PATENT DOCUMENT

Publication Number: US-10234659-B2
Application Number: US-201715472132-A
Country: US
Kind Code: B2

Title: Folded lens system with four refractive lenses

Abstract:
Compact folded lens systems are described that may be used in small form factor cameras. Lens systems are described that may include four lens elements with refractive power, with a light folding element such as a prism, located between a first lens element on the object side of the lens system and a second lens element, that redirects the light refracted from the first lens element from a first axis onto a second axis on which the other lens elements and a photosensor are arranged. The lens systems may include an aperture stop located behind the front vertex of the lens system, for example at the first lens element, and an optional infrared filter, for example located between the last lens element and a photosensor.

Claims:
What is claimed is: 
     
       1. A lens system, comprising:
 a plurality of elements arranged along a folded optical axis of the lens system, wherein the plurality of elements includes, in order along the folded optical axis from an object side to an image side:
 a first lens element on a first portion of the folded optical axis having a convex object-side surface in the paraxial region; 
 a light folding element configured to redirect light from the first lens element to a second portion of the folded optical axis; 
 a second lens element on the second portion of the folded optical axis; 
 a third lens element on the second portion of the folded optical axis having a concave image-side surface in the paraxial region; and 
 a fourth lens element on the second portion of the folded optical axis; 
 
 wherein the lens system provides a 35 mm equivalent focal length in the range of 55-140 mm and less than 6.5 mm of Z-height measured from a front vertex of the lens system to a rear vertex of the light folding element. 
 
     
     
       2. The lens system as recited in  claim 1 , wherein the first lens element has positive refractive power, and the second lens element has negative refractive power. 
     
     
       3. The lens system as recited in  claim 1 , wherein the lens system further comprises an aperture stop located between the object side of the lens system and the light folding element. 
     
     
       4. The lens system as recited in  claim 1 , wherein the lens system provides a 35 mm equivalent focal length in the range of 75-120 mm and less than 6 mm of Z-height measured from the front vertex of the lens system to the rear vertex of the folding element. 
     
     
       5. The lens system as recited in  claim 1 , wherein the first lens element has positive refractive power and is the only lens element on the object side of the light folding element. 
     
     
       6. The lens system as recited in  claim 1 , wherein the first and fourth lens elements are formed of optical materials with Abbe number Vd&gt;40, and the second lens element is formed of an optical material with Abbe number Vd&lt;30. 
     
     
       7. The lens system as recited in  claim 1 , wherein the first lens element is formed of an optical material with Abbe number Vd&gt;40, and the second lens element is formed of an optical material with Abbe number Vd&lt;30. 
     
     
       8. The lens system as recited in  claim 1 , wherein the lens system satisfies one or more of the relationships:
   0.4&lt;| f/f 1|&lt;1 
   0.8&lt;| f/f 2|&lt;1.6 
   0.05&lt;| R 4 f−R 4 r|/|R 4 f+R 4 r|&lt; 0.8 
 
       where f is effective focal length of the lens system, f1 is focal length of the first lens element, f2 is focal length of the second lens element, R4f is radius of curvature of the object-side surface of the fourth lens element, and R4r is radius of curvature of the image side surface of the fourth lens element. 
     
     
       9. The lens system as recited in  claim 1 , wherein at least one surface of at least one of the plurality of lens elements is aspheric. 
     
     
       10. The lens system as recited in  claim 1 , wherein at least one of the lens elements is formed of lightweight polymer or plastic material. 
     
     
       11. The lens system as recited in  claim 1 , wherein the light folding element is a prism. 
     
     
       12. The lens system as recited in  claim 11 , wherein an image side surface of the first lens element is flat/plano, and wherein the image side surface of the first lens element is in contact with the object side surface of the prism. 
     
     
       13. The lens system as recited in  claim 1 , wherein effective focal length of the lens system is within a range of 6.5 millimeters to 14 millimeters. 
     
     
       14. The lens system as recited in  claim 1 , wherein focal ratio (F/#) of the lens system is within a range of 2.2 to 3. 
     
     
       15. The lens system as recited in  claim 1 , wherein full field of view (FOV) of the lens system is within a range of 20.4° to 42.2°. 
     
     
       16. A camera, comprising:
 a photosensor configured to capture light projected onto a surface of the photosensor; and 
 a folded 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 comprises four refractive lens elements arranged along a folded optical axis of the camera from an object side to an image side and a light folding element located between a first and second lens element from the object side and configured to redirect light from a first axis onto a second axis; 
 wherein the folded lens system provides a 35 mm equivalent focal length in the range of 55-140 mm and less than 6.5 mm of Z-height measured from a front vertex of the lens system to a rear vertex of the folding element. 
 
     
     
       17. The camera as recited in  claim 16 , wherein effective focal length of the lens system is within a range of 6.5 millimeters to 14 millimeters, and wherein the photosensor is between 4 millimeters and 8 millimeters in a diagonal dimension. 
     
     
       18. The camera as recited in  claim 16 , wherein the photosensor is configured to move on one or more axes relative to the lens system to adjust focus of the camera. 
     
     
       19. 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 folded 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 proximate to the surface of the photosensor, wherein the lens system comprises four refractive lens elements arranged along a folded optical axis of the lens system from an object side to an image side and a light folding element configured to redirect light from the first lens element on the object side to a second portion of the folded optical axis; 
 
 wherein the lens system lens system provides a 35 mm equivalent focal length in the range of 55-140 mm and less than 6.5 mm of Z-height measured from a front vertex of the lens system to a rear vertex of the folding element. 
 
     
     
       20. The device as recited in  claim 19 , wherein the lens system further comprises at least one aperture stop located between a front vertex of the lens system and the light folding element.

