PATENT DOCUMENT

Publication Number: US-11933949-B2
Application Number: US-202017008524-A
Country: US
Kind Code: B2

Title: Freeform folded optical system

Abstract:
A freeform folded optical system that include two freeform prisms with optical power. At least one of the freeform prisms is configured to fold the optical axis twice. Thus, embodiments of the freeform folded optical system fold the optical axis three or four times. Folding the optical axis three or four times in the freeform prisms allows for long focal lengths required for telephoto lens applications without requiring additional lens elements between the prisms. In addition, the configuration of the freeform folded optical system provides reduced Z-axis height when compared to conventional folded lens systems with similar optical characteristics.

Claims:
What is claimed is: 
     
       1. An optical system, comprising:
 in order from an object side of the optical system to an image side of the optical system:
 a first freeform prism that includes:
 a first surface, a second surface, and a third surface, wherein an optical axis of the optical system traverses the first surface, the second surface, and the third surface, 
 wherein an angle θ between the first surface of the first freeform prism and the second surface of the first freeform prism is less than or equal to 35 degrees, 
 wherein the first surface is configured to transmit light incident from an object side into the first freeform prism, and to internally reflect at least a portion of the light that is reflected back to the first surface from within the first freeform prism, 
 wherein the light incident into the first freeform prism from the object side has no more than two internal reflections within the first freeform prism, 
 wherein at least one of the first surface, the second surface, or the third surface of the first freeform prism is a freeform surface; and 
 
 a second freeform prism that includes:
 a first surface, a second surface, and a third surface, wherein the optical axis of the optical system traverses the first surface, the second surface, and the third surface, 
 wherein the first surface is configured to input light exiting the first freeform prism, 
 wherein the light input through the first surface of the second freeform prism has a same direction of propagation as the light exiting the first freeform prism and has no more than two internal reflections within the second freeform prism, 
 wherein at least one of the first surface, the second surface, or the third surface of the second freeform prism is another freeform surface; 
 
 
 wherein the first freeform prism is configured to fold the optical axis of the optical system twice. 
 
     
     
       2. The optical system as recited in  claim 1 , wherein, to fold the optical axis of the optical system twice:
 the first surface of the first freeform prism receives light from an object field on the object side of the optical system and transmits the light to the second surface of the first freeform prism on a first portion of the optical axis; 
 the second surface of the first freeform prism reflects the light received on the first portion of the optical axis on to a second portion of the optical axis; and 
 the first surface of the first freeform prism reflects the light received on the second portion of the optical axis via total internal reflection on to a third portion of the optical axis; 
 wherein the third surface of the first freeform prism transmits the light on the third portion of the optical axis to the first surface of the second freeform prism. 
 
     
     
       3. The optical system as recited in  claim 2 , wherein the second freeform prism is configured to fold the optical axis of the optical system twice, wherein, to fold the optical axis of the optical system twice:
 the first surface of the second freeform prism receives light on the third portion of the optical axis and transmits the light to the second surface of the second freeform prism; 
 the second surface of the second freeform prism reflects the light received on the third portion of the optical axis via total internal reflection on to a fourth portion of the optical axis; and 
 the third surface of the second freeform prism reflects the light received on the fourth portion of the optical axis on to a fifth portion of the optical axis; 
 wherein the second surface of the second freeform prism transmits the light on the fifth portion of the optical axis to form an image at an image plane on the image side of the optical system. 
 
     
     
       4. The optical system as recited in  claim 2 , wherein the second freeform prism is configured to fold the optical axis of the optical system once, wherein, to fold the optical axis of the optical system once:
 the first surface of the second freeform prism receives light on the third portion of the optical axis and transmits the light to the second surface of the second freeform prism; 
 the second surface of the second freeform prism reflects the light received on the third portion of the optical axis on to a fourth portion of the optical axis; and 
 the third surface of the second freeform prism transmits the light on the fourth portion of the optical axis to form an image at an image plane on the image side of the optical system. 
 
     
     
       5. The optical system as recited in  claim 1 , further comprising an objective lens having positive refractive power and located on the object side of the first freeform prism, wherein light from an object field is refracted by the objective lens before entering the first surface of the first freeform prism. 
     
     
       6. The optical system as recited in  claim 5 , wherein the objective lens is a rotationally symmetric lens with at least one aspherical surface. 
     
     
       7. The optical system as recited in  claim 5 , wherein the objective lens is composed of an optical plastic material or of an optical glass material. 
     
     
       8. The optical system as recited in  claim 5 , wherein the objective lens is a doublet lens. 
     
     
       9. The optical system as recited in  claim 5 , wherein the optical system satisfies a condition:
   0.5&lt; B/A&lt; 1.0 
 where A is optical power of the optical system, and B is optical power of the objective lens. 
 
     
     
       10. The optical system as recited in  claim 5 , wherein the objective lens is composed of an optical material with Abbe number V d1  that satisfies a condition:
     V   d1 &gt;50. 
 
     
     
       11. The optical system as recited in  claim 5 , wherein an image plane formed by the optical system is parallel to a principal plane of the objective lens. 
     
     
       12. The optical system as recited in  claim 1 , wherein the first freeform prism is composed of an optical plastic material with Abbe number V d2  that satisfies a condition:
     V   d2 &gt;50; and 
 wherein the second freeform prism is composed of an optical plastic material with Abbe number V d3  that satisfies a condition:
     V   d3 &lt;25. 
 
 
     
     
       13. The optical system as recited in  claim 1 , wherein the optical system satisfies a condition:
   0.05&lt; AD&lt; 0.3 
 where A is optical power of the optical system, and D is semi-diagonal image height. 
 
     
     
       14. The optical system as recited in  claim 1 , wherein effective focal length f of the optical system is within a range of 9 to 31 millimeters. 
     
     
       15. The optical system as recited in  claim 1 , wherein F-number of the optical system is within a range of 2.0 to 4.0. 
     
     
       16. The optical system as recited in  claim 1 , wherein semi-diagonal image height of the optical system is within a range of 2.5 to 2.9 millimeters. 
     
     
       17. The optical system as recited in  claim 1 , wherein half field of view of the optical system is within a range of 4.5 degrees to 16 degrees. 
     
     
       18. The optical system as recited in  claim 1 , wherein 35 mm equivalent focal length of the optical system is within a range of 75 to 270 millimeters. 
     
     
       19. A camera, comprising, in order from an object side of the camera to an image side of the camera:
 an optical system comprising:
 a first freeform prism that includes:
 a first surface, a second surface, and a third surface, wherein an optical axis of the optical system traverses the first surface, the second surface, and the third surface, 
 wherein an angle θ between the first surface of the first freeform prism and the second surface of the first freeform prism is less than or equal to 35 degrees, 
 wherein the first surface is configured to transmit light incident from an object side into the first freeform prism, and to internally reflect at least a portion of the light that is reflected back to the first surface from within the first freeform prism, 
 wherein the light incident into the first freeform prism from the object side has no more than two internal reflections within the first freeform prism, 
 wherein at least one of the first surface, the second surface, or the third surface of the first freeform prism is a freeform surface; and 
 
 a second freeform prism that includes:
 a first surface, a second surface, and a third surface on the optical axis of the optical system, wherein at least one of the first surface, the second surface, or the third surface of the second freeform prism is another freeform surface; and 
 
 an image sensor configured to capture light projected onto a surface of the image sensor; 
 
 wherein the first freeform prism is configured to fold the optical axis of the optical system twice before transmitting light received from an object field on the object side of the camera to the second freeform prism; and 
 wherein the second freeform prism is configured to fold the optical axis of the optical system at least once before transmitting the light to form an image at an image plane at the surface of the image sensor and the light has no more than two internal reflections within the second freeform prism. 
 
     
     
       20. The optical system as recited in  claim 19 , further comprising an objective lens having positive refractive power and located on the object side of the first freeform prism, wherein the light from the object field is refracted by the objective lens before entering the first surface of the first freeform prism. 
     
     
       21. The optical system as recited in  claim 19 , further comprising an aperture stop located on the object side of the first freeform prism. 
     
     
       22. The optical system as recited in  claim 19 , further comprising an infrared filter located between the second freeform prism and the image sensor.

Description:
PRIORITY INFORMATION 
     This application claims benefit of priority of U.S. Provisional Application Ser. No. 62/907,456 entitled “FREEFORM FOLDED OPTICAL SYSTEM” filed Sep. 27, 2019, 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 folded optical systems. 
     Description of the Related Art 
     The advent of small, mobile multipurpose devices such as smartphones and tablet or pad devices has resulted in a need for high-resolution, small form factor cameras that are lightweight, compact, and capable of capturing high resolution, high quality images at low F-numbers for integration in the devices. However, due to limitations of conventional camera technology, conventional small cameras used in such devices tend to capture images at lower resolutions and/or with lower image quality than can be achieved with larger, higher quality cameras. Achieving higher resolution with small package size cameras generally requires use of 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 image sensors. However, as image sensors become more compact and powerful, demand for compact imaging lens systems with improved imaging quality performance has increased. In addition, there are increasing expectations for small form factor cameras to be equipped with higher pixel count and/or larger pixel size image sensors (one or both of which may require larger image sensors) while still maintaining a module height that is compact enough to fit into portable electronic devices. Thus, a challenge from an optical system design point of view is to provide an optical system that is capable of capturing high brightness, high resolution images under the physical constraints imposed by small form factor cameras. 
     SUMMARY OF EMBODIMENTS 
     Embodiments of a freeform folded optical system are described that may, for example, be used in small form factor cameras in mobile multipurpose devices such as smartphones and tablet or pad devices. Embodiments of the freeform folded optical system are described that include two freeform prisms with optical power and without a lens stack between the prisms. At least one of the freeform prisms is configured to fold the optical axis of the optical system twice. Thus, embodiments of the freeform folded optical system fold the optical axis three or four times. Folding the optical axis three or four times in the freeform prisms allows for long focal lengths required for telephoto lens applications without requiring additional lens elements between the prisms. In addition, the configuration of the freeform folded optical system provides reduced Z-axis height when compared to conventional folded lens systems with similar optical characteristics. 
     The folded optical system includes two freeform prisms. In at least some embodiments, each freeform prism is formed of an optical plastic material. Each freeform prism has more than three surfaces; however, only three of the surfaces of each freeform prism are discussed. 
     In embodiments of the folded optical system, the first freeform prism has a first surface that is a transmitting and total internal reflection (TIR) surface that transmits light received from an object field and reflects light received from a second surface of the first freeform prism by TIR to a third surface of the first freeform prism. The second surface of the first freeform prism is a reflecting surface coated with a mirror coating that reflects light received through the first surface of the first freeform prism back to the first surface of the first freeform prism. The third surface of the first freeform prism is a transmitting surface that transmits light received from the first surface of the first freeform prism. Thus, the first freeform prism folds the optical axis twice—once at the second surface, and again at the first surface. At least one of the three surfaces of the first freeform prism is a freeform surface. 
     In embodiments of the folded optical system that fold the optical axis four times, the second freeform prism has a first surface that is a transmitting surface that transmits light received from the first freeform prism to a second surface of the second freeform prism. The second surface of the second freeform prism is a transmitting and TIR surface that reflects light received through the first surface of the second freeform prism by TIR to the third surface of the second freeform prism and transmits light received from the third surface of the second freeform prism to form an image at an image plane. The third surface of the second freeform prism is a reflecting surface coated with a mirror coating that reflects light received from the second surface of the second freeform prism back to the second surface of the second freeform prism. Thus, in these embodiments, the second freeform prism folds the optical axis twice—once at the second surface, and again at the third surface. At least one of the three surfaces of the second freeform prism is a freeform surface. 
     In embodiments of the folded optical system that fold the optical axis three times, the second freeform prism has a first surface that is a transmitting surface that transmits light received from the first freeform prism to a second surface of the second freeform prism. The second surface of the second freeform prism is a reflecting surface that reflects light received through the first surface of the second freeform prism to the third surface of the second freeform prism. The second surface of the second freeform prism may be coated with a mirror coating, or alternatively may reflect light via total internal reflection. The third surface of the second freeform prism is a transmitting surface that transmits light received from the second surface of the second freeform prism to form an image at an image plane. Thus, in these embodiments, the second freeform prism folds the optical axis once, at the second surface. At least one of the three surfaces of the second freeform prism is a freeform surface. 
     In some embodiments, an objective lens may be located on the object side of the first freeform prism, for example to correct for aberrations in the optical system. In some embodiments, the objective lens is a rotationally symmetric lens. In some embodiments, at least one of the surfaces of the objective lens is aspherical. Using optical glass instead of plastic for the objective lens may, for example, aid in correcting aberrations. In some embodiments, the objective lens has positive refractive power. In some embodiments, the objective lens is composed of an optical plastic material. In some embodiments, the objective lens is composed of an optical glass material. Using optical glass instead of plastic for the objective lens may, for example, aid in correcting aberrations. In some embodiments, the objective lens is a doublet lens. 
     In some embodiments, the folded optical system may satisfy the following condition:
 
0.5 &lt;B/A&lt; 0.1.0  (1)
 
where A is the optical power of the overall optical system, and B is the optical power of the objective lens.
 
     In some embodiments, the folded optical system may satisfy the following condition:
 
0.05&lt; AD&lt; 0.3  (2)
 
where A is the optical power of the overall optical system, and D is the semi-diagonal image height.
 
     In some embodiments, the objective lens is composed of a material (either optical plastic or optical glass) with Abbe number V d1  that satisfies the following condition:
 
 V   d1 &gt;50.  (3)
 
     In some embodiments, the first freeform prism is composed of an optical plastic material with Abbe number V d2  that satisfies the following condition:
 
 V   d2 &gt;50.  (4)
 
     In some embodiments, the second freeform prism is composed of an optical plastic material with Abbe number V d3  that satisfies the following condition:
 
 V   d3 &lt;25.  (5)
 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A  illustrates a freeform folded optical system that folds the optical axis four times, according to some embodiments. 
         FIG.  1 B  illustrates a freeform folded optical system that folds the optical axis three times, according to some embodiments. 
         FIG.  2 A  illustrates a first example embodiment of a freeform folded optical system. 
         FIG.  2 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  2 A . 
         FIG.  2 C  shows distortion for the freeform folded optical system of  FIG.  2 A . 
         FIG.  3 A  illustrates a second example embodiment of a freeform folded optical system. 
         FIG.  3 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  3 A . 
         FIG.  3 C  shows distortion for the freeform folded optical system of  FIG.  3 A   
         FIG.  4 A  illustrates a third example embodiment of a freeform folded optical system. 
         FIG.  4 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  4 A . 
         FIG.  4 C  shows distortion for the freeform folded optical system of  FIG.  4 A . 
         FIG.  5 A  illustrates a fourth example embodiment of a freeform folded optical system. 
         FIG.  5 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  5 A . 
         FIG.  5 C  shows distortion for the freeform folded optical system of  FIG.  5 A . 
         FIG.  6 A  illustrates a fifth example embodiment of a freeform folded optical system. 
         FIG.  6 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  6 A . 
         FIG.  6 C  shows distortion for the freeform folded optical system of  FIG.  6 A . 
         FIG.  7 A  illustrates a sixth example embodiment of a freeform folded optical system. 
         FIG.  7 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  7 A . 
         FIG.  7 C  shows distortion for the freeform folded optical system of  FIG.  7 A . 
         FIG.  8 A  illustrates a sixth example embodiment of a freeform folded optical system. 
         FIG.  8 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  8 A . 
         FIG.  8 C  shows distortion for the freeform folded optical system of  FIG.  8 A . 
         FIG.  9    illustrates a freeform folded optical system that includes an objective lens composed of a glass material, according to some embodiments. 
         FIG.  10    illustrates a freeform folded optical system in which the objective lens is a doublet lens, according to some embodiments. 
         FIG.  11    illustrates a freeform folded optical system that does not include an objective lens, according to some embodiments. 
         FIG.  12    illustrates a freeform folded optical system that folds the optical axis three times rather than four times, according to some embodiments. 
         FIGS.  13 A through  13 C  compare an embodiment of the freeform folded optical system to a conventional folded lens system. 
         FIG.  14    provides labels for the optical elements and surfaces of the optical elements that are used in the Tables. 
         FIG.  15    is a flowchart of a method for capturing images using embodiments of a freeform folded optical system that folds the optical axis four times, according to some embodiments. 
         FIG.  16    is a flowchart of a method for capturing images using embodiments of a freeform folded optical system that folds the optical axis three times, according to some embodiments. 
         FIG.  17    illustrates an example computer system. 
     
