PATENT DOCUMENT

Publication Number: US-11347030-B2
Application Number: US-201815979776-A
Country: US
Kind Code: B2

Title: Imaging lens system

Abstract:
Compact lens systems are described that may be used in small form factor cameras. The lens systems may include seven lens elements with refractive power, and may provide low F-numbers with wide field of view while maintaining or improving imaging quality and package size when compared to other compact lens systems. The lens systems may, for example, provide a focal ratio of 1.85 or less, with full field of view of 75 degrees or more. The lens systems may conform to a criterion for compactness TTL/ImageH&lt;1.7, where TTL is the total track length of the lens system, and ImageH is the semi-diagonal image height of the image plane at the photosensor. Lens system parameters and relationships 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.

Claims:
What is claimed is: 
     
       1. A lens system, comprising:
 a plurality of refractive lens elements arranged along an optical axis of the lens system, wherein the plurality of lens elements includes, in order along the optical axis from an object side to an image side:
 a first lens element with positive refractive power; 
 a second lens element with refractive power; 
 a third lens element with negative refractive power; 
 a fourth lens element with positive refractive power; 
 a fifth lens element with refractive power; 
 a sixth lens element with positive refractive power; and 
 a seventh lens element with refractive power; 
 
 wherein Abbe number of the sixth lens element (Vd 6 ) satisfies Vd 6 &gt;45; 
 wherein the lens system satisfies the relationship:
   TTL/Image H &lt;1.7, 
 
 where TTL is total track length of the lens system, and ImageH is semi-diagonal image height at an image plane of the lens system; 
 wherein the second lens element has an Abbe number higher than respective Abbe numbers for the third and fifth lens elements; 
 wherein the lens system satisfies the relationship:
   ( R 9+ R 10)/( R 9− R 10)&lt;−2,
 
 
 where R 9  is radius of curvature of an object side surface of the fifth lens element and R 10  is radius of curvature of an image side surface of the fifth lens element; and 
 wherein an F-number of the lens system is within a range of 1.6 to 1.85. 
 
     
     
       2. The lens system as recited in  claim 1 , wherein the lens system satisfies the relationship:
   0.6&lt;( f   system   /f 12)&lt;1.4, 
 
       where f system  is effective focal length of the lens system and f 12  is composite focal length of the first and second lens elements. 
     
     
       3. The lens system as recited in  claim 1 , wherein the lens system satisfies the relationship:
   0.55&lt;| f   system   /f 3|+| f   system   /f 5|&lt;1.15, 
 
       where f system  is effective focal length of the lens system, f 3  is effective focal length of the third lens element, and f 5  is effective focal length of the fifth lens element. 
     
     
       4. The lens system as recited in  claim 1 , wherein the lens system satisfies the relationship:
   0.8&lt;( Vd 1+ Vd 3)/ Vd 2&lt;3, 
 
       where Vd 1 , Vd 2 , and Vd 3  are Abbe numbers of the first, second, and third lens elements, respectively. 
     
     
       5. The lens system as recited in  claim 1 , wherein the third lens element has a concave image-side surface in a paraxial region. 
     
     
       6. The lens system as recited in  claim 1 , wherein the fifth lens element has a concave object-side surface and a convex image-side surface. 
     
     
       7. The lens system as recited in  claim 1 , wherein an object-side surface and an image-side surface of the sixth lens element are aspheric, wherein the sixth lens element has a convex object-side surface in a paraxial region, and wherein the object side surface of the sixth lens element has at least one part being concave in a peripheral region. 
     
     
       8. The lens system as recited in  claim 1 , wherein an object-side surface and an image-side surface of the seventh lens element are aspheric, wherein the seventh lens element has a concave image-side surface in a paraxial region, wherein the object-side surface of the seventh lens element has at least one part being concave in a peripheral region, and wherein the image-side surface of the seventh lens element has at least one part being convex in a peripheral region. 
     
     
       9. The lens system as recited in  claim 1 , wherein the lens system further includes an aperture stop located between a front vertex of the lens system and the second lens element. 
     
     
       10. The lens system as recited in  claim 9 , wherein the lens system further includes at least one secondary stop located between the first lens element and the fifth lens element. 
     
     
       11. The lens system as recited in  claim 1 , wherein effective focal length f of the lens system is within a range of 3.4 to 5 mm, and full field of view of the lens system is within a range of 75 to 94 degrees. 
     
     
       12. The lens system as recited in  claim 1 , wherein TTL of the lens system is less than 6.8 mm. 
     
     
       13. A camera, comprising:
 a photosensor configured to capture light projected onto a surface of the photosensor; and 
 a lens system configured to refract light from an object field located in front of the camera to form an image of a scene at an image plane at or near the surface of the photosensor, wherein the lens system includes seven refractive lens elements arranged in order along an optical axis from a first lens element having a positive refractive power on an object side of the camera to a seventh lens element on an image side of the camera, including a fourth lens with positive refractive power and a sixth lens element with positive refractive power; 
 wherein the lens system satisfies the relationship:
   TTL/Image H &lt;1.7, 
 
 where TTL is total track length of the lens system, and ImageH is semi-diagonal image height at the image plane; and 
 wherein a second lens element in order along the optical axis has an Abbe number higher than respective Abbe numbers for a third lens element and a fifth lens element in order along the optical axis; 
 wherein Abbe number of the sixth lens (Vd 6 ) satisfies Vd 6 &gt;45; 
 wherein the lens system satisfies the relationship:
   ( R 9+ R 10)/( R 9− R 10)&lt;−2,
 
 
 where R 9  is radius of curvature of an object side surface of the fifth lens element and R 10  is radius of curvature of an image side surface of the fifth lens element; and 
 wherein an F-number of the lens system is within a range of 1.6 to 1.85. 
 
     
     
       14. The camera as recited in  claim 13 , wherein the lens system satisfies one or more of the relationships:
   0.6&lt;( f   system   /f 12)&lt;1.4, 
   0.55&lt;| f   system   /f 3|+| f   system   /f 5|&lt;1.15, 
   ( R 9+ R 10)/( R 9− R 10)&lt;−2,
 
   0.8&lt;( Vd 1+ Vd 3)/ Vd 2&lt;3, 
 
       where f system  is effective focal length of the lens system, f 12  is composite focal length of the first and second lens elements, f 3  is effective focal length of the third lens element, f 5  is effective focal length of the fifth lens element, R 9  is radius of curvature of an object side surface of the fifth lens element, R 10  is radius of curvature of an image side surface of the fifth lens element, and Vd 1 , Vd 2 , and Vd 3  are Abbe numbers of the first, second, and third lens elements, respectively. 
     
     
       15. The camera as recited in  claim 13 , wherein effective focal length f of the lens system is within a range of 3.4 to 5 mm, and full field of view of the lens system is within a range of 75 to 94 degrees. 
     
     
       16. The camera as recited in  claim 13 , wherein TTL of the lens system is less than 6.8 mm. 
     
     
       17. A device, comprising:
 one or more processors; 
 one or more cameras; and 
 a memory comprising program instructions executable by at least one of the one or more processors to control operations of the one or more cameras; 
 wherein at least one of the one or more cameras is a camera comprising:
 a photosensor configured to capture light projected onto a surface of the photosensor; and 
 a lens system configured to refract light from an object field located in front of the camera to form an image of a scene at an image plane at or near the surface of the photosensor, wherein the lens system includes seven refractive lens elements arranged in order along an optical axis from a first lens element having a positive refractive power on an object side of the camera to a seventh lens element on an image side of the camera, including a fourth lens with positive refractive power and a sixth lens element with positive refractive power; 
 wherein the lens system satisfies the relationship:
   TTL/Image H &lt;1.7, 
 
 where TTL is total track length of the lens system, and ImageH is semi-diagonal image height at the image plane; 
 wherein a second lens element in order along the optical axis has an Abbe number higher than respective Abbe numbers for a third lens element and a fifth lens element in order along the optical axis; 
 wherein Abbe number of the sixth lens element (Vd 6 ) satisfies Vd 6 &gt;45; 
 wherein the lens system satisfies the relationship:
   ( R 9+ R 10)/( R 9− R 10)&lt;−2,
 
 
 where R 9  is radius of curvature of an object side surface of the fifth lens element and R 10  is radius of curvature of an image side surface of the fifth lens element; and 
 wherein an F-number of the lens system is within a range of 1.6 to 1.85. 
 
 
     
     
       18. The device as recited in  claim 17 , wherein effective focal length f of the lens system is within a range of 3.4 to 5 mm, full field of view of the lens system is within a range of 75 to 94 degrees, and TTL of the lens system is less than 6.8 mm.

Description:
PRIORITY INFORMATION 
     This application claims benefit of priority of U.S. Provisional Application Ser. No. 62/522,594 entitled “IMAGING LENS SYSTEM” filed Jun. 20, 2017, the content of which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Technical Field 
     This disclosure relates generally to camera systems, and more specifically to high-resolution, 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 a compact imaging lens system including seven lens elements that may be used in a camera and that provide a low F-number (&lt;=2.1), wide field of view (e.g., 75 degrees or greater) and short total track length (e.g., 6.8 mm or less) 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 seven lens elements with refractive power arranged along an optical axis from a first lens element on the object side to a seventh lens on the image side. In embodiments, the first lens element has positive refractive power, the third lens element has negative refractive power, the fourth lens element has positive refractive power, and the sixth lens element has positive refractive power. The second, fifth, and seventh lens elements may have either positive or negative refractive power in various embodiments. Lens system parameters and relationships including but not limited to power distribution, lens shape, thickness, aperture location, 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 aperture stop located between the object side of the optical system and the third lens element for controlling the brightness of the optical system. In some embodiments, the aperture stop may be located at the first lens element at or behind the front vertex of the lens system. In some embodiments, the aperture stop may instead be located between the first and second lens elements. In some embodiments, the lens system may also include one or more internal or secondary stops, for example a secondary stop located at the object side surface of the fourth lens element, or two secondary stops, with one located at the image side surface of the second lens element and one located at the image side surface of the fourth lens element. The secondary stop(s) may, for example, help in aberration control in low F-number and wide FOV conditions by cutting off a percentage of the off-axis ray bundles. In some embodiments, the lens system may also 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 seventh lens element and the photosensor. 
     In some embodiments, the lens system may satisfy one or more of the following relationships:
 
0.6&lt;( f   system   /f 12)&lt;1.4
 
0.55 &lt;|f   system   /f 3 |+|f   system   /f 5|&lt;1.15
 
( R 9+ R 10)/( R 9− R 10)&lt;−2
 
0.8&lt;( Vd 1+ Vd 3)/ Vd 2&lt;3
 
 Vd 6&lt;45
 
where f system  is the effective focal length of the lens system, f 12  is the composite focal length of the first and second lens elements, f 3  is effective focal length of the third lens element, f 5  is effective focal length of the fifth lens element, R 9  is radius of curvature of the object side surface of the fifth lens element, R 10  is radius of curvature of the image side surface of the fifth lens element, and Vd 1 , Vd 2 , Vd 3 , and Vd 6  are the Abbe numbers of the first, second, third, and sixth lens elements, respectively.
 
