PATENT ABSTRACT
A five-piece optical lens for capturing image and a five-piece optical module for capturing image, along the optical axis in order from an object side to an image side, include a first lens with positive refractive power having a convex object-side surface; a second lens with refractive power; a third lens with refractive power; a fourth lens with refractive power; and a fifth lens with negative refractive power; and at least one of the image-side surface and object-side surface of each of the five lens elements are aspheric. The optical lens can increase aperture value and improve the imagining quality for use in compact cameras.

PATENT DESCRIPTION
BACKGROUND OF THE INVENTION 
       [0001]    1. Technical Field 
         [0002]    The present invention relates generally to an optical system, and more particularly to a compact optical image capturing system for an electronic device. 
         [0003]    2. Description of Related Art 
         [0004]    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. 
         [0005]    The conventional optical system of the portable electronic device usually has a three or four-piece lens. 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. An optical system with large aperture usually has several problems, such as large aberration, poor image quality at periphery of the image, and hard to manufacture. In addition, an optical system of wide-angle usually has large distortion. Therefore, the conventional optical system provides high optical performance as required. 
         [0006]    It is an important issue to increase the quantity of light entering the lens and the angle of field of the lens. In addition, the modern lens is also asked to have several characters, including high pixels, high image quality, small in size, and high optical performance. 
       BRIEF SUMMARY OF THE INVENTION 
       [0007]    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. 
         [0008]    The term and its definition to the lens parameter in the embodiment of the present are shown as below for further reference. 
         [0009]    The lens parameter related to a length or a height in the lens element: 
         [0010]    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 element to the image-side surface of the fifth lens element is denoted by InTL. A distance from the image-side surface of the fifth lens to the image plane is denoted by InB. InTL+InB=HOS. A distance from the first lens element to the second lens element is denoted by IN 12  (instance). A central thickness of the first lens element of the optical image capturing system on the optical axis is denoted by TP 1  (instance). 
         [0011]    The lens parameter related to a material in the lens: 
         [0012]    An Abbe number of the first lens element in the optical image capturing system is denoted by NA 1  (instance). A refractive index of the first lens element is denoted by Nd 1  (instance). 
         [0013]    The lens parameter related to a view angle in the lens: 
         [0014]    A view angle is denoted by AF. Half of the view angle is denoted by HAF. A major light angle is denoted by MRA. 
         [0015]    The lens parameter related to exit/entrance pupil in the lens 
         [0016]    An entrance pupil diameter of the optical image capturing system is denoted by HEP. 
         [0017]    The lens parameter related to a depth of the lens shape 
         [0018]    A distance in parallel with an optical axis from a maximum effective semi diameter position to an axial point on the object-side surface of the fifth lens is denoted by InRS 51  (instance). A distance in parallel with an optical axis from a maximum effective semi diameter position to an axial point on the image-side surface of the fifth lens is denoted by InRS 52  (instance). 
         [0019]    The lens parameter related to the lens shape: 
         [0020]    A critical point C is a tangent point on a surface of a specific lens, and the tangent point is tangent to a plane perpendicular to the optical axis and the tangent point cannot be a crossover point on the optical axis. To follow the past, a distance perpendicular to the optical axis between a critical point C 41  on the object-side surface of the fourth lens and the optical axis is HVT 41  (instance). A distance perpendicular to the optical axis between a critical point C 51  on the object-side surface of the fifth lens and the optical axis is HVT 51  (instance). A distance perpendicular to the optical axis between a critical point C 52  on the image-side surface of the fifth lens and the optical axis is HVT 52  (instance). The object-side surface of the fifth lens has one inflection point IF 511  which is nearest to the optical axis, and the sinkage value of the inflection point IF 511  is denoted by SGI 511 . A distance perpendicular to the optical axis between the inflection point IF 511  and the optical axis is HIF 511  (instance). The image-side surface of the fifth lens has one inflection point IF 521  which is nearest to the optical axis, and the sinkage value of the inflection point IF 521  is denoted by SGI 521  (instance). A distance perpendicular to the optical axis between the inflection point IF 521  and the optical axis is HIF 521  (instance). The object-side surface of the fifth lens has one inflection point IF 512  which is the second nearest to the optical axis, and the sinkage value of the inflection point IF 512  is denoted by SGI 512  (instance). A distance perpendicular to the optical axis between the inflection point IF 512  and the optical axis is HIF 512  (instance). The image-side surface of the fifth lens has one inflection point IF 522  which is the second nearest to the optical axis, and the sinkage value of the inflection point IF 522  is denoted by SGI 522  (instance). A distance perpendicular to the optical axis between the inflection point IF 522  and the optical axis is HIF 522  (instance). 
         [0021]    The lens element parameter related to an aberration: 
         [0022]    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. 
         [0023]    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. 
         [0024]    The optical image capturing system of the present invention includes a first lens, a second lens, a third lens, a fourth lens, and a fifth lens in order along an optical axis from an object side to an image side. These five lenses have 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: 
         [0000]      1.2 ≦f/HEP≦ 6.0; 0.5≦ HOS/f ≦5.0; 0&lt;Σ| InRS|/InTL≦ 3;
 
         [0025]    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 from an object-side surface of the first lens to the image plane; Σ|InRS| is a sum of InRSO and InRSI, where InRSO is a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the object-side surface to the point at the maximum effective semi diameter of the object-side surface, and InRSI is a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the image-side surface to the point at the maximum effective semi diameter of the image-side surface; and InTL is a distance in parallel with the optical axis between the object-side surface of the first lens and the image-side surface of the fourth lens. 
         [0026]    The present invention further provides an optical image capturing system, including a first lens, a second lens, a third lens, a fourth lens, and a fifth lens in order along an optical axis from an object side to an image side. The first lens has refractive power. The second lens has refractive power, and the third and the fourth lenses have refractive power. The fifth lens has negative refractive power, and both an object-side surface and an image-side surface thereof are aspheric surfaces. The optical image capturing system satisfies: 
         [0000]      1.2 ≦f/HEP≦ 6.0; 0.5≦ HOS/f ≦5.0; 0&lt;Σ| InRS|/InTL≦ 3; | TDT|&lt; 60%; and | ODT|≦ 50%;
 
         [0027]    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; HAF is a half of the view angle of the optical image capturing system; TDT is a TV distortion; ODT is an optical distortion; Σ|InRS| is a sum of InRSO and InRSI, where InRSO is a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the object-side surface to the point at the maximum effective semi diameter of the object-side surface, and InRSI is a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the image-side surface to the point at the maximum effective semi diameter of the image-side surface; and InTL is a distance in parallel with the optical axis between the object-side surface of the first lens and the image-side surface of the fourth lens. 
         [0028]    The present invention further provides an optical image capturing system, including a first lens, a second lens, a third lens, a fourth lens, and a fifth lens in order along an optical axis from an object side to an image side. At least two of these five lenses each has at least an inflection point on at least a surface thereof. The first lens has positive refractive power, and both an object-side surface and an image-side surface thereof are aspheric surfaces. The second and the third lens have refractive power, and the fourth lens has positive refractive power. The fifth lens has negative refractive power, and both an object-side surface and an image-side surface thereof are aspheric surfaces. The optical image capturing system satisfies: 
         [0000]      1.2 ≦f/HEP≦ 3.0; 0.5≦ HOS/f ≦3.0; 0&lt;Σ| InRS|/InTL≦ 3; | TDT|&lt; 60%; and | ODT|≦ 50%;
 
