Patent Publication Number: US-9835826-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 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 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 IN12 (instance). A central thickness of the first lens of the optical image capturing system on the optical axis is denoted by TP1 (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 NA1 (instance). A refractive index of the first lens is denoted by Nd1 (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 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 EHD11, the maximum effective half diameter of the image-side surface of the first lens is denoted by EHD12, the maximum effective half diameter of the object-side surface of the second lens is denoted by EHD21, the maximum effective half diameter of the image-side surface of the second lens is denoted by EHD22, 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 ARS11, the profile curve length of the maximum effective half diameter of the image-side surface of the first lens is denoted by ARS12, the profile curve length of the maximum effective half diameter of the object-side surface of the second lens is denoted by ARS21, the profile curve length of the maximum effective half diameter of the image-side surface of the second lens is denoted by ARS22, 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 start point and 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 ARE11, 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 ARE12, 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 ARE21, 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 ARE22, 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 InRS51 (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 InRS52 (the depth of the maximum effective semi diameter). The depth of the maximum effective semi diameter (sinkage) on the object-side surface of 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 C41 on the object-side surface of the fourth lens and the optical axis is HVT41 (instance), and a distance perpendicular to the optical axis between a critical point C42 on the image-side surface of the fourth lens and the optical axis is HVT42 (instance). A distance perpendicular to the optical axis between a critical point C51 on the object-side surface of the fifth lens and the optical axis is HVT51 (instance), and a distance perpendicular to the optical axis between a critical point C52 on the image-side surface of the fifth lens and the optical axis is HVT52 (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 IF511 which is nearest to the optical axis, and the sinkage value of the inflection point IF511 is denoted by SGI511 (instance). A distance perpendicular to the optical axis between the inflection point IF511 and the optical axis is HIF511 (instance). The image-side surface of the fifth lens has one inflection point IF521 which is nearest to the optical axis, and the sinkage value of the inflection point IF521 is denoted by SGI521 (instance). A distance perpendicular to the optical axis between the inflection point IF521 and the optical axis is HIF521 (instance). 
     The object-side surface of the fifth lens has one inflection point IF512 which is the second nearest to the optical axis, and the sinkage value of the inflection point IF512 is denoted by SGI512 (instance). A distance perpendicular to the optical axis between the inflection point IF512 and the optical axis is HIF512 (instance). The image-side surface of the fifth lens has one inflection point IF522 which is the second nearest to the optical axis, and the sinkage value of the inflection point IF522 is denoted by SGI522 (instance). A distance perpendicular to the optical axis between the inflection point IF522 and the optical axis is HIF522 (instance). 
     The object-side surface of the fifth lens has one inflection point IF513 which is the third nearest to the optical axis, and the sinkage value of the inflection point IF513 is denoted by SGI513 (instance). A distance perpendicular to the optical axis between the inflection point IF513 and the optical axis is HIF513 (instance). The image-side surface of the fifth lens has one inflection point IF523 which is the third nearest to the optical axis, and the sinkage value of the inflection point IF523 is denoted by SGI523 (instance). A distance perpendicular to the optical axis between the inflection point IF523 and the optical axis is HIF523 (instance). 
     The object-side surface of the fifth lens has one inflection point IF514 which is the fourth nearest to the optical axis, and the sinkage value of the inflection point IF514 is denoted by SGI514 (instance). A distance perpendicular to the optical axis between the inflection point IF514 and the optical axis is HIF514 (instance). The image-side surface of the fifth lens has one inflection point IF524 which is the fourth nearest to the optical axis, and the sinkage value of the inflection point IF524 is denoted by SGI524 (instance). A distance perpendicular to the optical axis between the inflection point IF524 and the optical axis is HIF524 (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 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 pass 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 pass 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 around 30 μm or around 30 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 around 20 μm or around 20 pixels. 
     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 imagining 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 1≦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 positive 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 positive refractive power. The fifth lens has refractive power, and both the object-side surface and the image-side surface thereof are aspheric surfaces. At least two lenses among the first lens to the fifth lens respectively have 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 1≦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 two lenses among the first to the fifth lenses has at least an inflection point on at least one surface thereof. The first lens has positive refractive power, and the second lens has refractive power. The third lens has refractive power. The fourth lens has positive refractive power. The fifth lens has negative refractive power, wherein the object-side surface and the image-side surface thereof are both aspheric surfaces. The optical image capturing system satisfies:
 