     In some embodiments, the lens system may satisfy a criterion for compactness as defined in the following relationship:
 
TTL/Image H&lt; 1.7
 
where TTL is the total track length of the lens system when focused at infinity, and where ImageH is the semi-diagonal image height on the image plane at the photosensor.
 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a cross-sectional illustration of a first embodiment of a lens system that includes seven lens elements. 
         FIG. 1B  is a graph illustrating the modulation transfer function (MTF) for a lens system as illustrated in  FIG. 1A . 
         FIG. 1C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 1A . 
         FIG. 2A  is a cross-sectional illustration of a second embodiment of a lens system that includes seven lens elements. 
         FIG. 2B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 2A . 
         FIG. 2C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 2A . 
         FIG. 3A  is a cross-sectional illustration of a third embodiment of a lens system that includes seven lens elements. 
         FIG. 3B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 3A . 
         FIG. 3C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 3A . 
         FIG. 4A  is a cross-sectional illustration of a fourth embodiment of a lens system that includes seven lens elements. 
         FIG. 4B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 4A . 
         FIG. 4C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 4A . 
         FIG. 5A  is a cross-sectional illustration of a fifth embodiment of a lens system that includes seven lens elements. 
         FIG. 5B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 5A . 
         FIG. 5C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 5A . 
         FIG. 6A  is a cross-sectional illustration of a sixth embodiment of a lens system that includes seven lens elements. 
         FIG. 6B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 6A . 
         FIG. 6C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 6A . 
         FIG. 7A  is a cross-sectional illustration of a seventh embodiment of a lens system that includes seven lens elements. 
         FIG. 7B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 7A . 
         FIG. 7C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 7A . 
         FIG. 8A  is a cross-sectional illustration of an eighth embodiment of a lens system that includes seven lens elements. 
         FIG. 8B  is a graph illustrating the MTF for a lens system as illustrated in  FIG. 8A . 
         FIG. 8C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system as illustrated in  FIG. 8A . 
         FIG. 9  is a flowchart of a method for capturing images using a camera as illustrated in  FIGS. 1A through 8C , according to some embodiments. 
         FIG. 10  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 compact lens system are described. Embodiments of a compact lens system including seven lens elements are described that may be used in the camera and that provide a low F-number (&lt;=2.1), wide field of view (e.g., 75 degrees or greater) and short total track length (e.g., 6.8 mm or less) 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. Embodiments of the lens system include seven lens elements with refractive power. Lens system parameters and relationships including but not limited to power distribution, lens shape, thickness, aperture location, 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. 
       FIGS. 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A  illustrate several example embodiments of lens systems that include seven refracting lens elements. The example embodiments may provide an F-number (focal ratio) of 1.85 or less, with focal length (f) of 5.0 mm or less, and a total track length (TTL) of less than 6.8 mm (assuming a semi-diagonal image height of 4.0). 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. 
     The refractive lens elements in embodiments of the lens system 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 =( V   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  FIGS. 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A , an example camera includes at least a compact lens system and a photosensor. The photosensor 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 may be 1.2 microns or less, although larger pixel sizes may be used. In a non-limiting example embodiment, the photosensor 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 example embodiments, an example photosensor with a full diagonal dimension of 8 mm (semi-diagonal 4 mm) may be used; however, larger or smaller photosensors may be used with appropriate adjustment of the lens system dimensions. 
     The lens system may also include an aperture stop located between the object side of the optical system and the third lens element for controlling the brightness of the optical system. In some embodiments, the aperture stop may be located at the first lens element at or behind the front vertex of the lens system. In some embodiments, the aperture stop may instead be located between the first and second lens elements. In some embodiments, the lens system may also include one or more secondary stops, for example a secondary stop located at the object side surface of the fourth lens element, or two secondary stops, with one located at the image side surface of the second lens element and one located at the image side surface of the fourth lens element. The secondary stop(s) may, for example, help in aberration control in low F-number and wide FOV conditions by cutting off a percentage of the off-axis ray bundles. 
     The camera may also, but does not necessarily, include an infrared (IR) filter, for example located between the last or seventh lens element of the lens system and the photosensor. The IR filter may, for example, be composed of a glass material. However, other materials may be used. In 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. Further note that the camera may also include other components than those illustrated and described herein. 
     In the camera, the lens system forms an image at an image plane (IP) at or near the surface of the photosensor. The image size for a distant object is directly proportional to the effective focal length f of a lens system. 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 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 the non-limiting example embodiments described herein, the lens system may be configured such that the effective focal length f of the lens system is within a range of 3.4 to 5 mm, and the F-number is within a range of 1.6 to 1.85. The lens system may, for example, be configured as shown in the examples 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. 1A , at f=4.996 mm, an F-number of 1.7 is achieved with an effective aperture of @2.94 mm. The example embodiments may, for example, be configured with a full field of view (FOV) within a range of 75 to 94 degrees. In some embodiments, photosensor with a full diagonal dimension of 8 mm (semi-diagonal 4 mm) may be used. The lens systems may satisfy a criterion for compactness as defined in the following relationship:
 
TTL/Image H&lt; 1.7
 
where TTL is the total track length of the lens system when focused at infinity, and where ImageH is the semi-diagonal image height on the image plane at the photosensor. Thus, TTL of the example embodiments may be less than 6.8 mm, assuming a semi-diagonal image height of 4 mm. Telephoto ratio (TTL/f) of an example embodiment with effective focal length f of about 5.0 and TTL of about 6.5 is thus at or about 1.3.
 
     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 may be adjustable. For example, in some embodiments, a lens system as described herein may be equipped with an adjustable iris (entrance pupil) or aperture stop. Using an adjustable aperture stop, the F-number (focal ratio, or f/#) may be dynamically varied within a range. For example, if the lens system is well corrected at f/1.7, at a given focal length f and FOV, then the focal ratio may be varied within a range of 1.4 to 8 (or higher) by adjusting the aperture stop assuming that the aperture stop can be adjusted to the F-number setting. In some embodiments, the lens system may be used at faster focal ratios (&lt;1.7) by adjusting the aperture stop at the same FOV (e.g. 81 degrees), possibly with degraded imaging quality performance, or with reasonably good performance at a smaller FOV. 
     While ranges of values may be given herein as examples for adjustable cameras and lens systems in which one or more optical parameters may be dynamically varied (e.g., using an adjustable aperture stop), embodiments of camera systems that include fixed (non-adjustable) lens systems in which values for optical and other parameters are within these ranges may be implemented. 
     Referring to the example embodiments as illustrated in  FIGS. 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A , an example camera includes at least a compact lens system and a photosensor. The camera may include an aperture stop, for example at the first lens element and at or behind the front vertex of the lens system as illustrated in  FIG. 1A , for controlling brightness of the optical system. In some embodiments, the aperture stop may instead be located between the first and second lens elements, for example as illustrated in  FIG. 2A . In some embodiments, the camera may also include one or more secondary stops, for example two secondary stops as illustrated in  FIG. 1A  or a single secondary stop as illustrated in  FIG. 2A . The camera may also, but does not necessarily, include an infrared (IR) filter, for example located between the lens system and the photosensor. The IR filter may act to reduce or eliminate interference of environmental noises on the photosensor and/or to block infrared radiation that could damage or adversely affect the photosensor, and may be configured so as to have no effect on f. 
     In embodiments, the lens system may include seven 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  with positive refractive power;   a second lens element L 2 ;   a third lens element L 3  with negative refractive power;   a fourth lens element L 4  with positive refractive power;   a fifth lens element L 5 ;   a sixth lens element L 6  with positive refractive power; and   a seventh lens element L 7 .       

     The second, fifth, and seventh lens elements may have either positive or negative refractive power in various embodiments. 
     In some embodiments the third lens element has a concave image-side surface in the paraxial region. 
     In some embodiments, the fifth lens element has a concave object-side surface and a convex image-side surface. 
     In some embodiments, the sixth lens element has a convex object-side surface in the paraxial region. In some embodiments, both the object-side surface and the image-side surface of the sixth lens element are aspheric. In some embodiments, the object-side surface has at least one part being concave near the peripheral region. 
     In some embodiments, the seventh lens element has a concave image-side surface in the paraxial region. In some embodiments, both the object-side surface and the image-side surface of the seventh lens element are aspheric. In some embodiments, the object-side surface has at least one part being concave near the peripheral region, and the image-side surface has at least one part being convex near the peripheral region. 
     In some embodiments, the lens system may satisfy one or more of the following relationships:
 
0.6&lt;( f   system   /f 12)&lt;1.4
 
0.55&lt;| f   system   /f 3|+| f   system   /f 5|&lt;1.15
 
( R 9+ R 10)/( R 9− R 10)&lt;−2
 
0.8&lt;( Vd 1+ Vd 3)/ Vd 2&lt;3
 
 Vd 6&gt;45
 
where f system  is the effective focal length of the lens system, f 12  is the composite focal length of the first and second lens elements, f 3  is effective focal length of the third lens element, f 5  is effective focal length of the fifth lens element, R 9  is radius of curvature of the object side surface of the fifth lens element, R 10  is radius of curvature of the image side surface of the fifth lens element, and Vd 1 , Vd 2 , Vd 3 , and Vd 6  are the Abbe numbers of the first, second, third, and sixth lens elements, respectively.
 
     Embodiments of a lens system may be implemented to be compact for use in small form factor cameras for consumer electronics products such as smartphones and tablet/pad devices. A criterion for compactness of the lens system may be defined in the following relationship:
 
TTL/Image H&lt; 1.7
 
where ImageH is the semi-diagonal image height on the image plane at the photosensor. Thus, in the example lens systems as defined in the Tables, total track length (TTL) is less than 6.8 mm assuming a photosensor with semi-diagonal image height of 4 mm is used. The relationship (TTL/ImageH&lt;1.7) for the example embodiments (6.8 mm/4 mm=1.7) is thus satisfied. Note that this criterion for compactness allows for proportionally longer TTL when using larger photosensors, and proportionally shorter TTL when using smaller photosensors. For example, TTL of a lens system for a photosensor with ImageH of about 3 mm would be less than 5.1 mm, and TTL of a lens system for a photosensor with ImageH of about 5 mm would be less than 8.5 mm.
 