         [0029]    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; HAF is a half of the view angle of the optical image capturing system; TDT is a TV distortion; ODT is an optical distortion; Σ|InRS| is a sum of InRSO and InRSI, where InRSO is a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the object-side surface to the point at the maximum effective semi diameter of the object-side surface, and InRSI is a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the image-side surface to the point at the maximum effective semi diameter of the image-side surface; and InTL is a distance in parallel with the optical axis between the object-side surface of the first lens and the image-side surface of the fourth lens. 
         [0030]    In an embodiment, the optical image capturing system further includes an image sensor with a size less than 1/1.2″ in diagonal, and the preferred size is 1/2.3″, and a pixel less than 1.4 μm. A preferable pixel size of the image sensor is less than 1.2 μm, and more preferable pixel size is less than 0.9 μm. A 16:9 image sensor is available for the optical image capturing system of the present invention. 
         [0031]    In an embodiment, the optical image capturing system of the present invention is available to high-quality (4K 2K, so called UHD and QHD) recording, and provides high quality of image. 
         [0032]    In an embodiment, a height of the optical image capturing system (HOS) can be reduced while |f 1 |&gt;f 5 . 
         [0033]    In an embodiment, when the lenses satisfy |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, at least one of the lenses from the second lens to the fourth lens could have weak positive refractive power or weak negative refractive power. The weak refractive power indicates that an absolute value of the focal length is greater than 10. When at least one of the lenses from the second lens to the fourth lens could have weak positive refractive power, it may share the positive refractive power of the first lens, and on the contrary, when at least one of the lenses from the second lens to the fourth lens could have weak negative refractive power, it may finely modify the aberration of the system. 
         [0034]    In an embodiment, the fifth lens has negative refractive power, and an image-side surface thereof is concave, it may reduce back focal length and size. Besides, the fifth lens has at least an inflection point on a surface thereof, which may reduce an incident angle of the light of an off-axis field of view and modify the aberration of the off-axis field of view. It is preferable that both surfaces of the fifth lens have at least an inflection point on a surface thereof. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0035]    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 
           [0036]      FIG. 1A  is a schematic diagram of a first preferred embodiment of the present invention; 
           [0037]      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; 
           [0038]      FIG. 1C  shows a curve diagram of TV distortion of the optical image capturing system of the first embodiment of the present application; 
           [0039]      FIG. 2A  is a schematic diagram of a second preferred embodiment of the present invention; 
           [0040]      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; 
           [0041]      FIG. 2C  shows a curve diagram of TV distortion of the optical image capturing system of the second embodiment of the present application; 
           [0042]      FIG. 3A  is a schematic diagram of a third preferred embodiment of the present invention; 
           [0043]      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; 
           [0044]      FIG. 3C  shows a curve diagram of TV distortion of the optical image capturing system of the third embodiment of the present application; 
           [0045]      FIG. 4A  is a schematic diagram of a fourth preferred embodiment of the present invention; 
           [0046]      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; 
           [0047]      FIG. 4C  shows a curve diagram of TV distortion of the optical image capturing system of the fourth embodiment of the present application; 
           [0048]      FIG. 5A  is a schematic diagram of a fifth preferred embodiment of the present invention; 
           [0049]      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; 
           [0050]      FIG. 5C  shows a curve diagram of TV distortion of the optical image capturing system of the fifth embodiment of the present application; 
           [0051]      FIG. 6A  is a schematic diagram of a sixth preferred embodiment of the present invention; 
           [0052]      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 
           [0053]      FIG. 6C  shows a curve diagram of TV distortion of the optical image capturing system of the sixth embodiment of the present application; 
           [0054]      FIG. 7A  is a schematic diagram of a seventh preferred embodiment of the present invention; 
           [0055]      FIG. 7B  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 seventh embodiment of the present application; and 
           [0056]      FIG. 7C  shows a curve diagram of TV distortion of the optical image capturing system of the seventh embodiment of the present application. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0057]    An optical image capturing system of the present invention includes a first lens, a second lens, a third lens, a forth lens, and a fifth lens from an object side to an image side with refractive power. The optical image capturing system further is provided with an image sensor at an image plane. 
         [0058]    The optical image capturing system works in three wavelengths, including 486.1 nm, 510 nm, 587.5 nm, and 656.2 nm, wherein 587.5 nm is the main reference wavelength, and 555 nm is the reference wavelength for obtaining the technical characters. 
         [0059]    The optical image capturing system of the present invention satisfies 0.5≦ΣPPR/|ΣNPR|≦2.5, and a preferable range is 1≦ΣPPR/|ΣNPR|≦2.0, 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 to control of an entire refractive power and an entire length of the optical image capturing system. 
         [0060]    HOS is a height of the optical image capturing system, and when the ratio of HOS/f approaches to 1, it is helpful to decrease of size and increase of imaging quality. 
         [0061]    In an embodiment, the optical image capturing system of the present invention satisfies 0&lt;ΣPP≦200 and f 1 /ΣPP≦0.85, where ΣPP is a sum of a focal length fp of each lens with positive refractive power, and ΣNP is a sum of a focal length fn of each lens with negative refractive power. It is helpful to control of focusing capacity of the system and redistribution of the positive refractive powers of the system to avoid the significant aberration in early time. The optical image capturing system further satisfies ΣNP&lt;−0.1 and 0.01≦f 5 /ΣNP≦0.85, which is helpful to control of an entire refractive power and an entire length of the optical image capturing system. 
         [0062]    The first lens has positive refractive power, and an object-side surface, which faces the object side, thereof is convex. It may modify the positive refractive power of the first lens as well as shorten the entire length of the system. 
         [0063]    The second lens has negative refractive power, which may correct the aberration of the first lens. 
         [0064]    The third lens has positive refractive power, which may share the positive refractive power of the first lens. It may share the positive refractive power of the first lens to reduce an increase of the aberration and reduce a sensitivity of the system. 
         [0065]    The fourth lens has positive refractive power, and an image-side surface thereof, which faces the image side, is convex. It may share the positive refractive power of the first lens to reduce an increase of the aberration and reduce a sensitivity of the system. 
         [0066]    The fifth lens has negative refractive power, and an image-side surface thereof, which faces the image side, is concave. It may shorten a rear focal length to reduce the size of the system. In addition, the fifth lens is provided with at least an inflection point on at least a surface to reduce an incident angle of the light of an off-axis field of view and modify the aberration of the off-axis field of view. It is preferable that each surface, the object-side surface and the image-side surface, of the fifth lens has at least an inflection point. 
         [0067]    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≦5.0, and a preferable range is 1≦HOS/HOI≦2.5 and 1≦HOS/f≦2, where HOI is height for image formation of the optical image capturing system, 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 to reduction of size of the system for used in compact cameras. 
         [0068]    The optical image capturing system of the present invention further is provided with an aperture to increase image quality. 
         [0069]    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, and a preferable range is 0.8≦InS/HOS≦1, where InS is a distance between the aperture and the image plane. It is helpful to size reduction and wide angle. 
         [0070]    The optical image capturing system of the present invention satisfies 0.45≦ΣTP/InTL≦0.95, 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 to the contrast of image and yield rate of manufacture, and provides a suitable back focal length for installation of other elements. 
         [0071]    The optical image capturing system of the present invention satisfies 0.1≦|R 1 /R 2 |≦5, and a preferable range is 0.1≦|R 1 /R 2 |≦4, where R 1  is a radius of curvature of the object-side surface of the first lens, and R 2  is a radius of curvature of the image-side surface of the first lens. It provides the first lens with a suitable refractive power to reduce the increase rate of the spherical aberration. 
         [0072]    The optical image capturing system of the present invention satisfies −200&lt;(R 9 −R 10 )/(R 9 +R 10 )&lt;30, where R 9  is a radius of curvature of the object-side surface of the fifth lens, and R 10  is a radius of curvature of the image-side surface of the fifth lens. It may modify the astigmatic field curvature. 
         [0073]    The optical image capturing system of the present invention satisfies 0&lt;IN 12 /f≦2.0, and a preferable range is 0.01≦IN 12 /f≦0.20, where IN 12  is a distance on the optical axis between the first lens and the second lens. It may correct chromatic aberration and improve the performance. 
         [0074]    The optical image capturing system of the present invention satisfies 0&lt;(TP 1 +IN 12 )/TP 2 ≦10, where TP 1  is a central thickness of the first lens on the optical axis, and TP 2  is a central thickness of the second lens on the optical axis. It may control the sensitivity of manufacture of the system and improve the performance. 
         [0075]    The optical image capturing system of the present invention satisfies 0.2≦(TP 5 +IN 45 )/TP 4 ≦3, where TP 4  is a central thickness of the fourth lens on the optical axis, TP 5  is a central thickness of the fifth lens on the optical axis, and N 45  is a distance between the fourth lens and the fifth lens. It may control the sensitivity of manufacture of the system and improve the performance. 
         [0076]    The optical image capturing system of the present invention satisfies 0.1≦(TP 2 +TP 3 +TP 4 )/ΣTP≦0.9, and a preferable range is 0.4≦(TP 2 +TP 3 +TP 4 )/ΣTP≦0.8, where TP 2  is a central thickness of the second lens on the optical axis, TP 3  is a central thickness of the third lens on the optical axis, TP 4  is a central thickness of the fourth lens on the optical axis, TP 5  is a central thickness of the fifth lens on the optical axis, and ΣTP is a sum of the central thicknesses of all the lenses on the optical axis. It may finely modify the aberration of the incident rays and reduce the height of the system. 
         [0077]    The optical image capturing system of the present invention satisfies 0≦|InRS 11 |+|InRS 12 |≦2 mm; and 1.01≦(|InRS 11 |+TP 1 +|InRS 12 |)/TP 1 ≦3, where InRS 11  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 a point at the maximum effective semi diameter of the object-side surface of the first lens, wherein InRS 11  is positive while the displacement is toward the image side, and InRS 11  is negative while the displacement is toward the object side; InRS 12  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 a point at the maximum effective semi diameter of the image-side surface of the first lens; and TP 1  is a central thickness of the first lens on the optical axis. It may control a ratio of the central thickness of the first lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0078]    The optical image capturing system of the present invention satisfies 0≦|InRS 21 |+|InRS 22 |≦2 mm; and 1.01≦(|InRS 21 |+TP 2 +|InRS 22 |)/TP 2 ≦5, where InRS 21  is 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 a point at the maximum effective semi diameter of the object-side surface of the first lens; InRS 22  is 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 a point at the maximum effective semi diameter of the image-side surface of the second lens; and TP 2  is a central thickness of the second lens on the optical axis. It may control a ratio of the central thickness of the second lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0079]    The optical image capturing system of the present invention satisfies 0≦|InRS 31 |+|InRS 32 |≦2 mm; and 1.01≦(|InRS 31 |+TP 3 +|InRS 32 |)/TP 3 ≦10, where InRS 31  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 a point at the maximum effective semi diameter of the object-side surface of the first lens; InRS 32  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 a point at the maximum effective semi diameter of the image-side surface of the third lens; and TP 3  is a central thickness of the third lens on the optical axis. It may control a ratio of the central thickness of the third lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0080]    The optical image capturing system of the present invention satisfies 0≦|InRS 41 |+|InRS 42 |≦2 mm; and 1.01≦(|InRS 41 |+TP 4 +|InRS 42 |)/TP 4 ≦10, where InRS 41  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 a point at the maximum effective semi diameter of the object-side surface of the first lens; InRS 42  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 a point at the maximum effective semi diameter of the image-side surface of the fourth lens; and TP 4  is a central thickness of the fourth lens on the optical axis. It may control a ratio of the central thickness of the fourth lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0081]    The optical image capturing system of the present invention satisfies 0≦|InRS 51 |+|InRS 52 |≦3 mm; and 1.01≦(|InRS 51 |+TP 5 +|InRS 52 |)/TP 5 ≦20, where InRS 51  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 a point at the maximum effective semi diameter of the object-side surface of the first lens; InRS 52  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 a point at the maximum effective semi diameter of the image-side surface of the fifth lens; and TP 5  is a central thickness of the fifth lens on the optical axis. It may control a ratio of the central thickness of the fifth lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0082]    The optical image capturing system of the present invention satisfies 0&lt;Σ|InRS|≦15 mm, where Σ|InRS| is of an sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point to the point at the maximum effective semi diameter, i.e. Σ|InRS|=InRSO+InRSI while InRSO is of a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the object-side surface to the point at the maximum effective semi diameter of the object-side surface, i.e. InRSO=|InRS 11 |+|InRS 21 |+|InRS 31 |+|InRS 41 |+|InRS 51 | and InRSI is of a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the image-side surface to the point at the maximum effective semi diameter of the image-side surface, i.e. InRSI=|InRS 12 |+|InRS 22 |+|InRS 32 |+|InRS 42 |+|InRS 52 |. It may increase the capability of modifying the off-axis view field aberration of the system. 
         [0083]    The optical image capturing system of the present invention satisfies 0&lt;Σ|InRS|/InTL≦3 and 0&lt;Σ|InRS|/HOS≦2. It may reduce the total height of the system as well as efficiently increase the capability of modifying the off-axis view field aberration of the system. 
         [0084]    The optical image capturing system of the present invention satisfies 0&lt;|InRS 41 |+|InRS 42 |+|InRS 51 |+|InRS 52 |≦5 mm; 0&lt;(|InRS 41 |+|InRS 42 |+|InRS 51 |+|InRS 52 |)/InTL≦2; and 0&lt;(|InRS 41 |+|InRS 42 |+|InRS 51 |+|InRS 52 |)/HOS≦2. It could increase the yield rate of manufacture of the two lenses, which are the first and the second closest to the image side, and increase the capability of modifying the off-axis view field aberration of the system. 
         [0085]    The optical image capturing system of the present invention satisfies HVT 41 ≧0 mm and HVT 42 ≧0 mm, where HVT 41  a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens and the optical axis; and HVT 42  a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fourth lens and the optical axis. It may efficiently modify the off-axis view field aberration of the system. 
         [0086]    The optical image capturing system of the present invention satisfies HVT 51 ≧0 mm and HVT 52 ≧0 mm, where HVT 51  a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens and the optical axis; and HVT 52  a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens and the optical axis. It may efficiently modify the off-axis view field aberration of the system. 
         [0087]    The optical image capturing system of the present invention satisfies 0.2≦HVT 52 /HOI≦0.9, and preferable is 0.3≦HVT 52 /HOI≦0.8. It is helpful to correction of the aberration of the peripheral view field. 
         [0088]    The optical image capturing system of the present invention satisfies 0≦HVT 52 /HOS≦0.5, and preferable is 0.2≦HVT 52 /HOS≦0.45. It is helpful to correction of the aberration of the peripheral view field. 
         [0089]    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 to correction of aberration of the system. 
         [0090]    An equation of aspheric surface is 
         [0000]        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)
 