1.2≦ f/HEP≦ 3.5; 0.5≦ HOS/f≦ 3.0; 0&lt; InTL/HOS&lt; 0.9; and 1≦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 of correcting 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 ARS11, the thickness of the first lens on the optical axis is TP1, and the ratio between these two parameters is ARS11/TP1; the profile curve length of the maximum effective half diameter of the image-side surface of the first lens is denoted by ARS12, and the ratio between ARS12 and TP1 is ARS12/TP1. The profile curve length of the maximum effective half diameter of the object-side surface of the second lens is denoted by ARS21, the thickness of the second lens on the optical axis is TP2, and the ratio between these two parameters is ARS21/TP2; the profile curve length of the maximum effective half diameter of the image-side surface of the second lens is denoted by ARS22, and the ratio between ARS22 and TP2 is ARS22/TP2. 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 of correcting 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 ARE11, the thickness of the first lens on the optical axis is TP1, and the ratio between these two parameters is ARE11/TP1; 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 ARE12, and the ratio between ARE12 and TP1 is ARE12/TP1. 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 ARE21, the thickness of the second lens on the optical axis is TP2, and the ratio between these two parameters is ARE21/TP2; 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 ARE22, and the ratio between ARE22 and TP2 is ARE22/TP2. 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 |f1|&gt;f5. 
     In an embodiment, when the lenses satisfy f2|+|f3|+|f4| and |f1|+|f5|, 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 finely 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 first lens can have positive refractive power, and an object-side surface, which faces the object side, thereof can be convex. It may modify the positive refractive power of the first lens as well as shorten the entire length of the system. 
     The second lens can have negative refractive power, and an object-side surface, which faces the object side, thereof can be convex. It may correct the aberration of the first lens. 
     The third lens can have positive refractive power, and an image-side surface, which faces the image side, thereof can be convex. It may share the positive refractive power of the first lens, which prevents excessively increasing the spherical aberration, and lowers the sensitivity of the optical image capturing system. 
     The fourth lens can have positive refractive power, wherein at least one surface of the fourth lens can have at least an inflection point thereon. It may effectively adjust the incidence angle on the fourth lens of each field of view to improve the spherical aberration. 
     The fifth lens has negative refractive power, and an image-side surface, which faces the image side, thereof can be concave. It may shorten the back focal length to keep the system miniaturized. Besides, the fifth has at least an inflection point on at least a surface thereof to reduce the incident angle of the off-axis view angle light. 
     The image sensor is provided on the image plane. The optical image capturing system of the present invention satisfies HOS/HOI≦3 and 0.5≦HOS/f≦2.5, and a preferable range is 1≦HOS/HOI≦2.5 and 1≦HOS/f≦2, 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 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 0.5≦InS/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/InTL≦0.9, 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&lt;|R1/R2|&lt;20, and a preferable range is 0.05&lt;|R1/R2|&lt;0.5, where R1 is a radius of curvature of the object-side surface of the first lens, and R2 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 −7&lt;(R9−R10)/(R9+R10)&lt;2, where R9 is a radius of curvature of the object-side surface of the fifth lens, and R10 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 IN12/f≦0.8, where IN12 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 IN45/f≦0.8, where IN45 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≦(TP1+IN12)/TP2≦10.0, where TP1 is a central thickness of the first lens on the optical axis, and TP2 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≦(TP5+IN45)/TP4≦10.0, where TP4 is a central thickness of the fourth lens on the optical axis, TP5 is a central thickness of the fifth lens on the optical axis, and IN45 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≦TP3/(IN23+TP3+IN34)&lt;1, where TP2 is a central thickness of the second lens on the optical axis, TP3 is a central thickness of the third lens on the optical axis, TP4 is a central thickness of the fourth lens on the optical axis, IN23 is a distance on the optical axis between the second lens and the third lens, IN34 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 finely 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≦HVT513 mm; 0 mm&lt;HVT52≦6 mm; 0≦HVT51/HVT52; 0 mm≦|SGC51|≦0.5 mm; 0 mm&lt;|SGC52|≦2 mm; and 0&lt;|SGC52|/(|SGC52|+TP5)≦0.9, where HVT51 a distance perpendicular to the optical axis between the critical point C51 on the object-side surface of the fifth lens and the optical axis; HVT52 a distance perpendicular to the optical axis between the critical point C52 on the image-side surface of the fifth lens and the optical axis; SGC51 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 C51; SGC52 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 C52. It is helpful to correct the off-axis view field aberration. 
     The optical image capturing system satisfies 0.2≦HVT52/HOI≦0.9, and preferably satisfies 0.3≦HVT52/HOI≦0.8. It may help to correct the peripheral aberration. 
     The optical image capturing system satisfies 0≦HVT52/HOS≦0.5, and preferably satisfies 0.2≦HVT52/HOS≦0.45. It may help to correct the peripheral aberration. 
     The optical image capturing system of the present invention satisfies 0&lt;SGI511/(SGI511+TP5)≦0.9; 0&lt;SGI521/(SGI521+TP5)≦0.9, and it is preferable to satisfy 0.1≦SGI511/(SGI511+TP5)≦0.6; 0.1≦SGI521/(SGI521+TP5)≦0.6, where SGI511 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 SGI521 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;SGI512/(SGI512+TP5)≦0.9; 0&lt;SGI522/(SGI522+TP5)≦0.9, and it is preferable to satisfy 0.1≦SGI512/(SGI512+TP5)≦0.6; 0.1≦SGI522/(SGI522+TP5)≦0.6, where SGI512 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 SGI522 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≦|HIF511|≦5 mm; 0.001 mm≦|HIF521|≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF511|≦3.5 mm; 1.5 mm≦|HIF521|≦3.5 mm, where HIF511 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, and HIF521 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≦|HIF512|≦5 mm; 0.001 mm≦|HIF522|≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF522|≦3.5 mm; 0.1 mm≦|HIF512|≦3.5 mm, where HIF512 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, and HIF522 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≦|HIF513|≦5 mm; 0.001 mm≦|HIF523|≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF523|≦3.5 mm; 0.1 mm≦|HIF513|≦3.5 mm, where HIF513 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, and HIF523 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≦|HIF514|≦5 mm; 0.001 mm≦|HIF524|≦5 mm, and it is preferable to satisfy 0.1 mm≦|HIF524|≦3.5 mm; 0.1 mm≦|HIF514|≦3.5 mm, where HIF514 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, and HIF524 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 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 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 that 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 dynamic focusing optical system. It is superior in 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. 
     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 positive 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  and the image-side surface  114  both have 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 ARS11, and a profile curve length of the maximum effective half diameter of the image-side surface of the first lens  110  is denoted by ARS12. 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 ARE11, 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 ARE12. A thickness of the first lens  110  on the optical axis is TP1. 
     The first lens satisfies SGI111=0.19728 mm; |SGI111|/(|SGI111|+TP1)=0.24340; SGI121=0.00216 mm; |SGI121|/(|SGI121|+TP1)=0.00351, where SGI111 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 SGI121 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 HIF111=0.81258 mm; HIF111/HOI=0.27700; HIF121=0.22793 mm; HIF121/HOI=0.07770, where HIF111 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, and HIF121 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 negative 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 ARS21, and a profile curve length of the maximum effective half diameter of the image-side surface of the second lens  120  is denoted by ARS22. 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 ARE21, 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 ARE22. A thickness of the second lens  120  on the optical axis is TP2. 
     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 SGI211, 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 SGI221. 
     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 HIF211, 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 HIF221. 
     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 concave aspheric surface. The object-side surface  132  and the image-side surface  134  both have two inflection points. A profile curve length of the maximum effective half diameter of an object-side surface of the third lens  130  is denoted by ARS31, and a profile curve length of the maximum effective half diameter of the image-side surface of the third lens  130  is denoted by ARS32. 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 ARE31, 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 ARE32. A thickness of the third lens  130  on the optical axis is TP3. 
     The third lens  130  satisfies SGI311=0.03298 mm; |SGI311|/(|SGI311|+TP3)=0.09002; SGI321=0.02042 mm; |SGI321|/(|SGI321|+TP3)=0.05772, where SGI311 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 SGI321 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. 
     The third lens  130  further satisfies SGI312=0.05207 mm; |SGI312|/(|SGI312|+TP3)=0.13510; SGI322=−0.02201 mm; |SGI322|/(|SGI322|+TP3)=0.06193, where SGI312 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 SGI322 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 HIF311=0.44853 mm; HIF311/HOI=0.15290; HIF321=0.44486 mm; HIF321/HOI=0.15165, where HIF311 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, and HIF321 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. 
     The third lens  130  further satisfies HIF312=0.90272 mm; HIF312/HOI=0.30773; HIF322=1.01361 mm; HIF322/HOI=0.34553, where HIF312 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, and HIF322 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 concave aspheric surface, and an image-side surface  144 , which faces the image side, is a convex aspheric surface. The image-side surface  144  has two inflection points. A profile curve length of the maximum effective half diameter of an object-side surface of the fourth lens  140  is denoted by ARS41, and a profile curve length of the maximum effective half diameter of the image-side surface of the fourth lens  140  is denoted by ARS42. 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 ARE41, 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 ARE42. A thickness of the fourth lens  140  on the optical axis is TP4. 
     The fourth lens  140  satisfies SGI421=−0.29255 mm; |SGI421|/(|SGI421|+TP4)=0.38267, where SGI411 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 SGI421 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. 
     The fourth lens  140  further satisfies SGI422=−0.48851 mm; |SGI422|/(|SGI4221+TP4)=0.50862, where SGI412 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 SGI422 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 HIF421=0.82535 mm; HIF421/HOI=0.28135, where HIF411 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, and HIF421 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. 
     The fourth lens  140  further satisfies HIF422=1.28471 mm; HIF422/HOI=0.43794, where HIF412 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, and HIF422 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 convex 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 two inflection points. A profile curve length of the maximum effective half diameter of an object-side surface of the fifth lens  150  is denoted by ARS51, and a profile curve length of the maximum effective half diameter of the image-side surface of the fifth lens  150  is denoted by ARS52. 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 ARE51, 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 ARE52. A thickness of the fifth lens  150  on the optical axis is TP5. 
     The fifth lens  150  satisfies SGI511=0.00673 mm; |SGI511|/(|SGI511|+TP5)=0.01323; SGI521=0.09725 mm; |SGI521|/(|SGI521|+TP5)=0.16225, where SGI511 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 SGI521 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 fifth lens  150  further satisfies SGI512=−0.11308 mm; |SGI512|/(|SGI512|+TP5)=0.18381; SGI522=−0.00604 mm; |SGI522|/(|SGI522|+TP5)=0.01188, where SGI512 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 SGI522 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 HIF511=0.27152 mm; HIF511/HOI=0.09256; HIF521=0.50870 mm; HIF521/HOI=0.17341, where HIF511 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, and HIF521 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 fourth lens  140  further satisfies HIF512=1.26187 mm; HIF512/HOI=0.43016; HIF512=2.13468 mm; HIF512/HOI=0.72769, where HIF512 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, and HIF522 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=3.68765 mm; f/HEP=2.05; and HAF=38 and tan(HAF)=0.7813, 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 f1=3.65523 mm; |f/f1|=1.0089; f5=−2.41708; and |f1|&gt;f5, where f1 is a focal length of the first lens  110 ; and f5 is a focal length of the fifth lens  150 . 
     The first embodiment further satisfies |f2|+|f3|+|f4|=20.3329; |f1|+|f5|=6.0723 and |f2|+|f3|+|f4|&gt;|f1|+|f5|, where f2 is a focal length of the second lens  120 , f3 is a focal length of the third lens  130 , f4 is a focal length of the fourth lens  140 , and f5 is a focal length of the fifth lens  150 . 
     The optical image capturing system  10  of the first embodiment further satisfies ΣPPR=f/f1+f/f3+f/f4=2.70744; ΣNPR=f/f2+f/f5=2.09358; ΣPPR/|ΣNPR|=1.29321; |f/f2|=0.5679; |f/f3|=0.3309; |f/f4|=1.3676; |f/f5|=0.83745; |f/f5|=1.5257, 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=4.48 mm; HOI=2.9335 mm; HOS/HOI=1.5272; HOS/f=1.2149; InS=4.2449 mm; and InS/HOS=0.9475, 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=2.2206 mm and ΣTP/InTL=0.6897, 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 |R1/R2|=0.1749, where R1 is a radius of curvature of the object-side surface  112  of the first lens  110 , and R2 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 (R9−R10)/(R9+R10)=0.6433, where R9 is a radius of curvature of the object-side surface  152  of the fifth lens  150 , and R10 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=f1+f3+f4=17.49479 and f1/(f1+f3+f4)=0.20893, 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 first lens  110  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=f2+f5=−8.91038 mm; and f5/(f2+f5)=0.27127, where f2 is a focal length of the second lens  120 , f5 is a focal length of the fifth lens  150 , and 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 avoid the significant aberration caused by the incident rays. 
     The optical image capturing system  10  of the first embodiment further satisfies IN12=0.0384098 mm and IN12/f=0.01042, where IN12 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 IN45=0.158316 mm; IN45/f=0.04293, where IN45 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 TP1=0.61326 mm; TP2=0.3 mm; TP3=0.33333 mm; and (TP1+IN12)/TP2=2.17223, where TP1 is a central thickness of the first lens  110  on the optical axis, TP2 is a central thickness of the second lens  120  on the optical axis, and TP3 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 TP4=0.47195 mm; TP5=0.50210 mm; and (TP5+IN45)/TP4=1.39935, where TP4 is a central thickness of the fourth lens  140  on the optical axis, TP5 is a central thickness of the fifth lens  150  on the optical axis, and IN45 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 TP2/TP3=0.90002; TP3/TP4=0.70628; TP4/TP5=0.93995; and TP3/(IN23+TP3+IN34)=0.64903, where IN34 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 InRS41=−0.3851 mm; InRS42=−0.586478 mm; |InRS41|/TP4=0.81598 and |InRS42|/TP4=1.24267, where InRS41 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; InRS42 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 TP4 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. 
     For the optical image capturing system  10  of the first embodiment, HVT41 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 HVT42 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 InRS51=−0.204125 mm; InRS52=−0.111733 mm; |InRS51|/TP5=0.40654 and |InRS52|/TP5=0.22253, where InRS51 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; InRS52 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 TP5 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 HVT51=0.512995 mm; HVT52=1.30753 mm; and HVT51/HVT52=0.3923, where HVT51 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 HVT52 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 HVT52/HOI=0.4457. 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 HVT52/HOS=0.2919. It is helpful for correction of the aberration of the peripheral view field of the optical image capturing system. 
     The second lens  120 , 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 NA5/NA3=1, where NA3 is an Abbe number of the third lens  130 ; and NA5 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|=0.639157%; |ODT|=2.52459%, 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 0.002 mm (the pixel size is 1.12 μm); 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 0.002 mm (the pixel size is 1.12 μm); 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 0.003 mm (the pixel size is 1.12 μm); 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 −0.003 mm (the pixel size is 1.12 μm); 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 −0.004 mm (the pixel size is 1.12 μm); 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 0.004 mm (the pixel size is 1.12 μm). 
     The parameters of the lenses of the first embodiment are listed in Table 1 and Table 2. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 f = 3.68765 mm; f/HEP = 2.05; HAF = 38 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 plane 
                   
                   
                   
                   
               
               
                 1 
                 Aperture/ 
                 1.66171 
                 0.613259 
                 Plastic 
                 1.5346 
                 56.07 
                 3.65523 
               
               
                   
                 1 st  lens 
               
               
                 2 
                   
                 9.5 
                 0.03841 
               
               
                 3 
                 2nd lens 
                 4.4103 
                 0.3 
                 Plastic 
                 1.6425 
                 22.465 
                 −6.4933 
               
               
                 4 
                   
                 2.09511 
                 0.3 
               
               
                 5 
                 3 rd  lens 
                 2.56592 
                 0.333326 
                 Plastic 
                 1.5346 
                 56.07 
                 11.1432 
               
               
                 6 
                   
                 4.29241 
                 0.502411 
               
               
                 7 
                 4 th  lens 
                 −2.11857 
                 0.471949 
                 Plastic 
                 1.5346 
                 56.07 
                 2.69636 
               
               
                 8 
                   
                 −0.92632 
                 0.158316 
               
               
                 9 
                 5 th  lens 
                 4.44003 
                 0.502104 
                 Plastic 
                 1.5346 
                 56.07 
                 −2.41708 
               
               
                 10 
                   
                 0.96379 
                 0.3 
               
               
                 11 
                 Infrared 
                 plane 
                 0.21 
                 BK7_SCH 
               
               
                   
                 rays filter 
               
               
                 12 
                   
                 plane 
                 0.75168 
               
               
                 13 
                 Image 
                 plane 
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; position of blocking light: blocking at the first surface with effective semi diameter of 1.8 mm; blocking at the fourth surface with effective semi diameter of 1.7 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k 
                 −5.756495 
                 −37.40291 
                 −108.1256 
                 −10.028056 
                 −21.141348 
                 10.107969 
                 1.254233 
               
               
                 A4 
                 1.38781E−01 
                 −2.38325E−01 
                 −1.20457E−01 
                 −9.87212E−03 
                 −7.40825E−03 
                 −6.56951E−02 
                 2.04125E−01 
               
               
                 A6 
                 −9.83402E−02  
                  6.48730E−01 
                  5.22423E−01 
                  2.85381E−01 
                 −1.42045E−01 
                 −8.49780E−02 
                 −6.07873E−01  
               
               
                 A8 
                 1.48089E−02 
                 −7.05647E−01 
                 −3.87104E−01 
                 −3.14387E−01 
                 −2.18016E−01 
                 −1.53175E−01 
                 2.13933E+00 
               
