PATENT DOCUMENT

Publication Number: US-11726304-B2
Application Number: US-202117329009-A
Country: US
Kind Code: B2

Title: Folded optical systems

Abstract:
Single fold optical systems that include a power prism and a lens stack including two or more refractive lens elements. The single fold optical system may provide a long mechanical back focus without increasing the Z-height of the optical system. Providing power on the prism may reduce the optical total length and reduce the X-length of the optical system. The single folded optical systems may provide reduced Z-axis height and reduced X-axis length when compared to conventional double folded optical systems with similar optical characteristics. In addition, the optical systems may include an anamorphic lens that is oriented to correct for astigmatism caused by surface errors of the reflective surface of the prism.

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 lens group comprising a power prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the first surface is a transmissive aspherical surface that provides positive refractive power for the prism, wherein the second surface is a reflective surface that folds the optical axis of the optical system, and wherein the third surface is a transmissive surface; and 
 a second lens group comprising two or more refractive lenses; and 
 
 wherein the optical system satisfies the conditional expressions:
   0.6&lt; B/A&lt; 2.3, 
 
 where A is power of the optical system, and B is power of the first lens group, and
   −0.2&lt; CD&lt; 0.1,
 
 
 
       where C is power of the second lens group, and D is length of the second lens group. 
     
     
       2. The optical system as recited in  claim 1 , further comprising an aperture stop located on the object side of the power prism. 
     
     
       3. The optical system as recited in  claim 1 , wherein the power prism is formed of an optical plastic material. 
     
     
       4. The optical system as recited in  claim 1 , wherein the power prism comprises a glass prism and a refractive lens composed of an optical plastic material attached to an object side surface of the glass prism. 
     
     
       5. The optical system as recited in  claim 1 , wherein the power prism comprises a glass prism and a refractive lens composed of an optical glass material attached to an object side surface of the glass prism. 
     
     
       6. The optical system as recited in  claim 1 , wherein Z-height of the optical system is 7.3 millimeters or less. 
     
     
       7. The optical system as recited in  claim 1 , wherein X-length of the optical system is 18 millimeters or less. 
     
     
       8. The optical system as recited in  claim 1 , wherein the second lens group consists of four refractive lens elements. 
     
     
       9. The optical system as recited in  claim 8 , wherein the four refractive lens elements comprise, in order from the object side of the optical system to the image side of the optical system:
 a first lens with positive refractive power, 
 a second lens with negative refractive power; 
 a third lens with negative refractive power; and 
 a fourth lens with positive refractive power. 
 
     
     
       10. The optical system as recited in  claim 8 , wherein a second lens in the second lens group from the object side of the optical system is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     
     
       11. The optical system as recited in  claim 10 , wherein the second lens is configured to be rotated 90 degrees to correct for a different amount of astigmatism caused by the second surface of the power prism. 
     
     
       12. The optical system as recited in  claim 8 , wherein at least one of the lenses in the second lens group is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     
     
       13. The optical system as recited in  claim 1 , further comprising a light folding element located on the image side of the second lens group and configured to fold the optical axis of the optical system a second time, wherein a second lens in the second lens group from the object side of the optical system is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     
     
       14. 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 lens group comprising a power prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the first surface is a transmissive aspherical surface that provides positive refractive power for the prism, wherein the second surface is a reflective surface that folds the optical axis of the optical system, and wherein the third surface is a transmissive surface; and 
 a second lens group comprising two or more refractive lenses; and 
 
 an image sensor configured to capture light projected onto a surface of the image sensor by the optical system; 
 wherein the optical system satisfies the conditional expression:
   0.6&lt; B/A&lt; 2.3, and 
   −0.2&lt; CD&lt; 0.1,
 
 
 where A is power of the optical system, B is power of the first lens group, C is power of the second lens group, and D is length of the second lens group. 
 
     
     
       15. The camera as recited in  claim 14 , wherein Z-height of the optical system is 7.3 millimeters or less, and wherein X-length of the optical system is 18 millimeters or less. 
     
     
       16. The camera as recited in  claim 14 , further comprising an aperture stop located on the object side of the power prism. 
     
     
       17. The camera as recited in  claim 14 , further comprising an infrared filter located between the second lens group and the image sensor. 
     
     
       18. The camera as recited in  claim 14 , wherein at least one of the lenses in the second lens group is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     
     
       19. An optical system, comprising:
 a prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the second surface is a reflective surface that folds the optical axis of the optical system and the third surface is a transmissive surface; and 
 one or more refractive lenses, wherein at least one of the one or more refractive lenses is an anamorphic lens configured to correct for astigmatism caused by the prism.

Description:
This application claims benefit of priority to U.S. Provisional Application Ser. No. 63/030,224, entitled “Folded Optical Systems,” filed May 26, 2020, and which is incorporated herein by reference 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 single fold optical systems that include a single prism with optical power (referred to as a power prism) and a lens stack including two or more refractive lens elements are described. The power prism may be referred to as a first lens group, and the lens stack may be referred to as a second lens group. The single folded optical systems may provide reduced Z-axis height and reduced X-axis length when compared to conventional double folded optical systems with similar optical characteristics. Embodiments of the single fold optical systems may, for example, be used in small form factor cameras in mobile multipurpose devices such as smartphones and tablet or pad devices. 
     In some embodiments, the power prism is formed of an optical plastic material, and the object side surface of the prism is a curved spherical or aspherical surface to provide refractive power. In some embodiments, the power prism is an optical glass triangular prism with a refractive lens formed of an optical plastic attached to the object side of the prism to provide refractive power. In some embodiments, the power prism is an optical glass triangular prism with a refractive lens formed of an optical glass attached to the object side of the prism. 
     In addition, embodiments of folded optical systems that include at least one anamorphic lens that is oriented to correct for aberrations including astigmatism caused by surface errors of the reflective surface of the prism(s) in the folded optical systems are described. An anamorphic lens as described herein may, for example, be used in embodiments of the single fold optical systems that include a single power prism as described herein. However, anamorphic lenses as described herein may also be used in other single fold optical systems or double fold optical systems to correct for aberrations including astigmatism caused by surface errors of the reflective surface(s) of the prism(s) in the folded optical systems. Anamorphic lenses as described herein may be used to correct for aberrations caused by the flat reflective surfaces of power prisms or triangular prisms or by the curved reflective surfaces of prisms such as freeform prisms. 
     A manufacturing process for folded optical systems that include anamorphic lenses to correct for aberrations including astigmatism caused by surface errors of the reflective surface(s) of the prism(s) is also described. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates an example single fold optical system that includes a power prism composed of an optical plastic, according to some embodiments. 
         FIG.  2    illustrates an example single fold optical system that includes a glass prism and a plastic lens on the object side of the prism, according to some embodiments. 
         FIG.  3    illustrates an example single fold optical system that includes a glass prism and a glass lens on the object side of the prism, according to some embodiments. 
         FIG.  4    illustrates example optical characteristics and performance metrics of an example optical system as illustrated in  FIG.  1   . 
         FIGS.  5 A and  5 B  compare a double fold optical system to a single fold optical system, according to some embodiments. 
         FIG.  6 A  illustrates another example single fold optical system that includes a power prism composed of an optical plastic, according to some embodiments. 
         FIG.  6 B  illustrates optical characteristics and performance metrics of the example optical system illustrated in  FIG.  6 A . 
         FIG.  7 A  illustrates another example single fold optical system that includes a glass prism and a plastic lens on the object side of the prism, according to some embodiments. 
         FIG.  7 B  illustrates optical characteristics and performance metrics of the example optical system illustrated in  FIG.  7 A . 
         FIG.  8 A  illustrates another example single fold optical system that includes a glass prism and a glass lens on the object side of the prism, according to some embodiments. 
         FIG.  8 B  illustrates optical characteristics and performance metrics of the example optical system illustrated in  FIG.  8 A . 
         FIG.  9 A  illustrates another example single fold optical system that includes a power prism, according to some embodiments. 
         FIG.  9 B  illustrates optical characteristics and performance metrics of the example optical system illustrated in  FIG.  9 A . 
         FIG.  10    is a flowchart of a method for capturing images using embodiments of a single fold optical system as illustrated in  FIGS.  1  through  9   , according to some embodiments. 
         FIG.  11    shows surfaces of an example single fold optical system as referred to in the Tables. 
         FIGS.  12 A through  12 D  illustrate using an anamorphic lens in a lens stack to correct aberrations including astigmatism caused by surface errors of the reflective surface of a prism in a folded optical system, according to some embodiments. 
         FIG.  13    illustrates using an anamorphic lens in a lens stack to correct aberrations including astigmatism caused by surface errors of the reflective surface of a prism in a double fold optical system, according to some embodiments. 
         FIG.  14    illustrates using an anamorphic lens to correct aberrations including astigmatism caused by a freeform prism, according to some embodiments. 
         FIG.  15    is a high-level flowchart of a method of manufacturing a folded optical system that includes an anamorphic lens oriented to correct for aberrations including astigmatism caused by surface errors of the reflective surface of a prism in a folded optical system, according to some embodiments. 
         FIG.  16    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 single fold 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 double folded optical systems may include two prisms and a lens stack including two or more refractive lens elements. A first prism redirects light from a first optical axis to the lens stack on a second optical axis. A second prism located at the image side of the lens stack folds the optical axis on to a third axis where an image is formed at an image plane at or near the surface of a photosensor. 
     Embodiments of single fold optical systems that include a single prism with optical power (referred to as a power prism) and a lens stack including two or more refractive lens elements as described herein may provide an optical system with long focal length and reduced thickness (Z-height) and X-length when compared to a double folded optical system with similar optical characteristics. In general, the Z-height of double folded optics is defined by the prism size and mechanical back focus. Embodiments of the single fold optical system may provide a long mechanical back focus without increasing the Z-height of the optical system. Providing power on the prism may reduce the optical total length and reduce the X-length of the optical system. 
     In some embodiments, the power prism in the single fold optical system is formed of an optical plastic material, and the object side surface of the prism is a curved spherical or aspherical surface to provide refractive power. In some embodiments, the power prism is an optical glass triangular prism with a refractive lens formed of an optical plastic attached to the object side of the prism to provide refractive power. A first surface of the lens may be an aspherical or spherical surface. In some embodiments, the power prism is an optical glass triangular prism with a refractive lens formed of an optical glass attached to the object side of the prism. A first surface of the lens may be an aspherical or spherical surface. Note that the power prism has more than three surfaces; however, only three of the surfaces of the power prism are discussed; an object side surface with curvature that provides refractive power; a reflective surface that acts to fold the optical axis; and an image side surface through which light from the reflective surface exits the power prism towards the lens stack or second lens group. 
     In addition, embodiments of folded optical systems that include at least one anamorphic lens that is oriented to correct for aberrations including astigmatism caused by surface errors of the reflective surface of the prism(s) in the folded optical systems are described. An anamorphic lens as described herein may, for example, be used in embodiments of the single fold optical systems that include a single power prism as described herein. However, anamorphic lenses as described herein may also be used in other single fold optical systems or double fold optical systems to correct for aberrations including astigmatism caused by surface errors of the reflective surface(s) of the prism(s) in the folded optical systems. Anamorphic lenses as described herein may be used to correct for aberrations caused by the flat reflective surfaces of power prisms or triangular prisms or by the curved reflective surfaces of prisms such as freeform prisms. Freeform optics involve optical designs with at least one 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 surface which has no translational or rotational symmetry about axes normal to the mean plane of the surface. 
     A manufacturing process for folded optical systems that include anamorphic lenses to correct for aberrations including astigmatism caused by surface errors of the reflective surface(s) of the prism(s) is also described. 
       FIGS.  1  through  3    illustrate side cutaway views of example embodiments of single fold optical systems as described herein. As shown in  FIGS.  1  through  3   , the single fold optical system may include:
         a first lens group that includes a power prism formed of an optical plastic material with an aspherical object side surface as shown in  FIG.  1   , or that includes a triangular glass prism with a positive lens formed of an optical plastic or glass material having an aspherical object side surface and a flat or plano image side surface attached to the object side surface of the prism as shown in  FIGS.  2  and  3   ; and   a second lens group that includes two or more refractive lens elements (four, in these embodiments). The refractive lenses in the second lens group may be formed of optical plastic or glass materials. In some embodiments, all of the refractive lenses in the second lens group may be formed of the same material. In some embodiments, at least two of the refractive lenses in the second lens group may be formed of different materials.       