     In the example embodiments, the lenses may be formed of various optical materials with various Abbe numbers; the materials and power configurations of lenses L 1  through L 7  may be selected to, for example, reduce chromatic aberrations. 
     Lens System  110   
       FIG. 1A  illustrates an example camera  100  with a lens system  110  that includes seven refractive lens elements, according to some embodiments. Tables 1A through 1F provide example values for various optical and physical parameters of camera  100  and lens system  110 . Lens system  110  may include seven 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  101  with positive refractive power;   a second lens element  102  with negative refractive power;   a third lens element  103  with negative refractive power;   a fourth lens element  104  with positive refractive power;   a fifth lens element  105  with refractive power;   a sixth lens element  106  with positive refractive power; and   a seventh lens element  107  with refractive power.       

     As shown in  FIG. 1A , lens system  110  system may include an aperture stop  130  at or near the object side surface of lens  101 , and two internal stops (secondary stop  132 A at the image side surface of lens  102 , and secondary stop  132 B at the image side surface of lens  104 ) in addition to the aperture stop  130 . The lens system  110  may be designed to compensate for loss of illumination and possible vignetting that may result from the internal stops  132 . The camera  100  may include an IR filter located between lens element  107  and photosensor  120 . 
     Lens system  110  may have an effective focal length f of 4.996, F-number of 1.7, and full field of view (FFOV) of 76.7 degrees. The relationship TTL/ImageH for lens system  110  is 1.57. Thus, assuming ImageH=4 mm, TTL of lens system  110  is about 6.28 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  110  is 2.804. Vd 6  for lens system  110  is 56.0. The relationship (f system /f 12 ) for lens system  110  is 0.707. The relationship|f system /f3|+|f system /f 5  for lens system  110  is 0.871. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  110  is −4.876. 
       FIG. 1B  is a graph illustrating the modulation transfer function (MTF) for a lens system  110  as illustrated in  FIG. 1A , according to some embodiments.  FIG. 1B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 1C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  110  as illustrated in  FIG. 1A , according to some embodiments. As shown in  FIG. 1C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  210   
       FIG. 2A  illustrates an example camera  200  with a lens system  210  that includes seven refractive lens elements, according to some embodiments. Tables 2A through 2F provide example values for various optical and physical parameters of camera  200  and lens system  210 . Lens system  210  may include seven 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  201  with positive refractive power;   a second lens element  202  with positive refractive power;   a third lens element  203  with negative refractive power;   a fourth lens element  204  with positive refractive power;   a fifth lens element  205  with refractive power;   a sixth lens element  206  with positive refractive power; and   a seventh lens element  207  with refractive power.       

     As shown in  FIG. 2A , lens system  210  system may include an aperture stop  230  at or near the image side surface of lens  201 , and a secondary stop  232  at the object side surface of lens  204 . The lens system  210  may be designed to compensate for loss of illumination and possible vignetting that may result from the internal stop  232 . The camera  200  may include an IR filter located between lens element  207  and photosensor  220 . 
     Lens system  210  may have an effective focal length f of 4.672, F-number of 1.6, and full field of view (FFOV) of 81.7 degrees. The relationship TTL/ImageH for lens system  210  is 1.584. Thus, assuming ImageH=4 mm, TTL of lens system  210  is about 6.336 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  210  is 1.34. Vd 6  for lens system  210  is 56.0. The relationship (f system /f 12 ) for lens system  210  is 0.999. The relationship|f system /f 3 |+|f system /f 5  for lens system  210  is 0.738. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  210  is −6.824. 
       FIG. 2B  is a graph illustrating the modulation transfer function (MTF) for a lens system  210  as illustrated in  FIG. 2A , according to some embodiments.  FIG. 2B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 2C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  210  as illustrated in  FIG. 2A , according to some embodiments. As shown in  FIG. 2C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  310   
       FIG. 3A  illustrates an example camera  300  with a lens system  310  that includes seven refractive lens elements, according to some embodiments. Tables 3A through 3F provide example values for various optical and physical parameters of camera  300  and lens system  310 . Lens system  310  may include seven 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  301  with positive refractive power;   a second lens element  302  with positive refractive power;   a third lens element  303  with negative refractive power;   a fourth lens element  304  with positive refractive power;   a fifth lens element  305  with refractive power;   a sixth lens element  306  with positive refractive power; and   a seventh lens element  307  with refractive power.       

     As shown in  FIG. 3A , lens system  310  system may include an aperture stop  330  at or near the image side surface of lens  301 , and a secondary stop  332  at the object side surface of lens  304 . The lens system  310  may be designed to compensate for loss of illumination and possible vignetting that may result from the internal stop  332 . The camera  300  may include an IR filter located between lens element  307  and photosensor  320 . 
     Lens system  310  may have an effective focal length f of 4.170, F-number of 1.7, and full field of view (FFOV) of 81.1 degrees. The relationship TTL/ImageH for lens system  310  is 1.587. Thus, assuming ImageH=4 mm, TTL of lens system  310  is about 6.348 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  310  is 1.36. Vd 6  for lens system  310  is 56.0. The relationship (f system /f 12 ) for lens system  310  is 1.125. The relationship|f system /f 3 +|f system /f 5  for lens system  310  is 0.792. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  310  is −6.865. 
       FIG. 3B  is a graph illustrating the modulation transfer function (MTF) for a lens system  310  as illustrated in  FIG. 3A , according to some embodiments.  FIG. 3B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 3C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  310  as illustrated in  FIG. 3A , according to some embodiments. As shown in  FIG. 3C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  410   
       FIG. 4A  illustrates an example camera  400  with a lens system  410  that includes seven refractive lens elements, according to some embodiments. Tables 4A through 4F provide example values for various optical and physical parameters of camera  400  and lens system  410 . Lens system  410  may include seven 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  401  with positive refractive power;   a second lens element  402  with positive refractive power;   a third lens element  403  with negative refractive power;   a fourth lens element  404  with positive refractive power;   a fifth lens element  405  with refractive power;   a sixth lens element  406  with positive refractive power; and   a seventh lens element  407  with refractive power.       

     As shown in  FIG. 4A , lens system  410  system may include an aperture stop  430  at or near the image side surface of lens  401 , and a secondary stop  432  at the object side surface of lens  404 . The lens system  410  may be designed to compensate for loss of illumination and possible vignetting that may result from the internal stop  432 . The camera  400  may include an IR filter located between lens element  407  and photosensor  420 . 
     Lens system  410  may have an effective focal length f of 3.797, F-number of 1.7, and full field of view (FFOV) of 86.5 degrees. The relationship TTL/ImageH for lens system  410  is 1.547. Thus, assuming ImageH=4 mm, TTL of lens system  410  is about 6.188 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  410  is 1.36. Vd 6  for lens system  410  is 56.0. The relationship (f system /f 12 ) for lens system  410  is 0.914. The relationship|f system /f 3 +|f system /f 5  for lens system  410  is 0.782. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  410  is −5.228. 
       FIG. 4B  is a graph illustrating the modulation transfer function (MTF) for a lens system  410  as illustrated in  FIG. 4A , according to some embodiments.  FIG. 4B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 4C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  410  as illustrated in  FIG. 4A , according to some embodiments. As shown in  FIG. 4C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  510   
       FIG. 5A  illustrates an example camera  500  with a lens system  510  that includes seven refractive lens elements, according to some embodiments. Tables 5A through 5F provide example values for various optical and physical parameters of camera  500  and lens system  510 . Lens system  510  may include seven 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  501  with positive refractive power;   a second lens element  502  with positive refractive power;   a third lens element  503  with negative refractive power;   a fourth lens element  504  with positive refractive power;   a fifth lens element  505  with refractive power;   a sixth lens element  506  with positive refractive power; and   a seventh lens element  507  with refractive power.       

     As shown in  FIG. 5A , lens system  510  system may include an aperture stop  530  between the image side surface of lens  501  and the object side surface of lens  502 . Lens system  510  may not include a secondary stop. 
     Lens system  510  may have an effective focal length f of 4.889, F-number of 1.75, and full field of view (FFOV) of 75.0 degrees. The relationship TTL/ImageH for lens system  510  is 1.594. Thus, assuming ImageH=4 mm, TTL of lens system  510  is about 6.376 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  510  is 1.34. Vd 6  for lens system  510  is 56.0. The relationship (f system /f12) for lens system  510  is 1.138. The relationship|f system /f 3 +|f system /f 5  for lens system  510  is 0.918. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  510  is −6.659. 
       FIG. 5B  is a graph illustrating the modulation transfer function (MTF) for a lens system  510  as illustrated in  FIG. 5A , according to some embodiments.  FIG. 5B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 5C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  510  as illustrated in  FIG. 5A , according to some embodiments. As shown in  FIG. 5C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  610   
       FIG. 6A  illustrates an example camera  600  with a lens system  610  that includes seven refractive lens elements, according to some embodiments. Tables 6A through 6F provide example values for various optical and physical parameters of camera  600  and lens system  610 . Lens system  610  may include seven 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  601  with positive refractive power;   a second lens element  602  with positive refractive power;   a third lens element  603  with negative refractive power;   a fourth lens element  604  with positive refractive power;   a fifth lens element  605  with refractive power;   a sixth lens element  606  with positive refractive power; and   a seventh lens element  607  with refractive power.       

     As shown in  FIG. 6A , lens system  610  system may include an aperture stop  630  at or near the image side surface of lens  601 , and a secondary stop  632  at the object side surface of lens  604 . The lens system  610  may be designed to compensate for loss of illumination and possible vignetting that may result from the internal stop  632 . The camera  600  may include an IR filter located between lens element  607  and photosensor  620 . 
     Lens system  610  may have an effective focal length f of 3.401, F-number of 1.79, and full field of view (FFOV) of 93.8 degrees. The relationship TTL/ImageH for lens system  610  is 1.534. Thus, assuming ImageH=4 mm, TTL of lens system  610  is about 6.136 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  610  is 1.35. Vd 6  for lens system  610  is 56.0. The relationship (f system /f 12 ) for lens system  610  is 0.811. The relationship|f system /f 3 |+|f system /f 5 | for lens system  610  is 0.812. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  610  is −3.707. 
       FIG. 6B  is a graph illustrating the modulation transfer function (MTF) for a lens system  610  as illustrated in  FIG. 6A , according to some embodiments.  FIG. 6B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 6C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  610  as illustrated in  FIG. 6A , according to some embodiments. As shown in  FIG. 6C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  710   
       FIG. 7A  illustrates an example camera  700  with a lens system  710  that includes seven refractive lens elements, according to some embodiments. Tables 7A through 7F provide example values for various optical and physical parameters of camera  700  and lens system  710 . Lens system  710  may include seven 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  with positive refractive power;   a second lens element  702  with positive refractive power;   a third lens element  703  with negative refractive power;   a fourth lens element  704  with positive refractive power;   a fifth lens element  705  with refractive power;   a sixth lens element  706  with positive refractive power; and   a seventh lens element  707  with refractive power.       

