Patent Publication Number: US-9835829-B2

Title: Optical image capturing system

Description:
BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present invention relates generally to an optical system, and more particularly to a compact optical image capturing system for an electronic device. 
     2. Description of Related Art 
     In recent years, with the rise of portable electronic devices having camera functionalities, the demand for an optical image capturing system is raised gradually. The image sensing device of the ordinary photographing camera is commonly selected from charge coupled device (CCD) or complementary metal-oxide semiconductor sensor (CMOS Sensor). In addition, as advanced semiconductor manufacturing technology enables the minimization of the pixel size of the image sensing device, the development of the optical image capturing system towards the field of high pixels. Therefore, the requirement for high imaging quality is rapidly raised. 
     The conventional optical system of the portable electronic device usually has three or four lenses. However, the optical system is asked to take pictures in a dark environment, in other words, the optical system is asked to have a large aperture. The conventional optical system provides high optical performance as required. 
     It is an important issue to increase the quantity of light entering the lens. In addition, the modern lens is also asked to have several characters, including high image quality. 
     BRIEF SUMMARY OF THE INVENTION 
     The aspect of embodiment of the present disclosure directs to an optical image capturing system and an optical image capturing lens which use combination of refractive powers, convex and concave surfaces of five-piece optical lenses (the convex or concave surface in the disclosure denotes the geometrical shape of an image-side surface or an object-side surface of each lens on an optical axis) to increase the quantity of incoming light of the optical image capturing system, and to improve imaging quality for image formation, so as to be applied to minimized electronic products. 
     The term and its definition to the lens parameter in the embodiment of the present are shown as below for further reference. 
     The lens parameter related to a length or a height in the lens: 
     A height for image formation of the optical image capturing system is denoted by HOI. A height of the optical image capturing system is denoted by HOS. A distance from the object-side surface of the first lens to the image-side surface of the fifth lens is denoted by InTL. A distance from the first lens to the second lens is denoted by IN 12  (instance). A central thickness of the first lens of the optical image capturing system on the optical axis is denoted by TP 1  (instance). 
     The lens parameter related to a material in the lens: 
     An Abbe number of the first lens in the optical image capturing system is denoted by NA 1  (instance). A refractive index of the first lens is denoted by Nd 1  (instance). 
     The lens parameter related to a view angle in the lens: 
     A view angle is denoted by AF. Half of the view angle is denoted by HAF. A major light angle is denoted by MRA. 
     The lens parameter related to exit/entrance pupil in the lens: 
     An entrance pupil diameter of the optical image capturing system is denoted by HEP. For any surface of any lens, a maximum effective half diameter (EHD) is a perpendicular distance between an optical axis and a crossing point on the surface where the incident light with a maximum viewing angle of the system passing the very edge of the entrance pupil. For example, the maximum effective half diameter of the object-side surface of the first lens is denoted by EHD 11 , the maximum effective half diameter of the image-side surface of the first lens is denoted by EHD 12 , the maximum effective half diameter of the object-side surface of the second lens is denoted by EHD 21 , the maximum effective half diameter of the image-side surface of the second lens is denoted by EHD 22 , and so on. 
     The lens parameter related to an arc length of the shape of a surface and a surface profile: 
     For any surface of any lens, a profile curve length of the maximum effective half diameter is, by definition, measured from a start point where the optical axis of the belonging optical image capturing system passes through the surface of the lens, along a surface profile of the lens, and finally to an end point of the maximum effective half diameter thereof. In other words, the curve length between the aforementioned start and end points is the profile curve length of the maximum effective half diameter, which is denoted by ARS. For example, the profile curve length of the maximum effective half diameter of the object-side surface of the first lens is denoted by ARS 11 , the profile curve length of the maximum effective half diameter of the image-side surface of the first lens is denoted by ARS 12 , the profile curve length of the maximum effective half diameter of the object-side surface of the second lens is denoted by ARS 21 , the profile curve length of the maximum effective half diameter of the image-side surface of the second lens is denoted by ARS 22 , and so on. 
     For any surface of any lens, a profile curve length of a half of the entrance pupil diameter (HEP) is, by definition, measured from a start point where the optical axis of the belonging optical image capturing system passes through the surface of the lens, along a surface profile of the lens, and finally to a coordinate point of a perpendicular distance where is a half of the entrance pupil diameter away from the optical axis. In other words, the curve length between the aforementioned stat point and the coordinate point is the profile curve length of a half of the entrance pupil diameter (HEP), and is denoted by ARE. For example, the profile curve length of a half of the entrance pupil diameter (HEP) of the object-side surface of the first lens is denoted by ARE 11 , the profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the first lens is denoted by ARE 12 , the profile curve length of a half of the entrance pupil diameter (HEP) of the object-side surface of the second lens is denoted by ARE 21 , the profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the second lens is denoted by ARE 22 , and so on. 
     The lens parameter related to a depth of the lens shape: 
     A distance in parallel with the optical axis from a point where the optical axis passes through to an end point of the maximum effective semi diameter on the object-side surface of the fifth lens is denoted by InRS 51  (the depth of the maximum effective semi diameter). A distance in parallel with the optical axis from a point where the optical axis passes through to an end point of the maximum effective semi diameter on the image-side surface of the fifth lens is denoted by InRS 52  (the depth of the maximum effective semi diameter). The depth of the maximum effective semi diameter (sinkage) on the object-side surface or the image-side surface of any other lens is denoted in the same manner. 
     The lens parameter related to the lens shape: 
     A critical point C is a tangent point on a surface of a specific lens, and the tangent point is tangent to a plane perpendicular to the optical axis and the tangent point cannot be a crossover point on the optical axis. To follow the past, a distance perpendicular to the optical axis between a critical point C 41  on the object-side surface of the fourth lens and the optical axis is HVT 41  (instance), and a distance perpendicular to the optical axis between a critical point C 42  on the image-side surface of the fourth lens and the optical axis is HVT 42  (instance). A distance perpendicular to the optical axis between a critical point C 51  on the object-side surface of the fifth lens and the optical axis is HVT 51  (instance), and a distance perpendicular to the optical axis between a critical point C 52  on the image-side surface of the fifth lens and the optical axis is HVT 52  (instance). A distance perpendicular to the optical axis between a critical point on the object-side or image-side surface of other lenses the optical axis is denoted in the same manner. 
     The object-side surface of the fifth lens has one inflection point IF 511  which is nearest to the optical axis, and the sinkage value of the inflection point IF 511  is denoted by SGI 511  (instance). A distance perpendicular to the optical axis between the inflection point IF 511  and the optical axis is HIF 511  (instance). The image-side surface of the fifth lens has one inflection point IF 521  which is nearest to the optical axis, and the sinkage value of the inflection point IF 521  is denoted by SGI 521  (instance). A distance perpendicular to the optical axis between the inflection point IF 521  and the optical axis is HIF 521  (instance). 
     The object-side surface of the fifth lens has one inflection point IF 512  which is the second nearest to the optical axis, and the sinkage value of the inflection point IF 512  is denoted by SGI 512  (instance). A distance perpendicular to the optical axis between the inflection point IF 512  and the optical axis is HIF 512  (instance). The image-side surface of the fifth lens has one inflection point IF 522  which is the second nearest to the optical axis, and the sinkage value of the inflection point IF 522  is denoted by SGI 522  (instance). A distance perpendicular to the optical axis between the inflection point IF 522  and the optical axis is HIF 522  (instance). 
     The object-side surface of the fifth lens has one inflection point IF 513  which is the third nearest to the optical axis, and the sinkage value of the inflection point IF 513  is denoted by SGI 513  (instance). A distance perpendicular to the optical axis between the inflection point IF 513  and the optical axis is HIF 513  (instance). The image-side surface of the fifth lens has one inflection point IF 523  which is the third nearest to the optical axis, and the sinkage value of the inflection point IF 523  is denoted by SGI 523  (instance). A distance perpendicular to the optical axis between the inflection point IF 523  and the optical axis is HIF 523  (instance). 
     The object-side surface of the fifth lens has one inflection point IF 514  which is the fourth nearest to the optical axis, and the sinkage value of the inflection point IF 514  is denoted by SGI 514  (instance). A distance perpendicular to the optical axis between the inflection point IF 514  and the optical axis is HIF 514  (instance). The image-side surface of the fifth lens has one inflection point IF 524  which is the fourth nearest to the optical axis, and the sinkage value of the inflection point IF 524  is denoted by SGI 524  (instance). A distance perpendicular to the optical axis between the inflection point IF 524  and the optical axis is HIF 524  (instance). 
     An inflection point, a distance perpendicular to the optical axis between the inflection point and the optical axis, and a sinkage value thereof on the object-side surface or image-side surface of other lenses is denoted in the same manner. 
     The lens parameter related to an aberration: 
     Optical distortion for image formation in the optical image capturing system is denoted by ODT. TV distortion for image formation in the optical image capturing system is denoted by TDT. Further, the range of the aberration offset for the view of image formation may be limited to 50%-100% field. An offset of the spherical aberration is denoted by DFS. An offset of the coma aberration is denoted by DFC. 
     Transverse aberration on an edge of an aperture is denoted by STA, which stands for STOP transverse aberration, and is used to evaluate the performance of one specific optical image capturing system. The transverse aberration of light in any field of view can be calculated with a tangential fan or a sagittal fan. More specifically, the transverse aberration caused when the longest operation wavelength (e.g., 650 nm or 656 nm) and the shortest operation wavelength (e.g., 470 nm or 486 nm) pass through the edge of the aperture can be used as the reference for evaluating performance. The coordinate directions of the aforementioned tangential fan can be further divided into a positive direction (upper light) and a negative direction (lower light). The longest operation wavelength which passes through the edge of the aperture has an imaging position on the image plane in a particular field of view, and the reference wavelength of the mail light (e.g., 555 nm or 587.5 nm) has another imaging position on the image plane in the same field of view. The transverse aberration caused when the longest operation wavelength passes through the edge of the aperture is defined as a distance between these two imaging positions. Similarly, the shortest operation wavelength which passes through the edge of the aperture has an imaging position on the image plane in a particular field of view, and the transverse aberration caused when the shortest operation wavelength passes through the edge of the aperture is defined as a distance between the imaging position of the shortest operation wavelength and the imaging position of the reference wavelength. The performance of the optical image capturing system can be considered excellent if the transverse aberrations of the shortest and the longest operation wavelength which pass through the edge of the aperture and image on the image plane in 0.7 field of view (i.e., 0.7 times the height for image formation HOI) are both less than 20 μm or 20 pixels. Furthermore, for a stricter evaluation, the performance cannot be considered excellent unless the transverse aberrations of the shortest and the longest operation wavelength which pass through the edge of the aperture and image on the image plane in 0.7 field of view are both less than 10 μm or 10 pixels. 
     The optical image capturing system has a maximum image height HOI on the image plane vertical to the optical axis. A transverse aberration at 0.7 HOI in the positive direction of the tangential fan after the longest operation wavelength passing through the edge of the aperture is denoted by PLTA; a transverse aberration at 0.7 HOI in the positive direction of the tangential fan after the shortest operation wavelength passing through the edge of the aperture is denoted by PSTA; a transverse aberration at 0.7 HOI in the negative direction of the tangential fan after the longest operation wavelength passing through the edge of the aperture is denoted by NLTA; a transverse aberration at 0.7 HOI in the negative direction of the tangential fan after the shortest operation wavelength passing through the edge of the aperture is denoted by NSTA; a transverse aberration at 0.7 HOI of the sagittal fan after the longest operation wavelength passing through the edge of the aperture is denoted by SLTA; a transverse aberration at 0.7 HOI of the sagittal fan after the shortest operation wavelength passing through the edge of the aperture is denoted by SSTA. 
     The present invention provides an optical image capturing system, in which the fifth lens is provided with an inflection point at the object-side surface or at the image-side surface to adjust the incident angle of each view field and modify the ODT and the TDT. In addition, the surfaces of the fifth lens are capable of modifying the optical path to improve the imaging quality. 
     The optical image capturing system of the present invention includes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and an image plane in order along an optical axis from an object side to an image side. The first lens has refractive power. Both the object-side surface and the image-side surface of the fifth lens are aspheric surfaces. The optical image capturing system satisfies:
 
1.2 ≦f /HEP≦6.0; 0.5≦HOS/ f ≦3.0; 0&lt;InTL/HOS&lt;0.9; and 0.9≦2(ARE/HEP)≦1.5;
 
     where f is a focal length of the optical image capturing system; HEP is an entrance pupil diameter of the optical image capturing system; HOS is a distance in parallel with the optical axis between an object-side surface, which face the object side, of the first lens and the image plane; InTL is a distance between the object-side surface of the first lens and the image-side surface of the fifth lens on the optical axis; ARE is a profile curve length measured from a start point where the optical axis of the belonging optical image capturing system passes through the surface of the lens, along a surface profile of the lens, and finally to a coordinate point of a perpendicular distance where is a half of the entrance pupil diameter away from the optical axis. 
     The present invention further provides an optical image capturing system, including a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and an image plane in order along an optical axis from an object side to an image side. The first lens has negative refractive power, wherein the object-side surface thereof can be convex near the optical axis. The second lens has refractive power. The third lens has refractive power. The fourth lens has refractive power. The fifth lens has refractive power. The object-side surface and the image-side surface of at least one lens among the first lens to the fifth lens are both aspheric surfaces. At least one lens among the first lens to the fifth lens has at least an inflection point on at least a surface thereof. At least one lens between the second lens and the fifth lens has positive refractive power. The optical image capturing system satisfies:
 
1.2 ≦f /HEP≦6.0; 0.5≦HOS/ f 3.0; 0&lt;InTL/HOS&lt;0.9; and 0.9≦2(ARE/HEP)≦1.5;
 
     where f is a focal length of the optical image capturing system; HEP is an entrance pupil diameter of the optical image capturing system; HOS is a distance in parallel with the optical axis between an object-side surface, which face the object side, of the first lens and the image plane; InTL is a distance between the object-side surface of the first lens and the image-side surface of the fifth lens on the optical axis; ARE is a profile curve length measured from a start point where the optical axis of the belonging optical image capturing system passes through the surface of the lens, along a surface profile of the lens, and finally to a coordinate point of a perpendicular distance where is a half of the entrance pupil diameter away from the optical axis. 
     The present invention further provides an optical image capturing system, including a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and an image plane, in order along an optical axis from an object side to an image side. The number of the lenses having refractive power in the optical image capturing system is five. At least one lens among the first to the fifth lenses has at least an inflection point on at least one surface thereof. The first lens has negative refractive power, and the second lens has refractive power. The third lens has positive refractive power. The fourth lens has refractive power. The fifth lens has refractive power. The object-side surface and the image-side surface of at least one lens among the first lens to the fifth lens are both aspheric surfaces. The optical image capturing system satisfies:
 
