Abstract:
The invention discloses a four-piece optical lens for capturing image and a four-piece optical module for capturing image. In order from an object side to an image side, the optical lens along the optical axis comprises a first lens with positive refractive power; a second lens with refractive power; a third lens with refractive power; and a fourth lens with refractive power; and wherein at least one of the image-side surface and object-side surface of each of the four lens elements is aspheric whereby the optical lens can increase aperture value and improve the imagining quality for use in compact cameras.

Description:
BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present invention relates generally to an optical system, and more particularly to a compact optical image capturing system for an electronic device. 
     2. Description of Related Art 
     In recent years, with the rise of portable electronic devices having camera functionalities, the demand for an optical image capturing system is raised gradually. The image sensing device of ordinary photographing camera is commonly selected from charge coupled device (CCD) or complementary metal-oxide semiconductor sensor (CMOS Sensor). In addition, as advanced semiconductor manufacturing technology enables the minimization of pixel size of the image sensing device, the development of the optical image capturing system towards the field of high pixels. Therefore, the requirement for high imaging quality is rapidly raised. 
     The conventional optical system of the portable electronic device usually has a two or three-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. 
     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. 
     SUMMARY OF THE INVENTION 
     The aspect of embodiment of the present disclosure directs to an optical image capturing system and an optical image capturing lens which use combination of refractive powers, convex and concave surfaces of four-piece optical lenses (the convex or concave surface in the disclosure denotes the geometrical shape of an image-side surface or an object-side surface of each lens on an optical axis) to increase the quantity of incoming light of the optical image capturing system, and to improve imaging quality for image formation, so as to be applied to minimized electronic products. 
     The term and its definition to the lens parameter in the embodiment of the present are shown as below for further reference. 
     The lens parameter related to a length or a height in the lens element: 
     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 fourth lens element is denoted by InTL. A distance from the image-side surface of the fourth 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). 
     The lens parameter related to a material in the lens: 
     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). 
     The lens parameter related to a view angle in the lens: 
     A view angle is denoted by AF. Half of the view angle is denoted by HAF. A major light angle is denoted by MRA. 
     The lens parameter related to exit/entrance pupil in the lens 
     An entrance pupil diameter of the optical image capturing system is denoted by HEP. 
     The lens parameter related to a depth of the lens shape 
     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 fourth lens is denoted by InRS 41  (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 fourth lens is denoted by InRS 42  (instance). 
     The lens parameter related to the lens shape: 
     A critical point C is a tangent point on a surface of a specific lens, and the tangent point is tangent to a plane perpendicular to the optical axis and the tangent point cannot be a crossover point on the optical axis. To follow the past, a distance perpendicular to the optical axis between a critical point C 31  on the object-side surface of the third lens and the optical axis is HVT 31  (instance). A distance perpendicular to the optical axis between a critical point C 32  on the image-side surface of the third lens and the optical axis is HVT 32  (instance). 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 42  on the image-side surface of the fourth lens and the optical axis is HVT 42  (instance). The object-side surface of the fourth lens has one inflection point IF 411  which is nearest to the optical axis, and the sinkage value of the inflection point IF 411  is denoted by SGI 411 . A distance perpendicular to the optical axis between the inflection point IF 411  and the optical axis is HIF 411  (instance). The image-side surface of the fourth lens has one inflection point IF 421  which is nearest to the optical axis, and the sinkage value of the inflection point IF 421  is denoted by SGI 421  (instance). A distance perpendicular to the optical axis between the inflection point IF 421  and the optical axis is HIF 421  (instance). The object-side surface of the fourth lens has one inflection point IF 412  which is the second nearest to the optical axis, and the sinkage value of the inflection point IF 412  is denoted by SGI 412  (instance). A distance perpendicular to the optical axis between the inflection point IF 412  and the optical axis is HIF 412  (instance). The image-side surface of the fourth lens has one inflection point IF 422  which is the second nearest to the optical axis, and the sinkage value of the inflection point IF 422  is denoted by SGI 422  (instance). A distance perpendicular to the optical axis between the inflection point IF 422  and the optical axis is HIF 422  (instance). 
     The lens element parameter related to an aberration: 
     Optical distortion for image formation in the optical image capturing system is denoted by ODT. TV distortion for image formation in the optical image capturing system is denoted by TDT. Further, the range of the aberration offset for the view of image formation may be limited to 50%-100% field. An offset of the spherical aberration is denoted by DFS. An offset of the coma aberration is denoted by DFC. 
     The present invention provides an optical image capturing system, in which the fourth 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 fourth lens are capable of modifying the optical path to improve the imagining quality. 
     The optical image capturing system of the present invention includes a first lens, a second lens, a third lens, and a fourth lens in order along an optical axis from an object side to an image side. The first lens has positive refractive power, and the fourth lens has refractive power. Both the object-side surface and the image-side surface of the fourth lens are aspheric surfaces. The optical image capturing system satisfies:
 
1.2≦ f/HEP≦ 3.5; 0.5≦ HOS/f≦ 3.0; 0 &lt;Σ|InRS|/InTL≦ 3;
 
     where f is a focal length of the optical image capturing system; HEP is an entrance pupil diameter of the optical image capturing system; HOS is a distance in parallel with the optical axis between an object-side surface, which face the object side, of the first lens and the image plane; InTL is a distance between the object-side surface of the first lens and the image-side surface of the third lens; 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 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 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. 
     The present invention further provides an optical image capturing system, including a first lens, a second lens, a third lens, and a fourth lens in order along an optical axis from an object side to an image side. The first lens has positive refractive power, and both the object-side surface and the image-side surface thereof are aspheric surfaces. The second lens has refractive power, and the third lens have refractive power. The fourth lens has refractive power, and both an object-side surface and an image-side surface thereof are aspheric surfaces. The optical image capturing system satisfies:
 
1.2 ≦f/HEP≦ 3.5; 0.5 ≦HOS/f≦ 3.0; 0 &lt;Σ|InRS|/InTL≦ 3 ;|TDT |&lt;60%; and | ODT |≦50%;
 
     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; InTL is a distance between the object-side surface of the first lens and the image-side surface of the third lens; 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 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 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. 
     The present invention further provides an optical image capturing system, including a first lens, a second lens, a third lens, and a fourth lens in order along an optical axis from an object side to an image side. The first lens has positive refractive power, and both an object-side surface and an image-side surface thereof are aspheric surfaces. The second lens has negative refractive power. The third lens has refractive power. The fourth lens has refractive power, and at least one inflection point on at least one surface thereof, wherein both an object-side surface and an image-side surface thereof are aspheric surfaces. The optical image capturing system satisfies:
 
1.2 ≦f/HEP ≦3.5; 0.4≦|tan( HAF )|≦3.0; 0.5 ≦HOS/f ≦3.0 ; |TDT |&lt;1.5%;| ODT |≦2.5%; and 0 &lt;Σ|InRS|/InTL≦ 3;
 