               
                 A10 
                 1.15374E−01 
                 −8.69580E−01 
                 −1.10771E+00 
                  1.71061E−01 
                  1.13457E+00 
                  4.25743E−01 
                 −5.07032E+00  
               
               
                 A12 
                 −3.13777E−01  
                  2.52433E+00 
                  2.35677E+00 
                 −1.72845E−01 
                 −1.93816E+00 
                 −5.41369E−01 
                 7.73531E+00 
               
               
                 A14 
                 3.46750E−01 
                 −2.06008E+00 
                 −1.64576E+00 
                  3.16095E−01 
                  1.52237E+00 
                  3.20124E−01 
                 −7.50886E+00  
               
               
                 A16 
                 −2.20591E−01  
                  5.87851E−01 
                  4.02589E−01 
                 −1.66614E−01 
                 −4.32668E−01 
                 −6.06884E−02 
                 4.44245E+00 
               
               
                 A18 
                 5.85201E−02 
                   
                   
                   
                   
                   
                 −1.44931E+00  
               
               
                 A20 
                   
                   
                   
                   
                   
                   
                 1.98717E−01 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Surface 
                 8 
                 9 
                 10 
               
               
                   
                   
               
               
                   
                 k 
                 −3.050304 
                   −8.22E+01 
                   −6.12E+00 
               
               
                   
                 A4 
                 −2.73876E−02 
                 −1.99350E−01 
                 −1.38370E−01 
               
               
                   
                 A6 
                 −1.42715E−01 
                  1.72190E−01 
                  1.04610E−01 
               
               
                   
                 A8 
                  5.28787E−01 
                 −1.52610E−01 
                 −6.87850E−02 
               
               
                   
                 A10 
                 −8.67084E−01 
                  1.07920E−01 
                  3.27680E−02 
               
               
                   
                 A12 
                  8.78194E−01 
                 −4.86280E−02 
                 −1.09030E−02 
               
               
                   
                 A14 
                 −5.28366E−01 
                  1.35410E−02 
                  2.45390E−03 
               
               
                   
                 A16 
                  1.79522E−01 
                 −2.27510E−03 
                 −3.55330E−04 
               
               
                   
                 A18 
                 −3.14470E−02 
                  2.12210E−04 
                  2.98290E−05 
               
               
                   
                 A20 
                  2.16525E−03 
                 −8.45910E−06 
                 −1.09730E−06 
               
               
                   
                   
               
            
           
         
       
     
     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/ 
                   
                 ARE/ 
               
               
                 ARE 
                 ½(HEP) 
                 value 
                 ½(HEP) 
                 HEP) % 
                 TP 
                 TP (%) 
               
               
                   
               
               
                 11 
                 0.899 
                 0.937 
                 0.038 
                 104.23% 
                 0.613 
                 152.86% 
               
               
                 12 
                 0.899 
                 0.902 
                 0.002 
                 100.24% 
                 0.613 
                 147.02% 
               
               
                 21 
                 0.899 
                 0.902 
                 0.003 
                 100.28% 
                 0.300 
                 300.66% 
               
               
                 22 
                 0.899 
                 0.933 
                 0.034 
                 103.75% 
                 0.300 
                 311.04% 
               
               
                 31 
                 0.899 
                 0.902 
                 0.003 
                 100.28% 
                 0.333 
                 270.59% 
               
               
                 32 
                 0.899 
                 0.902 
                 0.002 
                 100.23% 
                 0.333 
                 270.46% 
               
               
                 41 
                 0.899 
                 0.916 
                 0.016 
                 101.81% 
                 0.472 
                 194.03% 
               
               
                 42 
                 0.899 
                 0.971 
                 0.071 
                 107.93% 
                 0.472 
                 205.69% 
               
               
                 51 
                 0.899 
                 0.901 
                 0.002 
                 100.18% 
                 0.502 
                 179.46% 
               
               
                 52 
                 0.899 
                 0.922 
                 0.023 
                 102.55% 
                 0.502 
                 183.69% 
               
               
                   
               
               
                   
                   
                 ARS 
                 ARS − 
                 (ARS/ 
                   
                 ARS/ 
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 EHD)% 
                 TP 
                 TP (%) 
               
               
                   
               
               
                 11 
                 0.899 
                 0.937 
                 0.038 
                 104.23% 
                 0.613 
                 152.86% 
               
               
                 12 
                 0.969 
                 0.975 
                 0.006 
                 100.63% 
                 0.613 
                 159.05% 
               
               
                 21 
                 0.990 
                 0.994 
                 0.004 
                 100.39% 
                 0.300 
                 331.23% 
               
               
                 22 
                 0.979 
                 1.030 
                 0.051 
                 105.25% 
                 0.300 
                 343.39% 
               
               
                 31 
                 1.084 
                 1.089 
                 0.005 
                 100.48% 
                 0.333 
                 326.80% 
               
               
                 32 
                 1.147 
                 1.158 
                 0.011 
                 100.99% 
                 0.333 
                 347.48% 
               
               
                 41 
                 1.277 
                 1.363 
                 0.086 
                 106.77% 
                 0.472 
                 288.81% 
               
               
                 42 
                 1.534 
                 1.656 
                 0.123 
                 107.99% 
                 0.472 
                 350.93% 
               
               
                 51 
                 2.107 
                 2.135 
                 0.029 
                 101.36% 
                 0.502 
                 425.30% 
               
               
                 52 
                 2.348 
                 2.447 
                 0.099 
                 104.20% 
                 0.502 
                 487.30% 
               
               
                   
               
            
           
         
       
     
     The detail parameters of the first embodiment are listed in Table 1, in which the unit of 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, an aperture  200 , a first lens  210 , a second lens  220 , a third lens  230 , 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 positive 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 image-side surface  214  has an inflection point thereon. 
     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 convex 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 thereon. 
     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 concave aspheric surface. The image-side surface  234  has an inflection point. 
     The fourth lens  240  has positive refractive power, and is made of plastic. An object-side surface  242 , which faces the object side, is a convex aspheric surface, and an image-side surface  244 , which faces the image side, is a convex aspheric surface. The object-side surface  242  and the image-side surface  244  both have an inflection point. 
     The fifth lens  250  has negative refractive power, and is made of plastic. An object-side surface  252 , which faces the object side, is a concave surface, and an image-side surface  254 , 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  252  and the image-side surface  254  both have 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 |f2|+|f3|+|f4|=30.2470 mm; |f1|+|f5|=10.0680 mm; and |f2|+|f3|+|f4|&gt;|f1|+|f5|, where f2 is a focal length of the second lens  220 , f3 is a focal length of the third lens  230 , f4 is a focal length of the fourth lens  240 , and f5 is a focal length of the fifth lens  250 . 
     In the second embodiment, the first lens  210 , the third lens  230 , and the fourth lens  240  are positive lenses, and their focal lengths are f1, f3, and f4. The optical image capturing system of the second embodiment further satisfies ΣPP=f1+f3+f4=23.85400 mm; and f1/(f1+f4+f5)=0.27115, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  210  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the second embodiment further satisfies ΣNP=f2+f5=−16.46100 mm; and f5/(f2+f5)=0.21870, where f2 is a focal length of the second lens  220 , f5 is a focal length of the fifth lens  250 , and ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the fifth lens  250  to the other negative lens. 
     The parameters of the lenses of the second embodiment are listed in Table 3 and Table 4. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 f = 4.7290 mm; f/HEP = 1.4; HAF = 38 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 plane 
                 −0.697 
               
               
                 2 
                 1 st  lens 
                 2.232848064 
                 0.739 
                 Plastic 
                 1.565 
                 58.00 
                 6.468 
               
               
                 3 
                   
                 5.028687584 
                 0.661 
               
               
                 4 
                 2 nd  lens 
                 12.06855267 
                 0.233 
                 Plastic 
                 1.632 
                 23.40 
                 −12.861 
               
               
                 5 
                   
                 4.842481422 
                 0.057 
               
               
                 6 
                 3 rd  lens 
                 4.254871892 
                 0.650 
                 Plastic 
                 1.565 
                 58.00 
                 13.716 
               
               
                 7 
                   
                 8.879887183 
                 0.451 
               
               
                 8 
                 4 th  lens 
                 19.884118 
                 0.871 
                 Plastic 
                 1.632 
                 23.40 
                 3.670 
               
               
                 9 
                   
                 −2.603638355 
                 0.627 
               
               
                 10 
                 5 th  lens 
                 −2.736680111 
                 0.395 
                 Plastic 
                 1.607 
                 26.60 
                 −3.600 
               
               
                 11 
                   
                 11.82424296 
                 0.500 
               
               
                 12 
                 Infrared 
                 plane 
                 0.200 
                   
                 1.517 
                 64.13 
               
               
                   
                 rays filter 
               
               
                 13 
                   
                 plane 
                 0.616 
               
               
                 14 
                 Image 
                 plane 
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; position of blocking light: blocking at the fourth surface with effective semi diameter of 1.45 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                 −3.784543E−01  
                  4.278908E+00 
                 −2.568723E+01 
                 −3.179905E−01  
                 −1.333417E+01 
                 −4.380684E+01 
                  5.000000E+01 
               
               
                 A4 
                 1.858348E−03 
                 −7.552209E−04 
                 −1.162374E−02 
                 −1.349513E−02  
                 −1.351083E−02 
                 −1.671490E−02 
                  2.789542E−03 
               
               
                 A6 
                 4.320958E−03 
                 −2.642594E−03 
                 −8.580818E−03 
                 −1.739171E−03  
                  2.612062E−03 
                 −8.859523E−03 
                 −3.785614E−03 
               
               
                 A8 
                 −1.667584E−03  
                  2.553922E−04 
                 −1.398973E−03 
                 1.283871E−04 
                 −3.627635E−05 
                 −8.227024E−04 
                 −2.332744E−03 
               
               
                 A10 
                 2.397413E−04 
                 −4.166299E−06 
                  2.098229E−04 
                 1.638794E−04 
                 −8.533857E−05 
                  1.697300E−04 
                 −2.158309E−04 
               
               
                 A12 
                 1.572405E−04 
                 −2.384406E−05 
                  1.481413E−04 
                 3.745783E−05 
                 −6.435772E−06 
                  9.895643E−05 
                 −1.184346E−04 
               
               
                 A14 
                 −3.466209E−05  
                 −8.073829E−06 
                 −4.418428E−06 
                 6.275187E−05 
                  3.163929E−05 
                 −2.789651E−05 
                 −3.397791E−05 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Surface 
                 9 
                 10 
                 11 
               
               
                   
                   
               
               
                   
                 k 
                 −1.139048E+00 
                  3.642438E−01 
                 2.411216 
               
               
                   
                 A4 
                  2.462291E−02 
                 −4.765751E−03 
                 −2.66161E−02 
               
               
                   
                 A6 
                 −2.097541E−03 
                 −2.828003E−03 
                  1.55028E−03 
               
               
                   
                 A8 
                 −6.757196E−04 
                 −2.932639E−04 
                 −2.05990E−05 
               
               
                   