     In some embodiments of the single fold optical system, the first (object side) surface of the first lens group is aspherical, and the angle between the principal ray that passes through the first surface of the first lens group and the principal ray at an image plane formed on the image side of the second lens group may be, but is not necessarily, less than 90 degrees. 
     Embodiments of the single fold optical system may satisfy the following conditional expression:
 
0.6&lt; B/A&lt; 2.3,
 
where A is the power of the total optical system, and B is the power of the first lens group. If B/A is larger than the range expressed in the conditional expression, the amount of sag may be too large to manufacture. On the other hand, if B/A is smaller than the range expressed in the conditional expression, the X-length of optical system cannot be reduced effectively.
 
     Embodiments of the single fold optical system may satisfy the following conditional expression:
 
−0.2&lt; CD&lt; 0.1,
 
where C is the power of the second lens group, and D is the length of the second lens group. CD applies to the sensitivity of the second lens group. If CD is not within the range expressed in the conditional expression, the tolerance of second lens group may not be good and/or the size (length) of the second lens group may be enlarged.
 
     In some embodiments, the prism in the first lens group is composed of an optical material with an Abbe number V d  that satisfies the following condition:
 
 V   d &gt;50.
 
     Embodiments of the single fold optical system as described herein may have a Z-height of &lt;7.3 mm, and an X-length of &lt;18 mm. 
     In some embodiments, one or more of the optical elements in the optical system 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.). 
       FIG.  1    illustrates a single fold optical system that includes a power prism composed of an optical plastic, according to some embodiments. Optical system  100  may include a power prism  110  (also referred to as a first lens group) and a lens stack  120  (also referred to as a second lens group) that includes two or more refractive lenses. In this example, lens stack  120  includes four refractive lenses: lens  121 , lens  122 , lens  123 , and lens  124 . Note, however, that some embodiments may include more or fewer lenses in lens stack  120 . An aperture stop  102  may be located at or near the object side of the power prism  110 . 
     The power prism  110  may be formed of an optical plastic material. In some embodiments, the object side surface  112  of the prism  110  is a curved aspherical surface that provides positive refractive power for the prism  110 . A second surface  114  of the prism  110  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  112  of the prism  110  to thus fold the optical axis of the optical system  100 . The light reflected by the second surface  114  exits the prism  110  through a third flat or plano surface  116  to a first lens  121  in the lens stack  120 . The lenses in the lens stack  120  then refract the light to form an image at an image plane. 
       FIG.  1    shows an example lens stack  120  that includes four refractive lenses: lens  121  with positive refractive power, lens  122  with negative refractive power, lens  123  with negative refractive power, and lens  124  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  120 . In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  100  of  FIG.  1    may form an image at an image plane at or near a surface of an image sensor  140  located on the image side of the lens stack  120 . In some embodiments, an infrared (IR) filter  130  may be located between lens stack  120  and the image sensor  140 . The optical system  100 , sensor  140 , and filter  130  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  2    illustrates an example single fold optical system that includes a glass prism and a plastic lens on the object side of the prism, according to some embodiments. Optical system  200  may include a lens  204  formed of an optical plastic material and a prism  210  formed of an optical glass material (collectively referred to as a first lens group) and a lens stack  220  (also referred to as a second lens group) that includes two or more refractive lenses. In this example, lens stack  220  includes four refractive lenses: lens  221 , lens  222 , lens  223 , and lens  224 . Note, however, that some embodiments may include more or fewer lenses in lens stack  220 . An aperture stop  202  may be located at or near the object side of the lens  204 . 
     The prism  210  may be formed of an optical glass material. The object side surface  212  of the prism  210  is a flat or plano surface. A plastic lens  204  with positive refractive power may be attached to the object side surface  212  of the prism  210 , for example with an adhesive material. The object side surface of lens  204  may be a spherical or aspherical convex surface; the image side surface of lens  204  is a flat or plano surface. A second surface  214  of the prism  210  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  212  of the prism  210  to thus fold the optical axis of the optical system  200 . The light reflected by the second surface  214  exits the prism  210  through a third flat or plano surface  216  to a first lens  221  in the lens stack  220 . The lenses in the lens stack  220  then refract the light to form an image at an image plane. 
       FIG.  2    shows an example lens stack  220  that includes four refractive lenses: lens  221  with positive refractive power, lens  222  with negative refractive power, lens  223  with negative refractive power, and lens  224  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  220 . In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  200  of  FIG.  2    may form an image at an image plane at or near a surface of an image sensor  240  located on the image side of the lens stack  220 . In some embodiments, an infrared (IR) filter  230  may be located between lens stack  220  and the image sensor  240 . The optical system  200 , sensor  240 , and filter  230  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  3    illustrates an example single fold optical system that includes a glass prism and a glass lens on the object side of the prism, according to some embodiments. Optical system  300  may include a lens  304  formed of an optical glass material and a prism  310  formed of an optical glass material (collectively referred to as a first lens group) and a lens stack  320  (also referred to as a second lens group) that includes two or more refractive lenses. In this example, lens stack  320  includes four refractive lenses: lens  321 , lens  322 , lens  323 , and lens  324 . Note, however, that some embodiments may include more or fewer lenses in lens stack  320 . An aperture stop  302  may be located at or near the object side of the lens  304 . 
     The prism  310  may be formed of an optical glass material. The object side surface  312  of the prism  310  is a flat or plano surface. A glass lens  304  with positive refractive power may be attached to the object side surface  312  of the prism  310 , for example with an adhesive material. The object side surface of lens  304  may be a spherical or aspherical convex surface; the image side surface of lens  304  is a flat or plano surface. A second surface  314  of the prism  310  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  312  of the prism  310  to thus fold the optical axis of the optical system  300 . The light reflected by the second surface  314  exits the prism  310  through a third flat or plano surface  316  to a first lens  321  in the lens stack  320 . The lenses in the lens stack  320  then refract the light to form an image at an image plane. 
       FIG.  3    shows an example lens stack  320  that includes four refractive lenses: lens  321  with positive refractive power, lens  322  with negative refractive power, lens  223  with negative refractive power, and lens  324  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  320 . In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  300  of  FIG.  3    may form an image at an image plane at or near a surface of an image sensor  340  located on the image side of the lens stack  320 . In some embodiments, an infrared (IR) filter  330  may be located between lens stack  320  and the image sensor  340 . The optical system  300 , sensor  340 , and filter  330  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  4    illustrates example optical characteristics and performance metrics of an example optical system as illustrated in  FIG.  1   . The example optical system may have an X length of 15.5 millimeters (mm), and a Z height of 6.8 mm. Distortion of the optical systems may be &lt;+/−0.25%. The graphs show the modulation transfer function (MTF) of the single fold optical systems at infinity (inf) and at macro. 
       FIGS.  5 A and  5 B  compare a double fold optical system to a single fold optical system, according to some embodiments.  FIG.  5 A  shows an example conventional double folded optical system  500 A that includes, in order from an object side to an image side, a first prism that folds the optical axis a first time, a lens stack, and a second prism or mirror that folds the optical axis a second time; an image is formed at an image plane at or near a sensor. Z-height of the optical system  500 A may be about 7.1 mm, while X-length may be about 22.3 mm.  FIG.  5 B  shows an example embodiment of a single fold optical system  500 B as described herein that includes, in order from an object side to an image side, a first lens group (power prism) that folds the optical axis, and a second lens group (lens stack) that refracts light received from the first lens group to form an image at an image plane at or near a sensor. Z-height of the optical system  500 B may be about 6.8 mm, while X-length may be about 15.5 mm. 
     As shown in  FIGS.  5 A and  5 B , embodiments of the single fold optical system as described herein may provide an optical system with long focal length and reduced thickness (Z-height) and X-length when compared to a conventional double folded optical system with similar optical characteristics. In general, the Z-height of double folded optics is defined by the prism size and mechanical back focus. Embodiments of the single fold optical system may provide a long mechanical back focus without increasing, or even decreasing, the Z-height of the optical system. Providing power on the prism may reduce the optical total length and reduce the X-length of the optical system. 
       FIGS.  6 A- 6 B,  7 A- 7 B,  8 A- 8 B, and  9    illustrate side cutaway views of additional example embodiments of single fold optical systems as described herein. 
       FIG.  6 A  illustrates another example single fold optical system that includes a power prism composed of an optical plastic, according to some embodiments. Optical system  600  may include a power prism  610  (also referred to as a first lens group) and a lens stack  620  (also referred to as a second lens group) that includes four refractive lenses: lens  621 , lens  622 , lens  623 , and lens  624 . Note, however, that some embodiments may include more or fewer lenses in lens stack  620 . An aperture stop  602  may be located at or near the object side of the power prism  610 . 
     The power prism  610  may be formed of an optical plastic material. In some embodiments, the object side surface  612  of the prism  610  is a curved aspherical surface that provides positive refractive power for the prism  610 . A second surface  614  of the prism  610  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  612  of the power prism  610  to thus fold the optical axis of the optical system  600 . The light reflected by the second surface  614  exits the prism  610  through a third flat or plano surface  616  to a first lens  621  in the lens stack  620 . The lenses in the lens stack  612  then refract the light to form an image at an image plane. 
