is convex in the paraxial region. In some embodiments, L 1  is composed of a material with an Abbe number vd 1 , where 45&lt;vd 1 &lt;70. In some embodiments, L 1  satisfies the relationships: 
       |fsys/f 1 |&gt;0.5 
       0.8&lt;|R1+R2|/|R1−R2|&lt;1.5
 
     where fsys is the effective focal length of the lens system, f 1  is effective focal length of L  1 , and R 1  and R 2  are radius of curvature of the object side surface and the image side surface of L 1 , respectively. 
     In some embodiments, L 2  has negative refractive power. In some embodiments, the object side surface of L 2  is convex in the paraxial region. In some embodiments, L 2  is composed of a material with an Abbe number vd 2 , where  15 &lt;vd 2 &lt;30. In some embodiments, L2 satisfies the relationship: 
       |fsys/f2|&lt;0.5 
     where fsys is the effective focal length of the lens system, and f 2  is effective focal length of L 2 . 
     In some embodiments, L 3  has positive refractive power. In some embodiments, the object side surface of L 3  is concave in the paraxial region. In some embodiments, the image side surface of L 3  is convex in the paraxial region. In some embodiments, L 3  satisfies the relationships: 
       |fsys/f3|&gt;0.5;| 
       R5+R6|/|R5−R6|&lt;4
 
     where fsys is the effective focal length of the lens system, f 3  s effective focal length of L 3 , and R 5  and R 6  are radius of curvature of the object side surface and image side surface of L 3 , respectively. 
     In some embodiments, L 4  has negative refractive power. In some embodiments, the object side surface of L 4  is aspheric and has at least one part being concave along the lens. In some embodiments, the image side surface of L 4  is concave in the paraxial region and has at least one part being convex along the lens shape. In some embodiments, L 4  is composed of a material with an Abbe number vd 4 , where 15&lt;vd4 &lt;30. In some embodiments, L 4  satisfies the relationships: 
       −0.8&lt;fsys/f4∛−0.2
 
       1&lt;(R7+R8)/(R7−R8)&lt;4
 
     where fsys is the effective focal length of the lens system, f 4  is effective focal length of L 4 , and R 7  and R 8  are radius of curvature of the object side surface and the image side surface of L 4 , respectively. 
     In some embodiments, L 5  has refractive power. In some embodiments, the object side surface of L 5  is convex in the paraxial region, and the surface form is aspheric. In some embodiments, the image side surface of L 5  is concave in the paraxial region, and the surface form is aspheric. In some embodiments, L 5  is composed of a material with an Abbe number vd5, where 45 &lt;vd5 &lt;70. In some embodiments, L5 satisfies the relationships: 
       |fsys/f5|&lt;0.55 
       (R9+R10)/(R9- 31  R10)&gt;4
 