     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; InTL is a distance between the object-side surface of the first lens and the image-side surface of the third lens; 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 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 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. 
     In an embodiment, the optical image capturing system further includes an image sensor with a size less than 1/1.2″ in diagonal, a 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 1.12 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. 
     In an embodiment, the optical image capturing system of the present invention is available to high-quality (4K2K, so called UHD and QHD) recording, and provides high quality of image. 
     In an embodiment, a height of the optical image capturing system (HOS) can be reduced while |f 1 |&gt;f 4 . 
     In an embodiment, when the lenses satisfy |f 2 |+|f 3 |&gt;|f 1 |+|f 4 |, at least one of the lenses from the second lens to the third 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 third 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 third lens could have weak negative refractive power, it may finely modify the aberration of the system. 
     In an embodiment, the fourth lens can have negative refractive power, and an image-side surface thereof is concave, it may reduce back focal length and size. Besides, the fourth lens has at least an inflection point on at least a surface thereof, which may reduce an incident angle of the light of an off-axis field of view and modify the aberration of the off-axis field of view. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The present invention will be best understood by referring to the following detailed description of some illustrative embodiments in conjunction with the accompanying drawings, in which 
         FIG. 1A  is a schematic diagram of a first preferred embodiment of the present invention; 
         FIG. 1B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the first embodiment of the present application; 
         FIG. 1C  shows a curve diagram of TV distortion of the optical image capturing system of the first embodiment of the present application; 
         FIG. 2A  is a schematic diagram of a second preferred embodiment of the present invention; 
         FIG. 2B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the second embodiment of the present application; 
         FIG. 2C  shows a curve diagram of TV distortion of the optical image capturing system of the second embodiment of the present application; 
         FIG. 3A  is a schematic diagram of a third preferred embodiment of the present invention; 
         FIG. 3B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the third embodiment of the present application; 
         FIG. 3C  shows a curve diagram of TV distortion of the optical image capturing system of the third embodiment of the present application; 
         FIG. 4A  is a schematic diagram of a fourth preferred embodiment of the present invention; 
         FIG. 4B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the fourth embodiment of the present application; 
         FIG. 4C  shows a curve diagram of TV distortion of the optical image capturing system of the fourth embodiment of the present application; 
         FIG. 5A  is a schematic diagram of a fifth preferred embodiment of the present invention; 
         FIG. 5B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the fifth embodiment of the present application; 
         FIG. 5C  shows a curve diagram of TV distortion of the optical image capturing system of the fifth embodiment of the present application; 
         FIG. 6A  is a schematic diagram of a sixth preferred embodiment of the present invention; 
         FIG. 6B  shows curve diagrams of longitudinal spherical aberration, astigmatic field, and optical distortion of the optical image capturing system in the order from left to right of the sixth embodiment of the present application; 
         FIG. 6C  shows a curve diagram of TV distortion of the optical image capturing system of the sixth embodiment of the present application; 
         FIG. 7A  is a schematic diagram of a seventh preferred embodiment of the present invention; 
         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; 
         FIG. 7C  shows a curve diagram of TV distortion of the optical image capturing system of the seventh embodiment of the present application; 
         FIG. 8A  is a schematic diagram of a eighth preferred embodiment of the present invention; 
         FIG. 8B  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 eighth embodiment of the present application; and 
         FIG. 8C  shows a curve diagram of TV distortion of the optical image capturing system of the eighth embodiment of the present application. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An optical image capturing system of the present invention includes a first lens, a second lens, a third lens, and a forth lens from an object side to an image side. The optical image capturing system further is provided with an image sensor at an image plane. 
     The optical image capturing system works in three wavelengths, including 486.1 nm, 587.5 nm, and 656.2 nm, wherein 587.5 nm is the main reference wavelength, and 555 nm is adopted as the main reference wavelength for extracting features. 
     The optical image capturing system of the present invention satisfies 0.5≦ΣPPR/|ΣNPR|≦4.5, and a preferable range is 1≦ΣPPR/|ΣNPR|≦3.5, where PPR is a ratio of the focal length f of the optical image capturing system to a focal length fp of each of lenses with positive refractive power; NPR is a ratio of the focal length f of the optical image capturing system to a focal length fn of each of lenses with negative refractive power; 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. 
     HOS is a height of the optical image capturing system, and when the ratio of HOS/f approaches to 1, it is helpful for decrease of size and increase of imaging quality. 
     In an embodiment, the optical image capturing system of the present invention satisfies 0&lt;ΣPP≦200 and f 1 /ΣPP≦0.85, and a preferable range is 0&lt;ΣPP≦150 and 0.01≦f 1 /ΣPP≦0.6, 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 first lens can have 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. 
     The second lens has negative refractive power, which may correct the aberration of the first lens. 
     The third lens has positive refractive power, which may share the positive refractive power of the first lens. 
     The fourth 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 fourth 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 fourth lens has at least an inflection point. 
     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≦3.0, 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 for reduction of size of the system for used in compact cameras. 
     The optical image capturing system of the present invention further is provided with an aperture to increase image quality. 
     In the optical image capturing system of the present invention, the aperture could be a front aperture or a middle aperture, wherein the front aperture is provided between the object and the first lens, and the middle is provided between the first lens and the image plane. The front aperture provides a long distance between an exit pupil of the system and the image plane, which allows more elements to be installed. The middle could enlarge a view angle of view of the system and increase the efficiency of the image sensor. The optical image capturing system satisfies 0.5≦InS/HOS≦1.1, 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 for size reduction and wide angle. 
     The optical image capturing system of the present invention satisfies 0.45≦ΣTP/InTL&lt;0.95, where InTL is a distance between the object-side surface of the first lens and the image-side surface of the fourth lens, and ETP is a sum of central thicknesses of the lenses on the optical axis. It is helpful for the contrast of image and yield rate of manufacture, and provides a suitable back focal length for installation of other elements. 
     The optical image capturing system of the present invention satisfies 0.1≦|R 1 /R 2 |≦0.5, and a preferable range is 0.1≦|R 1 /R 2 |≦0.45, 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. 
     The optical image capturing system of the present invention satisfies −200&lt;(R 7 −R 8 )/(R 7 +R 8 )&lt;30, where R 7  is a radius of curvature of the object-side surface of the fourth lens, and R 8  is a radius of curvature of the image-side surface of the fourth lens. It may modify the astigmatic field curvature. 
     The optical image capturing system of the present invention satisfies 0&lt;IN 12 /f≦0.25, 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. 
     The optical image capturing system of the present invention satisfies 1≦(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. 
     The optical image capturing system of the present invention satisfies 0.2≦(TP 4 +IN 34 )/TP 4 ≦3, where 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, and IN 34  is a distance between the third lens and the fourth lens. It may control the sensitivity of manufacture of the system and improve the performance. 
     The optical image capturing system of the present invention satisfies 0.1≦(TP 2 +TP 3 )/ΣTP≦0.9, and a preferable range is 0.4≦(TP 2 +TP 3 )/ΣTP≦0.8. It may finely modify the aberration of the incident rays and reduce the height of the system. 
     The optical image capturing system of the present invention satisfies 0 mm&lt;|InRS 11 |+|InRS 12 |≦2 mm and 1.0≦(|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. 
     The optical image capturing system of the present invention satisfies 0 mm&lt;|InRS 21 |+|InRS 22 |≦2 mm; and 1.0≦(|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. 
     The optical image capturing system of the present invention satisfies 0 mm&lt;|InRS 31 |+|InRS 32 |≦2 mm; and 1.0≦(|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. 
     The optical image capturing system of the present invention satisfies 0 mm&lt;|InRS 41 |+|InRS 42 |≦5 mm; and 1.0&lt;(|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. 
     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 | 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 |. It may increase the capability of modifying the off-axis view field aberration of the system. 
     The optical image capturing system of the present invention satisfies 0&lt;Σ|InRS|/InTL≦3 and 0≦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. 
     The optical image capturing system of the present invention satisfies 0&lt;|InRS 31 |+|InRS 32 |+|InRS 41 |+|InRS 42 |≦8 mm; 0&lt;(|InRS 31 |+|InRS 32 |+|InRS 41 |+|InRS 42 |)/InTL≦3; and 0&lt;(|InRS 31 |+|InRS 32 |+|InRS 41 |+|InRS 42 |)/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. 
     The optical image capturing system of the present invention satisfies HVT 31 ≧0 mm and HVT 32 ≧0 mm, where HVT 31  a distance perpendicular to the optical axis between the critical point on the object-side surface of the third lens and the optical axis; and HVT 32  a distance perpendicular to the optical axis between the critical point on the image-side surface of the third lens and the optical axis. It may efficiently modify the off-axis view field aberration of the system. 
     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 critical 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 critical 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. 
     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 for correction of the aberration of the peripheral view field. 
     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 for correction of the aberration of the peripheral view field. 
     In an embodiment, the lenses of high Abbe number and the lenses of low Abbe number are arranged in an interlaced arrangement that could be helpful for correction of aberration of the system. 
     An equation of aspheric surface is
 
 z=ch   2 /[1+[1( k +1) c   2   h   2 ] 0.5   ]+A 4 h   4   +A 6 h   6   +A 8 h   8   +A 10 h   10   +A 12 h   12   +A 14 h   14   +A 16 h   16   +A 18 h   18   +A 20 h   20   (1)
 
