Patent Publication Number: US-10317644-B2

Title: Optical image capturing system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of Taiwan Patent Application No. 104118192, filed on Jun. 4, 2015, in the Taiwan Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present disclosure relates to an optical image capturing system, and more particularly to a compact optical image capturing system which can be applied to electronic products. 
     2. Description of the 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 directs towards the field of high pixels. Therefore, the requirement for high imaging quality is rapidly raised. 
     The traditional optical image capturing system of a portable electronic device comes with different designs, including a second-lens or a third-lens design. However, the requirement for the higher pixels and the requirement for a large aperture of an end user, like functionalities of micro filming and night view, or the requirement of wide view angle of the portable electronic device have been raised. But the optical image capturing system with the large aperture design often produces more aberration resulting in the deterioration of quality in peripherical image formation and difficulties of manufacturing, and the optical image capturing system with wide view angle design increases distortion rate in image formation, thus the optical image capturing system in prior arts cannot meet the requirement of the higher order camera lens module. 
     Therefore, how to effectively increase quantity of incoming light and view angle of the optical lenses, not only further improves total pixels and imaging quality for the image formation, but also considers the equity design of the miniaturized optical lenses, becomes a quite important issue. 
     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 the view angle of the optical lenses, and to improve total pixels and imaging quality for image formation, so as to be applied to minimized electronic products. 
     The term and its definition to the lens element parameter in the embodiment of the present invention are shown as below for further reference. 
     The Lens Element 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 element to an image plane is denoted by InB. InTL+InB=HOS. A distance from an aperture stop (aperture) to an image plane is denoted by InS. A distance from the first lens element to the second lens element is denoted by In12 (instance). A central thickness of the first lens element of the optical image capturing system on the optical axis is denoted by TP1 (instance). 
     The Lens Element Parameter Related to a Material in the Lens Element 
     An Abbe number of the first lens element in the optical image capturing system is denoted by NA1 (instance). A refractive index of the first lens element is denoted by Nd1 (instance). 
     The Lens Element Parameter Related to a View Angle in the Lens Element 
     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 Element Parameter Related to Exit/Entrance Pupil in the Lens Element 
     An entrance pupil diameter of the optical image capturing system is denoted by HEP. An entrance pupil diameter of the optical image capturing system is denoted by HEP. A maximum effective half diameter position of any surface of single lens element means the vertical height between the effective half diameter (EHD) and the optical axis where the incident light of the maximum view angle of the system passes through the farthest edge of the entrance pupil on the EHD of the surface of the lens element. For example, the maximum effective half diameter position of the object-side surface of the first lens element is denoted as EHD 11. The maximum effective half diameter position of the image-side of the first lens element is denoted as EHD12. The maximum effective half diameter position of the object-side surface of the second lens element is denoted as EHD21. The maximum half effective half diameter position of the image-side surface of the second lens element is denoted as EHD22. The maximum effective half diameter position of any surfaces of the remaining lens elements of the optical image capturing system can be referred as mentioned above. 
     The lens element parameter related to an arc length of the lens element shape and an outline of surface 
     A length of outline curve of the maximum effective half diameter position of any surface of a single lens element refers to a length of outline curve from an axial point on the surface of the lens element to the maximum effective half diameter position of the surface along an outline of the surface of the lens element and is denoted as ARS. For example, the length of outline curve of the maximum effective half diameter position of the object-side surface of the first lens element is denoted as ARS11. The length of outline curve of the maximum effective half diameter position of the image-side surface of the first lens element is denoted as ARS12. The length of outline curve of the maximum effective half diameter position of the object-side surface of the second lens element is denoted as ARS21. The length of outline curve of the maximum effective half diameter position of the image-side surface of the second lens element is denoted as ARS22. The lengths of outline curve of the maximum effective half diameter position of any surface of the other lens elements in the optical image capturing system are denoted in the similar way. 
     A length of outline curve of a half of an entrance pupil diameter (HEP) of any surface of a signal lens element refers to a length of outline curve of the half of the entrance pupil diameter (HEP) from an axial point on the surface of the lens element to a coordinate point of vertical height with a distance of the half of the entrance pupil diameter from the optical axis on the surface along the outline of the surface of the lens element and is denoted as ARE. For example, the length of the outline curve of the half of the entrance pupil diameter (HEP) of the object-side surface of the first lens element is denoted as ARE11. The length of the outline curve of the half of the entrance pupil diameter (HEP) of the image-side surface of the first lens element is denoted as ARE12. The length of the outline curve of the half of the entrance pupil diameter (HEP) of the object-side surface of the second lens element is denoted as ARE21. The length of the outline curve of the half of the entrance pupil diameter (HEP) of the image-side surface of the second lens element is denoted as ARS22. The lengths of outline curves of the half of the entrance pupil diameters (HEP) of any surface of the other lens elements in the optical image capturing system are denoted in the similar way. 
     The Lens Element Parameter Related to a Depth of the Lens Element Shape 
     A horizontal distance in parallel with an optical axis from a maximum effective half diameter position to an axial point on the object-side surface of the fourth lens element is denoted by InRS41 (instance). A horizontal distance in parallel with an optical axis from a maximum effective half diameter position to an axial point on the image-side surface of the fourth lens element is denoted by InRS42 (instance). 
     The Lens Element Parameter Related to the Lens Element Shape 
     A critical point C is a tangent point on a surface of a specific lens element, 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 C31 on the object-side surface of the third lens element and the optical axis is HVT31 (instance). A distance perpendicular to the optical axis between a critical point C32 on the image-side surface of the third lens element and the optical axis is HVT32 (instance). A distance perpendicular to the optical axis between a critical point C41 on the object-side surface of the fourth lens element and the optical axis is HVT41 (instance). A distance perpendicular to the optical axis between a critical point C42 on the image-side surface of the fourth lens element and the optical axis is HVT42 (instance). Distances perpendicular to the optical axis between critical points on the object-side surfaces or the image-side surfaces of other lens elements and the optical axis are denoted in the similar way described above. 
     The object-side surface of the fourth lens element has one inflection point IF411 which is nearest to the optical axis, and the sinkage value of the inflection point IF411 is denoted by SGI411. SGI411 is a horizontal shift distance in parallel with the optical axis from an axial point on the object-side surface of the fourth lens element to the inflection point which is nearest to the optical axis on the object-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF411 and the optical axis is HIF411 (instance). The image-side surface of the fourth lens element has one inflection point IF421 which is nearest to the optical axis and the sinkage value of the inflection point IF421 is denoted by SGI421 (instance). SGI421 is a horizontal shift distance in parallel with the optical axis from an axial point on the image-side surface of the fourth lens element to the inflection point which is nearest to the optical axis on the image-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF421 and the optical axis is HIF421 (instance). 
     The object-side surface of the fourth lens element has one inflection point IF412 which is the second nearest to the optical axis and the sinkage value of the inflection point IF412 is denoted by SGI412 (instance). SGI412 is a horizontal shift distance in parallel with the optical axis from an axial point on the object-side surface of the fourth lens element to the inflection point which is the second nearest to the optical axis on the object-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF412 and the optical axis is HIF412 (instance). The image-side surface of the fourth lens element has one inflection point IF422 which is the second nearest to the optical axis and the sinkage value of the inflection point IF422 is denoted by SGI422 (instance). SGI422 is a horizontal shift distance in parallel with the optical axis from an axial point on the image-side surface of the fourth lens element to the inflection point which is the second nearest to the optical axis on the image-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF422 and the optical axis is HIF422 (instance). 
     The object-side surface of the fourth lens element has one inflection point IF413 which is the third nearest to the optical axis and the sinkage value of the inflection point IF413 is denoted by SGI413 (instance). SGI413 is a horizontal shift distance in parallel with the optical axis from an axial point on the object-side surface of the fourth lens element to the inflection point which is the third nearest to the optical axis on the object-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF413 and the optical axis is HIF413 (instance). The image-side surface of the fourth lens element has one inflection point IF423 which is the third nearest to the optical axis and the sinkage value of the inflection point IF423 is denoted by SGI423 (instance). SGI423 is a horizontal shift distance in parallel with the optical axis from an axial point on the image-side surface of the fourth lens element to the inflection point which is the third nearest to the optical axis on the image-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF423 and the optical axis is HIF423 (instance). 
     The object-side surface of the fourth lens element has one inflection point IF414 which is the fourth nearest to the optical axis and the sinkage value of the inflection point IF414 is denoted by SGI414 (instance). SGI414 is a horizontal shift distance in parallel with the optical axis from an axial point on the object-side surface of the fourth lens element to the inflection point which is the fourth nearest to the optical axis on the object-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF414 and the optical axis is HIF414 (instance). The image-side surface of the fourth lens element has one inflection point IF424 which is the fourth nearest to the optical axis and the sinkage value of the inflection point IF424 is denoted by SGI424 (instance). SGI424 is a horizontal shift distance in parallel with the optical axis from an axial point on the image-side surface of the fourth lens element to the inflection point which is the fourth nearest to the optical axis on the image-side surface of the fourth lens element. A distance perpendicular to the optical axis between the inflection point IF424 and the optical axis is HIF424 (instance). 
     The inflection points on the object-side surfaces or the image-side surfaces of the other lens elements and the distances perpendicular to the optical axis thereof or the sinkage values thereof are denoted in the similar way described above. 
     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%. An offset of the spherical aberration is denoted by DFS. An offset of the coma aberration is denoted by DFC. 
     The lateral aberration of the stop is denoted as STA to assess the function of the specific optical image capturing system. The tangential fan or sagittal fan may be applied to calculate the STA of any view fields, and in particular, to calculate the STA of the maximum reference wavelength (e.g. 650 nm) and the minimum reference wavelength (e.g. 470 nm) for serve as the standard of the optimal function. The aforementioned direction of the tangential fan can be further defined as the positive (overhead-light) and negative (lower-light) directions. STA of the max operation wavelength is defined as the distance between the image position of the specific view field of max operation wavelength and the image position of the specific view field of the reference primary wavelength (e.g. wavelength of 555 nm), and STA of the minimum operation wavelength is defined as the distance between the image position of the specific view field of the minimum operation wavelength and the image position of the specific view field of the reference primary wavelength (e.g. wavelength of 555 nm) are assessed the function of the specific optical image capturing system to be optimal. Both STA of the max operation wavelength and STA of the minimum operation wavelength on the image position of vertical height with a distance from the optical axis to 70% HOI (i.e. 0.7 HOI), which are smaller than 20 μm, are served as the sample. The numerical, which are smaller than 10 μm, are also served as the sample. 
     A height for image formation on the image plane perpendicular to the optical axis in the optical image capturing system is denoted by HOI. A lateral aberration of the longest operation wavelength of a positive direction tangential fan of the optical image capturing system passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI is denoted as PLTA. A lateral aberration of the shortest operation wavelength of the positive direction tangential fan of the optical image capturing system passing through the edge of the entrance pupil and incident on the image plane by 0.7 HOI is denoted as PSTA. A lateral aberration of the longest operation wavelength of a negative direction tangential fan of the optical image capturing system passing through the edge of the entrance pupil and incident on the image plane by 0.7 HOI is denoted as NLTA. A lateral aberration of the shortest operation wavelength of a negative direction tangential fan of the optical image capturing system passing through the edge of the entrance pupil and incident on the image plane by 0.7 HOI is denoted as NSTA. A lateral aberration of the longest operation wavelength of a sagittal fan of the optical image capturing system passing through the edge of the entrance pupil and incident on the image plane by 0.7 HOI is denoted as SLTA. A lateral aberration of the shortest operation wavelength of the sagittal fan of the optical image capturing system passing through the edge of the entrance pupil and incident on the image plane by 0.7 HOI is denoted as SSTA. 
     The disclosure provides an optical image capturing system, an object-side surface or an image-side surface of the fourth lens element has inflection points, such that the angle of incidence from each view field to the fourth lens element can be adjusted effectively and the optical distortion and the TV distortion can be corrected as well. Besides, the surfaces of the fourth lens element may have a better optical path adjusting ability to acquire better imaging quality. 
     The disclosure provides an optical image capturing system, in order from an object side to an image side, including a first, second, third, fourth lens elements and an image plane. The first lens element has refractive power. An object-side surface and an image-side surface of the fourth lens element are aspheric. Focal lengths of the first through fourth lens elements are f1, f2, f3 and f4 respectively. A focal length of the optical image capturing system is f. An entrance pupil diameter of the optical image capturing system is HEP. A distance from an object-side surface of the first lens element to the image plane is HOS. A distance on the optical axis from the object-side surface of the first lens element to the image-side surface of the fourth lens element is InTL. A length of outline curve from an axial point on any surface of any one of the four lens elements to a coordinate point of vertical height with a distance of a half of the entrance pupil diameter from the optical axis on the surface along an outline of the surface is denoted as ARE. The following relations are satisfied: 1.2≤f/HEP≤6.0; 0.5≤HOS/f≤3.0; 0&lt;InTL/HOS&lt;0.9; and 1≤2(ARE/HEP)≤1.5. 
     The disclosure provides another optical image capturing system, in order from an object side to an image side, including a first, second, third, fourth lens elements and an image plane. The first lens element has positive refractive power and may have a convex object-side surface near the optical axis. An object-side surface and an image-side surface of the first lens element are aspheric. The second lens element has refractive power. The third lens element has refractive power. The fourth lens element has negative refractive power and an object-side surface and an image-side surface of the fourth lens element are aspheric. At least two lens elements among the first through fourth lens elements respectively have at least one inflection point on at least one surface thereof. At least one of the second through fourth lens elements has positive refractive power. Focal lengths of the first through fourth lens elements are f1, f2, f3 and f4 respectively. A focal length of the optical image capturing system is f. An entrance pupil diameter of the optical image capturing system is HEP. A distance from an object-side surface of the first lens element to the image plane is HOS. A distance on the optical axis from the object-side surface of the first lens element to the image-side surface of the fourth lens element is InTL A length of outline curve from an axial point on any surface of any one of the four lens elements to a coordinate point of vertical height with a distance of a half of the entrance pupil diameter from the optical axis on the surface along an outline of the surface is denoted as ARE. The following relations are satisfied: 1.2≤f/HEP≤6.0; 0.5≤HOS/f≤3.0; 0&lt;InTL/HOS&lt;0.9; and 1≤2 (ARE/HEP)≤1.5. 
     The disclosure provides another optical image capturing system, in order from an object side to an image side, including a first, second, third, fourth lens elements and an image plane. At least one surface among an object-side surface and an image-side surface of the fourth lens element has at least one inflection point. Wherein, the optical image capturing system consists of the four lens elements with refractive power and at least two lens elements among the first through third lens elements respectively have at least one inflection point on at least one surface thereof. The first lens element has positive refractive power. The second lens element has refractive power. The third lens element has refractive power. The fourth lens element has negative refractive power and an object-side surface and an image-side surface of the fourth lens element are aspheric. Focal lengths of the first through fourth lens elements are f1, f2, f3 and f4 respectively. A focal length of the optical image capturing system is f. An entrance pupil diameter of the optical image capturing system is HEP. A distance from an object-side surface of the first lens element to the image plane is HOS. A distance on the optical axis from the object-side surface of the first lens element to the image-side surface of the fourth lens element is InTL A length of outline curve from an axial point on any surface of any one of the four lens elements to a coordinate point of vertical height with a distance of a half of the entrance pupil diameter from the optical axis on the surface along an outline of the surface is denoted as ARE. The following relations are satisfied: 1.2≤f/HEP≤3.5; 0.5≤HOS/f≤3.0; 0&lt;InTL/HOS&lt;0.9; and 1≤2(ARE/HEP)≤1.5. 
     The length of the outline curve of any surface of a signal lens element in the maximum effective half diameter position affects the functions of the surface aberration correction and the optical path difference in each view field. The longer outline curve may lead to a better function of aberration correction, but the difficulty of the production may become inevitable. Hence, the length of the outline curve of the maximum effective half diameter position of any surface of a signal lens element (ARS) has to be controlled, and especially, the ratio relations (ARS/TP) between the length of the outline curve of the maximum effective half diameter position of the surface (ARS) and the thickness of the lens element to which the surface belongs on the optical axis (TP) has to be controlled. For example, the length of the outline curve of the maximum effective half diameter position of the object-side surface of the first lens element is denoted as ARS11, and the thickness of the first lens element on the optical axis is TP1, and the ratio between both of them is ARS11/TP1. The length of the outline curve of the maximum effective half diameter position of the image-side surface of the first lens element is denoted as ARS12, and the ratio between ARS12 and TP1 is ARS12/TP1. The length of the outline curve of the maximum effective half diameter position of the object-side surface of the second lens element is denoted as ARS21, and the thickness of the second lens element on the optical axis is TP2, and the ratio between both of them is ARS21/TP2. The length of the outline curve of the maximum effective half diameter position of the image-side surface of the second lens element is denoted as ARS22, and the ratio between ARS22 and TP2 is ARS22/TP2. The ratio relations between the lengths of the outline curve of the maximum effective half diameter position of any surface of the other lens elements and the thicknesses of the lens elements to which the surfaces belong on the optical axis (TP) are denoted in the similar way. 