         [0091]    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. 
         [0092]    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 to reduction of the height of the system. 
         [0093]    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. 
         [0094]    The optical image capturing system of the present invention further is provided with a diaphragm to increase image quality. 
         [0095]    In the optical image capturing system, the diaphragm could be a front diaphragm or a middle diaphragm, wherein the front diaphragm is provided between the object and the first lens, and the middle is provided between the first lens and the image plane. The front diaphragm provides a long distance between an exit pupil of the system and the image plane, which allows more elements to be installed. The middle diaphragm could enlarge a view angle of view of the system and increase the efficiency of the image sensor. The middle diaphragm is helpful to size reduction and wide angle. 
         [0096]    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. 
         [0097]    We provide several embodiments in conjunction with the accompanying drawings for the best understanding, which are: 
       First Embodiment 
       [0098]    As shown in  FIG. 1A  and  FIG. 1B , an optical image capturing system  100  of the first preferred embodiment of the present invention includes, along an optical axis from an object side to an image side, an aperture  100 , a first lens  110 , a second lens  120 , a third lens  130 , a fourth lens  140 , a fifth lens  150 , an infrared rays filter  170 , an image plane  180 , and an image sensor  190 . 
         [0099]    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, and the image-side surface has an inflection point. The first lens  110  satisfies SGI 121 =0.0387148 mm and |SGI 121 |/(|SGI 121 |+TP 1 )=0.061775374, where SGI 121  is a displacement in parallel with the optical axis from a point on the image-side surface of the first lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
         [0100]    The first lens  110  further satisfies HIF 121 =0.61351 mm and HIF 121 /HOI=0.209139253, where HIF 121  is a displacement perpendicular to the optical axis from a point on the image-side surface of the first lens, through which the optical axis passes, to the inflection point, which is the closest to the optical axis. 
         [0101]    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 concave aspheric surface, and an image-side surface  124  thereof, which faces the image side, is a convex aspheric surface, and the image-side surface  124  has an inflection point. The second lens  120  satisfies SGI 221 =−0.0657553 mm and |SGI 221 |/(|SGI 221 |+TP 2 )=0.176581512, where SGI 221  is 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. 
         [0102]    The second lens further satisfies HIF 221 =0.84667 mm and HIF 221 /HOI=0.288621101, where HIF 221  is 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. 
         [0103]    The third lens  130  has negative refractive power, and is made of plastic. An object-side surface  132 , which faces the object side, is a concave aspheric surface, and an image-side surface  134 , which faces the image side, is a convex aspheric surface, and each of them has two inflection points. The third lens  130  satisfies SGI 311 =−0.341027 mm; SGI 321 =−0.231534 mm and |SGI 311 |/(|SGI 311 |+TP 3 )=0.525237108 and |SGI 321 |/(|SGI 321 |+TP 3 )=0.428934269, where SGI 311  is a displacement in parallel with the optical axis, from a point on the object-side surface of the third lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 321  is a displacement in parallel with the optical axis, from a point on the image-side surface of the third lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
         [0104]    The third lens  130  satisfies SGI 312 =−0.376807 mm; SGI 322 =−0.382162 mm; |SGI 312 |/(|SGI 312 |+TP 5 )=0.550033428; |SGI 322 |/(|SGI 322 |+TP 3 )=0.55352345, where SGI 312  is a displacement in parallel with the optical axis, from a point on the object-side surface of the third lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis, and SGI 322  is a displacement in parallel with the optical axis, from a point on the image-side surface of the third lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the second closest to the optical axis. 
         [0105]    The third lens  130  further satisfies HIF 311 =0.987648 mm; HIF 321 =0.805604 mm; HIF 311 /HOI=0.336679052; and HIF 321 /HOI=0.274622124, where HIF 311  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the third lens, which is the closest to the optical axis, and the optical axis, and HIF 321  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the third lens, which is the closest to the optical axis, and the optical axis. 
         [0106]    The third lens  130  further satisfies HIF 312 =1.0493 mm; HIF 322 =1.17741 mm; HIF 312 /HOI=0.357695585; and HIF 322 /HOI=0.401366968, where HIF 312  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the third lens, which is the second the closest to the optical axis, and the optical axis, and HIF 322  is a distance perpendicular to the optical axis, between the inflection point on the image-side surface of the third lens, which is the second the closest to the optical axis, and the optical axis. 
         [0107]    The fourth lens  140  has positive refractive power, and is made of plastic. Both an object-side surface  142 , which faces the object side, and an image-side surface  144 , which faces the image side, thereof are convex aspheric surfaces, and the object-side surface  142  has an inflection point. The fourth lens  140  satisfies SGI 411 =0.0687683 mm and |SGI 411 |/(|SGI 411 |+TP 4 )=0.118221297, where SGI 411  is a displacement in parallel with the optical axis from a point on the object-side surface of the fourth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis. 
         [0108]    The fourth lens  140  further satisfies HIF 411 =0.645213 mm and HIF 411 /HOI=0.21994648, where HIF 411  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens, which is the closest to the optical axis, and the optical axis. 
         [0109]    The fifth lens  150  has negative refractive power, and is made of plastic. Both an object-side surface  152 , which faces the object side, and an image-side surface  154 , which faces the image side, thereof are concave aspheric surfaces. The object-side surface  152  has three inflection points, and the image-side surface  154  has an inflection point. The fifth lens  150  satisfies SGI 511 =−0.236079 mm; SGI 521 =0.023266 mm; |SGI 511 |/(|SGI 511 |+TP 5 )=0.418297214; and |SGI 521 |/(|SGI 521 |+TP 5 )=0.066177809, where SGI 511  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the closest to the optical axis, and SGI 521  is a displacement in parallel with the optical axis, from a point on the image-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the image-side surface, which is the closest to the optical axis. 
         [0110]    The fifth lens  150  further satisfies SGI 512 =−0.325042 mm and |SGI 512 |/(|SGI 512 |+TP 5 )=0.497505143, where SGI 512  is a displacement in parallel with the optical axis, from a point on the object-side surface of the fifth lens, through which the optical axis passes, to the inflection point on the object-side surface, which is the second closest to the optical axis. 
         [0111]    The fifth lens  150  further satisfies SGI 513 =−0.538131 mm; and |SGI 513 |/(|SGI 513 |+TP 5 )=0.621087839, where SGI 513  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 third closest to the optical axis. 
         [0112]    The fifth lens  150  further satisfies HIF 511 =1.21551 mm; HIF 521 =0.575738 mm; HIF 511 /HOI=0.414354866; and HIF 521 /HOI=0.196263167, where HIF 511  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the closest to the optical axis, and the optical axis, and HIF 521  is a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens, which is the closest to the optical axis, and the optical axis. 
         [0113]    The fifth lens  150  further satisfies HIF 512 =1.49061 mm and HIF 512 /HOI=0.508133629, where HIF 512  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the second the closest to the optical axis, and the optical axis. 
         [0114]    The fifth lens  150  further satisfies HIF 513 =2.00664 mm and HIF 513 /HOI=0.684042952, where HIF 513  is a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens, which is the third closest to the optical axis, and the optical axis. 
         [0115]    The infrared rays filter  170  is made of glass, and between the fifth lens  150  and the image plane  180 . The infrared rays filter  170  gives no contribution to the focal length of the system. 
         [0116]    The optical image capturing system of the first preferred embodiment has the following parameters, which are f=3.73172 mm; f/HEP=2.05; and HAF=37.5 degrees and tan(HAF)=0.7673, 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. 
         [0117]    The parameters of the lenses of the first preferred embodiment are f 1 =3.7751 mm; |f/f 1 |=0.9885; f 5 =−3.6601 mm; |f 1 |&gt;f 5 ; and |f 1 /f 5 |=1.0314, where f 1  is a focal length of the first lens  110 ; and f 5  is a focal length of the fifth lens  150 . 
         [0118]    The first preferred embodiment further satisfies |f 2 |+|f 3 |+|f 4 |=77.3594 mm; |f 1 |+|f 5 |=7.4352 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+f 5 |, where f 2  is a focal length of the second lens  120 ; f 3  is a focal length of the third lens  130 ; and f 4  is a focal length of the fourth lens  140 . 
         [0119]    The optical image capturing system of the first preferred embodiment further satisfies ΣPPR=f/f 1 +f/f 4 =1.9785; ΣNPR=f/f 2 +f/f 3 +f/f 5 =−1.2901; ΣPPR/|ΣNPR|=1.5336; |f/f 1 |=0.9885; |f/f 2 |=0.0676; |f/f 3 |=0.2029; |f/f 4 |=0.9900; and |f/f 5 |=1.0196, 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. 
         [0120]    The optical image capturing system of the first preferred embodiment further satisfies InTL+InB=HOS; HOS=4.5 mm; HOI=2.9335 mm; HOS/HOI=1.5340; HOS/f=1.2059; Intl/HOS=0.7597; and InS=4.19216 mm, 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  180 ; InS is a distance between the aperture  100  and the image plane  180 ; HOI is height for image formation of the optical image capturing system, i.e., the maximum image height; and InB is a distance between the image-side surface  154  of the fifth lens  150  and the image plane  180 . 
         [0121]    The optical image capturing system of the first preferred embodiment further satisfies ΣTP=2.044092 mm and ΣTP/InTL=0.5979, where ΣTP is a sum of the thicknesses of the lenses  110 - 150  with refractive power. It is helpful to the contrast of image and yield rate of manufacture, and provides a suitable back focal length for installation of other elements. 
         [0122]    The optical image capturing system of the first preferred embodiment further satisfies |R 1 /R 2 |=0.3261, where R 1  is a radius of curvature of the object-side surface  112  of the first lens  110 , and R 2  is a radius of curvature of the image-side surface  114  of the first lens  110 . It provides the first lens with a suitable positive refractive power to reduce the increase rate of the spherical aberration. 
         [0123]    The optical image capturing system of the first preferred embodiment further satisfies (R 9 −R 10 )/(R 9 +R 10 )=−2.9828, where R 9  is a radius of curvature of the object-side surface  152  of the fifth lens  150 , and R 10  is a radius of curvature of the image-side surface  154  of the fifth lens  150 . It may modify the astigmatic field curvature. 
         [0124]    The optical image capturing system of the first preferred embodiment further satisfies ΣPP=f 1 +f 4 =7.5444 mm and f 1 /(f 1 +f 4 )=0.5004, 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 the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0125]    The optical image capturing system of the first preferred embodiment further satisfies ΣNP=f 2 +f 3 +f 5 =−77.2502 mm and f 5 /(f 2 +f 3 +f 5 )=0.0474, where f 2 , f 3 , and f 5  are focal lengths of the second, the third, and the fifth lenses, 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 lenses to avoid the significant aberration caused by the incident rays. 
         [0126]    The optical image capturing system of the first preferred embodiment further satisfies IN 12 =0.511659 mm and IN 124 =0.1371, where IN 12  is a distance on the optical axis between the first lens  110  and the second lens  120 . It may correct chromatic aberration and improve the performance. 
         [0127]    The optical image capturing system of the first preferred embodiment further satisfies TP 1 =0.587988 mm; TP 2 =0.306624 mm; and (TP 1 +IN 12 )/TP 2 =3.5863, where TP 1  is a central thickness of the first lens  110  on the optical axis, and TP 2  is a central thickness of the second lens  120  on the optical axis. It may control the sensitivity of manufacture of the system and improve the performance. 
         [0128]    The optical image capturing system of the first preferred embodiment further satisfies TP 4 =0.5129 mm; TP 5 =0.3283 mm; and (TP 5 +IN 45 )/TP 4 =1.5095, where TP 4  is a central thickness of the fourth lens  140  on the optical axis, TP 5  is a central thickness of the fifth lens  150  on the optical axis, and N 45  is a distance on the optical axis between the fourth lens and the fifth lens. It may control the sensitivity of manufacture of the system and improve the performance. 
         [0129]    The optical image capturing system of the first preferred embodiment further satisfies TP 3 =0.3083 mm and (TP 2 +TP 3 +TP 4 )/ΣTP=0.5517, where TP 2 , TP 3 , and TP 4  are thicknesses on the optical axis of the second, the third, and the fourth lenses, and ΣTP is a sum of the central thicknesses of all the lenses with refractive power on the optical axis. It may finely modify the aberration of the incident rays and reduce the height of the system. 
         [0130]    The optical image capturing system of the first preferred embodiment |InRS 11 |=0.307838 mm; |InRS 12 |=0.0527214 mm; TP 1 =0.587988 mm; and (|InRS 11 |+TP 1 +|InRS 12 |)/TP 1 =1.613208773, where InRS 11  is a displacement in parallel with the optical axis from a point on the object-side surface  112  of the first lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  112  of the first lens; InRS 12  is a displacement in parallel with the optical axis from a point on the image-side surface  114  of the first lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  114  of the first lens; and TP 1  is a central thickness of the first lens  110  on the optical axis. It may control a ratio of the central thickness of the first lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0131]    The optical image capturing system of the first preferred embodiment |InRS 21 |=0.165699 mm; |InRS 22 |=0.0788662 mm; TP 2 =0.306624 mm; and (|InRS 21 |+TP 2 +|InRS 22 |)/TP 2 =1.797606189, where InRS 21  is a displacement in parallel with the optical axis from a point on the object-side surface  122  of the second lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  122  of the second lens; InRS 22  is a displacement in parallel with the optical axis from a point on the image-side surface  124  of the second lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  124  of the second lens; and TP 2  is a central thickness of the second lens  120  on the optical axis. It may control a ratio of the central thickness of the second lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0132]    The optical image capturing system of the first preferred embodiment |InRS 31 |=0.383103 mm; |InRS 32 |=−0.411894 mm; TP 3 =0.308255 mm; and (|InRS 31 |+TP 3 +|InRS 32 |)/TP 3 =3.57902386, where InRS 31  is a displacement in parallel with the optical axis from a point on the object-side surface  132  of the third lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  132  of the third lens; InRS 32  is a displacement in parallel with the optical axis from a point on the image-side surface  134  of the third lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  134  of the third lens; and TP 3  is a central thickness of the third lens  130  on the optical axis. It may control a ratio of the central thickness of the third lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0133]    The optical image capturing system of the first preferred embodiment |InRS 41 |=0.0384 mm; |InRS 42 |=0.263634 mm; TP 4 =0.512923 mm; (|InRS 41 |+TP 4 +|InRS 42 |)/TP 4 =1.588848619, where InRS 41  is a displacement in parallel with the optical axis from a point on the object-side surface  142  of the fourth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  142  of the fourth lens; InRS 42  is a displacement in parallel with the optical axis from a point on the image-side surface  144  of the fourth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  144  of the fourth lens; and TP 4  is a central thickness of the fourth lens  140  on the optical axis. It may control a ratio of the central thickness of the fourth lens and the effective semi diameter thickness (thickness ratio) to increase the yield rate of manufacture. 
         [0134]    The optical image capturing system of the first preferred embodiment further satisfies |InRS 51 |=0.576871 mm; |InRS 52 |=0.555284 mm; TP 5 =0.328302 mm; and (|InRS 51 |+TP 5 +|InRS 52 |)/TP 5 =4.448516914, where InRS 51  is a displacement in parallel with the optical axis from a point on the object-side surface  152  of the fifth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the object-side surface  152  of the fifth lens; InRS 52  is a displacement in parallel with the optical axis from a point on the image-side surface  154  of the fifth lens, through which the optical axis passes, to a point at the maximum effective semi diameter of the image-side surface  154  of the fifth lens; and TP 5  is a central thickness of the fifth lens  150  on the optical axis. It may control the positions of the maximum effective semi diameter on both surfaces of the fifth lens, correct the aberration of the spherical field of view, and reduce the size. 
         [0135]    The optical image capturing system of the first preferred embodiment satisfies InRSO=1.471911 mm; InRSI=1.3623996 mm; and Σ|InRS|=2.8343106 mm, where InRSO is of a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the object-side surface to the point at the maximum effective semi diameter of the object-side surface, i.e. InRSO=|InRS 11 |+|InRS 21 |+|InRS 31 |+|InRS 41 |+|InRS 51 |; InRSI is of a sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point on the image-side surface to the point at the maximum effective semi diameter of the image-side surface, i.e. InRSI=|InRS 12 |+|InRS 22 |+|InRS 32 |+|InRS 42 |+|InRS 52 |; and Σ|InRS| is of an sum of absolute values of the displacements in parallel with the optical axis of each lens with refractive power from the central point to the point at the maximum effective semi diameter, i.e. Σ|InRS|=InRSO+InRSI. It may efficiently increase the capability of modifying the off-axis view field aberration of the system. 
         [0136]    The optical image capturing system of the first preferred embodiment satisfies Σ|InRS|/InTL=0.856804897 and Σ|InRS|/HOS=0.632658616. It may reduce the total height of the system as well as efficiently increase the capability of modifying the off-axis view field aberration of the system. 
         [0137]    The optical image capturing system of the first preferred embodiment satisfies |InRS 41 |+|InRS 42 |+|InRS 51 |+|InRS 52 |=1.434189 mm; |InRS 41 |+|InRS 42 |+|InRS 51 |+|InRS 52 |)/InTL=0.433551693; and (|InRS 41 |+|InRS 42 |+|InRS 51 |+|InRS 52 |)/HOS=0.320131473. It may increase yield rate of the lenses of the first and the second closest to the image side as well as efficiently increase the capability of modifying the off-axis view field aberration of the system. 
         [0138]    The optical image capturing system of the first preferred embodiment satisfies HVT 41 =1.28509 mm and HVT 42 =0 mm, where HVT 41  a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens and the optical axis; and HVT 42  a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fourth lens and the optical axis. It may efficiently modify the aberration of the peripheral view field of the system. 
         [0139]    The optical image capturing system of the first preferred embodiment satisfies HVT 51 =0 mm; HVT 52 =1.06804 mm; and HVT 51 /HVT 52 =0, where HVT 51  a distance perpendicular to the optical axis between the inflection point on the object-side surface of the fifth lens and the optical axis; and HVT 52  a distance perpendicular to the optical axis between the inflection point on the image-side surface of the fifth lens and the optical axis. It may efficiently modify the aberration of the off-axis view field of the system. 
         [0140]    The optical image capturing system of the first preferred embodiment satisfies HVT 52 /HOI=0.364083859. It may efficiently modify the aberration of the off-axis view field of the system. 
         [0141]    The optical image capturing system of the first preferred embodiment satisfies HVT 52 /HOS=0.237342222. It may efficiently modify the aberration of the peripheral view field of the system. 
         [0142]    In the first embodiment, the first lens  110  and the fifth lens  150  are negative lenses. The optical image capturing system of the first preferred embodiment further satisfies NA 5 /NA 2 =2.5441, where NA 2  is an Abbe number of the second lens  120 , and NA 5  is an Abbe number of the fifth lens  150 . It may correct the aberration of the system. 
         [0143]    The optical image capturing system of the first preferred embodiment further satisfies |TDT|=0.6343% and |ODT|=2.5001%, where TDT is TV distortion; and ODT is optical distortion. 
         [0144]    The parameters of the lenses of the first embodiment are listed in Table 1 and Table 2. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 f = 3.73172 mm; f/HEP = 2.05; HAF = 37.5 deg; tan(HAF) = 0.7673 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive  
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 plane 
                 −0.30784 
                   