1.2 ≦f /HEP≦3.5; 0.5HOS/ f 3.0; 0&lt;InTL/HOS&lt;0.9; and 0.9≦2(ARE/HEP)≦1.5;
 
     where f is a focal length of the optical image capturing system; HEP is an entrance pupil diameter of the optical image capturing system; HOS is a distance in parallel with the optical axis between an object-side surface, which face the object side, of the first lens and the image plane; InTL is a distance between the object-side surface of the first lens and the image-side surface of the fifth lens on the optical axis; ARE is a profile curve length measured from a start point where the optical axis of the belonging optical image capturing system passes through the surface of the lens, along a surface profile of the lens, and finally to a coordinate point of a perpendicular distance where is a half of the entrance pupil diameter away from the optical axis. 
     For any surface of any lens, the profile curve length within the effective half diameter affects the ability of the surface to correct aberration and differences between optical paths of light in different fields of view. With longer profile curve length, the ability to correct aberration is better. However, the difficulty of manufacturing increases as well. Therefore, the profile curve length within the effective half diameter of any surface of any lens has to be controlled. The ratio between the profile curve length (ARS) within the effective half diameter of one surface and the thickness (TP) of the lens, which the surface belonged to, on the optical axis (i.e., ARS/TP) has to be particularly controlled. For example, the profile curve length of the maximum effective half diameter of the object-side surface of the first lens is denoted by ARS 11 , the thickness of the first lens on the optical axis is TP 1 , and the ratio between these two parameters is ARS 11 /TP 1 ; the profile curve length of the maximum effective half diameter of the image-side surface of the first lens is denoted by ARS 12 , and the ratio between ARS 12  and TP 1  is ARS 12 /TP 1 . The profile curve length of the maximum effective half diameter of the object-side surface of the second lens is denoted by ARS 21 , the thickness of the second lens on the optical axis is TP 2 , and the ratio between these two parameters is ARS 21 /TP 2 ; the profile curve length of the maximum effective half diameter of the image-side surface of the second lens is denoted by ARS 22 , and the ratio between ARS 22  and TP 2  is ARS 22 /TP 2 . For any surface of other lenses in the optical image capturing system, the ratio between the profile curve length of the maximum effective half diameter thereof and the thickness of the lens which the surface belonged to is denoted in the same manner. 
     For any surface of any lens, the profile curve length within a half of the entrance pupil diameter (HEP) affects the ability of the surface to correct aberration and differences between optical paths of light in different fields of view. With longer profile curve length, the ability to correct aberration is better. However, the difficulty of manufacturing increases as well. Therefore, the profile curve length within a half of the entrance pupil diameter (HEP) of any surface of any lens has to be controlled. The ratio between the profile curve length (ARE) within a half of the entrance pupil diameter (HEP) of one surface and the thickness (TP) of the lens, which the surface belonged to, on the optical axis (i.e., ARE/TP) has to be particularly controlled. For example, the profile curve length of a half of the entrance pupil diameter (HEP) of the object-side surface of the first lens is denoted by ARE 11 , the thickness of the first lens on the optical axis is TP 1 , and the ratio between these two parameters is ARE 11 /TP 1 ; the profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the first lens is denoted by ARE 12 , and the ratio between ARE 12  and TP 1  is ARE 12 /TP 1 . The profile curve length of a half of the entrance pupil diameter (HEP) of the object-side surface of the second lens is denoted by ARE 21 , the thickness of the second lens on the optical axis is TP 2 , and the ratio between these two parameters is ARE 21 /TP 2 ; the profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the second lens is denoted by ARE 22 , and the ratio between ARE 22  and TP 2  is ARE 22 /TP 2 . For any surface of other lenses in the optical image capturing system, the ratio between the profile curve length of a half of the entrance pupil diameter (HEP) thereof and the thickness of the lens which the surface belonged to is denoted in the same manner. 
     In an embodiment, a height of the optical image capturing system (HOS) can be reduced while |f 1 |&gt;f 5 . 
     In an embodiment, when |f 2 |+|f 3 |+|f 4 | and |f 1 |+|f 5 | of the lenses satisfy the aforementioned conditions, at least one lens among the second to the fourth lenses could have weak positive refractive power or weak negative refractive power. Herein the weak refractive power means the absolute value of the focal length of one specific lens is greater than 10. When at least one lens among the second to the fourth lenses has weak positive refractive power, it may share the positive refractive power of the first lens, and on the contrary, when at least one lens among the second to the fourth lenses has weak negative refractive power, it may fine turn and correct the aberration of the system. 
     In an embodiment, the fifth lens could have negative refractive power, and an image-side surface thereof is concave, it may reduce back focal length and size. Besides, the fifth lens can have at least an inflection point on at least a surface thereof, which may reduce an incident angle of the light of an off-axis field of view and correct the aberration of the off-axis field of view. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The present invention will be best understood by referring to the following detailed description of some illustrative embodiments in conjunction with the accompanying drawings, in which 
         FIG. 1A  is a schematic diagram of a first embodiment of the present invention; 
         FIG. 1B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the first embodiment of the present application; 
         FIG. 1C  shows a tangential fan and a sagittal fan of the optical image capturing system of the first embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of an aperture; 
         FIG. 2A  is a schematic diagram of a second embodiment of the present invention; 
         FIG. 2B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the second embodiment of the present application; 
         FIG. 2C  shows a tangential fan and a sagittal fan of the optical image capturing system of the second embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of an aperture; 
         FIG. 3A  is a schematic diagram of a third embodiment of the present invention; 
         FIG. 3B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the third embodiment of the present application; 
         FIG. 3C  shows a tangential fan and a sagittal fan of the optical image capturing system of the third embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of an aperture; 
         FIG. 4A  is a schematic diagram of a fourth embodiment of the present invention; 
         FIG. 4B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the fourth embodiment of the present application; 
         FIG. 4C  shows a tangential fan and a sagittal fan of the optical image capturing system of the fourth embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of an aperture; 
         FIG. 5A  is a schematic diagram of a fifth embodiment of the present invention; 
         FIG. 5B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the fifth embodiment of the present application; 
         FIG. 5C  shows a tangential fan and a sagittal fan of the optical image capturing system of the fifth embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of an aperture; 
         FIG. 6A  is a schematic diagram of a sixth embodiment of the present invention; 
         FIG. 6B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the sixth embodiment of the present application; and 
         FIG. 6C  shows a tangential fan and a sagittal fan of the optical image capturing system of the sixth embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of an aperture. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An optical image capturing system of the present invention includes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and an image plane from an object side to an image side. The optical image capturing system further is provided with an image sensor at an image plane. 
     The optical image capturing system can work in three wavelengths, including 486.1 nm, 587.5 nm, and 656.2 nm, wherein 587.5 nm is the main reference wavelength and is the reference wavelength for obtaining the technical characters. The optical image capturing system can also work in five wavelengths, including 470 nm, 510 nm, 555 nm, 610 nm, and 650 nm wherein 555 nm is the main reference wavelength, and is the reference wavelength for obtaining the technical characters. 
     The optical image capturing system of the present invention satisfies 0.5≦ΣPPR/|ΣNPR|≦3.0, and a preferable range is 1≦ΣPPR/|ΣNPR|≦2.5, where PPR is a ratio of the focal length f of the optical image capturing system to a focal length fp of each of lenses with positive refractive power; NPR is a ratio of the focal length f of the optical image capturing system to a focal length fn of each of lenses with negative refractive power; ΣPPR is a sum of the PPRs of each positive lens; and ΣNPR is a sum of the NPRs of each negative lens. It is helpful for control of an entire refractive power and an entire length of the optical image capturing system. 
     The image sensor is provided on the image plane. The optical image capturing system of the present invention satisfies HOS/HOI≦25 and 0.5≦HOS/f≦25, and a preferable range is 1≦HOS/HOI≦20 and 1≦HOS/f≦20, where HOI is a half of a diagonal of an effective sensing area of the image sensor, i.e., the maximum image height, and HOS is a height of the optical image capturing system, i.e. a distance on the optical axis between the object-side surface of the first lens and the image plane. It is helpful for reduction of the size of the system for used in compact cameras. 
     The optical image capturing system of the present invention further is provided with an aperture to increase image quality. 
     In the optical image capturing system of the present invention, the aperture could be a front aperture or a middle aperture, wherein the front aperture is provided between the object and the first lens, and the middle is provided between the first lens and the image plane. The front aperture provides a long distance between an exit pupil of the system and the image plane, which allows more elements to be installed. The middle could enlarge a view angle of view of the system and increase the efficiency of the image sensor. The optical image capturing system satisfies 0.2≦nS/HOS≦1.1, where InS is a distance between the aperture and the image plane. It is helpful for size reduction and wide angle. 
     The optical image capturing system of the present invention satisfies 0.1≦ΣTP/InTL0.9, where InTL is a distance between the object-side surface of the first lens and the image-side surface of the fifth lens, and ΣTP is a sum of central thicknesses of the lenses on the optical axis. It is helpful for the contrast of image and yield rate of manufacture and provides a suitable back focal length for installation of other elements. 
     The optical image capturing system of the present invention satisfies 0.01≦|R 1 /R 2 |&lt;100, and a preferable range is 0.05&lt;|R 1 /R 2 |&lt;80, where R 1  is a radius of curvature of the object-side surface of the first lens, and R 2  is a radius of curvature of the image-side surface of the first lens. It provides the first lens with a suitable positive refractive power to reduce the increase rate of the spherical aberration. 
     The optical image capturing system of the present invention satisfies −50&lt;(R 9 −R 10 )/(R 9 +R 10 )&lt;50, where R 9  is a radius of curvature of the object-side surface of the fifth lens, and R 10  is a radius of curvature of the image-side surface of the fifth lens. It may modify the astigmatic field curvature. 
     The optical image capturing system of the present invention satisfies IN 12 /f≦5.0, where IN 12  is a distance on the optical axis between the first lens and the second lens. It may correct chromatic aberration and improve the performance. 
     The optical image capturing system of the present invention satisfies IN 45 /f≦5.0, where IN 45  is a distance on the optical axis between the fourth lens and the fifth lens. It may correct chromatic aberration and improve the performance. 
     The optical image capturing system of the present invention satisfies 0.1≦(TP 1 +IN 12 )/TP 2 ≦50.0, where TP 1  is a central thickness of the first lens on the optical axis, and TP 2  is a central thickness of the second lens on the optical axis. It may control the sensitivity of manufacture of the system and improve the performance. 
     The optical image capturing system of the present invention satisfies 0.1≦(TP 5 +IN 45 )/TP 4 ≦50.0, where TP 4  is a central thickness of the fourth lens on the optical axis, TP 5  is a central thickness of the fifth lens on the optical axis, and IN 45  is a distance between the fourth lens and the fifth lens. It may control the sensitivity of manufacture of the system and improve the performance. 
     The optical image capturing system of the present invention satisfies 0.1≦TP 3 /(IN 23 +TP 3 +IN 34 )&lt;1, where TP 2  is a central thickness of the second lens on the optical axis, TP 3  is a central thickness of the third lens on the optical axis, TP 4  is a central thickness of the fourth lens on the optical axis, IN 23  is a distance on the optical axis between the second lens and the third lens, IN 34  is a distance on the optical axis between the third lens and the fourth lens, and InTL is a distance between the object-side surface of the first lens and the image-side surface of the fifth lens. It may fine tune and correct the aberration of the incident rays layer by layer, and reduce the height of the system. 
     The optical image capturing system satisfies 0 mm≦HVT 51 ≦3 mm; 0 mm&lt;HVT 52 ≦6 mm; 0≦HVT 51 /HVT 52 ; 0 mm≦|SGC 51 |≦0.5 mm; 0 mm&lt;|SGC 52 |≦2 mm; and 0&lt;|SGC 52 |/(|SGC 52 |+TP 5 )≦0.9, where HVT 51  a distance perpendicular to the optical axis between the critical point C 51  on the object-side surface of the fifth lens and the optical axis; HVT 52  a distance perpendicular to the optical axis between the critical point C 52  on the image-side surface of the fifth lens and the optical axis; SGC 51  is a distance in parallel with the optical axis between an point on the object-side surface of the fifth lens where the optical axis passes through and the critical point C 51 ; SGC 52  is a distance in parallel with the optical axis between an point on the image-side surface of the fifth lens where the optical axis passes through and the critical point C 52 . It is helpful to correct the off-axis view field aberration. 
     The optical image capturing system satisfies 0.2≦HVT 52 /HOI≦0.9, and preferably satisfies 0.3≦HVT 52 /HOI≦0.8. It may help to correct the peripheral aberration. 
     The optical image capturing system satisfies 0≦HVT 52 /HOS≦0.5, and preferably satisfies 0.2≦HVT 52 /HOS≦0.45. It may help to correct the peripheral aberration. 
     The optical image capturing system of the present invention satisfies 0&lt;SGI 511 /(SGI 511 +TP 5 )≦0.9; 0&lt;SGI 521 /(SGI 521 +TP 5 )≦0.9, and it is preferable to satisfy 0.1≦SGI 511 /(SGI 511 +TP 5 )≦0.6; 0.1≦SGI 521 /(SGI 521 +TP 5 )≦0.6, where SGI 511  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 521  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
     The optical image capturing system of the present invention satisfies 0&lt;SGI 512 /(SGI 512 +TP 5 )≦0.9; 0&lt;SGI 522 /(SGI 522 +TP 5 )≦0.9, and it is preferable to satisfy 0.1≦SGI 512 /(SGI 512 +TP 5 )≦0.6; 0.1≦SGI 522 /(SGI 522 +TP 5 )≦0.6, where SGI 512  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis, and SGI 522  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the second closest to the optical axis. 
     The optical image capturing system of the present invention satisfies 0.001 mm≦|HIF 511 |≦5 mm; 0.001 mm≦|HIF 521 |≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF 511 |≦3.5 mm; 1.5 mm≦|HIF 521 |≦3.5 mm, where HIF 511  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the closest to the optical axis, and the optical axis; HIF 521  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the closest to the optical axis, and the optical axis. 
     The optical image capturing system of the present invention satisfies 0.001 mm≦|HIF 512 |≦5 mm; 0.001 mm≦|HIF 522 |≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF 522 |≦3.5 mm; 0.1 mm≦|HIF 512 |≦3.5 mm, where HIF 512  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the second closest to the optical axis, and the optical axis; HIF 522  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the second closest to the optical axis, and the optical axis. 
     The optical image capturing system of the present invention satisfies 0.001 mm≦|HIF 513 |≦5 mm; 0.001 mm≦|HIF 523 |≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF 523 |≦3.5 mm; 0.1 mm≦|HIF 513 |≦3.5 mm, where HIF 513  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the third closest to the optical axis, and the optical axis; HIF 523  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the third closest to the optical axis, and the optical axis. 
     The optical image capturing system of the present invention satisfies 0.001 mm≦|HIF 514 |≦5 mm; 0.001 mm≦|HIF 524 |≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF 524 |≦3.5 mm; 0.1 mm≦|HIF 514 |≦3.5 mm, where HIF 514  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the fourth closest to the optical axis, and the optical axis; HIF 524  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the fourth closest to the optical axis, and the optical axis. 
     In an embodiment, the lenses of high Abbe number and the lenses of low Abbe number are arranged in an interlaced arrangement that could be helpful for correction of aberration of the system. 
     An equation of aspheric surface is
 