                 A10 
                 −3.295513E−04 
                  1.289687E−04 
                 −7.40315E−06 
               
               
                   
                 A12 
                 −1.507594E−04 
                  3.652351E−05 
                 −4.28619E−08 
               
               
                   
                 A14 
                  5.245853E−05 
                 −1.413866E−06 
                  2.77429E−08 
               
               
                   
                   
               
            
           
         
       
     
     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| 
               
               
                   
               
               
                 0.73114 
                 0.36770 
                 0.34478 
                 1.28856 
                 1.31361 
                 0.50292 
               
               
                   
               
               
                   
                   
                 ΣPPR/ 
               
               
                 ΣPPR 
                 ΣNPR 
                 |ΣNPR| 
                 IN12/f 
                 IN45/f 
                 |f2/f3| 
               
               
                   
               
               
                 2.36447 
                 1.68131 
                 1.40633 
                 0.13978 
                 0.13259 
                 0.93766 
               
               
                   
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                   
               
               
                 0.56131 
                 6.00858 
                 1.17336 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 |ODT|% 
                 |TDT|% 
               
               
                   
               
               
                 6.00000 
                 4.68400 
                 1.60428 
                 0.88383 
                 2.002 
                 1.152 
               
               
                   
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                   
               
               
                 1.07600 
                 0.00000 
                 0.00000 
                 0.93100 
                 0.00000 
                 0.00000 
               
               
                   
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                   
               
               
                 0.35846 
                 0.74627 
                 −1.183 
                 −0.763 
                 2.99494 
                 1.93165 
               
               
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                   
               
               
                 0.023 mm 
                 0.008 mm 
                 0.022 mm 
                 −0.001 mm 
                 0.012 mm 
                 0.005 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/ 
                   
                 ARE/ 
               
               
                 ARE 
                 ½(HEP) 
                 value 
                 ½(HEP) 
                 HEP) % 
                 TP 
                 TP (%) 
               
               
                   
               
               
                 11 
                 1.689 
                 1.926 
                 0.238 
                 114.06% 
                 0.739 
                 260.79% 
               
               
                 12 
                 1.610 
                 1.635 
                 0.025 
                 101.53% 
                 0.739 
                 221.29% 
               
               
                 21 
                 1.450 
                 1.458 
                 0.008 
                 100.53% 
                 0.233 
                 624.39% 
               
               
                 22 
                 1.553 
                 1.571 
                 0.018 
                 101.16% 
                 0.233 
                 672.78% 
               
               
                 31 
                 1.620 
                 1.635 
                 0.014 
                 100.89% 
                 0.650 
                 251.61% 
               
               
                 32 
                 1.689 
                 1.752 
                 0.064 
                 103.77% 
                 0.650 
                 269.73% 
               
               
                 41 
                 1.689 
                 1.816 
                 0.127 
                 107.53% 
                 0.871 
                 208.51% 
               
               
                 42 
                 1.689 
                 1.784 
                 0.096 
                 105.66% 
                 0.871 
                 204.88% 
               
               
                 51 
                 1.689 
                 1.882 
                 0.193 
                 111.41% 
                 0.395 
                 476.45% 
               
               
                 52 
                 1.689 
                 1.694 
                 0.005 
                 100.29% 
                 0.395 
                 428.91% 
               
               
                   
               
               
                   
                   
                 ARS 
                 ARS − 
                 (ARS/ 
                   
                 ARS/ 
               
               
                 ARS 
                 EHD 
                 value 
                 EHD 
                 EHD)% 
                 TP 
                 TP (%) 
               
               
                   
               
               
                 11 
                 1.690 
                 1.930 
                 0.239 
                 114.14% 
                 0.739 
                 261.22% 
               
               
                 12 
                 1.610 
                 1.635 
                 0.025 
                 101.53% 
                 0.739 
                 221.29% 
               
               
                 21 
                 1.450 
                 1.458 
                 0.008 
                 100.53% 
                 0.233 
                 624.39% 
               
               
                 22 
                 1.553 
                 1.571 
                 0.018 
                 101.16% 
                 0.233 
                 672.78% 
               
               
                 31 
                 1.620 
                 1.635 
                 0.014 
                 100.89% 
                 0.650 
                 251.61% 
               
               
                 32 
                 1.696 
                 1.764 
                 0.067 
                 103.97% 
                 0.650 
                 271.47% 
               
               
                 41 
                 1.712 
                 1.870 
                 0.158 
                 109.24% 
                 0.871 
                 214.73% 
               
               
                 42 
                 2.007 
                 2.204 
                 0.196 
                 109.77% 
                 0.871 
                 253.01% 
               
               
                 51 
                 2.197 
                 2.589 
                 0.392 
                 117.86% 
                 0.395 
                 655.57% 
               
               
                 52 
                 2.774 
                 2.799 
                 0.025 
                 100.92% 
                 0.395 
                 708.80% 
               
               
                   
               
            
           
         
       
     
     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) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF121 
                 1.43300 
                 HIF121/HOI 
                 0.38316 
                 SGI121 
                 0.20800 
                 |SGI121|/(|SGI121| + TP1) 
                 0.21964 
               
               
                 HIF211 
                 0.57400 
                 HIF211/HOI 
                 0.15348 
                 SGI211 
                 0.01200 
                 |SGI211|/(|SGI211| + TP2) 
                 0.04898 
               
               
                 HIF321 
                 0.55700 
                 HIF321/HOI 
                 0.14893 
                 SGI321 
                 0.01500 
                 |SGI321|/(|SGI321| + TP3) 
                 0.46147 
               
               
                 HIF411 
                 0.78300 
                 HIF411/HOI 
                 0.20936 
                 SGI411 
                 0.01600 
                 |SGI411|/(|SGI411| + TP4) 
                 0.01804 
               
               
                 HIF421 
                 1.83600 
                 HIF421/HOI 
                 0.49091 
                 SGI421 
                 −0.62900 
                 |SGI421|/(|SGI421| + TP4) 
                 0.41933 
               
               
                 HIF511 
                 1.84800 
                 HIF511/HOI 
                 0.49412 
                 SGI511 
                 −0.87100 
                 |SGI511|/(|SGI511| + TP5) 
                 0.68799 
               
               
                 HIF521 
                 0.52800 
                 HIF521/HOI 
                 0.14118 
                 SGI521 
                 0.01000 
                 |SGI521|/(|SGI521| + TP5) 
                 0.02469 
               
               
                   
               
            
           
         
       
     
     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, an aperture  300 , a first lens  310 , a second lens  320 , a third lens  330 , 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 positive 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 thereon, and the image-side surface  324  has two inflection points. 
     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 convex aspheric surface. The object-side surface  332  has two inflection points, and the image-side surface  334  has an inflection point. 
     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 concave aspheric surface, and an image-side surface  344 , which faces the image side, is a convex aspheric surface. The object-side surface  342  and the image-side surface  344  both have 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  and the image-side surface  354  both have 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 |f2|+|f3|+|f4|=66.4260 mm; |f1|+|f5|=8.4060 mm; and |f2|+|f3|+|f4|&gt;|f1|+|f5|, where f2 is a focal length of the second lens  320 , f3 is a focal length of the third lens  330 , f4 is a focal length of the fourth lens  340 , and f5 is a focal length of the fifth lens  350 . 
     In the third embodiment, the first lens  310 , the third lens  330 , and the fourth lenses  340  are positive lenses, and their focal lengths are f1, f3, and f4. The optical image capturing system of the third embodiment further satisfies ΣPP=f1+f3+f4=27.25000 mm; and f1/(f1+f3+f4)=0.23927, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  310  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the third embodiment further satisfies ΣNP=f245=−47.58200 mm; and f5/(f2+f5)=0.03964, where f2 is a focal length of the second lens  320 , f5 is a focal length of the fifth lens  350 , and ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the fifth lens  350  to the other negative lens. 
     The parameters of the lenses of the third embodiment are listed in Table 5 and Table 6. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 f = 4.215 mm; f/HEP = 1.4; HAF = 41.001 deg; 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 plane 
                 −0.687 
               
               
                 2 
                 1 st  lens 
                 2.107858171 
                 0.641 
                 Plastic 
                 1.565 
                 58.00 
                 6.520 
               
               
                 3 
                   
                 4.367280319 
                 0.588 
               
               
                 4 
                 2 nd  lens 
                 2.473705396 
                 0.200 
                 Plastic 
                 1.650 
                 21.40 
                 −45.696 
               
               
                 5 
                   
                 2.211841597 
                 0.240 
               
               
                 6 
                 3 rd  lens 
                 12.72336466 
                 0.459 
                 Plastic 
                 1.607 
                 26.60 
                 18.781 
               
               
                 7 
                   
                 −115.5951023 
                 0.328 
               
               
                 8 
                 4 th  lens 
                 −6.85096174 
                 1.056 
                 Plastic 
                 1.565 
                 58.00 
                 1.949 
               
               
                 9 
                   
                 −1.004506893 
                 0.050 
               
               
                 10 
                 5 th  lens 
                 8.497823382 
                 0.487 
                 Plastic 
                 1.607 
                 26.60 
                 −1.886 
               
               
                 11 
                   
                 0.992971286 
                 0.500 
               
               
                 12 
                 Infrared 
                 plane 
                 0.200 
                   
                 1.517 
                 64.13 
               
               
                   
                 rays 
               
               
                   
                 filter 
               
               
                 13 
                   
                 plane 
                 0.911 
               
               
                 14 
                 Image 
                 plane 
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; 
               
               
                 position of blocking light: blocking at the fourth surface with effective semi diameter of 1.300 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                 5.830556E−01 
                 3.712910E+00 
                 −6.501147E+00 
                 −1.394533E+00 
                 −9.280279E+00 
                 −5.000000E+01 
                 −4.801895E+01 
               
               
                 A4 
                 −1.070256E−02 
                 −7.838198E−03 
                 −3.172762E−02 
                 −5.387515E−02 
                 −3.164638E−02 
                 −2.452898E−02 
                 1.085675E−02 
               
               
                 A6 
                 4.253747E−03 
                 −2.806486E−03 
                 −2.314911E−02 
                 −6.561042E−03 
                 3.181452E−03 
                 −1.729713E−02 
                 −1.189420E−02 
               
               
                 A8 
                 −3.713903E−03 
                 4.001564E−03 
                 −3.023000E−03 
                 −1.428945E−03 
                 7.749236E−05 
                 2.644143E−03 
                 −3.513299E−03 
               
               
                 A10 
                 1.165929E−03 
                 −1.724823E−03 
                 −2.085009E−04 
                 2.183710E−03 
                 1.015903E−03 
                 −1.295418E−05 
                 1.106739E−03 
               
               
                 A12 
                 −1.931507E−04 
                 1.157773E−04 
                 −7.055315E−04 
                 −1.139975E−04 
                 3.414263E−04 
                 −1.597281E−04 
                 4.833231E−04 
               
               
                 A14 
                 −1.220784E−06 
                 7.657999E−05 
                 6.982472E−04 
                 8.224819E−05 
                 −1.010114E−04 
                 2.641922E−04 
                 −1.015426E−04 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 9 
                 10 
                 11 
               