       FIG.  6 A  shows an example lens stack  620  that includes four refractive lenses: lens  621  with positive refractive power, lens  622  with negative refractive power, lens  623  with negative refractive power, and lens  624  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  620 . In some embodiments, at least one surface of at least one of the lenses in the second lens group may be an aspherical surface. The refractive lenses in the second lens group may be formed of optical plastic or glass materials. In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  600  of  FIG.  6 A  may form an image at an image plane at or near a surface of an image sensor  640  located on the image side of the lens stack  620 . In some embodiments, an infrared (IR) filter  630  may be located between lens stack  620  and the image sensor  640 . The optical system  600 , sensor  640 , and filter  630  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  6 B  illustrates optical characteristics and performance metrics of the example optical system  600  illustrated in  FIG.  6 A . The example optical system  600  may have an X length of 17.2 millimeters (mm), and a Z height of 6.8 mm. Distortion of the optical systems may be &lt;+/−0.25%. The graphs show the modulation transfer function (MTF) of the single fold optical systems at infinity (inf) and at macro. 
       FIG.  7 A  illustrates another example single fold optical system that includes a glass prism and a plastic lens on the object side of the prism, according to some embodiments. Optical system  700  may include a lens  704  formed of an optical plastic material and a prism  710  formed of an optical glass material (collectively referred to as a first lens group) and a lens stack  720  (also referred to as a second lens group) that includes four refractive lenses: lens  721 , lens  722 , lens  723 , and lens  724 . Note, however, that some embodiments may include more or fewer lenses in lens stack  720 . An aperture stop  702  may be located at or near the object side of the lens  704 . 
     The prism  710  may be formed of an optical glass material. The object side surface  712  of the prism  710  is a flat or plano surface. A plastic lens  704  with positive refractive power may be attached to the object side surface  712  of the prism  710 , for example with an adhesive material. The object side surface of lens  704  may be a spherical or aspherical convex surface; the image side surface of lens  704  is a flat or plano surface. A second surface  714  of the prism  710  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  712  of the prism  710  to thus fold the optical axis of the optical system  700 . The light reflected by the second surface  714  exits the prism  710  through a third flat or plano surface  716  to a first lens  721  in the lens stack  720 . The lenses in the lens stack  720  then refract the light to form an image at an image plane. 
       FIG.  7 A  shows an example lens stack  720  that includes four refractive lenses: lens  721  with positive refractive power, lens  722  with negative refractive power, lens  723  with negative refractive power, and lens  724  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  720 . In some embodiments, at least one surface of at least one of the lenses in the second lens group may be an aspherical surface. The refractive lenses in the second lens group may be formed of optical plastic or glass materials. In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  700  of  FIG.  7 A  may form an image at an image plane at or near a surface of an image sensor  740  located on the image side of the lens stack  720 . In some embodiments, an infrared (IR) filter  730  may be located between lens stack  720  and the image sensor  740 . The optical system  700 , sensor  740 , and filter  730  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  7 B  illustrates optical characteristics and performance metrics of the example optical system  700  illustrated in  FIG.  7 A . The example optical system  700  may have an X length of 17.2 millimeters (mm), and a Z height of 6.5 mm. Distortion of the optical systems may be &lt;+/−0.25%. The graphs show the modulation transfer function (MTF) of the single fold optical systems at infinity (inf) and at macro. 
       FIG.  8 A  illustrates another example single fold optical system that includes a glass prism and a glass lens on the object side of the prism, according to some embodiments. Optical system  800  may include a lens  804  formed of an optical glass material and a prism  810  formed of an optical glass material (collectively referred to as a first lens group) and a lens stack  820  (also referred to as a second lens group) that includes four refractive lenses: lens  821 , lens  822 , lens  823 , and lens  824 . Note, however, that some embodiments may include more or fewer lenses in lens stack  820 . An aperture stop  802  may be located at or near the object side of the lens  804 . 
     The prism  810  may be formed of an optical glass material. The object side surface  812  of the prism  810  is a flat or plano surface. A glass lens  804  with positive refractive power may be attached to the object side surface  812  of the prism  8710 , for example with an adhesive material. The object side surface of lens  804  may be a spherical or aspherical convex surface; the image side surface of lens  804  is a flat or plano surface. A second surface  814  of the prism  810  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  812  of the prism  810  to thus fold the optical axis of the optical system  800 . The light reflected by the second surface  814  exits the prism  810  through a third flat or plano surface  816  to a first lens  821  in the lens stack  820 . The lenses in the lens stack  820  then refract the light to form an image at an image plane. 
       FIG.  8 A  shows an example lens stack  820  that includes four refractive lenses: lens  821  with positive refractive power, lens  822  with negative refractive power, lens  823  with negative refractive power, and lens  824  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  820 . In some embodiments, at least one surface of at least one of the lenses in the second lens group may be an aspherical surface. The refractive lenses in the second lens group may be formed of optical plastic or glass materials. In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  800  of  FIG.  8 A  may form an image at an image plane at or near a surface of an image sensor  840  located on the image side of the lens stack  820 . In some embodiments, an infrared (IR) filter  830  may be located between lens stack  820  and the image sensor  840 . The optical system  800 , sensor  840 , and filter  830  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  8 B  illustrates optical characteristics and performance metrics of the example optical system  800  illustrated in  FIG.  8 A . The example optical system  800  may have an X length of 17.2 millimeters (mm), and a Z height of 7.1 mm. Distortion of the optical systems may be &lt;+/−0.25%. The graphs show the modulation transfer function (MTF) of the single fold optical systems at infinity (inf) and at macro. 
       FIG.  9 A  illustrates another example single fold optical system that includes a power prism, according to some embodiments. Optical system  900  may include a power prism  910  (also referred to as a first lens group) and a lens stack  920  (also referred to as a second lens group) that includes four refractive lenses: lens  921 , lens  922 , lens  923 , and lens  924 . Note, however, that some embodiments may include more or fewer lenses in lens stack  920 . An aperture stop  902  may be located at or near the object side of the power prism  910 . 
     The power prism  910  may be formed of an optical plastic material. In some embodiments, the object side surface  912  of the prism  910  is a curved aspherical surface that provides positive refractive power for the prism  910 . A second surface  914  of the prism  910  is a flat or plano surface that reflects, via total internal reflection (TIR) or via a mirror coating, light received from an object field through the object side surface  912  of the power prism  910  to thus fold the optical axis of the optical system  900 . The light reflected by the second surface  914  exits the prism  910  through a third flat or plano surface  916  to a first lens  921  in the lens stack  920 . The lenses in the lens stack  912  then refract the light to form an image at an image plane. 
       FIG.  9 A  shows an example lens stack  920  that includes four refractive lenses: lens  921  with positive refractive power, lens  922  with negative refractive power, lens  923  with negative refractive power, and lens  924  with positive refractive power. Note, however, that some embodiments may include more or fewer lenses in lens stack  920 . In some embodiments, at least one surface of at least one of the lenses in the second lens group may be an aspherical surface. The refractive lenses in the second lens group may be formed of optical plastic or glass materials. In addition, the material, shape, power, power order, position, and distance between the lenses is given by way of example, and is not intended to be limiting. 
     The single fold optical system  900  of  FIG.  9 A  may form an image at an image plane at or near a surface of an image sensor  940  located on the image side of the lens stack  920 . In some embodiments, an infrared (IR) filter  930  may be located between lens stack  920  and the image sensor  940 . The optical system  900 , sensor  940 , and filter  930  (if present) may be components of a camera that may, for example, be used as a small form factor camera in mobile multipurpose devices such as smartphones and tablet or pad devices. 
       FIG.  9 B  illustrates optical characteristics and performance metrics of the example optical system  900  illustrated in  FIG.  9 A . The example optical system  900  may have an X length of 17.6 millimeters (mm), and a Z height of 7.2 mm. Distortion of the optical systems may be &lt;+/−0.25%. The graphs show the modulation transfer function (MTF) of the single fold optical systems at infinity (inf) and at macro. 
       FIG.  10    is a flowchart of a method for capturing images using embodiments of a single fold optical system as illustrated in  FIGS.  1  through  9   , according to some embodiments. As indicated at  1000 , light from an object field is received through an aperture at a first surface of a power prism. As indicated at  1010 , the first surface of the power prism refracts the light to a second (reflective) surface of the power prism. As indicated at  1020 , the second surface of the power prism reflects the light to a third surface of the power prism. As indicated at  1030 , the third surface of the prism transmits the light to a lens stack. As indicated at  1040 , the refractive lenses in the lens stack refract the light to form an image at an image plane at or near a surface of an image sensor. In some embodiments, an infrared filter may be positioned between the lens stack and the image sensor. 
     The following tables provide optical and physical characteristics of the example single fold lens systems described herein.  FIG.  11    shows surfaces of an example single fold optical system as referred to in the Tables. Each surface location is determined by the global coordinate based on Prism S1. 
     An aspherical surface may be defined as: 
             z   =           h   2     r       1   +       1   -         (     1   +   k     )     ⁢     h   2         r   2               +     A   ⁢           ⁢     h   2       +     Bh   2     +     Ch   2     +   …                 where   ⁢                       h   =         x   2     +     y   2               
and where radius of curvature r is:
 
