Patent Publication Number: US-2021165192-A1

Title: Compact folded lenses with large apertures

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/310,690 filed Dec. 17, 2018 (now allowed), which was a 371 application from international patent application No. PCT/IB2018/055450 filed Jul. 22, 2018, and claims the benefit of priority of U.S. provisional patent application No. 62/535,926 filed Jul. 23, 2017, which is incorporated herein by reference in its entirety. 
    
    
     FIELD 
     Embodiments disclosed herein relate to optical lenses, and more particularly, to folded optical lenses. 
     BACKGROUND 
     Cameras with folded optics (or simply “folded camera modules” or “folded cameras”) are known. In particular, such folded camera modules have been proposed for incorporation in electronic mobile devices such as cellphones or smartphones, e.g. as part of a multiple-camera structure that comprises two or more lens modules, where at least one of the lens modules is “folded”. One example is a two-camera structure (also referred to as “dual-camera” or “dual-aperture camera”) that may include one or two folded camera modules. 
     In a folded camera module structure, an optical path folding element (referred to hereinafter as “OPFE”), e.g. a prism or a mirror, is added to tilt the light propagation direction from a first direction (e.g. the direction perpendicular to the phone back surface) to a second direction (e.g. parallel to the phone back surface). If the folded camera module is part of a dual-aperture camera, this provides a folded optical path through one lens module (normally a “Tele” lens module). Such a camera is referred to herein as folded-lens dual-aperture camera or dual-aperture camera with folded lens. 
     As the dimensions of mobile devices (and in particular the thickness of devices such as smartphones) are being constantly reduced, compact camera dimensions are becoming an increasingly limiting factor on device thickness. Therefore, camera dimensions and in particular folded camera heights and lengths need to be further reduced. 
     SUMMARY 
     The presently disclosed subject matter includes various designs of folded cameras with designs of folded lenses that have large camera aperture area, reduced optical height, and that can support an image sensor with a large diagonal size relative to an optical height and in which most lens elements have circular apertures. 
     In this specification, the known in the art term “total track length” (TTL), which is shown and marked in the figures, is a property of a lens and includes (i.e. is a sum of) two parts TTL 1  and TTL 2  (see e.g. in  FIGS. 1B and 2B ): a first part measured along a first optical axis from a light entrance surface of a first lens element to a prism reflective surface, and a second part measured along a second optical axis from the prism reflective surface to an image sensor (e.g. CCD or CMOS sensor). In general, the angle between the first and second optical axes is a 90° angle, however in some examples of other angles, the value of the angle may be less than or greater than 90°. In the examples provided below, the TTL is measured when the lens is focused to infinity and includes a window (e.g. IR filter) positioned between the last lens element and the image sensor, as specified in the design values. 
     In this specification, the term “total lens length” (TLL), which is shown and marked in e.g. FIG. B, is a property of a lens defined as the distance along the second optical axis direction between an image plane at the image sensor and the furthest vertex of the first optical element. TLL is measured when the lens is focused to infinity and includes a window (e.g. IR filter) positioned between the last lens element and the image sensor, as specified in the design values. 
     In this specification the known in the art term “back focal length” (BFL), which is shown and marked in e.g.  FIG. 1B , is a property of a lens, which defined as the distance along the second optical axis direction between the image plane and the closest point of the last optical element to the image. 
     In this specification, the known in the art term “effective focal length” (EFL) is a property of a lens which has its regular meaning. EFL is defined as to be equal to the focal length of a single lens element having an equal magnification power as the entire lens (that has a few lens elements). 
     In this specification, “lens surface aperture” refers to the shape and size of a maximum optically useable lens element surface, i.e. all the surface with a sag defined by a lens formula. “Lens element apertures” or “lens apertures” refer to front and back surfaces of the lens. “Camera aperture” or “lens assembly aperture” refers to the lens aperture of the first lens element object side surface that is open to incoming light rays. 
     In this specification, each lens is designed for an image sensor having a sensor diagonal length (SDL) given in mm. SDL/2 is half of the sensor diagonal length. All sensors having SDL specified may be used with the combination of the given lens examples disclosed herein, e.g. sensors having 3:4 or 9:16 or 1:2 width-to-height ratio, etc. 
     In various exemplary embodiments, there are provided folded lens assemblies comprising, from an object side to an image side: a positive first lens element L 1  with a first optical axis and a first lens width W 1 , a light folding element, a negative second lens element L 2  and a plurality of additional lens elements L 3 -L N  with a common second optical axis, and an image sensor having a sensor diagonal length SDL, wherein the light folding element is configured to fold light from the first optical axis to the second optical axis, wherein each folded lens assembly has an optical height OH, wherein SDL/OH&gt;0.7 and wherein OH/W 1 &lt;1.1. 
     In an embodiment, SDL/OH&gt;1. 
     In an embodiment, OH/W 1 &lt;1. In an embodiment, OH/W 1 &lt;0.95. 
     In an embodiment, BFL/TTL&gt;0.2. In an embodiment, BFL/TTL&gt;0.35. 
     In an embodiment, the first lens element has a length A 1  such that OH/A 1 &lt;1.4. In an embodiment, OH/A 1 &lt;1.1. 
     In an embodiment, the second lens element L 2  may have circular aperture. 
     In an embodiment, a lens assembly includes at least two air gaps between lens elements that comply with the condition STD&lt;0.020, where STD is a normalized gap standard deviation and r norm  is a minimum value of half a gap between adjacent surfaces L i S 2  and L i+1 S 1 . In an embodiment with at least two air gaps, STD&lt;0.010. 
     In an embodiment, a lens assembly includes at least three air gaps between lens elements that comply with the condition STD&lt;0.035. In an embodiment with at least three air gaps, STD&lt;0.015. 
     In an embodiment, a lens assembly includes at least four air gaps between lens elements that comply with the condition STD&lt;0.050. In an embodiment with at least four air gaps, STD&lt;0.025 
     In some embodiments, a lens assembly includes, from the object side to the image side five lens elements, with a first element having positive refractive power, a second lens having negative refractive power and any one of the other elements having either positive or negative refractive power. For example, the power sign sequence of the lens elements may be PNPPN or PNPNP, where P refers to a positive lens element power and N refers to a negative lens element power. 
     In an embodiment, a lens assembly includes at least one air gap between lens elements that complies with the conditions STD&lt;0.01 and OA_Gap/TTL&lt; 1/80, where OA_Gap is an on-axis gap. In an embodiment, STD&lt;0.01 and OA_Gap/TTL&lt; 1/65. 
     In some embodiments, the first and second lens elements and a third lens element have respective Abbe numbers larger than 50, smaller than 30 and larger than 50. 
     In some embodiments, the second lens element and a third lens element have together a negative effective focal length. 
     In some embodiments, the first lens element has a focal length f 1  and f 1 /EFL&lt;0.7. In an embodiment, f 1 /EFL&lt;0.6. In an embodiment, the second lens element has a focal length f 2  and |f 2 /f 1 &lt;1. In an embodiment, |f 2 /f 1 |&lt;0.7. 
     In some embodiments, lens elements L 2  to L N  have circular apertures. 
     In some embodiments, TTL/EFL&lt;1.1. 
     In an embodiment, the apertures of the first lens element are cut along the second optical axis. 
     In an embodiment, TLL/EFL&lt;1. 
     In various exemplary designs, the optical powers of the first two lens elements L 1  and L 2  are significant contributors to the lens system low OH/W 1  and TTL/EFL ratios. This is achieved by the low (&lt;0.6) f 1 /EFL ratio and also the low (&lt;1) absolute value of the f 2 /f 1  ratio. The high (&gt;50) and low (&lt;30) Abby numbers of respectively L 1  and L 2  also contribute to reduce the lens system chromatic aberration. The L 3  to L N  lens elements contribute manly to reduction of aberrations (e.g. spherical, distortion, field curvature, etc.). The close proximity or small gaps between lens elements that results in a large (&gt;0.2) BFL/TL ratio contributes to the lens system supporting a large SDL/OH ratio. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Non-limiting examples of embodiments disclosed herein are described below with reference to figures attached hereto that are listed following this paragraph. Identical structures, elements or parts that appear in more than one figure are generally labeled with a same numeral in all the figures in which they appear. The drawings and descriptions are meant to illuminate and clarify embodiments disclosed herein and should not be considered limiting in any way. In the drawings: 
         FIG. 1A  shows a first embodiment of a folded camera, comprising an optical lens assembly disclosed herein in an isometric view; 
         FIG. 1B  shows the camera of  FIG. 1A  from a side view; 
         FIG. 1C  shows the camera of  FIG. 1A  from a top view: 
         FIG. 1D  shows the camera of  FIG. 1A  with light ray tracing from an object to an image sensor; 
         FIG. 1E  shows the camera of  FIG. 1A  in a housing: 
         FIG. 1F  shows a side cut of the camera of  FIG. 1E ; 
         FIG. 2A  shows a second embodiment of a folded camera, comprising an optical lens assembly, disclosed herein in an isometric view; 
         FIG. 2B  shows the folded camera of  FIG. 2A  from a side view; 
         FIG. 2C  shows the folded camera of  FIG. 2A  from a top view; 
         FIG. 2D  shows the camera of  FIG. 2A  with light ray tracing from an object to an image sensor; 
         FIG. 3  shows a third exemplary embodiment of a folded camera with light ray tracing from an object to an image sensor; 
         FIG. 4  shows a fourth exemplary embodiment of a folded camera with light ray tracing from an object to an image sensor; 
         FIG. 5  shows a fifth exemplary embodiment of a folded camera with light ray tracing from an object to an image sensor; 
         FIG. 6  shows a sixth exemplary embodiment of a folded camera with light ray tracing from an object to an image sensor; 
         FIG. 7  shows a seventh exemplar embodiment of a folded camera with light ray tracing from an object to an image sensor. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1A -IC show a first exemplary embodiment (also referred to as “Example 1”) of a folded camera disclosed herein and numbered  100 .  FIG. 1A  shows embodiment  100  in an isometric view,  FIG. 1B  shows embodiment  100  in a side view and  FIG. 1C  shows embodiment  100  in atop view. The element numbers in  FIG. 1A  apply also to  FIGS. 1B and 1C . 
     Folded camera  100  comprises a folded lens assembly (also simply referred to as “folded lens”)  102  and an image sensor  106 . Optionally, camera  100  may comprise a window (e.g. glass window)  114  that may serve for example as a dust cover for the image sensor and/or to filter infra-red (IR) light and prevent the IR light from reaching image sensor  106 . In an embodiment, folded lens assembly  102  comprises, in order from an object side to an image side, a first lens element L 1 , a light folding element (exemplarily a prism)  104 , and a plurality of lens elements L 2  . . . L N . In total, lens assembly  102  includes a plurality of N lens elements, for example (as in this embodiment) five lens elements marked L 1 , L 2 , L 3 , L 4  and L 5 . In other embodiments, a lens assembly may include another number of elements, for example N=4, 6 or 7, wherein the design principles disclosed herein with respect to five lens elements can be maintained with other (e.g. greater) number of lens elements. In general, L i  will mark the i th  lens element of any lens, where “i” is an integer between 1 and N. Each lens element L i  has an optical axis. Lens element L 1  has an optical axis (also referred to as “first optical axis”)  108 . Lens elements L 2  . . . L N  have a common optical axis (also referred to ass “second optical axis”)  110 . Prism  104  folds light arriving from an object or scene  116  and passing through lens element L 1  along a first optical path substantially parallel to first optical axis  108 , to a second optical path substantially parallel to second optical axis  110  toward image sensor  106 . Prism  104  has a light entering surface (or “plane”)  104   a , a light exiting surface (plane)  104   b  and a light folding surface (plane)  104   c . First optical axis  108  and second optical axis  110  intersect on plane  104   c . In an example, prism light exiting surface  104   b  is smaller than prism light entering surface  104   a , i.e. the diameter of light exiting surface  104   b  is smaller than the diameter of light entering surface  104   a . This feature allows the prism to be lower (have lower height) than the case of equal diameter of light entering and exiting surfaces. Thus, the optical height (OH, see  FIG. 1B  and definition below) of lens  102  can be reduced. According to some examples described herein, the ratio between the prism light exiting surface and the prism light entering surface dimensions can be less than 1.00. 
     Each lens element L i  has a respective focal length f i , given in Table 1 for all lens elements of all examples in this specification. Each lens element L i  has a respective height H i  measured along the direction of the first optical axis, see e.g.  FIG. 1F . 
     Each lens element L i  has a respective front surface L i S 1  and a respective rear surface L i S 2  where “i” is an integer between 1 and N. As used herein, the term “front surface” of each lens element refers to the surface of a lens element located closer to the entrance of the camera (camera object side) and the term “rear surface” refers to the surface of a lens element located closer to the image sensor (camera image side). The front surface and/or the rear surface can be in some cases aspherical. The front surface and/or the rear surface can be in some cases spherical. These options are, however, not limiting. Lens elements L 1  to L N  may be made from various materials, for example plastic or glass. Some lens elements may be made of different materials than other lens elements. 
     In the case of camera  100 , L 1 S 2  is the same surface as the prism light entering surface  104   a . However, in other cases there can be an air gap between the two surfaces (not shown). In the case of camera  100 , L 1  and the prism are made as two parts which are fixedly attached (e.g. glued) to each other. In other cases, they may be made as one part, e.g. by taking a prism and polishing its entrance surface to have optical power and serve as a lens. The optical design of the lens for such a case (L 1  and prism as one part) may be identical to the design of lens  102 , in which L 1 S 2  which has no optical power. In camera  100 , L 1  and the prism are made of the same material. In other embodiments, they may be made of different materials. 
     L 1  has two surfaces (L 1 S 1 , L 1 S 2 ), having two apertures that include two cuts (facets)  112   a  and  112   b . Therefore, lens element L 1  is referred to as a “cut lens”. The cuts enable the lens assembly to be lower and/or shorter, as shown in the drawings. The cuts in L 1  allow shortening the prism entrance surface and thereby the shortening of TLL. The shortening of the prism entrance surface also allows lowering of the prism exit surface and thereby the lowering of the optical height. 
     The aperture of L 1 S 1  is referred to herein as a “cut aperture”. As illustrated by way of example in  FIG. 1B , the length of L 1  (denoted A 1 ) is measured along the second optical axis direction, between cuts  112   a  and  112   b . As further illustrated by a way of example in  FIG. 1C , the width of L 1  (denoted W 1 ) is measured along a direction perpendicular to both directions of the first and second optical axes. A 1  and W 1  are likewise applied to all other examples provided herein. 
     Detailed optical data of camera  100  (Example 1) and of lens assembly  102  are given in Tables 2-4. R is the radius of curvature of a surface and T is the distance from the surface to the next surface along an optical axis. D is the optical diameter of the surface. D/2 expresses a “semi-diameter” or half of the diameter. The units of R, T, D, A and W are in millimeters (mm). Nd and Vd are respectively the refraction index and Abbe number of the lens element material residing between the surface and the next surface. “Offset” in various Tables (given in mm) is the displacement from the optical axis, information required for reconstructing a prism in optical design software. “Type” in Table 1 has the common meaning well known in the art. 
     Surface types are defined in Tables 2 and the coefficients for the surfaces are in Table 3:
         Standard Surfaces;   Aspherical surfaces, which are defined using Eq. 1 and their details given in table 4:       