 z=ch   2 /[1+[1( k+ 1) c   2   h   2 ] 0.5   ]+A 4 h   4   +A 6 h   6   +A 8 h   8   +A 10 h   10   +A 12 h   12   +A 14 h   14   +A 16 h   16   +A 18 h   18   +A 20 h   20 +  (1)
 
     where z is a depression of the aspheric surface; k is conic constant; c is reciprocal of the radius of curvature; and A4, A6, A8, A10, A12, A14, A16, A18, and A20 are high-order aspheric coefficients. 
     In the optical image capturing system, the lenses could be made of plastic or glass. The plastic lenses may reduce the weight and lower the cost of the system, and the glass lenses may control the thermal effect and enlarge the space for arrangement of the refractive power of the system. In addition, the opposite surfaces (object-side surface and image-side surface) of the first to the fifth lenses could be aspheric that can obtain more control parameters to reduce aberration. The number of aspheric glass lenses could be less than the conventional spherical glass lenses, which is helpful for reduction of the height of the system. 
     When the lens has a convex surface, which means that the surface is convex around a position, through which the optical axis passes, and when the lens has a concave surface, which means that the surface is concave around a position, through which the optical axis passes. 
     The optical image capturing system of the present invention could be applied in a dynamic focusing optical system. It is superior in the correction of aberration and high imaging quality so that it could be allied in lots of fields. 
     The optical image capturing system of the present invention could further include a driving module to meet different demands, wherein the driving module can be coupled with the lenses to move the lenses. The driving module can be a voice coil motor (VCM), which is used to move the lens for focusing, or can be an optical image stabilization (OIS) component, which is used to lower the possibility of having the problem of image blurring which is caused by subtle movements of the lens while shooting. 
     To meet different requirements, at least one lens among the first lens to the fifth lens of the optical image capturing system of the present invention can be a light filter, which filters out light of wavelength shorter than 500 nm. Such effect can be achieved by coating on at least one surface of the lens, or by using materials capable of filtering out short waves to make the lens. 
     We provide several embodiments in conjunction with the accompanying drawings for the best understanding, which are: 
     First Embodiment 
     As shown in  FIG. 1A  and  FIG. 1B , an optical image capturing system  10  of the first embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  110 , an aperture  100 , a second lens  120 , a third lens  130 , a fourth lens  140 , a fifth lens  150 , an infrared rays filter  180 , an image plane  190 , and an image sensor  192 .  FIG. 1C  shows a tangential fan and a sagittal fan of the optical image capturing system  10  of the first embodiment of the present application, and a transverse aberration diagram at 0.7 field of view when a longest operation wavelength and a shortest operation wavelength pass through an edge of the aperture  100 . 
     The first lens  110  has negative refractive power and is made of plastic. An object-side surface  112  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  114  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  112  has an inflection point thereon. A profile curve length of the maximum effective half diameter of an object-side surface of the first lens  110  is denoted by ARS 11 , and a profile curve length of the maximum effective half diameter of the image-side surface of the first lens  110  is denoted by ARS 12 . A profile curve length of a half of an entrance pupil diameter (HEP) of the object-side surface of the first lens  110  is denoted by ARE 11 , and a profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the first lens  110  is denoted by ARE 12 . A thickness of the first lens  110  on the optical axis is TP 1 . 
     The first lens satisfies SGI 111 =1.96546 mm; |SGI 111 |/(|SGI 111 |+TP 1 )=0.72369, where SGI 111  is a displacement in parallel with the optical axis from a point on the object-side surface of the first lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 121  is a displacement in parallel with the optical axis from a point on the image-side surface of the first lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
     The first lens satisfies HIF 111 =3.38542 mm; HIF 111 /HOI=0.90519, where HIF 111  is a displacement perpendicular to the optical axis from a point on the object-side surface of the first lens, through which the optical axis passes, to the inflection point, which is the closest to the optical axis; HIF 121  is a displacement perpendicular to the optical axis from a point on the image-side surface of the first lens, through which the optical axis passes, to the inflection point, which is the closest to the optical axis. 
     The second lens  120  has positive refractive power and is made of plastic. An object-side surface  122  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  124  thereof, which faces the image side, is a concave aspheric surface. A profile curve length of the maximum effective half diameter of an object-side surface of the second lens  120  is denoted by ARS 21 , and a profile curve length of the maximum effective half diameter of the image-side surface of the second lens  120  is denoted by ARS 22 . A profile curve length of a half of an entrance pupil diameter (HEP) of the object-side surface of the second lens  120  is denoted by ARE 21 , and a profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the second lens  120  is denoted by ARE 22 . A thickness of the second lens  120  on the optical axis is TP 2 . 
     For the second lens, a displacement in parallel with the optical axis from a point on the object-side surface of the second lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis is denoted by SGI 211 , and a displacement in parallel with the optical axis from a point on the image-side surface of the second lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis is denoted by SGI 221 . 
     For the second lens, a displacement perpendicular to the optical axis from a point on the object-side surface of the second lens, through which the optical axis passes, to the inflection point, which is the closest to the optical axis is denoted by HIF 211 , and a displacement perpendicular to the optical axis from a point on the image-side surface of the second lens, through which the optical axis passes, to the inflection point, which is the closest to the optical axis is denoted by HIF 221 . 
     The third lens  130  has positive refractive power and is made of plastic. An object-side surface  132 , which faces the object side, is a convex aspheric surface, and an image-side surface  134 , which faces the image side, is a convex aspheric surface. The object-side surface  132  has an inflection point. A profile curve length of the maximum effective half diameter of an object-side surface of the third lens  130  is denoted by ARS 31 , and a profile curve length of the maximum effective half diameter of the image-side surface of the third lens  130  is denoted by ARS 32 . A profile curve length of a half of an entrance pupil diameter (HEP) of the object-side surface of the third lens  130  is denoted by ARE 31 , and a profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the third lens  130  is denoted by ARE 32 . A thickness of the third lens  130  on the optical axis is TP 3 . 
     The third lens  130  satisfies SGI 311 =0.00388 mm; |SGI 311 |/(|SGI 311 |+TP 3 )=0.00414, where SGI 311  is a displacement in parallel with the optical axis, from a point on the object-side surface of the third lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 321  is a displacement in parallel with the optical axis, from a point on the image-side surface of the third lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
     For the third lens  130 , SGI 312  is a displacement in parallel with the optical axis, from a point on the object-side surface of the third lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis, and SGI 322  is a displacement in parallel with the optical axis, from a point on the image-side surface of the third lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis. 
     The third lens  130  further satisfies HIF 311 =0.38898 mm; HIF 311 /HOI=0.10400, where HIF 311  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the third lens, which is the closest to the optical axis, and the optical axis; HIF 321  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the third lens, which is the closest to the optical axis, and the optical axis. 
     For the third lens  130 , HIF 312  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the third lens, which is the second closest to the optical axis, and the optical axis; HIF 322  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the third lens, which is the second closest to the optical axis, and the optical axis. 
     The fourth lens  140  has positive refractive power and is made of plastic. An object-side surface  142 , which faces the object side, is a convex aspheric surface, and an image-side surface  144 , which faces the image side, is a convex aspheric surface. The object-side surface  142  has an inflection point. A profile curve length of the maximum effective half diameter of an object-side surface of the fourth lens  140  is denoted by ARS 41 , and a profile curve length of the maximum effective half diameter of the image-side surface of the fourth lens  140  is denoted by ARS 42 . A profile curve length of a half of an entrance pupil diameter (HEP) of the object-side surface of the fourth lens  140  is denoted by ARE 41 , and a profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the fourth lens  140  is denoted by ARE 42 . A thickness of the fourth lens  140  on the optical axis is TP 4 . 
     The fourth lens  140  satisfies SGI 421 =0.06508 mm; |SGI 421 |/(|SGI 421 |+TP 4 )=0.03459, where SGI 411  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fourth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 421  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fourth lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
     For the fourth lens  140 , SGI 412  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fourth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis, and SGI 422  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fourth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis. 
     The fourth lens  140  further satisfies HIF 421 =0.85606 mm; HIF 421 /HOI=0.22889, where HIF 411  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens, which is the closest to the optical axis, and the optical axis; HIF 421  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fourth lens, which is the closest to the optical axis, and the optical axis. 
     For the fourth lens  140 , HIF 412  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens, which is the second closest to the optical axis, and the optical axis; HIF 422  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fourth lens, which is the second closest to the optical axis, and the optical axis. 
     The fifth lens  150  has negative refractive power and is made of plastic. An object-side surface  152 , which faces the object side, is a concave aspheric surface, and an image-side surface  154 , which faces the image side, is a concave aspheric surface. The object-side surface  152  and the image-side surface  154  both have an inflection point. A profile curve length of the maximum effective half diameter of an object-side surface of the fifth lens  150  is denoted by ARS 51 , and a profile curve length of the maximum effective half diameter of the image-side surface of the fifth lens  150  is denoted by ARS 52 . A profile curve length of a half of an entrance pupil diameter (HEP) of the object-side surface of the fifth lens  150  is denoted by ARE 51 , and a profile curve length of a half of the entrance pupil diameter (HEP) of the image-side surface of the fifth lens  150  is denoted by ARE 52 . A thickness of the fifth lens  150  on the optical axis is TP 5 . 
     The fifth lens  150  satisfies SGI 511 =−1.51505 mm; |SGI 511 |/(|SGI 511 |+TP 5 )=0.70144; SGI 521 =0.01229 mm; |SGI 521 |/(|SGI 521 |+TP 5 )=0.01870, where SGI 511  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 521  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
     For the fifth lens  150 , SGI 512  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis, and SGI 522  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis. 
     The fifth lens  150  further satisfies HIF 511 =2.25435 mm; HIF 511 /HOI=0.60277; HIF 521 =0.82313 mm; HIF 521 /HOI=0.22009, where HIF 511  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the closest to the optical axis, and the optical axis; HIF 521  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the closest to the optical axis, and the optical axis. 
     For the fifth lens  150 , HIF 512  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the second closest to the optical axis, and the optical axis; HIF 522  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the second closest to the optical axis, and the optical axis. 
     The infrared rays filter  180  is made of glass and between the fifth lens  150  and the image plane  190 . The infrared rays filter  180  gives no contribution to the focal length of the system. 
     The optical image capturing system  10  of the first embodiment has the following parameters, which are f=3.03968 mm; f/HEP=1.6; HAF=50.001; and tan(HAF)=1.1918, where f is a focal length of the system; HAF is a half of the maximum field angle; and HEP is an entrance pupil diameter. 
     The parameters of the lenses of the first embodiment are f 1 =−9.24529 mm; |f/f 1 |=0.32878; f 5 =−2.32439; and |f 1 |&gt;f 5 , where f 1  is a focal length of the first lens  110 ; and f 5  is a focal length of the fifth lens  150 . 
     The first embodiment further satisfies |f 2 |+|f 3 |+|f 4 |=17.3009 mm; |f 1 |+|f 5 |=11.5697 mm and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 2  is a focal length of the second lens  120 , f 3  is a focal length of the third lens  130 , f 4  is a focal length of the fourth lens  140 , and f 5  is a focal length of the fifth lens  150 . 
     The optical image capturing system  10  of the first embodiment further satisfies ΣPPR=f/f 2 +f/f 3 +f/f 4 =1.86768; ΣNPR=f/f 1 +f/f 5 =−1.63651; ΣPPR/|ΣNPR|=1.14125; |f/f 2 |=0.47958; |f/f 3 |=0.38289; |f/f 4 |=1.00521; |f/f 5 |=1.30773, where PPR is a ratio of a focal length f of the optical image capturing system to a focal length fp of each of the lenses with positive refractive power; and NPR is a ratio of a focal length f of the optical image capturing system to a focal length fn of each of lenses with negative refractive power. 
     The optical image capturing system  10  of the first embodiment further satisfies InTL+BFL=HOS; HOS=10.56320 mm; HOI=3.7400 mm; HOS/HOI=2.8244; HOS/f=3.4751; InS=6.21073 mm; and InS/HOS=0.5880, where InTL is a distance between the object-side surface  112  of the first lens  110  and the image-side surface  154  of the fifth lens  150 ; HOS is a height of the image capturing system, i.e. a distance between the object-side surface  112  of the first lens  110  and the image plane  190 ; InS is a distance between the aperture  100  and the image plane  190 ; HOI is a half of a diagonal of an effective sensing area of the image sensor  192 , i.e., the maximum image height; and BFL is a distance between the image-side surface  154  of the fifth lens  150  and the image plane  190 . 
     The optical image capturing system  10  of the first embodiment further satisfies ΣTP=5.0393 mm; InTL=9.8514 mm and ΣTP/InTL=0.5115, where ΣTP is a sum of the thicknesses of the lenses  110 - 150  with refractive power. It is helpful for the contrast of image and yield rate of manufacture and provides a suitable back focal length for installation of other elements. 
     The optical image capturing system  10  of the first embodiment further satisfies |R 1 /R 2 |=1.9672, where R 1  is a radius of curvature of the object-side surface  112  of the first lens  110 , and R 2  is a radius of curvature of the image-side surface  114  of the first lens  110 . It provides the first lens with a suitable positive refractive power to reduce the increase rate of the spherical aberration. 
     The optical image capturing system  10  of the first embodiment further satisfies (R 9 −R 10 )/(R 9 +R 10 )=−1.1505, where R 9  is a radius of curvature of the object-side surface  152  of the fifth lens  150 , and R 10  is a radius of curvature of the image-side surface  154  of the fifth lens  150 . It may modify the astigmatic field curvature. 
     The optical image capturing system  10  of the first embodiment further satisfies ΣPP=f 2 +f 3 +f 4 =17.30090 mm; and f 2 /(f 2 +f 3 +f 4 )=0.36635, where ΣPP is a sum of the focal lengths fp of each lens with positive refractive power. It is helpful to share the positive refractive power of the second lens  120  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system  10  of the first embodiment further satisfies ΣNP=f 1 +f 5 =−11.56968 mm; and f 5 /(f 1 +f 5 )=0.20090, where ΣNP is a sum of the focal lengths fn of each lens with negative refractive power. It is helpful to share the negative refractive power of the fifth lens  150  to the other negative lens, which avoids the significant aberration caused by the incident rays. 
     The optical image capturing system  10  of the first embodiment further satisfies IN 12 =3.19016 mm; IN 12 /f=1.04951, where IN 12  is a distance on the optical axis between the first lens  110  and the second lens  120 . It may correct chromatic aberration and improve the performance. 
     The optical image capturing system  10  of the first embodiment further satisfies IN 45 =0.40470 mm; IN 45 /f=0.13314, where IN 45  is a distance on the optical axis between the fourth lens  140  and the fifth lens  150 . It may correct chromatic aberration and improve the performance. 
     The optical image capturing system  10  of the first embodiment further satisfies TP 1 =0.75043 mm; TP 2 =0.89543 mm; TP 3 =0.93225 mm; and (TP 1 +IN 12 )/TP 2 =4.40078, where TP 1  is a central thickness of the first lens  110  on the optical axis, TP 2  is a central thickness of the second lens  120  on the optical axis, and TP 3  is a central thickness of the third lens  130  on the optical axis. It may control the sensitivity of manufacture of the system and improve the performance. 
     The optical image capturing system  10  of the first embodiment further satisfies TP 4 =1.81634 mm; TP 5 =0.64488 mm; and (TP 5 +IN 45 )/TP 4 =0.57785, where TP 4  is a central thickness of the fourth lens  140  on the optical axis, TP 5  is a central thickness of the fifth lens  150  on the optical axis, and IN 45  is a distance on the optical axis between the fourth lens  140  and the fifth lens  150 . It may control the sensitivity of manufacture of the system and lower the total height of the system. 
     The optical image capturing system  10  of the first embodiment further satisfies TP 2 /TP 3 =0.96051; TP 3 /TP 4 =0.51325; TP 4 /TP 5 =2.81657; and TP 3 /(IN 23 +TP 3 +IN 34 )=0.43372, where IN 34  is a distance on the optical axis between the third lens  130  and the fourth lens  140 . It may control the sensitivity of manufacture of the system and lower the total height of the system. 
     The optical image capturing system  10  of the first embodiment further satisfies InRS 41 =−0.09737 mm; InRS 42 =−−1.31040 mm; |InRS 41 |/TP 4 =0.05361 and |InRS 42 |/TP 4 =0.72145, where InRS 41  is a displacement in parallel with the optical axis from a point on the object-side surface  142  of the fourth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  142  of the fourth lens; InRS 42  is a displacement in parallel with the optical axis from a point on the image-side surface  144  of the fourth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  144  of the fourth lens; and TP 4  is a central thickness of the fourth lens  140  on the optical axis. It is helpful for manufacturing and shaping of the lenses and is helpful to reduce the size. 
     The optical image capturing system  10  of the first embodiment further satisfies HVT 41 =1.41740 mm; HVT 42 =0, where HVT 41  a distance perpendicular to the optical axis between the critical point on the object-side surface  142  of the fourth lens and the optical axis; and HVT 42  a distance perpendicular to the optical axis between the critical point on the image-side surface  144  of the fourth lens and the optical axis. 
     The optical image capturing system  10  of the first embodiment further satisfies InRS 51 =−1.63543 mm; InRS 52 =−0.34495 mm; |InRS 51 |/TP 5 =2.53604 and |InRS 52 |/TP 5 =0.53491, where InRS 51  is a displacement in parallel with the optical axis from a point on the object-side surface  152  of the fifth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  152  of the fifth lens; InRS 52  is a displacement in parallel with the optical axis from a point on the image-side surface  154  of the fifth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  154  of the fifth lens; and TP 5  is a central thickness of the fifth lens  150  on the optical axis. It is helpful for manufacturing and shaping of the lenses and is helpful to reduce the size. 
     The optical image capturing system  10  of the first embodiment satisfies HVT 51 =0; HVT 52 =1.35891 mm; and HVT 51 /HVT 52 =0, where HVT 51  a distance perpendicular to the optical axis between the critical point on the object-side surface  152  of the fifth lens and the optical axis; and HVT 52  a distance perpendicular to the optical axis between the critical point on the image-side surface  154  of the fifth lens and the optical axis. 
     The optical image capturing system  10  of the first embodiment satisfies HVT 52 /HOI=0.36334. It is helpful for correction of the aberration of the peripheral view field of the optical image capturing system. 
     The optical image capturing system  10  of the first embodiment satisfies HVT 52 /HOS=0.12865. It is helpful for correction of the aberration of the peripheral view field of the optical image capturing system. 
     The third lens  130  and the fifth lens  150  have negative refractive power. The optical image capturing system  10  of the first embodiment further satisfies NA 5 /NA 3 =0.368966, where NA 3  is an Abbe number of the third lens  130 ; and NA 5  is an Abbe number of the fifth lens  150 . It may correct the aberration of the optical image capturing system. 
     The optical image capturing system  10  of the first embodiment further satisfies |TDT|=0.63350%; |ODT|=2.06135%, where TDT is TV distortion; and ODT is optical distortion. 
     For the fifth lens  150  of the optical image capturing system  10  in the first embodiment, a transverse aberration at 0.7 field of view in the positive direction of the tangential fan after the longest operation wavelength passing through the edge of the aperture  100  is denoted by PLTA, and is −0.042 mm; a transverse aberration at 0.7 field of view in the positive direction of the tangential fan after the shortest operation wavelength passing through the edge of the aperture  100  is denoted by PSTA, and is 0.056 mm; a transverse aberration at 0.7 field of view in the negative direction of the tangential fan after the longest operation wavelength passing through the edge of the aperture  100  is denoted by NLTA, and is −0.011 mm; a transverse aberration at 0.7 field of view in the negative direction of the tangential fan after the shortest operation wavelength passing through the edge of the aperture  100  is denoted by NSTA, and is −0.024 mm; a transverse aberration at 0.7 field of view of the sagittal fan after the longest operation wavelength passing through the edge of the aperture  100  is denoted by SLTA, and is −0.013 mm; a transverse aberration at 0.7 field of view of the sagittal fan after the shortest operation wavelength passing through the edge of the aperture  100  is denoted by SSTA, and is 0.018 mm. 
     The parameters of the lenses of the first embodiment are listed in Table 1 and Table 2. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 f = 3.03968 mm; f/HEP = 1.6; HAF = 50.0010 deg 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Surface 
                 Radius of curvature (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 4.01438621 
                 0.750 
                 plastic 
                 1.514 
                 56.80 
                 −9.24529 
               