     As shown in  FIG. 7A , lens system  710  system may include an aperture stop  730  between the image side surface of lens  701  and the object side surface of lens  702 . Lens system  710  may not include a secondary stop. 
     Lens system  710  may have an effective focal length f of 4.361, F-number of 1.65, and full field of view (FFOV) of 80.3 degrees. The relationship TTL/ImageH for lens system  710  is 1.600. Thus, assuming ImageH=4 mm, TTL of lens system  710  is about 6.4 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  710  is 1.34. Vd 6  for lens system  710  is 56.0. The relationship (f system /f 12 ) for lens system  710  is 0.943. The relationship|f system /f 3 +|f system /f 5  for lens system  710  is 0.868. The relationship (R 9 +R 10 )/(R 9 −R 10 ) for lens system  710  is −4.540. 
       FIG. 7B  is a graph illustrating the modulation transfer function (MTF) for a lens system  710  as illustrated in  FIG. 7A , according to some embodiments.  FIG. 7B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 7C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  710  as illustrated in  FIG. 7A , according to some embodiments. 
     As shown in  FIG. 7C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
     Lens System  810   
       FIG. 8A  illustrates an example camera  800  with a lens system  810  that includes seven refractive lens elements, according to some embodiments. Tables 8A through 8F provide example values for various optical and physical parameters of camera  800  and lens system  810 . Lens system  810  may include seven 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  with positive refractive power;   a second lens element  802  with positive refractive power;   a third lens element  803  with negative refractive power;   a fourth lens element  804  with positive refractive power;   a fifth lens element  805  with refractive power;   a sixth lens element  806  with positive refractive power; and   a seventh lens element  807  with refractive power.       

     As shown in  FIG. 8A , lens system  810  system may include an aperture stop  830  at or near the object side surface of lens  801 . Lens system  810  may not include a secondary stop. 
     Lens system  810  may have an effective focal length f of 4.431, F-number of 1.85, and full field of view (FFOV) of 79.7 degrees. The relationship TTL/ImageH for lens system  810  is 1.599. Thus, assuming ImageH=4 mm, TTL of lens system  810  is about 6.396 mm. The relationship (Vd 1 +Vd 3 )/Vd 2  for lens system  810  is 1.34. Vd 6  for lens system  810  is 56.0. The relationship (f system /f 12 ) for lens system  810  is 1.005. The relationship|f system /f 3 |+|f system /f 5  for lens system  810  is 0.844. The relationship R 9 +R 10 )/(R 9 −R 10 ) for lens system  810  is −5.516. 
       FIG. 8B  is a graph illustrating the modulation transfer function (MTF) for a lens system  810  as illustrated in  FIG. 8A , according to some embodiments.  FIG. 8B  shows the lens MTF evaluated at 0 field, 0.4 field, 0.7 field and full field respectively. MTFs are higher than 0.5 at 100 line pairs (lp)/mm, showing good contrast for high-resolution imaging and rendering high-quality images using high-resolution sensors. 
       FIG. 8C  shows the longitudinal spherical aberration, field curvature and distortion for a lens system  810  as illustrated in  FIG. 8A , according to some embodiments. As shown in  FIG. 8C , optical distortion across the field of view is controlled within 2.5%, while field curvature and astigmatism are well balanced across the field of view. 
       FIG. 9  is a high-level flowchart of a method for capturing images using a camera with a lens system that includes seven lens elements as illustrated in any of  FIGS. 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A , according to some embodiments. As indicated at  1200 , light from an object field in front of the camera is received at a first lens element of the camera. As indicated at  1202 , the first lens element refracts the light to a second lens element. As indicated at  1204 , the light is then refracted by the second lens element to a third lens element. As indicated at  1206 , the light is then refracted by the third lens element to a fourth lens element. As indicated at  1208 , the light is then refracted by the fourth lens element to a fifth lens element. As indicated at  1210 , the light is then refracted by the fifth lens element to a sixth lens element. As indicated at  1212 , the light is then refracted by the sixth lens element to a seventh lens element. As indicated at  1214 , the light is refracted by the seventh lens element to form an image at an image plane at or near the surface of a photosensor. As indicated at  1216 , the image is captured by the photosensor. 
     While not shown in  FIG. 9 , in some embodiments, the light may pass through an infrared filter that may for example be located between the seventh lens element and the photosensor. In some embodiments, an aperture stop may be located at the first lens element, and light from the object field may be received at the first lens element through the aperture stop. In some embodiments, the aperture stop may instead be located between the first and second lens elements, and light from the object field may be received at the first lens element of the camera and refracted through an aperture stop to the second lens element. In some embodiments, the lens system may also include one or more internal or secondary stops, for example a secondary stop located at the object side surface of the fourth lens element, or two secondary stops, with one located at the image side surface of the second lens element and one located at the image side surface of the fourth lens element. 
     In some embodiments, the seven lens elements referred to in  FIG. 9  may be configured as illustrated in any of  FIGS. 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A  and the corresponding Tables 1A-1F, 2A-2F, 3A-3F, 4A-4F, 5A-5F, 6A-6F, 7A-7F, and 8A-8F. 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 embodiment of the lens system and cameras as described in reference to  FIGS. 1A, 2A, 3A, 4A, 5A, 6A, 7A, and 8A . In the Tables, all dimensions are in millimeters (mm) unless otherwise specified. L 1 , L 2 , L 3 , L 4 , L 5 , L 6 , and L 7  stand for refractive lenses 1, 2, 3, 4, 5, 6, and 7, respectively. STOP stands for the camera aperture stop, and (ape) signifies a secondary stop. Object indicates the object plane, IRCF or filter indicates an infrared filter, and sensor indicates the camera photosensor. “S#” stands for surface number. The surface numbers (S#) of the elements as shown in the Tables are listed from a first surface 0 at the object plane to a last surface at the image plane/photosensor surface. A positive radius for a surface 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. f 35mm  is the 35 mm equivalent focal length of the lens system. V x  is the Abbe number of a respective lens element. Both f and f sys  stand for the effective focal length of the lens system, f 12  is the composite focal length of the first and second lens elements, f 3  is effective focal length of the third lens element, f 5  is effective focal length of the fifth lens element, R 9  is radius of curvature of the object side surface of the fifth lens element, R 10  is radius of curvature of the image side surface of the fifth lens element, and Vd 1 , Vd 2 , Vd 3 , and Vd 6  are the Abbe numbers of the first, second, third, and sixth lens elements, respectively. TTL is total track length of the lens system focusing at infinity conjugate and may be 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, 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   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 1A 
               
             
            
               
                   
               
               
                 (Lens system 110) 
               
               
                 Lens system 110 
               
               
                 Fno = 1.7, FFOV = 76.7 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                 Radius 
                 Thickness or 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 separation (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 Stop 
                 1 
                 Inf 
                 −0.445 
               
               
                 L1 
                 *2 
                 2.304 
                 0.783 
                 1.545 
                 56.0 
               
               
                   
                 *3 
                 88.900 
                 0.040 
               
               
                 L2 
                 *4 
                 3.841 
                 0.230 
                 1.608 
                 26.9 
               
               
                 (ape) 
                 *5 
                 2.195 
                 0.466 
               
               
                 L3 
                 *6 
                 18.743 
                 0.231 
                 1.671 
                 19.5 
               
               
                   
                 *7 
                 8.569 
                 0.238 
               
               
                 L4 
                 *8 
                 16.112 
                 0.606 
                 1.545 
                 56.0 
               
               
                 (ape) 
                 *9 
                 −4.953 
                 0.404 
               
               
                 L5 
                 *10 
                 −1.217 
                 0.370 
                 1.608 
                 26.9 
               
               
                   
                 *11 
                 −1.845 
                 0.040 
               
               
                 L6 
                 *12 
                 1.562 
                 0.498 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 3.300 
                 1.049 
               
               
                 L7 
                 *14 
                 −4.722 
                 0.380 
                 1.509 
                 56.5 
               
               
                   
                 *15 
                 6.051 
                 0.300 
               
               
                 IRCF 
                 16 
                 Inf 
                 0.210 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.448 
               
               
                 Sensor 
                 18 
                 0 
                 0 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 1B-1E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 110) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S2 
                 S3 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 −3.05320E−01 
                 5.81709E+01 
                 −5.91105E+00 
                 −5.82023E+00 
               
               
                 A4 
                 6.03196E−04 
                 −4.25193E−02 
                 −1.00340E−01 
                 −1.86991E−02 
               
               
                 A6 
                 6.34230E−03 
                 6.59107E−02 
                 1.19187E−01 
                 3.47875E−02 
               
               
                 A8 
                 −9.72174E−03 
                 −5.91249E−02 
                 −9.27288E−02 
                 −3.37461E−02 
               
               
                 A10 
                 6.11484E−03 
                 2.82565E−02 
                 5.10058E−02 
                 2.50671E−02 
               
               
                 A12 
                 −2.26515E−03 
                 −7.21506E−03 
                 −1.59579E−02 
                 −1.12741E−02 
               
               
                 A14 
                 2.21091E−04 
                 7.15565E−04 
                 2.43034E−03 
                 2.02348E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 110) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 −9.90000E+01 
                 −6.73586E+01 
                 −3.42875E+01 
                 −8.83380E−01 
               
               
                 A4 
                 −4.31764E−02 
                 −3.39999E−02 
                 −5.79503E−02 
                 −5.18251E−02 
               
               
                 A6 
                 2.02107E−02 
                 2.82806E−02 
                 5.21786E−02 
                 3.59111E−02 
               
               
                 A8 
                 −7.78648E−02 
                 −6.25213E−02 
                 −6.55491E−02 
                 −5.04804E−02 
               
               
                 A10 
                 7.66115E−02 
                 5.70290E−02 
                 5.21580E−02 
                 4.32790E−02 
               