               
                   
                   
               
               
                   
                 k 
                 −5.058414E+00 
                 −4.549012E+01 
                 −7.579484E+00 
               
               
                   
                 A4 
                 −2.637122E−02 
                 −5.595745E−02 
                 −3.757511E−02 
               
               
                   
                 A6 
                 2.898145E−03 
                 −3.022457E−03 
                 5.329524E−03 
               
               
                   
                 A8 
                 2.940576E−04 
                 2.536217E−03 
                 −5.263819E−04 
               
               
                   
                 A10 
                 −3.652221E−05 
                 −3.611607E−04 
                 −1.204141E−05 
               
               
                   
                 A12 
                 −4.750680E−05 
                 3.801710E−05 
                 5.148148E−06 
               
               
                   
                 A14 
                 1.244993E−05 
                 −2.133418E−05 
                 −4.264678E−07 
               
               
                   
                   
               
            
           
         
       
     
     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| 
               
               
                   
               
               
                 0.64647 
                 0.09224 
                 0.22443 
                 2.16265 
                 2.23489 
                 0.14268 
               
               
                   
               
               
                   
                   
                 ΣPPR/ 
               
               
                 ΣPPR 
                 ΣNPR 
                 |ΣNPR| 
                 IN12/f 
                 IN45/f 
                 |f2/f3| 
               
               
                   
               
               
                 3.03355 
                 2.32713 
                 1.30356 
                 0.13950 
                 0.01186 
                 2.43310 
               
               
                   
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                   
               
               
                 0.44693 
                 6.14500 
                 0.50852 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 |ODT|% 
                 |TDT|% 
               
               
                   
               
               
                 5.66000 
                 4.04900 
                 1.51337 
                 0.87862 
                 2.017 
                 1.091 
               
               
                   
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                   
               
               
                 1.79200 
                 0.00000 
                 0.67500 
                 1.57500 
                 0.18048 
                 0.11926 
               
               
                   
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                   
               
               
                 0.43573 
                 0.43466 
                 −0.911 
                 −0.621 
                 1.87064 
                 1.27515 
               
               
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                   
               
               
                 −0.014 mm 
                 0.005 mm 
                 0.027 mm 
                 −0.025 mm 
                 −0.002 mm 
                 0.019 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 
                 ½(HEP) 
                 value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 ARE/TP (%) 
               
               
                   
               
               
                 11 
                 1.505 
                 1.713 
                 0.208 
                 113.80% 
                 0.641 
                 267.34% 
               
               
                 12 
                 1.431 
                 1.460 
                 0.029 
                 102.02% 
                 0.641 
                 227.87% 
               
               
                 21 
                 1.300 
                 1.317 
                 0.017 
                 101.29% 
                 0.200 
                 658.37% 
               
               
                 22 
                 1.447 
                 1.467 
                 0.020 
                 101.36% 
                 0.200 
                 733.43% 
               
               
                 31 
                 1.505 
                 1.508 
                 0.003 
                 100.19% 
                 0.459 
                 328.64% 
               
               
                 32 
                 1.505 
                 1.535 
                 0.029 
                 101.96% 
                 0.459 
                 334.43% 
               
               
                 41 
                 1.505 
                 1.525 
                 0.020 
                 101.31% 
                 1.056 
                 144.40% 
               
               
                 42 
                 1.505 
                 1.654 
                 0.149 
                 109.90% 
                 1.056 
                 156.64% 
               
               
                 51 
                 1.505 
                 1.537 
                 0.032 
                 102.12% 
                 0.487 
                 315.65% 
               
               
                 52 
                 1.505 
                 1.541 
                 0.036 
                 102.41% 
                 0.487 
                 316.54% 
               
               
                   
               
               
                   
                   
                 ARS 
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 value 
                 ARS − EHD 
                 (ARS/EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 1.505 
                 1.713 
                 0.208 
                 113.80% 
                 0.641 
                 267.34% 
               
               
                 12 
                 1.431 
                 1.460 
                 0.029 
                 102.02% 
                 0.641 
                 227.87% 
               
               
                 21 
                 1.300 
                 1.317 
                 0.017 
                 101.29% 
                 0.200 
                 658.37% 
               
               
                 22 
                 1.447 
                 1.467 
                 0.020 
                 101.36% 
                 0.200 
                 733.43% 
               
               
                 31 
                 1.541 
                 1.545 
                 0.005 
                 100.30% 
                 0.459 
                 336.76% 
               
               
                 32 
                 1.593 
                 1.624 
                 0.031 
                 101.91% 
                 0.459 
                 353.82% 
               
               
                 41 
                 1.846 
                 1.874 
                 0.028 
                 101.52% 
                 1.056 
                 177.45% 
               
               
                 42 
                 1.986 
                 2.233 
                 0.247 
                 112.44% 
                 1.056 
                 211.46% 
               
               
                 51 
                 2.023 
                 2.459 
                 0.436 
                 121.56% 
                 0.487 
                 504.97% 
               
               
                 52 
                 2.768 
                 3.248 
                 0.480 
                 117.36% 
                 0.487 
                 667.01% 
               
               
                   
               
            
           
         
       
     
     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 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF211 
                 0.62000 
                 HIF211/HOI 
                 0.16578 
                 SGI211 
                 0.06600 
                 |SGI211|/(|SGI211| + TP2) 
                 0.24812 
               
               
                 HIF221 
                 0.75200 
                 HIF221/HOI 
                 0.20107 
                 SGI221 
                 0.10800 
                 |SGI221|/(|SGI221| + TP2) 
                 0.35065 
               
               
                 HIF222 
                 1.28700 
                 HIF222/HOI 
                 0.34412 
                 SGI222 
                 0.20200 
                 |SGI222|/(|SGI222| + TP2) 
                 0.50249 
               
               
                 HIF311 
                 0.46500 
                 HIF311/HOI 
                 0.12433 
                 SGI311 
                 0.00700 
                 |SGI311|/(|SGI311| + TP3) 
                 0.01502 
               
               
                 HIF312 
                 1.09000 
                 HIF312/HOI 
                 0.29144 
                 SGI312 
                 0.01000 
                 |SGI312|/(|SGI312| + TP3) 
                 0.02132 
               
               
                 HIF321 
                 1.35400 
                 HIF321/HOI 
                 0.36203 
                 SGI321 
                 −0.15500 
                 |SGI321|/(|SGI321| + TP3) 
                 0.25244 
               
               
                 HIF411 
                 1.49000 
                 HIF411/HOI 
                 0.39840 
                 SGI411 
                 −0.18700 
                 |SGI411|/(|SGI411| + TP4) 
                 0.15044 
               
               
                 HIF421 
                 1.69500 
                 HIF421/HOI 
                 0.45321 
                 SGI421 
                 −0.77200 
                 |SGI421|/(|SGI421| + TP4) 
                 0.42232 
               
               
                 HIF511 
                 0.38900 
                 HIF511/HOI 
                 0.10401 
                 SGI511 
                 0.00700 
                 |SGI511|/(|SGI511| + TP5) 
                 0.01417 
               
               
                 HIF521 
                 0.61800 
                 HIF521/HOI 
                 0.16524 
                 SGI521 
                 0.12800 
                 |SGI521|/(|SGI521| + TP5) 
                 0.20813 
               
               
                   
               
            
           
         
       
     
     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, an aperture  400 , a first lens  410 , 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 positive 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 object-side surface  412  and the image-side surface  414  both have an inflection point. 
     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 concave aspheric surface, and an image-side surface  424  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  422  and the image-side surface  424  respectively 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 concave aspheric surface. The object-side surface  432  and the image-side surface  434  both have an inflection point. 
     The fourth lens  440  has positive 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 convex aspheric surface. The image-side surface  444  has two inflection points. 
     The fifth lens  450  has negative 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 concave surface. It may help to shorten the back focal length to keep small in size. In addition, the object-side surface  452  and the image-side surface  454  both have 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  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 |f2|+|f3|+|f4|=19.5740 mm; |f1|+|f5|=13.3330 mm; and |f2|+|f3|+|f4|&gt;|f1|+|f5|, where f2 is a focal length of the second lens  420 , f3 is a focal length of the third lens  430 , f4 is a focal length of the fourth lens  440 , and f5 is a focal length of the fifth lens  450 . 
     In the fourth embodiment, the first lens  410 , the third lens  430 , and the fourth lenses  440  are positive lenses, and their focal lengths are f1, f3, and f4. The optical image capturing system of the fourth embodiment further satisfies ΣPP=f1+f3+f4=20.31800 mm and f1/(f1+f3+f4)=0.29772, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  410  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the fourth embodiment further satisfies ΣNP=f245=−12.58900 mm, and f5/(f2+f5)=0.57860, where f2 is a focal length of the second lens  420 , f5 is a focal length of the fifth lens  450 , and ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the fifth lens  450  to the other negative lens. 
     The parameters of the lenses of the fourth embodiment are listed in Table 7 and Table 8. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 f = 4.684 mm; f/HEP = 1.6; HAF = 38 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Light 
                 plane 
                 0.000 
               
               
                   
                 barrier 
               
               
                 2 
                 Aperture 
                 plane 
                 −0.229 
               
               
                 3 
                 1 st  lens 
                 2.227945464 
                 0.592 
                 Plastic 
                 1.565 
                 58.00 
                 6.049 
               
               
                 4 
                   
                 5.750957203 
                 0.334 
               
               
                 5 
                 2 nd  lens 
                 −1.398076791 
                 0.200 
                 Plastic 
                 1.632 
                 23.40 
                 −5.305 
               
               
                 6 
                   
                 −2.517640671 
                 0.050 
               
               
                 7 
                 3 rd  lens 
                 1.635304546 
                 0.518 
                 Plastic 
                 1.565 
                 58.00 
                 4.844 
               
               
                 8 
                   
                 3.580596971 
                 0.807 
               
               
                 9 
                 4 th  lens 
                 −7.613832378 
                 0.358 
                 Plastic 
                 1.565 
                 58.00 
                 9.425 
               
               
                 10 
                   
                 −3.192689176 
                 0.759 
               
               
                 11 
                 5 th  lens 
                 2.8468201 
                 0.553 
                 Plastic 
                 1.530 
                 55.80 
                 −7.284 
               
               
                 12 
                   
                 1.530127437 
                 0.400 
               
               
                 13 
                 Infrared 
                 plane 
                 0.200 
                   
                 1.517 
                 64.13 
               
               
                   
                 rays 
               
               
                   
                 filter 
               
               
                 14 
                   
                 plane 
                 0.889 
               
               
                 16 
                 Image 
                 plane 
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; 
               
               
                 position of blocking light: blocking at the first surface with effective semi diameter of 1.400 mm; 
               
               
                 blocking at the fifth surface with effective semi diameter of 1.200 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 k 
                 −1.232782E+00 
                 2.128054E+00 
                 −1.195825E+01 
                 −3.128485E+01 
                 −1.049579E+01 
                 2.777743E+00 
                 2.158668E+01 
               