     
       
         
           
             
               
                 
                   SAG 
                   = 
                   
                     
                       
                         c 
                          
                         
                           r 
                           2 
                         
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                                
                               
                                 c 
                                 2 
                               
                                
                               
                                 r 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         α 
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                        
                       
                         r 
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                         α 
                         2 
                       
                        
                       
                         r 
                         4 
                       
                     
                     + 
                     
                       
                         α 
                         3 
                       
                        
                       
                         r 
                         6 
                       
                     
                     + 
                     
                       
                         α 
                         4 
                       
                        
                       
                         r 
                         8 
                       
                     
                     + 
                     
                       
                         α 
                         5 
                       
                        
                       
                         r 
                         10 
                       
                     
                     + 
                     
                       
                         α 
                         6 
                       
                        
                       
                         r 
                         12 
                       
                     
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                         7 
                       
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                         r 
                         14 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     where r is the distance of a point in the optical surface from (and perpendicular to) the relevant optical axis (first or second), k is the conic coefficient, c=1/R, and a are coefficients given in Table 4. In the equation above as applied to lens  102  in folded camera  100 , coefficients α 1  and α 4  to α 7  are zero Note that, for any aspheric surface, the maximum value of r (“max r”) is the semi-diameter (D/2) of the respective surface.
         A “stop”, i.e. a surface that can block a portion of the light from reaching the image sensor, as known in the art. Stops are common in optical design. A stop may help to reduce stray light and improve optical quality of the image. The position of the stop surface in lens  102  (between the prism and L 2 ) is exemplary. In other embodiments, one or more stops may be located between other elements or even before L1. Yet other embodiments may not include a “stop”.   The reflective surface of the prism, also commonly known as a “mirror”.       