               
                 A12 
                 −3.84784E−02 
                 −2.33303E−02 
                 −1.86763E−02 
                 −1.50636E−02 
               
               
                 A14 
                 7.77245E−03 
                 3.93678E−03 
                 2.41644E−03 
                 1.81523E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 110) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 −5.26250E+00 
                 −8.26180E−01 
                 −7.07080E+00 
                 −6.65914E+00 
               
               
                 A4 
                 −2.09645E−02 
                 4.59461E−02 
                 2.55357E−02 
                 2.76443E−02 
               
               
                 A6 
                 −3.17745E−02 
                 −6.11074E−02 
                 −3.47440E−02 
                 −3.96580E−02 
               
               
                 A8 
                 2.74893E−02 
                 5.30175E−02 
                 1.40896E−02 
                 1.66250E−02 
               
               
                 A10 
                 3.91643E−03 
                 −2.35045E−02 
                 −3.25680E−03 
                 −3.96122E−03 
               
               
                 A12 
                 −7.41082E−03 
                 6.02808E−03 
                 3.70484E−04 
                 5.50090E−04 
               
               
                 A14 
                 2.07046E−03 
                 −8.14669E−04 
                 −1.55394E−05 
                 −4.11444E−05 
               
               
                 A16 
                 −1.84476E−04 
                 4.37640E−05 
                 −2.74692E−08 
                 1.27412E−06 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 110) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.25036E+01 
                 2.04150E−01 
               
               
                   
                 A4 
                 −7.53149E−02 
                 −6.62641E−02 
               
               
                   
                 A6 
                 7.20264E−03 
                 9.96535E−03 
               
               
                   
                 A8 
                 4.36238E−03 
                 7.56385E−04 
               
               
                   
                 A10 
                 −1.24385E−03 
                 −4.48416E−04 
               
               
                   
                 A12 
                 1.39735E−04 
                 5.79979E−05 
               
               
                   
                 A14 
                 −7.44489E−06 
                 −3.22535E−06 
               
               
                   
                 A16 
                 1.54848E−07 
                 6.69547E−08 
               
               
                   
                 A18 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
                 A20 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1F 
               
               
                   
               
               
                 Optical Definitions (Lens system 110) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 4.966 
                 Vd6 
                 56.0 
               
               
                 FNO 
                 1.7 
                 fsys/f12 
                 0.707 
               
               
                 FFOV [deg] 
                 76.7° 
                 |fsys/f3| + |fsys/f5| 
                 0.871 
               
               
                 TTL/ImaH 
                 1.57 
                 (R9 + R10)/(R9 − R10) 
                 −4.876 
               
               
                 (Vd1 + Vd3)/Vd2 
                 2.804 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2A 
               
             
            
               
                   
               
               
                 (Lens system 210) 
               
               
                 Lens system 210 
               
               
                 Fno = 1.6, FFOV = 81.7 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                 Radius 
                 Thickness or 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 separation (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 L1 
                 *1 
                 3.578 
                 0.483 
                 1.678 
                 55.3 
               
               
                   
                 *2 
                 52.982 
                 0.043 
               
               
                 Stop 
                 3 
                 Inf 
                 0.120 
               
               
                 L2 
                 *4 
                 145.648 
                 0.523 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −14.715 
                 0.050 
               
               
                 L3 
                 *6 
                 4.593 
                 0.280 
                 1.671 
                 19.5 
               
               
                   
                 *7 
                 2.864 
                 0.698 
               
               
                 L4(ape) 
                 *8 
                 99.332 
                 0.648 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −7.970 
                 0.275 
               
               
                 L5 
                 *10 
                 −1.782 
                 0.349 
                 1.671 
                 19.5 
               
               
                   
                 *11 
                 −2.394 
                 0.050 
               
               
                 L6 
                 *12 
                 2.262 
                 0.592 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 3.608 
                 0.554 
               
               
                 L7 
                 *14 
                 2.166 
                 0.606 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 1.490 
                 0.371 
               
               
                 Filter 
                 16 
                 Inf 
                 0.200 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.600 
               
               
                 Sensor 
                 18 
                 Inf 
                 0.000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 2B-2E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 210) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −2.71282E−02 
                 −5.23273E−02 
                 −1.64596E−02 
                 −1.20496E−02 
               
               
                 A6 
                 8.16881E−04 
                 −1.09116E−03 
                 −1.49108E−02 
                 6.89812E−04 
               
               
                 A8 
                 −1.57489E−02 
                 1.61222E−02 
                 4.70541E−02 
                 −7.05934E−03 
               
               
                 A10 
                 7.79285E−03 
                 −8.29321E−03 
                 −2.82823E−02 
                 3.00405E−03 
               
               
                 A12 
                 −9.83834E−04 
                 1.58985E−03 
                 6.28593E−03 
                 −5.47500E−04 
               
               
                 A14 
                 0.00000E+00 
                 0.00000E+00 
                 −4.08275E−04 
                 4.45386E−05 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 210) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −6.43880E−02 
                 −5.64974E−02 
                 −3.26388E−02 
                 −7.17908E−02 
               
               
                 A6 
                 3.83174E−02 
                 4.07390E−02 
                 −2.27384E−03 
                 3.55925E−02 
               
               
                 A8 
                 −1.74126E−02 
                 −2.08857E−02 
                 −4.62563E−03 
                 −4.01549E−02 
               
               
                 A10 
                 7.67743E−03 
                 1.11914E−02 
                 3.95460E−03 
                 2.77583E−02 
               
               
                 A12 
                 −1.44363E−03 
                 −3.42685E−03 
                 −2.15521E−03 
                 −8.87713E−03 
               
               
                 A14 
                 6.58250E−05 
                 5.04322E−04 
                 5.80626E−04 
                 1.01358E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 210) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 −1.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −3.98488E−03 
                 −3.31090E−02 
                 −1.53803E−02 
                 3.30002E−02 
               
               
                 A6 
                 7.45794E−02 
                 5.20492E−02 
                 −9.40289E−03 
                 −2.88821E−02 
               
               
                 A8 
                 −9.46661E−02 
                 −5.34014E−02 
                 2.51963E−03 
                 7.89116E−03 
               
               
                 A10 
                 7.78882E−02 
                 4.27456E−02 
                 −6.01357E−04 
                 −1.40434E−03 
               
               
                 A12 
                 −3.36808E−02 
                 −2.10036E−02 
                 7.92489E−05 
                 1.55224E−04 
               
               
                 A14 
                 7.33848E−03 
                 6.06106E−03 
                 −4.67992E−06 
                 −9.20854E−06 
               
               
                 A16 
                 −6.48765E−04 
                 −9.52611E−04 
                 1.10339E−07 
                 2.17414E−07 
               
               
                 A18 
                 0.00000E+00 
                 6.30441E−05 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A20 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 210) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −1.40707E−01 
                 −1.49167E−01 
               
               
                   
                 A6 
                 2.67349E−02 
                 4.41248E−02 
               
               
                   
                 A8 
                 −2.02152E−03 
                 −1.04189E−02 
               
               
                   
                 A10 
                 −1.06561E−05 
                 1.72727E−03 
               
               
                   
                 A12 
                 1.20801E−05 
                 −1.83282E−04 
               
               
                   
                 A14 
                 −7.51427E−07 
                 1.16981E−05 
               
               
                   
                 A16 
                 1.52768E−08 
                 −4.07483E−07 
               
               
                   
                 A18 
                 0.00000E+00 
                 5.94083E−09 
               
               
                   
                 A20 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2F 
               
               
                   
               
               
                 Optical Definitions (Lens system 210) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f [mm] 
                 4.672 
                 Vd6 
                 56.0 
               
               
                 FNO 
                 1.6 
                 fsys/f12 
                 0.999 
               
               
                 FFOV [deg] 
                 81.7° 
                 |fsys/f3| + |fsys/f5| 
                 0.738 
               
               
                 TTL/ImaH 
                 1.584 
                 (R9 + R10)/(R9 − R10) 
                 −6.824 
               
               
                 (Vd1 + Vd3)/Vd2 
                 1.34 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3A 
               
             
            
               
                   
               
               
                 (Lens system 310) 
               
               
                 Lens system 310 
               
               
                 Fno = 1.7, FFOV = 81.1 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                 Radius 
                 Thickness or 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 separation (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 L1 
                 *1 
                 3.193 
                 0.411 
                 1.678 
                 55.3 
               
               
                   
                 *2 
                 7.332 
                 −0.111 
               
               
                 Stop 
                 3 
                 Inf 
                 0.218 
               
               
                 L2 
                 *4 
                 4.279 
                 0.580 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −9.522 
                 0.050 
               
               
                 L3 
                 *6 
                 5.775 
                 0.270 
                 1.661 
                 20.4 
               
               
                   
                 *7 
                 2.841 
                 0.424 
               
               
                 L4(ape) 
                 *8 
                 −69.948 
                 0.524 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −6.479 
                 0.233 
               
               
                 L5 
                 *10 
                 −1.824 
                 0.300 
                 1.661 
                 20.4 
               
               
                   
                 *11 
                 −2.446 
                 0.050 
               
               
                 L6 
                 *12 
                 2.100 
                 0.633 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 2.697 
                 0.365 
               
               
                 L7 
                 *14 
                 1.941 
                 0.555 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 1.331 
                 0.298 
               
               
                 Filter 
                 16 
                 Inf 
                 0.200 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.600 
               
               
                 Sensor 
                 18 
                 Inf 
                 0 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 3B-3E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 310) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −6.58554E−02 
                 −1.36833E−01 
                 −7.13044E−02 
                 −1.72276E−02 
               
               
                 A6 
                 1.74384E−02 
                 3.63225E−03 
                 −1.26558E−02 
                 −1.08422E−02 
               
               
                 A8 
                 −6.82517E−02 
                 3.87808E−02 
                 9.76565E−02 
                 5.06073E−03 
               
               
                 A10 
                 5.26960E−02 
                 −2.38248E−02 
                 −7.43276E−02 
                 −1.70027E−04 
               
               
                 A12 
                 −1.78190E−02 
                 4.71206E−03 
                 2.36292E−02 
                 −1.27495E−03 
               
               
                 A14 
                 2.43257E−03 
                 0.00000E+00 
                 −3.46406E−03 
                 4.44916E−05 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 310) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −7.20658E−02 
                 −7.43458E−02 
                 −4.18224E−02 
                 −9.43632E−02 
               
               
                 A6 
                 1.34562E−02 
                 3.54564E−02 
                 2.91573E−03 
                 8.48390E−02 
               
