Optical image capturing system

This application claims priority from Taiwan Patent Application No. 105113328, filed on Apr. 28, 2016, in the Taiwan Intellectual Property Office, the content of which is hereby incorporated by reference in its entirety for all purposes.

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 peripheral 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.

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

The height of an image formed by the optical image capturing system is denoted by HOI. The 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, where 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 In 12 (example). A central thickness of the first lens element of the optical image capturing system on the optical axis is denoted by TP 1 (example).

The Lens Element Parameter Related to the Material in the Lens Element

An Abbe number of the first lens element in the optical image capturing system is denoted by NA 1 (example). A refractive index of the first lens element is denoted by Nd 1 (example).

The Lens Element Parameter Related to 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. A maximum effective half diameter (EHD) of any surface of a single lens element refers to a perpendicular height between the optical axis and an intersection point where the incident ray with the maximum view angle passes through the outmost edge of the entrance pupil and intersects with the surface of the lens element. For example, the maximum effective half diameter of the object-side surface of the first lens element is denoted by EHD 11 . The maximum effective half diameter of the image-side surface of the first lens element is denoted by EHD 12 . The maximum effective half diameter of the object-side surface of the second lens element is denoted by EHD 21 . The maximum effective half diameter of the image-side surface of the second lens element is denoted by EHD 22 . The maximum effective half diameters of any surfaces of other lens elements in the optical image capturing system are denoted in the similar way.

The Lens Element Parameter Related to an Arc Length of the Lens Element Shape and an Outline of Surface

A length of the maximum effective half diameter outline curve at any surface of a single lens element refers to an arc length of a curve, wherein the curve starts from an axial point on the surface of the lens element, travels along the surface outline of the lens element, and ends at the point which defines the maximum effective half diameter; and this arc length is denoted as ARS. For example, the length of the maximum effective half diameter outline curve of the object-side surface of the first lens element is denoted as ARS 11 . The length of the maximum effective half diameter outline curve of the image-side surface of the first lens element is denoted as ARS 12 . The length of the maximum effective half diameter outline curve of the object-side surface of the second lens element is denoted as ARS 21 . The length of the maximum effective half diameter outline curve of the image-side surface of the second lens element is denoted as ARS 22 . The lengths of the maximum effective half diameter outline curve of any surface of other lens elements in the optical image capturing system are denoted in the similar way.

A length of ½ entrance pupil diameter (HEP) outline curve of any surface of a single lens element refers to an arc length of curve, wherein the curve starts from an axial point on the surface of the lens element, travels along the surface outline of the lens element, and ends at a coordinate point on the surface where the vertical height from the optical axis to the coordinate point is equivalent to ½ entrance pupil diameter; and the arc length is denoted as ARE. For example, the length of the ½ entrance pupil diameter (HEP) outline curve of the object-side surface of the first lens element is denoted as ARE 11 . The length of the ½ entrance pupil diameter (HEP) outline curve of the image-side surface of the first lens element is denoted as ARE 12 . The length of the ½ entrance pupil diameter (HEP) outline curve of the object-side surface of the second lens element is denoted as ARE 21 . The length of the ½ entrance pupil diameter (HEP) outline curve of the image-side surface of the second lens element is denoted as ARE 22 . The lengths of the ½ entrance pupil diameter (HEP) outline curve 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 distance paralleling 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 InRS 41 (example). A distance paralleling 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 InRS 42 (example).

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 the axial point of the lens element surface. Furthermore, a perpendicular distance between a critical point C 31 on the object-side surface of the third lens element and the optical axis is HVT 31 (example). A perpendicular distance between a critical point C 32 on the image-side surface of the third lens element and the optical axis is HVT 32 (example). A perpendicular distance between a critical point C 41 on the object-side surface of the fourth lens element and the optical axis is HVT 41 (example). A perpendicular distance between a critical point C 42 on the image-side surface of the fourth lens element and the optical axis is HVT 42 (example). The perpendicular distances between the critical point on the image-side surface or object-side surface of other lens elements are denoted in similar fashion.

The object-side surface of the fourth lens element has one inflection point IF 411 which is nearest to the optical axis, and the sinkage value of the inflection point IF 411 is denoted by SGI 411 . SGI 411 is a horizontal shift distance paralleling 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 IF 411 and the optical axis is HIF 411 (example). The image-side surface of the fourth lens element has one inflection point IF 421 which is nearest to the optical axis and the sinkage value of the inflection point IF 421 is denoted by SGI 421 (example). SGI 421 is a horizontal shift distance paralleling 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 IF 421 and the optical axis is HIF 421 (example).