               
                 2 
                   
                 2.040696375 
                 3.602 
                   
                   
                   
                   
               
               
                 3 
                 Aperture 
                 plane 
                 −0.412 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 2.45222384 
                 0.895 
                 plastic 
                 1.565 
                 58.00 
                 6.33819 
               
               
                 5 
                   
                 6.705898264 
                 0.561 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 16.39663088 
                 0.932 
                 plastic 
                 1.565 
                 58.00 
                 7.93877 
               
               
                 7 
                   
                 −6.073735083 
                 0.656 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 4.421363446 
                 1.816 
                 plastic 
                 1.565 
                 58.00 
                 3.02394 
               
               
                 9 
                   
                 −2.382933539 
                 0.405 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −1.646639396 
                 0.645 
                 plastic 
                 1.650 
                 21.40 
                 −2.32439 
               
               
                 11 
                   
                 23.53222697 
                 0.100 
                   
                   
                   
                   
               
               
                 12 
                 Infrared 
                 plane 
                 0.200 
                 BK7_SCH 
                 1.517 
                 64.20 
                   
               
               
                   
                 rays filter 
                   
                   
                   
                   
                   
                   
               
               
                 13 
                   
                 plane 
                 0.412 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 plane 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                 1 
                 2 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 −1.882119E−01 
                 −1.927558E+00 
                 −6.483417E+00 
                 1.766123E+01 
                 −5.000000E+01 
               
               
                 A4 
                 7.686381E−04 
                 3.070422E−02 
                 5.439775E−02 
                 7.241691E−03 
                 −2.985209E−02 
               
               
                 A6 
                 4.630306E−04 
                 −3.565153E−03 
                 −7.980567E−03 
                 −8.359563E−03 
                 −7.175713E−03 
               
               
                 A8 
                 3.178966E−05 
                 2.062259E−03 
                 −3.537039E−04 
                 1.303430E−02 
                 4.284107E−03 
               
               
                 A10 
                 −1.773597E−05 
                 −1.571117E−04 
                 2.844845E−03 
                 −6.951350E−03 
                 −5.492349E−03 
               
               
                 A12 
                 1.620619E−06 
                 −4.694004E−05 
                 −1.025049E−03 
                 1.366262E−03 
                 1.232072E−03 
               
               
                 A14 
                 −4.916041E−08 
                 7.399980E−06 
                 1.913679E−04 
                 3.588298E−04 
                 −4.107269E−04 
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
               
                 Surface 
                 7 
                 8 
                 8 
                 9 
                 10 
               
               
                   
               
               
                 k 
                 −3.544648E+01 
                 −3.167522E+01 
                 −2.470764E+00 
                 −1.570351E+00 
                 4.928899E+01 
               
               
                 A4 
                 −6.315366E−02 
                 −1.903506E−03 
                 −2.346908E−04 
                 −4.250059E−04 
                 −4.625703E−03 
               
               
                 A6 
                 6.038040E−03 
                 −1.806837E−03 
                 2.481207E−03 
                 −1.591781E−04 
                 −7.108872E−04 
               
               
                 A8 
                 4.674156E−03 
                 −1.670351E−03 
                 −5.862277E−04 
                 −3.752177E−05 
                 3.429244E−05 
               
               
                 A10 
                 −8.031117E−03 
                 4.791024E−04 
                 −1.955029E−04 
                 −9.210114E−05 
                 2.887298E−06 
               
               
                 A12 
                 3.319791E−03 
                 −5.594125E−05 
                 1.880941E−05 
                 −1.101797E−05 
                 3.684628E−07 
               
               
                 A14 
                 −5.356799E−04 
                 3.704401E−07 
                 1.132586E−06 
                 3.536320E−06 
                 −4.741322E−08 
               
               
                 A16 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A18 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 A20 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                   
               
            
           
         
       
     
     The figures related to the profile curve lengths obtained based on Table 1 and Table 2 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 First embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE  
                 ARE- 
                 2(ARE/HEP)  
                   
                 ARE/TP  
               
               
                 ARE 
                 1/2(HEP)  
                 value 
                 1/2(HEP) 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.950 
                 0.958 
                 0.008 
                 100.87% 
                 0.750 
                 127.69% 
               
               
                 12 
                 0.950 
                 0.987 
                 0.037 
                 103.91% 
                 0.750 
                 131.53% 
               
               
                 21 
                 0.950 
                 0.976 
                 0.026 
                 102.74% 
                 0.895 
                 108.99% 
               
               
                 22 
                 0.950 
                 0.954 
                 0.004 
                 100.42% 
                 0.895 
                 106.52% 
               
               
                 31 
                 0.950 
                 0.949 
                 −0.001 
                  99.94% 
                 0.932 
                 101.83% 
               
               
                 32 
                 0.950 
                 0.959 
                 0.009 
                 100.93% 
                 0.932 
                 102.84% 
               
               
                 41 
                 0.950 
                 0.953 
                 0.003 
                 100.29% 
                 1.816 
                  52.45% 
               
               
                 42 
                 0.950 
                 0.970 
                 0.020 
                 102.15% 
                 1.816 
                  53.42% 
               
               
                 51 
                 0.950 
                 0.995 
                 0.045 
                 104.71% 
                 0.645 
                 154.24% 
               
               
                 52 
                 0.950 
                 0.949 
                 −0.001 
                  99.92% 
                 0.645 
                 147.18% 
               
               
                   
               
               
                   
                   
                 ARS  
                 ARS- 
                 (ARS/EHD)  
                   
                 ARS/TP  
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 3.459 
                 4.210 
                 0.751 
                 121.71% 
                 0.750 
                 561.03% 
               
               
                 12 
                 2.319 
                 3.483 
                 1.165 
                 150.24% 
                 0.750 
                 464.19% 
               
               
                 21 
                 1.301 
                 1.384 
                 0.084 
                 106.43% 
                 0.895 
                 154.61% 
               
               
                 22 
                 1.293 
                 1.317 
                 0.024 
                 101.87% 
                 0.895 
                 147.09% 
               
               
                 31 
                 1.400 
                 1.447 
                 0.047 
                 103.39% 
                 0.932 
                 155.22% 
               
               
                 32 
                 1.677 
                 1.962 
                 0.285 
                 116.97% 
                 0.932 
                 210.45% 
               
               
                 41 
                 2.040 
                 2.097 
                 0.057 
                 102.82% 
                 1.816 
                 115.48% 
               
               
                 42 
                 2.338 
                 2.821 
                 0.483 
                 120.67% 
                 1.816 
                 155.32% 
               
               
                 51 
                 2.331 
                 2.971 
                 0.639 
                 127.43% 
                 0.645 
                 460.64% 
               
               
                 52 
                 3.219 
                 3.267 
                 0.049 
                 101.51% 
                 0.645 
                 506.66% 
               
               
                   
               
            
           
         
       
     
     The detail parameters of the first embodiment are listed in Table 1, in which the unit of the radius of curvature, thickness, and focal length are millimeter, and surface 0-10 indicates the surfaces of all elements in the system in sequence from the object side to the image side. Table 2 is the list of coefficients of the aspheric surfaces, in which A1-A20 indicate the coefficients of aspheric surfaces from the first order to the twentieth order of each aspheric surface. The following embodiments have the similar diagrams and tables, which are the same as those of the first embodiment, so we do not describe it again. 
     Second Embodiment 
     As shown in  FIG. 2A  and  FIG. 2B , an optical image capturing system  20  of the second embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  210 , a second lens  220 , a third lens  230 , an aperture  200 , a fourth lens  240 , a fifth lens  250 , an infrared rays filter  280 , an image plane  290 , and an image sensor  292 .  FIG. 2C  is a transverse aberration diagram at 0.7 field of view of the second embodiment of the present application. 
     The first lens  210  has negative refractive power and is made of plastic. An object-side surface  212  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  214  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  212  has an inflection point. 
     The second lens  220  has negative refractive power and is made of plastic. An object-side surface  222  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  224  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  222  has an inflection point. 
     The third lens  230  has positive refractive power and is made of plastic. An object-side surface  232 , which faces the object side, is a convex aspheric surface, and an image-side surface  234 , which faces the image side, is a convex aspheric surface. 
     The fourth lens  240  has negative refractive power and is made of plastic. An object-side surface  242 , which faces the object side, is a concave aspheric surface, and an image-side surface  244 , which faces the image side, is a concave aspheric surface. The image-side surface  244  has an inflection point. 
     The fifth lens  250  has positive refractive power and is made of plastic. An object-side surface  252 , which faces the object side, is a convex surface, and an image-side surface  254 , which faces the image side, is a convex surface. It may help to shorten the back focal length to keep small in size. In addition, the image-side surface  254  both has an inflection point, which may reduce an incident angle of the light of an off-axis field of view and correct the aberration of the off-axis field of view. 
     The infrared rays filter  280  is made of glass and between the fifth lens  250  and the image plane  290 . The infrared rays filter  280  gives no contribution to the focal length of the system. 
     The optical image capturing system of the second embodiment satisfies |f 2 |+|f 3 |+|f 4 |=21.3374 mm; |f 1 |+|f 5 |=18.3654 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  210 , f 2  is a focal length of the second lens  220 , f 3  is a focal length of the third lens  230 , f 4  is a focal length of the fourth lens  240 , and f 5  is a focal length of the fifth lens  250 . 
     In the second embodiment, the optical image capturing system of the second embodiment further satisfies ΣPP=8.87594 mm; and f 3 /ΣPP=0.67791, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the third lens  230  to the other positive lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the second embodiment further satisfies ΣNP=−30.82683 mm; and f 1 /ΣNP=0.50302, where ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the first lens  210  to other negative lenses. 
     The parameters of the lenses of the second embodiment are listed in Table 3 and Table 4. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 f = 1.33168 mm; f/HEP = 1.8; HAF = 100 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 57.51654 
                 2.017047 
                 plastic 
                 1.565 
                 58 
                 −15.5065 
               