     In this specification, “height” of a part, an element, or of a group of parts or elements is defined as a distance in the direction of the first optical axis (Y direction in an exemplary coordinate system) between the lowermost point of the part/element/group and the upper-most point of the part/element/group. The term “upper” or “top” refers to a section of any part/element/group that is closer to and facing an imaged (photographed) object (e.g. object  116 ) along Y relative to other sections of the same part/element or group. The term “lower” or “bottom” refers to a section of any part/element/group that is farthest from and facing away from an imaged object along Y relative to other sections of the same part/element or group. For example, as seen in  FIG. 2B , the height of L 5  is the distance from a bottom-most part  118   a  of L 5  to a top-most part  118   b  of L 5  along the Y direction. The optical height (OH) of folded lens  102  (marked in  FIG. 1B ) is defined as the distance from the lowest of the bottom-most part of any of lens elements L 2  . . . L N  and prism  104  to the top-most part of lens element L 1 . For example, the optical height of folded lens  102  is measured from the bottom-most part of lens L 5  as this lens has the largest diameter. In this specification, f i  will denote the focal length of lens element L i . According to some examples, the following relationships holds: |f 1 |&gt;|f 3 |&gt;|f 2 |. According to some examples, the following relationships holds: |f 3 |&gt;|f 1 |&gt;|f 2 |. According to some examples, |f 3 |&gt;|f 2 |&gt;|f 1 |. 
     A known definition of F-number (F#) of a lens is the ratio of the lens effective focal length (EFL) to the diameter of the entrance pupil (d). 
     In this application, in some cases the entrance pupil is not circular. In such cases, d is replaced by an “equivalent” circular entrance pupil diameter of de given by: 
     
       
         
           
             
               
                 
                   
                     
                       d 
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                           4 
                           · 
                           entrance 
                         
                          
                         
                             
                         
                          
                         pupil 
                          
                         
                             
                         
                          
                         
                           area 
                           / 
                           π 
                         
                       
                     
                   
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                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     In this specification, a “gap” or an “air gap” refers to the space between consecutive lens elements. In the case of lens elements 1 and 2, it refers to the air space between the prism exit surface and the first surface of lens  2 . 
     A number of functions and constants per gap are defined:
         1. A “Gap i (r)” function, (where i is the lens element number and r is the same variable used in Eq. 1) is:
           a) for i=1: Gap i (r)=SAG(r) of L 2 S 1 +(the distance along the second optical axis between the prism exit surface and L 2 S 1 );   b) for i&gt;1: Gap i (r)=SAG(r) of L i+1 S 1 +(the distance along the second optical axis between L i S 2  and L i+1 S 1 )−SAG(r) of L i S 2 ;   c) for r=0, an “on-axis gap” (OA_Gap i ) is defined as Gap i (r=0);   
           2. A “gap average” (AVG i ) constant is given by:       

     
       
         
           
             
               
                 
                   
                     AVG 
                     i 
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
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                           = 
                           0 
                         
                         N 
                       
                        
                       
                         
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                           i 
                         
                          
                         
                           ( 
                           
                             
                               j 
                               · 
                               
                                 r 
                                 norm 
                               
                             
                             N 
                           
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     where j is a discrete variable that runs from 0 to N, where N is an integer&gt;10, and where r norm  is the minimum value D/2 of surfaces {L i S 2 , L i+1 S 1 }.
         3. A normalized gap standard deviation (STD i ) constant is given by:       

     
       
         
           
             
               
                 
                   
                     STD 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                         r 
                         norm 
                       
                     
                      
                     
                       
                         
                           1 
                           N 
                         
                          
                         
                           
                             ∑ 
                             
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                                     i 
                                   
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                                       N 
                                     
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                                   i 
                                 
                               
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                   ( 
                   
                     Eq 
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                   ) 
                 
               
             
           
         
       
     
     where r norm  the minimum value D/2 of surfaces {L i S 2 , L i+1 S 1 }, N is an integer&gt;10, and AVG i  is defined as in (Eq. 4). 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Ex 1 
                 Ex 2 
                 Ex 3 
                 Ex 4 
                 Ex 5 
                 Ex 6 
                 Ex 7 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 F# 
                 2.73 
                 2.63 
                 2.75 
                 2.75 
                 2.75 
                 2.75 
                 2.75 
               
               
                 EFL [mm] 
                 14.947 
                 14.956 
                 15.00 
                 14.960 
                 14.958 
                 14.961 
                 14.967 
               
               
                 TTL [mm] 
                 15.05 
                 15.61 
                 14.77 
                 14.60 
                 14.62 
                 14.79 
                 14.45 
               
               
                 TLL[mm] 
                 13.85 
                 14.31 
                 13.56 
                 13.25 
                 13.26 
                 13.43 
                 13.13 
               
               
                 BFL [mm] 
                 4.751 
                 4.515 
                 5.500 
                 5.275 
                 5.374 
                 5.297 
                 5.457 
               
               
                 TTL/EFL 
                 1.006 
                 1.043 
                 0.984 
                 0.975 
                 0.977 
                 0.988 
                 0.965 
               
               
                 BFL/TTL 
                 0.315 
                 0.289 
                 0.372 
                 0.361 
                 0.367 
                 0.358 
                 0.377 
               
               
                 A 1  [mm] 
                 4.8 
                 5.7 
                 4.7 
                 4.7 
                 4.7 
                 4.7 
                 4.7 
               
               
                 W 1  [mm] 
                 5.7 
                 5.7 
                 5.7 
                 5.7 
                 5.7 
                 5.7 
                 5.7 
               
               
                 W 1 /TTL 1   
                 1.583 
                 1.373 
                 1.599 
                 1.538 
                 1.536 
                 1.538 
                 1.549 
               
               
                 SDL [mm] 
                 5.86 
                 5.86 
                 5.86 
                 5.86 
                 5.86 
                 5.86 
                 5.86 
               
               
                 D(L N S 2 )/SDL 
                 0.607 
                 0.512 
                 0.619 
                 0.617 
                 0.616 
                 0.617 
                 0.615 
               
               
                 OH [mm] 
                 5.38 
                 6.05 
                 5.37 
                 5.51 
                 5.51 
                 5.51 
                 5.48 
               
               
                 OH/W 1   
                 0.943 
                 1.061 
                 0.942 
                 0.967 
                 0.968 
                 0.967 
                 0.962 
               
               
                 OH/A 1   
                 1.120 
                 1.061 
                 1.142 
                 1.173 
                 1.174 
                 1.173 
                 1.167 
               
               
                 SDL/OH 
                 1.089 
                 0.968 
                 1.091 
                 1.063 
                 1.063 
                 1.063 
                 1.069 
               
               
                 f 1  [mm] 0.587 μm 
                 8.87 
                 9.66 
                 8.72 
                 9.38 
                 9.36 
                 8.94 
                 9.13 
               
               
                 f 2  [mm] 0.587 μm 
                 −5.20 
                 −5.13 
                 −5.86 
                 −9.26 
                 −8.68 
                 −6.13 
                 −7.17 
               
               
                 f 3  [mm] 0.587 μm 
                 6.94 
                 5.91 
                 36.00 
                 −6855.9 
                 −8587.8 
                 4.92 
                 18.32 
               
               
                 f 4  [mm] 0.587 μm 
                 6.38 
                 6.03 
                 7.40 
                 8.70 
                 −11.26 
                 −14.95 
                 −6.59 
               
               
                 f 5  [mm] 0.587 μm 
                 −4.81 
                 −4.32 
                 −11.30 
                 −10.76 
                 8.17 
                 −12.24 
                 6.72 
               
               
                 f 1 /EFL 
                 0.593 
                 0.646 
                 0.581 
                 0.627 
                 0.626 
                 0.598 
                 0.610 
               
               
                 |f 2 /f 1 | 
                 0.586 
                 0.530 
                 0.672 
                 0.987 
                 0.926 
                 0.685 
                 0.785 
               
               
                 TTL/OA_Gap 1   
                 27.870 
                 41.696 
                 131.937 
                 150.447 
                 149.100 
                 138.803 
                 146.802 
               
               
                 TTL/OA_Gap 2   
                 86.450 
                 128.449 
                 254.474 
                 278.606 
                 279.280 
                 50.084 
                 258.256 
               