     where fsys is the effective focal length of the lens system, f 5  is effective focal length of L 5 , and R 9  and R 10  are radius of curvature of the object side surface and the image side surface of L 5 , respectively. 
     Example Embodiments 
       FIGS. 7A, 8A, 9A, 10A, 11A, 12A, 13A, and 14A  illustrate several example embodiments of a lens system as illustrated in  FIG. 1  that include five refracting lens elements and a front aperture stop. The example embodiments may provide an F-number (focal ratio) of 2.4 or less, field of view (FOV) of 82 degrees or more, focal length (f) of 3.0 mm or less, and a total track length (TTL) of 4 mm or less, with a semi-diagonal image height within a range of 2.0 to 2.7 mm. Note, however, that these examples are not intended to be limiting, and that variations on the various parameters given for the lens systems are possible while still achieving similar results. 
     Example Lens System  710   
       FIG. 7A  illustrates an example camera  700  with a lens system  710  that includes five refractive lens elements, according to some embodiments. Lens system  710  may have an effective focal length f of @2.4mm, F-number of 2.0, and field of view (FOV) of 95 degrees. Lens system  710  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  701 ; 
     a second lens element  702 ; 
     a third lens element  703 ; 
     a fourth lens element  704 ; and 
     a fifth lens element  705 . 
     As shown in  FIG. 7A , lens system  710  system may include a front aperture stop. The camera  700  may include an IR filter located between lens element  705  and a photosensor. A cover glass may be located on the object side of the lens system  710 .  FIG. 7B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  710  as illustrated in  FIG. 7A , according to some embodiments. Tables 1 through 3 provide details for example lens system  710 . 
     Example Lens System  810   
       FIG. 8A  illustrates an example camera  800  with a lens system  810  that includes five refractive lens elements, according to some embodiments. Lens system  810  may have an effective focal length f of @2.3mm, F-number of 2.0, and field of view (FOV) of 90 degrees. Lens system  810  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  801 ; 
     a second lens element  802 ; 
     a third lens element  803 ; 
     a fourth lens element  804 ; and 
     a fifth lens element  805 . 
     As shown in  FIG. 8A , lens system  810  system may include a front aperture stop. The camera  800  may include an IR filter located between lens element  805  and a photosensor. A cover glass may be located on the object side of the lens system  810 .  FIG. 8B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  810  as illustrated in  FIG. 8A , according to some embodiments. 
     Example Lens System  910   
       FIG. 9A  illustrates an example camera 900 with a lens system  910  that includes five refractive lens elements, according to some embodiments. Lens system  910  may have an effective focal length f of @2.52mm, F-number of 2.0, and field of view (FOV) of 90 degrees. Lens system  910  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  901 ; 
     a second lens element  902 ; 
     a third lens element  903 ; 
     a fourth lens element  904 ; and 
     a fifth lens element  905 . 
     As shown in  FIG. 9A , lens system  910  system may include a front aperture stop. The camera  900  may include an IR filter located between lens element  905  and a photosensor. A cover glass may be located on the object side of the lens system  910 .  FIG. 9B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  910  as illustrated in  FIG. 9A , according to some embodiments. 
     Example Lens System  1010   
       FIG. 10A  illustrates an example camera  1000  with a lens system  1010  that includes five refractive lens elements, according to some embodiments. Lens system  1010  may have an effective focal length f of @2.74mm, F-number of  2 . 0 , and field of view (FOV) of 85 degrees. Lens system  1010  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  1001 ; 
     a second lens element  1002 ; 
     a third lens element  1003   
     a fourth lens element  1004 ; and 
     a fifth lens element  1005 . 
     As shown in  FIG. 10A , lens system  1010  system may include a front aperture stop. The camera  1000  may include an IR filter located between lens element  1005  and a photosensor. A cover glass may be located on the object side of the lens system  1010 .  FIG. 10B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  1010  as illustrated in  FIG. 10A , according to some embodiments. 
     Example Lens System  1110   
       FIG. 11A  illustrates an example camera  1100  with a lens system  1110  that includes five refractive lens elements, according to some embodiments. Lens system  1110  may have an effective focal length f of @2.67mm, F-number of 2.0, and field of view (FOV) of 85 degrees. Lens system  1110  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  1101 ; 
     a second lens element  1102 ; 
     a third lens element  1103 ; 
     a fourth lens element  1104 ; and 
     a fifth lens element  1105 . 
     As shown in  FIG. 11A , lens system  1110  system may include a front aperture stop. The camera  1100  may include an IR filter located between lens element  1105  and a photosensor. A cover glass may be located on the object side of the lens system  1110 .  FIG. 11B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  1110  as illustrated in  FIG. 11A , according to some embodiments. 
     Example Lens System  1210   
       FIG. 12A  illustrates an example camera  1200  with a lens system  1210  that includes five refractive lens elements, according to some embodiments. Lens system  1210  may have an effective focal length f of @2.38mm, F-number of 2.0, and field of view (FOV) of 85 degrees. Lens system  1210  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  1201 ; 
     a second lens element  1202 ; 
     a third lens element  1203 ; 
     a fourth lens element  1204 ; and 
     a fifth lens element  1205 . 
     As shown in  FIG. 12A , lens system  1210  system may include a front aperture stop. The camera  1200  may include an IR filter located between lens element  1205  and a photosensor. A cover glass may be located on the object side of the lens system  1210 . FIG.  12 B is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  1210  as illustrated in  FIG. 12A , according to some embodiments. 