               
                 2 
                   
                 7.52712 
                 8.271781 
                   
                   
                   
                   
               
               
                 3 
                 2 nd  lens 
                 −60.0917 
                 4.001031 
                 plastic 
                 1.565 
                 58 
                 −12.6711 
               
               
                 4 
                   
                 8.35303 
                 17.47607 
                   
                   
                   
                   
               
               
                 5 
                 3 rd  lens 
                 4.38824 
                 4.366001 
                 plastic 
                 1.55 
                 56.5 
                 6.01708 
               
               
                 6 
                   
                 −8.81439 
                 0.05 
                   
                   
                   
                   
               
               
                 7 
                 Aperture 
                 plane 
                 1.453606 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −3.58683 
                 0.4 
                 plastic 
                 1.65 
                 21.4 
                 −2.64923 
               
               
                 9 
                   
                 3.5145 
                 0.110454 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 2.99373 
                 2.211261 
                 plastic 
                 1.565 
                 58 
                 2.85886 
               
               
                 11 
                   
                 −2.5883 
                 1 
                   
                   
                   
                   
               
               
                 12 
                 Infrared 
                 plane 
                 0.85 
                 NBK7 
                   
                   
                   
               
               
                   
                 rays filter 
                   
                   
                   
                   
                   
                   
               
               
                 13 
                   
                 plane 
                 1.843675 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 plane 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
               
               
                 k 
                 4.064015 
                 −0.541688 
                 −2.11709 
                 −0.405219 
                 −1.15074 
               
               
                 A4 
                 4.29560E−06 
                 −2.71683E−04 
                 9.35290E−06 
                 −1.84133E−04 
                 1.07769E−03 
               
               
                 A6 
                 −1.71152E−08 
                 −1.07076E−07 
                 −6.60979E−08 
                 −2.20024E−06 
                 −3.81712E−05 
               
               
                 A8 
                 −2.76748E−11 
                 2.06773E−11 
                 −4.90235E−10 
                 −2.29752E−08 
                 6.79373E−06 
               
               
                 A10 
                 4.72903E−14 
                 −5.18719E−14 
                 −3.19862E−12 
                 1.24733E−10 
                 −6.94540E−07 
               
               
                 A12 
                 −1.44839E−17 
                 1.35603E−13 
                 −2.50917E−15 
                 2.60744E−12 
                 1.21782E−13 
               
               
                 A14 
                 −6.89749E−20 
                 −3.71107E−15 
                 4.18487E−16 
                 6.29943E−15 
                 2.30237E−16 
               
               
                   
               
               
                 Surface 
                 6 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 12.263053 
                 −10.261077 
                 −18.845912 
                 −15.130709 
                 −1.072172 
               
               
                 A4 
                 5.53057E−03 
                 −1.76548E−02 
                 7.36539E−03 
                 4.48813E−03 
                 2.76592E−03 
               
               
                 A6 
                 −2.21158E−04 
                 −1.86828E−03 
                 −3.74230E−03 
                 −6.88623E−04 
                 −3.84611E−06 
               
               
                 A8 
                 −5.14730E−05 
                 1.06128E−03 
                 6.37415E−04 
                 9.17362E−05 
                 5.19716E−05 
               
               
                 A10 
                 2.27442E−05 
                 −1.81264E−04 
                 −5.53223E−05 
                 −3.42556E−06 
                 5.54782E−06 
               
               
                 A12 
                 1.21783E−13 
                 1.21783E−13 
                 1.21783E−13 
                 1.21783E−13 
                 1.21754E−13 
               
               
                 A14 
                 2.30285E−16 
                 2.30324E−16 
                 2.30289E−16 
                 2.30301E−16 
                 2.30386E−16 
               
               
                   
               
            
           
         
       
     
     An equation of the aspheric surfaces of the second embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the second embodiment based on Table 3 and Table 4 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Second embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f/f5 | 
                 | f1/f2 | 
               
               
                 0.08588 
                 0.10510 
                 0.22132 
                 0.50267 
                 0.46581 
                 1.22377 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/| ΣNPR | 
                 IN12/f 
                 IN45/f 
                 | f2/f3 | 
               
               
                 0.68712 
                 0.69364 
                 0.99060 
                 6.21154 
                 0.08294 
                 2.10586 
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                 0.18702 
                 2.57155 
                 5.80429 
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 ODT % 
                 TDT % 
               
               
                 44.04140  
                 40.35730  
                 13.55746  
                 0.17846 
                 −141.731     
                 148.358   
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                 0.00000 
                 0.00000 
                 0.00000 
                 0.00000 
                 0.00000 
                 0.00000 
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 | InRS51 |/TP5 
                 | InRS52 |/TP5 
               
               
                 0.91641 
                 10.91500  
                  0.549456 
                 −0.95495  
                 0.24848 
                 0.43186 
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.019 mm 
                 0.003 mm 
                 0.004 mm 
                 −0.008 mm 
                 0.010 mm 
                 0.002 mm 
               
               
                   
               
            
           
         
       
     
     The figures related to the profile curve lengths obtained based on Table 3 and Table 4 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Second embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE  
                 ARE- 
                 2(ARE/HEP)  
                   
                 ARE/TP  
               
               
                 ARE 
                 1/2(HEP) 
                 value 
                 1/2(HEP) 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.370 
                 0.369 
                 −0.00091 
                  99.75% 
                 2.017 
                 18.29% 
               
               
                 12 
                 0.370 
                 0.369 
                 −0.00076 
                  99.79% 
                 2.017 
                 18.30% 
               
               
                 21 
                 0.370 
                 0.369 
                 −0.00091 
                  99.75% 
                 4.001 
                  9.22% 
               
               
                 22 
                 0.370 
                 0.369 
                 −0.00079 
                  99.79% 
                 4.001 
                  9.23% 
               
               
                 31 
                 0.370 
                 0.369 
                 −0.00048 
                  99.87% 
                 4.366 
                  8.46% 
               
               
                 32 
                 0.370 
                 0.369 
                 −0.00081 
                  99.78% 
                 4.366 
                  8.45% 
               
               
                 41 
                 0.370 
                 0.370 
                 −0.00027 
                  99.93% 
                 0.400 
                 92.41% 
               
               
                 42 
                 0.370 
                 0.370 
                 −0.00030 
                  99.92% 
                 0.400 
                 92.40% 
               
               
                 51 
                 0.370 
                 0.370 
                 −0.00008 
                  99.98% 
                 2.211 
                 16.73% 
               
               
                 52 
                 0.370 
                 0.370 
                   0.00033 
                 100.09% 
                 2.211 
                 16.74% 
               
               
                   
               
               
                   
                   
                 ARS  
                 ARS- 
                 (ARS/EHD)  
                   
                 ARS/TP  
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 18.475  
                 18.834  
                   0.358  
                 101.94% 
                 2.017 
                 933.72%  
               
               
                 12 
                 10.526  
                 13.912  
                   3.385  
                 132.16% 
                 2.017 
                 689.71%  
               
               
                 21 
                 10.297  
                 10.360  
                   0.064  
                 100.62% 
                 4.001 
                 258.94%  
               
               
                 22 
                 7.320 
                 7.932 
                   0.613  
                 108.37% 
                 4.001 
                 198.25%  
               
               
                 31 
                 2.964 
                 3.195 
                   0.232  
                 107.82% 
                 4.366 
                 73.19% 
               
               
                 32 
                 1.644 
                 1.651 
                   0.007  
                 100.42% 
                 4.366 
                 37.81% 
               
               
                 41 
                 1.667 
                 1.740 
                   0.074  
                 104.41% 
                 0.400 
                 435.05%  
               
               
                 42 
                 2.078 
                 2.103 
                   0.025  
                 101.22% 
                 0.400 
                 525.72%  
               
               
                 51 
                 2.340 
                 2.411 
                   0.070  
                 103.00% 
                 2.211 
                 109.02%  
               
               
                 52 
                 2.491 
                 2.698 
                   0.207  
                 108.29% 
                 2.211 
                 122.00%  
               
               
                   
               
            
           
         
       
     
     The results of the equations of the second embodiment based on Table 3 and Table 4 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Values related to the inflection points of the second embodiment 
               
               
                 (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 16.3905 
                 HIF111/HOI 
                 5.04556 
                 SGI111 
                 2.53067 
                 |SGI111|/(|SGI111| + TP1) 
                 0.55647 
               
               
                 HIF211 
                 10.1609 
                 HIF211/HOI 
                 3.12787 
                 SGI211 
                 −0.86928 
                 |SGI211|/(|SGI211| + TP2) 
                 0.17849 
               
               
                 HIF421 
                 1.31733 
                 HIF421/HOI 
                 0.40552 
                 SGI421 
                 0.17941 
                 |SGI421|/(|SGI421| + TP4) 
                 0.30965 
               
               
                 HIF521 
                 1.92575 
                 HIF521/HOI 
                 0.59281 
                 SGI521 
                 −0.65782 
                 |SGI521|/(|SGI521| + TP5) 
                 0.22928 
               
               
                   
               
            
           
         
       
     
     Third Embodiment 
     As shown in  FIG. 3A  and  FIG. 3B , an optical image capturing system of the third embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  310 , a second lens  320 , a third lens  330 , an aperture  300 , a fourth lens  340 , a fifth lens  350 , an infrared rays filter  380 , an image plane  390 , and an image sensor  392 .  FIG. 3C  is a transverse aberration diagram at 0.7 field of view of the third embodiment of the present application. 
     The first lens  310  has negative refractive power and is made of plastic. An object-side surface  312  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  314  thereof, which faces the image side, is a concave aspheric surface. 
     The second lens  320  has negative refractive power and is made of plastic. An object-side surface  322  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  324  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  322  has an inflection point. 
     The third lens  330  has positive refractive power and is made of plastic. An object-side surface  332  thereof, which faces the object side, is a convex surface, and an image-side surface  334  thereof, which faces the image side, is a concave aspheric surface. 
     The fourth lens  340  has positive refractive power and is made of plastic. An object-side surface  342 , which faces the object side, is a convex aspheric surface, and an image-side surface  344 , which faces the image side, is a convex aspheric surface. The object-side surface  342  has an inflection point. 
     The fifth lens  350  has negative refractive power and is made of plastic. An object-side surface  352 , which faces the object side, is a convex surface, and an image-side surface  354 , which faces the image side, is a concave surface. It may help to shorten the back focal length to keep small in size. In addition, the object-side surface  352  has two inflection points, and the image-side surface  354  has an inflection point, which may reduce an incident angle of the light of an off-axis field of view and correct the aberration of the off-axis field of view. 
     The infrared rays filter  380  is made of glass and between the fifth lens  350  and the image plane  390 . The infrared rays filter  390  gives no contribution to the focal length of the system. 
     The optical image capturing system of the second embodiment satisfies |f 2 |+|f 3 |+|f 4 |=32.8735; |f 1 |+|f 5 |=50.1732 mm; and |f 2 |+|f 3 |+|f 4 |&lt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  310 , f 2  is a focal length of the second lens  320 , f 3  is a focal length of the third lens  330 , f 4  is a focal length of the fourth lens  340 , and f 5  is a focal length of the fifth lens  350 . 
     In the third embodiment, the optical image capturing system of the third embodiment further satisfies ΣPP=27.87392 mm; and f 3 /ΣPP=0.87453 mm, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the third lens  330  to the other positive lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the third embodiment further satisfies ΣNP=−55.17274 mm; and f 1 /ΣNP=0.61045, where ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the first lens  310  to other negative lenses. 
     The parameters of the lenses of the third embodiment are listed in Table 5 and Table 6. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 f = 1.35300 mm; f/HEP = 1.8; HAF = 89.9935 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 49.63375 
                 6.170876 
                 plastic 
                 1.565 
                 58 
                 −33.6801 
               
               
                 2 
                   
                 13.16671 
                 7.280717 
                   
                   
                   
                   
               
               
                 3 
                 2 nd  lens 
                 51.25803 
                 3.299971 
                 plastic 
                 1.535 
                 56.3 
                 −4.99954 
               
               
                 4 
                   
                 2.4926 
                 6.054966 
                   
                   
                   
                   
               
               
                 5 
                 3 rd  lens 
                 9.21507 
                 10 
                 plastic 
                 1.65 
                 21.4 
                 24.3765 
               
               
                 6 
                   
                 12.41776 
                 0.26997 
                   
                   
                   
                   
               
               
                 7 
                 Aperture 
                 plane 
                 0 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 3.84092 
                 2.886463 
                 plastic 
                 1.565 
                 58 
                 3.49742 
               
               
                 9 
                   
                 −2.98276 
                 0.05 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 83.58868 
                 3.093074 
                 plastic 
                 1.65 
                 21.4 
                 −16.4931 
               
               
                 11 
                   
                 9.43212 
                 0.5 
                   
                   
                   
                   
               
               
                 12 
                 Infrared 
                 plane 
                 0.85 
                   
                 1.517 
                 64.13 
                   
               
               
                   
                 rays filter 
                   
                   
                   
                   
                   
                   
               
               
                 13 
                   
                 plane 
                 0.765964 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 plane 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
               
               
                 k 
                 0 
                   0 
                   9.969201 
                 −0.824227 
                 −2.43075 
               
               
                 A4 
                   
                   1.94756E−20 
                   4.68977E−05 
                 −6.15481E−04 
                   2.12823E−04 
               
               
                 A6 
                   
                   2.53134E−37 
                 −4.92765E−07 
                   6.35197E−06 
                   2.12615E−06 
               
               
                 A8 
                   
                   0.00000E+00 
                 −3.49547E−09 
                   7.53165E−08 
                   1.30474E−07 
               
               
                 A10 
                   
                   0.00000E+00 
                 −8.67461E−12 
                 −6.18924E−10 
                 −7.98482E−10 
               
               
                 A12 
                   
                   2.73003E−14 
                   4.03535E−13 
                 −2.34914E−09 
                 −3.41240E−10 
               
               
                 A14 
                   
                 −6.66915E−16 
                 −1.45720E−15 
                   2.94267E−12 
                 −5.37050E−13 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 6 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                   45.300665 
                 −0.797324 
                   0 
                   44.089874 
                 −0.224934 
               
               
                 A4 
                    1.64567E−03 
                 −1.60862E−03 
                   5.99395E−16 
                  −8.32874E−03 
                   1.82396E−03 
               
               
                 A6 
                  −1.98445E−04 
                   3.97482E−04 
                   4.47827E−24 
                  −5.53577E−04 
                 −6.81997E−04 
               
               
                 A8 
                    1.28754E−04 
                 −2.22951E−04 
                   0.00000E+00 
                  −4.84292E−05 
                   4.79287E−05 
               
               
                 A10 
                  −1.21974E−05 
                   7.73063E−06 
                   0.00000E+00 
                  −2.32327E−05 
                   5.33395E−07 
               