                   
                   
                   
               
               
                 2 
                 1 st  lens 
                 1.48285 
                 0.587988 
                 plastic 
                 1.5441 
                 56.1 
                 3.77514 
               
               
                 3 
                   
                 4.54742 
                 0.511659 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 −9.33807 
                 0.306624 
                 plastic 
                 1.6425 
                 22.465 
                 −55.2008 
               
               
                 5 
                   
                 −12.8028 
                 0.366935 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 −1.02094 
                 0.308255 
                 plastic 
                 1.6425 
                 22.465 
                 −18.3893 
               
               
                 7 
                   
                 −1.2492 
                 0.05 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 2.18916 
                 0.512923 
                 plastic 
                 1.5441 
                 56.1 
                 3.7693 
               
               
                 9 
                   
                 −31.3936 
                 0.44596 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −2.86353 
                 0.328302 
                 plastic 
                 1.514 
                 57.1538 
                 −3.6601 
               
               
                 11 
                   
                 5.75188 
                 0.3 
                   
                   
                   
                   
               
               
                 12 
                 Filter 
                 plane 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 plane 
                 0.58424 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 plane  
                 −0.00289 
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 −1.83479 
                 −20.595808 
                 16.674705 
                 11.425456 
                 −4.642191 
               
               
                 A4 
                 6.89867E−02 
                  2.25678E−02 
                 −1.11828E−01 
                 −4.19899E−02 
                 −7.09315E−02 
               
               
                 A6 
                 2.35740E−02 
                 −6.17850E−02 
                 −6.62880E−02 
                 −1.88072E−02 
                  9.65840E−02 
               
               
                 A8 
                 −4.26369E−02  
                  5.82944E−02 
                 −3.35190E−02 
                 −6.98321E−02 
                 −7.32044E−03 
               
               
                 A10 
                 5.63746E−03 
                 −2.73938E−02 
                 −7.28886E−02 
                 −1.13079E−02 
                 −8.96740E−02 
               
               
                 A12 
                 7.46740E−02 
                 −2.45759E−01 
                  4.05955E−02 
                  6.79127E−02 
                 −3.70146E−02 
               
               
                 A14 
                 −6.93116E−02  
                  3.43401E−01 
                  1.60451E−01 
                  2.83769E−02 
                  5.00641E−02 
               
               
                 A16 
                 −2.04867E−02  
                 −1.28084E−01 
                  1.24448E−01 
                 −2.45035E−02 
                  7.50413E−02 
               
               
                 A18 
                 1.99910E−02 
                 −2.32031E−02 
                 −1.94856E−01 
                  2.90241E−02 
                 −5.10392E−02 
               
               
                 A20 
               
               
                   
               
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 −1.197201 
                 −20.458388 
                 −50 
                 −2.907359 
                 −50 
               
               
                 A4 
                 3.64395E−02 
                 −1.75641E−02 
                 −7.82211E−04 
                 −1.58711E−03 
                 −2.46339E−02 
               
               
                 A6 
                 2.22356E−02 
                 −2.87240E−03 
                 −2.47110E−04 
                 −3.46504E−03 
                  6.61804E−04 
               
               
                 A8 
                 7.09828E−03 
                 −2.56360E−04 
                 −3.78130E−04 
                  4.52459E−03 
                  1.54143E−04 
               
               
                 A10 
                 5.05740E−03 
                  7.39189E−05 
                 −1.22232E−04 
                  1.05841E−04 
                 −2.83264E−05 
               
               
                 A12 
                 −4.51124E−04  
                 −5.53116E−08 
                 −1.50294E−05 
                 −5.57252E−04 
                 −5.78839E−06 
               
               
                 A14 
                 −1.84003E−03  
                  8.16043E−06 
                 −5.41743E−07 
                  4.41714E−05 
                 −2.91861E−07 
               
               
                 A16 
                 −1.28118E−03  
                  2.10395E−06 
                  2.98820E−07 
                  1.80752E−05 
                  8.25778E−08 
               
               
                 A18 
                 4.09004E−04 
                 −1.21664E−06 
                  2.73321E−07 
                 −2.27031E−06 
                 −9.87595E−09 
               
               
                 A20 
               
               
                   
               
             
          
         
       
     
         [0145]    The detail parameters of the first preferred embodiment are listed in Table 1, in which the unit of radius of curvature, thickness, and focal length are millimeter, and surface 0-14 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 
       [0146]    As shown in  FIG. 2A  and  FIG. 2B , an optical image capturing system of the second preferred 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  270 , an image plane  280 , and an image sensor  290 . 
         [0147]    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 convex aspheric surface. The object-side surface  212  has an inflection point. 
         [0148]    The second lens  220  has negative refractive power, and is made of plastic. An object-side surface  222 , which faces the object side, thereof has a concave aspheric surface, and an image-side surface  224 , which faces the image side, thereof is a convex aspheric surface. The object-side surface  222  has an inflection point. 
         [0149]    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 concave aspheric surface, and an image-side surface  234 , which faces the image side, is a convex aspheric surface, and the object-side surface  232  has two inflection points, and the image-side surface  234  has an inflection point. 
         [0150]    The fourth lens  240  has positive refractive power, and is made of plastic. An object-side surface  242 , which faces the object side, thereof is a concave aspheric surface, and an image-side surface  244 , which faces the image side, thereof is a convex aspheric surface. The image-side surface  244  has an inflection point. 
         [0151]    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 aspheric surface, and an image-side surface  254 , which faces the image side, is a convex aspheric surface. The object-side surface  252  and the image-side surface  254  each has two inflection points. 
         [0152]    The infrared rays filter  270  is made of glass, and between the fifth lens  250  and the image plane  280 . The infrared rays filter  270  gives no contribution to the focal length of the system. 
         [0153]    The optical image capturing system of the second preferred embodiment has the following parameters, which are |f 2 |+|f 3 |+|f 4 |=13.4958 mm, |f 1 |+|f 5 |=4.7939 mm, and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  210 ; f 2  is a focal length of the second lens  220 ; f 3  is a focal length of the third lens  230 ; f 4  is a focal length of the fourth lens  240 ; and f 5  is a focal length of the fifth lens  250 . 
         [0154]    The optical image capturing system of the second preferred embodiment further satisfies TP 4 =0.3005 mm and TP 5 =0.2085 mm, where TP 4  is a thickness of the fourth lens on the optical axis, and TP 5  is a thickness of the fifth lens on the optical axis. 
         [0155]    In the second embodiment, the first, the third, and the fourth lenses  210 ,  230 , and  240  are positive lenses, and their focal lengths are f 1 , f 3 , and f 4 . 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 the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0156]    In the second preferred embodiment, the second and the fifth lenses  220  and  250  are negative lenses, and their focal lengths are f 2  and f 5 . 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 lenses to avoid the significant aberration caused by the incident rays. 
         [0157]    The parameters of the lenses of the second embodiment are listed in Table 3 and Table 4. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 f = 1.93325 mm; f/HEP = 1.6; HAF = 50.0016 deg; tan(HAF) = 1.1918 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 infinity 
                 0.017633 
                   
                   
                   
                   
               
               
                 2 
                 1 st  lens 
                 6.34633 
                 0.624774 
                 plastic 
                 1.565 
                 58 
                 2.00628 
               
               
                 3 
                   
                 −1.336 
                 0.360605 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 −0.52157 
                 0.302683 
                 plastic 
                 1.65 
                 21.4 
                 −5.97113 
               
               
                 5 
                   
                 −0.74004 
                 0.05 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 2.07971 
                 0.6 
                 plastic 
                 1.565 
                 58 
                 2.78602 
               
               
                 7 
                   
                 −5.87484 
                 0.082571 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −1.96145 
                 0.300517 
                 plastic 
                 1.65 
                 21.4 
                 4.73869 
               
               
                 9 
                   
                 −1.27516  
                 0.281239 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens  
                 −1.23794  
                 0.208473 
                 plastic 
                 1.65 
                 21.4 
                 −2.78765 
               
               
                 11 
                   
                 −4.09489 
                 0.1 
                   
                   
                   
                   
               
               
                 12 
                 Filter 
                 infinity 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 infinity 
                 0.399999 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 infinity 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 45.031907 
                 0.356363 
                 −1.43439 
                 −0.58633 
                 −49.844293 
               
               
                 A4 
                 −2.52361E−01 
                 −1.33782E−01 
                 3.01814E−02 
                  1.35453E−01 
                 −8.94730E−02 
               
               
                 A6 
                 −2.84452E−03 
                 −2.50516E−01 
                 5.25000E−02 
                  5.03572E−01 
                 −7.71751E−02 
               
               
                 A8 
                 −8.54592E−01 
                  6.38190E−01 
                 9.20756E−01 
                 −9.15919E−02 
                  2.05340E−02 
               
               
                 A10 
                 −6.92339E−01 
                 −6.62762E−01 
                 −1.02120E+00  
                 −3.94943E−01 
                  2.17466E−02 
               
               
                 A12 
                  5.73209E+00 
                 −3.84009E−01 
                 −2.55516E+00  
                 −3.07033E−03 
                  2.50633E−02 
               
               
                 A14 
                 −1.20415E+01 
                  1.02173E−01 
                 2.81468E+00 
                  1.74595E−01 
                 −1.30316E−02 
               
               
                   
               
             
          
           
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 20.2538 
                 0.954593 
                 −0.707723 
                 −0.370411 
                 −50 
               
               
                 A4 
                 −1.51946E−01  
                  1.11864E−01 
                 8.78621E−03 
                 1.04771E−03 
                 5.69996E−03 
               
               
                 A6 
                 1.33241E−02 
                 −5.43670E−02 
                 3.15861E−02 
                 3.61403E−02 
                 1.14704E−02 
               
               
                 A8 
                 1.40042E−02 
                  3.51006E−02 
                 6.13972E−03 
                 2.06494E−02 
                 −6.39985E−03  
               
               
                 A10 
                 −1.95596E−02  
                  8.13004E−03 
                 3.02339E−03 
                 2.03916E−03 
                 8.52755E−04 
               
               
                 A12 
                 8.57798E−03 
                 −8.69568E−03 
                 2.15703E−03 
                 −1.15268E−03  
                 1.74399E−04 
               
               
                 A14 
                 6.30220E−03 
                 −2.59224E−03 
                 −1.06288E−03  
                 −6.38058E−04  
                 −6.57554E−05  
               
               
                   
               
             
          
         
       
     
         [0158]    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. 
         [0159]    The exact parameters of the second embodiment based on Table 3 and Table 4 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Second embodiment 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 −0.01763  
                 −0.39029  
                 −0.58372  
                 −0.64448  
                 0.02742 
                 −0.37259  
               
               
                 InRS41 
                 InRS42 
                 InRS51 
                 InRS52 
                 HVT51 
                 HVT52 
               
               
                 −0.34836  
                 −0.44694  
                 −0.59122  
                 −0.17430  
                 0.00000 
                 0.00000 
               
               
                 |ODT| 
                 |TDT| 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
               
               
                 2.15553% 
                 1.23916% 
                 1.56835 
                 2.02860 
                 3.59695 
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS32| + |InRS41|)/IN34 
                 (|InRS42| + |InRS51|)/IN45 
               
               
                 1.27966 
                 1.02452 
                 8.7314 
                 3.6913 
               
             
          
           
               
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/InTL 
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/HOS 
               
               
                 0.55528 
                 0.44457 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f/f5| 
                 |f1/f2| 
               
               
                 0.96360 
                 0.32377 
                 0.69391 
                 0.40797 
                 0.69351 
                 0.33600 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.06548 
                 1.01727 
                 2.03041 
                 9.53099 
                 −8.75878  
                 0.21050 
               
               
                 f5/ΣNP 
                 IN12/f 
                 HVT52/HOI 
                 HVT52/HOS 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                 0.31827 
                 0.18653 
                 0.00000 
                 0.00000 
                 2.8359 
                 0.8361  
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 3.51086 
                 2.81086 
                 1.52646 
                 1.00502 
                 0.80062 
                 0.72449 
               