     Example Lens System  1310   
       FIG. 13A  illustrates an example camera  1300  with a lens system  1310  that includes five refractive lens elements, according to some embodiments. Lens system  1310  may have an effective focal length f of @2.69mm, F-number of 2.2, and field of view (FOV) of 85 degrees. Lens system  1310  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  1301 ; 
     a second lens element  1302 ; 
     a third lens element  1303 ; 
     a fourth lens element  1304 ; and 
     a fifth lens element  1305 . 
     As shown in  FIG. 13A , lens system  1310  system may include a front aperture stop. The camera  1300  may include an IR filter located between lens element  1305  and a photosensor. Unlike other embodiments, lens system  1310  does not include a cover glass.  FIG. 13B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  1310  as illustrated in  FIG. 13A , according to some embodiments. 
     Example Lens System  1410   
       FIG. 14A  illustrates an example camera  1400  with a lens system  1410  that includes five refractive lens elements, according to some embodiments. Lens system  1410  may have an effective focal length f of @2.61mm, F-number of 2.0, and field of view (FOV) of 88 degrees. Lens system  1410  may include five lens elements with refractive power, arranged along an optical axis AX in order from an object side to an image side: 
     a first lens element  1401 ; 
     a second lens element  1402 ; 
     a third lens element  1403 ; 
     a fourth lens element  1404 ; and 
     a fifth lens element  1405 . 
     As shown in  FIG. 14A , lens system  1410  system may include a front aperture stop. The camera  1400  may include an IR filter located between lens element  1405  and a photosensor. A cover glass may be located on the object side of the lens system  1410 .  FIG. 14B  is a graph illustrating the diffraction modulation transfer function (MTF) for a lens system  1410  as illustrated in  FIG. 14A , according to some embodiments. Tables 4 through 6 provide details for example lens system  710 . 
       FIG. 15  is a high-level flowchart of a method for capturing images using a camera with a lens system that includes five lens elements as illustrated in any of  FIGS. 1, 7A, 8A, 9A, 10A, 11A, 12A, 13A, and 14A , according to some embodiments. As indicated at  1200 , light from an object field in front of the camera is received through a front aperture stop at a first lens element of the camera. As indicated at  1902 , the first lens element refracts the light to a second lens element. As indicated at  1904 , the light is then refracted by the second lens element to a third lens element. As indicated at  1906 , the light is then refracted by the third lens element to a fourth lens element. As indicated at  1908 , the light is then refracted by the fourth lens element to a fifth lens element. As indicated at  1910 , the light is refracted by the fifth lens element to form an image at an image plane at or near the surface of a photosensor. As indicated at  1912 , the image is captured by the photosensor. 
     While not shown in  FIG. 15 , in some embodiments, the light may pass through an infrared filter that may for example be located between the fifth lens element and the photosensor. In some embodiments, the camera may include a cover glass located on the object side of the lens system. In some embodiments, the cover glass may have a small amount of refractive power. In some embodiments, the camera may include an optical actuator component located in front of the lens system that provides autofocus (AF) functionality for the camera. 
     In some embodiments, the five lens elements referred to in  FIG. 15  may be configured as illustrated in any of  FIGS. 7A, 8A, 9A, 10A, 11A, 12A, 13A, and 14A . However, note that variations on the examples given in the Figures and Tables are possible while achieving similar optical results. 
     Example Lens System Tables 
     The following Tables provide example values for various optical and physical parameters of the example lens systems  710  and  1410  as described in reference to  FIGS. 7A and 14A , respectively. In the Tables, all dimensions are in millimeters (mm) unless otherwise specified. L 1 , L 2 , L 3 , L 4 , and L 4  stand for refractive lenses 1, 2, 3, 4, and 5, respectively. The surface numbers of the elements as shown in the Tables are listed from a first surface  1  at a cover glass to a last surface at the image plane/photosensor surface. A positive radius indicates that the center of curvature is to the right (object side) of the surface. A negative radius indicates that the center of curvature is to the left (image side) of the surface. “Inf” stands for infinity (as used in optics). The thickness (or separation) is the axial distance to the next surface. Fno stands for F-number of the lens system. FFOV stands for full field of view. IRCF designates an infrared (IR) filter. Vdx is the Abbe number of a respective lens element. Both f and f sys  stand for the effective focal length of the lens system, while fx stands for focal length of a respective lens element. R 1  and R 2  are radius of curvature of the object side surface and the image side surface of L 1 , respectively. R 5  and R 6  are radius of curvature of the object side surface and image side surface of L 3 , respectively. R 7  and R 8  are radius of curvature of the object side surface and the image side surface of L 4 , respectively. R 9  and R 10  are radius of curvature of the object side surface and the image side surface of L 5 , respectively. ΔT 1  is the maximum local thickness delta of L 5 . ΔT 2  is local thickness delta regression of L 5 . TTL is total track length of the lens system focusing at infinity conjugate and is measured between the object side surface of lens  1  or the aperture stop, whichever comes closer to the object, to the image plane. ImaH is the semi-diagonal image height on the image plane. 
     For the materials of the lens elements and IR filter, a refractive index N d  at the helium d-line wavelength is provided, as well as an Abbe number V d  relative to the d-line and the C- and F-lines of hydrogen. The Abbe number, V d , may be defined by the equation: 
         V   d =( N   d −1)/( N   F   −N   C ),
 