               
                 TTL/OA_Gap 3   
                 97.510 
                 101.485 
                 35.102 
                 29.309 
                 38.463 
                 291.430 
                 26.310 
               
               
                 TTL/OA_Gap 4   
                 99.554 
                 100.425 
                 58.416 
                 134.274 
                 111.851 
                 71.467 
                 126.195 
               
               
                 STD 1   
                 0.022 
                 0.022 
                 0.007 
                 0.003 
                 0.004 
                 0.013 
                 0.007 
               
               
                 STD 2   
                 0.014 
                 0.004 
                 0.011 
                 0.028 
                 0.018 
                 0.038 
                 0.001 
               
               
                 STD 3   
                 0.001 
                 0.003 
                 0.056 
                 0.078 
                 0.056 
                 0.032 
                 0.049 
               
               
                 STD 4   
                 0.013 
                 0.014 
                 0.026 
                 0.012 
                 0.014 
                 0.031 
                 0.013 
               
               
                   
               
            
           
         
       
     
     Example 1 
       
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                 L 1 S 1   
                 Aspheric - 
                 4.326 
                 1.200 
                 1.487 
                 70.405 
                 2.400 
                 2.850 
               
               
                   
                   
                 Stop 
               
               
                 S 2   
                 L 1 S 2   
                 Prism 
                 Infinity 
                 2.400 
                 1.487 
                 70.405 
                 2.400 
                 2.850 
               
               
                   
                   
                 Entrance 
               
               
                 S 3   
                   
                 Prism 
                 Infinity 
                 −2.400 
                 1.487 
                 70.405 
                 — 
                 — 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 4   
                 * 
                 Prism Exit 
                 Infinity 
                 −0.540 
                   
                   
                 2.100 
                 2.850 
               
               
                   
               
               
                 * the prism exit surface includes a −0.3 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 5   
                 L 2 S 1   
                 Aspheric 
                 7.502 
                 −0.296 
                 1.639 
                 23.523 
                 1.450 
               
               
                 S 6   
                 L 2 S 2   
                 Aspheric 
                 −6.089 
                 −0.174 
                   
                   
                 1.400 
               
               
                 S 7   
                 L 3 S 1   
                 Aspheric 
                 −5.811 
                 −1.105 
                 1.534 
                 55.664 
                 1.500 
               
               
                 S 8   
                 L 3 S 2   
                 Aspheric 
                 9.627 
                 −0.154 
                   
                   
                 1.500 
               
               
                 S 9   
                 L 4 S 1   
                 Aspheric 
                 10.940 
                 −1.600 
                 1.639 
                 23.523 
                 1.500 
               
               
                 S 10   
                 L 4 S 2   
                 Aspheric 
                 3.143 
                 −0.151 
                   
                   
                 1.700 
               
               
                 S 11   
                 L 5 S 1   
                 Aspheric 
                 2.344 
                 −0.273 
                 1.534 
                 55.664 
                 1.700 
               
               
                 S 12   
                 L 5 S 2   
                 Aspheric 
                 27.026 
                 −4.151 
                   
                   
                 1.800 
               
               
                 S 13   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.516 
                 64.167 
                 2.900 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.400 
                   
                   
                 2.950 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 0.000 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 # 
                 k 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 1   
                 −0.305 
                 6.77E−05 
                  3.27E−06 
               
               
                   
                 S 5   
                 15.881 
                 −1.26E−02  
                 −1.55E−02 
               
               
                   
                 S 6   
                 6.600 
                 1.35E−02 
                 −5.89E−03 
               
               
                   
                 S 7   
                 −7.648 
                 2.29E−02 
                 −4.61E−03 
               
               
                   
                 S 8   
                 26.734 
                 4.59E−02 
                 −4.28E−03 
               
               
                   
                 S 9   
                 26.996 
                 4.53E−02 
                 −1.64E−03 
               
               
                   
                 S 10   
                 −0.292 
                 1.60E−02 
                 −5.36E−04 
               
               
                   
                 S 11   
                 −0.336 
                 8.70E−04 
                 −1.26E−03 
               
               
                   
                 S 12   
                 3.075 
                 −4.34E−03  
                  6.15E−04 
               
               
                   
                   
               
            
           
         
       
     
     According to one example, in camera  100 , the length A 1  (denoted in the figure as  128 ) of L 1  is 4.80 mm, while its width W 1  is 5.7 mm, the length being smaller than the width because of cuts  112   a  and  112   b . TLL is 13.85 mm and EFL is 15 mm. TTL 1  is 11.45 mm. TTL 2  is 3.60 mm. TTL (i.e. TTL 1 +TTL 2 ) is therefore 15.05 mm. The optical height OH is 5.38 mm. To further decrease OH, prism  104  can have a flat surface  104   d  parallel to light entering plane  104   a  and intersecting exit plane  104   b  and light folding plane  104   c . The apertures of L 1  are cut along the second optical axis  110 . The apertures of L 2 , L 3 , L 4  and L 5  are circular. Note that in some embodiments, some of the apertures of L 2 , L 3 , L 4  and L 5  may also have cuts. 
     In lens  102 , L 1  is a positive (i.e. with positive refractive optical power) lens element. L 2  is a negative (i.e. with negative refractive optical power) lens element. This holds true also for all other embodiments (i.e. Examples 2-7) disclosed herein. Lens elements L 5  to L n  may have any sign. In example 100. L 3  is positive, L 4  is positive and L 5  is negative. In other examples given here, L 3  is positive, L 4  is negative and L 5  is positive. In yet other examples given here, L3 is negative, L 4  is negative and L 5  is positive. Given the description and values listed above, it is evident that the optical height (5.38 mm) is smaller than 1.2×A 1  (4.80 mm)=5.76 mm, that the ratio TTL/EFL=1.0033 (smaller than 1.2 and even than 1.1) and that TLL/EFL&lt;1. According to some examples (see below), TTL/EFL&lt;1. 
       FIG. 1E  shows a folded camera  100 ′ like camera  100  housed in a housing  127 .  FIG. 1F  shows a cut along a line A-A in  FIG. 1E . Housing  127  may be used to protect optical elements from dust and mechanical damage. Housing  127  include an opening  128 . Light can enter lens  102  through opening  128 . In camera  100 ′, lens elements L 2  to L N  are housed in a lens barrel  150 . Lens barrel  150  can be used for example for mechanical protection, to prevent unwanted light entering the lens, and for mechanical alignment of lens elements L 2 -L N . A height H C  of camera  100 ′ is defined as the height from the lower most point of camera  100 ′ to the highest point of camera  100 ′. He may be substantially equal to the optical height OH plus a “penalty”  140 . Penalty  140  may be equal to the thickness of a bottom shield  125  (which is part of housing  127 ) and an air gap  144 . Air gap  142  may be required for the actuation of lens  102  (see below). In an example, bottom shield  125  may be 50-150 μm thick and air gap  144  may be 50-150 μm wide. Thus, in some examples, H C  may be equal to optical height OH plus 100 μm, or to OH plus 200 μm, or to OH plus 300 μm. 
     In addition to H C , in some cases, camera  100 ′ may have uneven height. That is, a section  132  of camera  100 ′ may have higher height than a section  134 . In some example, section  132  may include lens element L 1  and prism  104 , while section  134  may include lens elements L 2  to L N , and barrel  150 . A lower part of camera  100 ′ (section  134 ) is referred as “camera shoulder”, and a shoulder height is marked H S . Height H S  may be substantially equal to the height of barrel  150  (marked H B ) plus a penalty  140  plus a penalty  146 . Penalty  146  may be equal to the thickness of a top shield  126  (which is part of a housing  122 ) and an air gap  148 . Air gap  148  may be required for the actuation of lens  102  (see below). In an example, top shield  126  may be 50-150 μm thick and air gap  148  may be 50-150 μm wide. Thus, in some examples, H S  may be equal to the Ha plus 250 μm, or to OH plus 300 μm, or OH plus 500 μm. 
     Housing  122  may further comprise an actuator that may move (actuate, shift) folded lens  102  for focusing (or auto focusing—“AF”) and optical image stabilization (OIS). Focusing may be performed by shifting lens  102  relative to image sensor  108  along second optical axis  110 . OIS may be performed by shifting lens  102  along the two axes perpendicular to second optical axis  110 . 
       FIGS. 2A-2C  show a second exemplary embodiment (Example 2) of a folded camera disclosed herein and numbered  200 .  FIG. 2A  shows embodiment  200  in an isometric view,  FIG. 2B  shows camera  200  in a side view and  FIG. 2C  shows camera  200  in a top view. All elements in cameras  100  and  200  are identical except for first lens element L 1 , which in this embodiment lacks cuts such as  112   a  and  112   b . Therefore, the folded lens in camera  200  is marked  202  and is referred to as a “no cut lens”. Detailed optical data for the folded camera  200  and folded lens  202  is given in Tables 1 and 5-7. 
     Example 2 
       