     The length of outline curve of half of an entrance pupil diameter of any surface of a single lens element especially affects the functions of the surface aberration correction and the optical path difference in each shared view field. The longer outline curve may lead to a better function of aberration correction, but the difficulty of the production may become inevitable. Hence, the length of outline curve of half of an entrance pupil diameter of any surface of a single lens element has to be controlled, and especially, the ratio relationship between the length of outline curve of half of an entrance pupil diameter of any surface of a single lens element and the thickness on the optical axis has to be controlled. For example, the length of outline curve of the half of the entrance pupil diameter of the object-side surface of the first lens element is denoted as ARE11, and the thickness of the first lens element on the optical axis is TP1, and the ratio between both of them is ARE11/TP1. The length of outline curve of the half of the entrance pupil diameter of the image-side surface of the first lens element is denoted as ARE12, and the ratio between ARE12 and TP1 is ARE12/TP1. The length of outline curve of the half of the entrance pupil diameter of the object-side surface of the second lens element is denoted as ARE21, and the thickness of the second lens element on the optical axis is TP2, and the ratio between both of them is ARE21/TP2. The length of outline curve of the half of the entrance pupil diameter of the image-side surface of the second lens element is denoted as ARE22, and the ratio between ARE22 and TP2 is ARE22/TP2. The ratio relations between the lengths of the outline curve of half of the entrance pupil diameter of any surface of the other lens elements and the thicknesses of the lens elements to which the surfaces belong on the optical axis (TP) are denoted in the similar way. 
     The optical image capturing system described above may be configured to form the image on the image sensing device which is shorter than 1/1.2 inch in diagonal length. The preferred size of the image sensing device is 1/2.3 inch. The pixel size of the image sensing device is smaller than 1.4 micrometers (μm), preferably the pixel size thereof is smaller than 1.12 micrometers (μm). The best pixel size thereof is smaller than 0.9 micrometers (μm). Furthermore, the optical image capturing system is applicable to the image sensing device with aspect ratio of 16:9. 
     The optical image capturing system described above is applicable to the demand of video recording with above millions or ten millions-pixels (e.g. 4K2K or called UHD, QHD) and leads to a good imaging quality. 
     The height of optical system (HOS) may be reduced to achieve the minimization of the optical image capturing system when the absolute value of f1 is larger than f4 (|f1|&gt;f4). 
     When |f2|+|f3|&gt;|f1|+|f4|, at least one of the second through third lens elements may have weak positive refractive power or weak negative refractive power. The weak refractive power indicates that an absolute value of the focal length of a specific lens element is greater than 10. When at least one of the second through third lens elements has the weak positive refractive power, the positive refractive power of the first lens element can be shared, such that the unnecessary aberration will not appear too early. On the contrary, when at least one of the second through third lens elements has the weak negative refractive power, the aberration of the optical image capturing system can be corrected and fine tuned. 
     The fourth lens element may have negative refractive power and a concave image-side surface. Hereby, the back focal length is reduced for keeping the miniaturization, to miniaturize the lens element effectively. In addition, at least one of the object-side surface and the image-side surface of the fourth lens element may have at least one inflection point, such that the angle of incident with incoming light from an off-axis view field can be suppressed effectively and the aberration in the off-axis view field can be corrected further. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The detailed structure, operating principle and effects of the present disclosure will now be described in more details hereinafter with reference to the accompanying drawings that show various embodiments of the present disclosure as follows. 
         FIG. 1A  is a schematic view of the optical image capturing system according to the first embodiment of the present application. 
         FIG. 1B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system in the order from left to right according to the first embodiment of the present application. 
         FIG. 1C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the first embodiment of the present application. 
         FIG. 2A  is a schematic view of the optical image capturing system according to the second embodiment of the present application. 
         FIG. 2B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system in the order from left to right according to the second embodiment of the present application. 
         FIG. 2C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the second embodiment of the present application. 
         FIG. 3A  is a schematic view of the optical image capturing system according to the third embodiment of the present application. 
         FIG. 3B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system in the order from left to right according to the third embodiment of the present application. 
         FIG. 3C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the third embodiment of the present application. 
         FIG. 4A  is a schematic view of the optical image capturing system according to the fourth embodiment of the present application. 
         FIG. 4B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system in the order from left to right according to the fourth embodiment of the present application. 
         FIG. 4C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the fourth embodiment of the present application. 
         FIG. 5A  is a schematic view of the optical image capturing system according to the fifth embodiment of the present application. 
         FIG. 5B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system in the order from left to right according to the fifth embodiment of the present application. 
         FIG. 5C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the fifth embodiment of the present application. 
         FIG. 6A  is a schematic view of the optical image capturing system according to the sixth embodiment of the present application. 
         FIG. 6B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system in the order from left to right according to the sixth embodiment of the present application. 
         FIG. 6C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the sixth embodiment of the present application. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Reference will now be made in detail to the exemplary embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. Therefore, it is to be understood that the foregoing is illustrative of exemplary embodiments and is not to be construed as limited to the specific embodiments disclosed, and that modifications to the disclosed exemplary embodiments, as well as other exemplary embodiments, are intended to be included within the scope of the appended claims. These embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the inventive concept to those skilled in the art. The relative proportions and ratios of elements in the drawings may be exaggerated or diminished in size for the sake of clarity and convenience in the drawings, and such arbitrary proportions are only illustrative and not limiting in any way. The same reference numbers are used in the drawings and the description to refer to the same or like parts. 
     It will be understood that, although the terms ‘first’, ‘second’, ‘third’, etc., may be used herein to describe various elements, these elements should not be limited by these terms. The terms are used only for the purpose of distinguishing one component from another component. Thus, a first element discussed below could be termed a second element without departing from the teachings of embodiments. As used herein, the term “or” includes any and all combinations of one or more of the associated listed items. 
     An optical image capturing system, in order from an object side to an image side, includes a first, second, third and fourth lens elements with refractive power. The optical image capturing system may further include an image sensing device which is disposed on an image plane. 
     The optical image capturing system may use three sets of wavelengths which are 486.1 nm, 587.5 nm and 656.2 nm, respectively, wherein 587.5 nm is served as the primary reference wavelength and a reference wavelength for retrieving technical features. The optical image capturing system may also use five sets of wavelengths which are 470 nm, 510 nm, 555 nm, 610 nm and 650 nm, respectively, wherein 555 nm is served as the primary reference wavelength and a reference wavelength for retrieving technical features. 
     A ratio of the focal length f of the optical image capturing system to a focal length fp of each of lens elements with positive refractive power is PPR. A ratio of the focal length f of the optical image capturing system to a focal length fn of each of lens elements with negative refractive power is NPR. A sum of the PPR of all lens elements with positive refractive power is ΣPPR. A sum of the NPR of all lens elements with negative refractive powers is ΣNPR. It is beneficial to control the total refractive power and the total length of the optical image capturing system when following conditions are satisfied: 0.5≤ΣPPR/|ΣNPR|≤4.5. Preferably, the following relation may be satisfied: 1≤|ΣPPR/ΣNPR|≤3.5. 
     The height of the optical image capturing system is HOS. It will facilitate the manufacturing of miniaturized optical image capturing system which may form images with ultra high pixels when the specific ratio value of HOS/f tends to 1. 
     A sum of a focal length fp of each lens element with positive refractive power is ΣPP. A sum of a focal length fn of each lens element with negative refractive power is ENP. In one embodiment of the optical image capturing system of the present disclosure, the following relations are satisfied: 0&lt;ΣPP≤200 and f1/ΣPP≤0.85. Preferably, the following relations may be satisfied: 0&lt;ΣPP≤150 and 0.01≤f1/ΣPP≤0.7. Hereby, its beneficial to control the focus ability of the optical image capturing system and allocate the positive refractive power of the optical image capturing system appropriately, so as to suppress the significant aberration generating too early. 
     The first lens element may have positive refractive power, and it has a convex object-side surface. Hereby, strength of the positive refractive power of the first lens element can be fined-tuned, so as to reduce the total length of the optical image capturing system. 
     The second lens element may have negative refractive power. Hereby, the aberration generated by the first lens element can be corrected. 
     The third lens element may have positive refractive power. Hereby, the positive refractive power of the first lens element can be shared. 
     The fourth lens element may have negative refractive power and a concave image-side surface. Hereby, the back focal length is reduced for keeping the miniaturization, to miniaturize the lens element effectively. In addition, at least one of the object-side surface and the image-side surface of the fourth lens element may have at least one inflection point, such that the angle of incident with incoming light from an off-axis field of view can be suppressed effectively and the aberration in the off-axis field of view can be corrected further. Preferably, each of the object-side surface and the image-side surface may have at least one inflection point. 
     The optical image capturing system may further include an image sensing device which is disposed on an image plane. Half of a diagonal of an effective detection field of the image sensing device (imaging height or the maximum image height of the optical image capturing system) is HOI. A distance on the optical axis from the object-side surface of the first lens element to the image plane is HOS. The following relations are satisfied: HOS/HOI≤3 and 0.5≤HOS/f≤3.0. Preferably, the following relations may be satisfied: 1≤HOS/HOI≤2.5 and 1≤HOS/f≤2. Hereby, the miniaturization of the optical image capturing system can be maintained effectively, so as to be carried by lightweight portable electronic devices. 
     In addition, in the optical image capturing system of the disclosure, according to different requirements, at least one aperture stop may be arranged for reducing stray light and improving the imaging quality. 
     In the optical image capturing system of the disclosure, the aperture stop may be a front or middle aperture. The front aperture is the aperture stop between a photographed object and the first lens element. The middle aperture is the aperture stop between the first lens element and the image plane. If the aperture stop is the front aperture, a longer distance between the exit pupil and the image plane of the optical image capturing system can be formed, such that more optical elements can be disposed in the optical image capturing system and the efficiency of receiving images of the image sensing device can be raised. If the aperture stop is the middle aperture, the view angle of the optical image capturing system can be expended, such that the optical image capturing system has the same advantage that is owned by wide angle cameras. A distance from the aperture stop to the image plane is InS. The following relation is satisfied: 0.5≤InS/HOS≤1.1. Preferably, the following relation may be satisfied: 0.8≤InS/HOS≤1. Hereby, features of maintaining the minimization for the optical image capturing system and having wide-angle are available simultaneously. 
     In the optical image capturing system of the disclosure, a distance from the object-side surface of the first lens element to the image-side surface of the fourth lens element is InTL. A sum of central thicknesses of all lens elements with refractive power on the optical axis is ΣTP. The following relation is satisfied: 0.45≤ΣTP/InTL≤0.95. Preferably, the following relation may be satisfied: 0.6≤ΣTP/InTL≤0.9. Hereby, contrast ratio for the image formation in the optical image capturing system and defect-free rate for manufacturing the lens element can be given consideration simultaneously, and a proper back focal length is provided to dispose other optical components in the optical image capturing system. 
     A curvature radius of the object-side surface of the first lens element is R1. A curvature radius of the image-side surface of the first lens element is R2. The following relation is satisfied: 0.01≤|R1/R2|≤0.5. Hereby, the first lens element may have proper strength of the positive refractive power, so as to avoid the longitudinal spherical aberration to increase too fast. Preferably, the following relation may be satisfied: 0.01≤|R1/R2|≤0.4. 
     A curvature radius of the object-side surface of the fourth lens element is R9. A curvature radius of the image-side surface of the fourth lens element is R10. The following relation is satisfied: −200&lt;(R7−R8)/(R7+R8)&lt;30. Hereby, the astigmatism generated by the optical image capturing system can be corrected beneficially. 
     A distance between the first lens element and the second lens element on the optical axis is IN12. The following relation is satisfied: 0&lt;IN12/f≤0.25. Preferably, the following relation may be satisfied: 0.01≤IN12/f≤0.20. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance can be increased. 
     A distance between the second lens element and the third lens element on the optical axis is IN23. The following relation is satisfied: 0&lt;IN23/f≤0.25. Preferably, the following relation may be satisfied: 0.01≤IN23/f≤0.20. Hereby, the performance of the lens elements can be improved. 
     A distance between the third lens element and the fourth lens element on the optical axis is IN34. The following relation is satisfied: 0&lt;IN34/f≤0.25. Preferably, the following relation may be satisfied: 0.001≤IN34/f≤0.20. Hereby, the performance of the lens elements can be improved. 
     Central thicknesses of the first lens element and the second lens element on the optical axis are TP1 and TP2, respectively. The following relation is satisfied: 1≤(TP1+IN12)/TP2≤10. Hereby, the sensitivity produced by the optical image capturing system can be controlled, and the performance can be increased. 
     Central thicknesses of the third lens element and the fourth lens element on the optical axis are TP3 and TP4, respectively, and a distance between the aforementioned two lens elements on the optical axis is IN34. The following relation is satisfied: 0.2≤(TP4+IN34)/TP4≤3. Hereby, the sensitivity produced by the optical image capturing system can be controlled and the total height of the optical image capturing system can be reduced. 
     A distance between the second lens element and the third lens element on the optical axis is IN23. A total sum of distances from the first lens element to the fourth lens element on the optical axis is ΣTP. The following relation is satisfied: 0.01≤IN23/(TP2+IN23+TP3)≤0.5. Preferably, the following relation may be satisfied: 0.05≤IN23/(TP2+IN23+TP3)≤0.4. Hereby, the aberration generated by the process of moving the incident light can be adjusted slightly layer upon layer, and the total height of the optical image capturing system can be reduced. 
     In the optical image capturing system of the disclosure, a distance in parallel with an optical axis from a maximum effective diameter position to an axial point on the object-side surface  142  of the fourth lens element is InRS41 (InRS41 is positive if the horizontal displacement is toward the image-side surface, or InRS41 is negative if the horizontal displacement is toward the object-side surface). A distance in parallel with an optical axis from a maximum effective diameter position to an axial point on the image-side surface  144  of the fourth lens element is InRS42. A central thickness of the fourth lens element  140  on the optical axis is TP4. The following relations are satisfied: −1 mm≤InRS4|≤1 mm, −1 mm≤InRS42≤1 mm, 1 mm≤|InRS41|+|InRS42|≤2 mm, 0.01≤|InRS41|/TP4≤10 and 0.01≤|InRS42|/TP4≤10. Hereby, the maximum effective diameter position between both surfaces of the fourth lens element can be controlled, so as to facilitate the aberration correction of peripheral field of view of the optical image capturing system and maintain its miniaturization effectively. 
     In the optical image capturing system of the disclosure, a distance in parallel with an optical axis from an inflection point on the object-side surface of the fourth lens element which is nearest to the optical axis to an axial point on the object-side surface of the fourth lens element is denoted by SGI411. A distance in parallel with an optical axis from an inflection point on the image-side surface of the fourth lens element which is nearest to the optical axis to an axial point on the image-side surface of the fourth lens element is denoted by SGI421. The following relations are satisfied: 0&lt;SGI411/(SGI411+TP4)≤0.9 and 0&lt;SGI421/(SGI421+TP4)≤0.9. Preferably, the following relations may be satisfied: 0.01&lt;SGI411/(SGI411+TP4)≤0.7 and 0.01&lt;SGI421/(SGI421+TP4)≤0.7. 
     A distance in parallel with the optical axis from the inflection point on the object-side surface of the fourth lens element which is the second nearest to the optical axis to an axial point on the object-side surface of the fourth lens element is denoted by SGI412. A distance in parallel with an optical axis from an inflection point on the image-side surface of the fourth lens element which is the second nearest to the optical axis to an axial point on the image-side surface of the fourth lens element is denoted by SGI422. The following relations are satisfied: 0&lt;SGI412/(SGI412+TP4)≤0.9 and 0&lt;SGI422/(SGI422+TP4)≤0.9. Preferably, the following relations may be satisfied: 0.1≤SGI412/(SGI412+TP4)≤0.8 and 0.1≤SGI422/(SGI422+TP4)≤0.8. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens element which is nearest to the optical axis and the optical axis is denoted by HIF411. A distance perpendicular to the optical axis between an inflection point on the image-side surface of the fourth lens element which is nearest to the optical axis and an axial point on the image-side surface of the fourth lens element is denoted by HIF421. The following relations are satisfied: 0.01≤HIF411/HOI≤0.9 and 0.01≤HIF421/HOI≤0.9. Preferably, the following relations may be satisfied: 0.09≤HIF411/HOI≤0.5 and 0.09≤HIF421/HOI≤0.5. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens element which is the second nearest to the optical axis and the optical axis is denoted by HIF412. A distance perpendicular to the optical axis between an axial point on the image-side surface of the fourth lens element and an inflection point on the image-side surface of the fourth lens element which is the second nearest to the optical axis is denoted by HIF422. The following relations are satisfied: 0.01≤HIF412/HOI≤0.9 and 0.01≤HIF422/HOI≤0.9. Preferably, the following relations may be satisfied: 0.09≤HIF412/HOI≤0.8 and 0.09≤HIF422/HOI≤0.8. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens element which is the third nearest to the optical axis and the optical axis is denoted by HIF413. A distance perpendicular to the optical axis between an axial point on the image-side surface of the fourth lens element and an inflection point on the image-side surface of the fourth lens element which is the third nearest to the optical axis is denoted by HIF423. The following relations are satisfied: 0.001 mm≤|HIF413|≤5 mm and 0.001 mm≤|HIF423|≤5 mm. Preferably, the following relations may be satisfied: 0.1 mm≤|HIF423|≤3.5 mm and 0.1 mm≤HIF413|≤3.5 mm. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens element which is the fourth nearest to the optical axis and the optical axis is denoted by HIF414. A distance perpendicular to the optical axis between an axial point on the image-side surface of the fourth lens element and an inflection point on the image-side surface of the fourth lens element which is the fourth nearest to the optical axis is denoted by HIF424. The following relations are satisfied: 0.001 mm≤|HIF414|≤5 mm and 0.001 mm≤|HIF424|≤5 mm. Preferably, the following relations may be satisfied: 0.1 mm≤|HIF424|≤3.5 mm and 0.1 mm≤|HIF414|≤3.5 mm. 
     In one embodiment of the optical image capturing system of the present disclosure, the chromatic aberration of the optical image capturing system can be corrected by alternatively arranging the lens elements with large Abbe number and small Abbe number. 
     The above Aspheric formula 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 101 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 position value of the position along the optical axis and at the height h which reference to the surface apex; k is the conic coefficient, c is the reciprocal of curvature radius, and A4, A6, A8, A10, A12, A14, A16, A18, and A20 are high order aspheric coefficients.
 