Description:
PRIORITY INFORMATION 
     This application claims benefit of priority of U.S. Provisional Application Ser. No. 62/314,350 entitled “FOLDED TELEPHOTO LENS SYSTEMS” filed Mar. 28, 2016, the content of which is incorporated by reference herein in its entirety, and also claims benefit of priority of U.S. Provisional Application Ser. No. 62/334,398 entitled “FOLDED LENS SYSTEM WITH FOUR REFRACTIVE LENSES” filed May 10, 2016, 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 compact lens systems for high-resolution, small form factor camera 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 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 (also referred to as an image sensor) 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 system with improved imaging quality performance has increased. 
     SUMMARY OF EMBODIMENTS 
     Compact folded lens systems are described that may be used in small form factor cameras. Lens systems are described that may include four lens elements with refractive power, with a light folding element such as a prism located between a first lens element on the object side of the lens system and a second lens element that redirects the light refracted from the first lens element from a first axis onto a second axis on which the other lens elements and a photosensor are arranged. The lens systems may include an aperture stop located behind the front vertex of the lens system, for example at the first lens element, and an optional infrared filter, for example located between the last lens element and a photosensor of the camera. 
     Embodiments of the compact folded lens system may include four lens elements with refractive power and a light folding element such as a prism to fold the optical axis. The compact folded lens system may be configured to operate with a relatively narrow field of view and a 35 mm equivalent focal length (f 35mm ) in the telephoto range. For example, some embodiments of the compact folded lens system may provide a 35 mm equivalent focal length in the range of 55-140 mm, with less than 6.5 mm of Z-height to fit in a wide variety of portable electronics devices. 
     Through proper arrangement in materials, power and radius of curvature of the four lens elements with power, embodiments of the compact folded lens are capable of capturing high resolution, high quality images at good brightness level. In some embodiments, a first lens element from the object side of the lens system has a convex object-side surface in the paraxial region, and a third lens element has a concave image-side surface in the paraxial region. In some embodiments, a first lens element from the object side of the lens system has a convex object-side surface in the paraxial region, and a third lens element has a concave image-side surface in the paraxial region. In some embodiments, the first lens elements is formed of optical materials with Abbe number Vd&gt;40, and the second lens element is formed of an optical material with Abbe number Vd&lt;30. In some embodiments, the first and fourth lens elements are formed of optical materials with Abbe number Vd&gt;40, and the second lens element is formed of an optical material with Abbe number Vd&lt;30. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional illustration of a compact camera including an example embodiment of a compact folded lens system with four lens elements and a light folding element. 
         FIGS. 2A and 2B  show a camera that includes an example embodiment of a compact folded lens system that operates at F/2.4, with 31° full field of view (FOV). 
         FIG. 3  shows a camera that includes an example embodiment of a compact folded lens system that operates at F/2.4, with 28.1° full FOV. 
         FIG. 4  shows a camera that includes an example embodiment of a compact folded lens system that operates at F/2.2, with 42.2° full FOV. 
         FIG. 5  shows a camera that includes an example embodiment of a compact folded lens system that operates at F/2.6, with 23.7° full FOV. 
         FIG. 6  shows a camera that includes an example embodiment of a compact folded lens system that operates at F/2.4, with 31.2° full FOV. 
         FIG. 7  shows a camera that includes an example embodiment of a compact folded lens system that operates at F/3, with 20.4° full FOV. 
         FIG. 8  illustrates numbering of the surfaces in the example lens systems as used in the Tables. 
         FIG. 9  is a flowchart of a method for capturing images using cameras with lens systems as illustrated  FIGS. 1 through 7 , 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 compact folded lens system including four lens elements with refractive power, with a light folding element such as a prism located between a first lens element on the object side of the lens system and a second lens element that redirects the light refracted from the first lens element from a first axis onto a second axis on which the other lens elements and a photosensor are arranged. The lens system may include an aperture stop located behind the front vertex of the lens system, for example at the first lens element, and an optional infrared filter, for example located between the last lens element and the photosensor. The shapes, materials, and arrangements of the lens elements in the lens system may be selected to capture high resolution, high quality images. 
     Conventionally, compact imaging lenses can be designed with a non-folded optical axis that provide a 35 mm equivalent focal length (f 35mm ) of 50 mm-70 mm. However, the lens brightness (related to the focal ratio, or F/#, of the lens system) and image quality of these conventional compact lens designs are typically limited by the constraint in thickness (Z dimension) of portable electronics devices. It is difficult to further increase the lens effective focal length of these conventional compact lens designs due to the scaling relationship with respect to the lens dimensions. To overcome this limitation, a folding-prism or mirror may be used in embodiments to relieve the constraint in the Z dimension of the lens system. 
     Embodiments of the compact folded lens systems as described herein may provide high resolution, high quality imaging for small form factor cameras. Using an embodiment of the compact lens system, a camera may 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.  FIG. 10  illustrates an example device that may include one or more small form factor cameras that use embodiments of the compact folded lens systems as described herein. 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. 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. 
     Folded Lens Systems with Four Lens Elements 
       FIG. 1  is a cross-sectional illustration of a compact camera  100  including an example embodiment of a compact folded lens system  110  with four lens elements  101 - 104  and a light folding element  140  such as a prism that “folds” the optical axis of the lens system  110 . The camera  100  may also include an aperture stop  130 , an optional IR filter  150 , and a photosensor  120 . A compact camera  100  including an embodiment of the compact folded lens system  110  as illustrated in  FIG. 1  may, for example, be implemented in portable electronic devices such as mobile phones and tablets. For embodiments of a lens system  110  as illustrated in  FIG. 1 , the 35 mm equivalent focal length (f 35mm ) of the lens system  110  is longer than 50 mm. A compact folded lens system  110  having a long f 35mm  may, for example, be used stand-alone for telephoto photography, or can be paired with a wide-angle imaging lens in a dual-prime configuration to enable effective optical zoom for portable electronic devices. 
     Embodiments of a compact folded lens system  110  are described that include four lens elements  101 - 104  with refractive power and a light folding element  140  such as a prism to fold the optical axis. Embodiments of the compact folded lens system  110  may provide a 35 mm equivalent focal length in the range of 75-120 mm and less than 6 mm of Z-height to fit in a wide variety of portable electronics devices. With proper arrangement of materials and lens powers, embodiments of the compact folded lens system  110  are capable of capturing high brightness photos with high image quality. 
     As illustrated in the example camera  100  of  FIG. 1 , the compact folded lens system  110  includes four elements with refractive power and a light folding element  140  (e.g., a prism), in order from the object side to the image side of the lens system  100 : a first lens element  101  with positive refractive power; a folding element  140  such as a prism to fold the optical axis from AX 1  to AX 2 ; a second lens element  102  with negative refractive power; a third lens element  103  with refractive power; and a fourth lens element  104  with refractive power. An aperture stop  130  may be located between the object side of the lens system  110  and the folding element  140  for controlling the brightness of the optical system. 
     In some embodiments, the camera  100  includes an IR filter  150  to reduce or eliminate interference of environmental noises on the photosensor  120 . In some embodiments, the photosensor  120  and/or lens system  110  may be shifted along AX 2  to allow refocusing of the lens system  110  in between Infinity conjugate and Macro conjugate. In various embodiments, lens element  102 , lens element  103 , and/or lens element  104  may be round/circular, rectangular, or some other shape. 
     In embodiments of lens system  110 , one or more of the following requirements may be satisfied, for example to facilitate correction of aberrations across the field of view (FOV) for the lens system  110 :
         Lens element  101  has a convex object-side surface in the paraxial region.   Lens element  103  has a concave image-side surface in the paraxial region.   In various embodiments, the other lens surfaces of lens elements  101  through  104  may be concave, convex, or flat/plano (e.g., the lenses may be plano-concave or plano-convex lenses) in the paraxial region.   In some embodiments, at least one of the eight lens surfaces may be aspheric.   In some embodiments, at least one of the lens elements is made of lightweight polymer or plastic material.   In some embodiments, lens element  101  and lens element  104  are formed of optical materials with Abbe number Vd&gt;40, and lens element  102  is formed of an optical material with Abbe number Vd&lt;30. The material and power configurations of the lens elements  101 ,  102 , and  104  are selected for reduction of chromatic aberrations.   In some embodiments, lens element  103  is formed of optical material with no limit in Abbe number.       

       FIG. 1  shows an example camera  100  that includes an example embodiments of a compact folded lens system  110  that operates at F/2.4, 31° full field of view. Camera  100  includes a 5.04 mm diagonal photosensor  120 . The effective focal length (EFL) of the lens system  110  is 9 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  100  is as large as 77 mm. In some embodiments, the camera  100 /lens system  110  has the capability of autofocusing from 400 mm to Infinity conjugates. 
     The modulation transfer functions (MTFs) for lens system  110  when focused at Infinity and Macro (400 mm) conjugates, at all fields and both conjugates, are higher than 0.6 at 125 line pairs (lp)/mm spatial frequency and higher than 0.3 at 150 lp/mm spatial frequency, providing good contrast for high-resolution imaging. At both conjugates, the on-axis and off-axis aberrations for lens system  110  are well balanced across the FOV. At both conjugates, optical distortion across the FOV is controlled within 1%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  110 , as defined from the front vertex of lens element  101  to the rear vertex of the folding element  140  may be 4.9 mm. The lens system  110  is thus able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Folded Lens Systems with Four Lens Elements—Alternative Embodiments 
       FIGS. 2A through 7  show several alternative embodiments of compact cameras with compact folded lens systems with four lens elements and a light folding element such as a prism that “folds” the optical axis of the lens system. A compact camera including an embodiment of the compact folded lens systems as illustrated in  FIGS. 2A through 7  may, for example, be implemented in portable electronic devices such as mobile phones and tablets. The lens system and/or camera may also include an aperture stop, an optional infrared (IR) filter, and a photosensor. The compact folded lens systems as illustrated in  FIGS. 2A through 7  may be configured to operate with a relatively narrow field of view and a 35 mm equivalent focal length (f 35mm ) in the telephoto range. Compact cameras including the compact folded lens systems as illustrated in  FIGS. 2A through 7  may, for example, be used stand-alone for telephoto photography, or can be paired with a wide-angle imaging lens in a dual-prime configuration to enable effective optical zoom for portable electronic devices. 
     Embodiments of the compact folded lens system as illustrated in  FIGS. 2A through 7  may include four lens elements with refractive power and a light folding element such as a prism to fold the optical axis. Embodiments of the compact folded lens system as illustrated in  FIGS. 2A through 7  may provide a 35 mm equivalent focal length in the range of 55-140 mm and less than 6.5 mm of Z-height to fit in a wide variety of portable electronics devices. With proper arrangement in materials, power and radius of curvature of the three lens elements with power, embodiments of the compact folded lens system as illustrated in  FIGS. 2A through 7  are capable of capturing high resolution, high quality images at good brightness level. 
     Embodiments of the compact folded lens system as illustrated in  FIGS. 2A through 7  include four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element (lens  1 ) with positive refractive power, a folding element such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element (lens  2 ) with negative refractive power, a third lens element (lens  3 ) with refractive power, and a fourth lens element (lens  4 ) with refractive power. An aperture stop may be located between the object side of the lens system and the folding element for controlling the brightness of the optical system. In some embodiments, the lens system or camera includes an IR filter to reduce or eliminate interference of environmental noises on the image sensor (also referred to herein as a photosensor or sensor). In some embodiments, the photosensor may be shifted along AX 2  to allow refocusing of the lens system in between Infinity conjugate and Macro conjugate, for example for autofocus applications. Lenses  2 ,  3 , and  4  may be round/circular optical lenses, or may have a shape other than circular (e.g., rectangular or square, hexagonal, etc.) to reduce the camera module Z height. 
     In embodiments of the compact folded lens system as illustrated in  FIGS. 2A through 7 , one or more of the following requirements may be satisfied, for example to facilitate correction of aberrations across the field of view (FOV) for the lens system:
         Lens  1  has a convex object-side surface in the paraxial region.   Lens  3  has a concave image side surface in the paraxial region.   In various embodiments, the other lens surfaces of lenses  1  through  4  may be concave, convex, or flat/plano (e.g., the lenses may be plano-concave or plano-convex lenses) in the paraxial region.   In some embodiments, at least one of the eight lens surfaces may be aspheric.   In some embodiments, at least one of the lens elements is made of a lightweight polymer or plastic.   In some embodiments, Lens  1  is formed of optical materials with Abbe number Vd&gt;40, and Lens  2  is formed of an optical material with Abbe number Vd&lt;30. The material and power configurations of the lenses may, for example, be selected for reduction of chromatic aberrations.   In some embodiments, one or more of the following relationships may be met:
 