The object-side surface of the fourth lens element has one inflection point IF 412 which is the second nearest to the optical axis and the sinkage value of the inflection point IF 412 is denoted by SGI 412 (example), SGI 1412 is a horizontal shift distance paralleling 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 IF 412 and the optical axis is HIF 412 (example). The image-side surface of the fourth lens element has one inflection point IF 422 which is the second nearest to the optical axis and the sinkage value of the inflection point IF 422 is denoted by SGI 422 (example). SGI 422 is a horizontal shift distance paralleling the optical axis from an axial point on the image-side surface of the fourth lens element to the inflection point which is 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 IF 4222 and the optical axis is HIF 422 (example).

The object-side surface of the fourth lens element has one inflection point IF 413 which is the third nearest to the optical axis and the sinkage value of the inflection point IF 413 is denoted by SGI 413 (example). SGI 413 is a horizontal shift distance paralleling 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 d lens element. A distance perpendicular to the optical axis between the inflection point IF 413 and the optical axis is HIF 413 (example). The image-side surface of the fourth lens element has one inflection point IF 423 which is the third nearest to the optical axis and the sinkage value of the inflection point IF 423 is denoted by SGI 423 (example). SGI 423 is a horizontal shift distance paralleling 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 IF 423 and the optical axis is HIF 423 (example).

The object-side surface of the fourth lens element has one inflection point IF 414 which is the fourth nearest to the optical axis and the sinkage value of the inflection point IF 414 is denoted by SGI 414 (example). SGI 414 is a horizontal shift distance paralleling 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 IF 414 and the optical axis is HIF 414 (example). The image-side surface of the fourth lens element has one inflection point IF 424 which is the fourth nearest to the optical axis and the sinkage value of the inflection point IF 424 is denoted by SGI 424 (example). SGI 424 is a horizontal shift distance paralleling 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 IF 424 and the optical axis is HIF 424 (example).

The inflection points on the object-side surface or the image-side surface of the other lens elements and the perpendicular distances between them and the optical axis, 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. Furthermore, 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 transverse aberration of the edge of the aperture is defined as STOP Transverse Aberration (STA), which assesses the specific performance of the optical image capturing system. The tangential fan or sagittal fan may be applied to calculate the STA of any fields of view, and in particular, to calculate the STAs of the longest operation wavelength (e.g. 650 nm) and the shortest operation wavelength (e.g. 470 nm), which serve as the standard of the performance. The aforementioned direction of the tangential fan can be further defined as the positive (overhead-light) and negative (lower-light) directions. The STA of the max operation wavelength is defined as the distance between the position of the image formed when the max operation wavelength passing through the edge of the aperture strikes a specific field of view of the image plane and the image position of the reference primary wavelength (e.g. wavelength of 555 nm) on specific field of view of the image plane. Whereas the STA of the shortest operation wavelength is defined as the distance between the position of the image formed when the shortest operation wavelength passing through the edge of the aperture strikes a specific field of view of the image plane and the image position of the reference primary wavelength on a specific field of view of the image plane. The criteria for the optical image capturing system to be qualified as having excellent performance may be set as: both STA of the incident longest operation wavelength and the STA of the incident shortest operation wavelength at 70% of the field of view of the image plane (i.e. 0.7 HOI) have to be less than 100 μm or even less than 80 μm.

The optical image capturing system has a maximum image height HOI on the image plane perpendicular to the optical axis. A transverse aberration of the longest operation wavelength of visible light of a positive direction tangential fan of the optical image capturing system passing through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane is denoted as PLTA. A transverse aberration of the shortest operation wavelength of visible light of the positive direction tangential fan of the optical image capturing system passing through the edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane is denoted as PSTA. A transverse aberration of the longest operation wavelength of visible light of a negative direction tangential fan of the optical image capturing system passing through the edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane is denoted as NLTA. A transverse aberration of the shortest operation wavelength of visible light of a negative direction tangential fan of the optical image capturing system passing through the edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane is denoted as NSTA. A transverse aberration of the longest operation wavelength of visible light of a sagittal fan of the optical image capturing system passing through the edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane denoted as SLTA. A transverse aberration of the shortest operation wavelength of visible light of the sagittal fan of the optical image capturing system passing through the edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane 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 may have inflection points, such that the angle of incidence from each field of view 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 the order from an object side to an image side including a first, second, third and fourth lens elements and an image plane. The first lens element has refractive power. Focal lengths of the first through fourth lens elements are f 1 , f 2 , f 3 and f 4 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 on an optical axis 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. Half of the maximum viewable angle of the optical image capturing system is denoted by HAF; an outline curve starting from an axial point on any surface of any one of those lens elements, tracing along the outline of the surface, ending at a coordinate point on the surface that has a vertical height of ½ entrance pupil diameter from the optical axis, has a length denoted by ARE. The following conditions are satisfied: 1.0≤f/HEP≤10, 0 deg≤HAF≤150 deg, and 0.9≤2 (ARE/HEP)≤2.0.