               
                 HVT41 
                 HVT42 
               
               
                 0     
                 1.2547  
               
               
                   
               
               
                 (Reference wavelength: 555 nm) 
               
             
          
         
       
     
         [0160]    The exact parameters of the inflection points of the second embodiment based on Table 3 and Table 4 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Second embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HIF111 
                 0.23363 
                 HIF111/ 
                 0.10158 
                 SGI111 
                 0.00361 
                 |SGI111|/(|SG 
                 0.00574 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 I111| + TP1) 
                   
               
               
                 HIF211 
                 0.84012 
                 HIF211/ 
                 0.36527 
                 SGI211 
                 −0.53760 
                 |SGI211|/(|SG 
                 0.63978 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 I211| + TP2) 
                   
               
               
                 HIF311 
                 0.33107 
                 HIF311/ 
                 0.14394 
                 SGI311 
                 0.01994 
                 |SGI311|/(|SG 
                 0.03217 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 I311| + TP3) 
                   
               
               
                 HIF312 
                 0.94990 
                 HIF312/ 
                 0.41300 
                 SGI312 
                 0.00411 
                 |SGI312|/(|S 
                 0.00680 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 GI312| + TP3) 
                   
               
               
                 HIF321 
                 1.05523 
                 HIF321/ 
                 0.45880 
                 SGI321 
                 −0.27368 
                 |SGI321|/(|S 
                 0.31325 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 GI321| + TP3) 
                   
               
               
                 HIF421 
                 0.88795 
                 HIF421/ 
                 0.38606 
                 SGI421 
                 −0.29641 
                 |SGI421|/(|S 
                 0.49656 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 GI421| + TP4) 
                   
               
               
                 HIF511 
                 0.93204 
                 HIF511/ 
                 0.40524 
                 SGI511 
                 −0.35291 
                 |SGI511|/(|SG 
                 0.62865 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 I511| + TP5) 
                   
               
               
                 HIF512 
                 1.32311 
                 HIF512/ 
                 0.57527 
                 SGI512 
                 −0.56508 
                 |SGI512|/(|S 
                 0.73050 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 GI512| + TP5) 
                   
               
               
                 HIF521 
                 0.66633 
                 HIF521/ 
                 0.28971  
                 SGI521 
                 −0.04121 
                 |SGI521|/(|S 
                 0.16503 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 GI521| + TP5) 
                   
               
               
                 HIF522 
                 1.31490  
                 HIF522/ 
                 0.57170  
                 SGI522 
                 −0.08809 
                 |SGI522|/(|S 
                 0.29705 
               
               
                   
                   
                 HOI 
                   
                   
                   
                 GI522| + TP5) 
               
               
                   
               
             
          
         
       
     
       Third Embodiment 
       [0161]    As shown in  FIG. 3A  and  FIG. 3B , an optical image capturing system of the third preferred 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  370 , an image plane  380 , and an image sensor  390 . 
         [0162]    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 object-side surface  312  and the image-side surface  314  each has an inflection point. 
         [0163]    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 concave aspheric surface, and an image-side surface  324  thereof, which faces the image side, is a convex aspheric surface. 
         [0164]    The third lens  330  has positive refractive power, and is made of plastic. An object-side surface  332 , which faces the object side, is a concave aspheric surface, and an image-side surface  334  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  332  and the image-side surface  334  each has two inflection points. 
         [0165]    The fourth lens  340  has a positive refractive power, and is made of plastic. An object-side surface  342 , which faces the object side, is a convex aspheric surface, and an image-side surface  344 , which faces the image side, is a concave aspheric surface. The object-side surface  342  and the image-side surface  344  each has an inflection point. 
         [0166]    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 concave aspheric surface, and an image-side surface  354 , which faces the image side, is a concave aspheric surface. The object-side surface  352  and the image-side surface  354  each has two inflection points. 
         [0167]    The infrared rays filter  370  is made of glass, and between the fifth lens  350  and the image plane  380 . The infrared rays filter  370  gives no contribution to the focal length of the system. 
         [0168]    The parameters of the lenses of the third preferred embodiment are |f 2 |+|f 3 |+|f 4 |=202.8098 mm; |f 1 |+|f 5 |=104.5054 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  310 ; f 2  is a focal length of the second lens  320 ; f 3  is a focal length of the third lens  330 ; and f 4  is a focal length of the fourth lens  340 ; and f 5  is a focal length of the fifth lens  350 . 
         [0169]    The optical image capturing system of the third preferred embodiment further satisfies TP 4 =0.2673 mm and TP 5 =0.2000 mm, where TP 4  is a thickness of the fourth lens  340  on the optical axis, and TP 5  is a thickness of the fifth lens  350  on the optical axis. 
         [0170]    In the third embodiment, the first, the third, and the fourth lenses  310 ,  330 , and  340  are positive lenses, and their focal lengths are f 1 , f 3 , and f 4 . 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 the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0171]    In the third embodiment, the second and the fifth lenses  320  and  350  are negative lenses, and their focal lengths are f 2  and f 5 . 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 lenses. 
         [0172]    The parameters of the lenses of the third embodiment are listed in Table 5 and Table 6. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 f = 1.89674 mm; f/HEP = 1.8; HAF = 50.0004 deg; tan(HAF) = 1.1918 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 infinity 
                 −0.03471 
                   
                   
                   
                   
               
               
                 2 
                 1 st  lens 
                 2.46088 
                 0.352806 
                 plastic 
                 1.565 
                 58 
                 4.50541 
               
               
                 3 
                   
                 64.27998 
                 0.174833 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 −40.3709 
                 0.227909 
                 plastic 
                 1.65 
                 21.4 
                 −100 
               
               
                 5 
                   
                 −105.349 
                 0.139419 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 −1.47864 
                 0.633148 
                 plastic 
                 1.565 
                 58 
                 2.81017 
               
               
                 7 
                   
                 −0.88556 
                 0.05 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 0.72422 
                 0.267314 
                 plastic 
                 1.65 
                 21.4 
                 99.9996 
               
               
                 9 
                   
                 0.62529 
                 0.561558 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −2.46697 
                 0.2 
                 plastic 
                 1.65 
                 21.4 
                 −100 
               
               
                 11 
                   
                 −2.64574 
                 0.1 
                   
                   
                   
                   
               
               
                 12 
                 Filter 
                 infinity 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 infinity 
                 0.398029 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 infinity 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 3.774581 
                 50 
                 −50 
                 −50 
                 −11.248118 
               
               
                 A4 
                 −1.27776E−01 
                 −2.44011E−01 
                 −5.86009E−01 
                  2.36513E−02 
                  1.98506E−01 
               
               
                 A6 
                  2.13799E−01 
                 −7.52363E−01 
                  1.25579E−01 
                 −4.68147E−01 
                  1.16003E−01 
               
               
                 A8 
                 −2.98233E+00 
                  8.12823E−01 
                 −6.83208E+00 
                 −5.66557E−01 
                 −4.65992E−01 
               
               
                 A10 
                  1.06482E+01 
                 −1.19927E+00 
                  8.24455E+00 
                  6.12085E−01 
                 −8.65363E−01 
               
               
                 A12 
                 −1.81028E+01 
                 −1.60914E+00 
                  1.48387E+01 
                  1.68734E+00 
                  2.38624E+00 
               
               
                 A14 
                  2.70672E+00 
                 −1.63981E+00 
                 −3.27846E+01 
                 −2.25332E+00 
                 −1.47372E+00 
               
               
                   
               
             
          
           
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 −0.487673 
                 −2.117587 
                 −1.933793 
                 0.16588 
                 −50 
               
               
                 A4 
                 1.51371E−02 
                 −1.37589E−01 
                 −2.04027E−01 
                 1.82461E−01 
                  6.12158E−02 
               
               
                 A6 
                 5.74363E−02 
                 −6.54839E−02 
                  2.66797E−02 
                 −6.94817E−02  
                 −9.98377E−03 
               
               
                 A8 
                 2.06379E−02 
                  3.52743E−02 
                  8.29950E−03 
                 2.45908E−03 
                 −1.48972E−03 
               
               
                 A10 
                 7.54084E−02 
                 −6.82084E−05 
                 −4.14321E−03 
                 2.50411E−03 
                  1.01116E−05 
               
               
                 A12 
                 2.12285E−02 
                 −2.42746E−03 
                 −3.09744E−03 
                 7.55618E−04 
                  5.81835E−05 
               
               
                 A14 
                 −3.82437E−02  
                 −3.15518E−03 
                  1.13105E−03 
                 −3.56933E−04  
                 −5.44220E−06 
               
               
                   
               
             
          
         
       
     
         [0173]    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. 
         [0174]    The exact parameters of the third embodiment based on Table 5 and Table 6 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Third embodiment 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.04803 
                 −0.09708  
                 −0.22191  
                 −0.19421  
                 −0.15588  
                 −0.57798  
               
               
                 InRS41 
                 InRS42 
                 InRS51 
                 InRS52 
                 HVT51 
                 HVT52 
               
               
                 0.16198 
                 0.18874 
                 −0.22581  
                 −0.02035  
                 0.00000 
                 0.88211 
               
               
                 |ODT| 
                 |TDT| 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
               
               
                 2.00297% 
                 1.05445% 
                 0.81362 
                 1.07836 
                 1.89198 
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS32| + |InRS41|)/IN34 
                 (|InRS42| + |InRS51|)/IN45 
               
               
                 0.72573 
                 0.57246 
                 14.7993 
                 0.7382 
               
             
          
           
               
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/InTL 
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/HOS 
               
               
                 0.22895 
                 0.18060 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f/f5| 
                 |f1/f2| 
               
               
                 0.42099 
                 0.01897 
                 0.67496 
                 0.01897 
                 0.01897 
                 0.04505 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 1.11491 
                 0.03793 
                 29.39029  
                 107.31518  
                 −200.00000   
                 0.04198 
               
               
                 f5/ΣNP 
                 IN12/f 
                 HVT52/HOI 
                 HVT52/HOS 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                 0.50000 
                 0.09218 
                 0.38353 
                 0.26690 
                 1.1291  
                 0.1017  
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 3.30502 
                 2.60699 
                 1.43697 
                 0.98950 
                 0.78880 
                 0.64487 
               
               
                 HVT41 
                 HVT42 
               
               
                 1.01897 
                 1.12157 
               
               
                   
               
               
                 (Reference wavelength: 555 nm) 
               
             
          
         
       
     
         [0175]    The exact parameters of the inflection points of the third embodiment based on Table 5 and Table 6 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Third embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HIF111 
                 0.43436 
                 HIF11 
                 0.18885 
                 SGI111 
                 0.03474 
                 |SGI111|/(|SGI 
                 0.08963 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 111| + TP1) 
                   
               
               
                 HIF121 
                 0.07150 
                 HIF12 
                 0.03109 
                 SGI121 
                 0.00003 
                 |SGI121|/(|SGI 
                 0.00009 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 211| + TP1) 
                   
               
               
                 HIF311 
                 0.37521 
                 HIF31 
                 0.16313 
                 SGI311 
                 −0.03756 
                 |SGI311|/(|SGI 
                 0.05600 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 311| + TP3) 
                   
               
               
                 HIF312 
                 0.58333 
                 HIF31 
                 0.25362 
                 SGI312 
                 −0.06786 
                 |SGI312|/(|SGI 
                 0.09680 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 312| + TP3) 
                   
               
               
                 HIF321 
                 0.85798 
                 HIF32 
                 0.37303 
                 SGI321 
                 −0.43078 
                 |SGI321|/(|SGI 
                 0.40490 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 321| + TP3) 
                   
               
               
                 HIF322 
                 1.00769 
                 HIF32 
                 0.43813 
                 SGI322 
                 −0.56585 
                 |SGI322|/(|SGI 
                 0.47193 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 322| + TP3) 
                   
               
               
                 HIF411 
                 0.55733 
                 HIF41 
                 0.24232 
                 SGI411 
                 0.17245 
                 |SGI411|/(|SGI 
                 0.39214 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 411| + TP4) 
                   
               
               
                 HIF421 
                 0.56329 
                 HIF42 
                 0.24491 
                 SGI421 
                 0.19855 
                 |SGI421|/(|SGI 
                 0.42620 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 421| + TP4) 
                   
               
               
                 HIF511 
                 0.51545 
                 HIF51 
                 0.22411 
                 SGI511 
                 −0.04296 
                 |SGI511|/(|SGI 
                 0.17682 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 511| + TP5) 
                   
               
               
                 HIF512 
                 0.96137 
                 HIF51 
                 0.41799 
                 SGI512 
                 −0.09169 
                 |SGI512|/(|SGI 
                 0.31433 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 512| + TP5) 
                   
               
               
                 HIF521 
                 0.41312 
                 HIF52 
                 0.17962 
                 SGI521 
                 −0.02426 
                 |SGI521|/(|SGI 
                 0.10819 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 521| + TP5) 
                   
               
               
                 HIF522 
                 1.33207 
                 HIF52 
                 0.57916 
                 SGI522 
                 −0.01993 
                 |SGI522|/(|SGI 
                 0.09060 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 522| + TP5) 
               
               
                   
               
             
          
         
       
     