     where N F  and N C  are the refractive index values of the material at the F and C lines of hydrogen, respectively. 
     Referring to the Tables of aspheric coefficients (Tables 2A-2B and 5A-5B), the aspheric equation describing an aspherical surface may be given by: 
         Z =( cr   2 /(1 +sqrt [1−(1 +K ) c   2   r   2 ]))+ A   4   r   4   +A   6   r   6   +A   8   r   8   +A   10   r   10   +A   12   R   12   +A   14   r   14   +A   16   r   16   +A   18   r   18   +A   20   r   20  
 
     where Z is the sag of surface parallel to the z-axis (the z-axis and the optical axis are coincident in these example embodiments), r is the radial distance from the vertex, c is the curvature at the pole or vertex of the surface (the reciprocal of the radius of curvature of the surface), K is the conic constant, and A 4 −A 20  are the aspheric coefficients. In the Tables, “E” denotes the exponential notation (powers of 10). 
     Note that the values given in the following Tables for the various parameters in the various embodiments of the lens system are given by way of example and are not intended to be limiting. For example, one or more of the parameters for one or more of the surfaces of one or more of the lens elements in the example embodiments, as well as parameters for the materials of which the elements are composed, may be given different values while still providing similar performance for the lens system. In particular, note that some values in the Tables may be scaled up or down for larger or smaller implementations of a camera using an embodiment of a lens system as described herein. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Example lens system 710 
               
               
                 Lens system 710 
               
               
                 Fno = 2.0, FFOV = 95.0 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness 
                 Refractive 
                 Abbe 
               
               
                   
                 Surface 
                 Radius 
                 or separation 
                 Index 
                 Number 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 N d   
                 V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Cover.W 
                 1 
                 Inf 
                 0.800 
                 1.525 
                 54.5 
               
               
                   
                 2 
                 −194.000 
                 0.150 
               
               
                   
                 3 
                 Inf 
                 0.055 
               
               
                 Stop 
                 4 
                 Inf 
                 −0.055 
               
               
                 L1 
                 *5 
                 2.049 
                 0.527 
                 1.545 
                 56.0 
               
               
                   
                 *6 
                 −182.726 
                 0.231 
               
               
                 L2 
                 *7 
                 33.602 
                 0.251 
                 1.678 
                 19.5 
               
               
                   
                 *8 
                 6.457 
                 0.098 
               
               
                 L3 
                 *9 
                 −3.661 
                 0.876 
                 1.545 
                 56.0 
               
               
                   
                 *10 
                 −0.989 
                 0.050 
               
               
                 L4 
                 *11 
                 4.898 
                 0.350 
                 1.678 
                 19.5 
               
               
                   
                 *12 
                 2.044 
                 0.097 
               
               
                 L5 
                 *13 
                 0.777 
                 0.301 
                 1.545 
                 56.0 
               
               
                   
                 *14 
                 0.592 
                 0.386 
               
               
                 IRCF 
                 15 
                 Inf 
                 0.210 
                 1.517 
                 64.2 
               
               
                   
                 16 
                 Inf 
                 0.475 
               
               
                 Sensor 
                 17 
                 Inf 
                 0 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficient given below in Tables 2A and 2B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2A 
               
             
            
               
                   
               
               
                 Lens system 710, Aspheric Coefficients 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 K 
                 0.00000E+00 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −7.54068E−02  
                 −2.24360E−01 
                 −5.63451E−01  
                 −4.24662E−01  
                 −2.33007E−01  
               
               
                 A6 
                 2.31315E−01 
                 −2.45325E−01 
                 5.60572E−01 
                 1.44087E+00 
                 2.12497E+00 
               
               
                 A8 
                 −1.64698E+00  
                  2.65302E−01 
                 −5.39081E+00  
                 −6.99290E+00  
                 −8.17804E+00  
               