               
                 A8 
                 −8.11394E−03 
                 −4.69230E−02 
                 −1.13379E−02 
                 −1.11897E−01 
               
               
                 A10 
                 5.22935E−03 
                 4.15968E−02 
                 −5.92143E−03 
                 8.79651E−02 
               
               
                 A12 
                 2.69362E−03 
                 −1.84051E−02 
                 5.58574E−03 
                 −3.74362E−02 
               
               
                 A14 
                 −1.82612E−03 
                 3.45904E−03 
                 7.34867E−05 
                 6.13431E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 310) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 3.28957E−02 
                 −1.40719E−02 
                 −6.96766E−02 
                 −3.86811E−03 
               
               
                 A6 
                 7.71349E−02 
                 −2.15278E−03 
                 −5.50187E−02 
                 −3.33070E−02 
               
               
                 A8 
                 −1.76369E−01 
                 2.01486E−02 
                 6.83074E−02 
                 1.13522E−02 
               
               
                 A10 
                 2.05715E−01 
                 −1.68369E−02 
                 −5.66557E−02 
                 −1.86911E−03 
               
               
                 A12 
                 −1.23173E−01 
                 1.34296E−02 
                 2.64327E−02 
                 5.26583E−05 
               
               
                 A14 
                 3.66992E−02 
                 −6.46473E−03 
                 −6.59686E−03 
                 2.38391E−05 
               
               
                 A16 
                 −4.73956E−03 
                 1.14035E−03 
                 6.69854E−04 
                 −2.19638E−06 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 310) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −2.46059E−01 
                 −2.48564E−01 
               
               
                   
                 A6 
                 8.79845E−02 
                 1.12006E−01 
               
               
                   
                 A8 
                 −1.77438E−02 
                 −3.95552E−02 
               
               
                   
                 A10 
                 2.19122E−03 
                 9.55319E−03 
               
               
                   
                 A12 
                 −1.61012E−04 
                 −1.45744E−03 
               
               
                   
                 A14 
                 6.26070E−06 
                 1.33290E−04 
               
               
                   
                 A16 
                 −9.39698E−08 
                 −6.66546E−06 
               
               
                   
                 A18 
                 0.00000E+00 
                 1.40103E−07 
               
               
                   
                 A20 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3F 
               
               
                   
               
               
                 Optical Definitions (Lens system 310) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 4.170 
                 Vd6 
                 56.0 
               
               
                 Fno 
                 1.7 
                 fsys/f12 
                 1.125 
               
               
                 FFOV [deg] 
                 81.1° 
                 |fsys/f3| + |fsys/f5| 
                 0.792 
               
               
                 TTL/ImaH 
                 1.587 
                 (R9 + R10)/(R9 − R10) 
                 −6.865 
               
               
                 (Vd1 + Vd3)/Vd2 
                 1.36 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4A 
               
             
            
               
                   
               
               
                 (Lens system 410) 
               
               
                 Lens system 410 
               
               
                 Fno = 1.7, FFOV = 86.5 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 separation 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 L1 
                 *1 
                 3.588 
                 0.358 
                 1.545 
                 56.0 
               
               
                   
                 *2 
                 8.847 
                 −0.060 
               
               
                 Stop 
                 3 
                 Inf 
                 0.120 
               
               
                 L2 
                 *4 
                 11.245 
                 0.507 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −4.916 
                 0.050 
               
               
                 L3 
                 *6 
                 3.509 
                 0.270 
                 1.661 
                 20.4 
               
               
                   
                 *7 
                 2.301 
                 0.424 
               
               
                 L4(ape) 
                 *8 
                 −74.141 
                 0.621 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −3.772 
                 0.226 
               
               
                 L5 
                 *10 
                 −1.558 
                 0.300 
                 1.661 
                 20.4 
               
               
                   
                 *11 
                 −2.295 
                 0.050 
               
               
                 L6 
                 *12 
                 2.078 
                 0.514 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 2.960 
                 0.384 
               
               
                 L7 
                 *14 
                 1.506 
                 0.532 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 1.119 
                 0.362 
               
               
                 Filter 
                 16 
                 Inf 
                 0.150 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.650 
               
               
                 Sensor 
                 18 
                 Inf 
                 0 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 4B-4E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 410) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −6.87139E−02  
                 −1.41063E−01  
                 −5.76515E−02  
                 1.11166E−02 
               
               
                 A6 
                 −2.65343E−03  
                 5.47312E−03 
                 5.10669E−03 
                 −2.54870E−02  
               
               
                 A8 
                 −4.15509E−02  
                 5.35520E−02 
                 7.87667E−02 
                 4.34636E−03 
               
               
                 A10 
                 3.10852E−02 
                 −3.69744E−02  
                 −6.66509E−02  
                 1.58538E−03 
               
               
                 A12 
                 −6.08135E−03  
                 8.63873E−03 
                 2.07700E−02 
                 −3.04491E−03  
               
               
                 A14 
                 0.00000E+00 
                 0.00000E+00 
                 −3.50562E−03  
                 4.45543E−05 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 410) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −1.10115E−01  
                 −1.23015E−01  
                 −1.90886E−02  
                 −9.18985E−02  
               
               
                 A6 
                 1.44245E−02 
                 2.32806E−02 
                 −4.14665E−03  
                 9.37935E−02 
               
               
                 A8 
                 −1.44747E−02  
                 −2.00680E−02  
                 −4.68787E−03  
                 −1.07030E−01  
               
               
                 A10 
                 1.15125E−02 
                 1.80039E−02 
                 −6.09420E−03  
                 8.13471E−02 
               
               
                 A12 
                 −3.23143E−03  
                 −1.38860E−02  
                 3.68790E−03 
                 −3.68387E−02  
               
               
                 A14 
                 −1.80795E−03  
                 3.46148E−03 
                 6.26946E−05 
                 6.62134E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 410) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −1.06950E−01  
                 −1.16537E−01  
                 1.51213E−02 
                 1.04536E−01 
               
               
                 A6 
                 4.08189E−01 
                 1.99673E−01 
                 −1.11470E−01  
                 −1.22501E−01  
               
               
                 A8 
                 −5.87411E−01  
                 −2.22056E−01  
                 7.74218E−02 
                 5.20529E−02 
               
               
                 A10 
                 5.22040E−01 
                 1.65449E−01 
                 −4.36571E−02  
                 −1.32314E−02  
               
               
                 A12 
                 −2.61898E−01  
                 −6.96212E−02  
                 1.62368E−02 
                 1.96780E−03 
               
               
                 A14 
                 6.65130E−02 
                 1.47542E−02 
                 −3.48295E−03  
                 −1.52875E−04  
               
               
                 A16 
                 −6.47441E−03  
                 −1.14956E−03  
                 3.14821E−04 
                 4.62834E−06 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 410) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −2.77492E−01 
                 −2.99036E−01 
               
               
                   
                 A6 
                  9.44416E−02 
                  1.38233E−01 
               
               
                   
                 A8 
                 −1.85059E−02 
                 −4.91065E−02 
               
               
                   
                 A10 
                  2.30288E−03 
                  1.18103E−02 
               
               
                   
                 A12 
                 −1.82048E−04 
                 −1.78576E−03 
               
               
                   
                 A14 
                  8.52448E−06 
                  1.61024E−04 
               
               
                   
                 A16 
                 −1.85072E−07 
                 −7.88048E−06 
               
               
                   
                 A18 
                  0.00000E+00 
                  1.60650E−07 
               
               
                   
                 A20 
                  0.00000E+00 
                  0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4F 
               
               
                   
               
               
                 Optical Definitions (Lens system 410) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 3.797 
                 Vd6 
                 56.0 
               
               
                 Fno 
                 1.7 
                 fsys/f12 
                 0.914 
               
               
                 FFOV[deg] 
                 86.5° 
                 |fsys/f3| + |fsys/f5| 
                 0.782 
               
               
                 TTL/ImaH 
                 1.547 
                 (R9 + R10)/(R9 − R10) 
                 −5.228 
               
            
           
           
               
               
               
            
               
                 (Vd1 + Vd3)/Vd2 
                 1.36 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5A 
               
             
            
               
                   
               
               
                 (Lens system 510) 
               
               
                 Lens system 510 
               
               
                 Fno = 1.75, FFOV = 76.0 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 separation 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 L1 
                 *1 
                 2.799 
                 0.515 
                 1.678 
                 55.3 
               
               
                   
                 *2 
                 7.957 
                 0.156 
               
               
                 Stop 
                 3 
                 Inf 
                 −0.116 
               
               
                 L2 
                 *4 
                 8.824 
                 0.495 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −38.936 
                 0.061 
               
               
                 L3 
                 *6 
                 4.785 
                 0.300 
                 1.671 
                 19.5 
               
               
                   
                 *7 
                 2.687 
                 0.584 
               
               
                 L4 
                 *8 
                 62.271 
                 0.458 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −6.395 
                 0.300 
               
               
                 L5 
                 *10 
                 −1.624 
                 0.330 
                 1.671 
                 19.5 
               
               
                   
                 *11 
                 −2.198 
                 0.176 
               
               
                 L6 
                 *12 
                 2.137 
                 0.600 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 2.921 
                 0.630 
               
               
                 L7 
                 *14 
                 3.564 
                 0.574 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 1.969 
                 0.248 
               
               
                 Filter 
                 16 
                 Inf 
                 0.200 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.589 
               
               
                 Sensor 
                 18 
                 Inf 
                 0.000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 5B-5E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 510) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −2.87841E−02  
                 −7.74463E−02  
                 −3.22850E−02  
                 1.70938E−02 
               
               
                 A6 
                 1.20615E−02 
                 1.28363E−02 
                 −1.60390E−02  
                 −1.63784E−02  
               
               
                 A8 
                 −2.44465E−02  
                 2.36840E−02 
                 7.76458E−02 
                 −5.57964E−03  
               
               
                 A10 
                 1.18127E−02 
                 −1.49048E−02  
                 −5.07699E−02  
                 4.23043E−03 
               
               
                 A12 
                 −1.63924E−03  
                 3.22003E−03 
                 1.27979E−02 
                 −7.34848E−04  
               
               
                 A14 
                 0.00000E+00 
                 0.00000E+00 
                 −9.98944E−04  
                 8.74525E−05 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 510) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −6.96462E−02  
                 −8.41529E−02  
                 −3.88860E−02  
                 −4.47361E−02  
               
               
                 A6 
                 3.00360E−02 
                 5.68837E−02 
                 −1.27338E−02  
                 4.72656E−02 
               