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                 L 1 S 1   
                 Aspheric 
                 4.712 
                 1.300 
                 1.48749 
                 70.4058 
                 2.850 
                 2.850 
               
               
                 S 2   
                 L 1 S 2   
                 Prism 
                 Infin- 
                 2.850 
                 1.48749 
                 70.4058 
                 2.850 
                 2.850 
               
               
                   
                   
                 Entrance 
                 ity 
               
               
                 S 3   
                   
                 Prism 
                 Infin- 
                 −2.850 
                 1.48749 
                 70.4058 
                 — 
                 — 
               
               
                   
                   
                   
                 ity 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 4   
                 * 
                 Prism 
                 Infin- 
                 −0.169 
                   
                   
                 2.360 
                 2.850 
               
               
                   
                   
                 Exit 
                 ity 
               
               
                   
               
               
                 * the prism exit surface includes a −0.495 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 5   
                   
                 Standard - 
                 Infinity 
                 −0.206 
                   
                   
                 1.455 
               
               
                   
                   
                 Stop 
               
               
                 S 6   
                 L 2 S 1   
                 Aspheric 
                 7.821 
                 −0.296 
                 1.6397 
                 23.523 
                 1.436 
               
               
                 S 7   
                 L 2 S 2   
                 Aspheric 
                 −5.750 
                 −0.122 
                   
                   
                 1.407 
               
               
                 S 8   
                 L 3 S 1   
                 Aspheric 
                 −4.660 
                 −1.120 
                 1.5348 
                 55.664 
                 1.425 
               
               
                 S 9   
                 L 3 S 2   
                 Aspheric 
                 9.045 
                 −0.154 
                   
                   
                 1.465 
               
               
                 S 10   
                 L 4 S 1   
                 Aspheric 
                 12.330 
                 −1.600 
                 1.6397 
                 23.523 
                 1.412 
               
               
                 S 11   
                 L 4 S 2   
                 Aspheric 
                 3.090 
                 −0.155 
                   
                   
                 1.550 
               
               
                 S 12   
                 L 5 S 1   
                 Aspheric 
                 2.329 
                 −0.273 
                 1.5348 
                 55.664 
                 1.484 
               
               
                 S 13   
                 L 5 S 2   
                 Aspheric 
                 −350.821 
                 −3.905 
                   
                   
                 1.507 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.5168 
                 64.2 
                 2.930 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 −0.400 
                   
                   
                 2.930 
               
               
                 S 16   
                   
                 Standard 
                 Infinity 
                 0.000 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 # 
                 k 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 1   
                 −0.361 
                 9.14E−05 
                  3.24E−06 
               
               
                   
                 S 6   
                 18.000 
                 −1.09E−02  
                 −1.72E−03 
               
               
                   
                 S 7   
                 2.173 
                 1.72E−02 
                 −7.95E−03 
               
               
                   
                 S 8   
                 −4.968 
                 2.36E−02 
                 −6.40E−03 
               
               
                   
                 S 9   
                 22.508 
                 4.42E−02 
                 −4.56E−03 
               
               
                   
                 S 10   
                 19.512 
                 4.90E−02 
                 −2.09E−03 
               
               
                   
                 S 11   
                 −0.257 
                 1.90E−02 
                 −1.20E−03 
               
               
                   
                 S 12   
                 −0.219 
                 4.04E−03 
                 −2.14E−03 
               
               
                   
                 S 13   
                 91.000 
                 −2.45E−03  
                  4.74E−04 
               
               
                   
                   
               
            
           
         
       
     
     In folded camera  200 , A 1  and W 1  are 5.70 mm (i.e. in camera  200 , L 1  is circular). TTL is 14.31 mm and EFL is 15 mm, TTL 1  is 11.46 mm, TTL 2  is 4.15 mm (i.e., the total TTL=15.61 mm) and OH is 6.05 mm. As in folded camera  100 , the prism can have a flat surface parallel to the light entering plane and intersecting the light exiting plane and the light folding plane. In the example shown according to  FIG. 2 , the apertures of all lens elements are circular. 
     Given the description and values listed above, it is evident that the optical height (6.05 mm) is smaller than 1.2×A 1  (5.70 mm)=6.84 mm, and smaller even than 1.1×A 1  (=6.27 mm). The ratio TTL/EFL=1.0407, i.e. smaller than 1.2 and even smaller than 1.1. Also, TILL/EFL&lt;1. 
       FIG. 3  shows third exemplary embodiment of folded camera numbered  300  (“Example 3”) with lens  302  and light ray tracing from an object to the image sensor. Detailed optical data for the folded camera  300  and folded lens  302  is given in Tables 1 and 8-10. All elements in camera  300  except lens  302  are identical with elements in cameras  100  and  200 . 
     Example 3 
       
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                   
                 Standard - 
                 Infinity 
                 −0.905 
                   
                   
                 2.350 
                 2.850 
               
               
                   
                   
                 STOP 
               
               
                 S 2   
                 L 1 S 1   
                 Aspheric 
                 4.611 
                 1.214 
                 1.528 
                 76.975 
                 2.350 
                 2.850 
               
               
                 S 3   
                 L 1 S 2   
                 Prism 
                 Infinity 
                 2.350 
                 1.528 
                 76.975 
                 2.350 
                 2.850 
               
               
                   
                   
                 Entrance 
               
               
                 S 4   
                   
                 Prism 
                 Infinity 
                 −2.350 
                 1.528 
                 76.975 
                 — 
                 — 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 5   
                 * 
                 Prism Exit 
                 Infinity 
                 −0.112 
                   
                   
                 2.100 
                 2.850 
               
               
                   
               
               
                 * the prism exit surface includes a −0.265 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 9 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 6   
                 L 2 S 1   
                 Aspheric 
                 20.118 
                 −0.441 
                 1.651 
                 21.513 
                 1.815 
               
               
                 S 7   
                 L 2 S 2   
                 Aspheric 
                 −4.758 
                 −0.058 
                   
                   
                 1.718 
               
               
                 S 8   
                 L 3 S 1   
                 Aspheric 
                 −3.508 
                 −0.902 
                 1.535 
                 56.115 
                 1.736 
               
               
                 S 9   
                 L 3 S 2   
                 Aspheric 
                 −3.904 
                 −0.421 
                   
                   
                 1.658 
               
               
                 S 10   
                 L 4 S 1   
                 Aspheric 
                 −8.924 
                 −0.925 
                 1.651 
                 21.513 
                 1.652 
               
               
                 S 11   
                 L 4 S 2   
                 Aspheric 
                 10.049 
                 −0.253 
                   
                   
                 1.754 
               
               
                 S 12   
                 L 5 S 1   
                 Aspheric 
                 3.985 
                 −0.252 
                 1.535 
                 56.115 
                 1.723 
               
               
                 S 13   
                 L 5 S 2   
                 Aspheric 
                 11.922 
                 −4.790 
                   
                   
                 1.815 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.516 
                 64.167 
                 2.889 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 −0.500 
                   
                   
                 2.919 
               
               
                 S 16   
                   
                 Standard 
                 Infinity 
                 — 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 10 
               
               
                   
                   
               
               
                   
                 # 
                 K 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 2   
                 −0.874 
                 8.10E−04 
                 1.91E−05 
               
               
                   
                 S 6   
                 −129.217 
                 −2.12E−03  
                 −2.70E−04  
               
               
                   
                 S 7   
                 0.203 
                 4.80E−03 
                 −2.56E−03  
               
               
                   
                 S 8   
                 0.184 
                 1.64E−02 
                 −3.58E−03  
               
               
                   
                 S 9   
                 1.622 
                 2.67E−02 
                 −1.23E−03  
               
               
                   
                 S 10   
                 −22.269 
                 2.61E−02 
                 2.30E−03 
               
               
                   
                 S 11   
                 12.035 
                 2.21E−02 
                 9.77E−04 
               
               
                   
                 S 12   
                 1.931 
                 8.11E−03 
                 3.19E−04 
               
               
                   