     where z is a depression of the aspheric surface; k is conic constant; c is reciprocal of radius of curvature; and A 4 , A 6 , A 8 , A 10 , A 12 , A 14 , A 16 , A 18 , and A 20  are high-order aspheric coefficients. 
     In the optical image capturing system, the lenses could be made of plastic or glass. The plastic lenses may reduce the weight and lower the cost of the system, and the glass lenses may control the thermal effect and enlarge the space for arrangement of refractive power of the system. In addition, the opposite surfaces (object-side surface and image-side surface) of the first to the fourth lenses could be aspheric that can obtain more control parameters to reduce aberration. The number of aspheric glass lenses could be less than the conventional spherical glass lenses that is helpful for reduction of the height of the system. 
     When the lens has a convex surface, which means that the surface is convex around a position, through which the optical axis passes, and when the lens has a concave surface, which means that the surface is concave around a position, through which the optical axis passes. 
     The optical image capturing system of the present invention further is provided with a diaphragm to increase image quality. 
     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. 
     We provide several embodiments in conjunction with the accompanying drawings for the best understanding, which are: 
     [First Embodiment] 
     As shown in  FIG. 1A  and  FIG. 1B , an optical image capturing system  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 , an infrared rays filter  170 , an image plane  180 , and an image sensor  190 . 
     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 object-side surface  112  and the image-side surface  114  both have an inflection point respectively. SGI 111  is a displacement in parallel with the optical axis from a point on the object-side surface  112  of the first lens  110 , through which the optical axis passes, to the inflection point on the object-side surface  112 , which is the closest to the optical axis; SGI 121  is a displacement in parallel with the optical axis from a point on the image-side surface  114  of the first lens  110 , through which the optical axis passes, to the inflection point on the image-side surface  114 , which is the closest to the optical axis. 
     HIF 111  is a displacement perpendicular to the optical axis from a point on the object-side surface  112  of the first lens  110 , through which the optical axis passes, to the inflection point, which is the closest to the optical axis; HIF 121  is a displacement perpendicular to the optical axis from a point on the image-side surface  114  of the first lens  110 , through which the optical axis passes, to the inflection point, which is the closest to the optical axis. 
     The second lens  120  has negative refractive power, and is made of plastic. An object-side surface  122  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  124  thereof, which faces the image side, is a concave aspheric surface, and the object-side surface  122  and the image-side surface  124  both have an inflection point respectively. SGI 211  is a displacement in parallel with the optical axis from a point on the object-side surface  122  of the second lens  120 , through which the optical axis passes, to the inflection point on the object-side surface  122 , which is the closest to the optical axis; SGI 221  is a displacement in parallel with the optical axis from a point on the image-side surface  124  of the second lens  120 , through which the optical axis passes, to the inflection point on the image-side surface  124 , which is the closest to the optical axis. 
     HIF 211  is a displacement perpendicular to the optical axis from a point on the object-side surface  122  of the second lens  120 , through which the optical axis passes, to the inflection point, which is the closest to the optical axis; HIF 221  is a displacement perpendicular to the optical axis from a point on the image-side surface  124  of the second lens  120 , through which the optical axis passes, to the inflection point, which is the closest to the optical axis. 
     The third lens  130  has positive refractive power, and is made of plastic. An object-side surface  132 , which faces the object side, is a concave aspheric surface, and an image-side surface  134 , which faces the image side, is a convex aspheric surface, wherein the object-side surface  132  has two inflection points, while the image-side surface has an inflection point. SGI 311  is a displacement in parallel with the optical axis, from a point on the object-side surface  132  of the third lens  130 , through which the optical axis passes, to the inflection point on the object-side surface  132 , 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  134  of the third lens  130 , through which the optical axis passes, to the inflection point on the image-side surface  134 , which is the closest to the optical axis. 
     SGI 312  is a displacement in parallel with the optical axis, from a point on the object-side surface  132  of the third lens  130 , through which the optical axis passes, to the inflection point on the object-side surface  132 , which is the second closest to the optical axis. 
     HIF 311  is a distance perpendicular to the optical axis between the inflection point on the object-side surface  132  of the third lens  130 , 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  134  of the third lens  130 , which is the closest to the optical axis, and the optical axis. 
     HIF 312  is a distance perpendicular to the optical axis between the inflection point on the object-side surface  132  of the third lens  130 , which is the second the closest to the optical axis, and the optical axis. 
     The fourth lens  140  has negative refractive power, and is made of plastic. An object-side surface  142  thereof which faces the object side is a convex aspheric surface, while an image-side surface  144  thereof which faces the image side is a concave aspheric surface, and the object-side surface  142  has two inflection points, while the image-side surface  144  has an inflection point. SGI 411  is a displacement in parallel with the optical axis from a point on the object-side surface  142  of the fourth lens  140 , through which the optical axis passes, to the inflection point on the object-side surface  142 , which is the closest to the optical axis; SGI 421  is a displacement in parallel with the optical axis from a point on the image-side surface  144  of the fourth lens  140 , through which the optical axis passes, to the inflection point on the image-side surface  144 , which is the closest to the optical axis. 
     SGI 412  is a displacement in parallel with the optical axis, from a point on the object-side surface  142  of the fourth lens  140 , through which the optical axis passes, to the inflection point on the object-side surface  142 , which is the second closest to the optical axis. 
     HIF 411  is a distance perpendicular to the optical axis between the inflection point on the object-side surface  142  of the fourth lens  140 , which is the closest to the optical axis, and the optical axis; HIF 421  is a distance perpendicular to the optical axis between the inflection point on the image-side surface  142  of the fourth lens  140 , which is the closest to the optical axis, and the optical axis. 
     HIF 412  is a distance perpendicular to the optical axis between the inflection point on the object-side surface  142  of the fourth lens  140 , which is the second the closest to the optical axis, and the optical axis. 
     The infrared rays filter  170  is made of glass, and between the fourth lens  140  and the image plane  180 . The infrared rays filter  170  gives no contribution to the focal length of the system. 
     The optical image capturing system of the first preferred embodiment has the following parameters, which are f=1.32952 mm; f/HEP=1.83; 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. 
     The parameters of the lenses of the first preferred embodiment are f 1 =1.6074 mm; |f/f 1 |=0.8271; f 4 =−1.0098 mm; |f 1 |&gt;f 4 ; and |f 1 /f 4 |=1.5918, where f 1  is a focal length of the first lens  110 ; and f 4  is a focal length of the fourth lens  140 . 
     The first preferred embodiment further satisfies |f 2 |+|f 3 |=4.0717 mm; |f 1 |+|f 4 |=2.6172 mm; and |f 2 |+|f 3 |&gt;|f 1 |+|f 4 |, 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 . 
     The optical image capturing system of the first preferred embodiment further satisfies ΣPPR=f/f 1 +f/f 3 =2.4734; ΣNPR=f/f 2 +f/f 4 =−1.7239; ΣPPR/|ΣNPR|=1.4348; |f/f 2 |=0.4073; |f/f 3 |=1.6463; and |f/f 4 |=1.3166, where PPR is a ratio of a focal length f of the optical image capturing system to a focal length fp of each of the lenses with positive refractive power; and NPR is a ratio of a focal length f of the optical image capturing system to a focal length fn of each of lenses with negative refractive power. 
     The optical image capturing system of the first preferred embodiment further satisfies InTL+InB=HOS; HOS=1.8503 mm; HOI=1.0280 mm; HOS/HOI=1.7999; HOS/f=1.3917; InTL/HOS=0.6368; and InS/HOS=0.9584, where InTL is a distance between the object-side surface  112  of the first lens  110  and the image-side surface  144  of the fourth lens  140 ; 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  144  of the fourth lens  140  and the image plane  180 . 
     The optical image capturing system of the first preferred embodiment further satisfies ΣTP=0.9887 mm and ΣTP/InTL=0.8392, where ΣTP is a sum of the thicknesses of the lenses  110 - 140  with refractive power. It is helpful for the contrast of image and yield rate of manufacture, and provides a suitable back focal length for installation of other elements. 
     The optical image capturing system of the first preferred embodiment further satisfies |R 1 /R 2 |=0.1252, 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 refractive power to reduce the increase rate of the spherical aberration. 
     The optical image capturing system of the first preferred embodiment further satisfies (R 7 −R 8 )/(R 7 +R 8 )=0.4810, where R 7  is a radius of curvature of the object-side surface  142  of the fourth lens  140 , and R 8  is a radius of curvature of the image-side surface  144  of the fourth lens  140 . It may modify the astigmatic field curvature. 
     The optical image capturing system of the first preferred embodiment further satisfies ΣPP=f 1 +f 3 =2.4150 mm and f 1 /(f 1 +f 3 )=0.6656, 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 lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the first preferred embodiment further satisfies ΣNP=f 2 +f 4 =−4.2739 mm and f 4 /(f 2 +f 4 )=0.7637, where f 2 , and f 4  are focal lengths of the second and the fourth lenses  120 ,  140  respectively, 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 fourth lens  140  to the other negative lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the first preferred embodiment further satisfies IN 12 =0.0846 mm and IN 12 /f=0.0636, where IN 12  is a distance on the optical axis between the first lens  110  and the second lens  120 . It may correct chromatic aberration and improve the performance. 
     The optical image capturing system of the first preferred embodiment further satisfies TP 1 =0.2979 mm; TP 2 =0.1800 mm; and (TP 1 +IN 12 )/TP 2 =2.1251, 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. 
     The optical image capturing system of the first preferred embodiment further satisfies TP 3 =0.3308 mm; TP 4 =0.1800 mm; and (TP 4 +IN 34 )/TP 3 =0.6197, where TP 3  is a central thickness of the third lens  130  on the optical axis, TP 4  is a central thickness of the fourth lens  140  on the optical axis, and IN 34  is a distance on the optical axis between the third lens  130  and the fourth lens  140 . It may control the sensitivity of manufacture of the system and improve the performance. 
     The optical image capturing system of the first preferred embodiment further satisfies (TP 2 +TP 3 )/ΣTP=0.5166, where TP 2  and TP 3  are thicknesses on the optical axis of the second and the third lenses  120 ,  130 , 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. 
     The optical image capturing system of the first preferred embodiment further satisfies |InRS 11 |=0.07696 mm; |InRS 12 |=0.03415 mm; TP 1 =0.29793 mm; and (|InRS 11 |+TP 1 +|InRS 12 |)/TP 1 =1.3730, 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  110 , 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  110 ; InRS 12  is a displacement in parallel with the optical axis from a point on the image-side surface  114  of the first lens  110 , 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  110 ; 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. 
     The optical image capturing system of the first preferred embodiment further satisfies |InRS 21 |=0.04442 mm; |InRS 22 |=0.02844 mm; TP 2 =0.1800 mm; and (|InRS 21 |+TP 2 +|InRS 22 |)/TP 2 =1.4048, 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  120 , 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  120 ; InRS 22  is a displacement in parallel with the optical axis from a point on the image-side surface  124  of the second lens  120 , 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  120 ; 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. 
     The optical image capturing system of the first preferred embodiment further satisfies |InRS 31 |=0.00187 mm; |InRS 32 |=0.14522 mm; TP 3 =0.33081 mm; and (|InRS 31 |+TP 3 +|InRS 32 |)/TP 3 =1.4446, 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  130 , 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  130 ; InRS 32  is a displacement in parallel with the optical axis from a point on the image-side surface  134  of the third lens  130 , 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  130 ; 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. 
     The optical image capturing system of the first preferred embodiment further satisfies |InRS 41 |=0.03563 mm; |InRS 42 |=0.06429 mm; TP 4 =0.1800 mm; and (|InRS 41 |+TP 4 +|InRS 42 |)/TP 4 =1.5551, 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  140 , 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  140 ; InRS 42  is a displacement in parallel with the optical axis from a point on the image-side surface  144  of the fourth lens  140 , 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  140 ; 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. 
     The optical image capturing system of the first preferred embodiment satisfies InRSO=0.15888 mm; InRSI=0.27211 mm; and Σ|InRS|=0.43099 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 | 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 |. It may increase the capability of modifying the off-axis view field aberration of the system. 
     The optical image capturing system of the first preferred embodiment satisfies Σ|InRS|/InTL=0.36580 and Σ|InRS|/HOS=0.23293. 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. 
     The optical image capturing system of the first preferred embodiment satisfies |InRS 31 |+|InRS 32 |+|InRS 41 |+|InRS 42 |≦0.43099 mm; (|InRS 31 |+|InRS 32 |+|InRS 41 |+|InRS 42 |)/InTL≦0.20965; and (|InRS 31 |+|InRS 32 |+|InRS 41 |+|InRS 42 |)/HOS≦0.13350. 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. 
     The optical image capturing system of the first preferred embodiment further satisfies HVT 31 =0.2386 mm and HVT 32 =0.4759 mm, where HVT 31  is a distance perpendicular to the optical axis between a critical point C 31  on the object-side surface  132  of the third lens  130  and the optical axis; HVT 32  is a distance perpendicular to the optical axis between a critical point C 32  on the image-side surface  134  of the third lens  130  and the optical axis. It may modify the aberration of the off-axis field of view. 
     The optical image capturing system of the first preferred embodiment further satisfies HVT 41 =0.3200 mm; HVT 42 =0.5522 mm; and HVT 41 /HVT 42 =0.5795, where HVT 41  is a distance perpendicular to the optical axis between a critical point C 41  on the object-side surface  142  of the fourth lens  140  and the optical axis; HVT 42  is a distance perpendicular to the optical axis between a critical point C 42  on the image-side surface  144  of the fourth lens  140  and the optical axis. It may modify the aberration of the off-axis field of view. 
     The optical image capturing system of the first preferred embodiment further satisfies HVT 42 /HOI=0.5372. It may correct the aberration of the spherical field of view. 
     The optical image capturing system of the first preferred embodiment further satisfies HVT 42 /HOS=0.2985. It may correct the aberration of the spherical field of view. 
     The optical image capturing system of the first preferred embodiment further satisfies NA 4 /NA 2 =1, where NA 2  is an Abbe number of the second lens  120 , and NA 4  is an Abbe number of the fourth lens  140 . It may correct the aberration of the system. 
     The optical image capturing system of the first preferred embodiment further satisfies 0&lt;(|InRS 22 |+|InRS 31 |)/IN 23 =0.37938 and 0&lt;(|InRS 32 |+|InRS 41 |)/IN 34 =7.23406. It may increase the adjustment capacity of the difference of the optical path, and keep the miniature size. 
     The optical image capturing system of the first preferred embodiment further satisfies |TDT|=0.4353% and |ODT|=1.0353%, where TDT is TV distortion; and ODT is optical distortion. 
     The parameters of the lenses of the first embodiment are listed in Table 1 and Table 2. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 f = 1.3295 mm; f/HEP = 1.83; 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 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 0.78234 
                 0.29793 
                 plastic 
                 1.544 
                 56.06 
                 1.607 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 6.24733 
                 0.08459 
               
               
                 3 
                 2 nd  lens 
                 4.14538 
                 0.18000 
                 plastic 
                 1.642 
                 22.46 
                 −3.264 
               
               
                 4 
                   
                 1.37611 
                 0.07989 
               
               
                 5 
                 3 rd  lens 
                 −1.86793 
                 0.33081 
                 plastic 
                 1.544 
                 56.06 
                 0.808 
               
               
                 6 
                   
                 −0.37896 
                 0.02500 
               
               
                 7 
                 4 th  lens 
                 0.91216 
                 0.18000 
                 plastic 
                 1.544 
                 56.06 
                 −1.010 
               
               
                 8 
                   
                 0.31965 
                 0.17206 
               
               
                 9 
                 Filter 
                 plane 
                 0.21 
                 BK7_SCHOTT 
               
               
                 10 
                   
                 plane 
                 0.29 
               
               
                 11 
                 Image plane 
                 plane 
               
               
                 12 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the third surface is 0.36 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                   5.76611E−01 
                   0.00000E+00 
                   1.97452E+01 
                   7.33565E+00 
                   0.00000E+00 
                 −2.09962E+00 
                 −2.65841E+01 
                 −5.02153E+00 
               
               
                 A4 
                 −5.51709E−01 
                 −2.23956E+00 
                 −3.78546E+00 
                 −8.00950E−01 
                   3.04031E+00 
                   1.53566E+00 
                 −2.73583E+00 
                 −2.12382E+00 
               
               
                 A6 
                   1.84419E+00 
                 −2.09186E+00 
                 −4.83803E+00 
                 −1.41685E+01 
                 −7.06804E+00 
                 −5.62446E+00 
                   2.46306E+01 
                   1.01033E+01 
               
               
                 A8 
                 −5.57618E+01 
                 −3.33312E+01 
                 −1.43809E+02 
                   8.62437E+01 
                 −1.72158E+01 
                   1.96904E+01 
                 −2.14097E+02 
                 −4.02636E+01 
               
               
                 A10 
                   3.45594E+02 
                   3.76727E+02 
                   3.15322E+03 
                 −3.68614E+02 
                   8.52740E+01 
                   1.00740E+02 
                   1.17330E+03 
                   1.06276E+02 
               