    
    
     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(f), 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 freeform folded optical system are described that may, for example, be used in small form factor cameras in mobile multipurpose devices such as smartphones and tablet or pad devices. Conventional folded lens systems may include one or more prisms and a lens stack including one or more refractive lens elements. A first prism redirects light from a first optical axis to a second optical axis to thus provide a “folded” optical axis for the lens system. In some conventional folded lens systems, a second prism may be located at the image side of the lens stack to fold the optical axis on to a third axis. Using a prism to fold the optical axis may, for example, reduce the Z-height of the lens system, and thus may reduce the Z-height of a camera that includes the folded lens system. 
     Embodiments of the freeform folded optical system are described that include two freeform prisms with optical power and without a lens stack between the prisms. At least one of the freeform prisms is configured to fold the optical axis twice. Thus, in contrast to conventional folded lens systems in which one or two prisms fold the optical axis either once (one prism) or twice (two prisms), embodiments of the freeform folded optical system described herein fold the optical axis three or four times.  FIG.  1 A  illustrates a freeform folded optical system that folds the optical axis four times, according to some embodiments.  FIG.  1 B  illustrates a freeform folded optical system that folds the optical axis three times, according to some embodiments. Folding the optical axis three or four times in the freeform prisms with optical power allows for long focal lengths required for telephoto lens applications (e.g., an effective focal length within a range of 9 to 31 millimeters (mm)) while providing low F-numbers (e.g., within a range of 2.0 to 4.0) without requiring additional lens elements between the prisms. In addition, the configuration of the freeform folded optical system provides reduced Z-axis height when compared to conventional folded lens systems with similar optical characteristics as illustrated in  FIG.  12   . 
     Freeform optics involve optical designs with at least one freeform surface which has no translational or rotational symmetry about axes normal to the mean plane of the surface. A freeform prism is thus a prism that has at least one freeform surface which has no translational or rotational symmetry about axes normal to the mean plane of the surface. In general, if optical rays pass through a conventional rotationally symmetric surface with an angle, asymmetric aberrations may occur. Using a conventional rotationally symmetric surfaces for the prisms may thus degrade the optical performance of a folded optical system. Freeform surfaces can correct for those asymmetric aberrations. Thus, freeform surfaces may be used in the prisms of the folded optical systems as described herein to improve the optical performance of the optical systems, and also to help in reducing the Z-height of the folded optical systems. 
       FIG.  1 A  illustrates a freeform folded optical system that folds the optical axis four times, according to some embodiments. The folded optical system includes two freeform prisms  10  and  20 . In at least some embodiments, each freeform prism is formed of an optical plastic material. Each freeform prism has more than three surfaces; however, only three of the surfaces of each freeform prism are discussed. 
     Referring to the first freeform prism  10 , a first surface  11  is a transmitting and total internal reflection (TIR) surface that transmits light received from an object field and reflects light received from a second surface  12  in the prism by TIR to a third surface  13 . The second surface  12  is a reflecting surface coated with a mirror coating that reflects light received through the first surface  11  back to the first surface  11  in the prism. The third surface  13  is a transmitting surface that transmits light received from the first surface  11 . At least one of the three surfaces  11 ,  12 , and  13  is a freeform surface. 
     Referring to the second freeform prism  20 , a first surface  21  is a transmitting surface that transmits light received from the first prism  10  to a second surface  22  in the prism. The second surface  22  is a transmitting and TIR surface that reflects light received through the first surface  21  by TIR to the third surface  23  in the prism and transmits light received from the third surface  23  in the prism to form an image at an image plane. The third surface  23  is a reflecting surface coated with a mirror coating that reflects light received from the second surface  22  back to the second surface  22 . At least one of the three surfaces  21 ,  22 , and  23  is a freeform surface. 
     While not shown, in some embodiments, a first (objective) lens may be located on the object side of the first freeform prism  10 , for example to correct for aberrations in the optical system. In some embodiments, the objective lens is a rotationally symmetric lens. In some embodiments, at least one of the surfaces of the objective lens is aspherical. In some embodiments, the objective lens has positive refractive power. In some embodiments, the objective lens is composed of an optical plastic material. In some embodiments, the objective lens is composed of an optical glass material. Using optical glass instead of plastic for the objective lens may, for example, aid in correcting aberrations. In some embodiments, the objective lens is a doublet lens. 
     The following is a definition of an aspherical surface: 
             z   =           h   2     r       1   +       1   -         (     1   +   k     )     ⁢     h   2         r   2               +     A   ⁢     h   4       +     B   ⁢     h   6       +     C   ⁢     h   8       +   …                 h   =         x   2     +     y   2               
where z is the sag (the z-component of the displacement of the surface from the vertex, at distance r from the axis), k is a conic constant, and where:
 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Radius of curvature 
                 r 
               
               
                   
                   
               
             
            
               
                   
                 4th order 
                 (A) 
               
               
                   
                 6th order 
                 (B) 
               
               
                   
                 8th order 
                 (C) 
               
               
                   
                 10th order 
                 (D) 
               
               
                   
                 12th order 
                 (E) 
               
               
                   
                 14th order 
                 (F) 
               
               
                   
                   
               
            
           
         
       
     
     The folded optical system of  FIG.  1 A  may form an image at an image plane at or near a surface of an image sensor (not shown) located on the image side of the second freeform prism  20 . While not shown, an infrared (IR) filter may be located between the second surface  22  of the second freeform prism  20  and the image sensor. 
     While not shown, an aperture stop may be located at or near the object side of the first freeform prism  10 . In embodiments that include an objective lens on the object side of the first freeform prism  10 , the aperture stop may be located on the object side of the objective lens. 
     In at least some embodiments, an angle θ between the first surface  11  and the second surface  12  of the first freeform prism  10  may be less than or equal to 35 degrees, for example within a range of 29 to 35 degrees. For example, in some embodiments, angle θ may be 30 degrees. In some embodiments, angle θ may be determined as the angle between a mean plane of surface  11  and a mean plane of surface  12 . In some embodiments, angle θ may be determined by the average angle of surface  11  and of surface  12 . In conventional folded lens systems, the angle between a first surface of a first prism and a second (reflective) surface of the first prism is typically 45 degrees. Reducing the angle between the first  11  and second  12  surfaces in the first freeform prism  10  (and similarly reducing the angle between the second  22  and third  23  surfaces in the second freeform prism  20 ) helps to reduce the Z-height of the freeform folded optical system when compared to conventional folded lens systems, for example as illustrated in  FIG.  12   . 
     The freeform folded optical system of  FIG.  1 A  folds the optical axis four times. The second surface  12  of the first freeform prism  10  folds the optical axis from a first portion AX 1  to a second portion AX 2 . The first surface  11  of the first freeform prism  10  then folds the optical axis from the second portion AX 2  to a third portion AX 3 . The second surface  22  of the second prism  20  then folds the optical axis from the third portion AX 3  to a fourth portion AX 4 . The third surface  23  of the second prism  20  then folds the optical axis from the fourth portion AX 4  to a fifth portion AX 5 . 
       FIG.  15    is a flowchart of a method for capturing images using embodiments of a freeform folded optical system as illustrated in  FIG.  1 A  that folds the optical axis four times, according to some embodiments. As indicated at  2000 , light from an object field is received at a first surface  11  of a first freeform prism  10 . As indicated at  2010 , the first surface  11  of the first prism  10  transmits the light to a second surface  12  of the first prism  10 . As indicated at  2020 , the second surface  12  of the first prism  10  reflects the light to the first surface  11  of the first prism  10 . As indicated at  2030 , the first surface  11  of the first prism  10  reflects the light by TIR; the reflected light is transmitted through a third surface  13  of the first prism  10  to a first surface  21  of a second freeform prism  20 . 
     As indicated at  2040 , the first surface  21  of the second prism  20  transmits the light to a second surface  22  of the second prism  20 . As indicated at  2050 , the second surface  22  of the second prism  20  reflects the light by TIR to a third surface  23  of the second prism  20 . As indicated at  2060 , the third surface  23  of the second prism  20  reflects the light; the reflected light is transmitted through the second surface  22  of the second prism  20  to form an image at an image plane. 
       FIG.  1 B  illustrates a freeform folded optical system that folds the optical axis three times, according to some embodiments. The folded optical system includes two freeform prisms  50  and  60 . In at least some embodiments, each freeform prism is formed of an optical plastic material. Each freeform prism has more than three surfaces; however, only three of the surfaces of each freeform prism are discussed. 
     Referring to the first freeform prism  50 , a first surface  51  is a transmitting and TIR surface that transmits light received from an object field and reflects light received from a second surface  52  in the prism by TIR to a third surface  53 . The second surface  52  is a reflecting surface coated with a mirror coating that reflects light received through the first surface  51  back to the first surface  51  in the prism  50 . The third surface  53  is a transmitting surface that transmits light received from the first surface  51 . At least one of the three surfaces  51 ,  52 , and  53  is a freeform surface. 
     Referring to the second freeform prism  60 , a first surface  61  is a transmitting surface that transmits light received from the first prism  50  to a second surface  62  in the prism  60 . The second surface  62  is a reflecting surface that reflects light received through the first surface  61  to the third surface  63  in the prism  60 . The second surface  62  may be coated with a mirror coating, or alternatively may reflect light via total internal reflection. The third surface  63  is a transmitting surface that transmits light received from the second surface  62  to form an image at an image plane. At least one of the three surfaces  61 ,  62 , and  63  is a freeform surface. 
     While not shown, in some embodiments, a first (objective) lens may be located on the object side of the first freeform prism  60 , for example to correct for aberrations in the optical system. In some embodiments, the objective lens is a rotationally symmetric lens. In some embodiments, at least one of the surfaces of the objective lens is aspherical. In some embodiments, the objective lens has positive refractive power. In some embodiments, the objective lens is composed of an optical plastic material. In some embodiments, the objective lens is composed of an optical glass material. In some embodiments, the objective lens is a doublet lens. 
     The folded optical system of  FIG.  1 B  may form an image at an image plane at or near a surface of an image sensor (not shown) located on the image side of the second freeform prism  60 . While not shown, an infrared (IR) filter may be located between the third surface  63  of the second freeform prism  60  and the image sensor. 
     While not shown, an aperture stop may be located at or near the object side of the first freeform prism  50 . In embodiments that include an objective lens on the object side of the first freeform prism  50 , the aperture stop may be located on the object side of the objective lens. 
     In at least some embodiments, an angle θ between the first surface  51  and the second surface  52  of the first freeform prism  50  may be less than or equal to 35 degrees, for example within a range of 29 to 35 degrees. For example, in some embodiments, angle θ may be 30 degrees. In some embodiments, angle θ may be determined as the angle between a mean plane of surface  51  and a mean plane of surface  52 . In conventional folded lens systems, the angle between a first surface of a first prism and a second (reflective) surface of the first prism is typically 45 degrees. Reducing the angle between the first  51  and second  52  surfaces in the first freeform prism  50  (and similarly reducing the angle between the second  62  and third  63  surfaces in the second freeform prism  60 ) helps to reduce the Z-height of the freeform folded optical system when compared to conventional folded lens systems, for example as illustrated in  FIG.  12   . 
     The freeform folded optical system of  FIG.  1 B  folds the optical axis three times. The second surface  52  of the first freeform prism  50  folds the optical axis from a first portion AX 1  to a second portion AX 2 . The first surface  51  of the first freeform prism  50  then folds the optical axis from the second portion AX 2  to a third portion AX 3 . The second surface  62  of the second prism  60  then folds the optical axis from the third portion AX 3  to a fourth portion AX 4 . 
       FIG.  16    is a flowchart of a method for capturing images using embodiments of a freeform folded optical system as illustrated in  FIG.  1 B  that folds the optical axis three times, according to some embodiments. As indicated at  2100 , light from an object field is received at a first surface  51  of a first freeform prism  50 . As indicated at  2110 , the first surface  51  of the first prism  50  transmits the light to a second surface  52  of the first prism  50 . As indicated at  2120 , the second surface  52  of the first prism  50  reflects the light to the first surface  51  of the first prism  50 . As indicated at  2130 , the first surface  51  of the first prism  50  reflects the light by TIR; the reflected light is transmitted through a third surface  53  of the first prism  50  to a first surface  61  of a second freeform prism  60 . 
     As indicated at  2140 , the first surface  61  of the second prism  60  transmits the light to a second surface  62  of the second prism  60 . As indicated at  2150 , the second surface  62  of the second prism  60  reflects the light to a third surface  63  of the second prism  20 . As indicated at  2160 , the third surface  23  of the second prism  20  transmits the light to form an image at an image plane. 
     Example Embodiments 
       FIGS.  2 A through  8 C  show several example embodiments of freeform folded optical systems. These embodiments all include, in order along an optical axis from an object side of the system to an image side of the system, an objective lens, a first freeform optical prism, and a second freeform optical prism. In these embodiments, both the first freeform optical prism and the second freeform optical prism fold the optical axis twice as illustrated in  FIG.  1 A . 
     In these example embodiments, the objective lens is a rotationally symmetric singlet lens. In some embodiments, at least one of the surfaces of the objective lens is aspherical. In some embodiments, the objective lens has positive refractive power (i.e., is a converging lens). 
     In these example embodiments, the first freeform optical prism folds the optical axis twice, and the second freeform optical prism also folds the optical axis twice. A first surface of the first freeform optical prism is a transmitting and total internal reflection (TIR) surface, a second surface of the first freeform optical prism is a reflecting surface, and a third surface of the first freeform optical prism is a transmitting surface. A first surface of the second freeform optical prism is a transmitting surface, a second surface of the second freeform optical prism is a reflecting and TIR surface, and a third surface of the second freeform optical prism is a transmitting surface. The optical axis passes through the objective lens and the first surface of the first freeform optical prism and is folded by a mirror coating at the second surface of the first freeform optical prism. The optical axis is folded again at the first surface of the first freeform optical prism by TIR, passes through the third surface of the first freeform optical prism and the first surface of the second freeform optical prism, is folded by TIR at the second surface of the second freeform optical prism, and is folded again by a mirror coating at the third surface of the second freeform optical prism. The optical axis then passes through the second surface of the second freeform optical prism. 
     In these example embodiments, both the first freeform optical prism and the second freeform optical prism may have optical power. At least one surface of the first freeform optical prism and of the second freeform optical prism is a freeform surface. The objective lens, first freeform optical prism, and second freeform optical prism of the folded optical systems of  FIGS.  2 A through  8 C  affect light received from an object field to form an image at an image plane at or near a surface of an image sensor located on the image side of the second freeform prism. 
     The folded optical systems of  FIGS.  2 A through  8 C  may, but do not necessarily, include an infrared (IR) filter, for example located between the second surface of the second freeform prism and the image sensor. In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens (the principal plane is perpendicular to the optical axis of the objective lens). In these embodiments, referring to  FIG.  1   , AX 1  is thus parallel to AX 5 . 
     In these example embodiments, an angle θ between the first surface and the second surface of the first freeform prism may be less than or equal to 35 degrees, for example within a range of 29 to 35 degrees. For example, in some embodiments, angle A may be 30 degrees. In some embodiments, angle θ may be determined as the angle between a mean plane of the first surface of the first freeform prism and a mean plane of the second surface of the first freeform prism. In conventional folded lens systems, the angle between a first surface of a first prism and a second (reflective) surface of the first prism is typically 45 degrees. Reducing the angle between the first and second surfaces in the first freeform prism (and similarly reducing the angle between the second and third surfaces in the second freeform prism) helps to reduce the Z-height of the freeform folded optical system when compared to conventional folded lens systems, for example as illustrated in  FIG.  12   . 
     In these example embodiments, effective focal lengths are within a range of 9 to 31 millimeters (mm) while F-numbers are within a range of 2.0 to 4.0. Semi-diagonal image heights in these embodiments are within a range of 2.5 to 2.9 mm; 2.52 mm in the folded optical systems of  FIGS.  2 A through  7 C , and 2.822 in the folded optical system of  FIGS.  8 A through  8 C . Half field of view (FOV) in these embodiments fall within a range of 4.5 degrees to 16 degrees. These embodiments provide 35 mm equivalent focal lengths that fall within a range of 75 to 270 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of the objective lens, the first freeform prism, and the second freeform prism may be adjusted to provide freeform folded optical systems in which one or more of these optical characteristics is outside of these ranges. 
     In these example embodiments, the objective lens, the first freeform prism, and the second freeform prism are all formed of optical plastic materials. In some embodiments, one or more of the objective lens, first freeform prism, and second freeform prism may be formed using an injection molding process. However, in some embodiments, other methods may be used to form one or more of these elements (e.g., 3D printing, extrusion, blow molding, casting, rotomolding, die cast, overmolding, compression molding, computer numerical control (CNC) machining, thermoforming, etc.). In some embodiments, all three of these elements may be formed of the same optical plastic material. In some embodiments, at least two of the three elements are formed of different optical plastic materials. 
     The folded optical systems of  FIGS.  2 A through  8 C  may satisfy the following condition:
 
0.5&lt; B/A&lt; 0.1.0  (1)
 
where A is the optical power of the overall optical system, and B is the optical power of the objective lens. Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which an optical system or optical element converges or diverges light.
 
     The folded optical systems of  FIGS.  2 A through  8 C  may satisfy the following condition:
 
0.05&lt; AD&lt; 0.3  (2)
 
where A is the optical power of the overall optical system, and D is the semi-diagonal image height.
 