               
                 A10 
                 4.43718E+00 
                 −9.03303E−01 
                 1.55628E+01 
                 1.70595E+01 
                 1.66612E+01 
               
               
                 A12 
                 −6.54981E+00  
                  1.04281E+00 
                 −2.34623E+01  
                 −2.35796E+01  
                 −1.95817E+01  
               
               
                 A14 
                 3.03756E+00 
                 −9.50420E−01 
                 1.62935E+01 
                 1.89485E+01 
                 1.36595E+01 
               
               
                 A16 
                 0.00000E+00 
                 −1.70912E−01 
                 −3.65427E+00  
                 −8.32376E+00  
                 −5.30161E+00  
               
               
                 A18 
                 0.00000E+00 
                  0.00000E+00 
                 0.00000E+00 
                 1.56115E+00 
                 8.86355E−01 
               
               
                 A20 
                 0.00000E+00 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2B 
               
             
            
               
                   
               
               
                 Lens system 710, Aspheric Coefficients 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 K 
                 −1.00000E+00 
                 0.00000E+00 
                 −1.00000E+00 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                 A4 
                 −1.94019E−02 
                 1.15599E−01 
                  3.86776E−02 
                 −8.16695E−01 
                 −1.10499E+00 
               
               
                 A6 
                  2.13740E−02 
                 −4.57601E−01  
                 −3.41815E−01 
                  3.87565E−01 
                  1.06232E+00 
               
               
                 A8 
                 −5.74570E−02 
                 7.41619E−01 
                  4.14133E−01 
                 −6.40573E−02 
                 −8.03080E−01 
               
               
                 A10 
                  2.20338E−01 
                 −9.74199E−01  
                 −3.19359E−01 
                 −1.08281E−03 
                  4.41832E−01 
               
               
                 A12 
                 −4.25957E−01 
                 8.56136E−01 
                  1.56504E−01 
                 −4.48342E−03 
                 −1.65942E−01 
               
               
                 A14 
                  3.86038E−01 
                 −4.80696E−01  
                 −4.53415E−02 
                  4.16376E−03 
                  4.07746E−02 
               
               
                 A16 
                 −1.13319E−01 
                 1.55943E−01 
                  7.05167E−03 
                 −1.24009E−03 
                 −6.23311E−03 
               
               
                 A18 
                  2.24867E−03 
                 −2.17562E−02  
                 −4.55397E−04 
                  1.68211E−04 
                  5.36585E−04 
               
               
                 A20 
                  0.00000E+00 
                 0.00000E+00 
                  0.00000E+00 
                 −8.92759E−06 
                 −1.98606E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Lens system 710, Optical Definitions 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 2.399 
                 Vd4 
                 19.5 
               
               
                 Fno 
                 2.0 
                 fsys/f4 
                 −0.440 
               
               
                 FFOV[deg] 
                 95° 
                 (R7 + R8)/(R7 − R8) 
                 2.433 
               
               
                 TTL/(2*ImaH) 
                 0.764 
                 Vd5 
                 56.0 
               
               
                 Vd1 
                 56.0 
                 |fsys/f5| 
                 0.225 
               
               
                 |fsys/f1| 
                 0.646 
                 (R9 + R10)/(R9 − R10) 
                 7.383 
               
               
                 |R1 + R2|/|R1 − R2| 
                 0.978 
                 ΔT2/ΔT1 
                 0.63 
               
               
                 |fsys/f2| 
                 0.203 
                 Ym/SD 
                 0.57 
               
               
                 |fsys/f3| 
                 1.080 
                 Y4/SD 
                 0.42 
               
               
                 |R5 + R6|/|R5 − R6| 
                 1.740 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Example lens system 1410 
               
               
                 Lens system 1410 
               
               
                 Fno = 2.0, FFOV = 88.0 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness 
                 Refractive 
                 Abbe 
               
               
                   
                 Surface 
                 Radius 
                 or separation 
                 Index 
                 Number 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 N d   
                 V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Cover.W 
                 1 
                 Inf 
                 0.800 
                 1.525 
                 54.5 
               
               
                   
                 2 
                 −194.000 
                 0.150 
               
               
                   
                 3 
                 Inf 
                 0.093 
               
               
                 Stop 
                 4 
                 Inf 
                 −0.093 
               
               
                 L1 
                 *5 
                 1.644 
                 0.475 
                 1.545 
                 56.0 
               
               
                   