               
                 A12 
                 −1.49452E+03 
                 −1.16899E+03 
                 −1.72284E+04 
                   1.49654E+03 
                   4.79654E+02 
                 −2.01751E+02 
                 −3.91183E+03 
                 −1.77404E+02 
               
               
                 A14 
                   
                   
                   3.30750E+04 
                 −4.00967E+03 
                 −5.54044E+03 
                 −9.63345E+02 
                   7.77524E+03 
                   1.78638E+02 
               
               
                 A16 
                   
                   
                   
                   
                   1.16419E+04 
                 −5.33613E+00 
                 −8.46792E+03 
                 −1.05883E+02 
               
               
                 A18 
                   
                   
                   
                   
                   6.99649E+04 
                   6.97327E+03 
                   3.92598E+03 
                   3.92300E+01 
               
               
                 A20 
                   
                   
                   
                   
                 −3.30580E+05 
                 −4.71386E+03 
                 −6.97617E+01 
                 −1.03791E+01 
               
               
                   
               
             
          
         
       
     
     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] 
     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 , an infrared rays filter  270 , an image plane  280 , and an image sensor  290 . 
     The first lens  210  has positive refractive power, and is made of plastic. An object-side surface thereof, which faces the object side, is a convex aspheric surface, and an image-side surface thereof, which faces the image side, is a convex aspheric surface. 
     The second lens  220  has negative refractive power, and is made of plastic. An object-side surface  222  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  224  thereof, which faces the image side, is a concave aspheric surface. The object-side surface  222  has an inflection point, while the image-side surface  224  has two inflection points. 
     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. The object-side surface  232  has two inflection points, while the image-side surface  234  has an inflection point. 
     The fourth lens  240  has negative refractive power, and is made of plastic. An object-side surface  242  thereof, which faces the object side, is a convex surface, and an image-side surface  244  thereof, which faces the image side, is a concave aspheric surfaces. The object-side surface  242  has two inflection points, while the image-side surface  244  has an inflection point. 
     The infrared rays filter  270  is made of glass, and between the fourth lens  240  and the image plane  280 . The infrared rays filter  270  gives no contribution to the focal length of the system. 
     The optical image capturing system of the second preferred embodiment has the following parameters, which are |f 2 |+|f 3 |=2.8463 mm; |f 1 |+|f 4 |=2.1524 mm; and |f 2 |+|f 3 |&gt;|f 1 |+|f 4 |, 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 ; and f 4  is a focal length of the fourth lens  240 . 
     The optical image capturing system of the second preferred embodiment further satisfies TP 3 =0.3419 mm and TP 4 =0.1800 mm, where TP 3  is a thickness of the third lens  230  on the optical axis, and TP 4  is a thickness of the fourth lens  240  on the optical axis. 
     In the second embodiment, the first and the third lenses  210 ,  230  are positive lenses, and their focal lengths are f 1  and f 3  respectively. The optical image capturing system of the second preferred embodiment further satisfies ΣPP=f 1 +f 3 =2.0394 mm and f 1 /(f 1 +f 3 )=0.6445, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  210  to the other positive lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the second preferred embodiment further satisfies ΣNP=f 2 +f 4 =−2.9592 mm and f 4 /(f 2 +f 4 )=0.7168, where f 2  and f 4  are focal lengths of the second and the fourth lenses  220 ,  240 , and ΣNP is a sum of the focal lengths of each negative lens. It is helpful to share the negative refractive power of the fourth lens  240  to the other negative lens to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the first preferred embodiment further satisfies HVT 31 =0.2938 mm and HVT 32 =0.4785 mm, where HVT 31  is a distance perpendicular to the optical axis between a critical point C 31  on the object-side surface  132  of the third lens  130  and the optical axis; HVT 32  is a distance perpendicular to the optical axis between a critical point C 32  on the image-side surface  134  of the third lens  130  and the optical axis. 
     The optical image capturing system of the first preferred embodiment further satisfies HVT 41 =0.2727 mm and HVT 42 =0.5598 mm, where HVT 41  is a distance perpendicular to the optical axis between a critical point C 41  on the object-side surface  142  of the fourth lens  140  and the optical axis; HVT 42  is a distance perpendicular to the optical axis between a critical point C 42  on the image-side surface  144  of the fourth lens  140  and the optical axis. 
     The optical image capturing system of the first preferred embodiment further satisfies ΣPPR=f/f 1 +f/f 3 =2.81647; ΣNPR=f/f 2 +f/f 4 =2.19093; and ΣPPR/|ΣNPR|=1.28551, where ΣPPR is a sum of the positive refractive power of all the positive lenses, and ΣNPR is a sum of the negative refractive power of all the negative lenses. 
     The parameters of the lenses of the second embodiment are listed in Table 3 and Table 4. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 f = 1.3161 mm; f/HEP = 2.2; HAF = 37.4999 deg; tan(HAF) = 0.7673 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 0.79595 
                 0.28690 
                 plastic 
                 1.535 
                 56.05 
                 1.314 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 −5.39261 
                 0.06530 
               
               
                 3 
                 2nd lens 
                 −10.03368 
                 0.18000 
                 plastic 
                 1.636 
                 23.89 
                 −2.121 
               
               
                 4 
                   
                 1.58183 
                 0.09560 
               
               
                 5 
                 3rd lens 
                 −1.85091 
                 0.34192 
                 plastic 
                 1.535 
                 56.05 
                 0.725 
               
               
                 6 
                   
                 −0.34207 
                 0.02500 
               
               
                 7 
                 4th lens 
                 0.95031 
                 0.18000 
                 plastic 
                 1.535 
                 56.05 
                 −0.838 
               
               
                 8 
                   
                 0.28496 
                 0.17538 
               
               
                 9 
                 Filter 
                 plane 
                 0.21 
                 BK7_SCHOTT 
               
               
                 10 
                   
                 plane 
                 0.29 
               
               
                 11 
                 Image Plane 
                 plane 
               
               
                 12 
               
               
                   
               
               
                 Reference wavelength: 555 nm 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
               
               
                 k 
                 −2.63520E+00 
                 9.00000E+01 
                 7.02705E+01 
                 1.04836E+01 
                  0.00000E+00 
               
               
                 A4 
                  2.54572E−01 
                 −2.78473E+00  
                 −4.11735E+00  
                 −7.94187E−01  
                  2.01072E+00 
               
               
                 A6 
                 −2.39185E+00 
                 −6.41042E+00  
                 −4.75470E+00  
                 −1.16298E+01  
                 −2.19396E+00 
               
               
                 A8 
                 −1.44420E+01 
                 −2.59495E+01  
                 −1.17215E+02  
                 9.92997E+01 
                 −9.25098E+00 
               
               
                 A10 
                 −4.42055E+01 
                 8.80139E+02 
                 3.46562E+03 
                 −5.19480E+02  
                 −7.47034E+00 
               
               
                 A12 
                 −1.49091E+03 
                 −4.22124E+03  
                 −1.90911E+04  
                 1.88585E+03 
                  1.65866E+02 
               
               
                 A14 
                  0.00000E+00 
                 0.00000E+00 
                 3.30750E+04 
                 −4.00967E+03  
                 −1.97492E+03 
               
               
                 A16 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                  4.45806E+03 
               
               
                 A18 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                  6.99649E+04 
               
               
                 A20 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
                 −3.30580E+05 
               
               
                   
               
             
          
           
               
                   
                 Surface 
                 6 
                 7 
                 8 
               
               
                   
                   
               
               
                   
                 k 
                 −1.91663E+00 
                 −7.29999E+01 
                 −5.48399E+00 
               
               
                   
                 A4 
                  1.54783E+00 
                 −2.67149E+00 
                 −2.01478E+00 
               
               
                   
                 A6 
                 −6.19201E+00 
                  2.50952E+01 
                  9.86508E+00 
               
               
                   
                 A8 
                  2.06421E+01 
                 −2.14629E+02 
                 −4.00560E+01 
               
               
                   
                 A10 
                  9.70022E+01 
                  1.17159E+03 
                  1.06564E+02 
               
               
                   
                 A12 
                 −1.25083E+02 
                 −3.90951E+03 
                 −1.77622E+02 
               
               
                   
                 A14 
                 −9.73701E+02 
                  7.78461E+03 
                  1.77782E+02 
               
               
                   
                 A16 
                 −4.64315E+02 
                 −8.48455E+03 
                 −1.04877E+02 
               
               
                   
                 A18 
                  6.97327E+03 
                  3.92598E+03 
                  3.92300E+01 
               
               
                   
                 A20 
                 −4.71386E+03 
                 −6.97617E+01 
                 −1.03791E+01 
               
               
                   
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the second embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the second embodiment (with main reference wavelength as 555 nm) based on Table 3 and Table 4 are listed in the following table: 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Second embodiment (main reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.01337 
                 −0.05357 
                 −0.05604 
                 0.03101 
                 −0.00848 
                 −0.16816 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 −0.04642 
                 0.07249 
                 0.12431 
                 0.32523 
                 0.44954 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.38268 
                 0.24298 
                 0.4131 
                 8.5832 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.25160 
                 0.15975 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 1.00123 
                 0.62041 
                 1.81523 
                 1.57051 
                 0.61965 
                 2.92584 
               
               
                 Σ PPR 
                 Σ NPR 
                 Σ PPR/| Σ NPR| 
                 Σ PP 
                 Σ NP 
                 f1/Σ PP 
               
               
                 2.81647 
                 2.19093 
                 1.28551 
                 2.03945 
                 −2.95924 
                 0.64451 
               
               
                 f4/Σ NP 
                 IN12/f 
                 HVT41 
                 HVT42 
                 |ODT| 
                 |TDT| 
               
               
                 0.28317 
                 0.04962 
                 0.27270 
                 0.55978 
                 1.00310 
                 0.40309 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 Σ TP/InTL 
               
               
                 1.17472 
                 1.85011 
                 1.79972 
                 0.99277 
                 0.63495 
                 0.84175 
               
               
                 HVT31 
                 HVT32 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0.2938 
                 0.4785 
                 0.25787 
                 0.40274 
                 0.54453 
                 0.30257 
               
               
                   
               
             
          
         
       
     
     [Third Embodiment] 
     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 , an infrared rays filter  370 , an image plane  380 , and an image sensor  390 . 
     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, and the object-side surface  312  and the image-side surface  314  both have an inflection point respectively. 
     The second lens  320  has positive 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. 
     The third lens  330  has negative 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 , which faces the image side, is a convex aspheric surface, and the image-side surface  334  has an inflection point. 
     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  has two inflection points, while the image-side surface  344  has an inflection point. 
     The infrared rays filter  370  is made of glass, and between the fourth lens  340  and the image plane  380 . The infrared rays filter  370  gives no contribution to the focal length of the system. 
     The parameters of the lenses of the third preferred embodiment are |f 2 |+|f 3 |=3.2561 mm; |f 1 |+|f 4 |=4.3895 mm; and |f 2 |+|f 3 |&lt;|f 1 +|f 4 |, 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 . 
     The optical image capturing system of the third preferred embodiment further satisfies TP 3 =0.2115 mm and TP 4 =0.5131 mm, where TP 3  is a thickness of the third lens  330  on the optical axis, and TP 4  is a thickness of the fourth lens  340  on the optical axis. 
     The optical image capturing system of the third preferred embodiment further satisfies ΣPP=f 1 +f 2 +f 4 =6.3099 mm and f 1 /(f 1 +f 2 +f 4 )=0.3720, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  310  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the third preferred embodiment further satisfies ΣNP=f 3 =−1.3357 mm and f 3 /(f 3 )=1, where ΣNP is a sum of the focal lengths of each negative lens. 
     The parameters of the lenses of the third embodiment are listed in Table 5 and Table 6. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 f = 1.7488 mm; f/HEP = 1.82; HAF = 44.0009 deg; tan(HAF) = 0.9657 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 1.10194 
                 0.30074 
                 plastic 
                 1.53460 
                 56.04928 
                 2.34742 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 7.99086 
                 0.20524 
               