               
                 A8 
                 −1.11213E−02  
                 −3.42487E−02  
                 3.64131E−03 
                 −6.94547E−02  
               
               
                 A10 
                 3.85523E−03 
                 2.10999E−02 
                 −6.00617E−03  
                 5.11704E−02 
               
               
                 A12 
                 1.27146E−03 
                 −7.07483E−03  
                 1.75852E−03 
                 −1.93692E−02  
               
               
                 A14 
                 −5.84598E−04  
                 1.16314E−03 
                 5.65390E−04 
                 2.99051E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 510) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 −1.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 9.00794E−02 
                 1.17886E−02 
                 −7.23946E−02 
                 −1.61905E−02  
               
               
                 A6 
                 −5.06815E−04  
                 −3.59261E−03  
                  1.63035E−02 
                 −1.44504E−02  
               
               
                 A8 
                 −3.69265E−02  
                 1.23897E−02 
                 −8.32292E−03 
                 4.93190E−03 
               
               
                 A10 
                 5.39105E−02 
                 −9.22268E−03  
                  2.27821E−03 
                 −1.05531E−03  
               
               
                 A12 
                 −2.94572E−02  
                 5.53239E−03 
                 −3.35075E−04 
                 1.38287E−04 
               
               
                 A14 
                 7.41675E−03 
                 −1.76962E−03  
                  3.00073E−05 
                 −9.09815E−06  
               
               
                 A16 
                 −7.16588E−04  
                 2.10520E−04 
                 −1.28586E−06 
                 1.96984E−07 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 510) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −1.37976E−01 
                 −1.47241E−01 
               
               
                   
                 A6 
                  4.28089E−02 
                  5.31172E−02 
               
               
                   
                 A8 
                 −8.45973E−03 
                 −1.60379E−02 
               
               
                   
                 A10 
                  1.15443E−03 
                  3.35399E−03 
               
               
                   
                 A12 
                 −1.00644E−04 
                 −4.40049E−04 
               
               
                   
                 A14 
                  4.94238E−06 
                  3.42149E−05 
               
               
                   
                 A16 
                 −1.03363E−07 
                 −1.43279E−06 
               
               
                   
                 A18 
                  0.00000E+00 
                  2.47956E−08 
               
               
                   
                 A20 
                  0.00000E+00 
                  0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5F 
               
               
                   
               
               
                 Optical Definitions (Lens system 510) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 4.889 
                 Vd6 
                 56.0 
               
               
                 Fno 
                 1.75 
                 fsys/f12 
                 1.138 
               
               
                 FFOV[deg] 
                 75.0° 
                 |fsys/f3| + |fsys/f5| 
                 0.918 
               
               
                 TTL/ImaH 
                 1.594 
                 (R9 + R10)/(R9 − R10) 
                 −6.659 
               
            
           
           
               
               
               
            
               
                 (Vd1 + Vd3)/Vd2 
                 1.34 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6A 
               
             
            
               
                   
               
               
                 (Lens system 610) 
               
               
                 Lens system 610 
               
               
                 Fno = 1.79, FFOV = 93.8 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 separation 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 L1 
                 *1 
                 9.893 
                 0.301 
                 1.545 
                 56.0 
               
               
                   
                 *2 
                 −20.150 
                 −0.072 
               
               
                 Stop 
                 3 
                 Inf 
                 0.156 
               
               
                 L2 
                 *4 
                 −15.153 
                 0.470 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −2.755 
                 0.050 
               
               
                 L3 
                 *6 
                 2.749 
                 0.282 
                 1.671 
                 19.5 
               
               
                   
                 *7 
                 2.008 
                 0.367 
               
               
                 L4(ape) 
                 *8 
                 −12.915 
                 0.826 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −3.410 
                 0.169 
               
               
                 L5 
                 *10 
                 −1.554 
                 0.361 
                 1.671 
                 19.5 
               
               
                   
                 *11 
                 −2.702 
                 0.050 
               
               
                 L6 
                 *12 
                 2.178 
                 0.566 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 7.664 
                 0.258 
               
               
                 L7 
                 *14 
                 1.112 
                 0.439 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 0.881 
                 0.500 
               
               
                 Filter 
                 16 
                 Inf 
                 0.150 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.650 
               
               
                 Sensor 
                 18 
                 Inf 
                 0.000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 6B-6E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 610) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                  0.00000E+00 
               
               
                 A4 
                 −8.54874E−02  
                 −1.29422E−01  
                 −4.96919E−02  
                 −4.97829E−03 
               
               
                 A6 
                 −2.92135E−03  
                 1.65093E−02 
                 −8.55566E−03  
                 −2.87222E−02 
               
               
                 A8 
                 −3.23911E−02  
                 4.88389E−02 
                 8.24493E−02 
                  1.54703E−02 
               
               
                 A10 
                 3.41242E−02 
                 −4.11291E−02  
                 −7.80300E−02  
                 −8.82930E−03 
               
               
                 A12 
                 −8.18398E−03  
                 1.35679E−02 
                 2.26991E−02 
                 −3.46007E−03 
               
               
                 A14 
                 0.00000E+00 
                 0.00000E+00 
                 −4.86829E−03  
                 −7.69854E−04 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 7.04683E−13 
                  5.55645E−04 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 610) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −1.20944E−01 
                 −1.37693E−01  
                 −2.23939E−02  
                 −1.39867E−01  
               
               
                 A6 
                  1.37811E−02 
                 2.44784E−02 
                 −5.54065E−03  
                 1.03517E−01 
               
               
                 A8 
                 −1.82004E−02 
                 −2.74661E−02  
                 −9.66051E−03  
                 −1.05067E−01  
               
               
                 A10 
                  1.08938E−02 
                 1.73582E−02 
                 −4.75993E−03  
                 8.15255E−02 
               
               
                 A12 
                 −5.61416E−03 
                 −1.19012E−02  
                 4.47867E−03 
                 −3.68732E−02  
               
               
                 A14 
                 −1.54022E−03 
                 3.80138E−03 
                 3.70650E−04 
                 6.51606E−03 
               
               
                 A16 
                 −2.90552E−04 
                 1.19506E−05 
                 1.01270E−05 
                 1.93153E−05 
               
               
                 A18 
                  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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 610) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −1.24230E−01  
                 −1.66946E−01  
                 3.91676E−02 
                 2.42652E−01 
               
               
                 A6 
                 3.34553E−01 
                 2.03674E−01 
                 −1.15821E−01  
                 −2.28507E−01  
               
               
                 A8 
                 −3.48613E−01  
                 −1.36071E−01  
                 1.06102E−01 
                 1.15685E−01 
               
               
                 A10 
                 2.55101E−01 
                 6.36438E−02 
                 −8.87040E−02  
                 −4.03913E−02  
               
               
                 A12 
                 −1.06193E−01  
                 −1.58712E−02  
                 5.43856E−02 
                 9.83342E−03 
               
               
                 A14 
                 1.99169E−02 
                 9.73536E−04 
                 −2.22572E−02  
                 −1.64155E−03  
               
               
                 A16 
                 −6.87339E−04  
                 2.05965E−04 
                 5.69580E−03 
                 1.80004E−04 
               
               
                 A18 
                 0.00000E+00 
                 0.00000E+00 
                 −8.23279E−04  
                 −1.16281E−05  
               
               
                 A20 
                 0.00000E+00 
                 0.00000E+00 
                 5.10427E−05 
                 3.30815E−07 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 610) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −2.35121E−01 
                 −3.16279E−01 
               
               
                   
                 A6 
                  3.70422E−02 
                  1.25385E−01 
               
               
                   
                 A8 
                  5.00077E−03 
                 −3.94052E−02 
               
               
                   
                 A10 
                 −5.02644E−03 
                  8.58115E−03 
               
               
                   
                 A12 
                  1.73785E−03 
                 −1.13335E−03 
               
               
                   
                 A14 
                 −3.40303E−04 
                  7.46468E−05 
               
               
                   
                 A16 
                  3.81534E−05 
                 −4.81599E−07 
               
               
                   
                 A18 
                 −2.27502E−06 
                 −2.09744E−07 
               
               
                   
                 A20 
                  5.59302E−08 
                  8.12967E−09 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6F 
               
               
                   
               
               
                 Optical Definitions (Lens system 610) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 3.401 
                 Vd6 
                 56.0 
               
               
                 Fno 
                 1.79 
                 fsys/f12 
                 0.811 
               
               
                 FFOV[deg] 
                 93.8° 
                 |fsys/f3| + |fsys/f5| 
                 0.812 
               
               
                 TTL/ImaH 
                 1.534 
                 (R9 + R10)/(R9 − R10) 
                 −3.707 
               
            
           
           
               
               
               
            
               
                 (Vd1 + Vd3)/Vd2 
                 1.35 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7A 
               
             
            
               
                   
               
               
                 (Lens system 710) 
               
               
                 Lens system 710 
               
               
                 Fno = 1.65, FFOV = 80.3 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 separation 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 L1 
                 *1 
                 3.368 
                 0.454 
                 1.678 
                 55.3 
               
               
                   
                 *2 
                 26.231 
                 0.085 
               
               
                 Stop 
                 3 
                 Inf 
                 −0.035 
               
               
                 L2 
                 *4 
                 68.151 
                 0.447 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −15.443 
                 0.065 
               
               
                 L3 
                 *6 
                 3.535 
                 0.270 
                 1.671 
                 19.5 
               
               
                   
                 *7 
                 2.478 
                 0.557 
               
               
                 L4 
                 *8 
                 −194.992 
                 0.603 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −6.045 
                 0.231 
               
               
                 L5 
                 *10 
                 −1.641 
                 0.359 
                 1.671 
                 19.5 
               
               
                   
                 *11 
                 −2.568 
                 0.059 
               
               
                 L6 
                 *12 
                 2.214 
                 0.679 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 4.192 
                 0.450 
               
               
                 L7 
                 *14 
                 1.948 
                 0.650 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 1.416 
                 0.394 
               
               
                 Filter 
                 16 
                 Inf 
                 0.150 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.581 
               
               
                 Sensor 
                 18 
                 Inf 
                 0.000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 7B-7E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 710) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −3.44743E−02  
                 −6.27155E−02  
                 −1.11696E−02  
                 9.28600E−03 
               
               
                 A6 
                 6.74888E−03 
                 −5.09915E−03  
                 −2.28545E−02  
                 −9.71708E−03  
               