       Fourth Embodiment 
       [0176]    As shown in  FIG. 4A  and  FIG. 4B , an optical image capturing system of the fourth preferred 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  470 , an image plane  480 , and an image sensor  490 . 
         [0177]    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 convex aspheric surface. The object-side surface  412  has an inflection point. 
         [0178]    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. 
         [0179]    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 surfaces. The object-side surface  432  and the image-side surface  434  each has an inflection point. 
         [0180]    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 an inflection point. 
         [0181]    The fifth lens  450  has negative refractive power, and is made of plastic. An object-side surface  452  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  454  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  452  has two inflection points. 
         [0182]    The infrared rays filter  470  is made of glass, and between the fifth lens  450  and the image plane  480 . The infrared rays filter  470  gives no contribution to the focal length of the system. 
         [0183]    The optical image capturing system of the fourth preferred embodiment has the following parameters, which are |f 2 |+|f 3 |+|f 4 |=111.5795 mm; |f 1 |+|f 5 |=4.6065 mm; and |f 2 |+|f 3 |+f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  410 ; f 2  is a focal length of the second lens  420 ; f 3  is a focal length of the third lens  430 ; f 4  is a focal length of the fourth lens  440 ; and f 5  is a focal length of the fifth lens  450 . 
         [0184]    The optical image capturing system of the fourth preferred embodiment further satisfies TP 4 =0.3549 mm and TP 5 =0.2128 mm, where TP 4  is a thickness of the fourth lens  340  on the optical axis, and TP 5  is a thickness of the fifth lens  350  on the optical axis. 
         [0185]    In the fourth embodiment, the first, the third, and the fourth lenses  410 ,  430 , and  440  are positive lenses, and their focal lengths are f 1 , f 3 , and f 4 . 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 the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0186]    In the fourth embodiment, the second and the fifth lenses  420  and  450  are negative lenses, and their focal lengths are f 2  and f 5 . 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 lenses. 
         [0187]    The parameters of the lenses of the fourth embodiment are listed in Table 7 and Table 8. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 f = 2.24032 mm; f/HEP = 2.0; HAF = 44.9997 deg; tan(HAF) = 0.99999 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 infinity 
                 −0.00011 
                   
                   
                   
                   
               
               
                 2 
                 1 st  lens 
                 2.3859 
                 0.455696 
                 plastic 
                 1.565 
                 58 
                 2.77965 
               
               
                 3 
                   
                 −4.31753 
                 0.304833 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 −0.58392 
                 0.2 
                 plastic 
                 1.65 
                 21.4 
                 −100 
               
               
                 5 
                   
                 −0.66907 
                 0.05 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 2.53327 
                 0.445471 
                 plastic 
                 1.565 
                 58 
                 9.34231 
               
               
                 7 
                   
                 4.54799  
                 0.327203 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −5.49049 
                 0.354933 
                 plastic 
                 1.607 
                 26.6 
                 2.23718 
               
               
                 9 
                   
                 −1.12144 
                 0.299017 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −1.12502 
                 0.212847 
                 plastic 
                 1.65 
                 21.4 
                 −1.82689 
               
               
                 11 
                   
                 −20 
                 0.1 
                   
                   
                   
                   
               
               
                 12 
                 Filter 
                 infinity 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 infinity 
                 0.400001 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 infinity 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 4.442682 
                 32.315678 
                 −0.660854 
                 −0.526339 
                 4.449883 
               
               
                 A4 
                 −1.89322E−01 
                 −2.48747E−01 
                 4.74142E−02 
                 3.01434E−01 
                 −1.05620E−01 
               
               
                 A6 
                  9.51166E−02 
                 −2.57418E−01 
                 1.59176E+00 
                 6.70248E−01 
                  1.92902E−02 
               
               
                 A8 
                 −1.56481E+00 
                  1.03272E−01 
                 −2.76571E+00  
                 2.203 64E−01  
                 −5.81766E−02 
               
               
                 A10 
                  6.79105E−01 
                 −2.38772E+00 
                 1.74299E+00 
                 −1.45755E+00  
                 −1.33033E−02 
               
               
                 A12 
                  8.56159E+00 
                  7.25609E+00 
                 8.75531E−01 
                 3.15090E−01 
                  6.47676E−02 
               
               
                 A14 
                 −2.02654E+01 
                 −7.79129E+00 
                 −4.09041E+00  
                 5.15658E−01 
                 −7.76543E−02 
               
               
                   
               
             
          
           
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 −50 
                 −50 
                 −2.805809 
                 −0.287515 
                 50 
               
               
                 A4 
                 −5.73067E−02 
                  5.12532E−02 
                 −4.94351E−02 
                 2.74457E−03 
                 −2.73881E−02 
               
               
                 A6 
                 −8.36953E−02 
                 −1.28146E−01 
                  4.13884E−02 
                 5.50218E−02 
                 −1.13742E−02 
               
               
                 A8 
                  1.11455E−02 
                 −3.62072E−02 
                  2.11205E−02 
                 1.11704E−02 
                  2.15704E−03 
               
               
                 A10 
                  2.08931E−02 
                  1.24160E−02 
                  2.86160E−03 
                 3.52923E−03 
                  4.11311E−04 
               
               
                 A12 
                 −4.32293E−02 
                 −7.02362E−03 
                 −2.59366E−03 
                 2.67995E−03 
                  2.50272E−04 
               
               
                 A14 
                  1.26490E−02 
                 −2.22465E−02 
                 −2.37269E−03 
                 1.70752E−03 
                 −1.35717E−04 
               
               
                   
               
             
          
         
       
     
         [0188]    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. 
         [0189]    The exact parameters of the fourth embodiment based on Table 7 and Table 8 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Fourth embodiment 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.04352 
                 −0.21218  
                 −0.46078  
                 −0.45890  
                 0.10551 
                 −0.13996  
               
               
                 InRS41 
                 InRS42 
                 InRS51 
                 InRS52 
                 HVT51 
                 HVT52 
               
               
                 −0.30617  
                 −0.39203  
                 −0.63854  
                 −0.35904  
                 0.00000 
                 0.00000 
               
               
                 |ODT| 
                 |TDT| 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
               
               
                 2.02520% 
                 1.02303% 
                 1.55452 
                 1.56209 
                 3.11661 
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS32| + |InRS41|)/IN34 
                 (|InRS42| + |InRS51|)/IN45 
               
               
                 1.17608 
                 0.93033 
                 1.3634 
                 3.4465 
               
             
          
           
               
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/InTL 
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/HOS 
               
               
                 0.63991 
                 0.50620 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f/f5| 
                 |f1/f2| 
               
               
                 0.80597 
                 0.02240 
                 0.23980 
                 1.00140 
                 1.22630 
                 0.02780 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 fΣ/ΣPP 
               
               
                 2.04718 
                 1.24871 
                 1.63944 
                 14.35914  
                 −101.82689   
                 0.19358 
               
               
                 f5/ΣNP 
                 IN12/f 
                 HVT52/HOI 
                 HVT52/HOS 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                 0.01794 
                 0.13607 
                 0.00000 
                 0.00000 
                 3.0000  
                 1.6868  
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 3.35000 
                 2.65000 
                 1.45652 
                 0.99997 
                 0.79104 
                 0.62979 
               
               
                 HVT41 
                 HVT42 
               
               
                 0     
                 0     
               
               
                   
               
               
                 (Reference wavelength: 555 nm) 
               
             
          
         
       
     
         [0190]    The exact parameters of the inflection points of the fourth embodiment based on Table 7 and Table 8 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Fourth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HIF111 
                 0.39600 
                 HIF11 
                 0.17217 
                 SGI111 
                 0.02911 
                 |SGI111|/(|SG 
                 0.06004 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I111| + TP1) 
                   
               
               
                 HIF311 
                 0.69833 
                 HIF31 
                 0.30362 
                 SGI311 
                 0.08287 
                 |SGI311|/(|SG 
                 0.15684 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I311| + TP3) 
                   
               
               
                 HIF321 
                 0.37395 
                 HIF32 
                 0.16259 
                 SGI321 
                 0.01293 
                 |SGI321|/(|S 
                 0.02821 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI321| + TP3) 
                   
               
               
                 HIF421 
                 0.77942 
                 HIF42 
                 0.33888 
                 SGI421 
                 −0.23479 
                 |SGI421|/(|S 
                 0.39813 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI421| + TP4) 
                   
               
               
                 HIF511 
                 0.97232 
                 HIF51 
                 0.42275 
                 SGI511 
                 −0.43543 
                 |SGI511|/(|SG 
                 0.67167 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I511| + TP5) 
                   
               
               
                 HIF512 
                 1.21589 
                 HIF51 
                 0.52865 
                 SGI512 
                 −0.61584 
                 |SGI512|/|(S 
                 0.74315 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 GI512| + TP5) 
               
               
                   
               
             
          
         
       
     
       Fifth Embodiment 
       [0191]    As shown in  FIG. 5A  and  FIG. 5B , an optical image capturing system of the fifth preferred 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  570 , an image plane  580 , and an image sensor  590 . 
         [0192]    The first lens  510  has positive refractive power, and is made of plastic. An object-side surface  512  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  514  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  512  has an inflection point. 
         [0193]    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 object-side surface  522  has an inflection point, and the image-side surface  524  has two inflection points. 
         [0194]    The third lens  530  has positive refractive power, and is made of plastic. An object-side surface  532  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  534  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  532  and the image-side surface  534  each has two inflection points. 
         [0195]    The fourth lens  540  has a 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  each has an inflection point. 
         [0196]    The fifth lens  550  has negative refractive power, and is made of plastic. An object-side surface  552  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  554  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  552  has an inflection point, and the image-side surface  554  has two inflection points. 
         [0197]    The infrared rays filter  570  is made of glass, and between the fifth lens  550  and the image plane  580 . The infrared rays filter  570  gives no contribution to the focal length of the system. 
         [0198]    The parameters of the lenses of the fifth preferred embodiment are |f 2 |+|f 3 |+|f 4 |=92.9779 mm; |f 1 |+|f 5 |=4.2942 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  510 ; f 2  is a focal length of the second lens  520 ; f 3  is a focal length of the third lens  530 ; and f 4  is a focal length of the fourth lens  540 ; and f 5  is a focal length of the fifth lens  550 . 
         [0199]    The optical image capturing system of the fifth preferred embodiment further satisfies TP 4 =0.5394 mm and TP 5 =0.2217 mm, where TP 4  is a thickness of the fourth lens  540  on the optical axis, and TP 5  is a thickness of the fifth lens  550  on the optical axis. 
         [0200]    In the fifth preferred embodiment, the first, the third, and the fourth lenses  510 ,  530 , and  540  are positive lenses, and their focal lengths are f 1 , f 3 , and f 4 . 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 the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0201]    In the fifth preferred embodiment, the second and the fifth lenses  520  and  550  are negative lenses, and their focal lengths are f 2  and f 5 . 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 lenses to avoid the significant aberration caused by the incident rays. 
         [0202]    The parameters of the lenses of the fifth embodiment are listed in Table 9 and Table 10. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 f = 2.23522 mm; f/HEP = 2.2; HAF = 45.0001 deg; tan(HAF) = 1.0000 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 infinity 
                 0.021575 
                   
                   
                   
                   
               
               
                 2 
                 1 st  lens 
                 2.77865 
                 0.428111 
                 plastic 
                 1.565 
                 58 
                 2.66817 
               
               
                 3 
                   
                 −3.13322 
                 0.266153 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 −0.62603 
                 0.2 
                 plastic 
                 1.65 
                 21.4 
                 −74.452 
               
               
                 5 
                   
                 −0.71438 
                 0.05 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 1.22315 
                 0.222233 
                 plastic 
                 1.565 
                 58 
                 16.7359 
               
               
                 7 
                   
                 1.31193 
                 0.345874 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −2.00887 
                 0.539374 
                 plastic 
                 1.565 
                 58 
                 1.79 
               
               
                 9 
                   
                 −0.73957 
                 0.376755 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −1.00738 
                 0.221743 
                 plastic 
                 1.65 
                 21.4 
                 −1.62598 
               
               
                 11 
                   
                 −20 
                 0.1 
                   
                   
                   
                   
               
               
                 12 
                 Filter 
                 infinity 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 infinity 
                 0.399757 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 infinity 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 −7.99142 
                 −4.24192 
                 −0.888444 
                 −0.984164 
                 −15.787249 
               
               
                 A4 
                 −1.66690E−01 
                 −4.47564E−01 
                 5.13471E−02 
                  8.21572E−02 
                 1.26874E−01 
               
               
                 A6 
                  1.02722E−01 
                 −4.69434E−01 
                 1.64426E+00 
                  1.45754E+00 
                 −3.28325E−01  
               
               
                 A8 
                 −3.34310E+00 
                  1.21399E+00 
                 −4.42800E+00  
                 −4.89701E−01 
                 2.47475E−01 
               
               
                 A10 
                  6.65787E+00 
                 −5.97802E+00 
                 1.26191E+01 
                 −4.53862E+00 
                 1.30786E−01 
               
               
                 A12 
                  5.74827E+00 
                  1.50111E+01 
                 −3.05813E+01  
                  5.08335E+00 
                 −6.02370E−01  
               
               
                 A14 
                 −4.22341E+01 
                 −1.74337E+01 
                 2.70921E+01 
                 −1.27778E+00 
                 3.48094E−01 
               
               
                   
               
             
          
           
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 −12.912034 
                 1.133182 
                 −1.55392 
                 −0.427047 
                 −0.129932 
               
               
                 A4 
                 −1.06416E−01 
                 −1.77492E−01 
                 −1.32110E−01  
                 3.98307E−01 
                 7.91490E−02 
               