     In the folded optical systems of  FIGS.  2 A through  8 C , the objective lens is rotationally symmetric, and at least one of the two surfaces of the objective lens is aspherical. The objective lens may be composed of an optical plastic material (or, alternatively, of an optical glass material as illustrated in the example folded optical system of  FIGS.  8 A through  8 C ) with Abbe number V d1  that satisfies the following condition:
 
 V   d1 &gt;50.  (3)
 
     Using optical glass instead of plastic for the objective lens may, for example, reduce the thermal shift of focus and axial color aberrations. 
     In the folded optical systems of  FIGS.  2 A through  8 C , the first freeform prism is composed of an optical plastic material with Abbe number V d2  that satisfies the following condition:
 
 V   d2 &gt;50.  (4)
 
     In the folded optical systems of  FIGS.  2 A through  8 C , the second freeform prism is composed of an optical plastic material with Abbe number V d3  that satisfies the following condition:
 
 V   d3 &lt;25.  (5)
 
       FIG.  2 A  illustrates a first example embodiment of a freeform folded optical system.  FIG.  2 A  shows a cutaway view of a camera  100  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  140 , a first freeform optical prism  110 , and a second freeform optical prism  120 . The camera  100  may also include an image sensor  160  located on the image side of freeform optical prism  120 . The camera  100  may also include an aperture stop  130 , for example located on the object side of lens  140 . The camera  100  may also include an IR filter  150 , for example located between image sensor  160  and freeform optical prism  120 . The folded optical system of  FIG.  2 A  affects light received from an object field through aperture stop  130  to form an image at an image plane at or near a surface of the image sensor  160 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  140 . 
     Objective lens  140  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  140  may be aspherical. Objective lens  140  may have positive refractive power. Both freeform optical prism  110  and freeform optical prism  120  have optical power. At least one surface of freeform optical prism  110  and of freeform optical prism  120  is a freeform surface. 
     Freeform optical prism  110  folds the optical axis twice. A first surface  111  of freeform optical prism  110  is a transmitting and total internal reflection (TIR) surface, a second surface  112  of the freeform optical prism  110  is a reflecting surface, and a third surface  113  of freeform optical prism  110  is a transmitting surface. Freeform optical prism  120  also folds the optical axis twice. A first surface  121  of freeform optical prism  120  is a transmitting surface, a second surface  122  of freeform optical prism  120  is a reflecting and TIR surface, and a third surface  123  of freeform optical prism  120  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  2 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  2 A , effective focal length (f) is 10 mm, F-number is 2.0, semi-diagonal image height is 2.52 mm, half FOV is 14.1 degrees, and 35 mm equivalent focal length is 86 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  140 , freeform optical prism  110 , and freeform optical prism  120  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  100 . Tables 2A through 2K provide prescriptions for the optical elements of the example freeform folded optical system of camera  100 . 
       FIGS.  2 B and  2 C  illustrate optical performance for the freeform folded optical system of  FIG.  2 A .  FIG.  2 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  2 A . The frequency of MTF is 1251 p/mm.  FIG.  2 C  shows distortion for the freeform folded optical system of  FIG.  2 A . As shown by  FIGS.  2 B and  2 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  2 A  are good. 
       FIG.  3 A  illustrates a second example embodiment of a freeform folded optical system.  FIG.  3 A  shows a cutaway view of a camera  200  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  240 , a first freeform optical prism  210 , and a second freeform optical prism  220 . The camera  200  may also include an aperture stop, for example located on the object side of lens  240 . The camera  200  may also include an image sensor  260  located on the image side of freeform optical prism  220 . The camera  200  may also include an IR filter  250 , for example located between image sensor  260  and freeform optical prism  220 . The folded optical system of  FIG.  3 A  affects light received from an object field to form an image at an image plane at or near a surface of the image sensor  260 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  240 . 
     Objective lens  240  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  240  may be aspherical. Objective lens  240  may have positive refractive power. Both freeform optical prism  210  and freeform optical prism  220  have optical power. At least one surface of freeform optical prism  210  and of freeform optical prism  220  is a freeform surface. 
     Freeform optical prism  210  folds the optical axis twice. A first surface  211  of freeform optical prism  210  is a transmitting and total internal reflection (TIR) surface, a second surface  212  of the freeform optical prism  210  is a reflecting surface, and a third surface  213  of freeform optical prism  210  is a transmitting surface. Freeform optical prism  220  also folds the optical axis twice. A first surface  221  of freeform optical prism  220  is a transmitting surface, a second surface  222  of freeform optical prism  220  is a reflecting and TIR surface, and a third surface  223  of freeform optical prism  220  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  3 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  3 A , effective focal length is 12.24 mm, F-number is 2.0, semi-diagonal image height is 2.52 mm, half FOV is 11.6 degrees, and 35 mm equivalent focal length is 105 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  240 , freeform prism  210 , and freeform prism  220  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  200 . Tables 3A through 3K provide prescriptions for the optical elements of the example freeform folded optical system of camera  200 . 
       FIGS.  3 B and  3 C  illustrate optical performance for the freeform folded optical system of  FIG.  3 A .  FIG.  3 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  3 A . The frequency of MTF is 1251 p/mm.  FIG.  3 C  shows distortion for the freeform folded optical system of  FIG.  2 A . As shown by  FIGS.  3 B and  3 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  3 A  are good. 
       FIG.  4 A  illustrates a third example embodiment of a freeform folded optical system.  FIG.  4 A  shows a cutaway view of a camera  300  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  340 , a first freeform optical prism  310 , and a second freeform optical prism  320 . The camera  300  may also include an aperture stop, for example located on the object side of lens  340 . The camera  300  may also include an image sensor  360  located on the image side of freeform optical prism  320 . The camera  300  may also include an IR filter  350 , for example located between image sensor  360  and freeform optical prism  320 . The folded optical system of  FIG.  4 A  affects light received from an object field to form an image at an image plane at or near a surface of the image sensor  360 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  340 . 
     Objective lens  340  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  340  may be aspherical. Objective lens  340  may have positive refractive power. Both freeform optical prism  310  and freeform optical prism  320  have optical power. At least one surface of freeform optical prism  310  and of freeform optical prism  320  is a freeform surface. 
     Freeform optical prism  310  folds the optical axis twice. A first surface  311  of freeform optical prism  310  is a transmitting and total internal reflection (TIR) surface, a second surface  312  of the freeform optical prism  310  is a reflecting surface, and a third surface  313  of freeform optical prism  310  is a transmitting surface. Freeform optical prism  320  also folds the optical axis twice. A first surface  321  of freeform optical prism  320  is a transmitting surface, a second surface  322  of freeform optical prism  320  is a reflecting and TIR surface, and a third surface  323  of freeform optical prism  320  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  4 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  4 A , effective focal length is 15.3 mm, F-number is 2.2, semi-diagonal image height is 2.52 mm, half FOV is 9.4 degrees, and 35 mm equivalent focal length is 131 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  340 , freeform prism  310 , and freeform prism  320  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  300 . Tables 4A through 4K provide prescriptions for the optical elements of the example freeform folded optical system of camera  300 . 
       FIGS.  4 B and  4 C  illustrate optical performance for the freeform folded optical system of  FIG.  4 A .  FIG.  4 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  4 A . The frequency of MTF is 1251 p/mm.  FIG.  4 C  shows distortion for the freeform folded optical system of  FIG.  4 A . As shown by  FIGS.  4 B and  4 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  4 A  are good. 
       FIG.  5 A  illustrates a fourth example embodiment of a freeform folded optical system.  FIG.  5 A  shows a cutaway view of a camera  400  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  440 , a first freeform optical prism  410 , and a second freeform optical prism  420 . The camera  400  may also include an aperture stop, for example located on the object side of lens  440 . The camera  400  may also include an image sensor  460  located on the image side of freeform optical prism  420 . The camera  400  may also include an IR filter  450 , for example located between image sensor  460  and freeform optical prism  420 . The folded optical system of  FIG.  5 A  affects light received from an object field to form an image at an image plane at or near a surface of the image sensor  460 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  440 . 
     Objective lens  440  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  440  may be aspherical. Objective lens  440  may have positive refractive power. Both freeform optical prism  410  and freeform optical prism  420  have optical power. At least one surface of freeform optical prism  410  and of freeform optical prism  420  is a freeform surface. 
     Freeform optical prism  410  folds the optical axis twice. A first surface  411  of freeform optical prism  410  is a transmitting and total internal reflection (TIR) surface, a second surface  412  of the freeform optical prism  410  is a reflecting surface, and a third surface  413  of freeform optical prism  410  is a transmitting surface. Freeform optical prism  420  also folds the optical axis twice. A first surface  421  of freeform optical prism  420  is a transmitting surface, a second surface  422  of freeform optical prism  420  is a reflecting and TIR surface, and a third surface  423  of freeform optical prism  420  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  5 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  5 A , effective focal length is 18.36 mm, F-number is 2.3, semi-diagonal image height is 2.52 mm, half FOV is 7.8 degrees, and 35 mm equivalent focal length is 158 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  440 , freeform prism  410 , and freeform prism  420  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  400 . Tables 5A through 5K provide prescriptions for the optical elements of the example freeform folded optical system of camera  400 . 
       FIGS.  5 B and  5 C  illustrate optical performance for the freeform folded optical system of  FIG.  5 A .  FIG.  5 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  5 A . The frequency of MTF is 1251 p/mm.  FIG.  5 C  shows distortion for the freeform folded optical system of  FIG.  5 A . As shown by  FIGS.  5 B and  5 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  5 A  are good. 
       FIG.  6 A  illustrates a fifth example embodiment of a freeform folded optical system.  FIG.  6 A  shows a cutaway view of a camera  500  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  540 , a first freeform optical prism  510 , and a second freeform optical prism  520 . The camera  500  may also include an aperture stop, for example located on the object side of lens  540 . The camera  500  may also include an image sensor  560  located on the image side of freeform optical prism  520 . The camera  500  may also include an IR filter  550 , for example located between image sensor  560  and freeform optical prism  520 . The folded optical system of  FIG.  6 A  affects light received from an object field to form an image at an image plane at or near a surface of the image sensor  560 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  540 . 
     Objective lens  540  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  540  may be aspherical. Objective lens  540  may have positive refractive power. Both freeform optical prism  510  and freeform optical prism  520  have optical power. At least one surface of freeform optical prism  510  and of freeform optical prism  520  is a freeform surface. 
     Freeform optical prism  510  folds the optical axis twice. A first surface  511  of freeform optical prism  510  is a transmitting and total internal reflection (TIR) surface, a second surface  512  of the freeform optical prism  510  is a reflecting surface, and a third surface  513  of freeform optical prism  510  is a transmitting surface. Freeform optical prism  520  also folds the optical axis twice. A first surface  521  of freeform optical prism  520  is a transmitting surface, a second surface  522  of freeform optical prism  520  is a reflecting and TIR surface, and a third surface  523  of freeform optical prism  520  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  6 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  6 A , effective focal length is 24.48 mm, F-number is 3.2, semi-diagonal image height is 2.52 mm, half FOV is 5.9 degrees, and 35 mm equivalent focal length is 210 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  540 , freeform prism  510 , and freeform prism  520  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  500 . Tables 6A through 6K provide prescriptions for the optical elements of the example freeform folded optical system of camera  500 . 
       FIGS.  6 B and  6 C  illustrate optical performance for the freeform folded optical system of  FIG.  6 A .  FIG.  6 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  6 A . The frequency of MTF is 1251 p/mm.  FIG.  6 C  shows distortion for the freeform folded optical system of  FIG.  6 A . As shown by  FIGS.  6 B and  6 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  6 A  are good. 
       FIG.  7 A  illustrates a sixth example embodiment of a freeform folded optical system.  FIG.  7 A  shows a cutaway view of a camera  600  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  640 , a first freeform optical prism  610 , and a second freeform optical prism  620 . The camera  600  may also include an aperture stop, for example located on the object side of lens  640 . The camera  600  may also include an image sensor  660  located on the image side of freeform optical prism  620 . The camera  600  may also include an IR filter  650 , for example located between image sensor  660  and freeform optical prism  620 . The folded optical system of  FIG.  7 A  affects light received from an object field to form an image at an image plane at or near a surface of the image sensor  660 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  640 . 
     Objective lens  640  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  640  may be aspherical. Objective lens  640  may have positive refractive power. Both freeform optical prism  610  and freeform optical prism  620  have optical power. At least one surface of freeform optical prism  610  and of freeform optical prism  620  is a freeform surface. 
     Freeform optical prism  610  folds the optical axis twice. A first surface  611  of freeform optical prism  610  is a transmitting and total internal reflection (TIR) surface, a second surface  612  of the freeform optical prism  610  is a reflecting surface, and a third surface  613  of freeform optical prism  610  is a transmitting surface. Freeform optical prism  620  also folds the optical axis twice. A first surface  621  of freeform optical prism  620  is a transmitting surface, a second surface  622  of freeform optical prism  620  is a reflecting and TIR surface, and a third surface  623  of freeform optical prism  620  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  7 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  7 A , effective focal length is 30.6 mm, F-number is 4, semi-diagonal image height is 2.52 mm, half FOV is 4.7 degrees, and 35 mm equivalent focal length is 263 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  640 , freeform prism  610 , and freeform prism  620  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  600 . Tables 7A through 7K provide prescriptions for the optical elements of the example freeform folded optical system of camera  600 . 
       FIGS.  7 B and  7 C  illustrate optical performance for the freeform folded optical system of  FIG.  7 A .  FIG.  7 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  7 A . The frequency of MTF is 1251 p/mm.  FIG.  7 C  shows distortion for the freeform folded optical system of  FIG.  7 A . As shown by  FIGS.  7 B and  7 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  7 A  are good. 
       FIG.  8 A  illustrates a seventh example embodiment of a freeform folded optical system.  FIG.  8 A  shows a cutaway view of a camera  700  that may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  740 , a first freeform optical prism  710 , and a second freeform optical prism  720 . The camera  700  may also include an aperture stop, for example located on the object side of lens  740 . The camera  700  may also include an image sensor  760  located on the image side of freeform optical prism  720 . The camera  700  may also include an IR filter  750 , for example located between image sensor  760  and freeform optical prism  720 . The folded optical system of  FIG.  8 A  affects light received from an object field to form an image at an image plane at or near a surface of the image sensor  760 . In some embodiments, the image plane formed by the folded optical system is parallel to a principal plane of the objective lens  740 . 
     Objective lens  740  may be a rotationally symmetric singlet lens. At least one of the surfaces of objective lens  740  may be aspherical. Objective lens  740  may have positive refractive power. Objective lens  740  may be formed of an optical glass material. Using optical glass instead of plastic for the objective lens  740  may, for example, reduce the thermal shift of focus and axial color aberrations. Both freeform optical prism  710  and freeform optical prism  720  have optical power. At least one surface of freeform optical prism  710  and of freeform optical prism  720  is a freeform surface. 
     Freeform optical prism  710  folds the optical axis twice. A first surface  711  of freeform optical prism  710  is a transmitting and total internal reflection (TIR) surface, a second surface  712  of the freeform optical prism  710  is a reflecting surface, and a third surface  713  of freeform optical prism  710  is a transmitting surface. Freeform optical prism  720  also folds the optical axis twice. A first surface  721  of freeform optical prism  720  is a transmitting surface, a second surface  722  of freeform optical prism  720  is a reflecting and TIR surface, and a third surface  723  of freeform optical prism  720  is a transmitting surface. 
     The example freeform folded optical system shown in  FIG.  8 A  meets conditions 1 through 5 described above. In an example embodiment of a freeform folded optical system as shown in  FIG.  8 A , effective focal length is 17 mm, F-number is 2.8, semi-diagonal image height is 2.822 mm, half FOV is 9.4 degrees, and 35 mm equivalent focal length is 130 mm. Note, however, that shape, surface shape, spacing, materials, and other aspects of one or more of objective lens  740 , freeform prism  710 , and freeform prism  720  may be adjusted to change one or more of these optical characteristics. Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of camera  700 . 
       FIGS.  8 B and  8 C  illustrate optical performance for the freeform folded optical system of  FIG.  8 A .  FIG.  8 B  shows the modulation transfer function (MTF) for the freeform folded optical system of  FIG.  8 A . The frequency of MTF is 1251 p/mm.  FIG.  8 C  shows distortion for the freeform folded optical system of  FIG.  8 A . As shown by  FIGS.  8 B and  8 C , both the MTF and the distortion in the freeform folded optical system of  FIG.  8 A  are good. 
       FIGS.  9  through  12    illustrate various alternative embodiments of a freeform folded optical system. 
       FIG.  9    illustrates a freeform folded optical system that includes an objective lens composed of a glass material, according to some embodiments. A camera  900  may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  940 , a first freeform optical prism  910  that folds the optical axis twice, and a second freeform optical prism  920  that folds the optical axis twice. The camera  900  may also include an aperture stop, for example located on the object side of lens  940 . The camera  900  may also include an image sensor  960  located on the image side of freeform optical prism  920 . While not shown, the camera  900  may also include an IR filter, for example located between image sensor  960  and freeform optical prism  920 . 
     The freeform folded optical system of  FIG.  9    may correspond to or be similar to any of the example embodiments shown in  FIGS.  2 A through  8 C . The first freeform prism  910  and the second freeform prism  920  are formed of optical plastic materials. However, instead of being formed of an optical plastic material as in the example embodiments shown in  FIGS.  2 A through  7 C , lens  940  is a glass lens. In the example embodiment  800  shown in  FIGS.  8 A through  8 C , lens  740  is a glass lens. Using optical glass instead of plastic for the objective lens  940  may, for example, aid in correcting aberrations. More precisely, using optical glass instead of plastic for the objective lens  940  may reduce the thermal shift of focus and axial color aberrations. 
       FIG.  10    illustrates a freeform folded optical system in which the objective lens is a doublet lens, according to some embodiments. A camera  1000  may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, an objective lens  1040 , a first freeform optical prism  1010  that folds the optical axis twice, and a second freeform optical prism  1020  that folds the optical axis twice. The camera  1000  may also include an aperture stop, for example located on the object side of lens  1040 . The camera  1000  may also include an image sensor  1060  located on the image side of freeform optical prism  1020 . While not shown, the camera  1000  may also include an IR filter, for example located between image sensor  1060  and freeform optical prism  1020 . 
     The freeform folded optical system of  FIG.  10    may correspond to or be similar to any of the example embodiments shown in  FIGS.  2 A through  8 C . However, instead of being a singlet lens, lens  1040  is a doublet. Using a doublet lens for the objective lens  1040  may, for example, aid in correcting aberrations. In some embodiments, both of the lens elements in the doublet lens  1040  may be composed of optical plastic. Alternatively, one or both of the lens elements in the doublet lens may be composed of optical glass. 
       FIG.  11    illustrates a freeform folded optical system that does not include an objective lens, according to some embodiments. A camera  1100  may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, a first freeform optical prism  1110  that folds the optical axis twice, and a second freeform optical prism  1120  that folds the optical axis twice. The camera  1100  may also include an aperture stop, for example located on the object side of prism  1110 . The camera  1100  may also include an image sensor  1160  located on the image side of freeform optical prism  1120 . While not shown, the camera  1100  may also include an IR filter, for example located between image sensor  1160  and freeform optical prism  1120 . 
       FIG.  12    illustrates a freeform folded optical system that folds the optical axis three times rather than four times, according to some embodiments. A camera  1200  may include a freeform folded optical system that includes, in order along an optical axis from an object side of the system to an image side of the system, a first freeform optical prism  1210  that folds the optical axis twice, and a second freeform optical prism  1220  that folds the optical axis once. 
     Referring to the first freeform prism  1210 , a first surface  1211  is a transmitting and TIR surface that transmits light received from an object field and reflects light received from a second surface  1212  in the prism by TIR to a third surface  1213 . The second surface  1212  is a reflecting surface coated with a mirror coating that reflects light received through the first surface  1211  back to the first surface  1211  in the prism  101 . The third surface  1213  is a transmitting surface that transmits light received from the first surface  1211 . At least one of the three surfaces  1211 ,  1212 , and  1213  is a freeform surface. 
     Referring to the second freeform prism  1220 , a first surface  1221  is a transmitting surface that transmits light received from the first prism  1210  to a second surface  1222  in the prism  1220 . The second surface  1222  is a reflecting surface that reflects light received through the first surface  1221  to the third surface  1223  in the prism  1220 . The second surface  1222  may be coated with a mirror coating, or alternatively may reflect light via total internal reflection. The third surface  1223  is a transmitting surface that transmits light received from the second surface  1222  to form an image at an image plane. At least one of the three surfaces  1221 ,  1222 , and  1223  is a freeform surface. 
     The camera  1200  may also include an aperture stop, for example located on the object side of freeform optical prism  1210 . The camera  1200  may also include an image sensor  1260  located on the image side of freeform optical prism  1220 . While not shown, the camera  1200  may also include an IR filter, for example located between image sensor  1260  and freeform optical prism  1220 . While not shown, the camera  1200  may also include an objective lens located on the object side of freeform optical prism  1210 . The objective lens may be a singlet lens composed of optical plastic or glass, or a doublet lens that includes two optical plastic or glass lens elements. 
       FIGS.  13 A through  13 C  compare an embodiment of the freeform folded optical system to a conventional folded lens system.  FIG.  13 A  is a side view that compares a camera  1300  with a conventional folded lens system (top) to a camera with a freeform folded optical system (bottom), for example a camera  200  as illustrated in  FIG.  3 A . Camera  1300  has a conventional folded lens system that includes, in order from an object side to an image side, a first prism  1310 , a lens stack  1330 , and a second prism  1320 . The conventional folded lens system affects light received at an object side of the first prism  1310  to form an image at an image plane on the image side of the second prism  1320 . Camera  200  has a freeform folded optical system that includes, in order from an object side to an image side, a lens  240 , a first freeform prism  210 , and a second freeform prism  220 . The freeform folded optical system affects light received at an object side of lens  240  to form an image at an image plane on the image side of the second freeform prism  220 . 
     In conventional folded lens systems as shown in camera  1300 , the angle θ between a first surface of the first prism  1310  and a second (reflective) surface of the first prism  1310  is typically 45 degrees. Z-height of the example camera  1300  (measured from the object side surface of the first prism  1310  to the image plane) is 7.6 mm. In a freeform folded optical system as shown in camera  200 , the angle θ between a first surface of the first prism  210  and the second surface of the first prism  210  is less than or equal to 35 degrees, for example within a range of 29 to 35 degrees. For example, in some embodiments, angle A may be 30 degrees. Z-height of the example camera  200  (measured from the apex of the object side surface of lens  240  to the image plane) is 5 mm. Reducing the angle between the first and second surfaces in the first freeform prism  210  (and similarly reducing the angle between the second and third surfaces in the second freeform prism  220 ) thus helps to reduce the Z-height of a camera  200  including a freeform folded optical system significantly when compared cameras  1300  including conventional folded lens systems. 
     Embodiments of the freeform folded optical system as described herein may provide lower F-numbers at similar effective focal lengths when compared to conventional folded lens systems. For example, the example conventional folded lens system in camera  1300  may have an effective focal length of ˜12.24 mm, with an F-number of ˜2.2. The freeform folded optical system in camera  200  may have an effective focal length of 12.24 mm, with an F-number of 2.0. 
       FIG.  13 B  compares the modulation transfer function (MTF) of the conventional folded optical system in camera  1300  shown in  FIG.  13 A  to the MTF of the freeform folded optical system in camera  200  shown in  FIG.  13 A .  FIG.  13 C  compares distortion of the conventional folded optical system in camera  1300  shown in  FIG.  13 A  to distortion of the freeform folded optical system in camera  200  shown in  FIG.  13 A . As can be seen from  FIGS.  13 B and  13 C , the freeform folded optical system performs well when compared to the conventional folded optical system. 
     Numerical Examples and Tables 
     Table 1 provides values for various optical and physical parameters of the example freeform folded optical systems of cameras  100 ,  200 ,  300 ,  400 ,  500 ,  600 , and  700  as described in  FIGS.  2 A through  8 C , as well as ranges for some of the parameters. In Table 1, A is the optical power of the overall optical system, B is the optical power of the objective lens, and D is the semi-diagonal image height (SDIH). The optical elements (e.g., the objective lens, first prism, and second prism) are designated by d 1 , d 2 , and d 3 , respectively. N is the refractive index of a respective optical element (e.g., Nd 1  is the refractive index of the objective lens), and V is the Abbe number of a respective optical element (e.g., Vd 1  is the Abbe number of the objective lens). EFL is effective focal length of the system, and Fno is the F-number of the optical system. Angle θ is the angle between a first surface of the first prism and a second (reflective) surface of the first prism. Half FOV is half field of view, and 35 mm EFL is 35 mm equivalent focal length. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Parameter 
                 Range 
                 100 
                 200 
                 300 
                 400 
                 500 
                 600 
                 700 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 1/A 
                 — 
                 10 
                 12.24 
                 15.3 
                 18.36 
                 24.48 
                 30.6 
                 17 
               