     The optical image capturing system provided by the disclosure, the lens elements may be made of glass or plastic material. If plastic material is adopted to produce the lens elements, the cost of manufacturing will be lowered effectively. If lens elements are made of glass, the heat effect can be controlled and the designed space arranged for the refractive power of the optical image capturing system can be increased. Besides, the object-side surface and the image-side surface of the first through fourth lens elements may be aspheric, so as to obtain more control variables. Comparing with the usage of traditional lens element made by glass, the number of lens elements used can be reduced and the aberration can be eliminated. Thus, the total height of the optical image capturing system can be reduced effectively. 
     In addition, in the optical image capturing system provided by the disclosure, if the lens element has a convex surface, the surface of the lens element is convex adjacent to the optical axis. If the lens element has a concave surface, the surface of the lens element is concave adjacent to the optical axis. 
     Besides, in the optical image capturing system of the disclosure, according to different requirements, at least one aperture may be arranged for reducing stray light and improving the imaging quality. 
     The optical image capturing system of the disclosure can be adapted to the optical image capturing system with automatic focus if required. With the features of a good aberration correction and a high quality of image formation, the optical image capturing system can be used in various application fields. 
     The optical image capturing system of the disclosure can include a driving module according to the actual requirements. The driving module may be coupled with the lens elements to enable the lens elements producing displacement. The driving module described above may be the voice coil motor (VCM) which is applied to move the lens to focus, or may be the optical image stabilization (OIS) which is applied to reduce the distortion frequency owing to the vibration of the lens while shooting. 
     According to the above embodiments, the specific embodiments with figures are presented in detail as below. 
     The First Embodiment (Embodiment 1) 
     Please refer to  FIG. 1A  and  FIG. 1B .  FIG. 1A  is a schematic view of the optical image capturing system according to the first embodiment of the present application,  FIG. 1B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion curve of the optical image capturing system in the order from left to right according to the first embodiment of the present application, and  FIG. 1C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the first embodiment of the present application. As shown in  FIG. 1A , in order from an object side to an image side, the optical image capturing system includes an aperture stop  1 , a first lens element  110 , a second lens element  120 , a third lens element  130 , a fourth lens element  140 , an IR-bandstop filter  170 , an image plane  180 , and an image sensing device  190 . 
     The first lens element  110  has positive refractive power and it is made of plastic material. The first lens element  110  has a convex object-side surface  112  and a concave image-side surface  114 , both of the object-side surface  112  and the image-side surface  114  are aspheric. The object-side surface  112  and the image-side surface  114  have an inflection point respectively. The length of outline curve of the maximum effective half diameter position of the object-side surface of the first lens element is denoted as ARS11. The length of outline curve of the maximum effective half diameter position of the image-side surface of the first lens element is denoted as ARS12. The length of outline curve of a half of an entrance pupil diameter (HEP) of the object-side surface of the first lens element is denoted as ARE11, and the length of outline curve of the half of the entrance pupil diameter (HEP) of the image-side surface of the first lens element is denoted as ARE12. The thickness of the first lens element on the optical axis is TP1. 
     A distance in parallel with an optical axis from an inflection point on the object-side surface of the first lens element which is nearest to the optical axis to an axial point on the object-side surface of the first lens element is denoted by SGI111. A distance in parallel with an optical axis from an inflection point on the image-side surface of the first lens element which is nearest to the optical axis to an axial point on the image-side surface of the first lens element is denoted by SGI121. The following relations are satisfied: SGI111=0.2008 mm, SGI121=0.0113 mm, |SGI111|/(|SGI111|+TP1)=0.3018 and |SGI121|/(|SGI121|+TP1)=0.0238°. 
     A distance perpendicular to the optical axis from the inflection point on the object-side surface of the first lens element which is nearest to the optical axis to an axial point on the object-side surface of the first lens element is denoted by HIF111. A distance perpendicular to the optical axis from the inflection point on the image-side surface of the first lens element which is nearest to the optical axis to an axial point on the image-side surface of the first lens element is denoted by HIF121. The following relations are satisfied: HIF111=0.7488 mm, HIF121=0.4451 mm, HIF111/HOI=0.2552 and HIF121/HOI=0.1517. 
     The second lens element  120  has positive refractive power and it is made of plastic material. The second lens element  120  has a concave object-side surface  122  and a convex image-side surface  124 , and both of the object-side surface  122  and the image-side surface  124  are aspheric. The object-side surface  122  has an inflection point. The length of outline curve of the maximum effective half diameter position of the object-side surface of the second lens element is denoted as ARS21, and the length of outline curve of the maximum effective half diameter position of the image-side surface of the second lens element is denoted as ARS22. The length of outline curve of a half of an entrance pupil diameter (HEP) of the object-side surface of the second lens element is denoted as ARE21, and the length of outline curve of the half of the entrance pupil diameter (HEP) of the image-side surface of the second lens element is denoted as ARS22. The thickness of the second lens element on the optical axis is TP2. 
     A distance in parallel with an optical axis from an inflection point on the object-side surface of the second lens element which is nearest to the optical axis to an axial point on the object-side surface of the second lens element is denoted by SGI211. A distance in parallel with an optical axis from an inflection point on the image-side surface of the second lens element which is nearest to the optical axis to an axial point on the image-side surface of the second lens element is denoted by SGI221. The following relations are satisfied: SGI211=−0.1791 mm and |SGI211|/(|SGI211|+TP2)=0.3109. 
     A distance perpendicular to the optical axis from the inflection point on the object-side surface of the second lens element which is nearest to the optical axis to an axial point on the object-side surface of the second lens element is denoted by HIF211. A distance perpendicular to the optical axis from the inflection point on the image-side surface of the second lens element which is nearest to the optical axis to an axial point on the image-side surface of the second lens element is denoted by HIF221. The following relations are satisfied: HIF211=0.8147 mm and HIF211/HOI=0.2777. 
     The third lens element  130  has negative refractive power and it is made of plastic material. The third lens element  130  has a concave object-side surface  132  and a convex image-side surface  134 , and both of the object-side surface  132  and the image-side surface  134  are aspheric. The image-side surface  134  has an inflection point. The length of outline curve of the maximum effective half diameter position of the object-side surface of the third lens element is denoted as ARS31, and the length of outline curve of the maximum effective half diameter position of the image-side surface of the third lens element is denoted as ARS32. The length of outline curve of a half of an entrance pupil diameter (HEP) of the object-side surface of the third lens element is denoted as ARE31, and the length of outline curve of the half of the entrance pupil diameter (HEP) of the image-side surface of the third lens element is denoted as ARS32. The thickness of the third lens element on the optical axis is TP3. 
     A distance in parallel with an optical axis from an inflection point on the object-side surface of the third lens element which is nearest to the optical axis to an axial point on the object-side surface of the third lens element is denoted by SGI311. A distance in parallel with an optical axis from an inflection point on the image-side surface of the third lens element which is nearest to the optical axis to an axial point on the image-side surface of the third lens element is denoted by SGI321. The following relations are satisfied: SGI321=−0.1647 mm and |SGI321|/(|SGI321|+TP3)=0.1884. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the third lens element which is nearest to the optical axis and the optical axis is denoted by HIF311. A distance perpendicular to the optical axis from the inflection point on the image-side surface of the third lens element which is nearest to the optical axis to an axial point on the image-side surface of the third lens element is denoted by HIF321. The following relations are satisfied: HIF321=0.7269 mm and HIF321/HOI=0.2477. 
     The fourth lens element  140  has negative refractive power and it is made of plastic material. The fourth lens element  140  has a convex object-side surface  142  and a concave image-side surface  144 , both of the object-side surface  142  and the image-side surface  144  are aspheric, the object-side surface  142  has two inflection points and the image-side surface  144  has an inflection point. The length of outline curve of the maximum effective half diameter position of the object-side surface of the fourth lens element is denoted as ARS41, and the length of outline curve of the maximum effective half diameter position of the image-side surface of the fourth lens element is denoted as ARS42. The length of outline curve of a half of an entrance pupil diameter (HEP) of the object-side surface of the fourth lens element is denoted as ARE41, and the length of outline curve of the half of the entrance pupil diameter (HEP) of the image-side surface of the fourth lens element is denoted as ARS42. The thickness of the fourth lens element on the optical axis is TP4. 
     A distance in parallel with an optical axis from an inflection point on the object-side surface of the fourth lens element which is nearest to the optical axis to an axial point on the object-side surface of the fourth lens element is denoted by SGI411. A distance in parallel with an optical axis from an inflection point on the image-side surface of the fourth lens element which is nearest to the optical axis to an axial point on the image-side surface of the fourth lens element is denoted by SGI421. The following relations are satisfied: SGI411=0.0137 mm, SGI421=0.0922 mm, |SGI411|/(|SGI411|+TP4)=0.0155 and |SGI421|/(|SGI421|+TP4)=0.0956. 
     A distance in parallel with the optical axis from an inflection point on the object-side surface of the fourth lens element which is the second nearest to the optical axis to an axial point on the object-side surface of the fourth lens element is denoted by SGI412. The following relations are satisfied: SGI412=−0.1518 mm and |SGI412|/(|SGI412|+TP4)=0.1482. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens element which is nearest to the optical axis and the optical axis is denoted by HIF411. A distance perpendicular to the optical axis between the inflection point on the image-side surface of the fourth lens element which is nearest to the optical axis and the optical axis is denoted by HIF421. The following relations are satisfied: HIF411=0.2890 mm, HIF421=0.5794 mm, HIF411/HOI=0.0985 and HIF421/HOI=0.1975. 
     A distance perpendicular to the optical axis between the inflection point on the object-side surface of the fourth lens element which is the second nearest to the optical axis and the optical axis is denoted by HIF412. The following relations are satisfied: HIF412=1.3328 mm and HIF412/HOI=0.4543. 
     The IR-bandstop filter  170  is made of glass material without affecting the focal length of the optical image capturing system and it is disposed between the fourth lens element  140  and the image plane  180 . 
     In the optical image capturing system of the first embodiment, a focal length of the optical image capturing system is f, an entrance pupil diameter of the optical image capturing system is HEP, and half of a maximal view angle of the optical image capturing system is HAF. The detailed parameters are shown as below: f=3.4375 mm, f/HEP=2.23, HAF=39.69° and tan(HAF)=0.8299. 
     In the optical image capturing system of the first embodiment, a focal length of the first lens element  110  is f1 and a focal length of the fourth lens element  140  is f4. The following relations are satisfied: f1=3.2736 mm, |f/f1|=1.0501, f4=−8.3381 mm and |f1/f4|=0.3926. 
     In the optical image capturing system of the first embodiment, focal lengths of the second lens element  120  and the third lens element  130  are f2 and 13, respectively. The following relations are satisfied: |f2|+|f3|=10.0976 mm, |f1|+|f4|=11.6116 mm and |f2|+|f3|&lt;f1|+|f4|. 
     A ratio of the focal length f of the optical image capturing system to a focal length fp of each of lens elements with positive refractive power is PPR. A ratio of the focal length f of the optical image capturing system to a focal length fn of each of lens elements with negative refractive power is NPR. In the optical image capturing system of the first embodiment, a sum of the PPR of all lens elements with positive refractive power is ΣPPR=|f/f1|+|f/f2|=1.95585. A sum of the NPR of all lens elements with negative refractive powers is ΣNPR=|f/f3|+|f/f4|=0.95770 and ΣPPR/|ΣNPR|=2.04224. The following relations are also satisfied: |f/f1|=1.05009, |f/f2|=0.90576, |f/f3|=0.54543 and |f/f4|=0.41227. 
     In the optical image capturing system of the first embodiment, a distance from the object-side surface  112  of the first lens element to the image-side surface  144  of the fourth lens element is InTL. A distance from the object-side surface  112  of the first lens element to the image plane  180  is HOS. A distance from an aperture  100  to an image plane  180  is InS. Half of a diagonal length of an effective detection field of the image sensing device  190  is HOI. A distance from the image-side surface  144  of the fourth lens element to an image plane  180  is InB. The following relations are satisfied: InTL+InB=HOS, HOS=4.4250 mm, HOI=2.9340 mm, HOS/HOI=1.5082, HOS/f=1.2873, InTL/HOS=0.7191, InS=4.2128 mm and InS/HOS=0.95204. 
     In the optical image capturing system of the first embodiment, the sum of central thicknesses of all lens elements with refractive power on the optical axis is ΣTP. The following relations are satisfied: ΣTP=2.4437 mm and ΣTP/InTL=0.76793. Hereby, contrast ratio for the image formation in the optical image capturing system and defect-free rate for manufacturing the lens element can be given consideration simultaneously, and a proper back focal length is provided to dispose other optical components in the optical image capturing system. 
     In the optical image capturing system of the first embodiment, a curvature radius of the object-side surface  112  of the first lens element is R1. A curvature radius of the image-side surface  114  of the first lens element is R2. The following relation is satisfied: |R1/R2|=0.1853. Hereby, the first lens element may have proper strength of the positive refractive power, so as to avoid the longitudinal spherical aberration to increase too fast. 
     In the optical image capturing system of the first embodiment, a curvature radius of the object-side surface  142  of the fourth lens element is R7. A curvature radius of the image-side surface  144  of the fourth lens element is R8. The following relation is satisfied: (R7−R8)/(R7+R8)=0.2756. Hereby, the astigmatism generated by the optical image capturing system can be corrected beneficially. 
     In the optical image capturing system of the first embodiment, the focal lengths of the first lens element  110  and the second lens element  120  are f1 and f2, respectively. A sum of focal lengths of all lens elements with positive refractive power is ΣPP. The following relations are satisfied: ΣPP=f1+f2=7.0688 mm and f1/(f1+f2)=0.4631. Hereby, it is favorable for allocating the positive refractive power of the first lens element  110  to other positive lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the first embodiment, the focal lengths of the third lens element  130  and the fourth lens element  140  are f3 and f4, respectively. A sum of focal lengths of all lens elements with negative refractive power is ΣNP. The following relations are satisfied: ΣNP=f3+f4=−14.6405 mm and f4/(f3+f4)=0.5695. Hereby, it is favorable for allocating the negative refractive power of the fourth lens element  140  to other negative lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the first embodiment, a distance between the first lens element  110  and the second lens element  120  on the optical axis is IN12. The following relations are satisfied: IN12=0.3817 mm and IN12/f=0.11105. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance can be increased. 
     In the optical image capturing system of the first embodiment, a distance between the second lens element  120  and the third lens element  130  on the optical axis is IN23. The following relations are satisfied: IN23=0.0704 mm and IN23/f=0.02048. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance can be increased. 
     In the optical image capturing system of the first embodiment, a distance between the third lens element  130  and the fourth lens element  140  on the optical axis is IN34. The following relations are satisfied: IN34=0.2863 mm and IN34/f=0.08330. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance can be increased. 
     In the optical image capturing system of the first embodiment, central thicknesses of the first lens element  110  and the second lens element  120  on the optical axis are TP1 and TP2, respectively. The following relations are satisfied: TP1=0.46442 mm, TP2=0.39686 mm, TP1/TP2=1.17023 and (TP1+IN12)/TP2=2.13213. Hereby, the sensitivity produced by the optical image capturing system can be controlled, and the performance can be increased. 
     In the optical image capturing system of the first embodiment, central thicknesses of the third lens element  130  and the fourth lens element  140  on the optical axis are TP3 and TP4, respectively, and a distance between the aforementioned two lens elements on the optical axis is IN34. The following relations are satisfied: TP3=0.70989 mm, TP4=0.87253 mm, TP3/TP4=0.81359 and (TP4+IN34)/TP3=1.63248. Hereby, the sensitivity produced by the optical image capturing system can be controlled and the total height of the optical image capturing system can be reduced. 
     In the optical image capturing system of the first embodiment, the following relations are satisfied: IN23/(TP2+IN23+TP3)=0.05980. Hereby, the aberration generated by the process of moving the incident light can be adjusted slightly layer upon layer, and the total height of the optical image capturing system can be reduced. 
     A distance in parallel with an optical axis from a maximum effective diameter position to an axial point on the object-side surface  142  of the fourth lens element is InRS41. A distance in parallel with an optical axis from a maximum effective diameter position to an axial point on the image-side surface  144  of the fourth lens element is InRS42. A central thickness of the fourth lens element  140  on the optical axis is TP4. The following relations are satisfied: InRS41=−0.23761 mm, InRS42=−0.20206 mm, |InRS41|+|InRS42|=0.43967 mm, |InRS41|/TP4=0.27232 and |InRS42|/TP4=0.23158. Hereby, it is favorable to the manufacturing and formation of the lens elements and to maintain its miniaturization effectively. 
     In the optical image capturing system of the first embodiment, a distance perpendicular to the optical axis between a critical point C41 on the object-side surface  142  of the fourth lens element and the optical axis is HVT41. A distance perpendicular to the optical axis between a critical point C42 on the image-side surface  144  of the fourth lens element and the optical axis is HVT42. The following relations are satisfied: HVT41=0.5695 mm, HVT42=1.3556 mm and HVT41/HVT42=0.4201. Hereby, the aberration in the off-axis field of view can be corrected. 
     In the optical image capturing system of the first embodiment, the following relation is satisfied: HVT42/HOI=0.4620. Hereby, the aberration of surrounding field of view can be corrected. 
     In the optical image capturing system of the first embodiment, the following relation is satisfied: HVT42/HOS=0.3063. Hereby, the aberration of surrounding field of view can be corrected. 
     In the optical image capturing system of the first embodiment, an Abbe number of the first lens element is NA1. An Abbe number of the second lens element is NA2. An Abbe number of the third lens element is NA3. An Abbe number of the fourth lens element is NA4. The following relations are satisfied: |NA1−NA2|=0 and NA3/NA2=0.39921. Hereby, the chromatic aberration of the optical image capturing system can be corrected. 
     In the optical image capturing system of the first embodiment, TV distortion and optical distortion for image formation in the optical image capturing system are TDT and ODT, respectively. The following relations are satisfied: |TDT|=0.4% and |ODT|=2.5%. 
     In the optical image capturing system of the first embodiment, a lateral aberration of the longest operation wavelength of a positive direction tangential fan of the optical image capturing system passing through an edge of the aperture and incident on the image plane by 0.7 view field is denoted as PLTA, which is 0.001 mm (pixel size is 1.12 μm). A lateral aberration of the shortest operation wavelength of the positive direction tangential fan of the optical image capturing system passing through the edge of the aperture and incident on the image plane by 0.7 view field is denoted as PSTA, which is 0.004 mm (pixel size is 1.12 μm). A lateral aberration of the longest operation wavelength of a negative direction tangential fan of the optical image capturing system passing through the edge of the aperture and incident on the image plane by 0.7 view field is denoted as NLTA, which is 0.003 mm (pixel size is 1.12 μm). A lateral aberration of the shortest operation wavelength of a negative direction tangential fan of the optical image capturing system passing through the edge of the aperture and incident on the image plane by 0.7 view field is denoted as NSTA, which is −0.003 mm (pixel size is 1.12 μm). A lateral aberration of the longest operation wavelength of a sagittal fan of the optical image capturing system passing through the edge of the aperture and incident on the image plane by 0.7 view field is denoted as SLTA, which is 0.003 mm (pixel size is 1.12 μm). A lateral aberration of the shortest operation wavelength of the sagittal fan of the optical image capturing system passing through the edge of the aperture and incident on the image plane by 0.7 view field is denoted as SSTA, which is 0.004 mm (pixel size is 1.12 μm). 
     Please refer to the following Table 1 and Table 2. 
     The detailed data of the optical image capturing system of the first embodiment is as shown in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Data of the optical image capturing system 
               