               
                 A6 
                  9.17856E−02 
                  2.79443E−01 
                 1.05931E−01 
                 −1.48294E−01  
                 −7.67527E−02  
               
               
                 A8 
                 −1.19557E−01 
                  1.25483E−01 
                 6.32175E−02 
                 −5.64466E−02  
                 8.38386E−04 
               
               
                 A10 
                  1.48308E−01 
                 −5.83854E−02 
                 9.93323E−03 
                 1.96098E−03 
                 4.65567E−03 
               
               
                 A12 
                 −2.17718E−01 
                 −9.92883E−02 
                 2.62301E−02 
                 7.21207E−03 
                 1.18890E−03 
               
               
                 A14 
                  1.07526E−01 
                  4.95034E−02 
                 −1.99292E−02  
                 1.28124E−02 
                 −4.92270E−04  
               
               
                   
               
             
          
         
       
     
         [0203]    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. 
         [0204]    The exact parameters of the fifth embodiment based on Table 9 and Table 10 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Fifth embodiment 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.02197 
                 −0.20614  
                 −0.34870  
                 −0.32915  
                 0.11476 
                 0.09252 
               
               
                 InRS41 
                 InRS42 
                 InRS51 
                 InRS52 
                 HVT51 
                 HVT52 
               
               
                 −0.14692  
                 −0.48629  
                 −0.66529  
                 −0.35543  
                 0.00000 
                 0.00000 
               
               
                 |ODT| 
                 |TDT| 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
               
               
                 2.01568% 
                 1.06754% 
                 1.29763 
                 1.46952 
                 2.76716 
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS32| + |InRS41|)/IN34 
                 (|InRS42| + |InRS51|)/IN45 
               
               
                 1.04411 
                 0.82602 
                 0.6923 
                 3.0566 
               
             
          
           
               
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/InTL 
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/HOS 
               
               
                 0.62406 
                 0.49371 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f/f5| 
                 |f1/f2| 
               
               
                 0.83774 
                 0.03002 
                 0.13356 
                 1.24873 
                 1.37469 
                 0.03584 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.22002 
                 1.40471 
                 1.58041 
                 21.19407  
                 −76.07798  
                 0.12589 
               
               
                 f5/ΣNP 
                 IN12/f 
                 HVT52/HOI 
                 HVT52/HOS 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                 0.02137 
                 0.11907 
                 0.00000 
                 0.00000 
                 3.0003  
                 1.6029  
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 3.35000 
                 2.65024 
                 1.45652 
                 1.00644 
                 0.79112 
                 0.60804 
               
               
                 HVT41 
                 HVT42 
               
               
                  0.929707 
                 1.0347  
               
               
                   
               
               
                 (Reference wavelength: 555 nm) 
               
             
          
         
       
     
         [0205]    The exact parameters of the inflection points of the fifth embodiment based on Table 9 and Table 10 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Fifth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HIF111 
                 0.32213 
                 HIF11 
                 0.14005 
                 SGI111 
                 0.01627 
                 |SGI111|/(|SG 
                 0.03661 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I111| + TP1) 
                   
               
               
                 HIF211 
                 0.69303 
                 HIF21 
                 0.30132 
                 SGI211 
                 −0.33245 
                 |SGI211|/(|SG 
                 0.62438 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I211| + TP2) 
                   
               
               
                 HIF221 
                 0.47096 
                 HIF22 
                 0.20476 
                 SGI221 
                 −0.13861 
                 |SGI221|/(|S 
                 0.40935 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI221| + TP2) 
                   
               
               
                 HIF222 
                 0.60112 
                 HIF22 
                 0.26136 
                 SGI222 
                 −0.20015 
                 |SGI222|/(|S 
                 0.50018 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 GI222| + TP2) 
                   
               
               
                 HIF311 
                 0.54611 
                 HIF31 
                 0.23744 
                 SGI311 
                 0.08612 
                 |SGI311|/(|SG  
                 0.27930 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I311| + TP3) 
                   
               
               
                 HIF312 
                 0.98749 
                 HIF31 
                 0.42935 
                 SGI312 
                 0.11629 
                 |SGI312|/(|S 
                 0 34353 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 GI312| + TP3) 
                   
               
               
                 HIF321 
                 0.46209 
                 HIF32 
                 0.20091 
                 SGI321 
                 0.05907 
                 |SGI321|/(|S 
                 0.20998 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI321| + TP3) 
                   
               
               
                 HIF322 
                 1.03072 
                 HIF32 
                 0.44814 
                 SGI322 
                 0.09774 
                 |SGI322|/(|S 
                 0.30547 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 GI322| + TP3) 
                   
               
               
                 HIF411 
                 0.63305 
                 HIF41 
                 0.27524 
                 SGI411 
                 −0.11389 
                 |SGI411|/(|SG 
                 0.17434 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I411| + TP4) 
                   
               
               
                 HIF421 
                 0.72748 
                 HIF42 
                 0.31629 
                 SGI421 
                 −0.33514 
                 |SGI421|/(|S 
                 0.38323 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI421| + TP4) 
                   
               
               
                 HIF511 
                 1.14405 
                 HIF51 
                 0.49741 
                 SGI511 
                 −0.54764 
                 |SGI511|/(|SG  
                 0.71179 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I511| + TP5) 
                   
               
               
                 HIF521 
                 0.24889 
                 HIF52 
                 0.10821 
                 SGI521 
                 −0.00126 
                 |SGI521|/(|S 
                 0.00566 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI521| + TP5) 
                   
               
               
                 HIF522 
                 0.60470 
                 HIF52 
                 0.26291 
                 SGI522 
                 −0.00227 
                 |SGI522|/(|S 
                 0.01011 
               
               
                   
                   
                 2/HOI 
                   
                   
                   
                 GI522| + TP5) 
               
               
                   
               
             
          
         
       
     
       Sixth Embodiment 
       [0206]    As shown in  FIG. 6A  and  FIG. 6B , an optical image capturing system of the sixth preferred embodiment of the present invention includes, along an optical axis from an object side to an image side, a first lens  610 , an aperture  600 , a second lens  620 , a third lens  630 , a fourth lens  640 , a fifth lens  650 , an infrared rays filter  670 , an image plane  680 , and an image sensor  690 . 
         [0207]    The first lens  610  has negative refractive power, and is made of plastic. An object-side surface  612  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  614  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  612  has an inflection point. 
         [0208]    The second lens  620  has positive refractive power, and is made of plastic. An object-side surface  622  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  624  thereof, which faces the image side, is a convex aspheric surface. 
         [0209]    The third lens  630  has positive refractive power, and is made of plastic. An object-side surface  632  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  634  thereof, which faces the image side, is a convex aspheric surface. The image-side surface  634  has an inflection point. 
         [0210]    The fourth lens  640  has a 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. 
         [0211]    The fifth lens  650  has negative refractive power, and is made of plastic. An object-side surface  652  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  654  thereof, which faces the image side, is a convex aspheric surface. The image-side surface  654  has an inflection point. 
         [0212]    The infrared rays filter  670  is made of glass, and between the fifth lens  650  and the image plane  680 . The infrared rays filter  670  gives no contribution to the focal length of the system. 
         [0213]    The parameters of the lenses of the sixth preferred embodiment are |f 2 |+|f 3 |+|f 4 |=33.5491 mm; |f 1 |+|f 5 |=10.9113 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  610 ; f 2  is a focal length of the second lens  620 ; f 3  is a focal length of the third lens  630 ; and f 4  is a focal length of the fourth lens  640 ; and f 5  is a focal length of the fifth lens  650 . 
         [0214]    The optical image capturing system of the sixth preferred embodiment further satisfies TP 4 =1.1936 mm and TP 5 =0.4938 mm, where TP 4  is a thickness of the fourth lens  640  on the optical axis, and TP 5  is a thickness of the fifth lens  650  on the optical axis. 
         [0215]    In the sixth preferred embodiment, the second, the third, and the fourth lenses  620 ,  630 , and  640  are positive lenses, and their focal lengths are f 2 , f 3 , and f 4 . The optical image capturing system of the sixth preferred embodiment further satisfies ΣPP=f 2 +f 3 +f 4 =33.5491 mm and f 2 /(f 2 +f 3 +f 4 )=0.1012, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the second lens  620  to the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0216]    In the sixth preferred embodiment, the first and the fifth lenses  610  and  650  are negative lenses, and their focal lengths are f 2  and f 4 . The optical image capturing system of the sixth preferred embodiment further satisfies ΣNP=f 1 +f 5 =−10.9113 mm; and f 5 /(f 1 +f 5 )=0.3956, where 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 lenses to avoid the significant aberration caused by the incident rays. 
         [0217]    The parameters of the lenses of the sixth embodiment are listed in Table 11 and Table 12. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 f = 3.06009 mm; f/HEP = 2.0; HAF = 50.0007 deg; tan(HAF) = 1.1918 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive  
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material  
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens 
                 3.50904  
                 0.796742 
                 plastic 
                 1.514 
                 56.8 
                 −6.5946 
               
               
                 2 
                   
                 1.59356 
                 4.172675 
                   
                   
                   
                   
               
               
                 3 
                 Aperture 
                 infinity 
                 −0.36597 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 2.36495 
                 0.703695 
                 plastic 
                 1.565 
                 58 
                 3.39442 
               
               
                 5 
                   
                 −9.20538 
                 0.766828 
                   
                   
                   
                   
               
               
                 6 
                 3 rd  lens 
                 −3.96665  
                 0.773956 
                 plastic 
                 1.565 
                 58 
                 26.056 
               
               
                 7 
                   
                 −3.3475  
                 0.128823 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −19.1128 
                 1.193613 
                 plastic 
                 1.565 
                 58 
                 4.09863 
               
               
                 9 
                   
                 −2.11807 
                 0.384924 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −1.36773 
                 0.49381 
                 plastic 
                 1.65 
                 21.4 
                 −4.31667 
               
               
                 11 
                   
                 −3.02608 
                 0.1 
                   
                   
                   
                   
               
               
                 12 
                 Filter 
                 infinity 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 infinity 
                 1.623541 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 infinity 
                 0.027363 
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 −0.364446 
                 −0.797073 
                 −0.976489 
                 45.184506 
                 −4.955335 
               
               
                 A4 
                 3.03151E−03 
                 2.47474E−02 
                 1.19749E−02 
                 1.53107E−02 
                 −3.15766E−02 
               
               
                 A6 
                 3.11535E−04 
                 1.09227E−03 
                 3.29173E−03 
                 −8.86750E−03  
                 −7.36452E−03 
               
               
                 A8 
                 6.03641E−06 
                 2.11777E−03 
                 −1.41246E−03  
                 1.63700E−02 
                  9.93051E−03 
               
               
                 A10 
                 −1.90703E−05  
                 −1.38673E−04  
                 2.09487E−03 
                 −9.72154E−03  
                 −1.85429E−02 
               
               
                 A12 
                 1.68207E−06 
                 −2.43097E−05  
                 −1.07114E−03  
                 1.55553E−03 
                  8.34169E−03 
               
               
                 A14 
                 −4.42840E−08  
                 5.42793E−07 
                 4.80842E−05 
                 4.47459E−04 
                 −9.07537E−04 
               
               
                   
               
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 k 
                 −4.26661 
                 −17.215386 
                 0.01572 
                 −0.56999 
                 −1.957095 
               
               
                 A4 
                 −2.02516E−02 
                 −2.81080E−02 
                  1.04073E−02 
                  2.87988E−02 
                  4.78950E−03 
               
               
                 A6 
                 −1.45844E−02 
                  1.26828E−02 
                  4.37395E−04 
                 −1.68233E−04 
                 −4.65598E−04 
               
               
                 A8 
                  1.47638E−02 
                 −2.57367E−02 
                 −8.83115E−04 
                 −1.52077E−04 
                  1.47492E−04 
               
               
                 A10 
                 −8.52821E−03 
                  1.81999E−02 
                 −2.21655E−04 
                  2.58158E−05 
                 −1.37919E−05 
               
               
                 A12 
                 −3.64995E−05 
                 −8.19803E−03 
                 −4.19162E−05 
                 −6.96422E−06 
                  1.27305E−06 
               
               
                 A14 
                  8.24445E−04 
                  1.22153E−03 
                  5.89942E−06 
                  1.05801E−05 
                 −1.66946E−07 
               
               
                   
               
             
          
         
       
     
         [0218]    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. 
         [0219]    The exact parameters of the sixth embodiment based on Table 11 and Table 12 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Sixth embodiment 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 1.85151 
                 2.39057 
                 0.36630 
                 −0.08200  
                 −0.32310  
                 −0.42687  
               
               
                 InRS41 
                 InRS42 
                 InRS51 
                 InRS52 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                 −0.37068  
                 −1.05112  
                 −1.19340  
                 −0.63635  
                 2.4167  
                 1.2887  
               
               
                 |ODT| % 
                 |TDT| % 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
               
               
                 1.99808 
                 0.23490 
                 4.10499 
                 4.58691 
                 8.69190 
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS32| + |InRS41|)/IN34 
                 (|InRS42| + |InRS51|)/IN45 
               
               
                 0.96053 
                 0.79017 
                 6.19108 
                 5.83107 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.35932 
                 0.29560 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f/f5| 
                 |f1/f2| 
               
               
                 0.46403 
                 0.90151 
                 0.11744 
                 0.74661 
                 0.70890 
                 1.94278 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 IN12/f 
               