               
                 A4 
                 3.255861E−03 
                 −2.405748E−02 
                 3.342821E−02 
                 4.272929E−02 
                 3.959254E−02 
                 −4.515479E−02 
                 −4.161206E−03 
               
               
                 A6 
                 −4.099186E−03 
                 −3.209015E−02 
                 −3.127519E−03 
                 2.771634E−02 
                 −2.424518E−02 
                 1.288952E−02 
                 1.377771E−02 
               
               
                 A8 
                 −3.573271E−03 
                 1.015094E−02 
                 1.426844E−02 
                 1.799014E−03 
                 5.346692E−03 
                 −1.856368E−02 
                 −5.815097E−03 
               
               
                 A10 
                 1.400447E−03 
                 6.377118E−03 
                 −4.195191E−03 
                 −1.586526E−03 
                 −1.803348E−03 
                 6.219327E−03 
                 6.207399E−04 
               
               
                 A12 
                 −1.675061E−03 
                 −5.967127E−03 
                 −3.657407E−03 
                 −6.713441E−03 
                 1.391711E−03 
                 −9.279403E−04 
                 5.047959E−04 
               
               
                 A14 
                 2.800297E−04 
                 1.136842E−03 
                 1.338820E−03 
                 2.316695E−03 
                 −5.970768E−04 
                 −1.449320E−04 
                 −3.037476E−04 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 10 
                 11 
                 12 
               
               
                   
                   
               
               
                   
                 k 
                 −1.496856E+00 
                 −1.133905E−01 
                 −5.701014E+00 
               
               
                   
                 A4 
                 −4.179823E−02 
                 −2.328204E−01 
                 −8.643635E−02 
               
               
                   
                 A6 
                 3.031237E−02 
                 6.772130E−02 
                 2.169130E−02 
               
               
                   
                 A8 
                 −6.745533E−03 
                 −1.322223E−02 
                 −3.252516E−03 
               
               
                   
                 A10 
                 7.035514E−04 
                 −5.582678E−04 
                 −4.613532E−05 
               
               
                   
                 A12 
                 3.112372E−04 
                 7.028594E−04 
                 6.904817E−05 
               
               
                   
                 A14 
                 −1.169583E−04 
                 −1.032838E−04 
                 −6.086708E−06 
               
               
                   
                   
               
            
           
         
       
     
     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| 
               
               
                   
               
               
                 0.77434 
                 0.88294 
                 0.96697 
                 0.49698 
                 0.64305 
                 1.14025 
               
               
                   
               
               
                   
                   
                 ΣPPR/ 
               
               
                 ΣPPR 
                 ΣNPR 
                 |ΣNPR| 
                 IN12/f 
                 IN45/f 
                 |f2/f3| 
               
               
                   
               
               
                 2.23829 
                 1.52599 
                 1.46677 
                 0.07131 
                 0.16204 
                 1.09517 
               
               
                   
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                   
               
               
                 0.37673 
                 4.63000 
                 3.66480 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 |ODT|% 
                 |TDT|% 
               
               
                   
               
               
                 5.66000 
                 4.17100 
                 1.51337 
                 0.95972 
                 2.036 
                 1.057 
               
               
                   
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                   
               
               
                 0.00000 
                 0.00000 
                 0.68800 
                 1.25700 
                 0.18396 
                 0.12155 
               
               
                   
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                   
               
               
                 0.38610 
                 1.44693 
                 −0.927 
                 −0.84 
                 1.67631 
                 1.51899 
               
               
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                   
               
               
                 −0.002 mm 
                 0.002 mm 
                 0.019 mm 
                 0.019 mm 
                 0.006 mm 
                 0.005 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 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 ARE 
                 ½(HEP) 
                 ARE value 
                 ARE-½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 ARE/TP (%) 
               
               
                   
               
               
                 11 
                 1.339 
                 1.387 
                 0.049 
                 103.65% 
                 0.592 
                 234.43% 
               
               
                 12 
                 1.283 
                 1.286 
                 0.003 
                 100.24% 
                 0.592 
                 217.29% 
               
               
                 21 
                 1.200 
                 1.214 
                 0.014 
                 101.18% 
                 0.200 
                 607.10% 
               
               
                 22 
                 1.264 
                 1.273 
                 0.009 
                 100.73% 
                 0.200 
                 636.62% 
               
               
                 31 
                 1.459 
                 1.501 
                 0.042 
                 102.87% 
                 0.518 
                 289.64% 
               
               
                 32 
                 1.464 
                 1.481 
                 0.017 
                 101.17% 
                 0.518 
                 285.81% 
               
               
                 41 
                 1.464 
                 1.486 
                 0.022 
                 101.49% 
                 0.358 
                 414.95% 
               
               
                 42 
                 1.464 
                 1.507 
                 0.044 
                 102.98% 
                 0.358 
                 421.08% 
               
               
                 51 
                 1.464 
                 1.541 
                 0.077 
                 105.29% 
                 0.553 
                 278.66% 
               
               
                 52 
                 1.464 
                 1.481 
                 0.017 
                 101.17% 
                 0.553 
                 267.76% 
               
               
                   
               
               
                   
                   
                 ARS 
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 value 
                 ARS-EHD 
                 (ARS/EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 1.339 
                 1.387 
                 0.049 
                 103.65% 
                 0.592 
                 234.43% 
               
               
                 12 
                 1.283 
                 1.286 
                 0.003 
                 100.24% 
                 0.592 
                 217.29% 
               
               
                 21 
                 1.200 
                 1.214 
                 0.014 
                 101.18% 
                 0.200 
                 607.10% 
               
               
                 22 
                 1.264 
                 1.273 
                 0.009 
                 100.73% 
                 0.200 
                 636.62% 
               
               
                 31 
                 1.459 
                 1.501 
                 0.042 
                 102.87% 
                 0.518 
                 289.64% 
               
               
                 32 
                 1.537 
                 1.577 
                 0.039 
                 102.55% 
                 0.518 
                 304.27% 
               
               
                 41 
                 1.580 
                 1.659 
                 0.079 
                 105.01% 
                 0.358 
                 463.37% 
               
               
                 42 
                 1.732 
                 1.791 
                 0.059 
                 103.41% 
                 0.358 
                 500.24% 
               
               
                 51 
                 1.877 
                 2.335 
                 0.458 
                 124.39% 
                 0.553 
                 422.15% 
               
               
                 52 
                 2.526 
                 3.037 
                 0.511 
                 120.25% 
                 0.553 
                 549.16% 
               
               
                   
               
            
           
         
       
     
     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) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 1.03600 
                 HIF111/HOI 
                 0.27701 
                 SGI111 
                 0.23200 
                 |SGI111|/(|SGI111| + TP1) 
                 0.28155 
               
               
                 HIF121 
                 0.58300 
                 HIF121/HOI 
                 0.15588 
                 SGI121 
                 0.02600 
                 |SGI121|/(|SGI121| + TP1) 
                 0.04207 
               
               
                 HIF211 
                 0.57800 
                 HIF211/HOI 
                 0.15455 
                 SGI211 
                 −0.08500 
                 |SGI211|/(|SGI211| + TP2) 
                 0.29825 
               
               
                 HIF221 
                 0.45500 
                 HIF221/HOI 
                 0.12166 
                 SGI221 
                 −0.03200 
                 |SGI221|/(|SGI221| + TP2) 
                 0.13793 
               
               
                 HIF311 
                 1.02000 
                 HIF311/HOI 
                 0.27273 
                 SGI311 
                 0.22200 
                 |SGI311|/(|SGI311| + TP3) 
                 0.30000 
               
               
                 HIF321 
                 0.80000 
                 HIF321/HOI 
                 0.21390 
                 SGI321 
                 0.07600 
                 |SGI321|/(|SGI321| + TP3) 
                 0.12795 
               
               
                 HIF421 
                 1.14000 
                 HIF421/HOI 
                 0.30481 
                 SGI421 
                 −0.22000 
                 |SGI421|/(|SGI421| + TP4) 
                 0.38062 
               
               
                 HIF422 
                 1.52700 
                 HIF422/HOI 
                 0.40829 
                 SGI422 
                 −0.34300 
                 |SGI422|/(|SGI422| + TP4) 
                 0.48930 
               
               
                 HIF511 
                 0.37800 
                 HIF511/HOI 
                 0.10107 
                 SGI511 
                 0.02100 
                 |SGI511|/(|SGI511| + TP5) 
                 0.03659 
               
               
                 HIF521 
                 0.59400 
                 HIF521/HOI 
                 0.15882 
                 SGI521 
                 0.09000 
                 |SGI521|/(|SGI521| + TP5) 
                 0.13997 
               
               
                   
               
            
           
         
       
     
     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, an aperture  500 , a first lens  510 , a second lens  520 , 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 positive 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 an inflection point thereon. 
     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 convex aspheric surface. 
     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 concave aspheric surface, and an image-side surface  534 , which faces the image side, is a convex aspheric surface. The image-side surface  534  has two inflection points thereon. 
     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 concave aspheric surface, and an image-side surface  544 , which faces the image side, is a convex aspheric surface. The object-side surface  542  and the image-side surface  544  both have two inflection points. 
     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 convex surface, and an image-side surface  554 , 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  552  and the image-side surface  554  both have 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  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 |f2|+|f3|+|f4|=86.0870 mm; |f1|+|f5|=7.1540 mm; and |f2|+|f3|+|f4|&gt;|f1|+|f5|, where f2 is a focal length of the second lens  520 , f3 is a focal length of the third lens  530 , f4 is a focal length of the fourth lens  540 , and f5 is a focal length of the fifth lens  550 . 
     In the fifth embodiment, the first lens  510 , the third lens  530 , and the fourth lenses  540  are positive lenses, and their focal lengths are f1, f3, and f4. The optical image capturing system of the fifth embodiment further satisfies PP=f1+f3+f4=54.61300 mm; and f1/(f1+f3+f4)=0.08787, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  510  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the fifth embodiment further satisfies ΣNP=f245=−38.62800, and f5/(f2+f5)=0.06097, where f2 is a focal length of the second lens  520 , f5 is a focal length of the fifth lens  550 , and ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the fifth lens  550  to the other negative lens. 
     The parameters of the lenses of the fifth embodiment are listed in Table 9 and Table 10. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 f = 4.20882 mm; f/HEP = 1.6; HAF = 41.0001 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 Tickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 Radius of curvature (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 plane 
                 −0.54109 
               
               
                 2 
                 1 st  lens 
                 1.94778 
                 0.646688 
                 Plastic 
                 1.565 
                 58 
                 4.79873 
               
               
                 3 
                   
                 6.03771 
                 0.808171 
               
               
                 4 
                 2 nd  lens 
                 −4.39423 
                 0.296636 
                 Plastic 
                 1.65 
                 21.4 
                 −36.2728 
               
               
                 5 
                   
                 −5.53463 
                 0.108087 
               
               
                 6 
                 3 rd  lens 
                 −7.53982 
                 0.2 
                 Plastic 
                 1.65 
                 21.4 
                 47.431 
               