     4th order (A); 
     6th order (B); 
     8th order (C); 
     10th order (D); 
     12th order (E); and 
     14th order (F). 
     Table 1 provides ranges of optical and physical characteristics of the example embodiments shown in  FIGS.  1 ,  6 A,  7 A,  8 A, and  9 A . 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Charac- 
                   
                   
                 FIG.  
                 FIG.  
                 FIG.  
                 FIG.  
               
               
                 teristic 
                 Range 
                 FIG. 1 
                 6A 
                 7A 
                 8A 
                 9A 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 B/A 
                 0.6-2.3 
                 1.24 
                 0.81 
                 0.81 
                 0.81 
                 2.10 
               
               
                 CD 
                 −0.2-0.1  
                 −0.128 
                 0.047 
                 0.047 
                 0.046 
                 −0.106 
               
               
                 Vd1 
                 &gt;50 
                 55.97 
                 55.73 
                 55.73 
                 55.73 
                 55.73 
               
               
                 Z-height 
                 &lt;7.3 
                 6.8 
                 6.8 
                 6.5 
                 7.1 
                 7.2 
               
               
                 X-length 
                 &lt;18 
                 15.5 
                 17.2 
                 17.2 
                 17.2 
                 17.6 
               
               
                   
               
            
           
         
       
     
     Tables 2A through 2F provide optical and physical characteristics for the example single fold optical system as illustrated in  FIG.  1   . 
     Table 2A shows all surface positions based on the Prism S1 global coordinate for the example single fold optical system as illustrated in  FIG.  1   : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2A 
               
               
                   
               
               
                   
                 x 
                 z 
                 angle (α) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 aperture 
                 0 
                 0.3 
                 0 
               
               
                 Prism S1 
                 0.000 
                 0.000 
                 0 
               
               
                 Prism S2 
                 0.000 
                 3.800 
                 45 
               
               
                 Prism S3 
                 −3.400 
                 3.800 
                 90 
               
               
                 L1 S1 
                 −3.500 
                 3.800 
                 90 
               
               
                 L1S2 
                 −4.320 
                 3.800 
                 90 
               
               
                 L2S1 
                 −4.712 
                 3.800 
                 90 
               
               
                 L2S2 
                 −5.102 
                 3.800 
                 90 
               
               
                 L3S1 
                 −8.070 
                 3.800 
                 90 
               
               
                 L3S4 
                 −8.737 
                 3.800 
                 90 
               
               
                 L4S1 
                 −9.070 
                 3.800 
                 90 
               
               
                 L4S2 
                 −10.225 
                 3.800 
                 90 
               
               
                 IRcut S1 
                 −11.890 
                 3.800 
                 90 
               
               
                 IRcut S2 
                 −12.100 
                 3.800 
                 90 
               
               
                 image plane (INF) 
                 −12.200 
                 3.800 
                 90 
               
               
                   
               
            
           
         
       
     
     Tables 2B through 2D show aspherical values for the surfaces of the optical components for the example single fold optical system as illustrated in  FIG.  1   : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2B 
               
               
                   
               
               
                   
                 Prism S1 
                 L1S1 
                 L1S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 6.7203 
                 −5.2935 
                 14.2603 
               
               
                 4th order 
                 −4.26730E−04 
                 −2.88851E−03 
                 −1.48664E−03 
               
               
                 6th order 
                 −1.29339E−05 
                 −3.95461E−04 
                   9.32386E−04 
               
               
                 8th order 
                 −7.66845E−07 
                   9.90583E−05 
                 −6.91378E−05 
               
               
                 10th order 
                   6.66654E−08 
                 −1.12263E−05 
                 −3.43883E−06 
               
               
                 12th order 
                 −5.16169E−09 
                   2.23130E−06 
                   3.08245E−06 
               
               
                 14th order 
                   
                   4.49321E−07 
                 −2.03270E−07 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 2C 
               
               
                   
               
               
                   
                 L2S1 
                 L2S2 
                 L3S1 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −16.1429 
                 −2.7451 
                 3.7738 
               
               
                 4th order 
                   1.41735E−02 
                   1.19869E−02 
                   1.31664E−02 
               
               
                 6th order 
                 −6.22662E−04 
                 −2.57413E−03 
                 −2.21852E−03 
               
               
                 8th order 
                 −1.17735E−04 
                   4.39224E−04 
                   6.21870E−04 
               
               
                 10th order 
                 −3.12763E−05 
                 −5.79999E−04 
                 −1.72582E−04 
               
               
                 12th order 
                 −4.96180E−07 
                   2.09980E−04 
                   
               
               
                 14th order 
                 −4.53847E−07 
                 −4.24766E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 2D 
               
               
                   
               
               
                   
                 L3S2 
                 L4S1 
                 L4S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −10.1283 
                 −15.1458 
                 5.1079 
               
               
                 4th order 
                   1.57161E−02 
                   3.58922E−03 
                   266831E−03 
               
               
                 6th order 
                 −2.19959E−03 
                 −5.01016E−04 
                 −8.20924E−04 
               
               
                 8th order 
                   3.69265E−04 
                 −8.42268E−05 
                   9.61069E−05 
               
               
                 10th order 
                 −4.01054E−05 
                   3.08659E−05 
                 −2.99277E−05 
               
               
                 12th order 
                   
                 −4.44401E−06 
                   4.12343E−06 
               
               
                 14th order 
                   
                   2.08392E−07 
                 −2.22745E−07 
               
               
                   
               
            
           
         
       
     
     Table 2E shows material characteristics of the optical components for the example single fold optical system as illustrated in  FIG.  1   . Nd refers to refractive index, and Vd refers to Abbe number of the material. L1-L4 refer to the four lenses in the second lens group from the object side to the image side of the optical system: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 2E 
               
               
                   
               
               
                   
                   
                 Prism 
                 L1 
                 L2 
                 L3 
                 L4 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Nd 
                 1.544 
                 1.544 
                 1.671 
                 1.544 
                 1.671 
               
               
                   
                 Vd 
                 55.97 
                 55.97 
                 19.23 
                 55.97 
                 19.23 
               
               
                   
               
            
           
         
       
     
     Table 2F shows optical specifications for the example single fold optical system as illustrated in  FIG.  1   . EFL is effective focal length, and Fno is the F-number of the optical system: 
     
       
         
           
               
               
               
             
               
                 TABLE 2F 
               
               
                   
               
             
            
               
                   
                 EFL 
                 15.3 
               
               
                   
                 Fno 
                 3.0 
               
               
                   
                 semi-sensor diagonal 
                 2.52 
               
               
                   
                 Macro distance 
                 80 cm 
               
               
                   
               
            
           
         
       
     
     Tables 3A through 3F provide optical and physical characteristics for the example single fold optical system as illustrated in  FIG.  6 A . 
     Table 3A shows all surface positions based on the Prism S1 global coordinate for the example single fold optical system as illustrated in  FIG.  6 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 3A 
               
               
                   
               
               
                   
                 x 
                 z 
                 angle (α) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 aperture 
                 0 
                 0.28 
                 0 
               
               
                 Prism S1 
                 0.000 
                 0.000 
                 0 
               
               
                 Prism S2 
                 0.000 
                 3.450 
                 45 
               
               
                 Prism S3 
                 −3.100 
                 3.450 
                 90 
               
               
                 L1 S1 
                 −3.600 
                 3.450 
                 90 
               
               
                 L1S2 
                 −4.645 
                 3.450 
                 90 
               
               
                 L2S1 
                 −4.898 
                 3.450 
                 90 
               
               
                 L252 
                 −5.288 
                 3.450 
                 90 
               
               
                 L3S1 
                 −8.974 
                 3.450 
                 90 
               
               
                 L3S4 
                 −9.634 
                 3.450 
                 90 
               
               
                 L4S1 
                 −10.375 
                 3.450 
                 90 
               
               
                 L4S2 
                 −11.475 
                 3.450 
                 90 
               
               
                 IRcut S1 
                 −13.359 
                 3.450 
                 90 
               
               
                 IRcut S2 
                 −13.569 
                 3.450 
                 90 
               
               
                 image plane (INF) 
                 −13.669 
                 3.450 
                 90 
               
               
                   
               
            
           
         
       
     