               
                 A12 
                    2.20435E−09 
                   9.20194E−18 
                 −9.14115E−18 
                  −4.61660E−07 
                 −3.37863E−07 
               
               
                 A14 
                  −4.23398E−13 
                 −1.56560E−17 
                   8.21220E−18 
                    1.03426E−08 
                   1.49915E−08 
               
               
                   
               
            
           
         
       
     
     An equation of the aspheric surfaces of the third embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the third embodiment based on Table 5 and Table 6 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Third embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f/f5 | 
                 | f1/f2 | 
               
               
                 0.04017 
                 0.27062 
                 0.05550 
                 0.38686 
                 0.08203 
                 6.73664 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/| ΣNPR | 
                 IN12/f 
                 IN45/f 
                 | f2/f3 | 
               
               
                 0.44236 
                 0.39283 
                 1.12608 
                 5.38117 
                 0.03695 
                 0.20510 
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                 0.61256 
                 4.07628 
                 1.08890 
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 ODT % 
                 TDT % 
               
               
                 41.22200  
                 39.10600  
                 12.68369  
                 0.19760 
                 −100.027     
                 77.9207  
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                 0.00000 
                 0.00000 
                 0.58896 
                 0.00000 
                 0.18122 
                 0.01429 
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 | InRS51 |/TP5 
                 | InRS52 |/TP5 
               
               
                 0.33000 
                 3.46445 
                 −0.049915 
                  0.243398 
                 0.01614 
                 0.07869 
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.024 mm 
                 0.017 mm 
                 −0.018 mm 
                 0.020 mm 
                 −0.003 mm 
                 0.005 mm 
               
               
                   
               
            
           
         
       
     
     The figures related to the profile curve lengths obtained based on Table 5 and 
     Table 6 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Third embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE  
                 ARE- 
                 2(ARE/  
                   
                 ARE/TP  
               
               
                 ARE 
                 1/2(HEP) 
                 value 
                 1/2(HEP) 
                 HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.376 
                 0.375 
                 −0.00083 
                  99.78% 
                 6.171 
                  6.08% 
               
               
                 12 
                 0.376 
                 0.375 
                 −0.00078 
                  99.79% 
                 6.171 
                  6.08% 
               
               
                 21 
                 0.376 
                 0.375 
                 −0.00083 
                  99.78% 
                 3.300 
                  11.36% 
               
               
                 22 
                 0.376 
                 0.376 
                 0.00058 
                 100.15% 
                 3.300 
                  11.41% 
               
               
                 31 
                 0.376 
                 0.375 
                 −0.00073 
                  99.81% 
                 10.000 
                  3.75% 
               
               
                 32 
                 0.376 
                 0.375 
                 −0.00077 
                  99.79% 
                 10.000 
                  3.75% 
               
               
                 41 
                 0.376 
                 0.376 
                 −0.00024 
                  99.94% 
                 2.886 
                  13.01% 
               
               
                 42 
                 0.376 
                 0.376 
                 0.00016 
                 100.04% 
                 2.886 
                  13.03% 
               
               
                 51 
                 0.376 
                 0.375 
                 −0.00083 
                  99.78% 
                 3.093 
                  12.12% 
               
               
                 52 
                 0.376 
                 0.375 
                 −0.00073 
                  99.81% 
                 3.093 
                  12.13% 
               
               
                   
               
               
                   
                   
                 ARS  
                 ARS- 
                 (ARS/ 
                   
                 ARS/TP  
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 25.750 
                 27.073 
                 1.322 
                 105.13% 
                 6.171 
                 438.72% 
               
               
                 12 
                 12.259 
                 16.061 
                 3.802 
                 131.02% 
                 6.171 
                 260.28% 
               
               
                 21 
                 10.518 
                 10.617 
                 0.099 
                 100.94% 
                 3.300 
                 321.72% 
               
               
                 22 
                 4.763 
                 7.395 
                 2.632 
                 155.27% 
                 3.300 
                 224.10% 
               
               
                 31 
                 4.233 
                 4.384 
                 0.150 
                 103.55% 
                 10.000 
                  43.84% 
               
               
                 32 
                 1.358 
                 1.363 
                 0.004 
                 100.33% 
                 10.000 
                  13.63% 
               
               
                 41 
                 1.596 
                 1.638 
                 0.041 
                 102.59% 
                 2.886 
                  56.74% 
               
               
                 42 
                 2.047 
                 2.256 
                 0.209 
                 110.20% 
                 2.886 
                  78.16% 
               
               
                 51 
                 1.976 
                 1.997 
                 0.021 
                 101.06% 
                 3.093 
                  64.55% 
               
               
                 52 
                 2.446 
                 2.468 
                 0.022 
                 100.90% 
                 3.093 
                  79.80% 
               
               
                   
               
            
           
         
       
     
     The results of the equations of the third embodiment based on Table 5 and 
     Table 6 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Values related to the inflection points of the third embodiment 
               
               
                 (Reference wavelength: 555 nnn) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF211 
                 7.17352 
                 HIF211/HOI 
                 2.20724 
                 SGI211 
                 0.56778 
                 |SGI211|/(|SGI211| + TP2) 
                 0.14680 
               
               
                 HIF411 
                 0.79077 
                 HIF411/HOI 
                 0.24331 
                 SGI411 
                 −0.35438 
                 |SGI411|/(|SGI411| + TP4) 
                 0.10935 
               
               
                 HIF511 
                 0.34272 
                 HIF511/HOI 
                 0.10545 
                 SGI511 
                 0.00059 
                 |SGI511|/(|SGI511| + TP5) 
                 0.00019 
               
               
                 HIF512 
                 1.82902 
                 HIF512/HOI 
                 0.56278 
                 SGI512 
                 0.28955 
                 |SGI512|/(|SGI512| + TP5) 
                 0.08560 
               
               
                 HIF521 
                 2.12924 
                 HIF521/HOI 
                 0.65515 
                 SGI521  
                 0.23562 
                 |SGI521|/(|SGI521| + TP5) 
                 0.07078 
               
               
                   
               
            
           
         
       
     
     Fourth Embodiment 
     As shown in  FIG. 4A  and  FIG. 4B , an optical image capturing system  40  of the fourth embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  410 , an aperture  400 , a second lens  420 , a third lens  430 , a fourth lens  440 , a fifth lens  450 , an infrared rays filter  480 , an image plane  490 , and an image sensor  492 .  FIG. 4C  is a transverse aberration diagram at 0.7 field of view of the fourth embodiment of the present application. 
     The first lens  410  has negative refractive power and is made of plastic. An object-side surface  412  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  414  thereof, which faces the image side, is a concave aspheric surface. 
     The second lens  420  has negative refractive power and is made of plastic. An object-side surface  422  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  424  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  422  and the image-side surface  424  both have an inflection point. 
     The third lens  430  has positive refractive power and is made of plastic. An object-side surface  432  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  434  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  432  has an inflection point. 
     The fourth lens  440  has negative refractive power and is made of plastic. An object-side surface  442 , which faces the object side, is a concave aspheric surface, and an image-side surface  444 , which faces the image side, is a concave aspheric surface. 
     The fifth lens  450  has positive refractive power and is made of plastic. An object-side surface  452 , which faces the object side, is a convex surface, and an image-side surface  454 , which faces the image side, is a convex surface. It may help to shorten the back focal length to keep small in size. 
     The infrared rays filter  480  is made of glass and between the fifth lens  450  and the image plane  490 . The infrared rays filter  480  gives no contribution to the focal length of the system. 
     The optical image capturing system of the second embodiment satisfies |f 2 |+|f 3 |+|f 4 |=24.2854 mm; |f 1 |+|f 5 |=12.5933 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  410 , f 2  is a focal length of the second lens  420 , f 3  is a focal length of the third lens  430 , f 4  is a focal length of the fourth lens  440 , and f 5  is a focal length of the fifth lens  450 . 
     In the fourth embodiment, the optical image capturing system of the fourth embodiment further satisfies ΣPP=15.68241 mm; and f 3 /ΣPP=0.84738, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the third lens  430  to the other positive lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the fourth embodiment further satisfies ΣNP=−33.93998 mm; and f 1 /ΣNP=0.42508, where ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the first lens  410  to other negative lenses. 
     The parameters of the lenses of the fourth embodiment are listed in Table 7 and Table 8. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 f = 0.85370 mm; f/HEP = 1.8; HAF = 80.0032 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius  
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 of curvature (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 56.69581 
                 8 
                 plastic 
                 1.565 
                 58 
                 −8.80866 
               
               
                 2 
                   
                 4.3543 
                 17.07889 
                   
                   
                   
                   
               
               
                 3 
                 2 nd  lens 
                 49.68607 
                 1.425896 
                 plastic 
                 1.565 
                 58 
                 −17.2141 
               
               
                 4 
                   
                 8.07054 
                 12.41534 
                   
                   
                   
                   
               
               
                 5 
                 Aperture 
                 plane 
                 −0.33949 
                 plastic 
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 3.37181 
                 1.957908 
                   
                 1.565 
                 58 
                 3.90723 
               
               
                 7 
                   
                 −5.09692 
                 0.841654 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −11.6907 
                 0.402838 
                 plastic 
                 1.65 
                 21.4 
                 −3.16409 
               
               
                 9 
                   
                 2.55551 
                 0.113596 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 4.51333 
                 1.251703 
                 plastic 
                 1.565 
                 58 
                 3.78464 
               
               
                 11 
                   
                 −3.67781 
                 0.8 
                   
                   
                   
                   
               
               
                 12 
                 Infrared 
                 plane 
                 0.85 
                   
                 1.517 
                 64.13 
                   
               
               
                   
                 rays filter 
                   
                   
                   
                   
                   
                   
               
               
                 13 
                   
                 plane 
                 1.597782 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 plane 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 6 
               
               
                   
               
               
                 k 
                 1.440261 
                 −0.882584 
                   15.474721 
                   1.329643 
                 −1.777957 
               
               
                 A4 
                   
                 −2.42256E−04 
                    3.88845E−06 
                   1.92207E−04 
                   4.06841E−03 
               
               
                 A6 
                   
                   4.64768E−06 
                  −1.05379E−06 
                 −6.11009E−06 
                 −6.79747E−04 
               
               
                 A8 
                   
                   4.19833E−09 
                  −3.90435E−10 
                   1.42111E−06 
                   1.97809E−04 
               
               
                 A10 
                   
                   2.40979E−14 
                  −1.01661E−11 
                 −1.78650E−08 
                 −5.44745E−05 
               
               
                 A12 
                   
                 −7.06167E−13 
                    1.79656E−12 
                   4.24081E−20 
                 −1.78608E−19 
               
               
                 A14 
                   
                 −8.98687E−15 
                  −1.23863E−14 
                 −7.48428E−21 
                   4.70503E−23 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                   2.84218 
                   29.118433 
                 −4.78026 
                   1.642938 
                 −0.452729 
               
               
                 A4 
                   1.43420E−02 
                  −2.15386E−02 
                 −5.30632E−03 
                 −3.20956E−04 
                   6.98376E−03 
               
               
                 A6 
                 −3.36527E−03 
                    3.13942E−03 
                   4.56969E−04 
                 −6.60907E−04 
                   2.50386E−03 
               
               
                 A8 
                   6.43266E−04 
                    5.66152E−04 
                   3.87991E−04 
                   1.77597E−04 
                   8.07165E−05 
               
               
                 A10 
                 −8.50804E−05 
                  −1.58101E−04 
                 −6.66387E−05 
                 −8.89048E−06 
                   2.31349E−06 
               
               
                 A12 
                 −5.82874E−19 
                  −1.58113E−18 
                   6.71158E−20 
                   2.17312E−19 
                   2.15148E−18 
               
               
                 A14 
                   2.45073E−21 
                    3.67320E−20 
                   2.34160E−20 
                 −5.61147E−20 
                   1.28473E−20 
               
               
                   
               
            
           
         
       
     
     An equation of the aspheric surfaces of the fourth embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the fourth embodiment based on Table 7 and Table 8 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Fourth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f/f5 | 
                 | f1/f2 | 
               
               
                 0.09692 
                 0.04959 
                 0.21849 
                 0.26981 
                 0.22557 
                 0.51171 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/| ΣNPR | 
                 IN12/f 
                 IN45/f 
                 | f2/f3 | 
               
               
                 0.44406 
                 0.41632 
                 1.06664 
                 20.00574  
                 0.13306 
                 4.40570 
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                 0.13162 
                 17.58812  
                 3.38919 
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 ODT % 
                 TDT % 
               
               
                 46.38980  
                 43.14830  
                 14.27378  
                 0.16102 
                 −32.8438    
                 43.2316  
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                 0.00000 
                 0.00000 
                 0.00000 
                 1.83600 
                 0.00000 
                 0.00000 
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 | InRS51 |/TP5 
                 | InRS52 |/TP5 
               
               
                 0.72828 
                 4.86029 
                  0.613775 
                 −0.22181  
                 0.49035 
                 0.17721 
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.017 mm 
                 0.009 mm 
                 −0.021 mm 
                 0.009 mm 
                 0.002 mm 
                 −0.004 mm 
               
               
                   
               
            
           
         
       
     
     The figures related to the profile curve lengths obtained based on Table 7 and 
     Table 8 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Fourth embodiment (Reference wavelength: 555 nnn) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE  
                 ARE-1/2 
                 2(ARE/HEP)  
                   
                 ARE/TP  
               
               
                 ARE 
                 1/2(HEP) 
                 value 
                 (HEP) 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.237 
                 0.237 
                 −0.00014 
                  99.94% 
                 8.000 
                  2.96% 
               
               
                 12 
                 0.237 
                 0.237 
                 −0.00002 
                  99.99% 
                 8.000 
                  2.96% 
               
               
                 21 
                 0.237 
                 0.237 
                 −0.00014 
                  99.94% 
                 1.426 
                  16.62% 
               
               
                 22 
                 0.237 
                 0.237 
                 −0.00010 
                  99.96% 
                 1.426 
                  16.62% 
               
               
                 31 
                 0.237 
                 0.237 
                 0.00006 
                 100.02% 
                 1.958 
                  12.11% 
               
               
                 32 
                 0.237 
                 0.237 
                 −0.00005 
                  99.98% 
                 1.958 
                  12.11% 
               
               
                 41 
                 0.237 
                 0.237 
                 −0.00012 
                  99.95% 
                 0.403 
                  58.84% 
               
               
                 42 
                 0.237 
                 0.237 
                 0.00019 
                 100.08% 
                 0.403 
                  58.91% 
               
               
                 51 
                 0.237 
                 0.237 
                 −0.00003 
                  99.99% 
                 1.252 
                  18.94% 
               
               
                 52 
                 0.237 
                 0.237 
                 0.00002 
                 100.01% 
                 1.252 
                  18.95% 
               
               
                   
               
               
                   
                   
                 ARS  
                 ARS- 
                 (ARS/EHD)  
                   
                 ARS/TP  
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 22.611 
                 23.380 
                 0.768 
                 103.40% 
                 8.000 
                 292.25% 
               