               
                 f = 3.4375 mm, f/HEP = 2.23, HAF = 39.6900 deg; tan(HAF) = 0.8299 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Focal 
               
               
                 Surface # 
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 length 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 At infinity 
                   
                   
                   
                   
               
               
                 1 
                 Lens 1/Ape. 
                 1.466388 
                 0.464000 
                 Plastic 
                 1.535 
                 56.07 
                 3.274 
               
               
                   
                 stop 
               
               
                 2 
                   
                 7.914480 
                 0.382000 
               
               
                 3 
                 Lens 2 
                 −5.940659 
                 0.397000 
                 Plastic 
                 1.535 
                 56.07 
                 3.795 
               
               
                 4 
                   
                 −1.551401 
                 0.070000 
               
               
                 5 
                 Lens 3 
                 −0.994576 
                 0.710000 
                 Plastic 
                 1.642 
                 22.46 
                 −6.302 
               
               
                 6 
                   
                 −1.683933 
                 0.286000 
               
               
                 7 
                 Lens 4 
                 2.406736 
                 0.873000 
                 Plastic 
                 1.535 
                 56.07 
                 −8.338 
               
               
                 8 
                   
                 1.366640 
                 0.213000 
               
               
                 9 
                 IR-bandstop 
                 Plano 
                 0.210000 
                 BK7_SCHOTT 
                 1.517 
                 64.13 
               
               
                   
                 filter 
               
               
                 10 
                   
                 Plano 
                 0.820000 
               
               
                 11 
                 Image plane 
                 Plano 
               
               
                   
               
               
                 Reference wavelength = 555 nm, shield position: clear aperture (CA) of the eighth plano = 2.320 mm. 
               
            
           
         
       
     
     As for the parameters of the aspheric surfaces of the first embodiment, reference is made to Table 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface # 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
               
                 k = 
                 −1.595426E+00 
                 −7.056632E+00 
                 −2.820679E+01 
                 −1.885740E+00 
                 1.013988E−01 
                 −3.460337E+01 
               
               
                 A4 = 
                 −4.325520E−04 
                 −2.633963E−02 
                 −1.367865E−01 
                 −9.745260E−02 
                 2.504976E−01 
                 −9.580611E−01 
               
               
                 A6 = 
                 1.103749E+00 
                 2.088207E−02 
                 3.135755E−01 
                 −1.032177E+00 
                 −1.640463E+00 
                 3.303418E+00 
               
               
                 A8 = 
                 −8.796867E+00 
                 −1.122861E−01 
                 −6.149514E+00 
                 8.016230E+00 
                 1.354700E+01 
                 −8.544412E+00 
               
               
                 A10 = 
                 3.981982E+01 
                 −7.137813E−01 
                 3.883332E+01 
                 −4.215882E+01 
                 −6.223343E+01 
                 1.602487E+01 
               
               
                 A12 = 
                 −1.102573E+02 
                 2.236312E+00 
                 −1.463622E+02 
                 1.282874E+02 
                 1.757259E+02 
                 −2.036011E+01 
               
               
                 A14 = 
                 1.900642E+02 
                 −2.756305E+00 
                 3.339863E+02 
                 −2.229568E+02 
                 −2.959459E+02 
                 1.703516E+01 
               
               
                 A16 = 
                 −2.000279E+02 
                 1.557080E+00 
                 −4.566510E+02 
                 2.185571E+02 
                 2.891641E+02 
                 −8.966359E+00 
               
               
                 A18 = 
                 1.179848E+02 
                 −2.060190E+00 
                 3.436469E+02 
                 −1.124538E+02 
                 −1.509364E+02 
                 2.684766E+00 
               
               
                 A20 = 
                 −3.023405E+01 
                 2.029630E+00 
                 −1.084572E+02 
                 2.357571E+01 
                 3.243879E+01 
                 −3.481557E−01 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface # 
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 7 
                 8 
               
               
                   
                   
               
               
                   
                 k = 
                 −4.860907E+01 
                 −7.091499E+00 
               
               
                   
                 A4 = 
                 −2.043197E−01 
                 −8.148585E−02 
               
               
                   
                 A6 = 
                 6.516636E−02 
                 3.050566E−02 
               
               
                   
                 A8 = 
                 4.863926E−02 
                 −8.218175E−03 
               
               
                   
                 A10 = 
                 −7.086809E−02 
                 1.186528E−03 
               
               
                   
                 A12 = 
                 3.815824E−02 
                 −1.305021E−04 
               
               
                   
                 A14 = 
                 −1.032930E−02 
                 2.886943E−05 
               
               
                   
                 A16 = 
                 1.413303E−03 
                 −6.459004E−06 
               
               
                   
                 A18 = 
                 −8.701682E−05 
                 6.571792E−07 
               
               
                   
                 A20 = 
                 1.566415E−06 
                 −2.325503E−08 
               
               
                   
                   
               
            
           
         
       
     
     The relevant data of the length of outline curve may be deduced from Table 1 and Table 2. 
     
       
         
           
               
             
               
                   
               
               
                 First embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE 
                   
                   
                   
                 ARE/TP 
               
               
                 ARE 
                 ½(HEP) 
                 value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.771 
                 0.808 
                 0.037 
                 104.77% 
                 0.464 
                 173.90% 
               
               
                 12 
                 0.771 
                 0.771 
                 0.000 
                  99.99% 
                 0.464 
                 165.97% 
               
               
                 21 
                 0.771 
                 0.797 
                 0.026 
                 103.38% 
                 0.397 
                 200.80% 
               
               
                 22 
                 0.771 
                 0.828 
                 0.057 
                 107.37% 
                 0.397 
                 208.55% 
               
               
                 31 
                 0.771 
                 0.832 
                 0.061 
                 107.97% 
                 0.710 
                 117.25% 
               
               
                 32 
                 0.771 
                 0.797 
                 0.026 
                 103.43% 
                 0.710 
                 112.32% 
               
               
                 41 
                 0.771 
                 0.771 
                 0.000 
                 100.05% 
                 0.873 
                  88.39% 
               
               
                 42 
                 0.771 
                 0.784 
                 0.013 
                 101.69% 
                 0.873 
                  89.84% 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARS 
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 value 
                 ARS − EHD 
                 (ARS/EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.771 
                 0.808 
                 0.037 
                 104.77% 
                 0.464 
                 173.90% 
               
               
                 12 
                 0.812 
                 0.814 
                 0.002 
                 100.19% 
                 0.464 
                 175.25% 
               
               
                 21 
                 0.832 
                 0.877 
                 0.045 
                 105.37% 
                 0.397 
                 220.98% 
               
               
                 22 
                 0.899 
                 1.015 
                 0.116 
                 112.95% 
                 0.397 
                 255.83% 
               
               
                 31 
                 0.888 
                 0.987 
                 0.098 
                 111.07% 
                 0.710 
                 138.98% 
               
               
                 32 
                 1.197 
                 1.237 
                 0.041 
                 103.41% 
                 0.710 
                 174.31% 
               
               
                 41 
                 1.642 
                 1.689 
                 0.046 
                 102.81% 
                 0.873 
                 193.53% 
               
               
                 42 
                 2.320 
                 2.541 
                 0.221 
                 109.54% 
                 0.873 
                 291.23% 
               
               
                   
               
            
           
         
       
     
     Table 1 is the detailed structure data to the first embodiment in  FIG. 1A , wherein the unit of the curvature radius, the thickness, the distance, and the focal length is millimeters (mm). Surfaces 0-14 illustrate the surfaces from the object side to the image plane in the optical image capturing system. Table 2 is the aspheric coefficients of the first embodiment, wherein k is the conic coefficient in the aspheric surface formula, and A1-A20 are the first to the twentieth order aspheric surface coefficient. Besides, the tables in the following embodiments are referenced to the schematic view and the aberration graphs, respectively, and definitions of parameters in the tables are equal to those in the Table 1 and the Table 2, so the repetitious details will not be given here. 
     The Second Embodiment (Embodiment 2) 
     Please refer to  FIG. 2A ,  FIG. 2B  and  FIG. 2C ,  FIG. 2A  is a schematic view of the optical image capturing system according to the second embodiment of the present application,  FIG. 2B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion curve of the optical image capturing system in the order from left to right according to the second embodiment of the present application, and  FIG. 2C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the second embodiment of the present application. As shown in  FIG. 2A , in order from an object side to an image side, the optical image capturing system includes an aperture stop  200 , first lens element  210 , a second lens element  220 , a third lens element  230 , a fourth lens element  240 , an IR-bandstop filter  270 , an image plane  280 , and an image sensing device  290 . 
     The first lens element  210  has positive refractive power and it is made of plastic material. The first lens element  210  has a convex object-side surface  212  and a convex image-side surface  214 , both of the object-side surface  212  and the image-side surface  214  are aspheric, and the object-side surface  212  has an inflection point. 
     The second lens element  220  has negative refractive power and it is made of plastic material. The second lens element  220  has a concave object-side surface  222  and a concave image-side surface  224 , both of the object-side surface  222  and the image-side surface  224  are aspheric. The image-side surface  224  has an inflection point. 
     The third lens element  230  has positive refractive power and it is made of plastic material. The third lens element  230  has a concave object-side surface  232  and a convex image-side surface  234 , and both of the object-side surface  232  and the image-side surface  234  are aspheric. The object-side surface  232  has four inflection points and the image-side surface  234  has an inflection point. 
     The fourth lens element  240  has negative refractive power and it is made of plastic material. The fourth lens element  240  has a convex object-side surface  242  and a concave image-side surface  244 , both of the object-side surface  242  and the image-side surface  244  are aspheric, and the object-side surface  242  and the image-side surface  244  have an inflection point respectively. 
     The IR-bandstop filter  270  is made of glass material without affecting the focal length of the optical image capturing system and it is disposed between the fourth lens element  240  and the image plane  280 . 
     In the optical image capturing system of the second embodiment, focal lengths of the second lens element  220  through the fourth lens element  240  are f2, f3 and f4 respectively. The following relations are satisfied: |f2|+|f3|=12.7333 mm, |f1|+|f4|=9.0015 mm and |f2|+f3|&gt;|f1|+|f4|. 
     In the optical image capturing system of the second embodiment, the first lens element  210  and the third lens element  230  are positive lens elements, and focal lengths of the first lens element  210  and the third lens element  230  are f1 and f3, respectively. A sum of focal lengths of all lens elements with positive refractive power is ΣPP. The following relations is satisfied: ΣPP=f1+f3. Hereby, it is favorable for allocating the positive refractive power of the first lens element  210  to other positive lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the second embodiment, focal lengths of the second lens element  220  and the fourth lens element  240  are f2 and f4, respectively. A sum of focal lengths of all lens elements with negative refractive power is ΣNP. The following relation is satisfied: ΣNP=f2+f4. Hereby, it is favorable for allocating the negative refractive power of the fourth lens element  240  to other negative lens elements. 
     Please refer to the following Table 3 and Table 4. 
     The detailed data of the optical image capturing system of the second embodiment is as shown in Table 3. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Data of the optical image capturing system 
               
               
                 f = 2.3521 mm, f/HEP = 1.8, HAF = 43.9997 deg, tan(HAF) = 0.96568 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Focal 
               
               
                 Surface # 
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 length 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 At 
                   
                   
                   
                   
               
               
                   
                   
                   
                 infinity 
               
               
                 1 
                 Ape. stop 
                 Plano 
                 −0.050 
               
               
                 2 
                 Lens 1 
                 1.938213716 
                 0.671 
                 Plastic 
                 1.544 
                 56.09 
                 3.163 
               
               
                 3 
                   
                 −13.86250007 
                 −0.002 
               
               
                 4 
                 Shading 
                 Plano 
                 0.238 
               
               
                   
                 sheet 
               
               
                 5 
                 Lens 2 
                 −10.24620787 
                 0.223 
                 Plastic 
                 1.642 
                 22.46 
                 −10.176 
               
               
                 6 
                   
                 18.62755924 
                 0.160 
               
               
                 7 
                 Lens 3 
                 −0.850575158 
                 0.483 
                 Plastic 
                 1.544 
                 56.09 
                 2.557 
               
               
                 8 
                   
                 −0.634626709 
                 0.026 
               
               
                 9 
                 Lens 4 
                 1.326898506 
                 0.503 
                 Plastic 
                 1.544 
                 56.09 
                 −5.839 
               
               
                 10 
                   
                 0.811386372 
                 0.323 
               
               
                 11 
                 IR-bandstop 
                 Plano 
                 0.200 
                 BK7_SCHOTT 
                 1.517 
                 64.13 
               
               
                   
                 filter 
               
               
                 12 
                   
                 Plano 
                 0.800 
               
               
                 13 
                 Image plane 
                 Plano 
               
               
                   
               
               
                 Reference wavelength (d-line) = 555 nm 
               
            
           
         
       
     
     As for the parameters of the aspheric surfaces of the second embodiment, reference is made to Table 4. 
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface # 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −2.177737E+01 
                 −1.023100E+00 
                 −7.599347E−01 
                 −8.904065E+01 
                 −3.319907E−01 
                 −3.433203E+00 
               
               
                 A4 = 
                 3.966765E−01 
                 −4.104819E−01 
                 −9.969493E−01 
                 −2.819491E−01 
                 9.371477E−01 
                 −5.081457E−01 
               
               
                 A6 = 
                 −1.795462E+00 
                 3.881327E−01 
                 1.384998E+00 
                 5.198925E−01 
                 5.954294E−01 
                 −2.855486E−01 
               
               
                 A8 = 
                 7.459632E+00 
                 −2.566679E+00 
                 −1.688135E+01 
                 −3.276790E+00 
                 −2.960255E+00 
                 9.830284E+00 
               
               
                 A10 = 
                 −2.276732E+01 
                 6.682022E+00 
                 6.177807E+01 
                 6.622781E+00 
                 −3.996158E−01 
                 −4.553455E+01 
               
               
                 A12 = 
                 3.884892E+01 
                 −8.258319E+00 
                 −8.855541E+01 
                 −5.332789E+00 
                 9.467090E+00 
                 1.139317E+02 
               
               
                 A14 = 
                 −2.873114E+01 
                 3.376030E+00 
                 4.494460E+01 
                 1.447432E+00 
                 −1.050707E+01 
                 −1.697212E+02 
               
               
                 A16 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 3.619412E+00 
                 1.497546E+02 
               
               
                 A18 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −7.178255E+01 
               
               
                 A20 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.431978E+01 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface # 
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 9 
                 10 
               
               
                   
                   
               
               
                   
                 k = 
                 −2.343340E−01 
                 −6.182010E+00 
               
               
                   
                 A4 = 
                 −2.848821E−01 
                 −5.124499E−02 
               
               
                   
                 A6 = 
                 1.084163E−03 
                 2.352778E−02 
               
               
                   
                 A8 = 
                 1.326129E−01 
                 −1.229831E−01 
               
               
                   
                 A10 = 
                 −1.356432E−01 
                 2.146638E−01 
               
               
                   
                 A12 = 
                 −7.005224E−02 
                 −2.037958E−01 
               
               
                   
                 A14 = 
                 2.296250E−01 
                 1.144310E−01 
               
               
                   
                 A16 = 
                 −1.796832E−01 
                 −3.771172E−02 
               
               
                   
                 A18 = 
                 6.235645E−02 
                 6.718570E−03 
               
               
                   
                 A20 = 
                 −8.333592E−03 
                 −4.992218E−04 
               
               
                   
                   
               
            
           
         
       
     
     In the second embodiment, the presentation of the aspheric surface formula is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are equal to those in the first embodiment, so the repetitious details will not be given here. 
     The following contents may be deduced from Table 3 and Table 4. 
     