0.4&lt; |f/f 1|&lt;1
 
0.8&lt; |f/f 2|&lt;1.6
 
0.05&lt; |R 4 f−R 4 r|/|R 4 f+R 4 r |&lt;0.8
   where f is effective focal length of the lens system, f1 is focal length of lens  1 , f2 is focal length of lens  2 , R4f is radius of curvature of the object-side surface of lens  4 , and R4r is radius of curvature of the image side surface of lens  4 .       

     As shown in the example embodiment in  FIGS. 2A-2B , in some embodiments of a camera including compact folded lens system as illustrated in  FIGS. 2A through 7 , the photosensor may be moved on one or more axes relative to the lens system to adjust focus of the camera. Alternatively, in some embodiments, the lens system may be moved relative to the photosensor to adjust focus.  FIG. 2A  corresponds to the camera focused at a first position (infinity conjugate), and  FIG. 2B  corresponds to the camera focused at a second position (e.g., macro conjugate). While the focus positions are shown as examples, note that the camera may be focused at other positions in some embodiments. 
     As shown in the example embodiments in  FIGS. 2A-7 , in some embodiments of a compact folded lens system as described herein, the image side surface of the first lens element (lens  1 ) may be flat/plano (e.g., lens  1  may be plano-convex), and the image side surface of lens  1  may be at/in contact with the object side surface of the light folding prism to effectively form a single combined unit or element. The lens  1  and prism elements may be composed of the same type of material (e.g., a plastic material) or of different types of materials. In some embodiments, the lens  1  and prism elements may be cemented. Alternatively, the lens  1  and prism elements may be composed of the same type of material (e.g., a plastic material), and may be molded as a single combined unit or element. However, while not shown in the example Figures, in some embodiments the image side surface of lens  1  may be convex, concave, or flat-plano, and lens  1  and the folding element (prism) may be air-spaced. 
     Example Lens System  210   
       FIGS. 2A and 2B  show a camera  200  that includes an example embodiment of a compact folded lens system  210  that operates at F/2.4, with 31° full FOV. Camera  200  includes a 5.04 mm diagonal photosensor  220 . Lens system  210  includes four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element  201  with positive refractive power, a folding element  240  such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element  202  with negative refractive power, a third lens element  203  with refractive power, and a fourth lens element  204  with refractive power. An aperture stop  230  may be located between the object side of the lens system  210  and the folding element  240 , for example at or near the object side surface of lens element  201 , for controlling the brightness of the optical system. In some embodiments, the lens system  210  or camera  200  includes an IR filter  250  to reduce or eliminate interference of environmental noises on the photosensor  220 . 
     Tables 1-5 correspond to an embodiment of a lens system  210  as illustrated in  FIGS. 2A and 2B , and provide example values for various optical and physical parameters of the lens system  210  and camera  200  of  FIGS. 2A and 2B . The effective focal length (EFL) of the lens system  210  is 9 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  210  may be 77 mm. In some embodiments, the camera  200 /lens system  210  has the capability of autofocusing from 700 mm to Infinity conjugates. 
     As shown in  FIGS. 2A-2B , in some embodiments the photosensor  220  may be moved on one or more axes relative to the lens system  210  to adjust focus of the camera  200 .  FIG. 2A  corresponds to the camera  200  focused at a first position (infinity conjugate), and  FIG. 2B  corresponds to the camera  200  focused at a second position (700 mm in  FIG. 2B ). While the focus positions are shown as examples, note that the camera  200  may be focused at other positions in some embodiments. 
     The modulation transfer functions (MTFs) for lens system  210  when focused at Infinity and Macro (500 mm) conjugates, at all fields and both conjugates, are close to diffraction limited; the lens system  210  provides good contrast for high-resolution imaging. At both conjugates, on-axis and off-axis aberrations for lens system  210  are well balanced across the FOV. At both conjugates, optical distortion across the FOV is controlled within 2%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  210 , as defined from the front vertex of lens element  201  to the rear vertex of the folding element  240 , may be 4.85 mm. The lens system  210  is able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Example Lens System  310   
       FIG. 3  shows a camera  300  that includes an example embodiment of a compact folded lens system  310  that operates at F/2.4, with 28.1° full FOV. Camera  300  includes a 5.04 mm diagonal photosensor  320 . Lens system  310  includes four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element  301  with positive refractive power, a folding element  340  such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element  302  with negative refractive power, a third lens element  303  with refractive power, and a fourth lens element  304  with refractive power. An aperture stop  330  may be located between the object side of the lens system  310  and the folding element  340 , for example at or near the object side surface of lens element  301 , for controlling the brightness of the optical system. In some embodiments, the lens system  310  or camera  300  includes an IR filter  350  to reduce or eliminate interference of environmental noises on the photosensor  320 . 
     Tables 6-9 correspond to an embodiment of a lens system  310  as illustrated in  FIG. 3 , and provide example values for various optical and physical parameters of the lens system  310  and camera  300  of  FIG. 3 . The effective focal length (EFL) of the lens system  310  is 10 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  310  may be 86 mm. While not shown in  FIG. 3 , in some embodiments, the camera  300 /lens system  310  has the capability of autofocusing from Macro to Infinity conjugates. 
     The modulation transfer function (MTF) for lens system  310  is close to diffraction limited; the lens system  310  provides good contrast for high-resolution imaging. On-axis and off-axis aberrations for lens system  310  are well balanced across the FOV. Optical distortion across the FOV is controlled within 2%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  310 , as defined from the front vertex of lens element  301  to the rear vertex of the folding element  340 , may be 5.35 mm. The lens system  310  is able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Example Lens System  410   
       FIG. 4  shows a camera  400  that includes an example embodiment of a compact folded lens system  410  that operates at F/2.2, with 42.2° full FOV. Camera  400  includes a 5.04 mm diagonal photosensor  420 . Lens system  410  includes four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element  401  with positive refractive power, a folding element  440  such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element  402  with negative refractive power, a third lens element  403  with refractive power, and a fourth lens element  404  with refractive power. An aperture stop  430  may be located between the object side of the lens system  410  and the folding element  440 , for example at or near the object side surface of lens element  401 , for controlling the brightness of the optical system. In some embodiments, the lens system  410  or camera  400  includes an IR filter  450  to reduce or eliminate interference of environmental noises on the photosensor  420 . 
     Tables 10-13 correspond to an embodiment of a lens system  410  as illustrated in  FIG. 4 , and provide example values for various optical and physical parameters of the lens system  410  and camera  400  of  FIG. 4 . The effective focal length (EFL) of the lens system  410  is 6.6 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  410  may be 57 mm. While not shown in  FIG. 4 , in some embodiments, the camera  400 /lens system  410  has the capability of autofocusing from Macro to Infinity conjugates. 
     The modulation transfer function (MTF) for lens system  410  is higher than 0.6 at 125 lp/mm and higher than 0.3 at 250 lp/mm; the lens system  410  provides good contrast for high-resolution imaging. On-axis and off-axis aberrations for lens system  410  are well balanced across the FOV. Optical distortion across the FOV is controlled within 2%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  410 , as defined from the front vertex of lens element  401  to the rear vertex of the folding element  440 , may be 4.4 mm. The lens system  410  is able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Example Lens System  510   