                 *6 
                 14.907 
                 0.331 
               
               
                 L2 
                 *7 
                 −13.821 
                 0.308 
                 1.678 
                 19.5 
               
               
                   
                 *8 
                 8.973 
                 0.094 
               
               
                 L3 
                 *9 
                 −3.585 
                 0.683 
                 1.545 
                 56.0 
               
               
                   
                 *10 
                 −1.021 
                 0.132 
               
               
                 L4 
                 *11 
                 5.795 
                 0.351 
                 1.661 
                 20.4 
               
               
                   
                 *12 
                 2.521 
                 0.181 
               
               
                 L5 
                 *13 
                 1.019 
                 0.304 
                 1.545 
                 56.0 
               
               
                   
                 *14 
                 0.683 
                 0.463 
               
               
                 IRCF 
                 15 
                 Inf 
                 0.210 
                 1.517 
                 64.2 
               
               
                   
                 16 
                 Inf 
                 0.267 
               
               
                 Sensor 
                 17 
                 Inf 
                 0.000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficient given below in Tables 5A and 5B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5A 
               
             
            
               
                   
               
               
                 Lens system 1410, Aspheric Coefficients 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −6.24275E−02  
                 −1.37057E−01  
                 −3.59915E−01  
                 −2.13554E−01  
                 −4.52048E−02  
               
               
                 A6 
                 2.23284E−01 
                 −4.23746E−01  
                 −4.39085E−01  
                 5.07277E−01 
                 1.51194E+00 
               
               
                 A8 
                 −1.63066E+00  
                 2.19635E+00 
                 1.88564E+00 
                 −2.11887E+00  
                 −5.57055E+00  
               
               
                 A10 
                 4.40169E+00 
                 −9.80697E+00  
                 −7.83224E+00  
                 2.76632E+00 
                 8.74391E+00 
               
               
                 A12 
                 −6.56826E+00  
                 2.24440E+01 
                 1.63691E+01 
                 −5.19544E−01  
                 −6.55745E+00  
               
               
                 A14 
                 3.40374E+00 
                 −2.68699E+01  
                 −1.39927E+01  
                 −1.03380E+00  
                 2.18277E+00 
               
               
                 A16 
                 0.00000E+00 
                 1.29431E+01 
                 3.99334E+00 
                 4.90923E−01 
                 −2.00090E−01  
               
               
                 A18 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A20 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5B 
               
             
            
               
                   
               
               
                 Lens system 1410, Aspheric Coefficients 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 K 
                 −1.00000E+00  
                  0.00000E+00 
                 −1.00000E+00 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                 A4 
                 3.64445E−01 
                  5.94928E−01 
                  5.18526E−01 
                 −5.93494E−01 
                 −1.03243E+00 
               
               
                 A6 
                 −1.05724E+00  
                 −1.70827E+00 
                 −1.81221E+00 
                 −2.54816E−01 
                  9.35381E−01 
               
               
                 A8 
                 1.83472E+00 
                  2.07367E+00 
                  2.73183E+00 
                  8.81176E−01 
                 −6.39242E−01 
               
               
                 A10 
                 −1.88816E+00  
                 −1.04015E+00 
                 −2.59519E+00 
                 −7.33021E−01 
                  3.29479E−01 
               
               
                 A12 
                 1.14633E+00 
                 −6.33299E−01 
                  1.61912E+00 
                  3.27849E−01 
                 −1.20446E−01 
               
               
                 A14 
                 −3.45145E−01  
                  1.34852E+00 
                 −6.60214E−01 
                 −8.82522E−02 
                  2.93661E−02 
               
               
                 A16 
                 4.11800E−02 
                 −9.22652E−01 
                  1.69072E−01 
                  1.43255E−02 
                 −4.48247E−03 
               
               
                 A18 
                 0.00000E+00 
                  3.08356E−01 
                 −2.45783E−02 
                 −1.29522E−03 
                  3.85358E−04 
               
               
                 A20 
                 0.00000E+00 
                 −4.18203E−02 
                  1.53972E−03 
                  5.01917E−05 
                 −1.42048E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Lens system 1410, Optical Definitions 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 2.613 
                 Vd4 
                 20.4 
               
               
                 Fno 
                 2.0 
                 fsys/f4 
                 −0.374 
               
               
                 FFOV[deg] 
                 88° 
                 (R7 + R8)/(R7 − R8) 
                 2.540 
               