       
         
           
               
             
               
                   
               
               
                 Second embodiment (Primary reference wavelength = 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 InRS41 
                 InRS42 
                 HVT41 
                 HVT42 
                 | ODT | % 
                 | TDT | % 
               
               
                 0.07355 
                 0.03694 
                 1.02659 
                 1.20664 
                   1.27193 
                 0.65228 
               
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f1/f2 | 
                 | f2/f3 | 
               
               
                 0.74375 
                 0.23115 
                 0.91971 
                 0.40283 
                   0.31079 
                 3.97882 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/ 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                   
                   
                 | ΣNPR | 
                   
                   
                   
               
               
                 1.66345 
                 0.63398 
                 2.62381 
                 5.72004 
                 −16.01478 
                 0.55289 
               
               
                 f4/ΣNP 
                 IN12/f 
                 IN23/f 
                 IN34/f 
                 TP3/f 
                 TP4/f 
               
               
                 0.36460 
                 0.10033 
                 0.06813 
                 0.01103 
                  0.20553 
                 0.21398 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 2.30328 
                 3.62606 
                 1.57655 
                 0.98621 
                  0.63520 
                 0.81672 
               
            
           
           
               
               
               
               
               
            
               
                 (TP1 +  
                 (TP4 +  
                 TP1/TP2 
                 TP3/TP4 
                 IN23/(TP2 +  
               
               
                 IN12)/ 
                 IN34)/ 
                   
                   
                 IN23 + TP3) 
               
               
                 TP2 
                 TP3 
                   
                   
                   
               
               
                 4.05841 
                 1.09477 
                 3.00237 
                 0.96051 
                  0.18479 
               
               
                 | INRS41 |/ 
                 | INRS42 |/ 
                 HVT42/ 
                 HVT42/ 
                   
               
               
                 TP4 
                 TP4 
                 HOI 
                 HOS 
                   
               
               
                 0.14613 
                 0.07340 
                 0.52463 
                 0.33277 
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.016 mm 
                 −0.013 mm 
                 −0.013 mm 
                 −0.019 mm 
                 0.009 mm 
                 0.010 mm 
               
               
                   
               
            
           
         
       
     
     The following contents may be deduced from Table 3 and Table 4. 
     
       
         
           
               
             
               
                   
               
               
                 Related inflection point values of second embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 0.55297 
                 HIF111/HOI 
                 0.24042 
                 SGI111 
                 0.07443 
                 |SGI111|/(|SGI111| + TP1) 
                 0.09986 
               
               
                 HIF221 
                 0.12972 
                 HIF221/HOI 
                 0.05640 
                 SGI221 
                 0.00037 
                 |SGI221|/(|SGI221| + TP2) 
                 0.00167 
               
               
                 HIF311 
                 0.35995 
                 HIF311/HOI 
                 0.15650 
                 SGI311 
                 −0.06237 
                 |SGI311|/(|SGI311| + TP3) 
                 0.11427 
               
               
                 HIF312 
                 0.58401 
                 HIF312/HOI 
                 0.25392 
                 SGI312 
                 −0.11873 
                 |SGI312|/(|SGI312| + TP3) 
                 0.19717 
               
               
                 HIF313 
                 0.69370 
                 HIF313/HOI 
                 0.30161 
                 SGI313 
                 −0.14464 
                 |SGI313|/(|SGI313| + TP3) 
                 0.23029 
               
               
                 HIF314 
                 0.95222 
                 HIF314/HOI 
                 0.41401 
                 SGI314 
                 −0.17071 
                 |SGI314|/(|SGI314| + TP3) 
                 0.26097 
               
               
                 HIF321 
                 0.68143 
                 HIF321/HOI 
                 0.29627 
                 SGI321 
                 −0.30171 
                 |SGI321|/(|SGI321| + TP3) 
                 0.38427 
               
               
                 HIF411 
                 0.55156 
                 HIF411/HOI 
                 0.23981 
                 SGI411 
                 0.09313 
                 |SGI411|/(|SGI411| + TP4) 
                 0.15615 
               
               
                 HIF421 
                 0.54626 
                 HIF421/HOI 
                 0.23751 
                 SGI421 
                 0.12543 
                 |SGI421|/(|SGI421| + TP4) 
                 0.19949 
               
               
                   
               
            
           
         
       
     
     The numerical related to the length of outline curve is shown according to table 3 and table 4. 
     
       
         
           
               
             
               
                   
               
               
                 Second embodiment (Primary reference wavelength: 587.5 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARE 
                   
                   
                   
                 ARE/TP 
               
               
                 ARE 
                 ½(HEP) 
                 value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.653 
                 0.662 
                 0.008 
                 101.28% 
                 0.671 
                  98.63% 
               
               
                 12 
                 0.653 
                 0.666 
                 0.013 
                 101.97% 
                 0.671 
                  99.30% 
               
               
                 21 
                 0.653 
                 0.708 
                 0.055 
                 108.40% 
                 0.223 
                 316.94% 
               
               
                 22 
                 0.653 
                 0.657 
                 0.004 
                 100.57% 
                 0.223 
                 294.05% 
               
               
                 31 
                 0.653 
                 0.668 
                 0.015 
                 102.31% 
                 0.483 
                 138.27% 
               
               
                 32 
                 0.653 
                 0.723 
                 0.070 
                 110.68% 
                 0.483 
                 149.59% 
               
               
                 41 
                 0.653 
                 0.666 
                 0.013 
                 101.93% 
                 0.503 
                 132.32% 
               
               
                 42 
                 0.653 
                 0.675 
                 0.022 
                 103.38% 
                 0.503 
                 134.20% 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 ARS 
                   
                   
                   
                 ARS/ 
               
               
                 ARS 
                 EHD 
                 value 
                 ARS − EHD 
                 (ARS/EHD) % 
                 TP 
                 TP(%) 
               
               
                   
               
               
                 11 
                 0.672 
                 0.681 
                 0.009 
                 101.28% 
                 0.671 
                 101.49% 
               
               
                 12 
                 0.760 
                 0.800 
                 0.040 
                 105.26% 
                 0.671 
                 119.24% 
               
               
                 21 
                 0.765 
                 0.881 
                 0.117 
                 115.25% 
                 0.223 
                 394.29% 
               
               
                 22 
                 0.942 
                 0.987 
                 0.046 
                 104.86% 
                 0.223 
                 441.86% 
               
               
                 31 
                 0.988 
                 1.007 
                 0.019 
                 101.96% 
                 0.483 
                 208.31% 
               
               
                 32 
                 1.024 
                 1.144 
                 0.120 
                 111.71% 
                 0.483 
                 236.55% 
               
               
                 41 
                 1.396 
                 1.434 
                 0.038 
                 102.70% 
                 0.503 
                 284.81% 
               
               
                 42 
                 1.724 
                 1.834 
                 0.110 
                 106.38% 
                 0.503 
                 364.48% 
               
               
                   
               
            
           
         
       
     
     The Third Embodiment (Embodiment 3) 
     Please refer to  FIG. 3A ,  FIG. 3B  and  FIG. 3C ,  FIG. 3A  is a schematic view of the optical image capturing system according to the third embodiment of the present application,  FIG. 3B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion curve of the optical image capturing system in the order from left to right according to the third embodiment of the present application, and  FIG. 3C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the third embodiment of the present application. As shown in  FIG. 3A , in order from an object side to an image side, the optical image capturing system includes an aperture stop  300 , first lens element  310 , a second lens element  320 , a third lens element  330 , a fourth lens element  340 , an IR-bandstop filter  370 , an image plane  380 , and an image sensing device  390 . 
     The first lens element  310  has positive refractive power and it is made of plastic material. The first lens element  310  has a convex object-side surface  312  and a convex image-side surface  314 , both of the object-side surface  312  and the image-side surface  314  are aspheric. The object-side surface  312  has an inflection point. 
     The second lens element  320  has negative refractive power and it is made of plastic material. The second lens element  320  has a concave object-side surface  322  and a concave image-side surface  324 , both of the object-side surface  322  and the image-side surface  324  are aspheric. The image-side surface  324  has an inflection point. 
     The third lens element  330  has positive refractive power and it is made of plastic material. The third lens element  330  has a concave object-side surface  332  and a convex image-side surface  334 , both of the object-side surface  332  and the image-side surface  334  are aspheric. The object-side surface  332  and the image-side surface  334  have two inflection points respectively. 
     The fourth lens element  340  has negative refractive power and it is made of plastic material. The fourth lens element  340  has a convex object-side surface  342  and a concave image-side surface  344 , both of the object-side surface  342  and the image-side surface  344  are aspheric. The object-side surface  342  and the image-side surface  344  have an inflection point respectively. 
     The IR-bandstop filter  370  is made of glass material without affecting the focal length of the optical image capturing system and it is disposed between the fourth lens element  340  and the image plane  380 . 
     In the optical image capturing system of the third embodiment, focal lengths of the second lens element  320  through the fourth lens element  340  are f2, f3 and f4 respectively. The following relations are satisfied: |f2|+|f3|=12.9833 mm, |f1|+|f4|=9.0429 mm and |f2|+|f3|&gt;|f1|+|f4|. 
     In the optical image capturing system of the third embodiment, a sum of focal lengths of all lens elements with positive refractive power is ΣPP. The following relation is satisfied: ΣPP=f1+f3. Hereby, it is favorable for allocating the positive refractive power of the first lens element  310  to other positive lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the third embodiment, a sum of focal lengths of all lens elements with negative refractive power is ΣNP. The following relation is satisfied: ΣNP=f2+f4. Hereby, it is favorable for allocating the negative refractive power of the fourth lens element  340  to other negative lens elements. 
     Please refer to the following Table 5 and Table 6. 
     The detailed data of the optical image capturing system of the third embodiment is as shown in Table 5. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Data of the optical image capturing system 
               
               
                 f = 2.3542 mm, f/HEP = 1.8, HAF = 43.9999 deg, tan(HAF) = 0.96566 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Focal 
               
               
                 Surface# 
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 length 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 At infinity 
                   
                   
                   
                   
               
               
                 1 
                 Ape. stop 
                 Plano 
                 −0.050 
               
               
                 2 
                 Lens 1 
                 1.986765609 
                 0.680 
                 Plastic 
                 1.544 
                 56.09 
                 3.220 
               
               
                 3 
                   
                 −13.40015807 
                 0.001 
               
               
                 4 
                 Shading 
                 Plano 
                 0.241 
               
               
                   
                 sheet 
               
               
                 5 
                 Lens 2 
                 −13.01452693 
                 0.215 
                 Plastic 
                 1.642 
                 22.46 
                 −10.447 
               
               
                 6 
                   
                 14.18207262 
                 0.161 
               
               
                 7 
                 Lens 3 
                 −0.8587634 
                 0.489 
                 Plastic 
                 1.544 
                 56.09 
                 2.537 
               
               
                 8 
                   
                 −0.636720641 
                 0.025 
               
               
                 9 
                 Lens 4 
                 1.326929379 
                 0.505 
                 Plastic 
                 1.544 
                 56.09 
                 −5.823 
               
               
                 10 
                   
                 0.810330303 
                 0.328 
               
               
                 11 
                 IR-bandstop 
                 Plano 
                 0.200 
                 BK7_SCHOTT 
                 1.517 
                 64.13 
               
               
                   
                 filter 
               
               
                 12 
                   
                 Plano 
                 0.800 
               
               
                 13 
                 Image plane 
                 Plano 
               
               
                   
               
               
                 Reference wavelength (d-line) = 555 nm; The clear aperture of the fourth surface is 0.772 mm. 
               
            
           
         
       
     
     As for the parameters of the aspheric surfaces of the third embodiment, reference is made to Table 6. 
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface # 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −2.169835E+01 
                 −1.023100E+00 
                 −7.599347E−01 
                 −8.904065E+01 
                 −3.275003E−01 
                 −3.322399E+00 
               
               
                 A4 = 
                 3.443483E−01 
                 −4.339406E−01 
                 −1.074319E+00 
                 −3.676701E−01 
                 8.314431E−01 
                 −4.715007E−01 
               
               
                 A6 = 
                 −1.379554E+00 
                 7.417974E−01 
                 2.091521E+00 
                 9.884165E−01 
                 1.111260E+00 
                 −4.325835E−01 
               
               
                 A8 = 
                 5.339244E+00 
                 −4.263400E+00 
                 −1.998596E+01 
                 −4.427655E+00 
                 −4.256519E+00 
                 9.872267E+00 
               
               
                 A10 = 
                 −1.652800E+01 
                 1.105245E+01 
                 6.734218E+01 
                 8.030609E+00 
                 1.956255E+00 
                 −4.496641E+01 
               
               
                 A12 = 
                 2.928238E+01 
                 −1.397816E+01 
                 −9.254723E+01 
                 −6.142826E+00 
                 6.657354E+00 
                 1.122459E+02 
               
               
                 A14 = 
                 −2.269702E+01 
                 6.365437E+00 
                 4.572555E+01 
                 1.623563E+00 
                 −8.681680E+00 
                 −1.664824E+02 
               
               
                 A16 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 3.135416E+00 
                 1.458519E+02 
               
               
                 A18 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −6.931591E+01 
               
               
                 A20 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.370263E+01 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface # 
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 9 
                 10 
               
               
                   
               
               
                   
                 k = 
                 −2.348430E−01 
                 −6.195413E+00 
               
               
                   
                 A4 = 
                 −2.458901E−01 
                 −5.171263E−03 
               
               
                   
                 A6 = 
                 −1.216824E−01 
                 −1.343401E−01 
               
               
                   
                 A8 = 
                 2.401647E−01 
                 1.477699E−01 
               
               
                   
                 A10 = 
                 −3.358441E−02 
                 −6.426788E−02 
               
               
                   
                 A12 = 
                 −3.586247E−01 
                 −1.849741E−02 
               
               
                   
                 A14 = 
                 4.858174E−01 
                 3.434063E−02 
               
               
                   
                 A16 = 
                 −2.949679E−01 
                 −1.600035E−02 
               
               
                   
                 A18 = 
                 8.884417E−02 
                 3.377881E−03 
               
               
                   
                 A20 = 
                 −1.080120E−02 
                 −2.772887E−04 
               
               
                   
               
            
           
         
       
     
     The presentation of the aspheric surface formula in the third embodiment is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are equal to those in the first embodiment so the repetitious details will not be given here. 
     The following contents may be deduced from Table 5 and Table 6 
     
       
         
           
               
             
               
                   
               
               
                 Third embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 InRS41 
                 InRS42 
                 HVT41 
                 HVT42 
                 | ODT | % 
                 | TDT | % 
               
               
                 0.07135 
                 0.03343 
                 1.03331 
                 1.22145 
                  1.17137 
                 0.55154 
               
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f1/f2 | 
                 | f2/f3 | 
               
               
                 0.73113 
                 0.22535 
                 0.92807 
                 0.40428 
                  0.30822 
                 4.11837 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/ 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                   
                   
                 | ΣNPR | 
                   
                   
                   
               
               
                 1.65920 
                 0.62963 
                 2.63519 
                 5.75650 
                 −16.26973 
                 0.55935 
               
               
                 f4/ΣNP 
                 IN12/f 
                 IN23/f 
                 IN34/f 
                 TP3/f 
                 TP4/f 
               
               
                 0.35791 
                 0.10281 
                 0.06856 
                 0.01062 
                  0.20793 
                 0.21451 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 2.31755 
                 3.64581 
                 1.58513 
                 0.98629 
                  0.63567 
                 0.81514 
               
            
           
           
               
               
               
               
               
            
               
                 (TP1 +  
                 (TP4 +  
                 TP1/TP2 
                 TP3/TP4 
                 IN23/(TP2 +  
               
               
                 IN12)/ 
                 IN34)/ 
                   
                   
                 IN23 + TP3) 
               
               
                 TP2 
                 TP3 
                   
                   
                   
               
               
                 4.28663 
                 1.08274 
                 3.16098 
                 0.96930 
                  0.18640 
               
            
           
           
               
               
               
               
               
               
            
               
                 | INRS41 |/ 
                 | INRS42 |/ 
                 HVT42/ 
                 HVT42/ 
                   
                   
               
               
                 TP4 
                 TP4 
                 HOI 
                 HOS 
                   
                   
               
               
                 0.14129 
                 0.06620 
                 0.53107 
                 0.33503 
                   
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.015 mm 
                 −0.017 mm 
                 −0.014 mm 
                 −0.019 mm 
                 0.015 mm 
                 0.015 mm 
               
               
                   
               
            
           
         
       
     
     The following contents may be deduced from Table 5 and Table 6. 
     