               
                 1/B 
                 — 
                 14.071 
                 18.68 
                 23.06 
                 18.42 
                 26.0545 
                 39.9823 
                 17.885 
               
               
                 A 
                 — 
                 0.100 
                 0.082 
                 0.065 
                 0.054 
                 0.041 
                 0.033 
                 0.059 
               
               
                 B 
                 — 
                 0.071 
                 0.054 
                 0.043 
                 0.054 
                 0.038 
                 0.025 
                 0.056 
               
               
                 B/A 
                 0.5-1.0 
                 0.71 
                 0.66 
                 0.66 
                 0.997 
                 0.94 
                 0.77 
                 0.95 
               
               
                 D 
                   
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.82 
               
               
                 AD 
                 0.05-0.3  
                 0.252 
                 0.206 
                 0.165 
                 0.137 
                 0.103 
                 0.082 
                 0.166 
               
               
                 Nd1 
                 — 
                 1.544 
                 1.544 
                 1.545 
                 1.544 
                 1.544 
                 1.544 
                 1.589 
               
               
                 Nd2 
                 — 
                 1.544 
                 1.544 
                 1.545 
                 1.544 
                 1.544 
                 1.544 
                 1.544 
               
               
                 Nd3 
                 — 
                 1.671 
                 1.671 
                 1.640 
                 1.671 
                 1.671 
                 1.671 
                 1.640 
               
               
                 Vd1 
                 &gt;50 
                 55.97 
                 55.97 
                 55.96 
                 55.97 
                 55.97 
                 55.97 
                 61.14 
               
               
                 Vd2 
                 &gt;50 
                 55.97 
                 55.97 
                 55.96 
                 55.97 
                 55.97 
                 55.97 
                 55.96 
               
               
                 Vd3 
                 &lt;25 
                 19.23 
                 19.23 
                 23.52 
                 19.23 
                 19.23 
                 19.23 
                 23.52 
               
               
                 EFL 
                  9-31 
                 10 
                 12.24 
                 15.3 
                 18.36 
                 24.48 
                 30.6 
                 17 
               
               
                 Fno 
                 2.0-4.0 
                 2.0 
                 2.0 
                 2.2 
                 2.3 
                 3.2 
                 4.0 
                 2.8 
               
               
                 SDIH 
                 2.5-2.9 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.52 
                 2.822 
               
               
                 Angle θ 
                 29°-35° 
                 29° 
                 30° 
                 30° 
                 30° 
                 30° 
                 31° 
                 30° 
               
               
                 Half FOV 
                 4.5-16  
                 14.1 
                 11.6 
                 9.4 
                 7.8 
                 5.9 
                 4.7 
                 9.4 
               
               
                 35 mm EFL 
                  75-270 
                 86 
                 105 
                 131 
                 158 
                 210 
                 263 
                 130 
               
               
                   
               
            
           
         
       
     
     Tables 2A through 8K provide prescriptions for the optical elements of the example freeform folded optical systems of cameras  100 ,  200 ,  300 ,  400 ,  500 ,  600 , and  700  as described in reference to  FIGS.  2 A through  8 C .  FIG.  14    shows labels designating the optical elements and surfaces of the optical elements that are used in Tables 2A through 8K. The objective lens is designated L 1 , the first prism is designated P 1 , and the second prism is designated P 2 . From the object side of the system along the optical axis, the surfaces are designated as L 1 R 1 , L 1 R 2 , P 1 S 1 , P 1 S 2 , P 1 S 3 , P 2 S 1 , P 2 S 2 , and P 2 S 3 . Surface locations are determined by global coordinates based on L 1 R 1  (i.e., the apex of surface R 1  is an origin (0,0), with the Y and Z axes shown). While not shown in  FIG.  14   , an aperture stop may be located on the object side of the objective lens (L 1 ). The aperture stop and the image plane are also considered surfaces in the Tables. 
     Tables 2A through 2K provide prescriptions for the optical elements of the example freeform folded optical system of camera  100  as described in reference to  FIGS.  2 A through  2 C . Tables 2A through 2D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  100 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2A 
               
             
            
               
                   
                   
               
               
                   
                 L1 
                   
               
            
           
           
               
               
               
            
               
                   
                 R1 
                 R2 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Z 
                 0.0000E+00 
                 6.8500E−01 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                   
                 TABLE 2B 
               
             
            
               
                   
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 −1.8716E+00  
                 2.2204E−16 
                 −5.6451E+00  
               
               
                 Z 
                 7.7306E−01 
                 2.7689E+00 
                 2.5755E+00 
               
               
                 angle of each surface 
                 7.4250E+00 
                 −2.1580E+01  
                 5.7031E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                   
                 TABLE 2C 
               
             
            
               
                   
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 −5.8661E+00  
                 −1.0392E+01  
                 −1.1653E+01  
               
               
                 Z 
                 1.6063E+00 
                 3.7307E+00 
                 2.7882E+00 
               
               
                 angle of each surface 
                 6.4858E+01 
                 5.8192E+00 
                 −2.6610E+01  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2D 
               
               
                   
                   
               
               
                   
                 aperture 
                 Image plane 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 −1.0035E+01  
               
               
                   
                 Z 
                 −1.0000E−01  
                 5.0000E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Table 2E shows the aspherical coefficients of surfaces R 1  and R 2  of L 1  for the freeform folded optical system of camera  100 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2E 
               
               
                   
                   
               
               
                   
                 R1 
                 R2 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Radius of curvature 
                  9.6851E+00 
                 −3.5850E+01 
               
               
                   
                 4th order 
                 −4.1081E−04 
                 −2.2926E−04 
               
               
                   
                 6th order 
                 −3.4319E−07 
                  1.3412E−05 
               
               
                   
                 8th order 
                 −2.5887E−06 
                 −2.9379E−06 
               
               
                   
                 10th order 
                  1.4052E−07 
                  1.8324E−07 
               
               
                   
                   
               
            
           
         
       
     
     Tables 2F through 2H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the freeform folded optical system of camera  100 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 2F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 1.2328E−03 
                 Y2: 
                 4.3111E−03 
                 X2Y: 
                 3.6478E−04 
               
               
                 Y3: 
                 3.6150E−04 
                 X4: 
                 4.0324E−05 
                 X2Y2: 
                 −1.9567E−05  
               
               
                 Y4: 
                 −9.2506E−07  
                 X4Y: 
                 −2.5607E−05  
                 X2Y3: 
                 −7.2075E−06  
               
               
                 Y5: 
                 3.5850E−06 
                 X6: 
                 2.9916E−06 
                 X4Y2: 
                 6.1786E−07 
               
               
                 X2Y4: 
                 −9.9562E−07  
                 Y6: 
                 −1.1106E−07  
                 X6Y: 
                 2.6702E−07 
               
               
                 X4Y3: 
                 3.4933E−07 
                 X2Y5: 
                 −3.2195E−08  
                 Y7: 
                 2.9442E−08 
               
               
                 X8: 
                 −7.9587E−08  
                 X6Y2: 
                 6.5762E−08 
                 X4Y4: 
                 −7.2555E−09  
               
               
                 X2Y6: 
                 −6.3510E−08  
                 Y8: 
                 −1.4553E−09  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 5.1746E−04 
                 Y2: 
                 3.5742E−03 
                 X2Y: 
                 4.8065E−04 
               
               
                 Y3: 
                 9.8164E−04 
                 X4: 
                 5.5470E−05 
                 X2Y2: 
                 6.2326E−05 
               
               
                 Y4: 
                 1.0288E−04 
                 X4Y: 
                 −1.4649E−05  
                 X2Y3: 
                 −7.0812E−06  
               
               
                 Y5: 
                 1.3998E−05 
                 X6: 
                 9.0699E−07 
                 X4Y2: 
                 −4.8501E−06  
               
               
                 X2Y4: 
                 −6.8238E−06  
                 Y6: 
                 1.3164E−06 
                 X6Y: 
                 3.2005E−07 
               
               
                 X4Y3: 
                 5.9569E−07 
                 X2Y5: 
                 −2.1128E−07  
                 Y7: 
                 4.7924E−07 
               
               
                 X8: 
                 1.1881E−08 
                 X6Y2: 
                 6.1828E−07 
                 X4Y4: 
                 9.2337E−07 
               
               
                 X2Y6: 
                 1.5008E−07 
                 Y8: 
                 6.4118E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of curvature 
                 −5.4296E+00  
                   
                   
                   
                   
               
               
                 ZP1: 
                 1.1270E−01 
                 ZP3: 
                  7.7990E−02 
                 ZP4: 
                 −2.3789E−02 
               
               
                 ZP5: 
                 −5.6901E−03  
                 ZP9: 
                  6.1637E−03 
                 ZP10: 
                  1.8562E−02 
               
               
                 ZP11: 
                 3.1953E−03 
                 ZP12: 
                  1.4158E−02 
                 ZP13: 
                  1.9125E−02 
               
               
                 ZP19: 
                 7.1611E−03 
                 ZP20: 
                 −1.8737E−03 
                 ZP21: 
                  3.5065E−04 
               
               
                 ZP22: 
                 1.1161E−03 
                 ZP23: 
                  8.9128E−04 
                 ZP24: 
                 −2.4812E−03 
               
               
                 ZP25: 
                 −1.7085E−03  
                 ZP33: 
                 −1.1747E−04 
                 ZP34: 
                 −6.1182E−04 
               
               
                 ZP35: 
                 2.1134E−04 
                 ZP36: 
                 −1.6513E−03 
                 ZP37: 
                 −4.6628E−04 
               
               
                 ZP38: 
                 2.1694E−04 
                 ZP39: 
                 −3.6364E−04 
                 ZP40: 
                  8.3883E−04 
               
               
                 ZP41: 
                 2.7900E−04 
                 ZP51: 
                  3.2965E−04 
                 ZP52: 
                 −1.9495E−04 
               
               
                 ZP53: 
                 3.3374E−04 
                 ZP54: 
                 −1.6678E−04 
                 ZP55: 
                  4.3056E−04 
               
               
                 ZP56: 
                 1.6211E−04 
                 ZP57: 
                 −4.2780E−05 
                 ZP58: 
                  4.7369E−05 
               
               
                 ZP59: 
                 −8.1842E−05  
                 ZP60: 
                 −7.9380E−05 
                 ZP61: 
                 −8.1680E−05 
               
               
                 NRADIUS: 
                 3.0498E+00 
               
               
                   
               
            
           
         
       
     
     Tables 2I through 2K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  100 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 21 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of curvature 
                 −5.6610E+00  
                   
                   
                   
                   
               
               
                 ZP1: 
                 1.0952E+00 
                 ZP3: 
                  9.8386E−02 
                 ZP4: 
                 −2.7527E−02 
               
               
                 ZP5: 
                 3.0773E−02 
                 ZP9: 
                 −1.8532E−02 
                 ZP10: 
                  6.8280E−02 
               
               
                 ZP11: 
                 −1.0050E−02  
                 ZP12: 
                  5.0446E−04 
                 ZP13: 
                  1.3270E−02 
               
               
                 ZP19: 
                 −5.7044E−03  
                 ZP20: 
                  3.1674E−03 
                 ZP21: 
                  4.4215E−02 
               
               
                 ZP22: 
                 3.3890E−02 
                 ZP23: 
                 −9.7978E−03 
                 ZP24: 
                 −7.5249E−03 
               
               
                 ZP25: 
                 4.7831E−03 
                 ZP33: 
                 −4.6537E−03 
                 ZP34: 
                 −2.4610E−03 
               
               
                 ZP35: 
                 7.2143E−03 
                 ZP36: 
                 −1.7016E−02 
                 ZP37: 
                 −6.4307E−03 
               
               
                 ZP38: 
                 2.4255E−03 
                 ZP39: 
                 −2.5328E−04 
                 ZP40: 
                 −1.8655E−03 
               