                 S 13   
                 21.054 
                 3.37E−04 
                 3.10E−04 
               
               
                   
                   
               
            
           
         
       
     
     In folded camera  300  (Example 3 and Tables 8-10), A 1  and W 1  are respectively 4.7 mm and 5.7 mm (i.e. in camera  300 . L 1  is a cut lens). TLL is 13.56 mm and EFL is 15.00 mm, TTL 1  is 3.564 mm, TTL 2  is I1.206 mm (i.e., the total TTL=14.77 mm) and OH is 5.37 mm. As in folded camera  100  (surface  104   d ) or  200 , the prism can have a flat surface parallel to the light entering plane and intersecting the light exiting plane and the light folding plane that contributes to the reducing of OH. Note that in Examples 3-7 (as well as in Example 1), the apertures of all lens elements except for L 1  are circular. Note that in Example 2, all lens elements including L1 have circular apertures. 
     Given the description and values listed above, it is evident that the optical height (5.37 mm) is smaller than 1.2×A 1  (4.7 mm)=5.64 mm. The ratio TTL/EFL=0.984, i.e. smaller than 1.2 and even smaller than 1.1 and even smaller than 1. Also, TLL/EFL&lt;1. 
       FIG. 4  shows a fourth exemplary embodiment of a folded camera numbered  400  (Example 4) with a lens  402  and light ray tracing from an object to the image sensor. Detailed optical data for the folded camera  400  and folded lens  402  is given in Tables 1 and 11-13. All elements in camera  400  except lens  402  are identical with elements in cameras  100 ,  200  and  300 . 
     Example 4 
       
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 11 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                   
                 Standard - 
                 Infinity 
                 −1.057 
                   
                   
                 2.350 
                 2.850 
               
               
                   
                   
                 STOP 
               
               
                 S 2   
                 L 1 S 1   
                 Aspheric 
                 4.073 
                 1.355 
                 1.433 
                 95.232 
                 2.350 
                 2.850 
               
               
                 S 3   
                 L 1 S 2   
                 Prism 
                 Infinity 
                 2.350 
                 1.433 
                 95.232 
                 2.350 
                 2.850 
               
               
                   
                   
                 Entrance 
               
               
                 S 4   
                   
                 Prism 
                 Infinity 
                 −2.350 
                 1.433 
                 95.232 
                 — 
                 — 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 5   
                 * 
                 Prism Exit 
                 Infinity 
                 −0.097 
                   
                   
                 2.080 
                 2.850 
               
               
                   
               
               
                 * the prism exit surface includes a −0.270 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 12 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 6   
                 L 2 S 1   
                 Aspheric 
                 31.776 
                 −0.409 
                 1.651 
                 21.513 
                 1.806 
               
               
                 S 7   
                 L 2 S 2   
                 Aspheric 
                 −7.479 
                 −0.052 
                   
                   
                 1.716 
               
               
                 S 8   
                 L 3 S 1   
                 Aspheric 
                 −3.567 
                 −0.907 
                 1.535 
                 56.115 
                 1.730 
               
               
                 S 9   
                 L 3 S 2   
                 Aspheric 
                 −3.247 
                 −0.498 
                   
                   
                 1.619 
               
               
                 S 10   
                 L 4 S 1   
                 Aspheric 
                 −14.616 
                 −0.951 
                 1.651 
                 21.513 
                 1.622 
               
               
                 S 11   
                 L 4 S 2   
                 Aspheric 
                 9.021 
                 −0.109 
                   
                   
                 1.750 
               
               
                 S 12   
                 L 5 S 1   
                 Aspheric 
                 4.476 
                 −0.252 
                 1.535 
                 56.115 
                 1.740 
               
               
                 S 13   
                 L 5 S 2   
                 Aspheric 
                 20.463 
                 −4.566 
                   
                   
                 1.806 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.516 
                 64.167 
                 2.876 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 −0.500 
                   
                   
                 2.907 
               
               
                 S 16   
                   
                 Standard 
                 Infinity 
                 — 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 13 
               
               
                   
                   
               
               
                   
                 # 
                 K 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 2   
                 −0.303 
                  7.31E−05 
                 1.71E−06 
               
               
                   
                 S 6   
                 96.549 
                 −6.01E−03 
                 −6.90E−06  
               
               
                   
                 S 7   
                 10.219 
                 −5.99E−03 
                 3.20E−04 
               
               
                   
                 S 8   
                 −0.715 
                 −1.72E−03 
                 1.80E−04 
               
               
                   
                 S 9   
                 −3.213 
                 −3.61E−03 
                 9.19E−04 
               
               
                   
                 S 10   
                 −108.408 
                  1.13E−02 
                 3.97E−03 
               
               
                   
                 S 11   
                 −0.202 
                  6.62E−03 
                 3.68E−03 
               
               
                   
                 S 12   
                 3.281 
                 −1.18E−02 
                 2.17E−03 
               
               
                   
                 S 13   
                 95.038 
                 −2.74E−03 
                 4.32E−04 
               
               
                   
                   
               
            
           
         
       
     
     In folded camera  400  (Example 4 and Tables 11-13) A 1  and W 1  are respectively 4.7 and 5.7 mm. TLL is 13.25 mm and EFL is 14.96 mm, TTL 1  is 3.705 mm, TTL 2  is 10.895 mm (i.e., the total TTL=14.6 mm) and OH is 5.51 mm. As in folded camera  100  or  200 , the prism can have flat surface parallel to the light entering plane and intersecting the light exiting plane and the light folding plane. The apertures of all lens elements are circular. 
     Given the description and values listed above, it is evident that the optical height (5.51 mm) is smaller than 1.2×A 1  (4.7 mm)=5.64 mm. The ratio TTL/EFL=0.975, i.e. smaller than 1.2 and even smaller than 1.1 and even smaller than 1. Also TLL/EFL&lt;1. 
       FIG. 5  shows a fifth exemplary embodiment of a folded camera numbered  500  (“Example 5”) with a lens  502  and light ray tracing from an object to the image sensor. Detailed optical data for the folded camera  500  and folded lens  502  is given in Tables 1 and 14-16. All elements in camera  500  except lens  502  are identical with elements in cameras  100 ,  200 ,  300  and  400 . 
     Example 5 
       
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 14 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                   
                 Standard - 
                 Infinity 
                 −1.065 
                   
                   
                 2.350 
                 2.850 
               
               
                   
                   
                 STOP 
               
               
                 S 2   
                 L 1 S 1   
                 Aspheric 
                 4.062 
                 1.359 
                 1.433 
                 95.232 
                 2.350 
                 2.850 
               
               
                 S 3   
                 L 1 S 2   
                 Prism 
                 Infinity 
                 2.350 
                 1.433 
                 95.232 
                 2.350 
                 2.850 
               
               
                   
                   
                 Entrance 
               
               
                 S 4   
                   
                 Prism 
                 Infinity 
                 −2.350 
                 1.433 
                 95.232 
                 — 
                 — 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 5   
                 * 
                 Prism 
                 Infinity 
                 −0.098 
                   
                   
                 2.080 
                 2.850 
               
               
                   
                   
                 Exit 
               
               
                   
               
               
                 * the prism exit surface includes a −0.27 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 15 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 6   
                 L 2 S 1   
                 Aspheric 
                 52.828 
                 −0.649 
                 1.651 
                 21.513 
                 1.800 
               
               
                 S 7   
                 L 2 S 2   
                 Aspheric 
                 −6.365 
                 −0.052 
                   
                   
                 1.709 
               
               
                 S 8   
                 L 3 S 1   
                 Aspheric 
                 −3.970 
                 −0.906 
                 1.535 
                 56.115 
                 1.720 
               
               
                 S 9   
                 L 3 S 2   
                 Aspheric 
                 −3.651 
                 −0.380 
                   
                   
                 1.636 
               
               
                 S 10   
                 L 4 S 1   
                 Aspheric 
                 −7.218 
                 −0.446 
                 1.535 
                 56.115 
                 1.637 
               
               
                 S 11   
                 L 4 S 2   
                 Aspheric 
                 −3.214 
                 −0.131 
                   
                   
                 1.749 
               
               
                 S 12   
                 L 5 S 1   
                 Aspheric 
                 −4.056 
                 −0.531 
                 1.651 
                 21.513 
                 1.765 
               
               
                 S 13   
                 L 5 S 2   
                 Aspheric 
                 −16.194 
                 −4.665 
                   
                   
                 1.807 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.516 
                 64.167 
                 2.883 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 −0.500 
                   