       
         
           
               
             
               
                   
               
               
                 Related inflection point values of third embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 0.55540 
                 HIF111/HOI 
                 0.24148 
                 SGI111 
                 0.07296 
                 |SGI111|/(|SGI111| + TP1) 
                 0.09694 
               
               
                 HIF221 
                 0.13265 
                 HIF221/HOI 
                 0.05767 
                 SGI221 
                 0.00051 
                 |SGI221|/(|SGI221| + TP2) 
                 0.00237 
               
               
                 HIF311 
                 0.35942 
                 HIF311/HOI 
                 0.15627 
                 SGI311 
                 −0.06239 
                 |SGI311|/(|SGI311| + TP3) 
                 0.11305 
               
               
                 HIF312 
                 0.96665 
                 HIF312/HOI 
                 0.42028 
                 SGI312 
                 −0.15089 
                 |SGI312|/(|SGI312| + TP3) 
                 0.23562 
               
               
                 HIF321 
                 0.68195 
                 HIF321/HOI 
                 0.29650 
                 SGI321 
                 −0.30515 
                 |SGI321|/(|SGI321| + TP3) 
                 0.38400 
               
               
                 HIF322 
                 1.02845 
                 HIF322/HOI 
                 0.44715 
                 SGI322 
                 −0.41969 
                 |SGI322|/(|SGI322| + TP3) 
                 0.46161 
               
               
                 HIF411 
                 0.54324 
                 HIF411/HOI 
                 0.23619 
                 SGI411 
                 0.09206 
                 |SGI411|/(|SGI411| + TP4) 
                 0.15419 
               
               
                 HIF421 
                 0.54336 
                 HIF421/HOI 
                 0.23624 
                 SGI421 
                 0.12597 
                 |SGI421|/(|SGI421| + TP4) 
                 0.19964 
               
               
                   
               
            
           
         
       
     
     The numerical related to the length of outline curve is shown according to table 5 and table 6. 
     
       
         
           
               
             
               
                   
               
               
                 Third embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 ARE 
                 ½(HEP) 
                 ARE value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 ARE/TP (%) 
               
               
                   
               
               
                 11 
                 0.654 
                 0.661 
                 0.007 
                 101.13% 
                 0.680 
                 97.31% 
               
               
                 12 
                 0.654 
                 0.666 
                 0.012 
                 101.80% 
                 0.680 
                 97.96% 
               
               
                 21 
                 0.654 
                 0.710 
                 0.056 
                 108.50% 
                 0.215 
                 330.01% 
               
               
                 22 
                 0.654 
                 0.657 
                 0.003 
                 100.45% 
                 0.215 
                 305.53% 
               
               
                 31 
                 0.654 
                 0.668 
                 0.014 
                 102.17% 
                 0.489 
                 136.49% 
               
               
                 32 
                 0.654 
                 0.725 
                 0.071 
                 110.81% 
                 0.489 
                 148.03% 
               
               
                 41 
                 0.654 
                 0.666 
                 0.012 
                 101.89% 
                 0.505 
                 131.94% 
               
               
                 42 
                 0.654 
                 0.676 
                 0.022 
                 103.38% 
                 0.505 
                 133.87% 
               
               
                   
               
               
                 ARS 
                 EHD 
                 ARS value 
                 ARS − EHD 
                 (ARS/EHD) % 
                 TP 
                 ARS/TP (%) 
               
               
                   
               
               
                 11 
                 0.672 
                 0.680 
                 0.008 
                 101.13% 
                 0.680 
                 99.98% 
               
               
                 12 
                 0.760 
                 0.798 
                 0.038 
                 105.03% 
                 0.680 
                 117.46% 
               
               
                 21 
                 0.766 
                 0.886 
                 0.120 
                 115.69% 
                 0.215 
                 411.90% 
               
               
                 22 
                 0.946 
                 0.991 
                 0.045 
                 104.71% 
                 0.215 
                 460.75% 
               
               
                 31 
                 1.004 
                 1.023 
                 0.019 
                 101.90% 
                 0.489 
                 208.96% 
               
               
                 32 
                 1.038 
                 1.163 
                 0.125 
                 112.08% 
                 0.489 
                 237.68% 
               
               
                 41 
                 1.407 
                 1.448 
                 0.040 
                 102.85% 
                 0.505 
                 286.67% 
               
               
                 42 
                 1.745 
                 1.861 
                 0.116 
                 106.63% 
                 0.505 
                 368.43% 
               
               
                   
               
            
           
         
       
     
     The Fourth Embodiment (Embodiment 4) 
     Please refer to  FIG. 4A ,  FIG. 4B  and  FIG. 4C ,  FIG. 4A  is a schematic view of the optical image capturing system according to the fourth embodiment of the present application,  FIG. 4B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion curve of the optical image capturing system in the order from left to right according to the fourth embodiment of the present application, and  FIG. 4C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the fourth embodiment of the present application. As shown in  FIG. 4A , in order from an object side to an image side, the optical image capturing system includes an aperture stop  400 , first lens element  410 , a second lens element  420 , a third lens element  430 , a fourth lens element  440 , an IR-bandstop filter  470 , an image plane  480 , and an image sensing device  490 . 
     The first lens element  410  has positive refractive power and it is made of plastic material. The first lens element  410  has a convex object-side surface  412  and a concave image-side surface  414 , both of the object-side surface  412  and the image-side surface  414  are aspheric, and the object-side surface  412  and the image-side surface  414  have an inflection point respectively. 
     The second lens element  420  has negative refractive power and it is made of plastic material. The second lens element  420  has a convex object-side surface  422  and a concave image-side surface  424 , both of the object-side surface  422  and the image-side surface  424  are aspheric, and the object-side surface  422  has two inflection points and the image-side surface  424  has an inflection point. 
     The third lens element  430  has positive refractive power and it is made of plastic material. The third lens element  430  has a concave object-side surface  432  and a convex image-side surface  434 , both of the object-side surface  432  and the image-side surface  434  are aspheric, and the object-side surface  432  has two inflection points and the image-side surface  434  has an inflection point. 
     The fourth lens element  440  has negative refractive power and it is made of plastic material. The fourth lens element  440  has a convex object-side surface  442  and a concave image-side surface  444 , both of the object-side surface  442  and the image-side surface  444  are aspheric, and the object-side surface  442  and the image-side surface  444  have an inflection point respectively. 
     The IR-bandstop filter  470  is made of glass material without affecting the focal length of the optical image capturing system and it is disposed between the fourth lens element  440  and the image plane  480 . 
     In the optical image capturing system of the fourth embodiment, focal lengths of the second lens element  420  through the fourth lens element  440  are f2, f3 and f4 respectively. The following relations are satisfied: |f2|+|f3|=16.7265 mm, |f1|+|f4|=9.9617 mm and |f2|+|f3|&gt;|f1|+|f4|. 
     In the optical image capturing system of the fourth embodiment, a sum of focal lengths of all lens elements with positive refractive power is ΣPP. The following relation is satisfied: ΣPP=f1+f3. Hereby, it is favorable for allocating the positive refractive power of the first lens element  410  to other positive lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the fourth embodiment, a sum of focal lengths of all lens elements with negative refractive power is ΣNP. The following relation is satisfied: ΣNP=f2+f4. Hereby, it is favorable for allocating the negative refractive power of the fourth lens element  440  to other negative lens elements. 
     Please refer to the following Table 7 and Table 8. 
     The detailed data of the optical image capturing system of the fourth embodiment is as shown in Table 7. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Data of the optical image capturing system 
               
               
                 f = 2.3442 mm, f/HEP = 2.070, HAF = 44.0000 deg, tan(HAF) = 0.96569 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Focal 
               
               
                 Surface # 
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 length 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 At infinity 
                   
                   
                   
                   
               
               
                 1 
                 Ape. stop 
                 Plano 
                 −0.050 
                   
                   
                   
                   
               
               
                 2 
                 Lens 1 
                 1.54478222 
                 0.487 
                 Plastic 
                 1.544 
                 56.09 
                 3.082 
               
               
                 3 
                   
                 16.7930775 
                 0.001 
                   
                   
                   
                   
               
               
                 4 
                 Shading 
                 Plano 
                 0.240 
                   
                   
                   
                   
               
               
                   
                 sheet 
                   
                   
                   
                   
                   
                   
               
               
                 5 
                 Lens 2 
                 12.0808192 
                 0.200 
                 Plastic 
                 1.642 
                 22.46 
                 −13.701 
               
               
                 6 
                   
                 5.082491689 
                 0.186 
                   
                   
                   
                   
               
               
                 7 
                 Lens 3 
                 −0.89540048 
                 0.432 
                 Plastic 
                 1.544 
                 52.90 
                 3.025 
               
               
                 8 
                   
                 −0.679833885 
                 0.025 
                   
                   
                   
                   
               
               
                 9 
                 Lens 4 
                 1.365501136 
                 0.497 
                 Plastic 
                 1.544 
                 56.09 
                 −6.880 
               
               
                 10 
                   
                 0.872742597 
                 0.266 
                   
                   
                   
                   
               
               
                 11 
                 IR-band 
                 Plano 
                 0.200 
                 BK7_SCHOTT 
                 1.517 
                 64.13 
                   
               
               
                   
                 stop filter 
                   
                   
                   
                   
                   
                   
               
               
                 12 
                   
                 Plano 
                 0.800 
                   
                   
                   
                   
               
               
                 13 
                 Image 
                 Plano 
                   
                   
                   
                   
                   
               
               
                   
                 plane 
               
               
                   
               
               
                 Reference wavelength (d-line) = 555 nm; The clear aperture of the fourth surface is 0.723 mm. 
               
            
           
         
       
     
     As for the parameters of the aspheric surfaces of the fourth embodiment, reference is made to Table 8. 
     
       
         
           
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface # 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −1.731429E+01 
                 −2.676670E−06 
                 −3.678229E−02 
                 −8.998956E+01 
                 −1.130900E−01 
                 −3.865357E+00 
               
               
                 A4 = 
                 4.737695E−01 
                 −4.074658E−01 
                 −1.019036E+00 
                 −3.726537E−01 
                 8.180921E−01 
                 −8.631224E−01 
               
               
                 A6 = 
                 −1.039006E+00 
                 5.144696E−01 
                 4.333086E+00 
                 2.020889E+00 
                 −2.330334E+00 
                 1.636988E+00 
               
               
                 A8 = 
                 −1.297225E+00 
                 −4.728974E+00 
                 −3.499760E+01 
                 −9.038652E+00 
                 2.182057E+01 
                 5.831143E−01 
               
               
                 A10 = 
                 1.306553E+01 
                 1.163796E+01 
                 1.057741E+02 
                 1.733202E+01 
                 −8.031341E+01 
                 −1.396189E+01 
               
               
                 A12 = 
                 −3.028718E+01 
                 −1.319640E+01 
                 −1.367989E+02 
                 −1.528333E+01 
                 1.426075E+02 
                 4.769059E+01 
               
               
                 A14 = 
                 1.800632E+01 
                 3.838551E+00 
                 6.617539E+01 
                 5.116787E+00 
                 −1.245757E+02 
                 −8.343037E+01 
               
               
                 A16 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 4.329677E+01 
                 8.312053E+01 
               
               
                 A18 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −4.494637E+01 
               
               
                 A20 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.023251E+01 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface # 
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 7 
                 8 
               
               
                   
               
               
                   
                 k = 
                 −1.274781E−01 
                 −4.365098E+00 
               
               
                   
                 A4 = 
                 −5.256318E−01 
                 −3.166917E−01 
               
               
                   
                 A6 = 
                 5.968521E−01 
                 6.016502E−01 
               
               
                   
                 A8 = 
                 −1.021886E+00 
                 −1.060367E+00 
               
               
                   
                 A10 = 
                 1.431483E+00 
                 1.278886E+00 
               
               
                   
                 A12 = 
                 −1.581217E+00 
                 −1.021661E+00 
               
               
                   
                 A14 = 
                 1.282935E+00 
                 5.266889E−01 
               
               
                   
                 A16 = 
                 −6.792613E−01 
                 −1.670045E−01 
               
               
                   
                 A18 = 
                 2.030504E−01 
                 2.944449E−02 
               
               
                   
                 A20 = 
                 −2.576893E−02 
                 −2.201968E−03 
               
               
                   
               
            
           
         
       
     
     The presentation of the aspheric surface formula in the fourth embodiment is similar to that in the first embodiment. Besides the definitions of parameters in following tables are equal to those in the first embodiment so the repetitious details will not be given here. 
     The following contents may be deduced from Table 7 and Table 8. 
     
       
         
           
               
             
               
                   
               
               
                 Fourth embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 InRS41 
                 InRS42 
                 HVT41 
                 HVT42 
                 | ODT | % 
                 | TDT | % 
               
               
                 0.02514 
                 −0.01296 
                 0.86343 
                 1.07635 
                   1.88867 
                 1.26818 
               
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f1/f2 | 
                 | f2/f3 | 
               
               
                 0.76065 
                  0.17110 
                 0.77485 
                 0.34074 
                   0.22493 
                 4.52874 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/ 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                   
                   
                 | ΣNPR | 
                   
                   
                   
               
               
                 1.53550 
                  0.51183 
                 3.00001 
                 6.10722 
                 −20.58094 
                 0.50462 
               
               
                 f4/ΣNP 
                 IN12/f 
                 IN23/f 
                 IN34/f 
                 TP3/f 
                 TP4/f 
               
               
                 0.33428 
                  0.10288 
                 0.07955 
                 0.01071 
                   0.18449 
                 0.21193 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                 2.06950 
                  3.33500 
                 1.45000 
                 0.98501 
                  0.62054 
                 0.78121 
               
            
           
           
               
               
               
               
               
            
               
                 (TP1 +  
                 (TP4 +  
                 TP1/TP2 
                 TP3/TP4 
                 IN23/(TP2 +  
               
               
                 IN12)/ 
                 IN34)/ 
                   
                   
                 IN23 + TP3) 
               
               
                 TP2 
                 TP3 
                   
                   
                   
               
               
                 3.64301 
                  1.20675 
                 2.43709 
                 0.87055 
                  0.22771 
               
            
           
           
               
               
               
               
               
               
            
               
                 | INRS41 |/ 
                 | INRS42 |/ 
                 HVT42/ 
                 HVT42/ 
                   
                   
               
               
                 TP4 
                 TP4 
                 HOI 
                 HOS 
                   
                   
               
               
                 0.05060 
                  0.02609 
                 0.46798 
                 0.32274 
                   
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 0.013 mm 
                 0.012 mm 
                 −0.008 mm 
                 −0.013 mm 
                 −0.00014  
                 −0.002 mm 
               
               
                   
                   
                   
                   
                 mm 
               
               
                   
               
            
           
         
       
     
     The following contents may be deduced from Table 7 and Table 8. 
     
       
         
           
               
             
               
                   
               
               
                 Related inflection point values of fourth embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 0.49704 
                 HIF111/HOI 
                 0.21610 
                 SGI111 
                 0.07515 
                 |SGI111|/(|SGI111| + TP1) 
                 0.13358 
               
               
                 HIF121 
                 0.11212 
                 HIF121/HOI 
                 0.04875 
                 SGI121 
                 0.00031 
                 |SGI121|/(|SGI121| + TP1) 
                 0.00064 
               
               
                 HIF211 
                 0.08529 
                 HIF211/HOI 
                 0.03708 
                 SGI211 
                 0.00025 
                 |SGI211|/(|SGI211| + TP2) 
                 0.00124 
               
               
                 HIF212 
                 0.69466 
                 HIF212/HOI 
                 0.30202 
                 SGI212 
                 −0.18451 
                 |SGI212|/(|SGI212| + TP2) 
                 0.47985 
               
               
                 HIF221 
                 0.25246 
                 HIF221/HOI 
                 0.10977 
                 SGI221 
                 0.00484 
                 |SGI221|/(|SGI221| + TP2) 
                 0.02361 
               
               
                 HIF311 
                 0.37483 
                 HIF311/HOI 
                 0.16297 
                 SGI311 
                 −0.06701 
                 |SGI311|/(|SGI311| + TP3) 
                 0.13415 
               
               
                 HIF312 
                 0.66788 
                 HIF312/HOI 
                 0.29038 
                 SGI312 
                 −0.13602 
                 |SGI312|/(|SGI312| + TP3) 
                 0.23925 
               
               
                 HIF321 
                 0.60353 
                 HIF321/HOI 
                 0.26241 
                 SGI321 
                 −0.24416 
                 |SGI321|/(|SGI321| + TP3) 
                 0.36084 
               
               
                 HIF411 
                 0.44629 
                 HIF411/HOI 
                 0.19404 
                 SGI411 
                 0.05733 
                 |SGI411|/(|SGI411| + TP4) 
                 0.10346 
               
               
                 HIF421 
                 0.48273 
                 HIF421/HOI 
                 0.20988 
                 SGI421 
                 0.09815 
                 |SGI421|/(|SGI421| + TP4) 
                 0.16497 
               
               
                   
               
            
           
         
       
     
     The numerical related to the length of outline curve is shown according to table 7 and table 8. 
     