               
                 7 
                   
                 −6.13186 
                 0.093294 
               
               
                 8 
                 4 th  lens 
                 −3.80138 
                 1.17407 
                 Plastic 
                 1.565 
                 58 
                 2.38301 
               
               
                 9 
                   
                 −1.1079 
                 0.05 
               
               
                 10 
                 5 th  lens 
                 8.14431 
                 0.630687 
                 Plastic 
                 1.583 
                 30.2 
                 −2.35543 
               
               
                 11 
                   
                 1.14728 
                 0.5 
               
               
                 12 
                 Infrared 
                 plane 
                 0.2 
                   
                 1.517 
                 64.2 
               
               
                   
                 rays 
               
               
                   
                 filter 
               
               
                 13 
                   
                 plane 
                 0.952368 
               
               
                 14 
                 Image 
                 plane 
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; 
               
               
                 position of blocking light: blocking at the fourth surface with effective semi diameter of 1.200 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                 −1.747515 
                 12.497346 
                 6.846206 
                 10.112645 
                 32.701259 
                 14.397738 
                 −4.35146 
               
               
                 A4 
                 2.47064E−02 
                 −9.23431E−05 
                 −6.55236E−02 
                 −5.10135E−02 
                 −2.71571E−02 
                 −6.43261E−03 
                 6.85033E−03 
               
               
                 A6 
                 2.63578E−02 
                 −5.16140E−03 
                 5.68629E−03 
                 −4.25165E−04 
                 −1.72750E−02 
                 −1.19084E−02 
                 8.64035E−03 
               
               
                 A8 
                 −2.14518E−02 
                 2.86506E−03 
                 1.01153E−02 
                 2.02521E−02 
                 −7.56357E−03 
                 3.83696E−04 
                 −1.20470E−03 
               
               
                 A10 
                 5.29933E−03 
                 −3.33368E−03 
                 1.54374E−03 
                 −2.58657E−03 
                 4.58729E−03 
                 4.87453E−04 
                 −4.42725E−05 
               
               
                 A12 
                 4.40566E−03 
                 2.80284E−03 
                 −8.84763E−03 
                 −6.95606E−03 
                 6.12851E−03 
                 2.34424E−03 
                 1.36688E−05 
               
               
                 A14 
                 −1.95481E−03 
                 −1.36893E−03 
                 3.05936E−03 
                 1.23844E−03 
                 −4.10701E−03 
                 −4.32170E−04 
                 −9.47643E−06 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 9 
                 10 
                 11 
               
               
                   
                   
               
               
                   
                 k 
                 −4.039633 
                 −36.35709 
                 −6.835411 
               
               
                   
                 A4 
                 −3.44124E−02 
                 −4.64977E−02 
                 −3.17529E−02 
               
               
                   
                 A6 
                 7.21975E−03 
                 4.81182E−03 
                 5.00275E−03 
               
               
                   
                 A8 
                 7.67209E−04 
                 −1.08376E−04 
                 −5.51816E−04 
               
               
                   
                 A10 
                 1.04280E−04 
                 6.29657E−06 
                 −1.70537E−05 
               
               
                   
                 A12 
                 −4.74733E−05 
                 1.11587E−05 
                 8.26503E−06 
               
               
                   
                 A14 
                 −3.16518E−06 
                 −1.96697E−06 
                 −4.84460E−07 
               
               
                   
                   
               
            
           
         
       
     
     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| 
               
               
                   
               
               
                 0.87810 
                 0.11617 
                 0.08884 
                 1.76836 
                 1.78938 
                 0.13230 
               
               
                   
               
               
                   
                   
                 ΣPPR/ 
               
               
                 ΣPPR 
                 ΣNPR 
                 |ΣNPR| 
                 IN12/f 
                 IN45/f 
                 |f2/f3| 
               
               
                   
               
               
                 2.73530 
                 1.90556 
                 1.43543 
                 0.19174 
                 0.01187 
                 0.76475 
               
               
                   
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                   
               
               
                 0.49875 
                 4.89899 
                 0.58007 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 |ODT|% 
                 |TDT|% 
               
               
                   
               
               
                 5.66000 
                 4.00800 
                 1.51337 
                 0.90442 
                 2.003 
                 0.912 
               
               
                   
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                   
               
               
                 0.00000 
                 0.00000 
                 0.79500 
                 1.75100 
                 0.21257 
                 0.14046 
               
               
                   
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                   
               
               
                 1.48500 
                 0.17036 
                 −0.526 
                 −0.448 
                 0.83360 
                 0.70998 
               
               
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                   
               
               
                 −0.030 mm 
                 0.020 mm 
                 0.023 mm 
                 −0.011 mm 
                 −0.004 mm 
                 0.007 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 
                 ½(HEP) 
                 ARE value 
                 ARE-½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 ARE/TP (%) 
               
               
                   
               
               
                 11 
                 1.317 
                 1.462 
                 0.145 
                 110.98% 
                 0.647 
                 226.00% 
               
               
                 12 
                 1.275 
                 1.283 
                 0.008 
                 100.66% 
                 0.647 
                 198.46% 
               
               
                 21 
                 1.200 
                 1.259 
                 0.059 
                 104.91% 
                 0.297 
                 424.41% 
               
               
                 22 
                 1.295 
                 1.361 
                 0.065 
                 105.05% 
                 0.297 
                 458.72% 
               
               
                 31 
                 1.291 
                 1.402 
                 0.110 
                 108.55% 
                 0.200 
                 700.95% 
               
               
                 32 
                 1.317 
                 1.341 
                 0.024 
                 101.83% 
                 0.200 
                 670.54% 
               
               
                 41 
                 1.317 
                 1.327 
                 0.010 
                 100.74% 
                 1.174 
                 113.00% 
               
               
                 42 
                 1.317 
                 1.437 
                 0.120 
                 109.14% 
                 1.174 
                 122.43% 
               
               
                 51 
                 1.317 
                 1.319 
                 0.002 
                 100.16% 
                 0.631 
                 209.14% 
               
               
                 52 
                 1.317 
                 1.355 
                 0.038 
                 102.90% 
                 0.631 
                 214.86% 
               
               
                   
               
               
                   
                   
                 ARS 
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 value 
                 ARS-EHD 
                 (ARS/EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 1.317 
                 1.462 
                 0.145 
                 110.98% 
                 0.647 
                 226.00% 
               
               
                 12 
                 1.275 
                 1.283 
                 0.008 
                 100.66% 
                 0.647 
                 198.46% 
               
               
                 21 
                 1.200 
                 1.259 
                 0.059 
                 104.91% 
                 0.297 
                 424.41% 
               
               
                 22 
                 1.295 
                 1.361 
                 0.065 
                 105.05% 
                 0.297 
                 458.72% 
               
               
                 31 
                 1.291 
                 1.402 
                 0.110 
                 108.55% 
                 0.200 
                 700.95% 
               
               
                 32 
                 1.507 
                 1.535 
                 0.028 
                 101.85% 
                 0.200 
                 767.52% 
               
               
                 41 
                 1.822 
                 1.833 
                 0.011 
                 100.59% 
                 1.174 
                 156.14% 
               
               
                 42 
                 2.127 
                 2.356 
                 0.228 
                 110.72% 
                 1.174 
                 200.64% 
               
               
                 51 
                 2.462 
                 2.577 
                 0.115 
                 104.67% 
                 0.631 
                 408.56% 
               
               
                 52 
                 3.016 
                 3.376 
                 0.361 
                 111.97% 
                 0.631 
                 535.36% 
               
               
                   
               
            
           
         
       
     
     The results of the equations of the fifth embodiment based on Table 9 and Table 10 are listed in the following table: 
     
       
         
           
               
             
               
                   
               
               
                 Values related to the inflection points of the fifth embodiment 
               
               
                 (Reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF121 
                 1.09800 
                 HIF121/HOI 
                 0.29358 
                 SGI121 
                 0.10600 
                 |SGI121|/(|SGI121| + TP1) 
                 0.14077 
               
               
                 HIF321 
                 1.20100 
                 HIF321/HOI 
                 0.32112 
                 SGI321 
                 −0.17200 
                 |SGI321|/(|SGI321| + TP3) 
                 0.46237 
               
               
                 HIF322 
                 1.49700 
                 HIF322/HOI 
                 0.40027 
                 SGI322 
                 −0.23900 
                 |SGI322|/(|SGI322| + TP3) 
                 0.54442 
               
               
                 HIF411 
                 0.90500 
                 HIF411/HOI 
                 0.24198 
                 SGI411 
                 −0.09400 
                 |SGI411|/(|SGI411| + TP4) 
                 0.07413 
               
               
                 HIF412 
                 1.65100 
                 HIF412/HOI 
                 0.44144 
                 SGI412 
                 −0.16700 
                 |SGI412|/(|SGI412| + TP4) 
                 0.12453 
               
               
                 HIF421 
                 1.28200 
                 HIF421/HOI 
                 0.34278 
                 SGI421 
                 −0.51100 
                 |SGI421|/(|SGI421| + TP4) 
                 0.30326 
               
               
                 HIF422 
                 1.88000 
                 HIF422/HOI 
                 0.50267 
                 SGI422 
                 −0.82200 
                 |SGI422|/(|SGI422| + TP4) 
                 0.41182 
               
               
                 HIF511 
                 0.44600 
                 HIF511/HOI 
                 0.11925 
                 SGI511 
                 0.01000 
                 |SGI511|/(|SGI511| + TP5) 
                 0.01560 
               
               
                 HIF521 
                 0.70000 
                 HIF521/HOI 
                 0.18717 
                 SGI521 
                 0.14600 
                 |SGI521|/(|SGI521| + TP5) 
                 0.18790 
               
               
                   
               
            
           
         
       
     
     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, an aperture  600 , a first lens  610 , a second lens  620 , 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 positive 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 negative 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 concave aspheric surface. The object-side surface  622  and the image-side surface  624  respectively have 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 convex 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 positive refractive power, and is made of plastic. An object-side surface  642 , which faces the object side, is a concave aspheric surface, and an image-side surface  644 , which faces the image side, is a convex aspheric surface. The object-side surface  642  and the image-side surface  644  both have an inflection point. 
     The fifth lens  650  has negative refractive power, and is made of plastic. An object-side surface  652 , which faces the object side, is a convex surface, and an image-side surface  654 , which faces the image side, is a concave surface. The object-side surface  652  and the image-side surface  654  both have 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 |f2|+|f3|+|f4|=26.1024 mm; |f1|+|f5|=10.9792 mm; and |f2|+|f3|+|f4|&gt;|f1|+|f5|, where f2 is a focal length of the second lens  620 , f3 is a focal length of the third lens  630 , f4 is a focal length of the fourth lens  640 , and f5 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 f1, f3, and f4. The optical image capturing system of the sixth embodiment further satisfies ΣPP=f1+244=21.25779 mm; and f1/(f1+f3+f4)=0.35286, where f1 is a focal length of the first lens  610 , f3 is a focal length of the third lens  630 , f4 is a focal length of the fourth lens  640 , and ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  610  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=f2+f5=−15.82380 mm; and f5/(f2+f5)=0.21980, where f2 is a focal length of the second lens  620 , f5 is a focal length of the fifth lens  650 , and ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the fifth lens  650  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 = 4.68853 nm; f/HEP = 1.8; HAF = 38 deg 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 plane 
                 −0.161 
               