                   
                 2.914 
               
               
                 S 16   
                   
                 Standard 
                 Infinity 
                 — 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 16 
               
               
                   
                   
               
               
                   
                 # 
                 k 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 2   
                 −0.225 
                 −3.72E−05  
                 −3.37E−06  
               
               
                   
                 S 6   
                 2.287 
                 −1.24E−03  
                 1.30E−04 
               
               
                   
                 S 7   
                 3.112 
                 −5.95E−03  
                 1.01E−03 
               
               
                   
                 S 8   
                 −0.731 
                 −1.11E−03  
                 3.02E−04 
               
               
                   
                 S 9   
                 0.084 
                 2.12E−02 
                 −1.55E−03  
               
               
                   
                 S 10   
                 −24.608 
                 2.74E−02 
                 7.22E−04 
               
               
                   
                 S 11   
                 −10.147 
                 8.67E−04 
                 1.15E−03 
               
               
                   
                 S 12   
                 −13.144 
                 3.59E−03 
                 1.08E−03 
               
               
                   
                 S 13   
                 −14.426 
                 1.64E−02 
                 −1.25E−04  
               
               
                   
                   
               
            
           
         
       
     
     In folded camera  500  (Example 5 and Tables 14-16), A 1  and W 1  are respectively 4.7 and 5.7 mm. TLL is 13.26 mm and EFL is 14.958 mm, TTL 1  is 3.709 mm, TTL 2  is 10.911 mm (i.e., the total TTL=14.62 mm) and OH is 5.51 mm. As in folded camera  100  or  200 , the prism can have a flat surface parallel to the light entering plane and intersecting the light exiting plane and the light folding plane. The apertures of all lens elements are circular. 
     Given the description and values listed above, it is evident that the optical height (5.51 mm) is smaller than 1.2×A 1  (4.7 mm)=5.64 mm. The ratio TTL/EFL=0.977, i.e. smaller than 1.2 and even smaller than 1.1 and even smaller than 1. Also, TLL/EFL&lt;1. 
       FIG. 6  shows a sixth exemplary embodiment of a folded camera numbered  600  (Example 6) with a lens  602  and light ray tracing from an object to the image sensor. Detailed optical data for the folded camera  600  and folded lens  602  is given in Tables 1 and 17-19. All elements in camera  600  except lens  602  are identical with elements in cameras  100 ,  200 ,  300 ,  400  and  500 . 
     Example 6 
       
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 17 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                   
                 Standard - 
                 Infinity 
                 −1.060 
                   
                   
                 2.350 
                 2.850 
               
               
                   
                   
                 STOP 
               
               
                 S 2   
                 L 1 S 1   
                 Aspheric 
                 4.078 
                 1.355 
                 1.456 
                 90.900 
                 2.350 
                 2.850 
               
               
                 S 3   
                 L 1 S 2   
                 Prism 
                 Infinity 
                 2.350 
                 1.456 
                 90.900 
                 2.350 
                 2.850 
               
               
                   
                   
                 Entrance 
               
               
                 S 4   
                   
                 Prism 
                 Infinity 
                 −2.350 
                 1.456 
                 90.900 
                 — 
                 — 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 5   
                   
                 Prism 
                 Infinity 
                 −0.107 
                   
                   
                 2.080 
                 2.850 
               
               
                   
                   
                 Exit 
               
               
                   
               
               
                 *the prism exit surface includes a −0.27 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 18 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 6   
                 L 2 S 1   
                 Aspheric 
                 15.780 
                 −0.670 
                 1.651 
                 21.513 
                 1.767 
               
               
                 S 7   
                 L 2 S 2   
                 Aspheric 
                 −5.439 
                 −0.295 
                   
                   
                 1.653 
               
               
                 S 8   
                 L 3 S 1   
                 Aspheric 
                 −8.111 
                 −0.907 
                 1.651 
                 21.513 
                 1.653 
               
               
                 S 9   
                 L 3 S 2   
                 Aspheric 
                 5.073 
                 −0.051 
                   
                   
                 1.760 
               
               
                 S 10   
                 L 4 S 1   
                 Aspheric 
                 7.664 
                 −0.953 
                 1.651 
                 21.513 
                 1.789 
               
               
                 S 11   
                 L 4 S 2   
                 Aspheric 
                 37.777 
                 −0.207 
                   
                   
                 1.809 
               
               
                 S 12   
                 L 5 S 1   
                 Aspheric 
                 5.035 
                 −0.250 
                 1.535 
                 56.115 
                 1.809 
               
               
                 S 13   
                 L 5 S 2   
                 Aspheric 
                 22.129 
                 −4.588 
                   
                   
                 1.811 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.516 
                 64.167 
                 2.864 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 −0.500 
                   
                   
                 2.896 
               
               
                 S 16   
                   
                 Standard 
                 Infinity 
                 — 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 19 
               
               
                   
                   
               
               
                   
                 # 
                 K 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 2   
                 −0.283 
                 7.76E−05 
                 3.45E−06 
               
               
                   
                 S 6   
                 22.671 
                 −1.94E−04 
                 −1.43E−03  
               
               
                   
                 S 7   
                 6.703 
                  1.44E−02 
                 8.50E−05 
               
               
                   
                 S 8   
                 −31.425 
                  9.90E−03 
                 4.27E−03 
               
               
                   
                 S 9   
                 −35.446 
                 −2.24E−02 
                 5.67E−03 
               
               
                   
                 S 10   
                 −112.063 
                 −3.55E−02 
                 5.52E−03 
               
               
                   
                 S 11   
                 63.734 
                 −1.41E−03 
                 2.85E−04 
               
               
                   
                 S 12   
                 2.909 
                 −9.30E−03 
                 −2.48E−03  
               
               
                   
                 S 13   
                 113.315 
                 −6.41E−03 
                 −1.64E−03  
               
               
                   
                   
               
            
           
         
       
     
     In folded camera  600  (Example 6 and Tables 17-19), A 1  and W 1  are respectively 4.7 and 5.7 mm. TLL is 13.43 mm and EFL is 14.961 mm, TTL is 3.705 mm. TTL 2  is 11.085 mm (i.e., the total TTL=14.79 mm) and OH is 5.51 mm. As in folded camera  100  or  200 , the prism can have a flat surface parallel to the light entering plane and intersecting the light exiting plane and the light folding plane. The apertures of all lens elements are circular. 
     Given the description and values listed above, it is evident that the optical height (5.51 mm) is smaller than 1.2× A 1  (4.7 mm)=5.64 mm. The ratio TTL/EFL=0.988, i.e. smaller than 1.2 and even smaller than 1.1 and even smaller than 1. Also, TLL/EFL&lt;1. 
       FIG. 7  shows a seventh exemplary embodiment of a folded camera numbered  700  (Example 7) with a lens  702  and light ray tracing from an object to the image sensor. Detailed optical data for the folded camera  700  and folded lens  702  is given in Tables 1 and 20-22. All elements in camera  700  except lens  702  are identical with elements in cameras  100 ,  200 ,  300 ,  400 ,  500  and  600 . 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 20 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 A/2 
                 W/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 S 1   
                   
                 Standard - 
                 Infinity 
                 −1.024 
                   
                   
                 2.350 
                 2.850 
               
               
                   
                   
                 STOP 
               
               
                 S 2   
                 L 1 S 1   
                 Aspheric 
                 4.166 
                 1.328 
                 1.433 
                 95.232 
                 2.350 
                 2.850 
               
               
                 S 3   
                 L 1 S 2   
                 Prism 
                 Infinity 
                 2.350 
                 1.433 
                 95.232 
                 2.350 
                 2.850 
               
               
                   
                   
                 Entrance 
               
               
                 S 4   
                   
                 Prism 
                 Infinity 
                 −2.350 
                 1.433 
                 95.232 
                 — 
                 — 
               
               
                   
                   
                 Reflective 
               
               
                   
                   
                 face 
               
               
                 S 5   
                   
                 Prism 
                 Infinity 
                 −0.098 
                   
                   
                 2.080 
                 2.850 
               
               
                   
                   
                 Exit 
               
               
                   
               
               
                 *the prism exit surface includes a −0.27 mm offset. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 21 
               
               
                   
               
               
                   
                   
                   
                 R 
                 T 
                   
                   
                 D/2 
               
               
                 # 
                   
                 Type 
                 [mm] 
                 [mm] 
                 Nd 
                 Vd 
                 [mm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 S 6   
                 L 2 S 1   
                 Aspheric 
                 −25.077 
                 −0.253 
                 1.651 
                 21.513 
                 1.791 
               