       
         
           
               
             
               
                   
               
               
                 Fourth embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 ARE/TP 
               
               
                 ARE 
                 ½(HEP) 
                 ARE value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.586 
                 0.596 
                 0.010 
                 101.69% 
                 0.487 
                 122.27% 
               
               
                 12 
                 0.586 
                 0.591 
                 0.005 
                 100.91% 
                 0.487 
                 121.33% 
               
               
                 21 
                 0.586 
                 0.606 
                 0.020 
                 103.47% 
                 0.200 
                 303.18% 
               
               
                 22 
                 0.586 
                 0.586 
                 0.000 
                 100.07% 
                 0.200 
                 293.23% 
               
               
                 31 
                 0.586 
                 0.600 
                 0.014 
                 102.41% 
                 0.432 
                 138.77% 
               
               
                 32 
                 0.586 
                 0.641 
                 0.055 
                 109.36% 
                 0.432 
                 148.20% 
               
               
                 41 
                 0.586 
                 0.593 
                 0.007 
                 101.19% 
                 0.497 
                 119.37% 
               
               
                 42 
                 0.586 
                 0.602 
                 0.016 
                 102.78% 
                 0.497 
                 121.24% 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 ARS value 
                 ARS − EHD 
                 (ARS/EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.622 
                 0.631 
                 0.009 
                 101.52% 
                 0.487 
                 129.54% 
               
               
                 12 
                 0.710 
                 0.743 
                 0.033 
                 104.63% 
                 0.487 
                 152.40% 
               
               
                 21 
                 0.728 
                 0.788 
                 0.060 
                 108.19% 
                 0.200 
                 393.89% 
               
               
                 22 
                 0.848 
                 0.861 
                 0.013 
                 101.50% 
                 0.200 
                 430.35% 
               
               
                 31 
                 0.870 
                 0.892 
                 0.022 
                 102.47% 
                 0.432 
                 206.21% 
               
               
                 32 
                 0.948 
                 1.043 
                 0.095 
                 110.00% 
                 0.432 
                 241.19% 
               
               
                 41 
                 1.403 
                 1.424 
                 0.021 
                 101.52% 
                 0.497 
                 286.61% 
               
               
                 42 
                 1.730 
                 1.868 
                 0.138 
                 107.97% 
                 0.497 
                 376.05% 
               
               
                   
               
            
           
         
       
     
     The Fifth Embodiment (Embodiment 5) 
     Please refer to  FIG. 5A ,  FIG. 5B  and  FIG. 5C ,  FIG. 5A  is a schematic view of the optical image capturing system according to the fifths embodiment of the present application,  FIG. 5B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion curve of the optical image capturing system in the order from left to right according to the fifth embodiment of the present application, and  FIG. 5C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the fifth embodiment of the present application. As shown in  FIG. 5A , in order from an object side to an image side, the optical image capturing system includes an aperture stop  500 , a first lens element  510 , a second lens element  520 , a third lens element  530 , a fourth lens element  540 , an IR-bandstop filter  570 , an image plane  580 , and an image sensing device  590 . 
     The first lens element  510  has positive refractive power and it is made of plastic material. The first lens element  510  has a convex object-side surface  512  and a convex image-side surface  514 , both of the object-side surface  512  and the image-side surface  514  are aspheric, and the object-side surface  512  has an inflection point. 
     The second lens element  520  has negative refractive power and it is made of plastic material. The second lens element  520  has a convex object-side surface  522  and a concave image-side surface  524 , both of the object-side surface  522  and the image-side surface  524  are aspheric, and the image-side surface  524  has an inflection point. 
     The third lens element  530  has positive refractive power and it is made of plastic material. The third lens element  530  has a concave object-side surface  532  and a convex image-side surface  534 , and both of the object-side surface  532  and the image-side surface  534  are aspheric, and the object-side surface  532  and the image-side surface  534  have two inflection points respectively. 
     The fourth lens element  540  has negative refractive power and it is made of plastic material. The fourth lens element  540  has a convex object-side surface  542  and a concave image-side surface  544 , both of the object-side surface  542  and the image-side surface  544  are aspheric, and the object-side surface  542  and the image-side surface  544  have an inflection point respectively. 
     The IR-bandstop filter  570  is made of glass material without affecting the focal length of the optical image capturing system and it is disposed between the fourth lens element  540  and the image plane  580 . 
     In the optical image capturing system of the fifth embodiment, focal lengths of the second lens element  520  through the fourth lens element  540  are f2, f3 and f4 respectively. The following relations are satisfied: |f2|+|f3|=14.0488 mm, |f1|+|f4|=9.9629 mm and |f2|+|f3|&gt;|f1|+|f4|. 
     In the optical image capturing system of the fifth embodiment, a sum of focal lengths of all lens elements with positive refractive power is ΣPP. The following relation is satisfied: ΣPP=f1+f3. Hereby, it is favorable for allocating the positive refractive power of the first lens element  510  to other positive lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the fifth embodiment, a sum of focal lengths of all lens elements with negative refractive power is ΣNP. The following relation is satisfied: ΣNP=f2+f4. Hereby, it is favorable for allocating the negative refractive power of the fourth lens element  540  to other negative lens elements. 
     Please refer to the following Table 9 and Table 10. 
     The detailed data of the optical image capturing system of the fifth embodiment is as shown in Table 9. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 Data of the optical image capturing system 
               
               
                 f = 2.3442 mm, f/HEP = 2.050, HAF = 44.000 deg, tan(HAF) = 0.96569 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Focal 
               
               
                 Surface # 
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 length 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 At infinity 
                   
                   
                   
                   
               
               
                 1 
                 Ape. stop 
                 Plano 
                 −0.050 
                   
                   
                   
                   
               
               
                 2 
                 Lens 1 
                 1.791162158 
                 0.525 
                 Plastic 
                 1.544 
                 56.09 
                 3.099 
               
               
                 3 
                   
                 −27.29469639 
                 0.001 
                   
                   
                   
                   
               
               
                 4 
                 Shading 
                 Plano 
                 0.240 
                   
                   
                   
                   
               
               
                   
                 sheet 
                   
                   
                   
                   
                   
                   
               
               
                 5 
                 Lens 2 
                 192.2396163 
                 0.216 
                 Plastic 
                 1.642 
                 22.46 
                 −11.145 
               
               
                 6 
                   
                 6.953278033 
                 0.193 
                   
                   
                   
                   
               
               
                 7 
                 Lens 3 
                 −0.913380109 
                 0.451 
                 Plastic 
                 1.546 
                 54.48 
                 2.904 
               
               
                 8 
                   
                 −0.681500067 
                 0.025 
                   
                   
                   
                   
               
               
                 9 
                 Lens 4 
                 1.369493694 
                 0.522 
                 Plastic 
                 1.544 
                 56.09 
                 −6.864 
               
               
                 10 
                   
                 0.867955184 
                 0.278 
                   
                   
                   
                   
               
               
                 11 
                 IR-bandstop 
                 Plano 
                 0.200 
                 BK_7 
                 1.517 
                 64.13 
                   
               
               
                   
                 filter 
                   
                   
                   
                   
                   
                   
               
               
                 12 
                   
                 Plano 
                 0.800 
                   
                   
                   
                   
               
               
                 13 
                 Image plane 
                 Plano 
               
               
                   
               
               
                 Reference wavelength (d-line) = 555 nm; The clear aperture of the fourth surface is 0.728 mm. 
               
            
           
         
       
     
     As for the parameters of the aspheric surfaces of the fifth embodiment, reference is made to Table 10. 
     
       
         
           
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface # 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
               
                 k = 
                 −2.141502E+01 
                 −2.687513E−06 
                 −3.678229E−02 
                 −9.000000E+01 
                 −1.332714E−01 
                 −3.658620E+00 
               
               
                 A4 = 
                 4.700290E−01 
                 −3.732708E−01 
                 −9.826101E−01 
                 −3.445585E−01 
                 7.235676E−01 
                 −8.232659E−01 
               
               
                 A6 = 
                 −2.683426E+00 
                 −1.998799E−01 
                 3.226924E+00 
                 1.102678E+00 
                 −1.438860E+00 
                 1.198598E+00 
               
               
                 A8 = 
                 1.389267E+01 
                 4.282276E−01 
                 −2.577515E+01 
                 −3.424785E+00 
                 1.360767E+01 
                 2.281161E+00 
               
               
                 A10 = 
                 −5.256507E+01 
                 −4.690586E+00 
                 7.478240E+01 
                 3.549108E+00 
                 −4.606272E+01 
                 −1.926093E+01 
               
               
                 A12 = 
                 1.075951E+02 
                 1.398585E+01 
                 −8.865238E+01 
                 −2.747822E−01 
                 7.360258E+01 
                 5.804735E+01 
               
               
                 A14 = 
                 −9.322212E+01 
                 −1.408746E+01 
                 3.660682E+01 
                 −9.260552E−01 
                 −5.702299E+01 
                 −9.340076E+01 
               
               
                 A16 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 1.753693E+01 
                 8.549761E+01 
               
               
                 A18 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 −4.209504E+01 
               
               
                 A20 = 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 8.614764E+00 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface # 
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 9 
                 10 
               
               
                   
               
               
                   
                 k = 
                 −1.314189E−01 
                 −4.161514E+00 
               
               
                   
                 A4 = 
                 −4.761457E−01 
                 −2.784669E−01 
               
               
                   
                 A6 = 
                 3.201405E−01 
                 3.950550E−01 
               
               
                   
                 A8 = 
                 −2.647136E−01 
                 −5.603426E−01 
               
               
                   
                 A10 = 
                 1.281055E−01 
                 5.891637E−01 
               
               
                   
                 A12 = 
                 −3.566120E−03 
                 −4.285164E−01 
               
               
                   
                 A14 = 
                 −2.900744E−02 
                 2.060858E−01 
               
               
                   
                 A16 = 
                 5.858937E−03 
                 −6.204344E−02 
               
               
                   
                 A18 = 
                 5.235025E−03 
                 1.053173E−02 
               
               
                   
                 A20 = 
                 −1.882416E−03 
                 −7.669237E−04 
               
               
                   
               
            
           
         
       
     
     The presentation of the aspheric surface formula in the fifth embodiment is similar to that in the first embodiment. Besides the definitions of parameters in following tables are equal to those in the first embodiment so the repetitious details will not be given here. 
     The following contents may be deduced from Table 9 and Table 10. 
     
       
         
           
               
             
               
                   
               
               
                 Fifth embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 InRS41 
                 InRS42 
                 HVT41 
                 HVT42 
                 | ODT | % 
                 | TDT | % 
               
               
                 −0.00511 
                 −0.08752 
                 0.87050 
                 1.11365 
                   1.60000 
                 0.98180 
               
               
                 | f/f1 | 
                 | f/f2 | 
                 | f/f3 | 
                 | f/f4 | 
                 | f1/f2 | 
                 | f2/f3 | 
               
               
                  0.75645 
                  0.21035 
                 0.80715 
                 0.34153 
                  0.27807 
                 3.83725 
               
               
                 ΣPPR 
                 ΣNPR 
                 ΣPPR/ 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                   
                   
                 | ΣNPR |  
                   
                   
                   
               
               
                  1.56360 
                  0.55188 
                 2.83325 
                 6.00327 
                 −18.00837 
                 0.51622 
               
               
                 f4/ΣNP 
                 IN12/f 
                 IN23/f 
                 IN34/f 
                 TP3/f 
                 TP4/f 
               
               
                  0.38115 
                  0.10280 
                 0.08212 
                 0.01066 
                   0.19226 
                 0.22263 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOI 
                 InTL/HOS 
                 ΣTP/InTL 
               
               
                  2.17242 
                  3.45000 
                 1.50000 
                 0.98551 
                   0.62969 
                 0.78895 
               
            
           
           
               
               
               
               
               
            
               
                 (TP1 +  
                 (TP4 +  
                 TP1/TP2 
                 TP3/TP4 
                 IN23/(TP2 +  
               
               
                 IN12)/ 
                 IN34)/ 
                   
                   
                 IN23 + TP3) 
               
               
                 TP2 
                 TP3 
                   
                   
                   
               
               
                  3.54633 
                  1.21348 
                 2.43104 
                 0.86355 
                  0.22403 
               
            
           
           
               
               
               
               
               
               
            
               
                 | INRS41 |/ 
                 | INRS42 |/ 
                 HVT42/ 
                 HVT42/ 
                   
                   
               
               
                 TP4 
                 TP4 
                 HOI 
                 HOS 
                   
                   
               
               
                  0.00980 
                  0.16769 
                 0.48420 
                 0.32280 
                   
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 0.009 mm 
                 0.011 mm 
                 −0.010 mm 
                 −0.015 mm 
                 0.007 mm 
                 0.005 mm 
               
               
                   
               
            
           
         
       
     
     The following contents may be deduced from Table 9 and Table 10. 
     
       
         
           
               
             
               
                   
               
               
                 Related inflection point values of fifth embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 0.48673 
                 HIF111/HOI 
                 0.21162 
                 SGI111 
                 0.06155 
                 |SGI111|/(|SGI111| + TP1) 
                 0.10488 
               
               
                 HIF211 
                 0.02105 
                 HIF211/HOI 
                 0.009151 
                 SGI211 
                 0.000001 
                 |SGI211|/(|SGI211| + TP2) 
                 0.000005 
               
               
                 HIF221 
                 0.20504 
                 HIF221/HOI 
                 0.08915 
                 SGI221 
                 0.00243 
                 |SGI221|/(|SGI221| + TP2) 
                 0.011119 
               
               
                 HIF311 
                 0.38441 
                 HIF311/HOI 
                 0.16713 
                 SGI311 
                 −0.06918 
                 |SGI311|/(|SGI311| + TP3) 
                 0.13307 
               
               
                 HIF312 
                 0.91437 
                 HIF312/HOI 
                 0.39755 
                 SGI312 
                 −0.13308 
                 |SGI312|/(|SGI312| + TP3) 
                 0.22796 
               
               
                 HIF321 
                 0.61714 
                 HIF321/HOI 
                 0.26832 
                 SGI321 
                 −0.26044 
                 |SGI321|/(|SGI321| + TP3) 
                 0.36623 
               
               
                 HIF322 
                 0.97913 
                 HIF322/HOI 
                 0.42571 
                 SGI322 
                 −0.35946 
                 |SGI322|/(|SGI322| + TP3) 
                 0.44370 
               
               
                 HIF411 
                 0.44110 
                 HIF411/HOI 
                 0.19178 
                 SGI411 
                 0.05670 
                 |SGI411|/(|SGI411| + TP4) 
                 0.09800 
               
               
                 HIF421 
                 0.48507 
                 HIF421/HOI 
                 0.21090 
                 SGI421 
                 0.10087 
                 |SGI421|/(|SGI421| + TP4) 
                 0.16196 
               
               
                   
               
            
           
         
       
     
     The numerical related to the length of outline curve is shown according to table 9 and table 10. 
     