               
                 ZP41: 
                 1.5220E−03 
                 ZP51: 
                 −1.1014E−03 
                 ZP52: 
                  1.2248E−03 
               
               
                 ZP53: 
                 2.9369E−04 
                 ZP54: 
                  1.5656E−04 
                 ZP55: 
                  2.6684E−03 
               
               
                 ZP56: 
                 5.3612E−04 
                 ZP57: 
                  1.1697E−04 
                 ZP58: 
                 −1.1903E−04 
               
               
                 ZP59: 
                 6.5491E−05 
                 ZP60: 
                 −4.2175E−04 
                 ZP61: 
                  6.8164E−05 
               
               
                 NRADIUS: 
                 3.0498E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 7.3128E−03 
                 Y2: 
                 1.3389E−02 
                 X2Y: 
                 −8.6068E−04 
               
               
                 Y3: 
                 −7.0201E−04  
                 X4: 
                 2.0413E−04 
                 X2Y2: 
                  4.4963E−05 
               
               
                 Y4: 
                 −1.4962E−04  
                 X4Y: 
                 −2.9382E−05  
                 X2Y3: 
                 −2.3458E−05 
               
               
                 Y5: 
                 2.4463E−05 
                 X6: 
                 1.8794E−05 
                 X4Y2: 
                  5.9414E−06 
               
               
                 X2Y4: 
                 3.4009E−06 
                 Y6: 
                 −8.9834E−07  
                 X6Y: 
                 −9.1301E−06 
               
               
                 X4Y3: 
                 −1.7092E−06  
                 X2Y5: 
                 −2.8930E−07  
                 Y7: 
                 −1.8104E−09 
               
               
                 X8: 
                 5.5755E−07 
                 X6Y2: 
                 3.6949E−07 
                 X4Y4: 
                  2.1167E−07 
               
               
                 X2Y6: 
                 1.7270E−08 
                 Y8: 
                 2.5066E−09 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2K 
               
               
                   
               
               
                 P2S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                  2.0725E−02 
                 Y2: 
                 3.8371E−02 
                 X2Y: 
                 −2.4160E−03  
               
               
                 Y3: 
                 −2.6147E−03 
                 X4: 
                 2.3937E−04 
                 X2Y2: 
                 4.3054E−04 
               
               
                 Y4: 
                 −3.5917E−04 
                 X4Y: 
                 −1.9644E−04  
                 X2Y3: 
                 −8.0213E−05  
               
               
                 Y5: 
                  1.3522E−04 
                 X6: 
                 1.5783E−05 
                 X4Y2: 
                 4.8256E−05 
               
               
                 X2Y4: 
                 −5.6418E−06 
                 Y6: 
                 −1.3096E−05  
                 X6Y: 
                 −4.2369E−06  
               
               
                 X4Y3: 
                 −8.9815E−06 
                 X2Y5: 
                 3.5679E−06 
                 Y7: 
                 5.1763E−08 
               
               
                 X8: 
                 −1.7716E−07 
                 X6Y2: 
                 2.3145E−07 
                 X4Y4: 
                 8.3435E−07 
               
               
                 X2Y6: 
                 −4.9429E−07 
                 Y8: 
                 −1.1385E−08  
               
               
                   
               
            
           
         
       
     
     Tables 3A through 3K provide prescriptions for the optical elements of the example freeform folded optical system of camera  200  as described in reference to  FIGS.  3 A through  3 C . Tables 3A through 3D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  200 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3A 
               
             
            
               
                   
                   
               
               
                   
                 L1 
                   
               
            
           
           
               
               
               
            
               
                   
                 R1 
                 R2 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Z 
                 0.0000E+00 
                 7.7203E−01 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                   
                 TABLE 3B 
               
             
            
               
                   
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 −2.3961E+00  
                 −4.4409E−16  
                 −6.5438E+00  
               
               
                 Z 
                 1.1043E+00 
                 3.6551E+00 
                 2.5980E+00 
               
               
                 angle of each surface 
                 8.2193E+00 
                 −2.1605E+01  
                 5.7447E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                   
                 TABLE 3C 
               
             
            
               
                   
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 −6.0633E+00  
                 −1.0247E+01  
                 −1.2020E+01  
               
               
                 Z 
                 2.0153E+00 
                 3.9299E+00 
                 2.5971E+00 
               
               
                 angle of each surface 
                 6.5410E+01 
                 6.1751E+00 
                 −2.6530E+01  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3D 
               
               
                   
                   
               
               
                   
                 aperture 
                 Image plane 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 −1.1044E+01  
               
               
                   
                 Z 
                 0.0000E+00 
                 5.7500E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Table 3E shows the aspherical coefficients of surfaces R 1  and R 2  of L for the freeform folded optical system of camera  200 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3E 
               
               
                   
                   
               
               
                   
                 R1 
                 R2 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Radius of curvature 
                  1.2908E+01 
                 −4.7064E+01 
               
               
                   
                 4th order 
                 −2.5061E−04 
                 −1.0392E−04 
               
               
                   
                 6th order 
                 −1.8682E−06 
                 −9.1017E−07 
               
               
                   
                 8th order 
                 −6.1682E−07 
                 −4.5580E−07 
               
               
                   
                   
               
            
           
         
       
     
     Tables 3F through 3H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the example freeform folded optical system of camera  200 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 3F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −3.5095E−03 
                 Y2: 
                  2.9289E−03 
                 X2Y: 
                 5.5317E−04 
               
               
                 Y3: 
                  4.5481E−04 
                 X4: 
                  3.4693E−05 
                 X2Y2: 
                 −7.2200E−05  
               
               
                 Y4: 
                 −1.8307E−05 
                 X4Y: 
                 −1.0340E−05 
                 X2Y3: 
                 4.0330E−06 
               
               
                 Y5: 
                  4.0167E−06 
                 X6: 
                  2.8135E−06 
                 X4Y2: 
                 2.5033E−06 
               
               
                 X2Y4: 
                 −1.3309E−06 
                 Y6: 
                 −8.1114E−08 
                 X6Y: 
                 −2.9519E−07  
               
               
                 X4Y3: 
                  2.4244E−08 
                 X2Y5: 
                  1.3772E−07 
                 Y7: 
                 1.4765E−08 
               
               
                 X8: 
                 −1.0841E−07 
                 X6Y2: 
                 −1.6783E−07 
                 X4Y4: 
                 −1.0881E−07  
               
               
                 X2Y6: 
                 −5.1891E−08 
                 Y8: 
                 −1.4786E−09 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −3.7256E−03 
                 Y2: 
                 −1.3926E−03 
                 X2Y: 
                   5.5215E−04 
               
               
                 Y3: 
                   9.3941E−04 
                 X4: 
                   2.2343E−05 
                 X2Y2: 
                 −3.8240E−05 
               
               
                 Y4: 
                   5.5463E−05 
                 X4Y: 
                 −1.3872E−06 
                 X2Y3: 
                   3.4788E−06 
               
               
                 Y5: 
                   1.2334E−05 
                 X6: 
                   1.4161E−06 
                 X4Y2: 
                   1.0258E−06 
               
               
                 X2Y4: 
                 −4.8210E−07 
                 Y6: 
                   1.9497E−06 
                 X6Y: 
                 −2.5124E−07 
               
               
                 X4Y3: 
                   2.1663E−07 
                 X2Y5: 
                 −6.8913E−08 
                 Y7: 
                   4.3985E−07 
               
               
                 X8: 
                 −5.9539E−08 
                 X6Y2: 
                 −2.9123E−08 
                 X4Y4: 
                   4.1044E−08 
               
               
                 X2Y6: 
                 −9.2035E−08 
                 Y8: 
                   2.6111E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of 
                 −4.9093E+00 
                   
                   
                   
                   
               
               
                 curvature 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                   2.3020E−01 
                 ZP3: 
                  8.2483E−02 
                 ZP4: 
                 −8.4278E−02 
               
               
                 ZP5: 
                   3.5161E−01 
                 ZP9: 
                  6.9965E−02 
                 ZP10: 
                   4.0886E−02 
               
               
                 ZP11: 
                   1.5798E−03 
                 ZP12: 
                  4.6503E−02 
                 ZP13: 
                   7.0710E−02 
               
               
                 ZP19: 
                   2.7145E−02 
                 ZP20: 
                 −2.0862E−02 
                 ZP21: 
                   3.0212E−02 
               
               
                 ZP22: 
                   4.0310E−02 
                 ZP23: 
                 −1.6333E−02 
                 ZP24: 
                   4.5817E−03 
               
               
                 ZP25: 
                   9.0657E−03 
                 ZP33: 
                 −1.0761E−03 
                 ZP34: 
                 −1.0716E−02 
               
               
                 ZP35: 
                   1.6367E−02 
                 ZP36: 
                 −3.2069E−02 
                 ZP37: 
                 −1.6126E−02 
               
               
                 ZP38: 
                   7.3529E−03 
                 ZP39: 
                 −6.5426E−03 
                 ZP40: 
                   2.0706E−03 
               
               
                 ZP41: 
                   3.3486E−03 
                 ZP51: 
                   2.2953E−04 
                 ZP52: 
                 −5.2360E−04 
               
               
                 ZP53: 
                   1.9069E−03 
                 ZP54: 
                 −2.2496E−03 
                 ZP55: 
                   6.4244E−03 
               
               
                 ZP56: 
                   7.6338E−04 
                 ZP57: 
                 −2.3103E−04 
                 ZP58: 
                 −8.3918E−05 
               
               
                 ZP59: 
                 −1.0706E−04 
                 ZP60: 
                 −6.2087E−04 
                 ZP61: 
                   1.0956E−04 
               
               
                 NRADIUS: 
                   4.0000E+00 
               
               
                   
               
            
           
         
       
     
     Tables 3I through 3K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  200 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 3I 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of 
                 −5.9766E+00 
                   
                   
                   
                   
               
               
                 curvature 
                   
                   
                   
                   
                   
               
               
                 ZP5: 
                   4.0930E−01 
                 ZP9: 
                   7.1930E−01 
                 ZP10: 
                 −9.8304E−01 
               
               
                 ZP11: 
                 −5.2634E−01 
                 ZP12: 
                   2.7501E−01 
                 ZP13: 
                   1.5788E−01 
               
               
                 ZP19: 
                   2.9383E−01 
                 ZP20: 
                 −5.7483E−01 
                 ZP21: 
                   7.5375E−01 
               
               
                 ZP22: 
                   2.2443E−01 
                 ZP23: 
                 −2.5236E−01 
                 ZP24: 
                   9.5702E−02 
               
               
                 ZP25: 
                   6.9367E−02 
                 ZP33: 
                   2.0166E−02 
                 ZP34: 
                 −1.2217E−01 
               
               
                 ZP35: 
                   1.2633E−01 
                 ZP36: 
                 −1.5532E−01 
                 ZP37: 
                   2.8595E−02 
               
               
                 ZP38: 
                 −3.5080E−02 
                 ZP39: 
                 −5.5277E−02 
                 ZP40: 
                   2.4987E−02 
               
               
                 ZP41: 
                   1.2333E−02 
                 ZP51: 
                 −1.4053E−04 
                 ZP52: 
                   2.2209E−03 
               
               
                 ZP53: 
                 −1.6432E−03 
                 ZP54: 
                   1.5347E−02 
                 ZP55: 
                   2.1915E−02 
               
               
                 ZP56: 
                 −2.7735E−02 
                 ZP57: 
                   1.9440E−02 
                 ZP58: 
                 −1.2007E−02 
               
               
                 ZP59: 
                 −3.9521E−03 
                 ZP60: 
                 −8.2731E−04 
                 ZP61: 
                 −2.2128E−04 
               
               
                 NRADIUS: 
                   5.0000E+00 
                   
                   
                   
                   
               
               
                 Radius of 
                 −5.9766E+00 
                   
                   
                   
                   
               
               
                 curvature 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −6.3897E−04 
                 Y2: 
                   1.7737E−02 
                 X2Y: 
                 −8.2134E−04 
               
               
                 Y3: 
                 −3.7734E−04 
                 X4: 
                   2.2350E−04 
                 X2Y2: 
                 −9.9851E−05 
               
               
                 Y4: 
                 −1.1818E−04 
                 X4Y: 
                 −7.0096E−05 
                 X2Y3: 
                   2.1693E−06 
               
               
                 Y5: 
                   2.2662E−05 
                 X6: 
                   3.1002E−06 
                 X4Y2: 
                   1.1461E−05 
               
               
                 X2Y4: 
                   1.8293E−06 
                 Y6: 
                 −1.4023E−06 
                 X6Y: 
                 −1.1191E−06 
               
               
                 X4Y3: 
                 −3.4267E−06 
                 X2Y5: 
                 −6.2429E−07 
                 Y7: 
                 −1.2591E−07 
               
               
                 X8: 
                   5.3797E−08 
                 X6Y2: 
                 −1.1617E−07 
                 X4Y4: 
                   4.6304E−07 
               
               
                 X2Y6: 
                   6.3632E−08 
                 Y8: 
                   6.8996E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3K 
               
               
                   
               
               
                 P2S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                   3.2160E−03 
                 Y2: 
                   3.9372E−02 
                 X2Y: 
                 −1.1659E−03 
               
               
                 Y3: 
                 −2.0014E−03 
                 X4: 
                   2.7091E−04 
                 X2Y2: 
                   1.4532E−04 
               
               
                 Y4: 
                 −4.0006E−05 
                 X4Y: 
                 −1.8054E−04 
                 X2Y3: 
                 −6.9765E−05 
               
               
                 Y5: 
                   6.3982E−05 
                 X6: 
                   2.6133E−07 
                 X4Y2: 
                   3.2422E−05 
               
               
                 X2Y4: 
                   8.5557E−06 
                 Y6: 
                 −1.2349E−05 
                 X6Y: 
                   2.6745E−06 
               
               
                 X4Y3: 
                 −8.3419E−06 
                 X2Y5: 
                 −2.5074E−06 
                 Y7: 
                   7.7794E−07 
               
               
                 X8: 
                 −2.0461E−07 
                 X6Y2: 
                 −6.4072E−07 
                 X4Y4: 
                   1.4627E−06 
               
               
                 X2Y6: 
                   1.8704E−07 
                 Y8: 
                 −1.8362E−08 
               
               
                   
               
            
           
         
       
     
     Tables 4A through 4K provide prescriptions for the optical elements of the example freeform folded optical system of camera  300  as described in reference to  FIGS.  4 A through  4 C . Tables 4A through 4D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  300 . 
     
       
         
           
               
               
             
               
                 TABLE 4A 
               
             
            
               
                   
               
               
                   
                 L1 
               
            
           
           
               
               
               
            
               
                   
                 R1 
                 R2 
               
               
                   
               
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Z 
                 0.0000E+00 
                 1.0740E+00 
               
               
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 4B 
               
             
            
               
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                   0.0000E+00 
                   0.0000E+00 
                   0.0000E+00 
               
               
                 Y 
                 −2.8639E+00 
                   8.8818E−16 
                 −7.5501E+00 
               
               
                 Z 
                   1.2177E+00 
                   4.2679E+00 
                   2.8594E+00 
               
               
                 angle of each surface 
                   8.2147E+00 
                 −2.1598E+01 
                   5.7781E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 4C 
               
             
            
               
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                   0.0000E+00 
                   0.0000E+00 
                   0.0000E+00 
               
               
                 Y 
                 −6.8198E+00 
                 −1.2013E+01 
                 −1.4077E+01 
               
               
                 Z 
                   2.0627E+00 
                   4.4442E+00 
                   2.8914E+00 
               
               
                 angle of each surface 
                   6.5363E+01 
                   6.1548E+00 
                 −2.6527E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 4D 
               
               
                   
               
               
                   
                 aperture 
                 Image plane 
               
               
                   
               
             
            
               
                 X 
                 0.0000E+00 
                   0.0000E+00 
               
               
                 Y 
                 0.0000E+00 
                 −1.2623E+01 
               
               
                 Z 
                 4.5000E−01 
                   7.1001E+00 
               
               
                 angle of each surface 
                 0.0000E+00 
                   0.0000E+00 
               
               
                   
               
            
           
         
       
     
     Table 4E shows the aspherical coefficients of surfaces R 1  and R 2  of L 1  for the freeform folded optical system of camera  300 . 
     