               
                 3 
                 2 nd  lens 
                 −2.57494 
                 0.40303 
                 plastic 
                 1.53460 
                 56.04928 
                 1.92038 
               
               
                 4 
                   
                 −0.77590 
                 0.11157 
               
               
                 5 
                 3 rd  lens 
                 −0.33101 
                 0.21155 
                 plastic 
                 1.64250 
                 22.45544 
                 −1.33567 
               
               
                 6 
                   
                 −0.67089 
                 0.06000 
               
               
                 7 
                 4 th  lens 
                 0.58226 
                 0.51306 
                 plastic 
                 1.53460 
                 56.04928 
                 2.04210 
               
               
                 8 
                   
                 0.86075 
                 0.20560 
               
               
                 9 
                 Filter 
                 plane 
                 0.21 
                 BK7_SCHOTT 
                 1.51680 
                 64.13477 
                 Infinity 
               
               
                 10 
                   
                 plane 
                 0.51922 
               
               
                 11 
                 Image plane 
                 plane 
               
               
                 12 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the second surface is 0.45 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                 −4.11386E+00 
                   1.11609E+02 
                 −1.20457E+01 
                 −2.60894E+01 
                 −1.60828E+00 
                 −3.02168E+00 
                 −7.36240E+00 
                 −1.32421E+00 
               
               
                 A4 
                   6.45604E−02 
                 −2.79760E−01 
                 −1.55566E+00 
                 −2.78890E+00 
                   4.87451E+00 
                 −1.88477E+00 
                 −4.73940E−01 
                 −7.69448E−01 
               
               
                 A6 
                   9.37001E+00 
                 −1.70772E+00 
                   2.22043E+01 
                 −5.44108E+00 
                 −9.55485E+01 
                   1.08819E+01 
                   5.90018E−01 
                   1.03816E+00 
               
               
                 A8 
                 −2.08371E+02 
                   3.44420E+00 
                 −4.29093E+02 
                   2.44100E+02 
                   9.54312E+02 
                 −7.59696E+01 
                 −1.09086E+00 
                 −1.24944E+00 
               
               
                 A10 
                   2.45407E+03 
                 −5.70037E+01 
                   4.72722E+03 
                 −2.82690E+03 
                 −6.36131E+03 
                   4.43236E+02 
                   1.91543E+00 
                   1.15891E+00 
               
               
                 A12 
                 −1.74873E+04 
                   3.13103E+02 
                 −3.37154E+04 
                   1.77963E+04 
                   2.99146E+04 
                 −1.53273E+03 
                 −2.14594E+00 
                 −7.58232E−01 
               
               
                 A14 
                   7.67016E+04 
                 −1.14091E+03 
                   1.53196E+05 
                 −6.60567E+04 
                 −9.56348E+04 
                   3.13152E+03 
                   1.44027E+00 
                   3.27720E−01 
               
               
                 A16 
                 −2.03736E+05 
                   2.44076E+03 
                 −4.32864E+05 
                   1.44067E+05 
                   1.94093E+05 
                 −3.75205E+03 
                 −5.57990E−01 
                 −8.76837E−02 
               
               
                 A18 
                   2.99396E+05 
                 −2.82699E+03 
                   6.99029E+05 
                 −1.71204E+05 
                 −2.23641E+05 
                   2.43713E+03 
                   1.14320E−01 
                   1.29417E−02 
               
               
                 A20 
                 −1.86602E+05 
                   1.34465E+03 
                 −4.96564E+05 
                   8.55440E+04 
                   1.10909E+05 
                 −6.55460E+02 
                 −9.18324E−03 
                 −7.90229E−04 
               
               
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the third embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the third embodiment (with main reference wavelength as 555 nm) based on Table 5 and Table 6 are listed in the following table: 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.09255 
                 −0.01411 
                 −0.12423 
                 −0.32720 
                 −0.38369 
                 −0.29644 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 0.07620 
                 0.09088 
                 0.67668 
                 0.72863 
                 1.40530 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.77848 
                 0.51288 
                 6.3720 
                 6.2106 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.46932 
                 0.30920 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 0.74498 
                 0.91064 
                 1.30929 
                 0.85636 
                 1.22237 
                 1.43777 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.51199 
                 1.30929 
                 1.91859 
                 1.01175 
                 3.96248 
                 2.32016 
               
               
                 f4/ΣNP 
                 IN12/f 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 |ODT| 
                 |TDT| 
               
               
                 0.51536 
                 0.11736 
                 0.14853 
                 0.17714 
                 2.83850 
                 0.48954 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ETP/InTL 
               
               
                 1.80518 
                 2.74000 
                 1.52902 
                 0.96622 
                 0.65882 
                 0.79126 
               
               
                 HVT31 
                 HVT32 
                 HVT41 
                 HVT42 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0 
                 0 
                 0.72659 
                 1.01863 
                 0.56843 
                 0.37176 
               
               
                   
               
             
          
         
       
     
     [Fourth Embodiment] 
     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 , an infrared rays filter  470 , an image plane  480 , and an image sensor  490 . 
     The first lens  410  has positive refractive power, and is made of plastic. An object-side surface  412  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  414  thereof, which faces the image side, is a concave aspheric surface, and each of them has an inflection point respectively. 
     The second lens  420  has positive refractive power, and is made of plastic. An object-side surface thereof, which faces the object side, is a concave aspheric surface, and an image-side surface thereof, which faces the image side, is a convex aspheric surface. 
     The third lens  430  has negative refractive power, and is made of plastic. An object-side surface  432 , which faces the object side, is a concave aspheric surface, and an image-side surface  434 , which faces the image side, is a convex aspheric surface. The object-side surface  432  has two inflection points, while the image-side surface  434  has an inflection point. 
     The fourth lens  440  has positive refractive power, and is made of plastic. An object-side surface  442 , which faces the object side, is a convex aspheric surface, and an image-side surface  444 , which faces the image side, is a concave aspheric surface. The object-side surface  442  and the image-side surface  444  both have an inflection point respectively. 
     The infrared rays filter  470  is made of glass, and between the fourth lens  440  and the image plane  480 . The infrared rays filter  470  gives no contribution to the focal length of the system. 
     The optical image capturing system of the fourth preferred embodiment has the following parameters, which are |f 2 |+|f 3 |=4.3448 mm; |f 1 |+|f 4 |=3.9627 mm; and |f 2 |+|f 3 |&gt;|f 1 |+|f 4 |, 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 ; and f 4  is a focal length of the fourth lens  440 . 
     The optical image capturing system of the fourth preferred embodiment further satisfies TP 3 =0.1900 mm and TP 4 =0.5171 mm, where TP 3  is a thickness of the third lens on the optical axis, and TP 4  is a thickness of the fourth lens on the optical axis. 
     In the fourth embodiment, the optical image capturing system of the fourth preferred embodiment further satisfies ΣPP=f 1 +f 2 +f 4 =6.9824 mm and f 1 /(f 1 +f 2 +f 4 )=0.3392, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  410  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the fourth preferred embodiment further satisfies ΣNP=f 3 =−1.3251 mm and f 3 /(f 3 )=1, where ΣNP is a sum of the focal lengths of each negative lens. 
     The parameters of the lenses of the fourth embodiment are listed in Table 7 and Table 8. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 f = 1.7995 mm; f/HEP = 2.037; HAF = 44.0013 deg; tan(HAF) = 0.9657 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 1.06261 
                 0.27856 
                 plastic 
                 1.535 
                 56.05 
                 2.368 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 5.90448 
                 0.21824 
               
               
                 3 
                 2 nd  lens 
                 −3.07258 
                 0.28878 
                 plastic 
                 1.535 
                 56.05 
                 3.020 
               
               
                 4 
                   
                 −1.09535 
                 0.14992 
               
               
                 5 
                 3 rd  lens 
                 −0.34003 
                 0.19000 
                 plastic 
                 1.642 
                 22.46 
                 −1.325 
               
               
                 6 
                   
                 −0.68687 
                 0.06000 
               
               
                 7 
                 4 th  lens 
                 0.52196 
                 0.51706 
                 plastic 
                 1.535 
                 56.05 
                 1.594 
               
               
                 8 
                   
                 0.87651 
                 0.22691 
               
               
                 9 
                 Filter 
                 plane 
                 0.21 
                 BK7_SCHOTT 
                 1.517 
                 64.13 
                 Infinity 
               
               
                 10 
                   
                 plane 
                 0.48809 
               
               
                 11 
                 Image plane 
                 plane 
               
               
                 12 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the second surface is 0.477 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                 −4.11386E+00 
                   1.11609E+02 
                 −1.20457E+01 
                 −2.60894E+01 
                 −1.60828E+00 
                 −3.02168E+00 
                 −6.90987E+00 
                 −1.16395E+00 
               
               
                 A4 
                   1.89663E−01 
                 −4.42882E−01 
                 −1.64918E+00 
                 −1.26975E+00 
                   5.72303E+00 
                 −1.58295E+00 
                 −4.49130E−01 
                 −8.19241E−01 
               
               
                 A6 
                   7.83824E+00 
                 −1.24645E+00 
                   2.35185E+01 
                 −1.36831E+01 
                   9.42979E+01 
                   1.00231E+01 
                   5.93576E−01 
                   1.06732E+00 
               
               
                 A8 
                 −2.01070E+02 
                 −3.10954E−01 
                 −4.45396E+02 
                   2.85720E+02 
                   9.49136E+02 
                 −7.13304E+01 
                 −1.09774E+00 
                 −1.26303E+00 
               
               
                 A10 
                   2.43526E+03 
                 −5.27607E+01 
                   4.79314E+03 
                 −2.93450E+03 
                   6.37753E+03 
                   4.33436E+02 
                   1.90775E+00 
                   1.15763E+00 
               
               
                 A12 
                 −1.74872E+04 
                   3.13009E+02 
                 −3.37154E+04 
                   1.78985E+04 
                   2.99953E+04 
                 −1.52494E+03 
                 −2.14594E+00 
                 −7.56626E−01 
               
               
                 A14 
                   7.67016E+04 
                 −1.14091E+03 
                   1.53196E+05 
                 −6.60525E+04 
                   9.57659E+04 
                   3.12107E+03 
                   1.44027E+00 
                   3.28469E−01 
               
               
                 A16 
                 −2.03736E+05 
                   2.44076E+03 
                 −4.32864E+05 
                   1.44068E+05 
                   1.94093E+05 
                 −3.73817E+03 
                 −5.57990E−01 
                 −8.82160E−02 
               