       FIG. 5  shows a camera  500  that includes an example embodiment of a compact folded lens system  510  that operates at F/2.6, with 23.7° full FOV. Camera  500  includes a 5.04 mm diagonal photosensor  520 . Lens system  510  includes four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element  501  with positive refractive power, a folding element  540  such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element  502  with negative refractive power, a third lens element  503  with refractive power, and a fourth lens element  504  with refractive power. An aperture stop  530  may be located between the object side of the lens system  510  and the folding element  540 , for example at or near the object side surface of lens element  501 , for controlling the brightness of the optical system. In some embodiments, the lens system  510  or camera  500  includes an IR filter  550  to reduce or eliminate interference of environmental noises on the photosensor  520 . 
     Tables 14-17 correspond to an embodiment of a lens system  510  as illustrated in  FIG. 5 , and provide example values for various optical and physical parameters of the lens system  510  and camera  500  of  FIG. 5 . The effective focal length (EFL) of the lens system  510  is 12 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  510  may be 103 mm. While not shown in  FIG. 5 , in some embodiments, the camera  500 /lens system  510  has the capability of autofocusing from Macro to Infinity conjugates. 
     The modulation transfer function (MTF) for lens system  510  is close to diffraction limited; the lens system  510  provides good contrast for high-resolution imaging. On-axis and off-axis aberrations for lens system  510  are well balanced across the FOV. Optical distortion across the FOV is controlled within 2%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  510 , as defined from the front vertex of lens element  501  to the rear vertex of the folding element  540 , may be 5.85 mm. The lens system  510  is able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Example Lens System  610   
       FIG. 6  shows a camera  600  that includes an example embodiment of a compact folded lens system  610  that operates at F/2.4, with 31.2° full FOV. Camera  600  includes a 4.54 mm diagonal photosensor  620 . Lens system  610  includes four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element  601  with positive refractive power, a folding element  640  such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element  602  with negative refractive power, a third lens element  603  with refractive power, and a fourth lens element  604  with refractive power. An aperture stop  630  may be located between the object side of the lens system  610  and the folding element  640 , for example at or near the object side surface of lens element  601 , for controlling the brightness of the optical system. In some embodiments, the lens system  610  or camera  600  includes an IR filter  650  to reduce or eliminate interference of environmental noises on the photosensor  620 . 
     Tables 18-21 correspond to an embodiment of a lens system  610  as illustrated in  FIG. 6 , and provide example values for various optical and physical parameters of the lens system  610  and camera  600  of  FIG. 6 . The effective focal length (EFL) of the lens system  610  is 8.1 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  610  may be 77 mm. While not shown in  FIG. 6 , in some embodiments, the camera  600 /lens system  610  has the capability of autofocusing from Macro to Infinity conjugates. 
     The modulation transfer function (MTF) for lens system  610  is close to diffraction limited; the lens system  610  provides good contrast for high-resolution imaging. On-axis and off-axis aberrations for lens system  610  are well balanced across the FOV. Optical distortion across the FOV is controlled within 2%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  610 , as defined from the front vertex of lens element  601  to the rear vertex of the folding element  640 , may be 4.45 mm. The lens system  610  is able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Example Lens System  710   
       FIG. 7  shows a camera  700  that includes an example embodiment of a compact folded lens system  710  that operates at F/3, with 20.4° full FOV. Camera  700  includes a 5.04 mm diagonal photosensor  720 . Lens system  710  includes four lens elements with refractive power and a folding element such as a prism, in order from the object side to the image side of the lens system: a first lens element  701  with positive refractive power, a folding element  740  such as a prism to fold the optical axis from AX 1  to AX 2 , a second lens element  702  with negative refractive power, a third lens element  703  with refractive power, and a fourth lens element  704  with refractive power. An aperture stop  730  may be located between the object side of the lens system  710  and the folding element  740 , for example at or near the object side surface of lens element  701 , for controlling the brightness of the optical system. In some embodiments, the lens system  710  or camera  700  includes an IR filter  750  to reduce or eliminate interference of environmental noises on the photosensor  720 . 
     Tables 22-25 correspond to an embodiment of a lens system  710  as illustrated in  FIG. 7 , and provide example values for various optical and physical parameters of the lens system  710  and camera  700  of  FIG. 7 . The effective focal length (EFL) of the lens system  70  is 14 mm. Given the EFL and photosensor size, the 35 mm equivalent focal length of the camera  710  may be 120 mm. While not shown in  FIG. 7 , in some embodiments, the camera  700 /lens system  710  has the capability of autofocusing from Macro to Infinity conjugates. 
     The modulation transfer function (MTF) for lens system  710  is close to diffraction limited; the lens system  710  provides good contrast for high-resolution imaging. On-axis and off-axis aberrations for lens system  710  are well balanced across the FOV. Optical distortion across the FOV is controlled within 2%, while field curvature and astigmatism are well balanced across the FOV. 
     In some embodiments, Z-height of the example lens system  710 , as defined from the front vertex of lens element  701  to the rear vertex of the folding element  740 , may be 5.75 mm. The lens system  710  is able to fit into a wide variety of portable electronic devices including but not limited to smart phones and tablets. 
     Example Lens System Tables 
     The following Tables provide example values for various optical and physical parameters of the example embodiments of the lens systems and cameras as described in reference to  FIGS. 2A through 7 . Tables 1-5 correspond to an example embodiment of a lens system  210  as illustrated in  FIGS. 2A and 2B . Note that Tables 1-5 may also correspond to an example embodiment of a lens system  110  as illustrated in  FIG. 1 . Tables 6-9 correspond to an example embodiment of a lens system  310  as illustrated in  FIG. 3 . Tables 10-13 correspond to an example embodiment of a lens system  410  as illustrated in  FIG. 4 . Tables 14-17 correspond to an example embodiment of a lens system  510  as illustrated in  FIG. 5 . Tables 18-21 correspond to an example embodiment of a lens system  610  as illustrated in  FIG. 6 . Tables 22-25 correspond to an example embodiment of a lens system  710  as illustrated in  FIG. 7 . 
     In the Tables, all dimensions are in millimeters (mm) unless otherwise specified. L1, L2, L3, and L4 stand for refractive lenses  1 ,  2 ,  3 , and  4 , respectively. “S#” stands for surface number. A positive radius indicates that the center of curvature is to the right (object side) of the surface. A negative radius indicates that the center of curvature is to the left (image side) of the surface. “INF” stands for infinity (as used in optics). The thickness (or separation) is the axial distance to the next surface. FNO stands for F-number of the lens system. FOV stands for full field of view. f 35mm  is the 35 mm equivalent focal length of the lens system. V 1  is the Abbe number of the first lens element, and V 2  is the Abbe number of the second lens element. Both f and EFL stand for effective focal length of the lens system, f1 stands for focal length of the first lens element, and f2 stands for focal length of the second lens element. R4f is radius of curvature of the object-side surface of lens  4 , and R4r is radius of curvature of the image side surface of lens  4 . Z stands for Z-height of the lens system as defined from the front (image side) vertex of the lens system to the rear vertex of the folding element (e.g., prism), as shown in  FIG. 1 . REFL represents a reflective surface. 
     For the materials of the lens elements and IR filter, a refractive index N d  at the helium d-line wavelength is provided, as well as an Abbe number V d  relative to the d-line and the C- and F-lines of hydrogen. The Abbe number, V d , may be defined by the equation:
 
 V   d =( N   d −1)/( N   F   −N   C ),
 
where N F  and N C  are the refractive index values of the material at the F and C lines of hydrogen, respectively.
 