               
                 12 
                 8.597 
                 14.167 
                 5.570 
                 164.78% 
                 8.000 
                 177.09% 
               
               
                 21 
                 4.567 
                 4.572 
                 0.006 
                 100.12% 
                 1.426 
                 320.67% 
               
               
                 22 
                 3.715 
                 3.926 
                 0.211 
                 105.68% 
                 1.426 
                 275.32% 
               
               
                 31 
                 1.573 
                 1.629 
                 0.056 
                 103.55% 
                 1.958 
                  83.21% 
               
               
                 32 
                 1.609 
                 1.629 
                 0.020 
                 101.25% 
                 1.958 
                  83.19% 
               
               
                 41 
                 1.491 
                 1.508 
                 0.016 
                 101.08% 
                 0.403 
                 374.24% 
               
               
                 42 
                 1.533 
                 1.579 
                 0.046 
                 102.97% 
                 0.403 
                 391.86% 
               
               
                 51 
                 1.552 
                 1.586 
                 0.034 
                 102.22% 
                 1.252 
                 126.73% 
               
               
                 52 
                 1.591 
                 1.616 
                 0.025 
                 101.60% 
                 1.252 
                 129.12% 
               
               
                   
               
            
           
         
       
     
     The results of the equations of the fourth embodiment based on Table 7 and Table 8 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Values related to the inflection points of the fourth embodiment 
               
               
                 (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF121 
                 9.84337 
                 HIF121/HOI 
                 3.02873 
                 SGI121 
                 14.65000 
                 |SGI121|/(|SGI121| + TP1) 
                 0.64680 
               
               
                 HIF211 
                 5.81845 
                 HIF211/HOI 
                 1.79029 
                 SGI211 
                 0.32714 
                 |SGI211|/(|SGI211| + TP2) 
                 0.18661 
               
               
                 HIF212 
                 8.09399 
                 HIF212/HOI 
                 2.49046 
                 SGI212 
                 0.53217 
                 |SGI212|/(|SGI212| + TP2) 
                 0.27178 
               
               
                 HIF213 
                 9.00407 
                 HIF213/HOI 
                 2.77048 
                 SGI213 
                 0.60926 
                 |SGI213|/(|SGI213| + TP2) 
                 0.29937 
               
               
                 HIF421 
                 1.92260 
                 HIF421/HOI 
                 0.59157 
                 SGI421 
                 0.49885 
                 |SGI421|/(|SGI421| + TP4) 
                 0.55324 
               
               
                 HIF521 
                 1.20884 
                 HIF521/HOI 
                 0.37195 
                 SGI521 
                 −0.17858 
                 |SGI521|/(|SGI521| + TP5) 
                 0.12486 
               
               
                   
               
            
           
         
       
     
     Fifth Embodiment 
     As shown in  FIG. 5A  and  FIG. 5B , an optical image capturing system of the fifth embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  510 , a second lens  520 , an aperture  500 , a third lens  530 , a fourth lens  540 , a fifth lens  550 , an infrared rays filter  580 , an image plane  590 , and an image sensor  592 .  FIG. 5C  is a transverse aberration diagram at 0.7 field of view of the fifth embodiment of the present application. 
     The first lens  510  has negative refractive power and is made of plastic. An object-side surface  512 , which faces the object side, is a convex aspheric surface, and an image-side surface  514 , which faces the image side, is a concave aspheric surface. The image-side surface  514  has two inflection points. 
     The second lens  520  has negative refractive power and is made of plastic. An object-side surface  522  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  524  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  522  has an inflection point. 
     The third lens  530  has positive refractive power and is made of plastic. An object-side surface  532 , which faces the object side, is a convex aspheric surface, and an image-side surface  534 , which faces the image side, is a concave aspheric surface. The image-side surface  534  has an inflection point. 
     The fourth lens  540  has positive refractive power and is made of plastic. An object-side surface  542 , which faces the object side, is a convex aspheric surface, and an image-side surface  544 , which faces the image side, is a convex aspheric surface. The object-side surface  542  has an inflection point. 
     The fifth lens  550  has negative refractive power and is made of plastic. An object-side surface  552 , which faces the object side, is a concave surface, and an image-side surface  554 , which faces the image side, is a convex surface. The object-side surface  552  and the image-side surface  554  both have an inflection point. It may help to shorten the back focal length to keep small in size. 
     The infrared rays filter  580  is made of glass and between the fifth lens  550  and the image plane  590 . The infrared rays filter  580  gives no contribution to the focal length of the system. 
     The optical image capturing system of the second embodiment satisfies |f 2 |+|f 3 |+|f 4 |=32.3540 mm; |f 1 |+|f 5 |=17.2684 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 2  is a focal length of the second lens  520 , f 3  is a focal length of the third lens  530 , f 4  is a focal length of the fourth lens  540 , and f 5  is a focal length of the fifth lens  550 . 
     In the fifth embodiment, the optical image capturing system of the fifth embodiment further satisfies ΣPP=15.68241 mm; and f 3 /ΣPP=0.84738, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the third lens  530  to the other positive lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the fifth embodiment further satisfies ΣNP=−33.93998 mm; and f 1 /ΣNP=0.42508, where ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the first lens  510  to other negative lenses. 
     The parameters of the lenses of the fifth embodiment are listed in Table 9 and Table 10. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 f = 1.17413 mm; f/HEP = 1.8; HAF = 70 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius  
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 of curvature (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 40.22805 
                 7.97905 
                 plastic 
                 1.565 
                 58 
                 −14.4273 
               
               
                 2 
                   
                 6.30816 
                 21.79378 
                   
                   
                   
                   
               
               
                 3 
                 2 nd  lens 
                 −100.262 
                 1.208962 
                 plastic 
                 1.565 
                 58 
                 −16.6716 
               
               
                 4 
                   
                 10.4778 
                 12.54886 
                   
                   
                   
                   
               
               
                 5 
                 Aperture 
                 plane 
                 0.26643 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 4.29722 
                 0.829451 
                 plastic 
                 1.514 
                 56.8 
                 13.2889 
               
               
                 7 
                   
                 10.76718 
                 1.440879 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 3.52308 
                 3.112357 
                 plastic 
                 1.565 
                 58 
                 2.39351 
               
               
                 9 
                   
                 −1.50105 
                 0.097704 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −1.21547 
                 1.599487 
                 plastic 
                 1.65 
                 21.4 
                 −2.84108 
               
               
                 11 
                   
                 −5.32344 
                 1 
                   
                   
                   
                   
               
               
                 12 
                 Infrared 
                 plane 
                 0.85 
                   
                 1.517 
                 64.13 
                   
               
               
                   
                 rays filter 
                   
                   
                   
                   
                   
                   
               
               
                 13 
                   
                 plane 
                 1.00000 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 plane 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 6 
               
               
                   
               
               
                 k 
                 0.432575 
                 −0.794138 
                 −50 
                   3.124682 
                 −7.66839 
               
               
                 A4 
                   
                   1.38216E−05 
                    7.79532E−05 
                   3.03009E−04 
                   6.50228E−03 
               
               
                 A6 
                   
                 −1.65220E−06 
                  −1.87356E−07 
                 −2.83718E−05 
                 −8.72992E−04 
               
               
                 A8 
                   
                 −3.95917E−09 
                    9.86538E−11 
                   2.28052E−06 
                   1.33073E−04 
               
               
                 A10 
                   
                   2.09628E−10 
                  −4.14409E−11 
                 −3.98770E−08 
                 −1.00686E−05 
               
               
                 A12 
                   
                 −2.86973E−13 
                    1.42065E−12 
                 −3.17951E−12 
                   2.30144E−19 
               
               
                 A14 
                   
                 −3.08344E−15 
                  −6.59100E−15 
                   1.25435E−14 
                   8.76433E−20 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 −49.992715 
                 −3.526101 
                 −3.796562 
                 −3.268786 
                 −50 
               
               
                 A4 
                  −5.32697E−03 
                   1.68416E−03 
                 −7.46776E−04 
                   7.25558E−03 
                    1.73448E−02 
               
               
                 A6 
                    2.65009E−04 
                 −4.82435E−04 
                 −1.44832E−04 
                 −5.88601E−04 
                  −2.19366E−04 
               
               
                 A8 
                    9.64475E−05 
                   2.14704E−05 
                 −1.55010E−05 
                 −2.78615E−05 
                  −1.32293E−04 
               
               
                 A10 
                  −1.19181E−05 
                 −3.39621E−06 
                   1.16646E−06 
                   6.32027E−06 
                    1.31507E−05 
               
               
                 A12 
                  −2.13985E−19 
                   1.07881E−18 
                 −5.92227E−18 
                 −2.57488E−18 
                  −3.81495E−18 
               
               
                 A14 
                    4.21422E−19 
                 −3.94386E−20 
                 −4.16111E−19 
                   5.11577E−19 
                    1.03587E−18 
               
               
                   
               
            
           
         
       
     
     An equation of the aspheric surfaces of the fifth embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the fifth embodiment based on Table 9 and Table 10 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Fifth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f/f5 | 
                 | f1/f2 | 
               
               
                 0.08138 
                 0.07043 
                 0.08835 
                 0.49055 
                 0.41327 
                 0.86538 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/| ΣNPR | 
                 IN12/f 
                 IN45/f 
                 | f2/f3 | 
               
               
                 0.57890 
                 0.56508 
                 1.02446 
                 18.56166  
                 0.08321 
                 1.25455 
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                 0.05498 
                 24.62683  
                 0.54531 
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 ODT % 
                 TDT % 
               
               
                 53.72700  
                 50.87700  
                 16.53138  
                 0.18978 
                 19.9227  
                 17.9338  
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                 0.00000 
                 0.00000 
                 0.00000 
                 1.22904 
                 0.00000 
                 0.00000 
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 | InRS51 |/TP5 
                 | InRS52 |/TP5 
               
               
                 1.45754 
                 0.26650 
                 −1.11932  
                 0.25423 
                 0.69980 
                 0.15894 
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.023 mm 
                 0.004 mm 
                 −0.036 mm 
                 −0.014 mm 
                 0.016 mm 
                 0.006 mm 
               
               
                   
               
            
           
         
       
     
     The figures related to the profile curve lengths obtained based on Table 9 and Table 10 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Fifth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE  
                 ARE-1/2 
                 2(ARE/HEP)  
                   
                 ARE/TP  
               
               
                 ARE 
                 1/2(HEP) 
                 value 
                 (HEP) 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.326 
                 0.326 
                 −0.00014 
                  99.96% 
                 7.979 
                  4.09% 
               
               
                 12 
                 0.326 
                 0.326 
                 −0.00000 
                 100.00% 
                 7.979 
                  4.09% 
               
               
                 21 
                 0.326 
                 0.326 
                 −0.00015 
                  99.96% 
                 1.209 
                  26.97% 
               
               
                 22 
                 0.326 
                 0.326 
                 −0.00009 
                  99.97% 
                 1.209 
                  26.97% 
               
               
                 31 
                 0.326 
                 0.326 
                 0.00016 
                 100.05% 
                 0.829 
                  39.34% 
               
               
                 32 
                 0.326 
                 0.326 
                 −0.00010 
                  99.97% 
                 0.829 
                  39.31% 
               
               
                 41 
                 0.326 
                 0.326 
                 0.00031 
                 100.10% 
                 3.112 
                  10.49% 
               
               
                 42 
                 0.326 
                 0.328 
                 0.00222 
                 100.68% 
                 3.112 
                  10.55% 
               
               
                 51 
                 0.326 
                 0.330 
                 0.00337 
                 101.03% 
                 1.599 
                  20.60% 
               
               
                 52 
                 0.326 
                 0.326 
                 0.00003 
                 100.01% 
                 1.599 
                  20.39% 
               
               
                   
               
               
                   
                   
                 ARS  
                 ARS- 
                 (ARS/EHD)  
                   
                 ARS/TP  
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 21.812 
                 23.185 
                 1.373 
                 106.30% 
                 7.979 
                 290.57% 
               
               
                 12 
                 10.489 
                 15.996 
                 5.507 
                 152.50% 
                 7.979 
                 200.48% 
               
               
                 21 
                 4.343 
                 4.343 
                 −0.00024 
                  99.99% 
                 1.209 
                 359.20% 
               
               
                 22 
                 3.702 
                 3.830 
                 0.128 
                 103.46% 
                 1.209 
                 316.82% 
               
               
                 31 
                 1.956 
                 2.012 
                 0.056 
                 102.86% 
                 0.829 
                 242.52% 
               
               
                 32 
                 1.984 
                 1.985 
                 0.001 
                 100.06% 
                 0.829 
                 239.32% 
               
               
                 41 
                 2.181 
                 2.263 
                 0.083 
                 103.80% 
                 3.112 
                  72.72% 
               
               
                 42 
                 2.061 
                 2.247 
                 0.186 
                 109.03% 
                 3.112 
                  72.20% 
               
               
                 51 
                 1.974 
                 2.148 
                 0.174 
                 108.83% 
                 1.599 
                 134.28% 
               
               
                 52 
                 1.745 
                 1.749 
                 0.004 
                 100.24% 
                 1.599 
                 109.36% 
               
               
                   
               
            
           
         
       
     
     The results of the equations of the fifth embodiment based on Table 9 and Table 10 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Value related to the inflection points of the fifth embodiment 
               
               
                 (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF121 
                 12.2131 
                 HIF121/HOI 
                 3.75788 
                 SGI121 
                 16.11670 
                 |SGI121/(|SGI121| + TP1) 
                 0.66886 
               
               
                 HIF122 
                 13.4470 
                 HIF122/HOI 
                 4.13754 
                 SGI122 
                 20.31160 
                 |SGI122/(|SGI122| + TP1) 
                 0.71796 
               
               
                 HIF211 
                 3.25212 
                 HIF211/HOI 
                 1.00065 
                 SGI211 
                 −0.04358 
                 |SGI211/(|SGI211| + TP2) 
                 0.03480 
               
               
                 HIF321 
                 1.02590 
                 HIF321/HOI 
                 0.31566 
                 SGI321 
                 0.03890 
                 |SGI321/(|SGI321| + TP3) 
                 0.04480 
               
               
                 HIF411 
                 1.92902 
                 HIF411/HOI 
                 0.59354 
                 SGI411 
                 0.45431 
                 |SGI411/(|SGI411| + TP4) 
                 0.12738 
               
               
                 HIF511 
                 1.41443 
                 HIF511/HOI 
                 0.43521 
                 SGI511 
                 −0.52130 
                 |SGI511/(|SGI511| + TP5) 
                 0.24580 
               
               
                 HIF521 
                 0.64114 
                 HIF521/HOI 
                 0.19727 
                 SGI521 
                 −0.03054 
                 |SGI521/(|SGI521| + TP5) 
                 0.01874 
               
               
                   
               
            
           
         
       
     