               
                 1.76556 
                 1.17293 
                 1.50526 
                 33.54905  
                 −10.91127  
                 1.24399 
               
               
                 f1/ΣPP 
                 f5/ΣNP 
                 HVT51 
                 HVT52 
                 HVT52/HOI 
                 HVT52/HOS 
               
               
                 0.10118 
                 0.39562 
                 0.00000 
                 0.00000 
                 0.00000 
                 0.00000 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 11.00000  
                 9.04910 
                 2.94118 
                 0.54823 
                 0.82265 
                 0.43781 
               
               
                 HVT41 
                 HVT42 
               
               
                 0     
                 0     
               
               
                   
               
               
                 (Reference wavelength: 555 nm) 
               
             
          
         
       
     
         [0220]    The exact parameters of the inflection points of the sixth embodiment based on Table 11 and Table 12 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Sixth embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HIF111 
                 2.68797 
                 HIF11 
                 0.718709 
                 SGI111 
                 1.25958 
                 |SGI111|/(|SG 
                 0.61254 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I111| + TP1) 
                   
               
               
                 HIF321 
                 1.35714 
                 HIF32 
                 0.362872 
                 SGI321 
                 −0.35849 
                 |SGI321|/(|S 
                 0.316563 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI321| + TP3) 
                   
               
               
                 HIF521 
                 1.81195 
                 HIF52 
                 0.484479 
                 SGI521 
                 −0.454608 
                 |SGI521|/(|S 
                 0.479333 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI521| + TP5) 
               
               
                   
               
             
          
         
       
     
       Seventh Embodiment 
       [0221]    As shown in  FIG. 7A  and  FIG. 7B , an optical image capturing system of the seventh preferred embodiment of the present invention includes, along an optical axis from an object side to an image side, an aperture  700 , a first lens  710 , a second lens  720 , a third lens  730 , a fourth lens  740 , a fifth lens  750 , an infrared rays filter  770 , an image plane  780 , and an image sensor  790 . 
         [0222]    The first lens  710  has positive refractive power, and is made of plastic. An object-side surface  712  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  714  thereof, which faces the image side, is a concave aspheric surface, and the object-side surface  712  has an inflection point. The object-side surface  712  and the image-side surface  714  each has an inflection point. 
         [0223]    The second lens  720  has negative refractive power, and is made of plastic. An object-side surface  722  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  724  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  722  and the image-side surface  724  each has an inflection point. 
         [0224]    The third lens  730  has positive refractive power, and is made of plastic. An object-side surface  732  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  734  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  732  and the image-side surface  734  each has an inflection point. 
         [0225]    The fourth lens  740  has a positive refractive power, and is made of plastic. An object-side surface  742 , which faces the object side, is a concave aspheric surface, and an image-side surface  744 , which faces the image side, is a convex aspheric surface. The image-side surface  744  has an inflection point. 
         [0226]    The fifth lens  750  has negative refractive power, and is made of plastic. An object-side surface  752  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  754  thereof, which faces the image side, is a convex aspheric surface. The object-side surface  752  has an inflection point. 
         [0227]    The infrared rays filter  770  is made of glass, and between the fifth lens  750  and the image plane  780 . The infrared rays filter  770  gives no contribution to the focal length of the system. 
         [0228]    The parameters of the lenses of the seventh preferred embodiment are |f 2 |+|f 3 |+|f 4 |=108.1231 mm; |f 1 |+|f 5 |=4.4501 mm; and |f 2 |+|f 3 |+|f 4 |&gt;|f 1 |+|f 5 |, where f 1  is a focal length of the first lens  710 ; f 2  is a focal length of the second lens  720 ; f 3  is a focal length of the third lens  730 ; and f 4  is a focal length of the fourth lens  740 ; and f 5  is a focal length of the fifth lens  750 . 
         [0229]    The optical image capturing system of the seventh preferred embodiment further satisfies TP 4 =0.4123 mm and TP 5 =0.2464 mm, where TP 4  is a thickness of the fourth lens  740  on the optical axis, and TP 5  is a thickness of the fifth lens  750  on the optical axis. 
         [0230]    In the seventh preferred embodiment, the second, the third, and the fourth lenses  720 ,  730 , and  740  are positive lenses, and their focal lengths are f 2 , f 3 , and f 4 . The optical image capturing system of the seventh preferred embodiment further satisfies ΣPP=f 2 +f 3 +f 4 =33.5491 mm and f 2 /(f 2 +f 3 +f 4 )=0.1014, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the second lens  720  to the other positive lenses to avoid the significant aberration caused by the incident rays. 
         [0231]    In the seventh preferred embodiment, the first and the fifth lenses  710  and  750  are negative lenses, and their focal lengths are f 2  and f 4 . The optical image capturing system of the seventh preferred embodiment further satisfies ΣNP=f 1 +f 5 =−10.9133 mm; and f 5 /(f 1 +f 5 )=0.3957, where 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  750  to the other negative lenses to avoid the significant aberration caused by the incident rays. 
         [0232]    The parameters of the lenses of the seventh embodiment are listed in Table 13 and Table 14. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
             
             
               
                   
               
               
                 f = 2.8743 mm; f/HEP = 2.4; HAF = 38.0001 deg; tan(HAF) = 0.7813 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 infinity 
                   
                   
                   
                   
               
               
                 1 
                 Aperture 
                 infinity 
                 −0.17585 
                   
                   
                   
                   
               
               
                 2 
                 1 st  lens 
                 1.01744 
                 0.405021 
                 plastic 
                 1.565 
                 58 
                 2.22849 
               
               
                 3 
                   
                 4.47852 
                 0.121586 
                   
                   
                   
                   
               
               
                 4 
                 2 nd  lens 
                 −2.5835 
                 0.2 
                 plastic 
                 1.65 
                 21.4 
                 −5.51039 
               
               
                 5 
                   
                 −9.35269 
                 0.172935 
                   
                   
                   
                   
               
               
                 7 
                 3 rd  lens 
                 3.06317 
                 0.243614 
                 plastic 
                 1.514 
                 56.8 
                 100 
               
               
                 7 
                   
                 3.16851 
                 0.299424 
                   
                   
                   
                   
               
               
                 8 
                 4 th  lens 
                 −1.54523 
                 0.41225 
                 plastic 
                 1.565 
                 58 
                 2.61267 
               
               
                 9 
                   
                 −0.82914 
                 0.548975 
                   
                   
                   
                   
               
               
                 10 
                 5 th  lens 
                 −1.07898 
                 0.246444 
                 plastic 
                 1.514 
                 56.8 
                 −2.22161 
               
               
                 13 
                   
                 −20 
                 0.1 
                   
                   
                   
                   
               
               
                 14 
                 Filter 
                 infinity 
                 0.2 
                   
                 1.517 
                 64.2 
                   
               
               
                 13 
                   
                 infinity 
                 0.39975 
                   
                   
                   
                   
               
               
                 14 
                 Image 
                 infinity 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
                   
                   
                   
                   
                   
                   
               
               
                   
               
               
                 Reference wavelength: 555 nm 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k 
                 −0.152901 
                 −38.451303 
                 7.562493 
                 50 
                 −20.487904 
               
               
                 A4 
                 1.19267E−04 
                 −6.26509E−02 
                  1.07254E−01 
                 6.88242E−02 
                 −6.72385E−01 
               
               
                 A7 
                 2.28986E−01 
                 −5.00591E−01 
                  6.78776E−01 
                 1.28062E+00 
                  5.85516E−01 
               
               
                 A8 
                 −1.11601E+00  
                  1.64822E+00 
                 −1.71636E−01 
                 −8.34550E−01  
                 −5.69296E−01 
               
               
                 A10 
                 1.28574E+00 
                 −3.99700E+00 
                 −1.07367E−01 
                 3.65176E+00 
                 −4.15553E+00 
               
               
                 A14 
                 2.48434E+00 
                 −5.01272E+00 
                 −1.23328E+01 
                 −1.49115E+01  
                  1.38904E+01 
               
               
                 A14 
                 −9.55224E+00  
                  1.28688E+01 
                  2.42747E+01 
                 2.43969E+01 
                 −1.43165E+01 
               
               
                   
               
             
          
           
               
                 Surface 
                 7 
                 8 
                 9 
                 10 
                 13 
               
               
                   
               
               
                 k 
                 −49.400115 
                 1.206381 
                 −1.049906 
                 −0.446708 
                 0.124678 
               
               
                 A4 
                 −2.63281E−01 
                 −1.98332E−01 
                 −7.79871E−02  
                 2.73518E−01 
                  3.77385E−04 
               
               
                 A7 
                 −9.40536E−02 
                  2.87990E−01 
                 2.81316E−02 
                 −1.19550E−01  
                 −2.97516E−02 
               
               
                 A8 
                 −1.19613E−02 
                  2.39851E−02 
                 7.82816E−02 
                 1.11863E−02 
                 −3.22781E−03 
               
               
                 A10 
                  1.35360E−01 
                 −1.96868E−01 
                 3.15953E−02 
                 2.46330E−03 
                  1.08130E−03 
               
               
                 A14 
                 −8.16158E−01 
                 −2.91138E−01 
                 −2.79742E−02  
                 −6.26277E−03  
                  2.78344E−04 
               
               
                 A14 
                  3.76051E−01 
                 −9.10928E−02 
                 7.83309E−04 
                 5.63434E−03 
                 −2.14299E−04 
               
               
                   
               
             
          
         
       
     
         [0233]    An equation of the aspheric surfaces of the seventh embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
         [0234]    The exact parameters of the seventh embodiment based on Table 13 and Table 14 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Seventh embodiment 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.20170 
                 −0.00332  
                 −0.04677  
                 0.06006 
                 −0.05731  
                 −0.10092  
               
               
                 InRS41 
                 InRS42 
                 InRS51 
                 InRS52 
                 HVT51 
                 HVT52 
               
               
                 −0.35035  
                 −0.56260  
                 −0.73934  
                 −0.71124  
                 0.00000 
                 0.00000 
               
               
                 |ODT|% 
                 |TDT|% 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
               
               
                 1.99981 
                 1.11665 
                 1.39546 
                 1.43814 
                 2.83360 
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS32| + |InRS41|)/IN34 
                 (|InRS42| + |InRS51|)/IN45 
               
               
                 1.06918 
                 0.84585 
                 1.5071 
                 2.3716 
               
             
          
           
               
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/InTL 
                 (|InRS41| + |InRS42| + |InRS51| + |InRS52|)/HOS 
               
               
                 0.89181 
                 0.70553 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f/f5| 
                 |f1/f2| 
               
               
                 1.28980 
                 0.52161 
                 0.02874 
                 1.10014 
                 1.29379 
                 0.40442 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.41868 
                 1.81541 
                 1.33231 
                 104.84116  
                 −7.73200  
                 0.02126 
               
               
                 f5/ΣNP 
                 IN12/f 
                 HVT52/HOI 
                 HVT52/HOS 
                 |InRS51|/TP5 
                 |InRS52|/TP5 
               
               
                 0.28733 
                 0.04230 
                 0.00000 
                 0.00000 
                 3.0000  
                 2.8860  
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 3.35000 
                 2.65025 
                 1.45652 
                 0.94751 
                 0.79112 
                 0.56875 
               
               
                 HVT41 
                 HVT42 
               
               
                 0     
                 0     
               
               
                   
               
               
                 (Reference wavelength: 555 nm) 
               
             
          
         
       
     
         [0235]    The exact parameters of the inflection points of the seventh embodiment based on Table 13 and Table 14 are listed in the following table: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Seventh embodiment (Reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 HIF111 
                 0.59342 
                 HIF11 
                 0.25801 
                 SGI111 
                  0.18587 
                 |SGI111|/(|SG 
                 0.31455 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I111| + TP1) 
                   
               
               
                 HIF121 
                 0.31590 
                 HIF12 
                 0.13735 
                 SGI121 
                  0.00966 
                 |SGI121|/(|S 
                 0.02331 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI121| + TP1) 
                   
               
               
                 HIF211 
                 0.38443 
                 HIF21 
                 0.16714 
                 SGI211 
                 −0.02575 
                 |SGI211|/(|SG 
                 0.11407 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I211| + TP2) 
                   
               
               
                 HIF221 
                 0.21188 
                 HIF22 
                 0.09212 
                 SGI221 
                 −0.00216 
                 |SGI221|/(|S 
                 0.01071 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI221| + TP2) 
                   
               
               
                 HIF311 
                 0.19746 
                 HIF31 
                 0.08585 
                 SGI311 
                  0.00525 
                 |SGI311|/(|SG 
                 0.02110 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I311| + TP3) 
                   
               
               
                 HIF321 
                 0.25171 
                 HIF32 
                 0.10944 
                 SGI321 
                  0.00825 
                 |SGI321|/(|S 
                 0.03276 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI321| + TP3) 
                   
               
               
                 HIF421 
                 0.81500 
                 HIF42 
                 0.35435 
                 SGI421 
                 −0.40503 
                 |SGI421|/(|S 
                 0.49558 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 GI421| + TP4) 
                   
               
               
                 HIF511 
                 1.24342 
                 HIF51 
                 0.54062 
                 SGI511 
                 −0.61472 
                 |SGI511|/(|SG 
                 0.71382 
               
               
                   
                   
                 1/HOI 
                   
                   
                   
                 I511| + TP5) 
               
               
                   
               
             
          
         
       
     
         [0236]    It must be pointed out that the embodiments described above are only some preferred 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.