     Referring to the Tables of aspheric coefficients (Tables, 2A-2B, 7A-7B, 11A-11B, 15A-15B, 19A-19B, and 23A-23B), the aspheric equation describing an aspherical surface may be given by:
 
 Z =( cr   2 /(1+sqrt[1−(1+ K ) c   2   r   2 ]))+ A   4   r   4   +A   6   r   6   +A   8   r   8   +A   10   r   10   +A   12   R   12   +A   14   r   14   +A   16   r   16   +A   18   r   18   +A   20   r   20  
 
where Z is the sag of surface parallel to the z-axis (the z-axis and the optical axis are coincident in these example embodiments), r is the radial distance from the vertex, c is the curvature at the pole or vertex of the surface (the reciprocal of the radius of curvature of the surface), K is the conic constant, and A 4 -A 20  are the aspheric coefficients. In the Tables, “E” denotes the exponential notation (powers of 10).
 
     Note that the values given in the following Tables for the various parameters in the various embodiments of the lens system are given by way of example and are not intended to be limiting. For example, one or more of the parameters for one or more of the surfaces of one or more of the lens elements in the example embodiments, as well as parameters for the materials of which the elements are composed, may be given different values while still providing similar performance for the lens system. In particular, note that some values in the Tables may be scaled up or down for larger or smaller implementations of a camera using an embodiment of a lens system as described herein. 
     Further note that surface numbers (S#) of the elements in the various embodiments of the lens system 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.  FIG. 8  illustrates numbering of the surfaces as used in the Tables. As shown in  FIG. 8 , in some embodiments of a compact folded lens system as described herein, the image side surface of the first lens element (lens  1 ) may be flat/plano (e.g., lens  1  may be plano-convex), and the image side surface of lens  1  may be at/in contact with the object side surface of the light folding prism  40  to effectively form a single combined unit or element. In these embodiments, the image side surface of lens  1  and the object side surface of the prism  40  form and are designated as a single surface, and the surfaces are numbered as illustrated in  FIG. 8 : 
     S 0 —Object plane 
     S 1 —Aperture stop 
     S 2 —Lens  1 , object side surface 
     S 3 —Prism  40 , image side surface 
     S 4 —Prism  40 , reflective surface 
     S 5 —Prism, object side surface 
     S 6 —Lens  2 , object side surface 
     S 7 —Lens  2 , image side surface 
     S 8 —Lens  3 , object side surface 
     S 9 —Lens  3 , image side surface 
     S 10 —Lens  4 , object side surface 
     S 11 —Lens  4 , image side surface 
     S 12 —IR filter  50 , object side surface 
     S 13 —IR filter  50 , image side surface 
     S 14 —Photosensor  20 , image plane 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Lens system 210 
               
               
                 Fno = 2.4, EFL = 9 mm, FOV = 31°, f 35 mm  = 77 mm 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                 Refractive 
                 Abbe 
               
               
                 Element 
                 Surface (S#) 
                 Radius (mm) 
                 separation (mm) 
                   
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 INF 
                 INF **1 
                   
                   
                   
               
               
                 Stop 
                 1 
                 INF 
                 −0.4253 
               
               
                 L1 
                 *2 
                  4.1390 
                  0.7090 
                   
                 1.513 
                 56.6 
               
               
                 Prism 
                 3 
                 INF 
                  2.0645 
                   
                 1.755 
                 27.6 
               
               
                   
                 Decenter (1) 
               
               
                   
                 4 
                 INF 
                 −2.0645 
                 REFL 
               
               
                   
                 Bend (1) 
               
               
                   
                 5 
                 INF 
                 −0.1000 
               
               
                 L2 
                 *6 
                 −6.2180 
                 −0.7980 
                   
                 1.651 
                 21.5 
               
               
                   
                 *7 
                 −2.6800 
                 −1.4810 
               
               
                 L3 
                 *8 
                 −3.3300 
                 −1.5000 
                   
                 1.545 
                 55.9 
               
               
                   
                 *9 
                 −6.4860 
                 −0.9520 
               
               
                 L4 
                 *10 
                 −3.5860 
                 −0.9080 
                   
                 1.545 
                 55.9 
               
               
                   
                 *11 
                 −2.7010 
                 −1.0750 
               
               
                 IR filter 
                 12 
                 INF 
                 −0.2100 
                   
                 1.517 
                 64.2 
               
               
                   
                 13 
                 INF 
                 −0.1000 
               
               
                   
                 14 
                 INF 
                 0 **2 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 2A-2B) 
               
               
                 **Annotates zoom parameters (values given in Table 4) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2A 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 210) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 S2 
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A4 
                 1.075350E−04 
                   2.439694E−02 
                 3.791761E−02 
                 3.637417E−03 
                   8.231862E−03 
               
               
                 A6 
                 1.207931E−05 
                 −1.069533E−03 
                 −2.010331E−03   
                 3.931192E−04 
                 −3.641826E−03 
               
               
                 A8 
                 0.000000E+00 
                 −3.872791E−05 
                 6.218673E−05 
                 1.643827E−05 
                   8.834411E−04 
               
               
                 A10 
                 0.000000E+00 
                 −7.475811E−06 
                 1.687762E−05 
                 8.500108E−06 
                 −1.430153E−04 
               
               
                 A12 
                 0.000000E+00 
                   4.716422E−06 
                 1.483912E−06 
                 0.000000E+00 
                   1.552517E−05 
               
               
                 A14 
                 0.000000E+00 
                   0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −1.067392E−06 
               
               
                 A16 
                 0.000000E+00 
                   0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                   0.000000E+00 
               
               
                 A18 
                  0.00000E+00 
                    0.00000E+00 
                  0.00000E+00 
                  0.00000E+00 
                    0.00000E+00 
               
               
                 A20 
                  0.00000E+00 
                    0.00000E+00 
                  0.00000E+00 
                  0.00000E+00 
                    0.00000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 210) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
            
               
                   
                 S10 
                 S11 
               
               
                   
               
            
           
           
               
               
               
            
               
                 K 
                 0 
                 0 
               
               
                 A4 
                 4.424514E−02 
                 4.864336E−02 
               
               
                 A6 
                 −2.698281E−03   
                 −3.955844E−03   
               
               
                 A8 
                 −2.784513E−04   
                 2.948393E−04 
               
               
                 A10 
                 1.678942E−05 
                 −1.358085E−05   
               
               
                 A12 
                 0.000000E+00 
                 −1.191172E−06   
               
               
                 A14 
                 0.000000E+00 
                 3.605321E−07 
               
               
                 A16 
                   0.00E+00 
                   0.00E+00 
               
               
                 A18 
                  0.00000E+00 
                  0.00000E+00 
               
               
                 A20 
                  0.00000E+00 
                  0.00000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Decentering Constants (Lens System 210) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Decenter 
                 X 
                 Y 
                 Z 
                 Alpha(deg) 
                 Beta(deg) 
                 Gamma (deg) 
               
               
                   
               
               
                 D(1) and 
                 0 
                 0 
                 0 
                 45 
                 0 
                 0 
               
               
                 Bend (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Zoom Parameters (Lens System 210) 
               
            
           
           
               
               
               
               
            
               
                   
                 **Zoom parameters 
                 Position-1 
                 Position-2 
               
               
                   
                   
               
               
                   
                 **1 
                 Infinity 
                     700 mm 
               
               
                   
                 **2 
                 0.000 
                 −0.115 mm 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 Optical Definitions (Lens system 210) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 EFL 
                   9 mm 
                 V 1   
                 56.6 
               
               
                   
                 FNO 
                 2.4 
                 V 2   
                 21.5 
               
               
                   
                 FOV 
                 31° 
                 |f/f1| 
                 0.64 
               
               
                   
                 f 35 mm   
                   77 mm 
                 |f/f2| 
                 1.14 
               
               
                   
                 Z 
                 4.85 mm 
                 |R4f − R4r|/|R4f + R4r| 
                 0.14 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Lens system 310 
               
               
                 Fno = 2.4, EFL = 10 mm, FOV = 28.1°, f 35 mm  = 86 mm 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                 Refractive 
                 Abbe 
               
               
                 Element 
                 Surface (S#) 
                 Radius (mm) 
                 separation (mm) 
                   
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 INF 
                 INF 
                   
                   
                   
               
               
                 Stop 
                 1 
                 INF 
                 −0.5000 
               
               
                 L1 
                 *2 
                  4.3690 
                 0.7780 
                   
                 1.513 
                 56.6 
               
               
                 Prism 
                 3 
                 INF 
                 2.2830 
                   
                 1.755 
                 27.6 
               
               
                   
                 Decenter (1) 
               
               
                   