     Tables 3B through 3D show aspherical values for the surfaces of the optical components for the example single fold optical system as illustrated in  FIG.  6 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 3B 
               
               
                   
               
               
                   
                 Prism S1 
                 L1S1 
                 L1S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 10.1475 
                 -4.5962 
                 24.1370 
               
               
                 4th order 
                 −5.10336E−04 
                 −4.96952E−03 
                 −6.96106E−03 
               
               
                 6th order 
                   1.31446E−07 
                   3.25426E−04 
                   2.34753E−03 
               
               
                 8th order 
                 −8.33779E−07 
                 −2.59701E−05 
                 −5.13966E−04 
               
               
                 10th order 
                   1.26361E−07 
                   3.54569E−05 
                   1.47389E−04 
               
               
                 12th order 
                 −5.84423E−09 
                 −7.43090E−06 
                 −1.18246E−05 
               
               
                 14th order 
                   
                   1.91989E−06 
                   1.99593E−07 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 3C 
               
               
                   
               
               
                   
                 L2S1 
                 L2S2 
                 L3S1 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −5.8392 
                 −2.7004 
                 7.9220 
               
               
                 4th order 
                   2.08846E−02 
                   2.80123E−02 
                   4.36643E−02 
               
               
                 6th order 
                 −6.99973E−03 
                 −1.15153E−02 
                 −8.56777E−03 
               
               
                 8th order 
                   9.61573E−04 
                   2.21425E−03 
                   4.95687E−04 
               
               
                 10th order 
                 −3.49028E−05 
                 −6.01848E−04 
                 −4.46371E−05 
               
               
                 12th order 
                 −8.47955E−07 
                   1.40503E−04 
                   
               
               
                 14th order 
                 −2.38157E−06 
                 −2.85205E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 3D 
               
               
                   
               
               
                   
                 L3S2 
                 L4S1 
                 L4S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −5.3114 
                 −81.4716 
                 6.5864 
               
               
                 4th order 
                   3.90863E−02 
                 −1.94553E−03 
                   8.73233E−04 
               
               
                 6th order 
                 −8.82724E−03 
                   1.24447E−03 
                 −2.40538E−04 
               
               
                 8th order 
                   1.21063E−03 
                 −3.53784E−04 
                   4.64840E−05 
               
               
                 10th order 
                 −9.15778E−05 
                   8.00536E−05 
                 −2.44547E−06 
               
               
                 12th order 
                   
                 −7.42994E−06 
                   1.63492E−06 
               
               
                 14th order 
                   
                   4.81112E−07 
                 −3.05210E−08 
               
               
                   
               
            
           
         
       
     
     Table 3E shows material characteristics of the optical components for the example single fold optical system as illustrated in  FIG.  6 A . Nd refers to refractive index, and Vd refers to Abbe number of the material. L1-L4 refer to the four lenses in the second lens group from the object side to the image side of the optical system: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 3E 
               
               
                   
               
               
                   
                   
                 Prism 
                 L1 
                 L2 
                 L3 
                 L4 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Nd 
                 1.535 
                 1.544 
                 1.671 
                 1.544 
                 1.671 
               
               
                   
                 Vd 
                 55.73 
                 55.97 
                 19.23 
                 55.97 
                 19.23 
               
               
                   
               
            
           
         
       
     
     Table 3F shows optical specifications for the example single fold optical system as illustrated in  FIG.  6 A . EFL is effective focal length, and Fno is the F-number of the optical system: 
     
       
         
           
               
               
               
             
               
                 TABLE 3F 
               
               
                   
               
             
            
               
                   
                 EFL 
                 15.37 
               
               
                   
                 Fno 
                 3.0 
               
               
                   
                 semi-sensor diagonal 
                 2.52 
               
               
                   
                 Macro distance 
                 125 cm 
               
               
                   
               
            
           
         
       
     
     Tables 4A through 4F provide optical and physical characteristics for the example single fold optical system as illustrated in  FIG.  7 A . 
     Table 4A shows all surface positions based on the Prism S1 global coordinate for the example single fold optical system as illustrated in  FIG.  7 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 4A 
               
               
                   
               
               
                   
                 x 
                 z 
                 angle (α) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 aperture 
                 0 
                 0.28 
                 0 
               
               
                 Prism S1 
                 0.000 
                 0.000 
                 0 
               
               
                 Prism inner surface 
                 0.000 
                 0.349 
                 0 
               
               
                 Prims S2 
                 0.000 
                 3.134 
                 45 
               
               
                 Prism S3 
                 −2.785 
                 3.134 
                 90 
               
               
                 L1 S1 
                 −4.220 
                 3.134 
                 90 
               
               
                 L1S2 
                 −5.265 
                 3.134 
                 90 
               
               
                 L2S1 
                 −5.518 
                 3.134 
                 90 
               
               
                 L2S2 
                 −5.908 
                 3.134 
                 90 
               
               
                 L3S1 
                 −9.594 
                 3.134 
                 90 
               
               
                 L3S2 
                 −10.254 
                 3.134 
                 90 
               
               
                 L4S1 
                 −10.995 
                 3.134 
                 90 
               
               
                 L4S2 
                 −12.095 
                 3.134 
                 90 
               
               
                 IRcut S1 
                 −13.946 
                 3.134 
                 90 
               
               
                 IRcut S2 
                 −14.156 
                 3.134 
                 90 
               
               
                 image plane (INF) 
                 −14.256 
                 3.134 
                 90 
               
               
                   
               
            
           
         
       
     
     Tables 4B through 4D show aspherical values for the surfaces of the optical components for the example single fold optical system as illustrated in  FIG.  7 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 4B 
               
               
                   
               
               
                   
                 Prism S1 
                 L1S1 
                 L1S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 9.6677 
                 −4.5962 
                 24.1370 
               
               
                 4th order 
                 −5.32525E−04 
                 −4.96952E−03 
                 −6.96106E−03 
               
               
                 6th order 
                 −8.96273E−06 
                   3.25426E−04 
                   2.34753E−03 
               
               
                 8th order 
                   1.55564E−06 
                 −2.59701E−05 
                 −5.13966E−04 
               
               
                 10th order 
                 −1.69683E−07 
                   3.54569E−05 
                   1.47389E−04 
               
               
                 12th order 
                   7.82692E−09 
                 −7.43090E−06 
                 −1.18246E−05 
               
               
                 14th order 
                   
                   1.91989E−06 
                   1.99593E−07 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 4C 
               
               
                   
               
               
                   
                 L2S1 
                 L2S2 
                 L3S1 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −5.8392 
                 −2.7004 
                 7.9220 
               
               
                 4th order 
                   2.08846E−02 
                   2.80123E−02 
                   4.36643E−02 
               
               
                 6th order 
                 −6.99973E−03 
                 −1.15153E−02 
                 −8.56777E−03 
               
               
                 8th order 
                   9.61573E−04 
                   2.21425E−03 
                   4.95687E−04 
               
               
                 10th order 
                 −3.49028E−05 
                 −6.01848E−04 
                 −4.46371E−05 
               
               
                 12th order 
                 −8.47955E−07 
                   1.40503E−04 
                   
               
               
                 14th order 
                 −2.38157−06 
                 −2.85205E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 4D 
               
               
                   
               
               
                   
                 L3S2 
                 L4S1 
                 L4S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −5.3114 
                 −81.4716 
                 6.5864 
               
               
                 4th order 
                   3.90863E−02 
                 −1.94553E−03 
                   8.73233E−04 
               
               
                 6th order 
                 −8.82724E−03 
                   1.24447E−03 
                 −2.40538E−04 
               
               
                 8th order 
                   1.21063E−03 
                 −3.53784E−04 
                   4.64840E−05 
               
               
                 10th order 
                 −9.15778E−05 
                   8.00536E−05 
                 −2.44547E−06 
               
               
                 12th order 
                   
                 −7.42994E−06 
                   1.63492E−06 
               
               
                 14th order 
                   
                   4.81112E−07 
                 −3.05210E−08 
               
               
                   
               
            
           
         
       
     
     Table 4E shows material characteristics of the optical components for the example single fold optical system as illustrated in  FIG.  7 A . Nd refers to refractive index, and Vd refers to Abbe number of the material. L1-L4 refer to the four lenses in the second lens group from the object side to the image side of the optical system: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 4E 
               
               
                   
               
               
                   
                   
                 Prism 
                 L1 
                 L2 
                 L3 
                 L4 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Nd 
                 1.514 
                 1.834 
                 1.544 
                 1.671 
                 1.544 
               
               
                   
                 Vd 
                 51.35 
                 37.16 
                 55.97 
                 19.23 
                 55.97 
               
               
                   
               
            
           
         
       
     
     Table 4F shows optical specifications for the example single fold optical system as illustrated in  FIG.  7 A . EFL is effective focal length, and Fno is the F-number of the optical system: 
     
       
         
           
               
               
               
             
               
                 TABLE 4F 
               
               
                   
               
             
            
               
                   
                 EFL 
                 15.3 
               
               
                   
                 Fno 
                 3.0 
               
               
                   
                 semi-sensor diagonal 
                 2.52 
               
               
                   
                 Macro distance 
                 125 cm 
               
               
                   
               
            
           
         
       
     
     Tables 5A through 5F provide optical and physical characteristics for the example single fold optical system as illustrated in  FIG.  8 A . 
     Table 5A shows all surface positions based on the Prism S1 global coordinate for the example single fold optical system as illustrated in  FIG.  8 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 5A 
               
               
                   
               
               
                   
                 x 
                 z 
                 angle (α) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 aperture 
                 0 
                 0.28 
                 0 
               
               
                 Prism S1 
                 0.000 
                 0.000 
                 0 
               
               
                 Prism inner surface 
                 0.000 
                 0.700 
                 0 
               