       
         
           
               
               
               
             
               
                 TABLE 4E 
               
               
                   
               
               
                   
                 R1 
                 R2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                   1.3779E+01 
                 −1.4250E+02 
               
               
                 4th order 
                 −6.9632E−05 
                   8.3882E−07 
               
               
                 6th order 
                   3.4866E−06 
                   8.5677E−06 
               
               
                 8th order 
                   3.7304E−07 
                   2.4073E−07 
               
               
                   
               
            
           
         
       
     
     Tables 4F through 4H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the freeform folded optical system of camera  300 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 4F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −4.1030E−03 
                 Y2: 
                 −2.0438E−03 
                 X2Y: 
                   3.0841E−04 
               
               
                 Y3: 
                   2.1374E−04 
                 X4: 
                   7.4688E−05 
                 X2Y2: 
                 −5.8378E−05 
               
               
                 Y4: 
                 −2.7081E−05 
                 X4Y: 
                 −8.1083E−06 
                 X2Y3: 
                   2.7833E−06 
               
               
                 Y5: 
                   1.3664E−06 
                 X6: 
                   1.0048E−06 
                 X4Y2: 
                   8.0682E−07 
               
               
                 X2Y4: 
                 −1.5666E−06 
                 Y6: 
                 −2.3636E−07 
                 X6Y: 
                 −3.7678E−07 
               
               
                 X4Y3: 
                 −7.0892E−08 
                 X2Y5: 
                   2.0387E−07 
                 Y7: 
                   5.3612E−09 
               
               
                 X8: 
                   1.7177E−08 
                 X6Y2: 
                   9.2501E−09 
                 X4Y4: 
                   1.1531E−08 
               
               
                 X2Y6: 
                 −1.0276E−08 
                 Y8: 
                 −1.0023E−10 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −4.0517E−03 
                 Y2: 
                 −6.4299E−03 
                 X2Y: 
                   1.9527E−04 
               
               
                 Y3: 
                   1.9196E−04 
                 X4: 
                   4.2377E−05 
                 X2Y2: 
                 −3.5460E−05 
               
               
                 Y4: 
                 −1.9359E−05 
                 X4Y: 
                 −3.1760E−06 
                 X2Y3: 
                 −1.1339E−06 
               
               
                 Y5: 
                 −6.9096E−07 
                 X6: 
                 −7.4827E−07 
                 X4Y2: 
                 −2.1279E−06 
               
               
                 X2Y4: 
                 −2.8271E−06 
                 Y6: 
                 −7.7148E−07 
                 X6Y: 
                 −2.1208E−07 
               
               
                 X4Y3: 
                 −4.6639E−08 
                 X2Y5: 
                 −7.0024E−08 
                 Y7: 
                 −6.0365E−08 
               
               
                 X8: 
                   7.7508E−08 
                 X6Y2: 
                   2.2880E−07 
                 X4Y4: 
                   2.7047E−07 
               
               
                 X2Y6: 
                   1.3074E−07 
                 Y8: 
                   1.2554E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius 
                 −5.2022E+00 
                   
                   
                   
                   
               
               
                 of cur- 
                   
                   
                   
                   
                   
               
            
           
           
               
               
            
               
                 vature 
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 ZP1: 
                   4.3990E−01 
                 ZP3: 
                   8.0953E−01 
                 ZP4: 
                  6.3020E−02 
               
               
                 ZP5: 
                   6.2129E−01 
                 ZP9: 
                   2.2885E−01 
                 ZP10: 
                  3.3807E−02 
               
               
                 ZP11: 
                   1.1773E−01 
                 ZP12: 
                   5.9172E−02 
                 ZP13: 
                  2.3739E−01 
               
               
                 ZP19: 
                   4.9033E−02 
                 ZP20: 
                 −2.7243E−02 
                 ZP21: 
                 −6.0975E−02 
               
               
                 ZP22: 
                 −3.4146E−02 
                 ZP23: 
                   2.2046E−02 
                 ZP24: 
                 −7.1215E−05 
               
               
                 ZP25: 
                   4.8177E−02 
                 ZP33: 
                   1.5254E−02 
                 ZP34: 
                 −2.2465E−02 
               
               
                 ZP35: 
                   3.4118E−03 
                 ZP36: 
                   2.9765E−03 
                 ZP37: 
                   4.3637E−04 
               
               
                 ZP38: 
                 −4.5495E−03 
                 ZP39: 
                 −5.7368E−03 
                 ZP40: 
                   8.2263E−03 
               
               
                 ZP41: 
                   1.1196E−02 
                 NRADIUS: 
                   5.0000E+00 
               
               
                   
               
            
           
         
       
     
     Tables 4I through 4K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  300 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 4I 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius 
                 −7.1912E+00 
                   
                   
                   
                   
               
               
                 of cur- 
                   
                   
                   
                   
                   
               
            
           
           
               
               
            
               
                 vature 
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 ZP1: 
                   1.8375E+00 
                 ZP3: 
                   8.5303E−01 
                 ZP4: 
                   1.0826E+00 
               
               
                 ZP5: 
                   4.9466E−01 
                 ZP9: 
                   7.5084E−01 
                 ZP10: 
                 −1.8544E+00 
               
               
                 ZP11: 
                 −9.6105E−01 
                 ZP12: 
                   5.7025E−01 
                 ZP13: 
                   4.4681E−01 
               
               
                 ZP19: 
                   3.9429E−01 
                 ZP20: 
                 −1.1961E+00 
                 ZP21: 
                   9.9587E−01 
               
               
                 ZP22: 
                   3.1859E−01 
                 ZP23: 
                 −4.7837E−01 
                 ZP24: 
                   2.9845E−01 
               
               
                 ZP25: 
                   1.5519E−01 
                 ZP33: 
                   9.9804E−02 
                 ZP34: 
                 −3.2426E−01 
               
               
                 ZP35: 
                   2.0437E−01 
                 ZP36: 
                 −7.8131E−02 
                 ZP37: 
                   4.5649E−02 
               
               
                 ZP38: 
                   4.3533E−03 
                 ZP39: 
                 −8.8371E−02 
                 ZP40: 
                   6.1961E−02 
               
               
                 ZP41: 
                   4.4628E−02 
                 NRADIUS: 
                   6.2500E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −3.3900E−03 
                 Y2: 
                   1.2000E−02 
                 X2Y: 
                 −2.6583E−04 
               
               
                 Y3: 
                 −8.9382E−05 
                 X4: 
                   2.3106E−04 
                 X2Y2: 
                 −1.7748E−04 
               
               
                 Y4: 
                 −5.6288E−05 
                 X4Y: 
                 −7.6938E−05 
                 X2Y3: 
                   8.5945E−06 
               
               
                 Y5: 
                 −8.7135E−07 
                 X6: 
                   8.5941E−06 
                 X4Y2: 
                   1.8457E−05 
               
               
                 X2Y4: 
                   7.7362E−07 
                 Y6: 
                 −5.2980E−07 
                 X6Y: 
                 −6.2832E−07 
               
               
                 X4Y3: 
                 −3.3326E−06 
                 X2Y5: 
                   5.8876E−07 
                 Y7: 
                   4.1715E−07 
               
               
                 X8: 
                 −1.5106E−07 
                 X6Y2: 
                 −2.2790E−07 
                 X4Y4: 
                   2.5596E−07 
               
               
                 X2Y6: 
                 −1.0205E−07 
                 Y8: 
                 −3.7415E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4K 
               
               
                   
               
               
                 P2S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −6.2694E−04 
                 Y2: 
                  3.1710E−02 
                 X2Y: 
                 −5.6440E−04 
               
               
                 Y3: 
                 −1.1796E−03 
                 X4: 
                  2.9229E−04 
                 X2Y2: 
                 −2.3184E−04 
               
               
                 Y4: 
                 −9.9880E−05 
                 X4Y: 
                 −1.3183E−04 
                 X2Y3: 
                  1.9399E−05 
               
               
                 Y5: 
                  2.9709E−05 
                 X6: 
                  2.2939E−06 
                 X4Y2: 
                  3.5026E−05 
               
               
                 X2Y4: 
                 −6.4207E−07 
                 Y6: 
                 −8.7850E−06 
                 X6Y: 
                  9.4914E−07 
               
               
                 X4Y3: 
                 −6.9571E−06 
                 X2Y5: 
                  4.6764E−07 
                 Y7: 
                  2.1291E−06 
               
               
                 X8: 
                 −5.1533E−08 
                 X6Y2: 
                 −4.2400E−07 
                 X4Y4: 
                  7.6908E−07 
               
               
                 X2Y6: 
                 −1.0919E−07 
                 Y8: 
                 −2.0390E−07 
               
               
                   
               
            
           
         
       
     
     Tables 5A through 5K provide prescriptions for the optical elements of the example freeform folded optical system of camera  400  as described in reference to  FIGS.  5 A through  5 C . Tables 5A through 5D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  400 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 5A 
               
             
            
               
                   
                   
               
               
                   
                   
                 L1 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Z 
                 0.0000E+00 
                 1.2612E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 5B 
               
             
            
               
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                  0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
               
               
                 Y 
                 −2.8396E+00 
                  0.0000E+00 
                 −7.4975E+00 
               
               
                 Z 
                  1.4331E+00 
                  4.4448E+00 
                  3.0119E+00 
               
               
                 angle of each surface 
                  8.2004E+00 
                 −2.1657E−01 
                  5.7494E−01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 5C 
               
             
            
               
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                  0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
               
               
                 Y 
                 −6.2664E+00 
                 −1.1940E+01 
                 −1.4589E+01 
               
               
                 Z 
                  1.6720E+00 
                  4.2998E+00 
                  2.3059E+00 
               
               
                 angle of each surface 
                  6.5148E−01 
                  6.0616E+00 
                 −2.6513E−01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 5D 
               
               
                   
                   
               
               
                   
                   
                 aperture 
                 Image plane 
               
               
                   
                   
               
             
            
               
                   
                 X 
                 0.0000E+00 
                  0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 −1.2624E+01 
               
               
                   
                 Z 
                 0.0000E+00 
                  7.0000E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                  0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Table 5E shows the aspherical coefficients of surfaces R 1  and R 2  of L 1  for the freeform folded optical system of camera  400 . 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 5E 
               
               
                   
                   
               
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
             
            
               
                   
                 Radius of curvature 
                  1.0031E+01 
                  2.2229E+04 
               
               
                   
                 4th order 
                 −2.2896E−05 
                  3.5394E−05 
               
               
                   
                 6th order 
                 −1.6868E−06 
                 −2.1342E−06 
               
               
                   
                 8th order 
                  5.3139E−08 
                  7.8283E−08 
               
               
                   
                 10th order 
                 −4.0851E−09 
                 −3.6425E−09 
               
               
                   
                   
               
            
           
         
       
     
     Tables 5F through 5H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the freeform folded optical system of camera  400 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 5F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −4.5543E−04 
                 Y2: 
                  6.4053E−04 
                 X2Y: 
                 −2.3979E−04 
               
               
                 Y3: 
                  1.9895E−04 
                 X4: 
                 −3.9579E−06 
                 X2Y2: 
                  3.0698E−08 
               
               
                 Y4: 
                 −2.2450E−05 
                 X4Y: 
                  2.8192E−06 
                 X2Y3: 
                 −2.7515E−06 
               
               
                 Y5: 
                  2.0284E−06 
                 X6: 
                  4.4608E−07 
                 X4Y2: 
                 −8.2259E−07 
               
               
                 X2Y4: 
                  2.4269E−08 
                 Y6: 
                 −2.0299E−07 
                 X6Y: 
                 −1.5154E−07 
               
               
                 X4Y3: 
                  9.0080E−08 
                 X2Y5: 
                 −2.2847E−08 
                 Y7: 
                  1.7511E−08 
               
               
                 X8: 
                 −4.9405E−09 
                 X6Y2: 
                  2.3692E−08 
                 X4Y4: 
                 −1.6216E−08 
               
               
                 X2Y6: 
                 −5.1094E−09 
                 Y8: 
                 −2.0773E−09 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −1.6273E−03 
                 Y2: 
                 −2.4812E−03 
                 X2Y: 
                  2.2888E−05 
               
               
                 Y3: 
                  3.2143E−04 
                 X4: 
                 −5.7852E−06 
                 X2Y2: 
                 −2.6798E−05 
               
               
                 Y4: 
                 −3.9699E−06 
                 X4Y: 
                 −1.3602E−07 
                 X2Y3: 
                 −2.4113E−06 
               
               
                 Y5: 
                  9.6929E−07 
                 X6: 
                  3.1876E−07 
                 X4Y2: 
                  8.8558E−08 
               
               
                 X2Y4: 
                 −5.4202E−08 
                 Y6: 
                  1.4351E−07 
                 X6Y: 
                 −2.0160E−08 
               
               
                 X4Y3: 
                 −3.0249E−08 
                 X2Y5: 
                 −9.1154E−08 
                 Y7: 
                 −3.5094E−08 
               
               
                 X8: 
                 −1.3766E−08 
                 X6Y2: 
                 −2.4974E−08 
                 X4Y4: 
                 −4.1940E−08 
               
               
                 X2Y6: 
                 −3.7645E−08 
                 Y8: 
                 −1.2102E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of 
                 −6.3097E+00 
                   
                   
                   
                   
               
               
                 curvature 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                  4.8394E−01 
                 ZP3: 
                  4.8168E−01 
                 ZP4: 
                  2.1211E−01 
               
               
                 ZP5: 
                  8.1466E−01 
                 ZP9: 
                 −4.5111E−02 
                 ZP10: 
                  3.8402E−01 
               
               
                 ZP11: 
                  4.6161E−02 
                 ZP12: 
                 −2.2978E−02 
                 ZP13: 
                  1.4383E−01 
               
               
                 ZP19: 
                 −1.8961E−02 
                 ZP20: 
                  1.0007E−01 
                 ZP21: 
                  1.3601E−01 
               
               
                 ZP22: 
                  6.2411E−01 
                 ZP23: 
                 −7.9147E−02 
                 ZP24: 
                  6.4665E−02 
               
               
                 ZP25: 
                  1.2522E−02 
                 ZP33: 
                  1.4510E−02 
                 ZP34: 
                 −2.1825E−02 
               
               
                 ZP35: 
                  7.9700E−02 
                 ZP36: 
                 −4.9564E−01 
                 ZP37: 
                 −4.3220E−01 
               
               
                 ZP38: 
                  1.6732E−01 
                 ZP39: 
                 −7.9496E−02 
                 ZP40: 
                  5.2080E−02 
               
               
                 ZP41: 
                 −2.1835E−02 
                 ZP51: 
                  2.4908E−03 
                 ZP52: 
                  1.1218E−02 
               
               
                 ZP53: 
                  2.8213E−03 
                 ZP54: 
                 −6.5446E−02 
                 ZP55: 
                  1.6333E−01 
               
               
                 ZP56: 
                  1.4409E−01 
                 ZP57: 
                 −6.2183E−02 
                 ZP58: 
                  1.7172E−02 
               
               
                 ZP59: 
                 −1.2107E−02 
                 ZP60: 
                  8.6648E−03 
                 ZP61: 
                 −5.0489E−03 
               
               
                 NRADIUS: 
                  6.0000E+00 
               
               
                   
               
            
           
         
       
     
     Tables 5I through 5K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  400 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 5I 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of 
                 −6.7292E+00 
                   
                   
                   
                   
               
               
                 curvature 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                  2.3755E+00 
                 ZP3: 
                  1.1681E+00 
                 ZP4: 
                  9.5930E−01 
               
               
                 ZP5: 
                  4.1826E−01 
                 ZP9: 
                  8.8117E−01 
                 ZP10: 
                 −6.0724E−01 
               
               
                 ZP11: 
                 −5.4366E−01 
                 ZP12: 
                  4.5785E−01 
                 ZP13: 
                  2.3040E−01 
               
               
                 ZP19: 
                  4.7024E−01 
                 ZP20: 
                 −1.1643E+00 
                 ZP21: 
                  4.0108E+00 
               
               
                 ZP22: 
                  6.6523E+00 
                 ZP23: 
                 −4.6990E−01 
                 ZP24: 
                  1.6282E−01 
               
               
                 ZP25: 
                  1.6400E−01 
                 ZP33: 
                  1.5319E−01 
                 ZP34: 
                 −3.4682E−01 
               
               
                 ZP35: 
                  9.0065E−01 
                 ZP36: 
                 −7.9447E+00 
                 ZP37: 
                 −6.4993E+00 
               
               
                 ZP38: 
                  7.7843E−01 
                 ZP39: 
                 −1.1310E−01 
                 ZP40: 
                 −3.4355E−02 
               
               
                 ZP41: 
                  2.9440E−02 
                 ZP51: 
                 −4.7922E−03 
                 ZP52: 
                  4.5851E−02 
               
               
                 ZP53: 
                 −6.5913E−03 
                 ZP54: 
                 −8.6574E−01 
                 ZP55: 
                  3.9292E+00 
               
               
                 ZP56: 
                  1.8646E+00 
                 ZP57: 
                 −4.6809E−01 
                 ZP58: 
                 −3.2108E−02 
               
               
                 ZP59: 
                 −3.2491E−02 
                 ZP60: 
                  8.6424E−04 
                 ZP61: 
                  3.4461E−04 
               
               
                 NRADIUS: 
                  7.5000E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                  6.9182E−03 
                 Y2: 
                  1.6072E−02 
                 X2Y: 
                 −2.0157E−03 
               
               
                 Y3: 
                  2.7670E−04 
                 X4: 
                  5.0748E−05 
                 X2Y2: 
                  1.9051E−04 
               
               
                 Y4: 
                 −8.6587E−05 
                 X4Y: 
                  3.0146E−06 
                 X2Y3: 
                 −3.5129E−05 
               
               
                 Y5: 
                 −5.6475E−06 
                 X6: 
                  9.4523E−07 
                 X4Y2: 
                 −6.7788E−06 
               
               
                 X2Y4: 
                  2.4293E−06 
                 Y6: 
                  1.2289E−07 
                 X6Y: 
                  2.4807E−07 
               
               
                 X4Y3: 
                  2.7042E−06 
                 X2Y5: 
                  4.1284E−07 
                 Y7: 
                  2.6102E−07 
               
               
                 X8: 
                  2.0806E−07 
                 X6Y2: 
                 −4.1283E−07 
                 X4Y4: 
                 −2.8925E−07 
               
               
                 X2Y6: 
                 −3.4697E−08 
                 Y8: 
                 −2.8260E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5K 
               
               
                   
               
               
                 P2S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                  8.1546E−03 
                 Y2: 
                  2.9680E−02 
                 X2Y: 
                 −2.5720E−03 
               
               
                 Y3: 
                 −7.8572E−04 
                 X4: 
                 −7.0060E−07 
                 X2Y2: 
                  4.3181E−04 
               
               
                 Y4: 
                 −3.9084E−05 
                 X4Y: 
                  2.3016E−05 
                 X2Y3: 
                 −8.0333E−05 
               