                 4 
                 INF 
                 −2.2830 
                 REFL 
               
               
                   
                 Bend (1) 
               
               
                   
                 5 
                 INF 
                 −0.0500 
               
               
                 L2 
                 *6 
                 −6.3250 
                 −0.6420 
                   
                 1.651 
                 21.5 
               
               
                   
                 *7 
                 −2.7690 
                 −1.3860 
               
               
                 L3 
                 *8 
                 −3.2130 
                 −1.4870 
                   
                 1.545 
                 55.9 
               
               
                   
                 *9 
                 −8.0790 
                 −0.9960 
               
               
                 L4 
                 *10 
                 −8.9340 
                 −0.8610 
                   
                 1.545 
                 55.9 
               
               
                   
                 *11 
                 −3.9490 
                 −1.5500 
               
               
                 IR filter 
                 12 
                 INF 
                 −0.2100 
                   
                 1.517 
                 64.2 
               
               
                   
                 13 
                 INF 
                 −0.1000 
               
               
                   
                 14 
                 INF 
                 0.0000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 7A-7B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7A 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 310) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 S2 
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A4 
                 −1.185992E−04  
                 2.418232E−02 
                 3.555325E−02 
                 1.824810E−03 
                 2.536181E−03 
               
               
                 A6 
                 −4.993100E−06  
                 −1.831987E−03  
                 −2.448378E−03  
                 5.056339E−04 
                 −6.020578E−04  
               
               
                 A8 
                 0.000000E+00 
                 −1.015260E−05  
                 1.020881E−04 
                 −7.150725E−07  
                 1.855878E−04 
               
               
                 A10 
                 0.000000E+00 
                 9.750139E−06 
                 1.063693E−05 
                 2.004868E−06 
                 1.754149E−05 
               
               
                 A12 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −3.933255E−06  
               
               
                 A14 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.541867E−07 
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 310) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S10 
                 S11 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 A4 
                 4.430967E−02 
                 4.249250E−02 
               
               
                   
                 A6 
                 −1.271181E−03  
                 −3.916083E−03  
               
               
                   
                 A8 
                 −2.677368E−04  
                 1.401346E−04 
               
               
                   
                 A10 
                 1.277254E−05 
                 −4.477309E−06  
               
               
                   
                 A12 
                 −3.214856E−07  
                 3.308677E−08 
               
               
                   
                 A14 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A16 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A18 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A20 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Decentering Constants (Lens System 310) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Decenter 
                 X 
                 Y 
                 Z 
                 Alpha(deg) 
                 Beta(deg) 
                 Gamma (deg) 
               
               
                   
               
               
                 D(1) and 
                 0 
                 0 
                 0 
                 45 
                 0 
                 0 
               
               
                 Bend (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 Optical Definitions (Lens system 310) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 EFL 
                 10 mm 
                 V 1   
                 56.6 
               
               
                   
                 FNO 
                     2.4 
                 V 2   
                 21.5 
               
               
                   
                 FOV 
                 28.1° 
                 |f/f1| 
                 0.67 
               
               
                   
                 f 35 mm   
                 86 mm 
                 |f/f2| 
                 1.24 
               
               
                   
                 Z 
                 5.35 mm     
                 |R4f − R4r|/|R4f + R4r| 
                 0.39 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 Lens system 410 
               
               
                 Fno = 2.2, EFL = 6.6 mm, FOV = 42.2°, f 35 mm  = 57 mm 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                 Refractive 
                 Abbe 
               
               
                 Element 
                 Surface (S#) 
                 Radius (mm) 
                 separation (mm) 
                   
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 INF 
                 INF 
                   
                   
                   
               
               
                 Stop 
                 1 
                 INF 
                 −0.2820 
               
               
                 L1 
                 *2 
                 3.2470 
                 0.6170 
                   
                 1.513 
                 56.6 
               
               
                 Prism 
                 3 
                 INF 
                 1.8725 
                   
                 1.755 
                 27.6 
               
               
                   
                 Decenter (1) 
               
               
                   
                 4 
                 INF 
                 −1.8725 
                 REFL 
               
               
                   
                 Bend (1) 
               
               
                   
                 5 
                 INF 
                 −0.0500 
               
               
                 L2 
                 *6 
                 −5.5010 
                 −0.6170 
                   
                 1.661 
                 20.4 
               
               
                   
                 *7 
                 −2.2820 
                 −0.3780 
               
               
                 L3 
                 *8 
                 −5.3630 
                 −0.8000 
                   
                 1.545 
                 55.9 
               
               
                   
                 *9 
                 4.9180 
                 −1.0650 
               
               
                 L4 
                 *10 
                 −11.8660 
                 −0.5000 
                   
                 1.545 
                 55.9 
               
               
                   
                 *11 
                 −2.5020 
                 −0.8070 
               
               
                 IR filter 
                 12 
                 INF 
                 −0.2100 
                   
                 1.517 
                 64.2 
               
               
                   
                 13 
                 INF 
                 −0.1000 
               
               
                   
                 14 
                 INF 
                 0.0000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 11A-11B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 11A 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 410) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 S2 
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A4 
                 −1.185992E−04  
                 2.418232E−02 
                 3.555325E−02 
                 1.824810E−03 
                 2.536181E−03 
               
               
                 A6 
                 −4.993100E−06  
                 −1.831987E−03  
                 −2.448378E−03  
                 5.056339E−04 
                 −6.020578E−04  
               
               
                 A8 
                 0.000000E+00 
                 −1.015260E−05  
                 1.020881E−04 
                 −7.150725E−07  
                 1.855878E−04 
               
               
                 A10 
                 0.000000E+00 
                 9.750139E−06 
                 1.063693E−05 
                 2.004868E−06 
                 1.754149E−05 
               
               
                 A12 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −3.933255E−06  
               
               
                 A14 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.541867E−07 
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 11B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 410) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S10 
                 S11 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 A4 
                 4.430967E−02 
                 4.249250E−02 
               
               
                   
                 A6 
                 −1.271181E−03  
                 −3.916083E−03  
               
               
                   
                 A8 
                 −2.677368E−04  
                 1.401346E−04 
               
               
                   
                 A10 
                 1.277254E−05 
                 −4.477309E−06  
               
               
                   
                 A12 
                 −3.214856E−07  
                 3.308677E−08 
               
               
                   
                 A14 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A16 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A18 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A20 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 Decentering Constants (Lens System 410) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Decenter 
                 X 
                 Y 
                 Z 
                 Alpha(deg) 
                 Beta(deg) 
                 Gamma (deg) 
               
               
                   
               
               
                 D(1) and 
                 0 
                 0 
                 0 
                 45 
                 0 
                 0 
               
               
                 Bend (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 13 
               
               
                   
               
               
                 Optical Definitions (Lens system 410) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 EFL 
                 6.6 mm 
                 V 1   
                 56.6 
               
               
                   
                 FNO 
                     2.2 
                 V 2   
                 20.4 
               
               
                   
                 FOV 
                 42.2° 
                 |f/f1| 
                 0.59 
               
               
                   
                 f 35 mm   
                  57 mm 
                 |f/f2| 
                 1.04 
               
               
                   
                 Z 
                 4.4 mm 
                 |R4f − R4r|/|R4f + R4r| 
                 0.65 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 Lens system 510 
               
               
                 Fno = 2.6, EFL = 12 mm, FOV = 23.7°, f 35 mm  = 103 mm 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                 Refractive 
                 Abbe 
               
               
                 Element 
                 Surface (S#) 
                 Radius (mm) 
                 separation (mm) 
                   
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 INF 
                 INF 
                   
                   
                   
               
               
                 Stop 
                 1 
                 INF 
                 −0.5376 
               
               
                 L1 
                 *2 
                  4.9890 
                 0.8240 
                   
                 1.513 
                 56.6 
               
               
                 Prism 
                 3 
                 INF 
                 2.5020 
                   
                 1.755 
                 27.6 
               
               
                   
                 Decenter (1) 
               
               
                   
                 4 
                 INF 
                 −2.5020 
                 REFL 
               
               
                   
                 Bend (1) 
               
               
                   
                 5 
                 INF 
                 −0.0500 
               
               
                 L2 
                 *6 
                 −5.9940 
                 −0.5980 
                   
                 1.651 
                 21.5 
               
               
                   