               
                 A18 
                   2.99396E+05 
                 −2.82699E+03 
                   6.99029E+05 
                 −1.71204E+05 
                 −2.23641E+05 
                   2.43713E+03 
                   1.14320E−01 
                   1.29417E−02 
               
               
                 A20 
                 −1.86602E+05 
                   1.34465E+03 
                 −4.96564E+05 
                   8.55440E+04 
                   1.10909E+05 
                 −6.55460E+02 
                 −9.18324E−03 
                 −7.90229E−04 
               
               
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the fourth embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the fourth embodiment (with main reference wavelength as 555 nm) based on Table 7 and Table 8 are listed in the following table: 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Fourth embodiment (main reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.08569 
                 −0.02436 
                 −0.13024 
                 −0.23075 
                 −0.31306 
                 −0.24465 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 0.09386 
                 −0.02821 
                 0.62285 
                 0.52797 
                 1.15082 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.67594 
                 0.43798 
                 3.6273 
                 5.6419 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.39927 
                 0.25871 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 0.75976 
                 0.59591 
                 1.35802 
                 1.12873 
                 0.78434 
                 2.27888 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.48440 
                 1.35802 
                 1.82943 
                 1.04339 
                 4.61393 
                 2.26997 
               
               
                 f4/ΣNP 
                 IN12/f 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 |ODT| 
                 |TDT| 
               
               
                 0.34553 
                 0.12128 
                 0.18153 
                 0.05456 
                 2.77932 
                 1.07666 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ETP/InTL 
               
               
                 1.70256 
                 2.62756 
                 1.46627 
                 0.96739 
                 0.64796 
                 0.74852 
               
               
                 HVT31 
                 HVT32 
                 HVT41 
                 HVT42 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0 
                 0.7088 
                 0.78677 
                 0.96171 
                 0.53667 
                 0.36601 
               
               
                   
               
             
          
         
       
     
     [Fifth Embodiment] 
     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 , an infrared rays filter  570 , an image plane  580 , and an image sensor  590 . 
     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 concave aspheric surface, wherein the object-side surface  512  and the image-side surface  514  both have an inflection point respectively. 
     The second lens  520  has positive refractive power, and is made of plastic. An object-side surface  522  thereof, which faces the object side, is a concave aspheric surface, and an image-side surface  524  thereof, which faces the image side, is a convex aspheric surface. 
     The third lens  530  has negative refractive power, and is made of plastic. An object-side surface  532 , which faces the object side, is a concave aspheric surface, and an image-side surface  534 , which faces the image side, is a convex aspheric surface. The image-side surface  534  has an inflection point. 
     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 convex aspheric surface, and an image-side surface  544 , which faces the image side, is a concave aspheric surface. The object-side surface  542  has two inflection points, while the image-side surface  544  has an inflection point. 
     The infrared rays filter  570  is made of glass, and between the fourth lens  540  and the image plane  580 . The infrared rays filter  570  gives no contribution to the focal length of the system. 
     The parameters of the lenses of the fifth preferred embodiment are |f 2 |+|f 3 |=7.6703 mm; |f 1 |+|f 4 |=7.7843 mm; and |f 2 |+|f 3 |&gt;|f 1 |+|f 4 |, 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 . 
     The optical image capturing system of the fifth preferred embodiment further satisfies TP 3 =0.3996 mm and TP 4 =0.9713 mm, where TP 3  is a thickness of the third lens  530  on the optical axis, and TP 4  is a thickness of the fourth lens  540  on the optical axis. 
     The optical image capturing system of the fifth preferred embodiment further satisfies ΣPP=f 1 +f 2 +f 4 =13.1419 mm and f 1 /(f 1 +f 2 +f 4 )=0.2525, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  510  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the fifth preferred embodiment further satisfies ΣNP=f 3 =−2.3127 mm; and f 3 /(f 3 )=1, where ΣNP is a sum of the focal lengths of each negative lens. 
     The parameters of the lenses of the fifth embodiment are listed in Table 9 and Table 10. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 f = 3.4320 mm; f/HEP = 2.28; HAF = 39.5498 deg; tan(HAF) = 0.8258 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 1.50982 
                 0.61808 
                 plastic 
                 1.53460 
                 56.04928 
                 3.31779 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 8.53969 
                 0.32873 
               
               
                 3 
                 2 nd  lens 
                 −6.01490 
                 0.35414 
                 plastic 
                 1.53460 
                 56.04928 
                 5.35759 
               
               
                 4 
                   
                 −1.98450 
                 0.11553 
               
               
                 5 
                 3rd lens 
                 −1.05901 
                 0.39958 
                 plastic 
                 1.64250 
                 22.45544 
                 −2.31270 
               
               
                 6 
                   
                 −4.15119 
                 0.20863 
               
               
                 7 
                 4 th  lens 
                 1.15231 
                 0.97132 
                 plastic 
                 1.53460 
                 56.04928 
                 4.46650 
               
               
                 8 
                   
                 1.56696 
                 0.17398 
               
               
                 9 
                 Filter 
                 plane 
                 0.61 
                 BK_7 
                 1.51680 
                 64.13477 
               
               
                 10 
                   
                 plane 
                 0.67 
               
               
                 11 
                 Image plane 
                 plane 
               
               
                 12 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the third surface is 0.72 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                   1.91608E+00 
                 −9.90000E+01 
                   3.12661E+01 
                 −7.96538E+00 
                 −8.30362E−01 
                 −6.96585E+00 
                 −1.18798E+01 
                 −7.01760E−01 
               
               
                 A4 
                 −1.04983E−01 
                 −7.00916E−02 
                 −1.45169E−01 
                 −4.53803E−01 
                 −5.41253E−01 
                 −1.20350E+00 
                 −4.13567E−01 
                 −2.64281E−01 
               
               
                 A6 
                   5.81412E−01 
                   1.32838E−01 
                   6.30379E−01 
                   1.53028E+00 
                   2.79171E+00 
                   3.66683E+00 
                   2.54369E−01 
                   1.37894E−01 
               
               
                 A8 
                 −6.71811E+00 
                 −9.11601E−01 
                 −1.13291E+01 
                 −1.23692E+01 
                 −1.51326E+01 
                 −8.89633E+00 
                 −2.66026E−03 
                 −6.37186E−02 
               
               
                 A10 
                   3.53193E+01 
                   7.64045E−01 
                   6.80561E+01 
                   4.61028E+01 
                   5.13829E+01 
                   1.65534E+01 
                 −1.50320E−01 
                   2.24580E−02 
               
               
                 A12 
                 −1.10122E+02 
                   3.05178E+00 
                 −2.37992E+02 
                 −9.64720E+01 
                 −9.52092E+01 
                 −2.06411E+01 
                   1.19574E−01 
                 −6.02309E−03 
               
               
                 A14 
                   2.06492E+02 
                 −9.34726E+00 
                   4.98312E+02 
                   1.17099E+02 
                   9.23444E+01 
                   1.65593E+01 
                 −4.20365E−02 
                   1.12736E−03 
               
               
                 A16 
                 −2.29728E+02 
                   8.04581E+00 
                 −6.30979E+02 
                 −7.95639E+01 
                 −3.38893E+01 
                 −8.18699E+00 
                   7.84666E−03 
                 −1.32311E−04 
               
               
                 A18 
                   1.38592E+02 
                 −1.22151E+00 
                   4.48459E+02 
                   2.63131E+01 
                 −1.04010E+01 
                   2.27325E+00 
                 −7.49829E−04 
                   8.32178E−06 
               
               
                 A20 
                 −3.50697E+01 
                   1.40638E−01 
                 −1.38023E+02 
                 −3.19378E+00 
                   8.37135E+00 
                 −2.71850E−01 
                   2.89993E−05 
                 −2.16110E−07 
               
               
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the fifth embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the fifth embodiment (with main reference wavelength as 555 nm) based on Table 9 and Table 10 are listed in the following table: 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Fifth embodiment (main reference wavelength: 555nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.19256 
                 −0.01037 
                 −0.14846 
                 −0.33742 
                 −0.36837 
                 −0.25666 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 −0.19362 
                 −0.25529 
                 0.90301 
                 0.85974 
                 1.76275 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.58836 
                 0.39612 
                 6.1091 
                 2.1582 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.35846 
                 0.24134 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 1.03444 
                 0.64059 
                 1.48400 
                 0.76840 
                 0.61927 
                 2.31660 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.44343 
                 1.48400 
                 1.64652 
                 1.00509 
                 9.82409 
                 3.30099 
               
               
                 f4/ΣNP 
                 IN12/f 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 |ODT| 
                 |TDT| 
               
               
                 0.45465 
                 0.09578 
                 0.19933 
                 0.26283 
                 2.01839 
                 1.61834 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ETP/InTL 
               
               
                 2.99601 
                 4.44999 
                 1.55812 
                 0.95673 
                 0.67326 
                 0.78208 
               
               
                 HVT31 
                 HVT32 
                 HVT41 
                 HVT42 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0 
                 1.0084 
                 0.61419 
                 1.21734 
                 0.42624 
                 0.27356 
               
               
                   
               
             
          
         
       
     
     [Sixth Embodiment] 
     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, an aperture  600 , a first lens  610 , a second lens  620 , a third lens  630 , a fourth lens  640 , an infrared rays filter  670 , an image plane  680 , and an image sensor  690 . 
     The first lens  610  has positive 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 surfaces. The object-side surface  612  and the image-side surface  614  both have an inflection point respectively. 
     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 concave aspheric surface, and an image-side surface  624  thereof which faces the image side is a convex aspheric surface. 
     The third lens  630  has negative refractive power, and is made of plastic. An object-side surface  632 , which faces the object side, is a concave aspheric surface, and an image-side surface  634 , which faces the image side, is a convex aspheric surface. The object-side surface  632  has two inflection points, while the image-side surface  634  has an inflection point. 
     The fourth lens  640  has positive refractive power, and is made of plastic. An object-side surface  642 , which faces the object side, is a convex aspheric surface, and an image-side surface  644 , which faces the image side, is a concave aspheric surface, and the object-side surface  642  has two inflection points, while the image-side surface  644  has an inflection point. 
     The infrared rays filter  670  is made of glass, and between the fourth lens  640  and the image plane  680 . The infrared rays filter  670  gives no contribution to the focal length of the system. 
     The optical image capturing system of the sixth preferred embodiment has the following parameters, which are |f 2 |+|f 3 |=5.7804 mm; If |f 1 |+|f 4 |=8.0922 mm; and |f 2 |+|f 3 |&lt;|f 1 |+|f 4 |. 
     The optical image capturing system of the sixth preferred embodiment further satisfies TP 3 =0.5226 mm and TP 4 =0.8727 mm, where TP 3  is a thickness of the third lens on the optical axis, and TP 4  is a thickness of the fourth lens on the optical axis. 
     The optical image capturing system of the sixth preferred embodiment further satisfies ΣPP=f 1 ±f 2 +f 4 =11.8154 mm and f 1 /(f 1 +f 2 +f 4 )=0.2908, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  610  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the sixth preferred embodiment further satisfies ΣNP=f 3 =−2.0572 mm and f 3 /(f 3 )=1, where ΣNP is a sum of the focal lengths of each negative lens. 
     The parameters of the lenses of the sixth embodiment are listed in Table 11 and Table 12. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 f = 3.4357 mm; f/HEP = 2.441; HAF = 39.5499 deg; tan(HAF) = 0.8258 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 1.37505 
                 0.39474 
                 plastic 
                 1.53460 
                 56.04928 
                 3.43574 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 4.87501 
                 0.48225 
               