     Sixth Embodiment 
     As shown in  FIG. 6A  and  FIG. 6B , an optical image capturing system of the sixth embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  610 , a second lens  620 , an aperture  600 , a third lens  630 , a fourth lens  640 , a fifth lens  650 , an infrared rays filter  680 , an image plane  690 , and an image sensor  692 .  FIG. 6C  is a transverse aberration diagram at 0.7 field of view of the sixth embodiment of the present application. 
     The first lens  610  has negative refractive power and is made of plastic. An object-side surface  612 , which faces the object side, is a convex aspheric surface, and an image-side surface  614 , which faces the image side, is a concave aspheric surface. The object-side surface  612  and the image-side surface  614  both have an inflection point. 
     The second lens  620  has positive refractive power and is made of plastic. An object-side surface  622  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  624  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  622  has an inflection point. 
     The third lens  630  has positive refractive power and is made of plastic. An object-side surface  632 , which faces the object side, is a concave aspheric surface, and an image-side surface  634 , which faces the image side, is a convex aspheric surface. The object-side surface  632  has an inflection point. 
     The fourth lens  640  has negative refractive power and is made of plastic. An object-side surface  642 , which faces the object side, is a convex aspheric surface, and an image-side surface  644 , which faces the image side, is a convex aspheric surface. The object-side surface  642  has two inflection points, and the image-side surface  644  has an inflection point. 
     The fifth lens  650  has positive refractive power and is made of plastic. An object-side surface  652 , which faces the object side, is a concave surface, and an image-side surface  654 , which faces the image side, is a concave surface. The object-side surface  652  has two inflection points, and the image-side surface  654  has an inflection point. It may help to shorten the back focal length to keep small in size. In addition, it may reduce an incident angle of the light of an off-axis field of view and correct the aberration of the off-axis field of view. 
     The infrared rays filter  680  is made of glass and between the fifth lens  650  and the image plane  690 . The infrared rays filter  680  gives no contribution to the focal length of the system. 
     The optical image capturing system of the second embodiment satisfies |f 2 |+|f 3 |+|f 4 |=8.4735 mm; |f 1 |+|f 5 |=8.9495 mm; and |f 2 |+|f 3 |+|f 4 |&lt;|f 1 |+|f 5 |, where f 2  is a focal length of the second lens  620 , f 3  is a focal length of the third lens  630 , f 4  is a focal length of the fourth lens  640 , and f 5  is a focal length of the fifth lens  650 . 
     In the sixth embodiment, the first lens  610 , the third lens  630 , and the fourth lenses  640  are positive lenses, and their focal lengths are f 1 , f 3 , and f 4 . The optical image capturing system of the sixth embodiment further satisfies ΣPP=11.46338 mm; and f 3 /ΣPP=0.15626, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the third lens  630  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the sixth embodiment further satisfies ΣNP=−5.95967 mm; and f 1 /ΣNP=0.56425, where ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the first lens  610  to the other negative lens to avoid the significant aberration caused by the incident rays. 
     The parameters of the lenses of the sixth embodiment are listed in Table 11 and Table 12. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 f = 2.86808 mm; f/HEP = 2.427; HAF = 59.98930 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius  
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 of curvature (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 500 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 80 
                 0.525587 
                 plastic 
                 1.5346 
                 56.07 
                 −3.36272 
               
               
                 2 
                   
                 1.75976 
                 0.84 
                   
                   
                   
                   
               
               
                 3 
                 2 nd  lens 
                 2.50746 
                 0.482655 
                 plastic 
                 1.5346 
                 56.07 
                 4.0853 
               
               
                 4 
                   
                 −16.2005 
                 0.176572 
                   
                   
                   
                   
               
               
                 5 
                 Aperture/ 
                 3.58683 
                 1.140171 
                 plastic 
                 1.544 
                 55.9671 
                 1.79129 
               
               
                   
                 3 rd  lens 
                   
                   
                   
                   
                   
                   
               
               
                 6 
                   
                 −1.19312 
                 0.107572 
                   
                   
                   
                   
               
               
                 7 
                 4 th  lens 
                 −0.52484 
                 0.390937 
                 plastic 
                 1.6425 
                 22.465 
                 −2.59695 
               
               
                 8 
                   
                 −0.98628 
                 0.025 
                   
                   
                   
                   
               
               
                 9 
                 5 th  lens 
                 1.47792 
                 1.18381 
                 plastic 
                 1.544 
                 55.9671 
                 5.58679 
               
               
                 10 
                   
                 2.05696 
                 0.485665 
                   
                   
                   
                   
               
               
                 11 
                 Infrared 
                 plane 
                 0.21 
                 BK_7 
                 1.517 
                 64.13 
                   
               
               
                   
                 rays filter 
                   
                   
                   
                   
                   
                   
               
               
                 12 
                   
                 plane 
                 0.912032 
                   
                   
                   
                   
               
               
                 13 
                 Image  
                 plane 
                 0 
                   
                   
                   
                   
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; the position of blocking light: blocking at the second surface with effective semi diameter of 0.96 mm; blocking at the sixth surface with effective semi diameter of 0.99100243 mm; blocking at the eighth surface with effective semi diameter of 1.321298916 mm; blocking at the tenth surface with effective semi diameter of 2.491334616 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
               
               
                 k 
                 −5.03000E+02 
                   2.82082E−01 
                 −2.81667E−01 
                   6.18050E+02 
                 −8.67154E+00 
               
               
                 A4 
                   1.56330E+00 
                   2.81910E−01 
                 −2.87192E−02 
                 −1.99638E−01 
                 −2.07474E−01 
               
               
                 A6 
                 −3.03630E+00 
                 −1.26529E−01 
                   1.56940E−01 
                 −7.43995E−01 
                 −4.28819E−02 
               
               
                 A8 
                   4.04600E+00 
                   1.05290E+00 
                 −1.44078E+00 
                   1.27258E+01 
                 −3.83914E−01 
               
               
                 A10 
                   2.58410E+00 
                 −5.79479E+00 
                   5.25994E+00 
                 −1.17552E+02 
                   1.45579E+00 
               
               
                 A12 
                 −2.67010E+01 
                   1.85953E+01 
                 −1.14969E+01 
                   6.44464E+02 
                 −5.01920E+00 
               
               
                 A14 
                   5.90370E+01 
                 −3.43207E+01 
                   1.33073E+01 
                 −2.16063E+03 
                   9.08970E+00 
               
               
                 A16 
                 −6.69520E+01 
                   3.66455E+01 
                 −9.32783E+00 
                   4.33535E+03 
                 −9.45118E+00 
               
               
                 A18 
                   3.93600E+01 
                 −2.08628E+01 
                   3.61733E+00 
                 −4.78357E+03 
                   5.61873E+00 
               
               
                 A20 
                 −9.46730E+00 
                   4.82551E+00 
                 −5.94958E−01 
                   2.25196E+03 
                 −1.41300E+00 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 6 
                 7 
                 8 
                 9 
                 10 
               
               
                   
               
               
                 k 
                 −2.30231E+01 
                 −3.51400E+00 
                 −3.71880E+00 
                 −1.00547E+00 
                 −1.53590E+01 
               
               
                 A4 
                 −1.53729E+00 
                 −9.41775E−01 
                   1.34105E−01 
                 −2.25483E−01 
                   5.44650E+00 
               
               
                 A6 
                   4.99856E+00 
                   4.93538E+00 
                   5.53718E−01 
                   1.72556E−01 
                 −7.42230E+01 
               
               
                 A8 
                 −1.23474E+01 
                 −1.36981E+01 
                 −1.52715E+00 
                 −1.24767E−01 
                   2.51900E+02 
               
               
                 A10 
                   2.15799E+01 
                   2.45281E+01 
                   2.13619E+00 
                   6.38251E−02 
                 −6.17910E+01 
               
               
                 A12 
                 −2.58352E+01 
                 −2.88164E+01 
                 −1.84328E+00 
                 −2.11807E−02 
                 −2.63260E+03 
               
               
                 A14 
                   2.01272E+01 
                   2.15397E+01 
                   9.95443E−01 
                   4.35764E−03 
                   9.22460E+03 
               
               
                 A16 
                 −9.64398E+00 
                 −9.67225E+00 
                 −3.27089E−01 
                 −5.26526E−04 
                 −1.49020E+04 
               
               
                 A18 
                   2.58796E+00 
                   2.32583E+00 
                   5.98985E−02 
                   3.39000E−05 
                   1.17850E+04 
               
               
                 A20 
                 −3.01617E−01 
                 −2.22032E−01 
                 −4.68891E−03 
                 −8.92970E−07 
                 −3.62630E+03 
               
               
                   
               
            
           
         
       
     
     An equation of the aspheric surfaces of the sixth embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the sixth embodiment based on Table 11 and Table 12 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Sixth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f/f5 | 
                 | f1/f2 | 
               
               
                 0.66179 
                 0.54474 
                 1.24236 
                 0.85694 
                 0.39834 
                 0.82313 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/| ΣNPR | 
                 IN12/f 
                 IN45/f 
                 | f2/f3 | 
               
               
                 2.18544 
                 1.51873 
                 1.43899 
                 0.37746 
                 0.01123 
                 2.28065 
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                 0.80050 
                 2.82932 
                 3.09208 
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 ODT % 
                 TDT % 
               
               
                 6.48000 
                 4.87230 
                 2.09709 
                 0.72207 
                 −20.2428    
                 20.2233  
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                 0.00000 
                 0.93469 
                 1.64180 
                 1.79310 
                 0.53133 
                 0.25336 
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 | InRS51 |/TP5 
                 | InRS52 |/TP5 
               
               
                 0.42332 
                 2.91651 
                  0.285797 
                  0.0076329 
                 0.24142 
                 0.00645 
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.004 mm 
                 0.008 mm 
                 0.013 mm 
                 0.012 mm 
                 0.003 mm 
                 0.002 mm 
               
               
                   
               
            
           
         
       
     
     The figures related to the profile curve lengths obtained based on Table 11 and Table 12 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Sixth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE  
                 ARE- 
                 2(ARE/  
                   
                 ARE/TP  
               
               
                 ARE 
                 1/2(HEP) 
                 value 
                 1/2(HEP) 
                 HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.460 
                 0.459 
                 −0.00038 
                  99.92% 
                 0.526 
                  87.35% 
               
               
                 12 
                 0.460 
                 0.467 
                 0.00781 
                 101.70% 
                 0.526 
                  88.91% 
               
               
                 21 
                 0.460 
                 0.461 
                 0.00190 
                 100.41% 
                 0.483 
                  95.60% 
               
               
                 22 
                 0.460 
                 0.460 
                 0.00010 
                 100.02% 
                 0.483 
                  95.22% 
               
               
                 31 
                 0.460 
                 0.459 
                 −0.00007 
                  99.99% 
                 1.140 
                  40.30% 
               
               
                 32 
                 0.460 
                 0.473 
                 0.01311 
                 102.85% 
                 1.140 
                  41.45% 
               
               
                 41 
                 0.460 
                 0.493 
                 0.03337 
                 107.26% 
                 0.391 
                 126.08% 
               
               
                 42 
                 0.460 
                 0.469 
                 0.00916 
                 101.99% 
                 0.391 
                 119.88% 
               
               
                 51 
                 0.460 
                 0.464 
                 0.00488 
                 101.06% 
                 1.184 
                  39.23% 
               
               
                 52 
                 0.460 
                 0.462 
                 0.00230 
                 100.50% 
                 1.184 
                  39.01% 
               
               
                   
               
               
                   
                   
                 ARS  
                 ARS- 
                 (ARS/ 
                   
                 ARS/TP  
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 1.662 
                 1.741 
                 0.079 
                 104.76% 
                 0.526 
                 331.21% 
               
               
                 12 
                 0.960 
                 1.174 
                 0.214 
                 122.34% 
                 0.526 
                 223.46% 
               
               
                 21 
                 0.733 
                 0.738 
                 0.005 
                 100.74% 
                 0.483 
                 152.89% 
               
               
                 22 
                 0.610 
                 0.613 
                 0.003 
                 100.46% 
                 0.483 
                 126.94% 
               
               
                 31 
                 0.713 
                 0.715 
                 0.002 
                 100.29% 
                 1.140 
                  62.71% 
               
               
                 32 
                 0.991 
                 1.164 
                 0.173 
                 117.41% 
                 1.140 
                 102.05% 
               
               
                 41 
                 1.024 
                 1.147 
                 0.123 
                 112.01% 
                 0.391 
                 293.42% 
               
               
                 42 
                 1.321 
                 1.343 
                 0.021 
                 101.62% 
                 0.391 
                 343.45% 
               
               
                 51 
                 1.887 
                 1.919 
                 0.032 
                 101.70% 
                 1.184 
                 162.07% 
               
               
                 52 
                 2.464 
                 2.576 
                 0.111 
                 104.52% 
                 1.184 
                 217.59% 
               
               
                   
               
            
           
         
       
     
     The results of the equations of the sixth embodiment based on Table 11 and Table 12 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Values related to the inflection points of the sixth embodiment 
               
               
                 (Reference wavelength: 555 nnn) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 1.47227 
                 HIF111/HOI 
                 0.47646 
                 SGI111 
                 0.31329 
                 |SGI111/(|SGI111| + TP1) 
                 0.37346 
               
               
                 HIF121 
                 0.95363 
                 HIF121/HOI 
                 0.30862 
                 SGI121 
                 0.54047 
                 |SGI121/(|SGI121| + TP1) 
                 0.50698 
               
               
                 HIF211 
                 0.55923 
                 HIF211/HOI 
                 0.18098 
                 SGI211 
                 0.05926 
                 |SGI211/(|SGI211| + TP2) 
                 0.10935 
               
               
                 HIF311 
                 0.30660 
                 HIF311/HOI 
                 0.09922 
                 SGI311 
                 0.01103 
                 |SGI311/(|SGI311| + TP3) 
                 0.00958 
               
               
                 HIF411 
                 0.55057 
                 HIF411/HOI 
                 0.17818 
                 SGI411 
                 −0.21628 
                 |SGI411/(|SGI411| + TP4) 
                 0.35618 
               
               
                 HIF412 
                 0.79077 
                 HIF412/HOI 
                 0.25591 
                 SGI412 
                 −0.35438 
                 |SGI412/(|SGI412| + TP4) 
                 0.47547 
               
               
                 HIF421 
                 0.44107 
                 HIF421/HOI 
                 0.14274 
                 SGI421 
                 −0.08049 
                 |SGI421/(|SGI421| + TP4) 
                 0.17074 
               
               
                 HIF511 
                 0.73656 
                 HIF511/HOI 
                 0.23837 
                 SGI511 
                 0.13638 
                 |SGI511/(|SGI511| + TP5) 
                 0.10330 
               
               
                 HIF512 
                 1.82902 
                 HIF512/HOI 
                 0.59192 
                 SGI512 
                 0.28955 
                 |SGI512/(|SGI512| + TP5) 
                 0.19652 
               
               
                 HIF521 
                 0.96915 
                 HIF521/HOI 
                 0.31364 
                 SGI521 
                 0.15622 
                 |SGI521/(|SGI521| + TP5) 
                 0.11658 
               
               
                   
               
            
           
         
       
     
     It must be pointed out that the embodiments described above are only some embodiments of the present invention. All equivalent structures which employ the concepts disclosed in this specification and the appended claims should fall within the scope of the present invention.