The disclosure also provides an optical image capturing system, in an order from an object side to an image side including a first, second, third and fourth lens elements and an image plane. The first lens element has refractive power. The second lens element has refractive power. The third lens element has refractive power. The fourth lens element has refractive power. At least two lens elements among the first to 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 f 1 , f 2 , f 3 and f 4 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 on the optical axis 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. Half of the maximum viewable angle of the optical image capturing system is denoted by HAF. An outline curve starting from an axial point on any surface of any one of those lens elements, tracing along the outline of the surface, ending at a coordinate point on the surface that has a vertical height of ½ entrance pupil diameter from the optical axis is defined, and the length of the outline curve is denoted by ARE. The following conditions are satisfied: 1.0≤f/HEP≤10, 0° (degree)≤HAF≤150° (deg), and 0.95≤2 (ARE/HEP)≤2.0.

The disclosure further provides an optical image capturing system, in an order from an object side to an image side including a first, second, third and fourth lens elements and an image plane. At least one of the object-side surface and the image-side surface of the fourth lens element has at least one inflection point, wherein there are four lens elements having refractive power in the optical image capturing system. The first lens element has refractive power. The second lens element has refractive power. The third lens element has refractive power. The fourth lens element has refractive power. Focal lengths of the first through fourth lens elements are f 1 , f 2 , f 3 and f 4 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 on the optical axis 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. Half of the maximum viewable angle of the optical image capturing system is denoted by HAF. An outline curve starting from an axial point on any surface of any one of those lens elements, tracing along the outline of the surface, ending at a coordinate point on the surface that has a vertical height of ½ entrance pupil diameter from the optical axis is defined, and the length of the outline curve is denoted by ARE. The following conditions are satisfied: 1.0≤f/HEP≤10, 0° (degree)≤HAF≤150° (deg), and 0.9≤2 (ARE/HEP)≤2.0.

The length of the outline curve of any surface of single lens element within the range of maximum effective half diameter affects the performance in correcting the surface aberration and the optical path difference between the rays in each field of view. The longer outline curve may lead to a better performance in aberration correction, but the difficulty of the production may become higher. Hence, the length of the outline curve (ARS) of any surface of a single lens element within the range of the maximum effective half diameter has to be controlled, and especially, the proportional relationship (ARS/TP) between the length of the outline curve (ARS) of the surface within the range of the maximum effective half diameter and the central thickness (TP) of the lens element to which the surface belongs on the optical axis has to be controlled. For example, the length of the maximum effective half diameter outline curve of the object-side surface of the first lens element is denoted as ARS 11 , and the central thickness of the first lens element on the optical axis is TP 1 , and the ratio between both of them is ARS 11 /TP 1 . The length of the maximum effective half diameter outline curve of the image-side surface of the first lens element is denoted as ARS 12 , and the ratio between ARS 12 and TP 1 is ARS 12 /TP 1 . The length of the maximum effective half diameter outline curve of the object-side surface of the second lens element is denoted as ARS 21 , and the central thickness of the second lens element on the optical axis is TP 2 , and the ratio between both of them is ARS 21 /TP 2 . The length of the maximum effective half diameter outline curve of the image-side surface of the second lens element is denoted as ARS 22 , and the ratio between ARS 22 and TP 2 is ARS 22 /TP 2 . The proportional relationships between the lengths of the maximum effective half diameter outline curve of any surface of the other lens elements and the central thicknesses of the lens elements to which the surfaces belong on the optical axis (TP) are denoted in the similar way.