               
                 TTL/(2*ImaH) 
                 0.754 
                 Vd5 
                 56.0 
               
               
                 Vd1 
                 56.0 
                 |fsys/f5| 
                 0.489 
               
               
                 |fsys/f1| 
                 0.782 
                 (R9 + R10)/(R9 − R10) 
                 5.059 
               
               
                 |R1 + R2|/|R1 − R2| 
                 1.248 
                 ΔT2/ΔT1 
                 0.50 
               
               
                 |fsys/f2| 
                 0.327 
                 Ym/SD 
                 0.59 
               
               
                 |fsys/f3| 
                 1.094 
                 Y4/SD 
                 0.4 
               
               
                 |R5 + R6|/|R5 − R6| 
                 1.796 
               
               
                   
               
            
           
         
       
     
     Example Computing Device 
       FIG. 16  illustrates an example computing device, referred to as computer system  2000 , that may include or host embodiments of a camera with a lens system as illustrated in  FIGS. 1 through 15 . In addition, computer system  2000  may implement methods for controlling operations of the camera and/or for performing image processing of images captured with the camera. In different embodiments, computer system  2000  may be any of various types of devices, including, but not limited to, a personal computer system, desktop computer, laptop, notebook, tablet or pad device, slate, or netbook computer, mainframe computer system, handheld computer, workstation, network computer, a camera, a set top box, a mobile device, a wireless phone, a smartphone, a consumer device, video game console, handheld video game device, application server, storage device, a television, a video recording device, a peripheral device such as a switch, modem, router, or in general any type of computing or electronic device. 
     In the illustrated embodiment, computer system  2000  includes one or more processors  2010  coupled to a system memory  2020  via an input/output (I/O) interface  2030 . Computer system  2000  further includes a network interface  2040  coupled to I/O interface  2030 , and one or more input/output devices  2050 , such as cursor control device  2060 , keyboard  2070 , and display(s)  2080 . Computer system  2000  may also include one or more cameras  2090 , for example one or more cameras as described above with respect to  FIGS. 1 through 15 , which may also be coupled to I/O interface  2030 , or one or more cameras as described above with respect to  FIGS. 1 through 15  along with one or more other cameras such as conventional wide-field cameras. 
     In various embodiments, computer system  2000  may be a uniprocessor system including one processor  2010 , or a multiprocessor system including several processors  2010  (e.g., two, four, eight, or another suitable number). Processors  2010  may be any suitable processor capable of executing instructions. For example, in various embodiments processors  2010  may be general-purpose or embedded processors implementing any of a variety of instruction set architectures (ISAs), such as the x86, PowerPC, SPARC, or MIPS ISAs, or any other suitable ISA. In multiprocessor systems, each of processors  2010  may commonly, but not necessarily, implement the same ISA. 
     System memory  2020  may be configured to store program instructions  2022  and/or data  2032  accessible by processor  2010 . In various embodiments, system memory  2020  may be implemented using any suitable memory technology, such as static random access memory (SRAM), synchronous dynamic RAM (SDRAM), nonvolatile/Flash-type memory, or any other type of memory. In the illustrated embodiment, program instructions  2022  may be configured to implement various interfaces, methods and/or data for controlling operations of camera  2090  and for capturing and processing images with integrated camera  2090  or other methods or data, for example interfaces and methods for capturing, displaying, processing, and storing images captured with camera  2090 . In some embodiments, program instructions and/or data may be received, sent or stored upon different types of computer-accessible media or on similar media separate from system memory  2020  or computer system  2000 . 
     In one embodiment, I/O interface  2030  may be configured to coordinate I/O traffic between processor  2010 , system memory  2020 , and any peripheral devices in the device, including network interface  2040  or other peripheral interfaces, such as input/output devices  2050 . In some embodiments, I/O interface  2030  may perform any necessary protocol, timing or other data transformations to convert data signals from one component (e.g., system memory  2020 ) into a format suitable for use by another component (e.g., processor  2010 ). In some embodiments, I/O interface  2030  may include support for devices attached through various types of peripheral buses, such as a variant of the Peripheral Component Interconnect (PCI) bus standard or the Universal Serial Bus (USB) standard, for example. In some embodiments, the function of I/O interface  2030  may be split into two or more separate components, such as a north bridge and a south bridge, for example. Also, in some embodiments some or all of the functionality of I/O interface  2030 , such as an interface to system memory  2020 , may be incorporated directly into processor  2010 . 