               
                 S 7   
                 L 2 S 2   
                 Aspheric 
                 −3.922 
                 −0.056 
                   
                   
                 1.715 
               
               
                 S 8   
                 L 3 S 1   
                 Aspheric 
                 −4.023 
                 −0.906 
                 1.535 
                 56.115 
                 1.721 
               
               
                 S 9   
                 L 3 S 2   
                 Aspheric 
                 −6.284 
                 −0.549 
                   
                   
                 1.646 
               
               
                 S 10   
                 L 4 S 1   
                 Aspheric 
                 −7.945 
                 −0.431 
                 1.535 
                 56.115 
                 1.615 
               
               
                 S 11   
                 L 4 S 2   
                 Aspheric 
                 −2.399 
                 −0.115 
                   
                   
                 1.754 
               
               
                 S 12   
                 L 5 S 1   
                 Aspheric 
                 −3.472 
                 −0.563 
                 1.651 
                 21.513 
                 1.773 
               
               
                 S 13   
                 L 5 S 2   
                 Aspheric 
                 −15.725 
                 −4.747 
                   
                   
                 1.803 
               
               
                 S 14   
                   
                 Standard 
                 Infinity 
                 −0.210 
                 1.516 
                 4.167 
                 2.877 
               
               
                 S 15   
                   
                 Standard 
                 Infinity 
                 −0.500 
                   
                   
                 2.908 
               
               
                 S 16   
                   
                 Standard 
                 Infinity 
                 — 
                   
                   
                 3.030 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 22 
               
               
                   
                   
               
               
                   
                 # 
                 K 
                 α 2   
                 α 3   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 S 2   
                 −0.373 
                 1.69E−04 
                  7.56E−06 
               
               
                   
                 S 6   
                 −30.531 
                 5.01E−03 
                 −1.01E−03 
               
               
                   
                 S 7   
                 −0.953 
                 4.25E−03 
                 −1.57E−03 
               
               
                   
                 S 8   
                 −5.260 
                 −3.33E−03  
                 −1.47E−03 
               
               
                   
                 S 9   
                 −22.816 
                 1.13E−02 
                 −1.86E−03 
               
               
                   
                 S 10   
                 −91.835 
                 4.26E−02 
                 −8.24E−04 
               
               
                   
                 S 11   
                 −8.964 
                 7.03E−03 
                  2.50E−04 
               
               
                   
                 S 12   
                 −13.635 
                 4.43E−03 
                 −2.45E−04 
               
               
                   
                 S 13   
                 −36.786 
                 2.05E−02 
                 −2.06E−03 
               
               
                   
                   
               
            
           
         
       
     
     In folded camera  700  (Example 7 and Tables 20-22), A 1  and W 1  are respectively 4.7 and 5.7 mm. TLL is 13.13 mm and EFL is 14.967 mm. TTL 1  is 3.678 mm. TTL 2  is 10.772 mm (i.e., the total TTL=14.45 mm) and OH is 5.48 mm. As in other folded cameras, the prism can have a flat surface parallel to the light entering plane and intersecting the light exiting plane and the light folding plane. The apertures of all lens elements are circular. 
     Given the description and values listed above, it is evident that the optical height (5.48 mm) is smaller than 1.2×A 1  (4.7 mm)=5.64 mm. The ratio TTL/EFL=0.965, i.e. smaller than 1.2 and even smaller than 1.1 and even smaller than 1. Also, TLL/EFL&lt;1. 
     Table 23 summarizes the design characteristics and parameters as they appear in the examples listed above. These characteristics helps to achieve the goal of a compact folded lens with large lens assembly aperture: 
     “AA”: AA 1 ≡BFL/TTL&gt;0.2, AA 2 ≡BFL/TTL&gt;0.28, AA 3 ≡BFL/TTL&gt;0.35;
 
“BB”: BB 1 ≡OH/A 1 &lt;1.4, BB 2 ≡OH/A 1 &lt;1.2, BB 3 ≡OH/A 1 &lt;1.1;
 
“CC”: CC 1 ≡OH/W 1 &lt;1.1, CC 2 ≡OH/W 1 &lt;1.00, CC 3 ≡OH/W 1 &lt;0.95;
 
“DD”: At least two gaps that comply with DD 1 ≡STD&lt;0.020, DD 2 ≡STD&lt;0.015, DD 3 ≡STD&lt;0.010;
 
“EE”: At least 3 gaps that comply with EE 1 ≡STD&lt;0.035, EE 2 ≡STD&lt;0.025, EE 3 ≡STD&lt;0.015;
 
“FF”: At least 4 gaps that comply with FF 1 ≡STD&lt;0.050, FF 2 ≡STD&lt;0.035, FF 3 ≡STD&lt;0.025:
 
“GG”: GG 1 ≡SDL/OH&gt;0.7, GG 2 ≡SDL/OH&gt;0.85, GG 3 ≡SDL/OH&gt;1;
 
“HH”: a power sign sequence;
 
“II”: At least 1 gap that complies with II 1 ≡STD&lt;0.01 and OA_Gap/TTL&lt;1/80, II 2 ≡STD&lt;0.015 and OA_Gap/TTL&lt;1/65;
 
“JJ”: Abbe number sequence of lens element 1, 2 and 3 can be respectively larger than 50, smaller than 30 and larger than 50;
 
“KK”: Effective focal length of combined lens elements 2 and 3 is negative:
 
“LL”: LL 1 ≡f1/EFL&lt;0.7, LL 2 ≡f1/EFL&lt;0.6;
 
“MM”: MM 1 ≡|f 2 /f 1 |&lt;1, MM 2 ≡|f 2 /f 1 &lt;0.7; and
 
“NN”: L 2  to L N  have circular apertures.
 
     Table 23 indicates whether a parameter or a condition is fulfilled (symbol “✓”) or not fulfilled (symbol “x”) in each Example. The cited examples are brought in order to illustrate the principles of the disclosed subject matter and should not be construed as limiting. Other examples are also contemplated within the scope of the presently disclosed subject matter. 
     
       
         
           
               
               
             
               
                   
                 TABLE 23 
               
             
            
               
                   
                   
               
               
                   
                 Example 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 EX1 
                 EX2 
                 EX3 
                 EX4 
                 EX5 
                 EX6 
                 EX7 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 AA 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 AA 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 AA 3   
                 x 
                 x 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 BB 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 BB 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 BB 3   
                 x 
                 ✓ 
                 x 
                 x 
                 x 
                 x 
                 x 
               
               
                 CC 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 CC 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 CC 3   
                 ✓ 
                 x 
                 ✓ 
                 x 
                 x 
                 x 
                 x 
               
               
                 DD 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 DD 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 ✓ 
               
               
                 DD 3   
                 x 
                 ✓ 
                 x 
                 x 
                 x 
                 x 
                 ✓ 
               
               
                 EE 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 EE 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 ✓ 
                 x 
                 ✓ 
               
               
                 EE 3   
                 ✓ 
                 ✓ 
                 x 
                 x 
                 x 
                 x 
                 ✓ 
               
               
                 FF 1   
                 ✓ 
                 ✓ 
                 x 
                 x 
                 x 
                 ✓ 
                 ✓ 
               
               
                 FF 2   
                 ✓ 
                 ✓ 
                 x 
                 x 
                 x 
                 x 
                 x 
               
               
                 FF 3   
                 ✓ 
                 ✓ 
                 x 
                 x 
                 x 
                 x 
                 x 
               
               
                 GG 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 GG 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 GG 3   
                 ✓ 
                 x 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 HH 
                 PNPPN 
                 PNPPN 
                 PNPPN 
                 PNNPN 
                 PNNNP 
                 PNPNN 
                 PNPNP 
               
               
                 II 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 ✓ 
               
               
                 II 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 JJ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 KK 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 ✓ 
               
               
                 LL 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 LL 2   
                 ✓ 
                 x 
                 ✓ 
                 x 
                 x 
                 ✓ 
                 ✓ 
               
               
                 MM 1   
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                 MM 2   
                 ✓ 
                 ✓ 
                 ✓ 
                 x 
                 x 
                 ✓ 
                 x 
               
               
                 NN 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
                 ✓ 
               
               
                   
               
            
           
         
       
     
     While this disclosure describes a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of such embodiments may be made. In general, the disclosure is to be understood as not limited by the specific embodiments described herein, but only by the scope of the appended claims. 
     All references mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual reference was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present application.