               
                 3 
                 2 nd  lens 
                 −5.64751 
                 0.36141 
                 plastic 
                 1.53460 
                 56.04928 
                 3.72326 
               
               
                 4 
                   
                 −1.50824 
                 0.13838 
               
               
                 5 
                 3rd lens 
                 −0.89310 
                 0.52263 
                 plastic 
                 1.64250 
                 22.45544 
                 −2.05715 
               
               
                 6 
                   
                 −3.33251 
                 0.22392 
               
               
                 7 
                 4 th  lens 
                 1.05425 
                 0.87270 
                 plastic 
                 1.53460 
                 56.04928 
                 4.65641 
               
               
                 8 
                   
                 1.29716 
                 0.17398 
               
               
                 9 
                 Filter 
                 plane 
                 0.61 
                 BK_7 
                 1.51680 
                 64.13477 
               
               
                 10 
                   
                 plane 
                 0.67 
               
               
                 11 
                 Image plane 
                 plane 
               
               
                 12 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the fifth surface is 0.84291 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k 
                   8.09170E−01 
                   3.53697E+01 
                   3.24901E+01 
                 −6.13868E+00 
                 −2.34427E−01 
                 −6.13591E+00 
                 −9.87167E+00 
                 −4.83890E+00 
               
               
                 A4 
                 −4.43062E−02 
                 −6.29081E−02 
                 −1.48904E−01 
                 −5.55294E−01 
                 −3.33293E−01 
                 −1.18661E+00 
                 −4.76987E−01 
                 −1.93095E−01 
               
               
                 A6 
                   4.60275E−01 
                 −1.10186E−01 
                   4.50578E−01 
                   1.99199E+00 
                   2.95033E+00 
                   3.67935E+00 
                   3.20089E−01 
                   1.26435E−01 
               
               
                 A8 
                 −6.08161E+00 
                   2.01953E−01 
                 −1.07366E+01 
                 −1.30027E+01 
                 −1.47850E+01 
                 −8.96834E+00 
                   1.05767E−03 
                 −6.18637E−02 
               
               
                 A10 
                   3.48125E+01 
                 −1.63820E+00 
                   6.66110E+01 
                   4.62836E+01 
                   5.10227E+01 
                   1.65676E+01 
                 −1.59616E−01 
                   2.26025E−02 
               
               
                 A12 
                 −1.13221E+02 
                   3.15908E+00 
                 −2.40552E+02 
                 −9.50780E−01 
                 −9.61802E−01 
                 −2.05674E+01 
                   1.19574E−01 
                 −6.08902E−03 
               
               
                 A14 
                   2.15144E+02 
                 −3.48735E+00 
                   5.12952E+02 
                   1.14955E+02 
                   9.39723E+01 
                   1.64749E+01 
                 −4.20365E−02 
                   1.12005E−03 
               
               
                 A16 
                 −2.36436E+02 
                   1.48079E+00 
                 −6.45513E+02 
                 −7.88321E+01 
                 −3.45958E+01 
                 −8.16248E+00 
                   7.84666E−03 
                 −1.29548E−04 
               
               
                 A18 
                   1.38592E+02 
                 −1.22151E+00 
                   4.48459E+02 
                   2.63131E+01 
                 −1.04010E+01 
                   2.27325E+00 
                 −7.49829E−04 
                   8.32178E−06 
               
               
                 A20 
                 −3.50697E+01 
                   1.40638E−01 
                 −1.38023E+02 
                 −3.19378E+00 
                   8.37135E+00 
                 −2.71850E−01 
                   2.89993E−05 
                 −2.16110E−07 
               
               
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the sixth embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the sixth embodiment (with main reference wavelength as 555 nm) based on Table 11 and Table 12 are listed in the following table: 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Sixth embodiment (main reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.19070 
                 0.02842 
                 −0.16242 
                 −0.36086 
                 −0.38418 
                 −0.31651 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 −0.17292 
                 −0.18713 
                 0.91021 
                 0.89292 
                 1.80313 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.60184 
                 0.40520 
                 5.3842 
                 2.1857 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.35405 
                 0.23837 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 0.99999 
                 0.92277 
                 1.67013 
                 0.73784 
                 0.92278 
                 1.80991 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/|ΣNPR| 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                 2.66060 
                 1.67013 
                 1.59305 
                 1.37859 
                 8.37967 
                 2.49221 
               
               
                 f4/ΣNP 
                 IN12/f 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 |ODT| 
                 |TDT| 
               
               
                 0.55568 
                 0.14037 
                 0.19814 
                 0.21443 
                 1.87598 
                 1.47595 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 2.99602 
                 4.45000 
                 1.55812 
                 0.95715 
                 0.67326 
                 0.71811 
               
               
                 HVT31 
                 HVT32 
                 HVT41 
                 HVT42 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0 
                 1.1365 
                 0.61754 
                 1.17747 
                 0.41228 
                 0.26460 
               
               
                   
               
             
          
         
       
     
     [Seventh Embodiment] 
     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  770 , a fourth lens  740 , an infrared rays filter  770 , an image plane  780 , and an image sensor  790 . 
     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 convex aspheric surface, and the object-side surface  712  has an inflection point. 
     The second lens  720  has positive 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 third lens  730  has negative refractive power, and is made of plastic. An object-side surface  732 , which faces the object side, is a concave aspheric surface, and an image-side surface  734 , which faces the image side, is a convex aspheric surface. The image-side surface  732  has two inflection points, while the image-side surface  734  has an inflection point. 
     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 convex aspheric surface, and an image-side surface  744 , which faces the image side, is a concave aspheric surface. The object-side surface  742  and the image-side surface  744  both have an inflection point respectively. 
     The infrared rays filter  770  is made of glass, and between the fourth lens  740  and the image plane  780 . The infrared rays filter  770  gives no contribution to the focal length of the system. 
     The parameters of the lenses of the third preferred embodiment are |f 2 |+|f 3 |=6.3879 mm; |f 1 |+|f 4 |=7.3017 mm; and |f 2 |+|f 3 |&lt;|f 1 |+|f 4 |, where f 1  is a focal length of the first lens  710 ; f 2  is a focal length of the second lens  720 ; f 7  is a focal length of the third lens  730 ; and f 4  is a focal length of the fourth lens  740 . 
     The optical image capturing system of the third preferred embodiment further satisfies TP 3 =0.342 mm and TP 4 =0.876 mm, where TP 3  is a thickness of the third lens  730  on the optical axis, and TP 4  is a thickness of the fourth lens  740  on the optical axis. 
     The optical image capturing system of the third preferred embodiment further satisfies ΣPP=f 1 +f 2 +f 4 =10.9940 mm and f 1 /(f 1 +f 2 +f 4 )=0.2801, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  710  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the third preferred embodiment further satisfies ΣNP=f 3 =−2.6956 mm and f 3 /(f 3 )=1, where ΣNP is a sum of the focal lengths of each negative lens. 
     The parameters of the lenses of the third embodiment are listed in Table 13 and Table 14. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
             
             
               
                   
               
               
                 f = 2.6019 mm; f/HEP = 1.600; HAF = 40.700 deg; tan(HAF) = 0.8601 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 1.71292 
                 0.38171 
                 plastic 
                 1.54410 
                 56.06368 
                 3.07935 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 −82.93521 
                 0.06127 
               
               
                 3 
                 Shading 
                 plane 
                 0.32214 
               
               
                   
                 Sheet 
               
               
                 4 
                 2 nd  lens 
                 −2.99453 
                 0.55905 
                 plastic 
                 1.54410 
                 56.06368 
                 3.69227 
               
               
                 5 
                   
                 −1.28410 
                 0.18224 
               
               
                 6 
                 3 rd  lens 
                 −0.49647 
                 0.34177 
                 plastic 
                 1.64250 
                 22.45544 
                 −2.69561 
               
               
                 7 
                   
                 −0.88152 
                 0.03097 
               
               
                 8 
                 4 th  lens 
                 1.05292 
                 0.87625 
                 plastic 
                 1.53460 
                 56.04928 
                 4.22234 
               
               
                 9 
                   
                 1.39616 
                 0.40577 
               
               
                 10 
                 Filter 
                 plane 
                 0.21 
                 BK7 
                 1.51680 
                 64.13477 
               
               
                 11 
                   
                 plane 
                 0.51339 
               
               
                 12 
                 Image plane 
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the third surface is 0.675 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 k 
                 −8.09736E−01 
                   9.90000E+01 
                   1.38546E+01 
                 −4.78421E+00 
                 −3.91527E+00 
                 −1.53405E+00 
                 −1.19640E+01 
                 −5.30860E+00 
               
               
                 A4 
                   3.11337E−04 
                 −1.47267E−01 
                 −2.45721E−01 
                 −2.55177E−01 
                 −1.04737E+00 
                 −8.42553E−02 
                 −3.47164E−02 
                 −5.45854E−02 
               
               
                 A6 
                 −4.23221E−01 
                   2.05335E−01 
                   1.11283E+00 
                 −1.35694E+00 
                   1.91291E+00 
                   1.14144E−01 
                 −1.11575E−01 
                 −3.54359E−03 
               
               
                 A8 
                   1.99682E+00 
                 −2.29326E+00 
                 −7.97159E+00 
                   5.61291E+00 
                 −1.03818E+00 
                   4.85341E−01 
                   1.55890E−01 
                   1.43811E−02 
               
               
                 A10 
                 −8.98568E+00 
                   6.67714E+00 
                   2.67059E+01 
                 −1.27982E+01 
                   8.28666E−02 
                 −5.78511E−01 
                 −1.02888E−01 
                 −8.50527E−03 
               
               
                 A12 
                   2.55814E+01 
                 −1.26431E+01 
                 −4.89500E+01 
                   1.83626E+01 
                 −7.20630E−01 
                   1.37111E−01 
                   3.67156E−02 
                   2.28063E−03 
               
               
                 A14 
                 −4.56047E+01 
                   1.25240E+01 
                   4.32986E+01 
                 −1.54412E+01 
                   8.84894E−01 
                   8.58529E−02 
                 −6.09560E−03 
                 −2.76813E−04 
               
               
                 A16 
                   3.35356E+01 
                 −4.95913E+00 
                 −1.11707E+01 
                   5.47973E+00 
                 −3.65905E−01 
                 −3.73888E−02 
                   1.92810E−04 
                   9.06057E−06 
               
               
                 A18 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
               
               
                 A20 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
                   0.00000E+00 
               