                 *7 
                 −3.0150 
                 −2.0714 
               
               
                 L3 
                 *8 
                 −3.2000 
                 −1.5670 
                   
                 1.545 
                 55.9 
               
               
                   
                 *9 
                 −4.3040 
                 −1.0600 
               
               
                 L4 
                 *10 
                 −5.6600 
                 −0.6990 
                   
                 1.545 
                 55.9 
               
               
                   
                 *11 
                 −4.2910 
                 −2.3200 
               
               
                 IR filter 
                 12 
                 INF 
                 −0.2100 
                   
                 1.517 
                 64.2 
               
               
                   
                 13 
                 INF 
                 −0.1000 
               
               
                   
                 14 
                 INF 
                 0.0000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 15A-15B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 15A 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 510) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 S2 
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A4 
                 −6.582527E−05  
                 2.037533E−02 
                 2.884337E−02 
                 1.642463E−03 
                 3.926273E−03 
               
               
                 A6 
                 2.046512E−06 
                 −1.110012E−03  
                 −1.366167E−03  
                 1.480820E−04 
                 −2.248217E−03  
               
               
                 A8 
                 0.000000E+00 
                 0.000000E+00 
                 3.673243E−05 
                 7.238769E−05 
                 6.422383E−04 
               
               
                 A10 
                 0.000000E+00 
                 0.000000E+00 
                 2.273830E−06 
                 −1.946842E−06  
                 −8.971135E−05  
               
               
                 A12 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.268152E−05 
               
               
                 A14 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −1.218277E−06  
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 15B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 510) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S10 
                 S11 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 A4 
                 4.679289E−02 
                 4.674529E−02 
               
               
                   
                 A6 
                 −3.481463E−03  
                 −5.658225E−03  
               
               
                   
                 A8 
                 2.305817E−04 
                 6.688362E−04 
               
               
                   
                 A10 
                 −1.991886E−05  
                 −7.402455E−05  
               
               
                   
                 A12 
                 −1.788224E−06  
                 3.598719E−06 
               
               
                   
                 A14 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A16 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A18 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A20 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 16 
               
             
            
               
                   
               
               
                 Decentering Constants (Lens System 510) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Decenter 
                 X 
                 Y 
                 Z 
                 Alpha(deg) 
                 Beta(deg) 
                 Gamma (deg) 
               
               
                   
               
               
                 D(1) and 
                 0 
                 0 
                 0 
                 45 
                 0 
                 0 
               
               
                 Bend (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 17 
               
               
                   
               
               
                 Optical Definitions (Lens system 510) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 EFL 
                  12 mm 
                 V 1   
                 56.6 
               
               
                   
                 FNO 
                     2.6 
                 V 2   
                 21.5 
               
               
                   
                 FOV 
                 23.7° 
                 |f/f1| 
                 0.70 
               
               
                   
                 f 35 mm   
                 103 mm 
                 |f/f2| 
                 1.20 
               
               
                   
                 Z 
                 5.85 mm  
                 |R4f − R4r|/|R4f + R4r| 
                 0.14 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 18 
               
             
            
               
                   
               
               
                 Lens system 610 
               
               
                 Fno = 2.4, EFL = 8.1 mm, FOV = 31.2°, f 35 mm  = 77 mm 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                 Refractive 
                 Abbe 
               
               
                 Element 
                 Surface (S#) 
                 Radius (mm) 
                 separation (mm) 
                   
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 INF 
                 INF 
                   
                   
                   
               
               
                 Stop 
                 1 
                 INF 
                 −0.3656 
               
               
                 L1 
                 *2 
                 3.7650 
                 0.6490 
                   
                 1.513 
                 56.6 
               
               
                 Prism 
                 3 
                 INF 
                 1.8980 
                   
                 1.755 
                 27.6 
               
               
                   
                 Decenter (1) 
               
               
                   
                 4 
                 INF 
                 −1.8980 
                 REFL 
               
               
                   
                 Bend (1) 
               
               
                   
                 5 
                 INF 
                 −0.1000 
               
               
                 L2 
                 *6 
                 −5.7300 
                 −0.5780 
                   
                 1.651 
                 21.5 
               
               
                   
                 *7 
                 −2.4180 
                 −1.0040 
               
               
                 L3 
                 *8 
                 −2.9820 
                 −1.3460 
                   
                 1.545 
                 55.9 
               
               
                   
                 *9 
                 −10.2080 
                 −0.7800 
               
               
                 L4 
                 *10 
                 −4.7340 
                 −0.8650 
                   
                 1.545 
                 55.9 
               
               
                   
                 *11 
                 −2.6520 
                 −1.2270 
               
               
                 IR filter 
                 12 
                 INF 
                 −0.2100 
                   
                 1.517 
                 64.2 
               
               
                   
                 13 
                 INF 
                 −0.1000 
               
               
                   
                 14 
                 INF 
                 0.0000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 19A-19B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 19A 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 610) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 S2 
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A4 
                 −2.360340E−04  
                 3.402370E−02 
                 5.016939E−02 
                 1.819421E−03 
                 7.779075E−03 
               
               
                 A6 
                 −2.111947E−05  
                 −3.386172E−03  
                 −4.162309E−03  
                 9.935049E−04 
                 −4.046032E−03  
               
               
                 A8 
                 0.000000E+00 
                 7.735521E−06 
                 2.891013E−04 
                 −3.703260E−05  
                 1.280125E−03 
               
               
                 A10 
                 0.000000E+00 
                 1.696235E−05 
                 1.413009E−05 
                 1.094440E−05 
                 −2.265344E−04  
               
               
                 A12 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 3.220049E−05 
               
               
                 A14 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −3.230947E−06  
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 19B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 610) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S10 
                 S11 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 A4 
                 6.462879E−02 
                 6.507028E−02 
               
               
                   
                 A6 
                 −3.617937E−03  
                 −6.851818E−03  
               
               
                   
                 A8 
                 −4.038654E−04  
                 4.452252E−04 
               
               
                   
                 A10 
                 −1.039311E−05  
                 −5.908594E−06  
               
               
                   
                 A12 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A14 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A16 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A18 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A20 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 20 
               
             
            
               
                   
               
               
                 Decentering Constants (Lens System 610) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Decenter 
                 X 
                 Y 
                 Z 
                 Alpha(deg) 
                 Beta(deg) 
                 Gamma (deg) 
               
               
                   
               
               
                 D(1) and 
                 0 
                 0 
                 0 
                 45 
                 0 
                 0 
               
               
                 Bend (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 21 
               
               
                   
               
               
                 Optical Definitions (Lens system 610) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 EFL 
                 8.1 mm 
                 V 1   
                 56.6 
               
               
                   
                 FNO 
                     2.4 
                 V 2   
                 21.5 
               
               
                   
                 FOV 
                 31.2° 
                 |f/f1| 
                 0.63 
               
               
                   
                 f 35 mm   
                  77 mm 
                 |f/f2| 
                 1.18 
               
               
                   
                 Z 
                 4.45 mm  
                 |R4f − R4r|/|R4f + R4r| 
                 0.28 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 22 
               
             
            
               
                   
               
               
                 Lens system 710 
               
               
                 Fno = 3.0, EFL = 14 mm, FOV = 20.4°, f 35 mm  = 120 mm 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness or 
                   
                 Refractive 
                 Abbe 
               
               
                 Element 
                 Surface (S#) 
                 Radius (mm) 
                 separation (mm) 
                   
                 Index N d   
                 Number V d   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Object 
                 0 
                 INF 
                 INF 
                   
                   
                   
               
               
                 Stop 
                 1 
                 INF 
                 −0.5231 
               
               
                 L1 
                 *2 
                  5.2200 
                 0.8040 
                   
                 1.513 
                 56.6 
               
               
                 Prism 
                 3 
                 INF 
                 2.4750 
                   
                 1.755 
                 27.6 
               
               
                   
                 Decenter (1) 
               
               
                   
                 4 
                 INF 
                 −2.4750 
                 REFL 
               
               
                   
                 Bend (1) 
               
               
                   
                 5 
                 INF 
                 −0.0500 
               
               
                 L2 
                 *6 
                 −5.6950 
                 −0.5640 
                   
                 1.651 
                 21.5 
               
               
                   
                 *7 
                 −3.0700 
                 −2.4640 
               
               
                 L3 
                 *8 
                 −3.0760 
                 −1.4990 
                   
                 1.545 
                 55.9 
               
               
                   