       
         
           
               
             
               
                   
               
               
                 Fifth embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 ARE/TP 
               
               
                 ARE 
                 ½(HEP) 
                 ARE value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.572 
                 0.578 
                 0.006 
                 101.05% 
                 0.525 
                 109.99% 
               
               
                 12 
                 0.572 
                 0.577 
                 0.005 
                 100.85% 
                 0.525 
                 109.77% 
               
               
                 21 
                 0.572 
                 0.590 
                 0.019 
                 103.27% 
                 0.216 
                 273.27% 
               
               
                 22 
                 0.572 
                 0.571 
                  −0.00042 
                  99.93% 
                 0.216 
                 264.42% 
               
               
                 31 
                 0.572 
                 0.585 
                 0.013 
                 102.30% 
                 0.451 
                 129.78% 
               
               
                 32 
                 0.572 
                 0.625 
                 0.053 
                 109.35% 
                 0.451 
                 138.73% 
               
               
                 41 
                 0.572 
                 0.578 
                 0.006 
                 101.07% 
                 0.522 
                 110.72% 
               
               
                 42 
                 0.572 
                 0.587 
                 0.016 
                 102.74% 
                 0.522 
                 112.56% 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 ARS value 
                 ARS − EHD 
                 (ARS/EHD)% 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.598 
                 0.604 
                 0.006 
                 101.05% 
                 0.525 
                 115.01% 
               
               
                 12 
                 0.710 
                 0.741 
                 0.031 
                 104.37% 
                 0.525 
                 141.07% 
               
               
                 21 
                 0.729 
                 0.798 
                 0.070 
                 109.58% 
                 0.216 
                 369.50% 
               
               
                 22 
                 0.882 
                 0.901 
                 0.019 
                 102.16% 
                 0.216 
                 416.89% 
               
               
                 31 
                 0.942 
                 0.959 
                 0.016 
                 101.73% 
                 0.451 
                 212.72% 
               
               
                 32 
                 0.986 
                 1.095 
                 0.109 
                 111.02% 
                 0.451 
                 243.00% 
               
               
                 41 
                 1.387 
                 1.413 
                 0.026 
                 101.86% 
                 0.522 
                 270.73% 
               
               
                 42 
                 1.749 
                 1.883 
                 0.134 
                 107.66% 
                 0.522 
                 360.73% 
               
               
                   
               
            
           
         
       
     
     The Sixth Embodiment (Embodiment 6) 
     Please refer to  FIG. 6A ,  FIG. 6B  and  FIG. 6C ,  FIG. 6A  is a schematic view of the optical image capturing system according to the sixth Embodiment of the present application,  FIG. 6B  is longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion curve of the optical image capturing system in the order from left to right according to the sixth Embodiment of the present application, and  FIG. 6C  is a lateral aberration diagram of tangential fan, sagittal fan, the longest operation wavelength and the shortest operation wavelength passing through an edge of the entrance pupil and incident on the image plane by 0.7 HOI according to the sixth embodiment of the present application. As shown in  FIG. 6A , in order from an object side to an image side, the optical image capturing system includes a first lens element  610 , an aperture stop  600 , a second lens element  620 , a third lens element  630 , a fourth lens element  640 , an IR-bandstop filter  670 , an image plane  680 , and an image sensing device  690 . 
     The first lens element  610  has positive refractive power and it is made of plastic material. The first lens element  610  has a convex object-side surface  612  and a concave image-side surface  614 , both of the object-side surface  612  and the image-side surface  614  are aspheric, and the object-side surface  612  and the image-side surface  614  have an inflection point respectively. 
     The second lens element  620  has positive refractive power and it is made of plastic material. The second lens element  620  has a concave object-side surface  622  and a convex image-side surface  624 , and both of the object-side surface  622  and the image-side surface  624  are aspheric. 
     The third lens element  630  has negative refractive power and it is made of plastic material. The third lens element  630  has a concave object-side surface  632  and a convex image-side surface  634 , both of the object-side surface  632  and the image-side surface  634  are aspheric, and the image-side surface  634  has an inflection point. 
     The fourth lens element  640  has positive refractive power and it is made of plastic material. The fourth lens element  640  has a convex object-side surface  642  and a concave image-side surface  644 , both of the object-side surface  642  and the image-side surface  644  are aspheric. The object-side surface  642  has two inflection points and the image-side surface  644  has an inflection point. 
     The IR-bandstop filter  670  is made of glass material without affecting the focal length of the optical image capturing system and it is disposed between the fourth lens element  640  and the image plane  680 . 
     In the optical image capturing system of the sixth Embodiment, focal lengths of the second lens element  620  through the fourth lens element  640  are f2, f3 and f4 respectively. The following relations are satisfied: |f2|+|f3|=7.6703 mm and |f1|+|f4|=7.7843 mm. 
     In the optical image capturing system of the sixth Embodiment, a sum of focal lengths of all lens elements with positive refractive power is ΣPP. The following relations are satisfied: ΣPP=f1+f3. Hereby, it is favorable for allocating the positive refractive power of the first lens element  610  to other positive lens elements and the significant aberrations generated in the process of moving the incident light can be suppressed. 
     In the optical image capturing system of the sixth Embodiment, a sum of focal lengths of all lens elements with negative refractive power is ΣNP. The following relations are satisfied: ΣNP-f2+f4. Hereby, it is favorable for allocating the negative refractive power of the fourth lens element  640  to other negative lens elements. 
     Please refer to the following Table 11 and Table 12. 
     The detailed data of the optical image capturing system of the sixth Embodiment is as shown in Table 11. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 Data of the optical image capturing system 
               
               
                 f = 3.4320 mm; f/HEP = 2.28; HAF = 39.5498 deg; tan(HAF) = 0.8258 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Focal 
               
               
                 Surface # 
                 Curvature Radius 
                 Thickness 
                 Material 
                 Index 
                 Abbe # 
                 length 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 0 
                 Object 
                 Plano 
                 600 
                 mm 
                   
                   
                   
                   
               
               
                 1 
                 Shading 
                 Plano 
                 0.000 
                   
                   
                   
                   
                   
               
               
                   
                 sheet 
                   
                   
                   
                   
                   
                   
                   
               
               
                 2 
                 Ape. Stop/ 
                 1.509818182 
                 0.618 
                   
                 Plastic 
                 1.535 
                 56.07 
                 3.318 
               
               
                   
                 Lens 1 
                   
                   
                   
                   
                   
                   
                   
               
               
                 3 
                   
                 8.53969299 
                 0.329 
                   
                   
                   
                   
                   
               
               
                 4 
                 Lens 2 
                 −6.014903199 
                 0.354 
                   
                 Plastic 
                 1.535 
                 56.07 
                 5.358 
               
               
                 5 
                   
                 −1.984502862 
                 0.116 
                   
                   
                   
                   
                   
               
               
                 6 
                 Lens 3 
                 −1.059010347 
                 0.400 
                   
                 Plastic 
                 1.642 
                 22.46 
                 −2.313 
               
               
                 7 
                   
                 −4.151190913 
                 0.209 
                   
                   
                   
                   
                   
               
               
                 8 
                 Lens 4 
                 1.152314669 
                 0.971 
                   
                 Plastic 
                 1.535 
                 56.07 
                 4.467 
               
               
                 9 
                   
                 1.5669645 
                 0.174 
                   
                   
                   
                   
                   
               
               
                 10 
                 IR-bandstop 
                 Plano 
                 0.610 
                   
                 BK_7 
                 1.517 
                 64.13 
                 1E+18 
               
               
                   
                 filter 
                   
                   
                   
                   
                   
                   
                   
               
               
                 11 
                   
                 Plano 
                 0.670 
                   
                   
                   
                   
                   
               
               
                 12 
                 Image plane 
                 Plano 
                 0.000 
               
               
                   
               
               
                 Reference wavelength = 555 nm, shield position: clear aperture (CA) of the first plano = 0.72 mm, clear aperture (CA) of the fourth plano = 0.72 mm. 
               
            
           
         
       
     
     As for the parameters of the aspheric surfaces of the sixth Embodiment, reference is made to Table 12. 
     
       
         
           
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 Aspheric Coefficients 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Surface # 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 k = 
                 1.916080E+00 
                 −9.900000E+01 
                 3.126612E+01 
                 −7.965379E+00 
                 −8.303619E−01 
                 −6.965851E+00 
               
               
                 A4 = 
                 −1.049827E−01 
                 −7.009159E−02 
                 −1.451689E−01 
                 −4.538029E−01 
                 −5.412535E−01 
                 −1.203501E+00 
               
               
                 A6 = 
                 5.814123E−01 
                 1.328381E−01 
                 6.303788E−01 
                 1.530283E+00 
                 2.791713E+00 
                 3.666830E+00 
               
               
                 A8 = 
                 −6.718107E+00 
                 −9.116008E−01 
                 −1.132911E+01 
                 −1.236917E+01 
                 −1.513262E+01 
                 −8.896333E+00 
               
               
                 A10 = 
                 3.531928E+01 
                 7.640451E−01 
                 6.805609E+01 
                 4.610285E+01 
                 5.138291E+01 
                 1.655336E+01 
               
               
                 A12 = 
                 −1.101217E+02 
                 3.051780E+00 
                 −2.379915E+02 
                 −9.647195E+01 
                 −9.520918E+01 
                 −2.064112E+01 
               
               
                 A14 = 
                 2.064916E+02 
                 −9.347255E+00 
                 4.983122E+02 
                 1.170989E+02 
                 9.234444E+01 
                 1.655931E+01 
               
               
                 A16 = 
                 −2.297285E+02 
                 8.045808E+00 
                 −6.309790E+02 
                 −7.956394E+01 
                 −3.388934E+01 
                 −8.186992E+00 
               
               
                 A18 = 
                 1.385918E+02 
                 −1.221506E+00 
                 4.484590E+02 
                 2.631311E+01 
                 −1.040105E+01 
                 2.273253E+00 
               
               
                 A20 = 
                 −3.506966E+01 
                 1.406385E−01 
                 −1.380228E+02 
                 −3.193777E+00 
                 8.371347E+00 
                 −2.718499E−01 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Surface # 
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 8 
                 9 
               
               
                   
               
               
                   
                 k = 
                 −1.187975E+01 
                 −7.017602E−01 
               
               
                   
                 A4 = 
                 −4.135674E−01 
                 −2.642810E−01 
               
               
                   
                 A6 = 
                 2.543691E−01 
                 1.378942E−01 
               
               
                   
                 A8 = 
                 −2.660257E−03 
                 −6.371856E−02 
               
               
                   
                 A10 = 
                 −1.503202E−01 
                 2.245800E−02 
               
               
                   
                 A12 = 
                 1.195738E−01 
                 −6.023087E−03 
               
               
                   
                 A14 = 
                 −4.203653E−02 
                 1.127358E−03 
               
               
                   
                 A16 = 
                 7.846661E−03 
                 −1.323108E−04 
               
               
                   
                 A18 = 
                 −7.498286E−04 
                 8.321783E−06 
               
               
                   
                 A20 = 
                 2.899932E−05 
                 −2.161104E−07 
               
               
                   
               
            
           
         
       
     
     In the sixth Embodiment, the presentation of the aspheric surface formula is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are equal to those in the first embodiment, so the repetitious details will not be given here. 
     The following contents may be deduced from Table 11 and Table 12. 
     
       
         
           
               
             
               
                   
               
               
                 Sixth Embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 InRS41 
                 InRS42 
                 HVT41 
                 HVT42 
                 | ODT | % 
                 | TDT | % 
               
               
                 −0.19362 
                 −0.25529 
                 0.61419 
                 1.21734 
                  2.01839 
                  1.61834 
               
               
                 | 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/ 
                 ΣPP 
                 ΣNP 
                 f1/ΣPP 
               
               
                   
                   
                 | ΣNPR | 
                   
                   
                   
               
               
                  2.51843 
                  1.40899 
                 1.78740 
                 1.00509 
                  9.82409 
                  3.30099 
               
               
                 f4/ΣNP 
                 IN12/f 
                 IN23/f 
                 IN34/f 
                 TP3/f 
                 TP4 /f 
               
               
                  0.45465 
                  0.09578 
                 0.03366 
                 0.06079 
                  0.11643 
                  0.28302 
               
               
                 InTL 
                 HOS 
                 HOS/HOI 
                 InS/HOS 
                 InTL/ 
                 ΣTP/InTL 
               
               
                   
                   
                   
                   
                 HOS 
                   
               
               
                  2.99601 
                  4.44999 
                 1.55812 
                 0.95673 
                  0.67326 
                  0.78208 
               
            
           
           
               
               
               
               
               
            
               
                 (TP1 +  
                 (TP4 +  
                 TP1/TP2 
                 TP3/TP4 
                 IN23/(TP2 +  
               
               
                 IN12)/ 
                 IN34)/ 
                   
                   
                 IN23 + TP3) 
               
               
                 TP2 
                 TP3 
                   
                   
                   
               
               
                  2.67357 
                  2.95298 
                 1.74532 
                 0.41138 
                  0.13291 
               
            
           
           
               
               
               
               
               
               
            
               
                 | INRS41 |/ 
                 | INRS42 |/ 
                 HVT42/ 
                 HVT42/ 
                   
                   
               
               
                 TP4 
                 TP4 
                 HOI 
                 HOS 
                   
                   
               
               
                  0.19933 
                  0.26283 
                 0.42624 
                 0.27356 
                   
                   
               
               
                 PLTA 
                 PSTA 
                 NLTA 
                 NSTA 
                 SLTA 
                 SSTA 
               
               
                 −0.00049  
                  0.00375  
                 0.01012  
                 0.00160  
                 −0.00428  
                 −0.00062  
               
               
                 mm 
                 mm 
                 mm 
                 mm 
                 mm 
                 mm 
               
               
                   
               
            
           
         
       
     
     The following contents may be deduced from Table 11 and Table 12. 
     
       
         
           
               
             
               
                   
               
               
                 Related inflection point values of sixth Embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 HIF111 
                 0.74316 
                 HIF111/HOI 
                 0.26021 
                 SGI111 
                 0.18567 
                 |SGI111|/ 
                 0.23101 
               
               
                   
                   
                   
                   
                   
                   
                 (|SGI111| + TP1) 
                   
               
               
                 HIF121 
                 0.32842 
                 HIF121/HOI 
                 0.11499 
                 SGI121 
                 0.00534 
                 |SGI121|/(|SGI121| + 
                 0.00857 
               
               
                   
                   
                   
                   
                   
                   
                 TP1) 
                   
               
               
                 HIF321 
                 0.70196 
                 HIF321/HOI 
                 0.24579 
                 SGI321 
                 −0.15758 
                 |SGI321|/(|SGI321| + 
                 0.28283 
               
               
                   
                   
                   
                   
                   
                   
                 TP3) 
                   
               
               
                 HIF411 
                 0.29817 
                 HIF411/HOI 
                 0.10440 
                 SGI411 
                 0.03024 
                 |SGI411|/ 
                 0.03019 
               
               
                   
                   
                   
                   
                   
                   
                 (|SGI411| + TP4) 
                   
               
               
                 HIF412 
                 1.21277 
                 HIF412/HOI 
                 0.42464 
                 SGI412 
                 −0.12205 
                 |SGI412|/ 
                 0.11163 
               
               
                   
                   
                   
                   
                   
                   
                 (|SGI412| + TP4) 
                   
               
               
                 HIF421 
                 0.55723 
                 HIF421/HOI 
                 0.19511 
                 SGI421 
                 0.07815 
                 |SGI421|/(|SGI421| + 
                 0.07446 
               
               
                   
                   
                   
                   
                   
                   
                 TP4) 
               
               
                   
               
            
           
         
       
     
     The numerical related to the length of outline curve is shown according to table 11 and table 12. 
     
       
         
           
               
             
               
                   
               
               
                 Sixth Embodiment (Primary reference wavelength: 555 nm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 ARE/TP 
               
               
                 ARE 
                 ½(HEP) 
                 ARE value 
                 ARE − ½(HEP) 
                 2(ARE/HEP) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.720 
                 0.747 
                 0.027 
                 103.78% 
                 0.618 
                 120.93% 
               
               
                 12 
                 0.752 
                 0.753 
                 0.001 
                 100.18% 
                 0.618 
                 121.81% 
               
               
                 21 
                 0.720 
                 0.752 
                 0.032 
                 104.46% 
                 0.354 
                 212.38% 
               
               
                 22 
                 0.758 
                 0.829 
                 0.072 
                 109.46% 
                 0.354 
                 234.19% 
               
               
                 31 
                 0.758 
                 0.838 
                 0.080 
                 110.57% 
                 0.400 
                 209.65% 
               
               
                 32 
                 0.758 
                 0.789 
                 0.031 
                 104.11% 
                 0.400 
                 197.41% 
               
               
                 41 
                 0.758 
                 0.761 
                 0.004 
                 100.48% 
                 0.971 
                  78.37% 
               
               
                 42 
                 0.758 
                 0.768 
                 0.010 
                 101.36% 
                 0.971 
                  79.06% 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 ARS/TP 
               
               
                 ARS 
                 EHD 
                 ARS value 
                 ARS − EHD 
                 (ARS/EHD) % 
                 TP 
                 (%) 
               
               
                   
               
               
                 11 
                 0.720 
                 0.747 
                 0.027 
                 103.78% 
                 0.618 
                 120.93% 
               
               
                 12 
                 0.752 
                 0.753 
                 0.001 
                 100.18% 
                 0.618 
                 121.81% 
               
               
                 21 
                 0.720 
                 0.752 
                 0.032 
                 104.46% 
                 0.354 
                 212.38% 
               
               
                 22 
                 0.810 
                 0.917 
                 0.107 
                 113.21% 
                 0.354 
                 258.97% 
               
               
                 31 
                 0.826 
                 0.924 
                 0.098 
                 111.92% 
                 0.400 
                 231.24% 
               
               
                 32 
                 1.040 
                 1.085 
                 0.045 
                 104.31% 
                 0.400 
                 271.50% 
               
               
                 41 
                 1.349 
                 1.406 
                 0.057 
                 104.24% 
                 0.971 
                 144.76% 
               
               
                 42 
                 2.078 
                 2.237 
                 0.160 
                 107.68% 
                 0.971 
                 230.32% 
               
               
                   
               
            
           
         
       
     
     The above-mentioned descriptions represent merely the exemplary embodiment of the present disclosure, without any intention to limit the scope of the present disclosure thereto. Various equivalent changes, alternations or modifications based on the claims of present disclosure are all consequently viewed as being embraced by the scope of the present disclosure.