               
                 2 
                 1 st  lens 
                 3.01192719 
                 0.733 
                 Plastic 
                 1.565 
                 58.00 
                 7.501 
               
               
                 3 
                   
                 9.421637837 
                 0.507 
               
               
                 4 
                 2 nd  lens 
                 3.43459039 
                 0.354 
                 Plastic 
                 1.650 
                 21.40 
                 −12.346 
               
               
                 5 
                   
                 2.312881196 
                 0.381 
               
               
                 6 
                 3 rd lens 
                 31.28111475 
                 0.939 
                 Plastic 
                 1.565 
                 58.00 
                 10.566 
               
               
                 7 
                   
                 −7.326192096 
                 0.565 
               
               
                 8 
                 4 th  lens 
                 −3.376711742 
                 0.871 
                 Plastic 
                 1.565 
                 58.00 
                 3.191 
               
               
                 9 
                   
                 −1.287601945 
                 0.050 
               
               
                 10 
                 5 th  lens 
                 2.900744957 
                 0.780 
                 Plastic 
                 1.583 
                 30.20 
                 −3.478 
               
               
                 11 
                   
                 1.078636748 
                 0.600 
               
               
                 12 
                 Infrared 
                 plane 
                 0.200 
                   
                 1.517 
                 64.13 
               
               
                   
                 rays 
               
               
                   
                 filter 
               
               
                 13 
                   
                 plane 
                 1.063 
               
               
                 14 
                 Image 
                 plane 
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm; 
               
               
                 position of blocking light: blocking at the first surface with effective semi diameter of 1.8 mm; 
               
               
                 blocking at the fourth surface with effective semi diameter of 1.7 mm. 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                 −4.535402E+00 
                 −2.715541E+01 
                 −1.260125E+01 
                 −5.105631E+00 
                 5.000000E+01 
                 −1.859382E+01 
                 −1.670156E+01 
               
               
                 A4 
                 2.082750E−02 
                 −1.073248E−02 
                 −5.261525E−02 
                 −3.206506E−02 
                 −9.901981E−03 
                 −1.596918E−02 
                 −1.526929E−02 
               
               
                 A6 
                 7.145606E−04 
                 3.186801E−03 
                 −5.093252E−03 
                 −7.282021E−04 
                 7.496969E−04 
                 −3.446354E−03 
                 −3.824708E−04 
               
               
                 A8 
                 −2.543825E−03 
                 −1.975121E−03 
                 −1.592440E−03 
                 1.658718E−03 
                 −4.089758E−05 
                 8.044274E−04 
                 −6.977028E−04 
               
               
                 A10 
                 8.565422E−04 
                 −6.414664E−04 
                 5.578372E−04 
                 −3.523094E−04 
                 8.234584E−05 
                 1.656935E−05 
                 −1.403571E−04 
               
               
                 A12 
                 2.729945E−04 
                 4.532820E−04 
                 2.855392E−04 
                 −1.912872E−04 
                 −4.010367E−04 
                 −1.337763E−04 
                 −1.648954E−05 
               
               
                 A14 
                 −2.170476E−04 
                 −2.132353E−04 
                 −3.628428E−04 
                 4.530383E−05 
                 7.916187E−05 
                 1.688031E−05 
                 1.256451E−05 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 9 
                 10 
                 11 
               
               
                   
                   
               
               
                   
                 k 
                 −3.375565E+00 
                 −1.442939E+01 
                 −4.631718E+00 
               
               
                   
                 A4 
                 −2.365253E−02 
                 −1.723102E−02 
                 −1.698217E−02 
               
               
                   
                 A6 
                 1.681813E−03 
                 −2.048496E−03 
                 8.623572E−04 
               
               
                   
                 A8 
                 −2.547813E−04 
                 3.394994E−05 
                 −7.206398E−05 
               
               
                   
                 A10 
                 −1.681747E−04 
                 5.267951E−05 
                 −2.098743E−08 
               
               
                   
                 A12 
                 −1.593035E−05 
                 8.642871E−06 
                 6.974444E−07 
               
               
                   
                 A14 
                 1.076519E−05 
                 −2.259826E−06 
                 −6.501014E−08 
               
               
                   
                   
               
            
           
         
       
     
     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| 
               
               
                   
               
               
                 0.62505 
                 0.37977 
                 0.44373 
                 1.46946 
                 1.34801 
                 0.60758 
               
               
                   
               
               
                   
                   
                 ΣPPR/ 
               
               
                 ΣPPR 
                 ΣNPR 
                 |ΣNPR| 
                 IN12/f 
                 IN45/f 
                 |f2/f3| 
               
               
                   
               
               
                 2.53825 
                 1.72779 
                 1.46908 
                 0.10804 
                 0.01066 
                 1.16843 
               
               
                   
               
            
           
           
               
               
               
            
               
                 TP3/(IN23 + TP3 + IN34) 
                 (TP1 + IN12)/TP2 
                 (TP5 + IN45)/TP4 
               
               
                   
               
               
                 0.49811 
                 3.50429 
                 0.95237 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 HOS 
                 InTL 
                 HOS/HOI 
                 InS/HOS 
                 |ODT|% 
                 |TDT|% 
               
               
                   
               
               
                 7.04095 
                 5.17843 
                 1.88261 
                 0.97708 
                 2.06837 
                 1.12761 
               
               
                   
               
               
                 HVT41 
                 HVT42 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                   
               
               
                 0.00000 
                 0.00000 
                 1.39547 
                 2.10022 
                 0.37312 
                 0.19819 
               
               
                   
               
               
                 TP2/TP3 
                 TP3/TP4 
                 InRS51 
                 InRS52 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                   
               
               
                 0.37669 
                 1.07753 
                 −0.482666 
                 −0.318016 
                 0.61902 
                 0.40786 
               
               
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                   
               
               
                 0.002 mm 
                 −0.012 mm 
                 0.005 mm 
                 −0.006 mm 
                 0.008 mm 
                 0.001 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 
                 ½(HEP) 
                 ARE value 
                 ARE-½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 ARE/TP (%) 
               
               
                   
               
               
                 11 
                 1.302 
                 1.347 
                 0.045 
                 103.43% 
                 0.733 
                 183.85% 
               
               
                 12 
                 1.302 
                 1.303 
                 0.001 
                 100.06% 
                 0.733 
                 177.87% 
               
               
                 21 
                 1.302 
                 1.313 
                 0.011 
                 100.84% 
                 0.354 
                 371.37% 
               
               
                 22 
                 1.302 
                 1.320 
                 0.017 
                 101.34% 
                 0.354 
                 373.23% 
               
               
                 31 
                 1.302 
                 1.302 
                 −0.0001 
                  99.99% 
                 0.939 
                 138.72% 
               
               
                 32 
                 1.302 
                 1.317 
                 0.015 
                 101.15% 
                 0.939 
                 140.32% 
               
               
                 41 
                 1.302 
                 1.329 
                 0.027 
                 102.05% 
                 0.871 
                 152.56% 
               
               
                 42 
                 1.302 
                 1.426 
                 0.124 
                 109.51% 
                 0.871 
                 163.71% 
               
               
                 51 
                 1.302 
                 1.311 
                 0.008 
                 100.65% 
                 0.780 
                 168.12% 
               
               
                 52 
                 1.302 
                 1.370 
                 0.068 
                 105.18% 
                 0.780 
                 175.69% 
               
               
                   
               
               
                 ARS 
                 EHD 
                 ARS value 
                 ARS-EHD 
                 (ARS/EHD) % 
                 TP 
                 ARS/TP (%) 
               
               
                   
               
               
                 11 
                 1.468 
                 1.528 
                 0.061 
                 104.13% 
                 0.733 
                 208.57% 
               
               
                 12 
                 1.536 
                 1.550 
                 0.014 
                 100.88% 
                 0.733 
                 211.53% 
               
               
                 21 
                 1.521 
                 1.612 
                 0.091 
                 105.95% 
                 0.354 
                 455.85% 
               
               
                 22 
                 1.847 
                 1.880 
                 0.034 
                 101.82% 
                 0.354 
                 531.65% 
               
               
                 31 
                 1.871 
                 1.923 
                 0.052 
                 102.80% 
                 0.939 
                 204.83% 
               
               
                 32 
                 2.055 
                 2.366 
                 0.311 
                 115.15% 
                 0.939 
                 252.05% 
               
               
                 41 
                 2.090 
                 2.367 
                 0.277 
                 113.27% 
                 0.871 
                 271.71% 
               
               
                 42 
                 2.199 
                 2.733 
                 0.534 
                 124.31% 
                 0.871 
                 313.71% 
               
               
                 51 
                 2.517 
                 2.767 
                 0.250 
                 109.93% 
                 0.780 
                 354.84% 
               
               
                 52 
                 3.246 
                 3.742 
                 0.496 
                 115.27% 
                 0.780 
                 479.86% 
               
               
                   
               
            
           
         
       
     
     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 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 1.33860 
                 HIF111/HOI 
                 0.35791 
                 SGI111 
                 0.31505 
                 |SGI111|/(|SGI111| + TP1) 
                 0.30071 
               
               
                 HIF121 
                 0.81088 
                 HIF121/HOI 
                 0.21681 
                 SGI121 
                 0.02919 
                 |SGI121|/(|SGI121| + TP1) 
                 0.03832 
               
               
                 HIF211 
                 0.54056 
                 HIF211/HOI 
                 0.14453 
                 SGI211 
                 0.03523 
                 |SGI211|/(|SGI211| + TP2) 
                 0.09059 
               
               
                 HIF221 
                 0.79896 
                 HIF221/HOI 
                 0.21363 
                 SGI221 
                 0.11126 
                 |SGI221|/(|SGI221| + TP2) 
                 0.23933 
               
               
                 HIF311 
                 0.53885 
                 HIF311/HOI 
                 0.14408 
                 SGI311 
                 0.00384 
                 |SGI311|/(|SGI311| + TP3) 
                 0.00408 
               
               
                 HIF411 
                 1.97823 
                 HIF411/HOI 
                 0.52894 
                 SGI411 
                 −0.76038 
                 |SGI411|/(|SGI411| + TP4) 
                 0.46603 
               
               
                 HIF421 
                 1.95709 
                 HIF421/HOI 
                 0.52329 
                 SGI421 
                 −1.20467 
                 |SGI421|/(|SGI421| + TP4) 
                 0.58031 
               
               
                 HIF511 
                 0.74546 
                 HIF511/HOI 
                 0.19932 
                 SGI511 
                 0.07504 
                 |SGI511|/(|SGI511| + TP5) 
                 0.08779 
               
               
                 HIF521 
                 0.88388 
                 HIF521/HOI 
                 0.23633 
                 SGI521 
                 0.24377 
                 |SGI521|/(|SGI521| + TP5) 
                 0.23817 
               
               
                   
               
            
           
         
       
     
     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.