                 *9 
                 −3.5620 
                 −1.4890 
               
               
                 L4 
                 *10 
                 12.6070 
                 −0.7620 
                   
                 1.545 
                 55.9 
               
               
                   
                 *11 
                 26.1350 
                 −2.7660 
               
               
                 IR filter 
                 12 
                 INF 
                 −0.2100 
                   
                 1.517 
                 64.2 
               
               
                   
                 13 
                 INF 
                 −0.1000 
               
               
                   
                 14 
                 INF 
                 0.0000 
               
               
                   
               
               
                 *Annotates aspheric surfaces (aspheric coefficients given in Tables 23A-23B) 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 23A 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 710) 
               
            
           
           
               
               
            
               
                   
                 Surface (S#) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 S2 
                 S6 
                 S7 
                 S8 
                 S9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A4 
                 −2.745195E−05  
                 2.036332E−02 
                 2.867198E−02 
                 2.551997E−03 
                 2.400665E−04 
               
               
                 A6 
                 4.097874E−06 
                 −1.192201E−03  
                 −1.661519E−03  
                 3.767858E−04 
                 1.776187E−05 
               
               
                 A8 
                 0.000000E+00 
                 −1.332816E−05  
                 5.296870E−05 
                 −7.901097E−06  
                 −1.579635E−05  
               
               
                 A10 
                 0.000000E+00 
                 6.595165E−06 
                 7.881696E−06 
                 5.689791E−06 
                 1.479408E−05 
               
               
                 A12 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 3.285398E−07 
               
               
                 A14 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −6.354672E−08  
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 23B 
               
             
            
               
                   
               
               
                 Aspheric Coefficients (Lens System 710) 
               
            
           
           
               
               
               
            
               
                   
                 Surface (S#) 
                   
               
            
           
           
               
               
               
            
               
                   
                 S10 
                 S11 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 K 
                 0 
                 0 
               
               
                   
                 A4 
                 3.006845E−02 
                 2.597292E−02 
               
               
                   
                 A6 
                 −4.706480E−04  
                 −1.734303E−03  
               
               
                   
                 A8 
                 −5.268048E−06  
                 1.066114E−04 
               
               
                   
                 A10 
                 1.030203E−05 
                 1.158703E−06 
               
               
                   
                 A12 
                 0.000000E+00 
                 −5.999168E−07  
               
               
                   
                 A14 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A16 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A18 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                 A20 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 24 
               
             
            
               
                   
               
               
                 Decentering Constants (Lens System 710) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Decenter 
                 X 
                 Y 
                 Z 
                 Alpha(deg) 
                 Beta(deg) 
                 Gamma (deg) 
               
               
                   
               
               
                 D(1) and 
                 0 
                 0 
                 0 
                 45 
                 0 
                 0 
               
               
                 Bend (1) 
               
               
                   
               
            
           
         
       
     
                     TABLE 25               Optical Definitions (Lens system 710)                                                        EFL    14 mm   V 1     56.6           FNO       3.0   V 2     21.5           FOV   20.4°   |f/f1|   0.78           f 35 mm     120 mm   |f/f2|   1.26           Z   5.75 mm    |R4f − R4r|/|R4f + R4r|   0.35                        
Example Flowchart
 
       FIG. 9  is a high-level flowchart of a method for capturing images using a camera with a lens system that includes four lens elements and a folding element as illustrated in  FIGS. 1 through 8 , according to some embodiments. As indicated at  2500 , light from an object field in front of the camera is received at a first lens element of the camera through an aperture stop. In some embodiments, the aperture stop may be located at the first lens element and behind the front vertex of the lens system. As indicated at  2502 , the first lens element refracts the light on a first axis AX 1  to a light folding element such as a prism. As indicated at  2504 , the light is redirected by the folding element to a second lens element on a second axis AX 2 . As indicated at  2506 , the light is then refracted by the second lens element to a third lens element on the second axis AX 2 . As indicated at  2508 , the light is then refracted by the third lens element to a fourth lens element on the second axis AX 2 . As indicated at  2510 , the light is then refracted by the fourth lens element to form an image at an image plane at or near the surface of a photosensor. As indicated at  2514 , the image is captured by the photosensor. While not shown, in some embodiments, the light may pass through an infrared filter that may for example be located between the fourth lens element and the photosensor. 
     In some embodiments, the elements referred to in  FIG. 9  may be configured as illustrated in  FIGS. 1 through 7 . However, note that variations on the example as given in the Figures are possible while achieving similar optical results. 
     Example Computing Device 
       FIG. 10  illustrates an example computing device, referred to as computer system  4000 , that may include or host embodiments of the camera as illustrated in  FIGS. 1 through 9 . In addition, computer system  4000  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  4000  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 mobile multipurpose 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, or in general any type of computing or electronic device. 
     In the illustrated embodiment, computer system  4000  includes one or more processors  4010  coupled to a system memory  4020  via an input/output (I/O) interface  4030 . Computer system  4000  further includes a network interface  4040  coupled to I/O interface  4030 , and one or more input/output devices  4050 , such as cursor control device  4060 , keyboard  4070 , and display(s)  4080 . Computer system  4000  may also include one or more cameras  4090 , for example one or more cameras as described above with respect to  FIGS. 1 through 9 , which may also be coupled to I/O interface  4030 , or one or more cameras as described above with respect to  FIGS. 1 through 9  along with one or more other cameras such as wide-field cameras. 
     In various embodiments, computer system  4000  may be a uniprocessor system including one processor  4010 , or a multiprocessor system including several processors  4010  (e.g., two, four, eight, or another suitable number). Processors  4010  may be any suitable processor capable of executing instructions. For example, in various embodiments processors  4010  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  4010  may commonly, but not necessarily, implement the same ISA. 
     System memory  4020  may be configured to store program instructions  4022  and/or data  4032  accessible by processor  4010 . In various embodiments, system memory  4020  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  4022  may be configured to implement various interfaces, methods and/or data for controlling operations of camera  4090  and for capturing and processing images with integrated camera  4090  or other methods or data, for example interfaces and methods for capturing, displaying, processing, and storing images captured with camera  4090 . 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  4020  or computer system  4000 . 
     In one embodiment, I/O interface  4030  may be configured to coordinate I/O traffic between processor  4010 , system memory  4020 , and any peripheral devices in the device, including network interface  4040  or other peripheral interfaces, such as input/output devices  4050 . In some embodiments, I/O interface  4030  may perform any necessary protocol, timing or other data transformations to convert data signals from one component (e.g., system memory  4020 ) into a format suitable for use by another component (e.g., processor  4010 ). In some embodiments, I/O interface  4030  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  4030  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  4030 , such as an interface to system memory  4020 , may be incorporated directly into processor  4010 . 
     Network interface  4040  may be configured to allow data to be exchanged between computer system  4000  and other devices attached to a network  4085  (e.g., carrier or agent devices) or between nodes of computer system  4000 . Network  4085  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  4040  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  4050  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  4000 . Multiple input/output devices  4050  may be present in computer system  4000  or may be distributed on various nodes of computer system  4000 . In some embodiments, similar input/output devices may be separate from computer system  4000  and may interact with one or more nodes of computer system  4000  through a wired or wireless connection, such as over network interface  4040 . 
     As shown in  FIG. 10 , memory  4020  may include program instructions  4022 , which may be processor-executable to implement any element or action to support integrated camera  4090 , including but not limited to image processing software and interface software for controlling camera  4090 . In some embodiments, images captured by camera  4090  may be stored to memory  4020 . In addition, metadata for images captured by camera  4090  may be stored to memory  4020 . 
     Those skilled in the art will appreciate that computer system  4000  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  4000  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  4000  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  4000  may be transmitted to computer system  4000  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: 20170328
Publication Date: 20190319
Grant Date: 20190319
Priority Date: 20160328
Inventors: YAO, YUHONG
SHINOHARA, YOSHIKAZU
Assignee: APPLE INC
CPC Classifications: [{"code": "G02B27/0025", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/004", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04N5/23212", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0065", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B27/0025", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0065", "inventive": true, "first": true, "tree": "[]"}, {"code": "G03B30/00", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/004", "inventive": true, "first": false, "tree": "[]"}, {"code": "H04N23/67", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0065", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/004", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B27/0025", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/004", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0065", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/0015", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/004", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0065", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/18", "inventive": true, "first": false, "tree": "[]"}]
Family ID: 58489443