               
                 A8 
                 −2.96218E−02  
                 2.72039E−02 
                 7.69463E−02 
                 −9.62688E−03  
               
               
                 A10 
                 1.55924E−02 
                 −1.52393E−02  
                 −5.26124E−02  
                 5.24733E−03 
               
               
                 A12 
                 −2.21316E−03  
                 3.28068E−03 
                 1.40864E−02 
                 −9.15930E−04  
               
               
                 A14 
                 0.00000E+00 
                 0.00000E+00 
                 −1.09968E−03  
                 2.48834E−04 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 710) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −7.32015E−02  
                 −8.04783E−02  
                 −3.26817E−02  
                 −7.74378E−02  
               
               
                 A6 
                 2.60355E−02 
                 4.62935E−02 
                 −6.23032E−03  
                 6.26289E−02 
               
               
                 A8 
                 −1.44950E−02  
                 −3.49531E−02  
                 2.17401E−03 
                 −6.82425E−02  
               
               
                 A10 
                 5.26982E−03 
                 2.27973E−02 
                 −4.85828E−03  
                 4.92366E−02 
               
               
                 A12 
                 1.39273E−03 
                 −7.83022E−03  
                 1.71949E−03 
                 −1.83752E−02  
               
               
                 A14 
                 −6.60225E−04  
                 1.17663E−03 
                 2.96148E−04 
                 2.63725E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 710) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 −1.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 4.05724E−02 
                 −3.86026E−02  
                 −6.18155E−02 
                 1.02626E−02 
               
               
                 A6 
                 3.09326E−04 
                 2.05060E−02 
                  3.38178E−02 
                 −1.73677E−03  
               
               
                 A8 
                 3.80031E−02 
                 2.28231E−02 
                 −1.91914E−02 
                 −4.53206E−03  
               
               
                 A10 
                 −3.48428E−02  
                 −2.75874E−02  
                  5.51249E−03 
                 1.73567E−03 
               
               
                 A12 
                 1.94087E−02 
                 1.36669E−02 
                 −8.64167E−04 
                 −2.91549E−04  
               
               
                 A14 
                 −6.10262E−03  
                 −3.27438E−03  
                  6.82043E−05 
                 2.41326E−05 
               
               
                 A16 
                 7.94906E−04 
                 3.04947E−04 
                 −2.05288E−06 
                 −7.96272E−07  
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 710) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −1.72955E−01 
                 −1.72321E−01 
               
               
                   
                 A6 
                  5.19549E−02 
                  6.08467E−02 
               
               
                   
                 A8 
                 −1.06579E−02 
                 −1.69687E−02 
               
               
                   
                 A10 
                  1.52322E−03 
                  3.18908E−03 
               
               
                   
                 A12 
                 −1.36015E−04 
                 −3.87618E−04 
               
               
                   
                 A14 
                  6.61824E−06 
                  2.95229E−05 
               
               
                   
                 A16 
                 −1.32761E−07 
                 −1.28364E−06 
               
               
                   
                 A18 
                  0.00000E+00 
                  2.41956E−08 
               
               
                   
                 A20 
                  0.00000E+00 
                  0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7F 
               
               
                   
               
               
                 Optical Definitions (Lens system 710) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 f[mm] 
                 4.361 
                 Vd6 
                 56.0 
               
               
                 Fno 
                 1.65 
                 fsys/f12 
                 0.943 
               
               
                 FFOV[deg] 
                 80.3° 
                 |fsys/f3| + |fsys/f5| 
                 0.868 
               
               
                 TTL/ImaH 
                 1.600 
                 (R9 + R10)/(R9 − R10) 
                 −4.540 
               
            
           
           
               
               
               
            
               
                 (Vd1 + Vd3)/Vd2 
                 1.34 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8A 
               
             
            
               
                   
               
               
                 (Lens system 810) 
               
               
                 Lens system 810 
               
               
                 Fno = 1.85, FFOV = 79.7 deg 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 separation 
                 Refractive 
                 Abbe 
               
               
                 Element 
                 # 
                 (mm) 
                 (mm) 
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 Inf 
                 Inf 
                   
                   
               
               
                 Stop 
                 1 
                 Inf 
                 −0.094 
               
               
                 L1 
                 *2 
                 3.205 
                 0.466 
                 1.678 
                 55.3 
               
               
                   
                 *3 
                 19.147 
                 0.050 
               
               
                 L2 
                 *4 
                 29.478 
                 0.603 
                 1.545 
                 56.0 
               
               
                   
                 *5 
                 −15.167 
                 0.064 
               
               
                 L3 
                 *6 
                 4.972 
                 0.270 
                 1.671 
                 19.5 
               
               
                   
                 *7 
                 2.959 
                 0.486 
               
               
                 L4 
                 *8 
                 40.884 
                 0.486 
                 1.545 
                 56.0 
               
               
                   
                 *9 
                 −7.986 
                 0.257 
               
               
                 L5 
                 *10 
                 −1.646 
                 0.337 
                 1.671 
                 19.5 
               
               
                   
                 *11 
                 −2.375 
                 0.095 
               
               
                 L6 
                 *12 
                 2.131 
                 0.635 
                 1.545 
                 56.0 
               
               
                   
                 *13 
                 4.027 
                 0.383 
               
               
                 L7 
                 *14 
                 2.887 
                 0.747 
                 1.545 
                 56.0 
               
               
                   
                 *15 
                 1.697 
                 0.319 
               
               
                 Filter 
                 16 
                 Inf 
                 0.200 
                 1.517 
                 64.2 
               
               
                   
                 17 
                 Inf 
                 0.600 
               
               
                 Sensor 
                 18 
                 Inf 
                 0.000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 8B-8E) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 810) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S2 
                 S3 
                 S4 
                 S5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −3.33453E−02  
                 −6.59874E−02  
                 −1.39071E−02  
                 1.77924E−02 
               
               
                 A6 
                 2.21206E−03 
                 −6.54625E−04  
                 −7.27079E−03  
                 −1.05580E−02  
               
               
                 A8 
                 −2.87575E−02  
                 2.59976E−02 
                 7.34537E−02 
                 −8.42516E−03  
               
               
                 A10 
                 1.64859E−02 
                 −1.59665E−02  
                 −5.23493E−02  
                 4.91074E−03 
               
               
                 A12 
                 −2.75046E−03  
                 3.12712E−03 
                 1.39528E−02 
                 −1.02281E−03  
               
               
                 A14 
                 0.00000E+00 
                 0.00000E+00 
                 −1.25200E−03  
                 1.94067E−04 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8C 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 810) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 −6.51317E−02  
                 −7.50044E−02  
                 −3.88245E−02  
                 −7.80156E−02  
               
               
                 A6 
                 1.21691E−02 
                 3.71948E−02 
                 3.05634E−03 
                 6.19215E−02 
               
               
                 A8 
                 −1.26592E−02  
                 −3.26568E−02  
                 −2.36015E−03  
                 −6.76501E−02  
               
               
                 A10 
                 5.00387E−03 
                 2.21537E−02 
                 −4.55367E−03  
                 4.93059E−02 
               
               
                 A12 
                 1.51365E−03 
                 −7.80729E−03  
                 1.59262E−03 
                 −1.83492E−02  
               
               
                 A14 
                 −5.56235E−04  
                 1.20591E−03 
                 2.33908E−04 
                 2.65054E−03 
               
               
                 A16 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8D 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 810) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 S10 
                 S11 
                 S12 
                 S13 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 K 
                 0.00000E+00 
                 0.00000E+00 
                 −1.00000E+00 
                 0.00000E+00 
               
               
                 A4 
                 4.59427E−02 
                 −1.39717E−02  
                 −3.91461E−02 
                 4.51843E−02 
               
               
                 A6 
                 4.33340E−02 
                 4.25585E−03 
                 −7.45644E−03 
                 −5.12982E−02  
               
               
                 A8 
                 −6.56422E−02  
                 2.10136E−02 
                  4.00291E−03 
                 1.95552E−02 
               
               
                 A10 
                 7.27541E−02 
                 −1.57416E−02  
                 −1.53258E−03 
                 −4.87089E−03  
               
               
                 A12 
                 −3.72528E−02  
                 6.98548E−03 
                  3.02585E−04 
                 7.40813E−04 
               
               
                 A14 
                 8.88956E−03 
                 −1.80096E−03  
                 −2.94270E−05 
                 −5.97926E−05  
               
               
                 A16 
                 −8.01808E−04  
                 1.90153E−04 
                  1.24868E−06 
                 1.93110E−06 
               
               
                 A18 
                 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 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8E 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 810) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S14 
                 S15 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 −1.00000E+00 
                 −1.00000E+00 
               
               
                   
                 A4 
                 −1.33823E−01 
                 −1.44219E−01 
               
               
                   
                 A6 
                  3.52857E−02 
                  5.07328E−02 
               
               
                   
                 A8 
                 −6.17338E−03 
                 −1.49682E−02 
               
               
                   
                 A10 
                  8.75308E−04 
                  3.19899E−03 
               
               
                   
                 A12 
                 −8.79522E−05 
                 −4.40498E−04 
               
               
                   
                 A14 
                  4.94928E−06 
                  3.63818E−05 
               
               
                   
                 A16 
                 −1.12493E−07 
                 −1.63487E−06 
               
               
                   
                 A18 
                  0.00000E+00 
                  3.06948E−08 
               
               
                   
                 A20 
                  0.00000E+00 
                  0.00000E+00 
               
               
                   
                   
               
            
           
         
       
     
                     TABLE 8F               Optical Definitions (Lens system 810)                                                f[mm]   4.431   Vd6   56.0       Fno   1.85   fsys/f12   1.005       FFOV[deg]   79.7°   |fsys/f3| + |fsys/f5|   0.844       TTL/ImaH   1.599   (R9 + R10)/(R9 − R10)   −5.516                         (Vd1 + Vd3)/Vd2   1.34                    
Example Computing Device
 
       FIG. 10  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. 1A through 9 . 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. 1A through 9 , which may also be coupled to I/O interface  2030 , or one or more cameras as described above with respect to  FIGS. 1A through 9  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. 10 , 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.

Metadata:
Filing Date: 20180515
Publication Date: 20220531
Grant Date: 20220531
Priority Date: 20170620
Inventors: YAO, YUHONG
SHINOHARA, YOSHIKAZU
LIAO, LIN-YAO
Assignee: APPLE INC
CPC Classifications: [{"code": "G02B9/64", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B9/64", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0045", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/0045", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B9/64", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0045", "inventive": true, "first": true, "tree": "[]"}]
Family ID: 64657301