               
                 Prims S2 
                 0.000 
                 3.612 
                 45 
               
               
                 Prism S3 
                 −2.912 
                 3.612 
                 90 
               
               
                 L1 S1 
                 −4.177 
                 3.612 
                 90 
               
               
                 L1S2 
                 −5.222 
                 3.612 
                 90 
               
               
                 L2S1 
                 −5.475 
                 3.612 
                 90 
               
               
                 L2S2 
                 −5.865 
                 3.612 
                 90 
               
               
                 L3S1 
                 −9.551 
                 3.612 
                 90 
               
               
                 L3S2 
                 −10.211 
                 3.612 
                 90 
               
               
                 L4S1 
                 −10.952 
                 3.612 
                 90 
               
               
                 L4S2 
                 −12.052 
                 3.612 
                 90 
               
               
                 IRcut S1 
                 −13.792 
                 3.612 
                 90 
               
               
                 IRcut S2 
                 −14.002 
                 3.612 
                 90 
               
               
                 image plane (INF) 
                 −14.102 
                 3.612 
                 90 
               
               
                   
               
            
           
         
       
     
     Tables 5B through 5D show aspherical values for the surfaces of the optical components for the example single fold optical system as illustrated in  FIG.  8 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 5B 
               
               
                   
               
               
                   
                 Prism S1 
                 L1S1 
                 L1S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 10.9936 
                 −4.5962 
                 24.1370 
               
               
                 4th order 
                 −4.47670E−04 
                 −4.96952E−03 
                 −6.96106E−03 
               
               
                 6th order 
                 −1.61255E−06 
                   3.25426E−04 
                   2.34753E−03 
               
               
                 8th order 
                 −1.31071E−07 
                 −2.59701E−05 
                 −5.13966E−04 
               
               
                 10th order 
                   3.27852E−08 
                   3.54569E−05 
                   1.47389E−04 
               
               
                 12th order 
                 −1.37757E−09 
                 −7.43090E−06 
                 −1.18246E−05 
               
               
                 14th order 
                   
                   1.91989E−06 
                   1.99593E−07 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 5C 
               
               
                   
               
               
                   
                 L2S1 
                 L2S2 
                 L3S1 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −5.8392 
                 −2.7004 
                 7.9220 
               
               
                 4th order 
                   2.08846E−02 
                   2.80123E−02 
                   4.36643E−02 
               
               
                 6th order 
                 −6.99973E−03 
                 −1.15153E−02 
                 −8.56777E−03 
               
               
                 8th order 
                   9.61573E−04 
                   2.21425E−03 
                   4.95687E−04 
               
               
                 10th order 
                 −3.49028E−05 
                 −6.01848E−04 
                 −4.46371E−05 
               
               
                 12th order 
                 −8.47955E−07 
                   1.40503E−04 
                   
               
               
                 14th order 
                 −2.38157E−06 
                 −2.85205E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 5D 
               
               
                   
               
               
                   
                 L3S2 
                 L4S1 
                 L4S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −5.3114 
                 −81.4716 
                 6.5864 
               
               
                 4th order 
                   3.90863E−02 
                 −1.94553E−03 
                   8.73233E−04 
               
               
                 6th order 
                 −8.82724E−03 
                   1.24447E−03 
                 −2.40538E−04 
               
               
                 8th order 
                   1.21063E−03 
                 −3.53784E−04 
                   4.64840E−05 
               
               
                 10th order 
                 −9.15778E−05 
                   8.00536E−05 
                 −2.44547E−06 
               
               
                 12th order 
                   
                 −7.42994E−06 
                   1.63492E−06 
               
               
                 14th order 
                   
                   4.81112E−07 
                 −3.05210E−08 
               
               
                   
               
            
           
         
       
     
     Table 5E shows material characteristics of the optical components for the example single fold optical system as illustrated in  FIG.  8 A . Nd refers to refractive index, and Vd refers to Abbe number of the material. L1-L4 refer to the four lenses in the second lens group from the object side to the image side of the optical system: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 5E 
               
               
                   
               
               
                   
                   
                 Prism 
                 L1 
                 L2 
                 L3 
                 L4 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Nd 
                 1.583 
                 1.834 
                 1.544 
                 1.671 
                 1.544 
               
               
                   
                 Vd 
                 59.38 
                 37.16 
                 55.97 
                 19.23 
                 55.97 
               
               
                   
               
            
           
         
       
     
     Table 5F shows optical specifications for the example single fold optical system as illustrated in  FIG.  8 A . EFL is effective focal length, and Fno is the F-number of the optical system: 
     
       
         
           
               
               
               
             
               
                 TABLE 5F 
               
               
                   
               
             
            
               
                   
                 EFL 
                 15.3 
               
               
                   
                 Fno 
                 3.0 
               
               
                   
                 semi-sensor diagonal 
                 2.52 
               
               
                   
                 Macro distance 
                 125 cm 
               
               
                   
               
            
           
         
       
     
     Tables 6A through 6F provide optical and physical characteristics for the example single fold optical system as illustrated in  FIG.  9 A . 
     Table 6A shows all surface positions based on the Prism S1 global coordinate for the example single fold optical system as illustrated in  FIG.  9 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 6A 
               
               
                   
               
               
                   
                 x 
                 z 
                 angle (α) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 aperture 
                 0 
                 0.7 
                 0 
               
               
                 Prism S1 
                 0.000 
                 0.000 
                 0 
               
               
                 Prism S2 
                 0.000 
                 3.700 
                 45 
               
               
                 Prism S3 
                 −3.300 
                 3.700 
                 90 
               
               
                 L1 S1 
                 −3.400 
                 3.700 
                 90 
               
               
                 L1S2 
                 −3.992 
                 3.700 
                 90 
               
               
                 L2S1 
                 −4.092 
                 3.700 
                 90 
               
               
                 L2S2 
                 −4.488 
                 3.700 
                 90 
               
               
                 L3S1 
                 −8.250 
                 3.700 
                 90 
               
               
                 L3S4 
                 −8.829 
                 3.700 
                 90 
               
               
                 L4S1 
                 −11.202 
                 3.700 
                 90 
               
               
                 L4S2 
                 −12.600 
                 3.700 
                 90 
               
               
                 IRcut S1 
                 −13.990 
                 3.700 
                 90 
               
               
                 IRcut S2 
                 −14.200 
                 3.700 
                 90 
               
               
                 image plane (INF) 
                 −14.300 
                 3.700 
                 90 
               
               
                   
               
            
           
         
       
     
     Tables 6B through 6D show aspherical values for the surfaces of the optical components for the example single fold optical system as illustrated in  FIG.  9 A : 
     
       
         
           
               
               
               
               
             
               
                 TABLE 6B 
               
               
                   
               
               
                   
                 Prism S1 
                 L1S1 
                 L1S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 5.6321 
                 −11.6936 
                 21.5932 
               
               
                 4th order 
                 −2.68374E−04 
                 −2.40165E−03 
                 −1.27735E−03 
               
               
                 6th order 
                 −7.96206E−06 
                   9.06400E−04 
                   1.10220E−03 
               
               
                 8th order 
                   2.54679E−07 
                   1.27434E−05 
                 −1.35119E−04 
               
               
                 10th order 
                 −5.97297E−08 
                   1.21772E−05 
                   1.10012E−05 
               
               
                 12th order 
                   2.34852E−09 
                 −9.78359E−06 
                   1.83952E−05 
               
               
                 14th order 
                   
                   3.15343E−06 
                 −1.67661E−06 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 6C 
               
               
                   
               
               
                   
                 L2S1 
                 L2S2 
                 L3S1 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −298.9651 
                 −4.7109 
                 5.5578 
               
               
                 4th order 
                   2.63966E−03 
                 −1.33363E−03 
                 −2.38091E−02 
               
               
                 6th order 
                 −2.23391E−03 
                 −2.71636E−03 
                   1.24316E−02 
               
               
                 8th order 
                   3.72586E−04 
                   4.30366E−04 
                 −1.91564E−03 
               
               
                 10th order 
                   9.73830E−05 
                   2.05012E−04 
                 −8.41607E−05 
               
               
                 12th order 
                 −3.53637E−05 
                 −1.05166E−04 
                   1.12014E−04 
               
               
                 14th order 
                   3.18196E−06 
                   1.25474E−05 
                 −2.07762E−05 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 6D 
               
               
                   
               
               
                   
                 L3S2 
                 L4S1 
                 L4S2 
               
               
                   
               
             
            
               
                 Radius of curvature 
                 −7.7071 
                 −20.8157 
                 7.0734 
               
               
                 4th order 
                 −2.99254E−02 
                 −5.62662E−03 
                 −7.04620E−04 
               
               
                 6th order 
                   1.16934E−02 
                   1.10755E−04 
                 −5.93634E−04 
               
               
                 8th order 
                 −8.47579E−04 
                 −6.24552E−05 
                   2.81487E−05 
               
               
                 10th order 
                 −3.95495E−04 
                   2.98711E−05 
                   4.61457E−06 
               
               
                 12th order 
                   1.22802E−04 
                 −4.10901E−06 
                   1.30778E-−07 
               
               
                 14th order 
                 −1.28792E−05 
                   2.54296E−07 
                 −6.59262E−10 
               
               
                   
               
            
           
         
       
     
     Table 6E shows material characteristics of the optical components for the example single fold optical system as illustrated in  FIG.  9 A . Nd refers to refractive index, and Vd refers to Abbe number of the material. L1-L4 refer to the four lenses in the second lens group from the object side to the image side of the optical system: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 6E 
               
               
                   
               
               
                   
                   
                 Prism 
                 L1 
                 L2 
                 L3 
                 L4 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Nd 
                 1.535 
                 1.544 
                 1.671 
                 1.544 
                 1.671 
               
               
                   
                 Vd 
                 55.73 
                 55.97 
                 19.23 
                 55.97 
                 19.23 
               