               
                 Y5: 
                 −9.3595E−06 
                 X6: 
                 −1.1998E−06 
                 X4Y2: 
                 −1.7497E−05 
               
               
                 X2Y4: 
                  6.4297E−06 
                 Y6: 
                  1.4123E−06 
                 X6Y: 
                  4.3808E−07 
               
               
                 X4Y3: 
                  3.5705E−06 
                 X2Y5: 
                  2.3803E−07 
                 Y7: 
                  2.4785E−07 
               
               
                 X8: 
                  9.5021E−08 
                 X6Y2: 
                 −6.6709E−08 
                 X4Y4: 
                 −2.4073E−07 
               
               
                 X2Y6: 
                 −6.7071E−08 
                 Y8: 
                 −3.8233E−08 
               
               
                   
               
            
           
         
       
     
     Tables 6A through 6K provide prescriptions for the optical elements of the example freeform folded optical system of camera  500  as described in reference to  FIGS.  6 A through  6 C . Tables 6A through 6D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  500 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 6A 
               
             
            
               
                   
                   
               
               
                   
                   
                 L1 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Z 
                 0.0000E+00 
                 9.1331E−01 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 6B 
               
             
            
               
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                  0.0000E+00 
                 0.0000E+00 
                  0.0000E+00 
               
               
                 Y 
                 −2.7510E+00 
                 0.0000E+00 
                 −7.2396E+00 
               
               
                 Z 
                  1.6615E+00 
                 4.5652E+00 
                  3.3919E+00 
               
               
                 angle of each surface 
                  8.3182E+00 
                 −2.1726E−01 
                  5.7051E−01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 6C 
               
             
            
               
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                  0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
               
               
                 Y 
                 −6.2521E+00 
                 −1.2392E+01 
                 −1.5580E+01 
               
               
                 Z 
                  1.8189E+00 
                  4.7268E+00 
                  2.3114E+00 
               
               
                 angle of each surface 
                  6.4657E−01 
                  5.9020E+00 
                 −2.6427E−01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 6D 
               
               
                   
                   
               
               
                   
                   
                 aperture 
                 Image plane 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 −1.3011E+01 
               
               
                   
                 Z 
                 0.0000E+00 
                 7.0000E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Table 6E shows the aspherical coefficients of surfaces R 1  and R 2  of L 1  for the freeform folded optical system of camera  500 . 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 6E 
               
               
                   
                   
               
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Radius of curvature 
                 1.1108E+01 
                 4.9615E+01 
               
               
                   
                 4th order 
                 −7.8523E−05 
                 −2.3386E−05 
               
               
                   
                 6th order 
                 −3.1053E−07 
                 1.5326E−06 
               
               
                   
                 8th order 
                 3.6348E−08 
                 4.0305E−08 
               
               
                   
                   
               
            
           
         
       
     
     Tables 6F through 6H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the freeform folded optical system of camera  500 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 6F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 X2: 
                 −1.2574E−03 
               
               
                   
                 Y2: 
                 −3.4899E−03 
               
               
                   
                 X2Y: 
                 −9.3471E−05 
               
               
                   
                 Y3: 
                 3.0175E−04 
               
               
                   
                 X4: 
                 1.0196E−05 
               
               
                   
                 X2Y2: 
                 −8.4511E−06 
               
               
                   
                 Y4: 
                 −3.1020E−05 
               
               
                   
                 X4Y: 
                 4.5054E−06 
               
               
                   
                 X2Y3: 
                 2.4496E−06 
               
               
                   
                 Y5: 
                 2.1977E−06 
               
               
                   
                 X6: 
                 −3.1450E−07 
               
               
                   
                 X4Y2: 
                 −7.6725E−07 
               
               
                   
                 X2Y4: 
                 −2.7463E−07 
               
               
                   
                 Y6: 
                 −9.2808E−08 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 X2: 
                 −5.3713E−03 
               
               
                   
                 Y2: 
                 −9.7583E−03 
               
               
                   
                 X2Y: 
                 6.8529E−05 
               
               
                   
                 Y3: 
                 2.0767E−04 
               
               
                   
                 X4: 
                 1.8023E−06 
               
               
                   
                 X2Y2: 
                 −2.5461E−05 
               
               
                   
                 Y4: 
                 −1.2655E−05 
               
               
                   
                 X4Y: 
                 3.3642E−07 
               
               
                   
                 X2Y3: 
                 −5.2884E−07 
               
               
                   
                 Y5: 
                 −9.4009E−07 
               
               
                   
                 X6: 
                 −4.9775E−07 
               
               
                   
                 X4Y2: 
                 −1.0824E−06 
               
               
                   
                 X2Y4: 
                 −7.5822E−07 
               
               
                   
                 Y6: 
                 −2.2155E−07 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Radius of curvature 
                 −7.0171E+00 
               
               
                   
                 ZP1: 
                 6.2089E−01 
               
               
                   
                 ZP3: 
                 1.2815E+00 
               
               
                   
                 ZP4: 
                 2.3659E+00 
               
               
                   
                 ZP5: 
                 1.0846E+00 
               
               
                   
                 ZP9: 
                 −3.0334E−01 
               
               
                   
                 ZP10: 
                 −7.3919E−01 
               
               
                   
                 ZP11: 
                 −7.6865E−01 
               
               
                   
                 ZP12: 
                 1.3237E+00 
               
               
                   
                 ZP13: 
                 −2.7353E−01 
               
               
                   
                 ZP19: 
                 −3.3278E−01 
               
               
                   
                 ZP20: 
                 −2.4673E−01 
               
               
                   
                 ZP21: 
                 7.5606E−01 
               
               
                   
                 ZP22: 
                 1.0313E−01 
               
               
                   
                 ZP23: 
                 −1.8634E−01 
               
               
                   
                 ZP24: 
                 4.3999E−01 
               
               
                   
                 ZP25: 
                 −1.4850E−01 
               
               
                   
                 ZP33: 
                 −6.7682E−02 
               
               
                   
                 ZP34: 
                 −8.6103E−02 
               
               
                   
                 ZP35: 
                 1.9254E−01 
               
               
                   
                 ZP36: 
                 −5.3608E−02 
               
               
                   
                 ZP37: 
                 5.8097E−02 
               
               
                   
                 ZP38: 
                 2.5860E−02 
               
               
                   
                 ZP39: 
                 −5.0847E−02 
               
               
                   
                 ZP40: 
                 7.0788E−02 
               
               
                   
                 ZP41: 
                 −3.9819E−02 
               
               
                   
                 NRADIUS: 
                 8.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Tables 6I through 6K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  500 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 6I 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Radius of curvature 
                 −6.7659E+00 
               
               
                   
                 ZP1: 
                 2.7976E+00 
               
               
                   
                 ZP3: 
                 2.7250E+00 
               
               
                   
                 ZP4: 
                 3.1104E+00 
               
               
                   
                 ZP5: 
                 2.4097E−01 
               
               
                   
                 ZP9: 
                 8.4945E−01 
               
               
                   
                 ZP10: 
                 6.9713E−01 
               
               
                   
                 ZP11: 
                 1.5345E+01 
               
               
                   
                 ZP12: 
                 4.3060E−01 
               
               
                   
                 ZP13: 
                 4.8787E−01 
               
               
                   
                 ZP19: 
                 6.4501E−01 
               
               
                   
                 ZP20: 
                 −1.8877E+00 
               
               
                   
                 ZP21: 
                 −1.0193E+00 
               
               
                   
                 ZP22: 
                 −1.2919E+01 
               
               
                   
                 ZP23: 
                 5.1161E+00 
               
               
                   
                 ZP24: 
                 1.4155E−01 
               
               
                   
                 ZP25: 
                 2.5003E−01 
               
               
                   
                 ZP33: 
                 5.1597E−01 
               
               
                   
                 ZP34: 
                 −9.6561E−01 
               
               
                   
                 ZP35: 
                 7.9243E−01 
               
               
                   
                 ZP36: 
                 2.7432E+00 
               
               
                   
                 ZP37: 
                 3.9039E+00 
               
               
                   
                 ZP38: 
                 −1.7259E+00 
               
               
                   
                 ZP39: 
                 8.6447E−01 
               
               
                   
                 ZP40: 
                 −8.7006E−02 
               
               
                   
                 ZP41: 
                 −7.5066E−04 
               
               
                   
                 NRADIUS: 
                 1.0000E+01 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 X2: 
                 5.8481E−03 
               
               
                   
                 Y2: 
                 1.4979E−02 
               
               
                   
                 X2Y: 
                 −2.2908E−03 
               
               
                   
                 Y3: 
                 9.9992E−04 
               
               
                   
                 X4: 
                 1.7355E−04 
               
               
                   
                 X2Y2: 
                 6.6700E−05 
               
               
                   
                 Y4: 
                 −6.3692E−05 
               
               
                   
                 X4Y: 
                 −3.3311E−05 
               
               
                   
                 X2Y3: 
                 1.0893E−05 
               
               
                   
                 Y5: 
                 −1.8513E−05 
               
               
                   
                 X6: 
                 −3.0405E−07 
               
               
                   
                 X4Y2: 
                 2.0500E−06 
               
               
                   
                 X2Y4: 
                 −1.6597E−06 
               
               
                   
                 Y6: 
                 9.5906E−07 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6K 
               
               
                   
               
               
                 P2S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 X2: 
                 −6.7780E−03 
               
               
                   
                 Y2: 
                 2.7419E−02 
               
               
                   
                 X2Y: 
                 −2.5576E−03 
               
               
                   
                 Y3: 
                 −6.2003E−05 
               
               
                   
                 X4: 
                 1.3028E−04 
               
               
                   
                 X2Y2: 
                 2.1446E−04 
               
               
                   
                 Y4: 
                 −1.2590E−04 
               
               
                   
                 X4Y: 
                 −3.9522E−06 
               
               
                   
                 X2Y3: 
                 −2.7222E−05 
               
               
                   
                 Y5: 
                 3.1668E−06 
               
               
                   
                 X6: 
                 −4.5754E−06 
               
               
                   
                 X4Y2: 
                 −2.0350E−06 
               
               
                   
                 X2Y4: 
                 2.0963E−07 
               
               
                   
                 Y6: 
                 1.1836E−07 
               
               
                   
                   
               
            
           
         
       
     
     Tables 7A through 7K provide prescriptions for the optical elements of the example freeform folded optical system of camera  600  as described in reference to  FIGS.  7 A through  7 C . Tables 7A through 7D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  600 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 7A 
               
             
            
               
                   
                   
               
               
                   
                   
                 L1 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Z 
                 0.0000E+00 
                 1.2180E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 7B 
               
             
            
               
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 −2.9889E+00 
                 4.4409E−16 
                 −6.9575E+00 
               
               
                 Z 
                 1.9879E+00 
                 5.1213E+00 
                 4.7729E+00 
               
               
                 angle of each surface 
                 8.8143E+00 
                 −2.1824E+01 
                 5.7860E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 7C 
               
             
            
               
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 X 
                 0.0000E+00 
                 0.0000E+00 
                 0.0000E+00 
               
               
                 Y 
                 −6.3392E+00 
                 −1.2987E+01 
                 −1.6172E+01 
               
               
                 Z 
                 1.8786E+00 
                 5.0713E+00 
                 2.6522E+00 
               
               
                 angle of each surface 
                 6.4345E+01 
                 5.7788E+00 
                 −2.6394E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 7D 
               
               
                   
                   
               
               
                   
                   
                 aperture 
                 Image plane 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 −1.3080E+01 
               
               
                   
                 Z 
                 0.0000E+00 
                 7.5000E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Table 7E shows the aspherical coefficients of surfaces R 1  and R 2  of L 1  for the freeform folded optical system of camera  600 . 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 7E 
               
               
                   
                   
               
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Radius of curvature  
                 9.2029E+00 
                 1.5192E+01 
               
               
                   
                 4th order 
                 1.0982E−04 
                 2.4752E−04 
               
               
                   
                 6th order 
                 2.7779E−06 
                 4.9210E−06 
               
               
                   
                 8th order 
                 1.4634E−07 
                 1.6847E−07 
               
               
                   
                   
               
            
           
         
       
     
     Tables 7F through 7H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the freeform folded optical system of camera  600 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 7F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 X2: 
                 −8.2779E−04 
               
               
                   
                 Y2: 
                 −5.9148E−03 
               
               
                   
                 X2Y: 
                 −2.4660E−04 
               
               
                   
                 Y3: 
                 5.5736E−04 
               
               
                   
                 X4: 
                 −1.1282E−06 
               
               
                   
                 X2Y2: 
                 −8.4651E−06 
               
               
                   
                 Y4: 
                 −5.7940E−05 
               
               
                   
                 X4Y: 
                 6.0643E−06 
               
               
                   
                 X2Y3: 
                 4.2961E−06 
               
               
                   
                 Y5: 
                 4.5389E−06 
               
               
                   
                 X6: 
                 −4.9393E−07 
               
               
                   
                 X4Y2: 
                 −9.2749E−07 
               
               
                   
                 X2Y4: 
                 −4.6152E−07 
               
               
                   
                 Y6: 
                 −2.0114E−07 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 X2: 
                 −9.0426E−03 
               
               
                   
                 Y2: 
                 −1.4448E−02 
               
               
                   
                 X2Y: 
                 −2.4112E−05 
               
               
                   
                 Y3: 
                 2.6340E−04 
               
               
                   
                 X4: 
                 −9.0849E−06 
               
               
                   
                 X2Y2: 
                 −3.4202E−05 
               
               
                   
                 Y4: 
                 −1.5518E−05 
               
               
                   
                 X4Y: 
                 4.5692E−07 
               
               
                   
                 X2Y3: 
                 −4.4335E−07 
               
               
                   
                 Y5: 
                 −8.4713E−07 
               
               
                   
                 X6: 
                 −3.5078E−07 
               
               
                   
                 X4Y2: 
                 −5.7510E−07 
               
               
                   
                 X2Y4: 
                 −3.8514E−07 
               
               
                   
                 Y6: 
                 −1.5611E−07 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Radius  
                 −8.6358E+00 
                   
                   
               
               
                 of 
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 curva- 
                   
                   
                   
                   
                   
               
               
                 ture 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                  2.2487E+00 
                 ZP3: 
                  2.0577E+00 
                 ZP4: 
                  3.1844E+00 
               
               
                 ZP5: 
                  2.7106E+00 
                 ZP9: 
                 −5.7599E−01 
                 ZP10: 
                 −1.7279E+00 
               
               
                 ZP11: 
                  1.3733E−01 
                 ZP12: 
                  1.1627E+00 
                 ZP13: 
                 −1.8046E−01 
               
               
                 ZP19: 
                 −3.1012E−01 
                 ZP20: 
                 −2.0870E+00 
                 ZP21: 
                 −9.0824E−01 
               
               
                 ZP22: 
                  2.7265E+00 
                 ZP23: 
                  1.7344E+00 
                 ZP24: 
                  3.7931E−01 
               
               
                 ZP25: 
                 −2.7709E−01 
                 ZP33: 
                 −1.5751E−01 
                 ZP34: 
                 −5.7027E−01 
               
               
                 ZP35: 
                  7.1266E−01 
                 ZP36: 
                  9.7281E−01 
                 ZP37: 
                 −1.6562E−01 
               
               
                 ZP38: 
                 −2.2530E−02 
                 ZP39: 
                  2.3460E−01 
                 ZP40: 
                  1.6191E−01 
               
               
                 ZP41: 
                 −1.2848E−01 
                 NRADIUS: 
                  1.0000E+01 
               
               
                   
               
            
           
         
       
     
     Tables 7I through 7K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  600 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 7I 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius  
                 −7.1904E+00 
                   
                   
                   
                   
               
               
                 of 
                   
                   
                   
                   
                   
               
               
                 curva- 
                   
                   
                   
                   
                   
               
               
                 ture 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                  3.6301E+00 
                 ZP3: 
                  4.0054E+00 
                 ZP4: 
                  2.1121E+00 
               
               
                 ZP5: 
                  4.3072E−01 
                 ZP9: 
                  1.0196E+00 
                 ZP10: 
                  2.3775E+00 
               
               
                 ZP11: 
                  5.3816E+00 
                 ZP12: 
                  5.9378E−01 
                 ZP13: 
                  4.7426E−01 
               
               
                 ZP19: 
                  9.4246E−01 
                 ZP20: 
                 −1.8285E+00 
                 ZP21: 
                 −5.4785E+01 
               
               
                 ZP22: 
                 −6.4703E+01 
                 ZP23: 
                  5.9021E+00 
                 ZP24: 
                  5.3321E−01 
               
               
                 ZP25: 
                  2.3571E−01 
                 ZP33: 
                  6.5779E−01 
                 ZP34: 
                 −7.1924E−01 
               
               
                 ZP35: 
                 −8.9669E+00 
                 ZP36: 
                  1.8550E+01 
                 ZP37: 
                  9.4747E+00 
               
               
                 ZP38: 
                 −1.1673E+01 
                 ZP39: 
                  2.2152E+00 
                 ZP40: 
                 −2.6436E−01 
               
               
                 ZP41: 
                 −6.3642E−02 
                 NRADIUS: 
                  1.2500E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                  1.4914E−02 
                 Y2: 
                  1.3470E−02 
                 X2Y: 
                 −3.8041E−03 
               
               
                 Y3: 
                  1.1921E−03 
                 X4: 
                  2.0673E−04 
                 X2Y2: 
                 −7.3145E−05 
               
               
                 Y4: 
                  5.6914E−05 
                 X4Y: 
                 −3.1082E−05 
                 X2Y3: 
                  6.5040E−05 
               
               
                 Y5: 
                 −7.3318E−06 
                 X6: 
                 −1.4514E−06 
                 X4Y2: 
                  1.1472E−06 
               