               
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the third embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the third embodiment (with main reference wavelength as 555 nm) based on Table 13 and Table 14 are listed in the following table: 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Seventh embodiment (main reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.10245 
                 −0.04085 
                 −0.18437 
                 −0.44347 
                 −0.51083 
                 −0.37921 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 0.11772 
                 0.04936 
                 0.91538 
                 0.91289 
                 1.82827 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.66352 
                 0.47065 
                 5.2365 
                 16.0459 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.38366 
                 0.27214 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 0.84495 
                 0.70469 
                 0.96524 
                 0.61622 
                 0.83400 
                 1.36973 
               
               
                 Σ PPR 
                 Σ NPR 
                 Σ PPR/| Σ NPR| 
                 Σ PP 
                 Σ NP 
                 f1/Σ PP 
               
               
                 2.16586 
                 0.96524 
                 2.24387 
                 0.38374 
                 7.91461 
                 8.02457 
               
               
                 f4/Σ NP 
                 IN12/f 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 |ODT| 
                 |TDT| 
               
               
                 0.53349 
                 0.14736 
                 0.13435 
                 0.05633 
                 2.57432 
                 0.27626 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 Σ TP/InTL 
               
               
                 2.75540 
                 3.88456 
                 1.68894 
                 0.97363 
                 0.70932 
                 0.78347 
               
               
                 HVT31 
                 HVT32 
                 HVT41 
                 HVT42 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0 
                 0 
                 1.11330 
                 1.39937 
                 0.60842 
                 0.36024 
               
               
                   
               
             
          
         
       
     
     [Eighth Embodiment] 
     As shown in  FIG. 8A  and  FIG. 8B , 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  800 , a first lens  810 , a second lens  820 , a third lens  880 , a fourth lens  840 , an infrared rays filter  870 , an image plane  880 , and an image sensor  890 . 
     The first lens  810  has positive refractive power, and is made of plastic. An object-side surface  812  thereof, which faces the object side, is a convex aspheric surface, and an image-side surface  814  thereof, which faces the image side, is a concave aspheric surface, and the object-side surface  812  and the image-side surface  814  both have an inflection point respectively. 
     The second lens  820  has negative refractive power, and is made of plastic. An object-side surface  822  thereof which faces the object side is a concave aspheric surface, and an image-side surface  824  thereof which faces the image side is a convex aspheric surface. 
     The third lens  830  has positive refractive power, and is made of plastic. An object-side surface  832 , which faces the object side, is a concave aspheric surface, and an image-side surface  834 , which faces the image side, is a convex aspheric surface. The object-side surface  832  has two inflection points, while the image-side surface  834  has an inflection point. 
     The fourth lens  840  has a negative refractive power, and is made of plastic. An object-side surface  842 , which faces the object side, is a convex aspheric surface, and an image-side surface  844 , which faces the image side, is a concave aspheric surface. The object-side surface  842  and the image-side surface  844  both have an inflection point respectively. 
     The infrared rays filter  870  is made of glass, and between the fourth lens  840  and the image plane  880 . The infrared rays filter  870  gives no contribution to the focal length of the system. 
     The parameters of the lenses of the third preferred embodiment are |f 2 |+|f 3 |=5.7651 mm; |f 1 |+|f 4 |=7.6347 mm; and |f 2 |+|f 3 |&lt;|f 1 |+|f 4 |, where f 1  is a focal length of the first lens  810 ; f 2  is a focal length of the second lens  820 ; f 3  is a focal length of the third lens  830 ; and f 4  is a focal length of the fourth lens  840 . 
     The optical image capturing system of the third preferred embodiment further satisfies TP 3 =0.342 mm and TP 4 =0.876 mm, where TP 3  is a thickness of the third lens  830  on the optical axis, and TP 4  is a thickness of the fourth lens  840  on the optical axis. 
     The optical image capturing system of the third preferred embodiment further satisfies ΣPP=f 1 +f 2 +f 4 =10.8016 mm and f 1 /(f 1 +f 2 +f 4 )=0.3169, where ΣPP is a sum of the focal lengths of each positive lens. It is helpful to share the positive refractive power of the first lens  810  to other positive lenses to avoid the significant aberration caused by the incident rays. 
     The optical image capturing system of the third preferred embodiment further satisfies ΣNP=f 3 =−2.598 mm and f 3 /(f 3 )=1, where ΣNP is a sum of the focal lengths of each negative lens. 
     The parameters of the lenses of the third embodiment are listed in Table 15 and Table 16. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 15 
               
             
             
               
                   
               
               
                 f = 2.602 mm; f/HEP = 2.051; HAF = 40.700 deg; tan(HAF) = 0.8601 
               
             
          
           
               
                   
                 Radius of curvature 
                 Thickness 
                   
                 Refractive 
                 Abbe 
                 Focal length 
               
               
                 Surface 
                 (mm) 
                 (mm) 
                 Material 
                 index 
                 number 
                 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 Object 
                 plane 
                 600 
                   
                   
                   
                   
               
               
                 1 
                 1 st  lens/ 
                 1.56137 
                 0.38171 
                 plastic 
                 1.54410 
                 56.06368 
                 3.42296 
               
               
                   
                 Aperture 
               
               
                 2 
                   
                 8.67919 
                 0.06127 
               
               
                 3 
                 Shading 
                 plane 
                 0.32214 
               
               
                   
                 Sheet 
               
               
                 4 
                 2 nd  lens 
                 −4.18777 
                 0.55905 
                 plastic 
                 1.54410 
                 56.06368 
                 3.16687 
               
               
                 5 
                   
                 −1.28128 
                 0.18224 
               
               
                 6 
                 3 rd  lens 
                 −0.49776 
                 0.34177 
                 plastic 
                 1.64250 
                 22.45544 
                 −2.59818 
               
               
                 7 
                   
                 −0.89764 
                 0.03097 
               
               
                 8 
                 4 th  lens 
                 1.05854 
                 0.87625 
                 plastic 
                 1.53460 
                 56.04928 
                 4.21178 
               
               
                 9 
                   
                 1.41631 
                 0.40577 
               
               
                 10 
                 Filter 
                 plane 
                 0.21 
                 BK7 
                 1.51680 
                 64.13477 
               
               
                 11 
                   
                 plane 
                 0.51339 
               
               
                 12 
                 Image plane 
                 plane 
               
               
                   
               
               
                 Reference wavelength: 555 nm. 
               
               
                 The clear aperture of the second surface is 0.45 mm. 
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 16 
               
             
             
               
                   
               
               
                 Coefficients of the aspheric surfaces 
               
             
          
           
               
                 Surface 
                 1 
                 2 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 k 
                   7.06758E−01 
                   9.90000E+01 
                   2.84329E+01 
                 −1.70758E+00 
                 −3.83499E+00 
                 −1.24082E+00 
                 −1.19640E+01 
                 −5.05896E+00 
               
               
                 A4 
                 −2.69167E−02 
                 −1.32998E−01 
                 −3.08525E−01 
                 −1.68528E−01 
                 −1.10160E+00 
                 −4.87334E−02 
                 −4.41395E−02 
                 −5.77518E−02 
               
               
                 A6 
                 −2.77792E−01 
                   2.62372E−01 
                   1.32713E+00 
                 −1.48439E+00 
                   1.86752E+00 
                   8.80821E−02 
                 −1.22090E−01 
                 −2.03495E−03 
               
               
                 A8 
                   1.66898E+00 
                 −2.14319E+00 
                 −9.10404E+00 
                   5.71121E+00 
                 −9.76525E−01 
                   4.32119E−01 
                   1.60177E−01 
                   1.42962E−02 
               
               
                 A10 
                 −8.42648E+00 
                   6.37998E+00 
                   2.90907E+01 
                 −1.28499E+01 
                   1.60948E−01 
                 −5.85268E−01 
                 −1.02654E−01 
                 −8.55909E−03 
               
               
                 A12 
                   2.55814E+01 
                 −1.26431E+01 
                 −5.13915E+01 
                   1.87544E+01 
                 −6.70051E−01 
                   2.00849E−01 
                   3.61092E−02 
                   2.27967E−03 
               
               
                 A14 
                 −4.56047E+01 
                   1.25240E+01 
                   4.32838E+01 
                 −1.58331E+01 
                   7.96067E−01 
                   6.41102E−02 
                 −5.79879E−03 
                 −2.69472E−04 
               
               
                 A16 
                   3.35356E+01 
                 −4.95913E+00 
                 −1.11707E+01 
                   5.47973E+00 
                 −3.65905E−01 
                 −3.73888E−02 
                   1.92810E−04 
                   9.06057E−06 
               
               
                 A18 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 A20 
               
               
                   
               
             
          
         
       
     
     An equation of the aspheric surfaces of the third embodiment is the same as that of the first embodiment, and the definitions are the same as well. 
     The exact parameters of the third embodiment (with main reference wavelength as 555 nm) based on Table 15 and Table 16 are listed in the following table: 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
           
               
                   
               
               
                 Eighth embodiment (main reference wavelength: 555 nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 InRS11 
                 InRS12 
                 InRS21 
                 InRS22 
                 InRS31 
                 InRS32 
               
               
                 0.12642 
                 −0.00468 
                 −0.17792 
                 −0.46224 
                 −0.53216 
                 −0.42421 
               
               
                 InRS41 
                 InRS42 
                 InRSO 
                 InRSI 
                 Σ|InRS| 
                   
               
               
                 0.08198 
                 0.14557 
                 0.91848 
                 1.03670 
                 1.95518 
                   
               
             
          
           
               
                 Σ|InRS|/InTL 
                 Σ|InRS|/HOS 
                 (|InRS22| + |InRS31|)/IN23 
                 (|InRS32| + |InRS41|)/IN34 
               
               
                 0.70958 
                 0.50332 
                 5.4565 
                 16.3449 
               
             
          
           
               
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/InTL 
                 (|InRS31| + |InRS32| + |InRS41| + |InRS42|)/HOS 
               
               
                 0.42967 
                 0.30478 
               
             
          
           
               
                 |f/f1| 
                 |f/f2| 
                 |f/f3| 
                 |f/f4| 
                 |f1/f2| 
                 |f2/f3| 
               
               
                 0.76013 
                 0.82160 
                 1.00143 
                 0.61776 
                 1.08087 
                 1.21888 
               
               
                 Σ PPR 
                 Σ NPR 
                 Σ PPR/| Σ NPR| 
                 ΣPP 
                 Σ NP 
                 f1/Σ PP 
               
               
                 2.19949 
                 1.00143 
                 2.19635 
                 0.82478 
                 7.37865 
                 4.15015 
               
               
                 f4/Σ NP 
                 IN12/f 
                 |InRS41|/TP4 
                 |InRS42|/TP4 
                 |ODT| 
                 |TDT| 
               
               
                 0.57081 
                 0.14736 
                 0.09356 
                 0.16613 
                 2.50131 
                 0.25090 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 Σ TP/InTL 
               
               
                 2.75540 
                 3.88456 
                 1.68894 
                 0.96746 
                 0.70932 
                 0.78347 
               
               
                 HVT31 
                 HVT32 
                 HVT41 
                 HVT42 
                 HVT42/HOI 
                 HVT42/HOS 
               
               
                 0 
                 0 
                 0.98319 
                 1.41703 
                 0.61610 
                 0.36479 
               
               
                   
               
             
          
         
       
     
     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.