               
                   
               
            
           
         
       
     
     Table 6F shows optical specifications for the example single fold optical system as illustrated in  FIG.  9 A . EFL is effective focal length, and Fno is the F-number of the optical system: 
                             TABLE 6F                      EFL   22.03           Fno   4.0           semi-sensor diagonal   2.268           Macro distance   175 cm                    
Anamorphic Lenses in Folded Optical Systems
 
     Folded optical systems such as the single fold optical systems illustrated in  FIGS.  1  through  11    include at least one prism with a reflective, flat second surface to fold the optical axis of the optical system. However, surface errors of the reflective surface of the prism(s) in folded optical systems may cause aberrations, in particular astigmatism, in the optical system. In other words, while ideally perfectly flat, the reflective surface of the prism will typically be flat within some tolerance level (e.g., a few microns) of the manufacturing process. Thus, the second (reflective) surface may be slightly curved, which results in the aforementioned aberrations. Using a glass prism may help to limit these aberrations when compared to plastic prisms, as glass can be polished to provide a tighter tolerance level in the manufacturing process than plastic. However, the reflective surface of a glass prism can only be guaranteed to be flat within some tolerance level. Further, due to variations in the manufacturing process, different groups or batches of prisms (whether glass or plastic) may vary in the “flatness” of the second, reflective surface. 
     In an optical system with astigmatism, rays that propagate in two perpendicular planes have different foci. For example, if an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. 
     Embodiments of folded optical systems that include at least one anamorphic lens that is configured and oriented to correct for aberrations including astigmatism caused by surface errors of the reflective surface of the prism(s) in the folded optical systems are described. An anamorphic lens as described herein may, for example, be used in embodiments of the single fold optical systems that include a single power prism as described in reference to  FIGS.  1  through  11   . However, anamorphic lenses as described herein may also be used in other single fold optical systems or double fold optical systems to correct for aberrations including astigmatism caused by surface errors of the reflective surface(s) of the prism(s) in the folded optical systems. Anamorphic lenses as described herein may be used to correct for astigmatism caused by the flat reflective surfaces of power prisms or triangular prisms, or by the curved reflective surfaces of prisms such as freeform prisms. 
     A spherical lens has one or two curved (concave or convex) surfaces. The curvature of the surface(s) is the same on all axes (e.g., on an X and Y axis). Spherical lenses pass the image to the sensor without affecting the aspect ratio. An anamorphic lens has at least one curved (convex or concave) surface in which the curvature is different on at least one axis (e.g., different on the X axis than on the Y axis). The effective surface of an anamorphic lens may thus be oval, rather than round as in typical spherical lenses. Anamorphic lenses thus distort the image, squeezing it in one direction (e.g., horizontally) while leaving the other (e.g., vertical) aspect unaffected. Aspherical lenses can be designed and manufactured with different curvatures on different axes to correct for aberrations (e.g., astigmatism) caused by surface errors (e.g., curvature in one or more directions) of the reflective surfaces of prisms used in folded optical systems. In a folded telephoto optical system, an anamorphic lens may be used to correct the astigmatism by up to 20 μm without creating a distortion problem, as the effect on distortion of the anamorphic lens is relatively small. 
     The astigmatism caused by the reflective surface of prisms may differ. For example, one batch of prisms may have more, or less, surface error and thus more, or less, astigmatism than another batch of prisms, or the “direction” of the astigmatism may be different. Thus, in embodiments, the anamorphic lens may be configured to be rotated 90 degrees to correct for differing astigmatism in different prisms. In addition, two or more different anamorphic lenses with different amounts or orientations of curvature to correct for different levels of astigmatism may be provided, and a correct anamorphic lens and orientation of the lens may be selected for use with one or more prisms. For example, one anamorphic lens may be configured to correct for 2 micros of astigmatism, another for 10 microns of astigmatism, another for 20 microns of astigmatism, and so on. 
     A manufacturing process for folded optical systems that include anamorphic lenses to correct for aberrations including astigmatism caused by surface errors of the reflective surface(s) of the prism(s) is also described. 
       FIGS.  12 A through  12 D  illustrate using an anamorphic lens in a lens stack to correct aberrations including astigmatism caused by surface errors of the reflective surface of a prism in a single fold optical system, according to some embodiments.  FIG.  12 A  shows an example single fold lens system as shown in  FIG.  1    that includes a power prism  1210  with a reflective surface  1214 . In this example, the second lens  1222  in the lens stack  1220  has been replaced with an anamorphic lens as shown in  FIGS.  12 B and  12 C  to correct for astigmatism caused by surface errors (curvature) of the reflective surface  1214 .  FIGS.  12 B and  12 C  show that the curvature of the second (object side) surface of the anamorphic lens  1222  is different on the X axis than on the Y axis. To correct for differing astigmatism caused by the reflective surface  1214  of prism  1210 , the lens  1222  may be rotated 90 degrees. Alternatively, a different anamorphic lens  1222  with different curvature to correct for a different level of astigmatism may be selected and used with the prism  1210 . 
     While  FIG.  12 A  shows an anamorphic lens as the second lens  1222  in lens stack  1220 , an anamorphic lens may instead be used at other lenses in the optical system  1200 , for example as the first lens in the lens stack  1220 . In some embodiments, more than one anamorphic lens may be used in an optical system  1200 . 
       FIG.  12 D  graphically illustrates correcting for astigmatism in an example optical system  1200  with an anamorphic lens  1222  as illustrated in  FIGS.  12 A through  11 C . (A)( 0 ) shows an ideal MTF for the optical system, (A)( 1 ) shows MTF with +0.2 microns of astigmatism, and (A)( 1 ) shows MTF with −0.2 microns of astigmatism. (B)( 1 ) shows correction of MTF with anamorphic lens  1122  oriented at azimuth 0 degrees to correct for the astigmatism of (A)( 1 ), and (B)( 2 ) shows correction of MTF with anamorphic lens  1122  oriented at azimuth 90 degrees to correct for the astigmatism of (A)( 2 ). 
       FIG.  13    illustrates using an anamorphic lens  1322  in a lens stack  1320  to correct aberrations including astigmatism caused by surface errors of the reflective surface  1314  of a first prism  1310  in a double fold optical system  1300  that includes two light folding elements (e.g., a first and second prism, or a first prism and a mirror), according to some embodiments. In this example, the second lens  1322  in the lens stack  1320  has been replaced with an anamorphic lens, for example as shown in  FIGS.  11 B and  11 C , to correct for astigmatism caused by surface errors (curvature) of the reflective surface  1314  of the first prism  1310 . To correct for differing astigmatism caused by the reflective surface  1314  of prism  1310 , the lens  1322  may be rotated 90 degrees. Alternatively, a different anamorphic lens  1322  with different curvature to correct for a different level of astigmatism may be selected and used with the prism  1310 . 
     While  FIG.  13    shows an anamorphic lens as the second lens  1322  in lens stack  1320 , an anamorphic lens may instead be used at other lenses in the optical system  1300 , for example as the first lens in the lens stack  1320 . In some embodiments, more than one anamorphic lens may be used in an optical system  1300 . 
       FIG.  14    illustrates using an anamorphic lens to correct aberrations including astigmatism caused by a freeform prism, according to some embodiments. As previously mentioned, freeform optics involve optical designs with at least one 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 surface which has no translational or rotational symmetry about axes normal to the mean plane of the surface. Example folded optical system  1400  includes, in order from an object side to an image side, an anamorphic lens  1410 , a first freeform prism  1420 , and a second freeform prism  1430 . The optical system  1400  may also include an aperture stop, for example located between anamorphic lens  1410  and freeform prism  1420 . Light from an object field is refracted by anamorphic lens  1410  to surface S 1  of freeform prism  1420 . The light is refracted by surface S 1  to surface S 2 , which reflects the light back to surface S 1 , thus folding the optical axis once. Surface S 1  reflects the light to surface S 3 , thus folding the optical axis a second time. The light is refracted by surface S 3  to surface S 4  of freeform prism  1430 . Surface S 4  refracts the light to surface S 5 , which reflects the light to surface S 6 , thus folding the optical axis a third time. Surface S 6  reflects the light to surface S 5 , thus folding the optical axis a fourth time. Surface S 5  refracts the light received from surface S 6  to form an image at an image plane, for example at or near the surface of a sensor. 
     The optical system  1400  of  FIG.  14    is given by way of example. For example, an optical system may include only one freeform prism, may include a freeform prism and a standard prism or power prism, and/or may include additional spherical, aspherical, or anamorphic lenses. In this example, anamorphic lens  1410  is configured correct for astigmatism caused by one or more surfaces of the two freeform prisms, for example astigmatism caused by surface S 2  of freeform prism  1420 . To correct for differing astigmatism caused by the freeform prism(s), the anamorphic lens  1410  may be rotated 90 degrees. Alternatively, a different anamorphic lens  1410  with different curvature to correct for a different level of astigmatism may be selected and used with the freeform prism(s). 
       FIG.  15    is a high-level flowchart of a method of manufacturing a folded optical system that includes an anamorphic lens oriented to correct for aberrations including astigmatism caused by surface errors of the reflective surface of a prism in a folded optical system, according to some embodiments. As indicated at  1500 , optical performance of one or more prisms may be measured to determine astigmatism caused by the reflective surface of the prism(s). Various methods may be used to measure the astigmatism of a prism, including but not limited to optical measurement methods (e.g., to measure MTF of the prism) and physical measurement methods (e.g., to directly measure surface error of the reflective surface). As indicated at  1510 , an anamorphic lens may be selected according to the measured astigmatism of the prism(s). As previously noted, different anamorphic lenses with different levels of correction may be provided. As indicated at  1520 , folded optical systems including the prisms and lenses including the selected anamorphic lens oriented to correct for the measured astigmatism may be assembled. As previously noted, an anamorphic lens may be rotated 90 degrees depending on the measured astigmatism. This process may be repeated, for example for different batches of prisms. 
     Example Computing Device 
       FIG.  16    illustrates an example computing device, referred to as computer system  3000 , that may include or host embodiments of a camera with a folded optical system as illustrated in  FIGS.  1  through  14   . 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 single fold optical system as described above with respect to  FIGS.  1  through  14   . 
     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.  16   , 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. 
     The following clauses describe various aspects of optical systems, cameras, and/or methods incorporating embodiments as described above. 
     Clause 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 lens group comprising a power prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the first surface is a transmissive aspherical surface that provides positive refractive power for the prism, wherein the second surface is a reflective surface that folds the optical axis of the optical system, and wherein the third surface is a transmissive surface; and   a second lens group comprising two or more refractive lenses; and   
           wherein the optical system satisfies the conditional expression:
 
0.6&lt; B/A&lt; 2.3,
   where A is power of the optical system, and B is power of the first lens group.       