     Network interface  2040  may be configured to allow data to be exchanged between computer system  2000  and other devices attached to a network  2085  (e.g., carrier or agent devices) or between nodes of computer system  2000 . Network  2085  may in various embodiments include one or more networks including but not limited to Local Area Networks (LANs) (e.g., an Ethernet or corporate network), Wide Area Networks (WANs) (e.g., the Internet), wireless data networks, some other electronic data network, or some combination thereof. In various embodiments, network interface  2040  may support communication via wired or wireless general data networks, such as any suitable type of Ethernet network, for example; via telecommunications/telephony networks such as analog voice networks or digital fiber communications networks; via storage area networks such as Fibre Channel SANs, or via any other suitable type of network and/or protocol. 
     Input/output devices  2050  may, in some embodiments, include one or more display terminals, keyboards, keypads, touchpads, scanning devices, voice or optical recognition devices, or any other devices suitable for entering or accessing data by computer system  2000 . Multiple input/output devices  2050  may be present in computer system  2000  or may be distributed on various nodes of computer system  2000 . In some embodiments, similar input/output devices may be separate from computer system  2000  and may interact with one or more nodes of computer system  2000  through a wired or wireless connection, such as over network interface  2040 . 
     As shown in  FIG. 16 , memory  2020  may include program instructions  2022 , which may be processor-executable to implement any element or action to support integrated camera  2090 , including but not limited to image processing software and interface software for controlling camera  2090 . In some embodiments, images captured by camera  2090  may be stored to memory  2020 . In addition, metadata for images captured by camera  2090  may be stored to memory  2020 . 
     Those skilled in the art will appreciate that computer system  2000  is merely illustrative and is not intended to limit the scope of embodiments. In particular, the computer system and devices may include any combination of hardware or software that can perform the indicated functions, including computers, network devices, Internet appliances, PDAs, wireless phones, pagers, video or still cameras, etc. Computer system  2000  may also be connected to other devices that are not illustrated, or instead may operate as a stand-alone system. In addition, the functionality provided by the illustrated components may in some embodiments be combined in fewer components or distributed in additional components. Similarly, in some embodiments, the functionality of some of the illustrated components may not be provided and/or other additional functionality may be available. 
     Those skilled in the art will also appreciate that, while various items are illustrated as being stored in memory or on storage while being used, these items or portions of them may be transferred between memory and other storage devices for purposes of memory management and data integrity. Alternatively, in other embodiments some or all of the software components may execute in memory on another device and communicate with the illustrated computer system  2000  via inter-computer communication. Some or all of the system components or data structures may also be stored (e.g., as instructions or structured data) on a computer-accessible medium or a portable article to be read by an appropriate drive, various examples of which are described above. In some embodiments, instructions stored on a computer-accessible medium separate from computer system 2000 may be transmitted to computer system 2000 via transmission media or signals such as electrical, electromagnetic, or digital signals, conveyed via a communication medium such as a network and/or a wireless link. Various embodiments may further include receiving, sending or storing instructions and/or data implemented in accordance with the foregoing description upon a computer-accessible medium. Generally speaking, a computer-accessible medium may include a non-transitory, computer-readable storage medium or memory medium such as magnetic or optical media, e.g., disk or DVD/CD-ROM, volatile or non-volatile media such as RAM (e.g. SDRAM, DDR, RDRAM, SRAM, etc.), ROM, etc. In some embodiments, a computer-accessible medium may include transmission media or signals such as electrical, electromagnetic, or digital signals, conveyed via a communication medium such as network and/or a wireless link. 
     The methods described herein may be implemented in software, hardware, or a combination thereof, in different embodiments. In addition, the order of the blocks of the methods may be changed, and various elements may be added, reordered, combined, omitted, modified, etc. Various modifications and changes may be made as would be obvious to a person skilled in the art having the benefit of this disclosure. The various embodiments described herein are meant to be illustrative and not limiting. Many variations, modifications, additions, and improvements are possible. Accordingly, plural instances may be provided for components described herein as a single instance. Boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of claims that follow. Finally, structures and functionality presented as discrete components in the example configurations may be implemented as a combined structure or component. These and other variations, modifications, additions, and improvements may fall within the scope of embodiments as defined in the claims that follow.