               
                 X2Y4: 
                 −4.5996E−06 
                 Y6: 
                 −3.2421E−07 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7K 
               
               
                   
               
               
                 P2S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −9.8263E−03 
                 Y2: 
                  2.5527E−02 
                 X2Y: 
                 −3.3991E−03 
               
               
                 Y3: 
                  3.0296E−04 
                 X4: 
                  1.0784E−04 
                 X2Y2: 
                  1.1260E−04 
               
               
                 Y4: 
                 −5.1418E−05 
                 X4Y: 
                  3.3765E−05 
                 X2Y3: 
                  2.6094E−05 
               
               
                 Y5: 
                  2.3030E−06 
                 X6: 
                 −6.0219E−06 
                 X4Y2: 
                 −3.1429E−06 
               
               
                 X2Y4: 
                 −4.8442E−06 
                 Y6: 
                 −2.0877E−07 
               
               
                   
               
            
           
         
       
     
     Tables 8A through 8K provide prescriptions for the optical elements of the example freeform folded optical system of camera  700  as described in reference to  FIGS.  8 A through  8 C . Tables 8A through 8D show the local coordinates and angles of all surfaces based on the R 1  global coordinate for the freeform folded optical system of camera  700 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 8A 
               
             
            
               
                   
                   
               
               
                   
                   
                 L1 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
               
                   
                 X 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                 Z 
                 0.0000E+00 
                 7.3293E−01 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                 0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 8B 
               
             
            
               
                   
               
               
                   
                 P1 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                  0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
               
               
                 Y 
                 −2.2048E+00 
                  0.0000E+00 
                 −5.9749E+00 
               
               
                 Z 
                  9.0635E−01 
                  3.2256E+00 
                  1.4497E+00 
               
               
                 angle of each surface 
                  8.5942E+00 
                 −2.1775E+01 
                  5.7593E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 8C 
               
             
            
               
                   
               
               
                   
                 P2 
               
            
           
           
               
               
               
               
            
               
                   
                 S1 
                 S2 
                 S3 
               
               
                   
               
               
                 X 
                  0.0000E+00 
                  0.0000E+00 
                  0.0000E+00 
               
               
                 Y 
                 −5.3875E+00 
                 −9.7960E+00 
                 −1.2352E+01 
               
               
                 Z 
                  1.5501E+00 
                  3.6006E+00 
                  1.6748E+00 
               
               
                 angle of each surface 
                  6.5056E+01 
                  6.0282E+00 
                 −2.6500E+01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 8D 
               
               
                   
                   
               
               
                   
                   
                 aperture 
                 Image plane 
               
               
                   
                   
               
             
            
               
                   
                 X 
                 0.0000E+00 
                  0.0000E+00 
               
               
                   
                 Y 
                 0.0000E+00 
                 −1.1139E+01 
               
               
                   
                 Z 
                 3.5000E−01 
                  6.0000E+00 
               
               
                   
                 angle of each surface 
                 0.0000E+00 
                  0.0000E+00 
               
               
                   
                   
               
            
           
         
       
     
     Table 8E shows the aspherical coefficients of surfaces R 1  and R 2  of L 1  for the freeform folded optical system of camera  700 . 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 8E 
               
               
                   
                   
               
               
                   
                   
                 R1 
                 R2 
               
               
                   
                   
               
             
            
               
                   
                 Radius of curvature 
                  1.0303E+01 
                  3.9988E+02 
               
               
                   
                 4th order 
                 −1.7141E−04 
                 −3.7221E−05 
               
               
                   
                 6th order 
                 −1.4999E−05 
                 −1.4028E−05 
               
               
                   
                 8th order 
                  2.6285E−06 
                  4.2961E−06 
               
               
                   
                 10th order 
                  1.3792E−07 
                 −9.8908E−08 
               
               
                   
                 12th order 
                 −5.5907E−08 
                 −3.7433E−08 
               
               
                   
                 14th order 
                  4.4768E−09 
                  4.0716E−09 
               
               
                   
                   
               
            
           
         
       
     
     Tables 8F through 8H show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 1  for the freeform folded optical system of camera  700 . XY polynomial coefficients are shown for S 1  and S 2 , and Standard Zernike coefficients are shown for S 3 . 
     
       
         
           
               
             
               
                 TABLE 8F 
               
               
                   
               
               
                 P1S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −7.9880E−03 
                 Y2: 
                 −3.4768E−03 
                 X2Y: 
                  6.0415E−04 
               
               
                 Y3: 
                  2.7953E−04 
                 X4: 
                  1.4429E−04 
                 X2Y2: 
                 −8.9651E−05 
               
               
                 Y4: 
                 −4.9715E−05 
                 X4Y: 
                  7.2540E−06 
                 X2Y3: 
                  8.6021E−06 
               
               
                 Y5: 
                  3.6989E−06 
                 X6: 
                  7.7453E−08 
                 X4Y2: 
                 −8.4114E−07 
               
               
                 X2Y4: 
                 −1.0365E−06 
                 Y6: 
                 −4.3165E−07 
                 X6Y: 
                 −1.3002E−06 
               
               
                 X4Y3: 
                  1.2342E−06 
                 X2Y5: 
                  1.4087E−07 
                 Y7: 
                 −1.3709E−09 
               
               
                 X8: 
                  8.7000E−08 
                 X6Y2: 
                  2.7905E−08 
                 X4Y4: 
                 −2.3965E−07 
               
               
                 X2Y6: 
                 −2.0211E−08 
                 Y8: 
                 −8.2973E−10 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8G 
               
               
                   
               
               
                 P1S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −5.7357E−03 
                 Y2: 
                 −9.2301E−03 
                 X2Y: 
                  3.6677E−04 
               
               
                 Y3: 
                  1.9103E−04 
                 X4: 
                  6.5377E−05 
                 X2Y2: 
                 −8.7112E−05 
               
               
                 Y4: 
                 −5.2402E−05 
                 X4Y: 
                  4.2696E−06 
                 X2Y3: 
                  7.2807E−07 
               
               
                 Y5: 
                 −2.2677E−06 
                 X6: 
                 −9.1284E−07 
                 X4Y2: 
                 −5.0035E−07 
               
               
                 X2Y4: 
                 −1.4888E−06 
                 Y6: 
                 −7.3623E−07 
                 X6Y: 
                 −6.3168E−07 
               
               
                 X4Y3: 
                 −6.3965E−08 
                 X2Y5: 
                  1.2354E−09 
                 Y7: 
                 −2.3532E−07 
               
               
                 X8: 
                  1.7557E−08 
                 X6Y2: 
                 −1.2032E−07 
                 X4Y4: 
                 −1.8183E−07 
               
               
                 X2Y6: 
                 −1.5204E−07 
                 Y8: 
                 −7.6984E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8H 
               
               
                   
               
               
                 P1S3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of 
                 −5.4072E+00 
                   
                   
                   
                   
               
               
                 curvature 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                  4.3990E−01 
                 ZP3: 
                  1.2804E+00 
                 ZP4: 
                 −3.8088E−01 
               
               
                 ZP5: 
                  5.0347E−01 
                 ZP9: 
                 −1.1152E−01 
                 ZP10: 
                  5.6146E−01 
               
               
                 ZP11: 
                  4.0343E−01 
                 ZP12: 
                 −3.3755E−01 
                 ZP13: 
                  2.8137E−01 
               
               
                 ZP19: 
                 −2.8827E−01 
                 ZP20: 
                  2.6649E−01 
                 ZP21: 
                 −1.9589E−01 
               
               
                 ZP22: 
                 −1.1702E−01 
                 ZP23: 
                  8.9485E−02 
                 ZP24: 
                 −1.4055E−01 
               
               
                 ZP25: 
                  1.2273E−01 
                 ZP33: 
                 −5.5987E−02 
                 ZP34: 
                  1.6748E−02 
               
               
                 ZP35: 
                  6.8211E−03 
                 ZP36: 
                  1.5670E−01 
                 ZP37: 
                  7.5871E−02 
               
               
                 ZP38: 
                  1.7911E−03 
                 ZP39: 
                 −1.8299E−02 
                 ZP40: 
                 −2.2971E−02 
               
               
                 ZP41: 
                  2.1558E−02 
                 ZP51: 
                 −3.6876E−03 
                 ZP52: 
                  8.2867E−04 
               
               
                 ZP53: 
                  1.9005E−02 
                 ZP54: 
                  5.7853E−03 
                 ZP55: 
                 −2.7646E−02 
               
               
                 ZP56: 
                  1.6117E−02 
                 ZP57: 
                 −8.9737E−03 
                 ZP58: 
                  8.7488E−03 
               
               
                 ZP59: 
                 −2.4040E−03 
                 ZP60: 
                 −5.9937E−04 
                 ZP61: 
                  1.1786E−03 
               
               
                 NRADIUS: 
                  5.0000E+00 
               
               
                   
               
            
           
         
       
     
     Tables 8I through 8K show the aspherical coefficients of surfaces S 1 , S 2 , and S 3 , respectively, of P 2  for the freeform folded optical system of camera  700 . Standard Zernike coefficients are shown for S 1 , and XY polynomial coefficients are shown for S 2  and S 3 . 
     
       
         
           
               
             
               
                 TABLE 8I 
               
               
                   
               
               
                 P2S1 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius of 
                 −5.1556E+00 
                   
                   
                   
                   
               
               
                 curvature 
                   
                   
                   
                   
                   
               
               
                 ZP1: 
                  1.8375E+00 
                 ZP3: 
                  1.2560E+00 
                 ZP4: 
                  1.6337E+00 
               
               
                 ZP5: 
                  5.3144E−01 
                 ZP9: 
                  7.3174E−01 
                 ZP10: 
                 −7.1290E−01 
               
               
                 ZP11: 
                 −1.7417E+00 
                 ZP12: 
                  5.7043E−01 
                 ZP13: 
                  5.5825E−01 
               
               
                 ZP19: 
                  1.9900E−01 
                 ZP20: 
                 −3.9167E−01 
                 ZP21: 
                 −1.2886E+00 
               
               
                 ZP22: 
                 −1.6970E+00 
                 ZP23: 
                 −1.2217E+00 
                 ZP24: 
                  3.1918E−01 
               
               
                 ZP25: 
                  2.0290E−01 
                 ZP33: 
                  1.3053E−01 
                 ZP34: 
                 −1.3405E−01 
               
               
                 ZP35: 
                 −2.2998E−02 
                 ZP36: 
                  6.1069E+00 
                 ZP37: 
                  2.7587E+00 
               
               
                 ZP38: 
                  2.5648E−01 
                 ZP39: 
                 −4.6007E−01 
                 ZP40: 
                  1.2644E−01 
               
               
                 ZP41: 
                 −9.6945E−03 
                 ZP51: 
                  3.9591E−03 
                 ZP52: 
                  2.3508E−02 
               
               
                 ZP53: 
                  8.0958E−02 
                 ZP54: 
                  5.8805E−01 
                 ZP55: 
                 −2.0554E+00 
               
               
                 ZP56: 
                 −2.3005E−03 
                 ZP57: 
                 −1.1504E−01 
                 ZP58: 
                  1.5088E−01 
               
               
                 ZP59: 
                 −5.1378E−02 
                 ZP60: 
                  2.3046E−02 
                 ZP61: 
                 −1.0302E−02 
               
               
                 NRADIUS: 
                  6.2500E+00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8J 
               
               
                   
               
               
                 P2S2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 X2: 
                 −1.1340E−02 
                 Y2: 
                  1.6512E−02 
                 X2Y: 
                 −2.7502E−04 
               
               
                 Y3: 
                 −1.8888E−04 
                 X4: 
                  2.1645E−04 
                 X2Y2: 
                 −2.0331E−04 
               
               
                 Y4: 
                 −1.4999E−04 
                 X4Y: 
                 −4.7643E−05 
                 X2Y3: 
                  2.0657E−05 
               
               
                 Y5: 
                  9.0283E−06 
                 X6: 
                  4.5142E−06 
                 X4Y2: 
                  1.3405E−05 
               
               
                 X2Y4: 
                 −3.5349E−06 
                 Y6: 
                 −2.8475E−07 
                 X6Y: 
                 −5.1346E−07 
               
               
                 X4Y3: 
                 −7.8525E−06 
                 X2Y5: 
                  1.4279E−06 
                 Y7: 
                  2.7125E−07 
               
               
                 X8: 
                  1.0757E−07 
                 X6Y2: 
                 −3.7044E−07 
                 X4Y4: 
                  1.4527E−06 
               
               
                 X2Y6: 
                 −1.8478E−07 
                 Y8: 
                 −2.8463E−08 
               
               
                   
               
            
           
         
       
     
                     TABLE 8K               P2S3                                                        X2:   −1.3993E−02   Y2:    3.3766E−02   X2Y:   −5.8411E−04       Y3:   −1.5314E−03   X4:    3.6632E−04   X2Y2:   −3.5607E−04       Y4:   −1.7846E−04   X4Y:   −1.3935E−04   X2Y3:    7.0493E−05       Y5:    5.3756E−05   X6:   −6.7060E−06   X4Y2:    4.0670E−05       X2Y4:   −1.2422E−05   Y6:   −1.3515E−05   X6Y:    3.1502E−06       X4Y3:   −1.1946E−05   X2Y5:    2.4983E−06   Y7:    2.9738E−06       X8:    2.0636E−07   X6Y2:   −6.8609E−07   X4Y4:    1.6853E−06       X2Y6:   −3.4509E−07   Y8:   −2.8111E−07                    
Example Computing Device
 
       FIG.  17    illustrates an example computing device, referred to as computer system  3000 , that may include or host embodiments of a camera with a freeform folded optical system as illustrated in  FIGS.  1  through  16   . In addition, computer system  3000  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  3000  may be any of various types of devices, including, but not limited to, a personal computer system, desktop computer, laptop, notebook, tablet or pad device, slate, or netbook computer, mainframe computer system, handheld computer, workstation, network computer, a camera, a set top box, a mobile device, a wireless phone, a smartphone, a consumer device, video game console, handheld video game device, application server, storage device, a television, a video recording device, a peripheral device such as a switch, modem, router, or in general any type of computing or electronic device. 
     In the illustrated embodiment, computer system  3000  includes one or more processors  3010  coupled to a system memory  3020  via an input/output (I/O) interface  3030 . Computer system  3000  further includes a network interface  3040  coupled to I/O interface  3030 , and one or more input/output devices  3050 , such as cursor control device  3060 , keyboard  3070 , and display(s)  3080 . Computer system  3000  may also include one or more cameras  3090 , for example at least one camera that includes a freeform folded optical system as described above with respect to  FIGS.  1  through  16   . 
     In various embodiments, computer system  3000  may be a uniprocessor system including one processor  3010 , or a multiprocessor system including several processors  3010  (e.g., two, four, eight, or another suitable number). Processors  3010  may be any suitable processor capable of executing instructions. For example, in various embodiments processors  3010  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  3010  may commonly, but not necessarily, implement the same ISA. 
     System memory  3020  may be configured to store program instructions  3022  and/or data  3032  accessible by processor  3010 . In various embodiments, system memory  3020  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  3022  may be configured to implement various interfaces, methods and/or data for controlling operations of camera  3090  and for capturing and processing images with integrated camera  3090  or other methods or data, for example interfaces and methods for capturing, displaying, processing, and storing images captured with camera  3090 . 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  3020  or computer system  3000 . 
     In one embodiment, I/O interface  3030  may be configured to coordinate I/O traffic between processor  3010 , system memory  3020 , and any peripheral devices in the device, including network interface  3040  or other peripheral interfaces, such as input/output devices  3050 . In some embodiments, I/O interface  3030  may perform any necessary protocol, timing or other data transformations to convert data signals from one component (e.g., system memory  3020 ) into a format suitable for use by another component (e.g., processor  3010 ). In some embodiments, I/O interface  3030  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  3030  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  3030 , such as an interface to system memory  3020 , may be incorporated directly into processor  3010 . 
     Network interface  3040  may be configured to allow data to be exchanged between computer system  3000  and other devices attached to a network  3085  (e.g., carrier or agent devices) or between nodes of computer system  3000 . Network  3085  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  3040  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  3050  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  3000 . Multiple input/output devices  3050  may be present in computer system  3000  or may be distributed on various nodes of computer system  3000 . In some embodiments, similar input/output devices may be separate from computer system  3000  and may interact with one or more nodes of computer system  3000  through a wired or wireless connection, such as over network interface  3040 . 
     As shown in  FIG.  17   , memory  3020  may include program instructions  3022 , which may be processor-executable to implement any element or action to support integrated camera  3090 , including but not limited to image processing software and interface software for controlling camera(s)  3090 . In some embodiments, images captured by camera(s)  3090  may be stored to memory  3020 . In addition, metadata for images captured by camera(s)  3090  may be stored to memory  3020 . 
     Those skilled in the art will appreciate that computer system  3000  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  3000  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  3000  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  3000  may be transmitted to computer system  3000  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: 20200831
Publication Date: 20240319
Grant Date: 20240319
Priority Date: 20190927
Inventors: SAIGA, TAKEYOSHI
Assignee: APPLE INC
CPC Classifications: [{"code": "G02B13/02", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B5/04", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B7/1805", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B7/04", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B13/007", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B17/0848", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/02", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B1/04", "inventive": true, "first": false, "tree": "[]"}, {"code": "G03B30/00", "inventive": true, "first": false, "tree": "[]"}, {"code": "G03B17/17", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B17/023", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/007", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B17/0832", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B17/0856", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B17/0816", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B5/04", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B7/04", "inventive": false, "first": false, "tree": "[]"}, {"code": "G02B7/1805", "inventive": true, "first": false, "tree": "[]"}]
Family ID: 75161887