     Clause 2. The optical system as recited in clause 1, wherein the optical system satisfies the conditional expression:
 
−0.2&lt; CD&lt; 0.1,
 
where C is power of the second lens group, and D is length of the second lens group.
 
     Clause 3. The optical system as recited in clause 1, further comprising an aperture stop located on the object side of the power prism. 
     Clause 4. The optical system as recited in clause 1, wherein the power prism is formed of an optical plastic material. 
     Clause 5. The optical system as recited in clause 1, wherein the power prism comprises a glass prism and a refractive lens composed of an optical plastic material attached to an object side surface of the glass prism. 
     Clause 6. The optical system as recited in clause 1, wherein the power prism comprises a glass prism and a refractive lens composed of an optical glass material attached to an object side surface of the glass prism. 
     Clause 7. The optical system as recited in clause 1, wherein Z-height of the optical system is 7.3 millimeters or less. 
     Clause 8. The optical system as recited in clause 1, wherein X-length of the optical system is 18 millimeters or less. 
     Clause 9. The optical system as recited in clause 1, wherein the second lens group consists of four refractive lens elements. 
     Clause 10. The optical system as recited in clause 9, wherein the four refractive lens elements comprise, in order from the object side of the optical system to the image side of the optical system: 
     a first lens with positive refractive power, 
     a second lens with negative refractive power; 
     a third lens with negative refractive power; and 
     a fourth lens with positive refractive power. 
     Clause 11. The optical system as recited in clause 9, wherein a second lens in the second lens group from the object side of the optical system is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     Clause 12. The optical system as recited in clause 11, wherein the second lens is configured to be rotated 90 degrees to correct for a different amount of astigmatism caused by the second surface of the power prism. 
     Clause 13. The optical system as recited in clause 9, wherein at least one of the lenses in the second lens group is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     Clause 14. The optical system as recited in clause 1, further comprising a light folding element located on the image side of the second lens group and configured to fold the optical axis of the optical system a second time, wherein a second lens in the second lens group from the object side of the optical system is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     Clause 15. 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 lens group comprising a power prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the first surface is a transmissive aspherical surface that provides positive refractive power for the prism, wherein the second surface is a reflective surface that folds the optical axis of the optical system, and wherein the third surface is a transmissive surface; and   a second lens group comprising two or more refractive lenses; and   
           an image sensor configured to capture light projected onto a surface of the image sensor by the optical system;   wherein the optical system satisfies the conditional expression:
 
0.6&lt; B/A&lt; 2.3, and
 
−0.2&lt; CD&lt; 0.1,
   where A is power of the optical system, B is power of the first lens group, C is power of the second lens group, and D is length of the second lens group.       

     Clause 16. The camera as recited in clause 15, wherein Z-height of the optical system is 7.3 millimeters or less, and wherein X-length of the optical system is 18 millimeters or less. 
     Clause 17. The camera as recited in clause 15, further comprising an aperture stop located on the object side of the power prism. 
     Clause 18. The camera as recited in clause 15, further comprising an infrared filter located between the second lens group and the image sensor. 
     Clause 19. The camera as recited in clause 15, wherein at least one of the lenses in the second lens group is an anamorphic lens configured to correct for astigmatism caused by the second surface of the power prism. 
     Clause 20. An optical system, comprising:
         a prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the second surface is a reflective surface that folds the optical axis of the optical system and the third surface is a transmissive surface; and   one or more refractive lenses, wherein at least one of the one or more refractive lenses is an anamorphic lens configured to correct for astigmatism caused by the prism.       

     Clause 21. The optical system as recited in clause 20, wherein the first surface of the prism is a transmissive aspherical surface. 
     Clause 22. The optical system as recited in clause 20, wherein the anamorphic lens is configured to be rotated 90 degrees to correct for a different amount of astigmatism caused by the prism. 
     Clause 23. The optical system as recited in clause 20, wherein the optical system comprises four refractive lenses located on an image side of the prism, wherein a second lens of the four refractive lenses from an object side of the optical system is the anamorphic lens configured to correct for astigmatism caused by the prism. 
     Clause 24. The optical system as recited in clause 23, wherein the second lens is configured to be rotated 90 degrees to correct for a different amount of astigmatism caused by the prism. 
     Clause 25. The optical system as recited in clause 20, wherein the one or more refractive lenses are located on an image side of the prism, the optical system further comprising a light folding element located on the image side of the one or more lenses and configured to fold the optical axis of the optical system a second time. 
     Clause 26. The optical system as recited in clause 20, wherein the prism is a power prism with positive refractive power. 
     Clause 27. The optical system as recited in clause 20, further comprising a refractive lens with positive refractive power attached to an object side surface of the prism. 
     Clause 28. The optical system as recited in clause 20, further comprising an aperture stop located on an object side of the prism. 
     Clause 29. The optical system as recited in clause 20, wherein the prism is a freeform prism. 
     Clause 30. The optical system as recited in clause 29, wherein the optical system further comprises a second freeform prism 
     Clause 31. The optical system as recited in clause 20, wherein the anamorphic lens is located on an object side of the prism. 
     Clause 32. The optical system as recited in clause 20, wherein the anamorphic lens is located on an image side of the prism. 
     Clause 33. A camera, comprising, in order from an object side of the camera to an image side of the camera:
         an optical system comprising:
           a prism that includes a first surface, a second surface, and a third surface on an optical axis of the optical system, wherein the second surface is a reflective surface that folds the optical axis of the optical system, and the third surface is a transmissive surface; and   one or more refractive lenses, wherein at least one of the one or more refractive lenses is an anamorphic lens configured to correct for astigmatism caused by the prism; and   
           an image sensor configured to capture light projected onto a surface of the image sensor by the optical system.       

     Clause 34. The camera as recited in clause 33, wherein the first surface of the prism is a transmissive aspherical surface. 
     Clause 35. The camera as recited in clause 33, wherein the optical system comprises four refractive lenses located on an image side of the prism, wherein a second lens of the four refractive lenses from the object side of the optical system is the anamorphic lens configured to correct for astigmatism caused by the prism, and wherein the second lens is configured to be rotated 90 degrees to correct for a different amount of astigmatism caused by the prism. 
     Clause 36. The camera as recited in clause 33, further comprising a light folding element located between the four refractive lenses and the image sensor and configured to fold the optical axis of the optical system a second time. 
     Clause 37. The camera as recited in clause 33, further comprising an aperture stop located on the object side of the prism. 
     Clause 38. The camera as recited in clause 33, further comprising an infrared filter located between the lens group and the image sensor. 
     Clause 39. The camera as recited in clause 33, wherein the prism is a power prism with positive refractive power. 
     Clause 40. The camera as recited in clause 33, wherein the prism is a freeform prism. 
     Clause 41. The camera as recited in clause 40, wherein the optical system further comprises a second freeform prism 
     Clause 42. The camera as recited in clause 33, wherein the anamorphic lens is located on an object side of the prism. 
     Clause 43. The camera as recited in clause 33, wherein the anamorphic lens is located on an image side of the prism. 
     Clause 44. A method, comprising:
         forming one or more prisms of an optical glass or plastic material, wherein each prism includes a first surface, a second reflective surface, and a third transmissive surface on an optical axis;   measuring optical performance of the one or more prisms to determine astigmatism caused by the prisms;   selecting one or more anamorphic lenses according to the determined astigmatism of the one or more prisms; and   assembling one or more optical systems, each optical system including:
           a first lens group including the prism; and   a second lens group including one or more refractive lens elements, wherein at least one of the one or more refractive lens elements is an anamorphic lens oriented to correct for the determined astigmatism of the respective prism.   
               

     Clause 45. The method as recited in clause 44, wherein the optical system further includes a second prism located on an image side of the second lens group. 
     Clause 46. The method as recited in clause 44, wherein the prism is a power prism. 
     Clause 47. The method as recited in clause 45, wherein the prism is a freeform prism.

Metadata:
Filing Date: 20210524
Publication Date: 20230815
Grant Date: 20230815
Priority Date: 20200526
Inventors: SAIGA, TAKEYOSHI
Assignee: APPLE INC
CPC Classifications: [{"code": "G02B13/007", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/003", "inventive": true, "first": false, "tree": "[]"}, {"code": "G03B17/17", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/007", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B9/60", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/007", "inventive": true, "first": true, "tree": "[]"}, {"code": "G02B13/08", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0045", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B9/60", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/0045", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/08", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/003", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/007", "inventive": true, "first": false, "tree": "[]"}, {"code": "G03B17/17", "inventive": true, "first": false, "tree": "[]"}, {"code": "G02B13/003", "inventive": true, "first": false, "tree": "[]"}, {"code": "G03B17/17", "inventive": true, "first": false, "tree": "[]"}]
Family ID: 76502847