The length of ½ entrance pupil diameter outline curve of any surface of a single lens element especially affects the performance of the surface in correcting the aberration in the shared region of each field of view, and the performance in correcting the optical path difference among each field of view. The longer outline curve may lead to a better function of aberration correction, but the difficulty of the production may become higher. Hence, the length of ½ entrance pupil diameter outline curve of any surface of a single lens element has to be controlled, and especially, the proportional relationship between the length of ½ entrance pupil diameter outline curve of any surface of a single lens element and the central thickness on the optical axis has to be controlled. For example, the length of the ½ entrance pupil diameter outline curve of the object-side surface of the first lens element is denoted as ARE 11 , and the central thickness of the first lens element on the optical axis is TP 1 , and the ratio thereof is ARE 11 /TP 1 . The length of the ½ entrance pupil diameter outline curve of the image-side surface of the first lens element is denoted as ARE 12 , and the central thickness of the first lens element on the optical axis is TP 1 , and the ratio thereof is ARE 12 /TP 1 . The length of the ½ entrance pupil diameter outline curve of the object-side surface of the first lens element is denoted as ARE 21 , and the central thickness of the second lens element on the optical axis is TP 2 , and the ratio thereof is ARE 21 /TP 2 . The length of the ½ entrance pupil diameter outline curve of the image-side surface of the second lens element is denoted as ARE 22 , and the central thickness of the second lens element on the optical axis is TP 2 , and the ratio thereof is ARE 22 /TP 2 . The proportional relationship of the remaining lens elements of the optical image capturing system can be computed in 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 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. 4K and 2K videos or the so-called UHD and 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 f 1 is larger than f 1 (|f 1 |>f 4 ).

When the relationship |f 2 |+|f 3 |>|f 1 |+|f 4 | is satisfied, 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 and 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 the image-side surface thereof may be a concave surface. With this configuration, the back focal distance of the optical image capturing system may be shortened and the system may be minimized. Besides, at least one surface of the fourth lens element may possess at least one inflection point, which is capable of effectively reducing the incident angle of the off-axis rays of the field of view, thereby further correcting the off-axis aberration.

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 invention.

FIG. 1B shows the 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 invention.

FIG. 1C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the first embodiment of the present invention.

FIG. 2A is a schematic view of the optical image capturing system according to the second embodiment of the present invention.

FIG. 2B shows the 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 invention.

FIG. 2C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the second embodiment of the present invention.

FIG. 3A is a schematic view of the optical image capturing system according to the third embodiment of the present invention.

FIG. 3B shows the 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 invention.

FIG. 3C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the third embodiment of the present invention.

FIG. 4A is a schematic view of the optical image capturing system according to the fourth embodiment of the present invention.

FIG. 4B shows the 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 invention.

FIG. 4C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the fourth embodiment of the present invention.

FIG. 5A is a schematic view of the optical image capturing system according to the fifth embodiment of the present invention.

FIG. 5B shows the 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 invention.

FIG. 5C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the fifth embodiment of the present invention.

FIG. 6A is a schematic view of the optical image capturing system according to the sixth embodiment of the present invention.

FIG. 6B shows the 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 invention.

FIG. 6C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the sixth embodiment of the present invention.

An optical image capturing system, in the order from an object side to an image side, includes a first, second, third and fourth lens elements with refractive power and an image plane. 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 operation 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 to obtain technical features of the optical system. 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 to obtain technical features of the optical system.

A ratio of the focal length f of the optical image capturing system to a focal length fp of each lens element 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 lens element with negative refractive power is NPR. A sum of the PPR of all lens elements with positive refractive powers is ΣPPR. A sum of the NPR of all lens elements with negative refractive powers is ΣNPR. The total refractive power and the total length of the optical image capturing system can be controlled easily when following conditions are satisfied: 0.5≤ΣPPR/|ΣNPR|≤4.5. Preferably, the following condition may be satisfied: 1≤ΣPPR/|ΣNPR|≤3.5.

The height of the optical image capturing system is HOS. When the value of the ratio, i.e. HOS/f approaches 1, it would be easier to manufacture the miniaturized optical image capturing system capable of ultra-high pixel image formation.

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 ΣNP. In one embodiment of the optical image capturing system of the present disclosure, the following conditions are satisfied: 0<ΣPP≤200 and f 1 /ΣPP≤0.85. Preferably, the following relations may be satisfied: 0<ΣPP≤150 and 0.01≤f 1 /ΣPP≤0.7. As a result, the optical image capturing system will have better control over the focusing, and the positive refractive power of the optical system can be distributed appropriately, so as to suppress any premature formation of noticeable aberration.

The first lens element may have positive refractive power, and it has a convex object-side surface. Hereby, the magnitude 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. With this configuration, the back focal length is reduced in order to keep the size of the optical system small. 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, which is capable of effectively reducing the incident angle of the off-axis rays of the field of view, thereby further correcting the off-axis aberration. 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 conditions 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 condition 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 condition 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 R 1 . A curvature radius of the image-side surface of the first lens element is R 2 . The following condition is satisfied: 0.01≤|R 1 /R 2 |≤0.5. Hereby, the first lens element may have a suitable magnitude of positive refractive power, so as to avoid the longitudinal spherical aberration to increase too fast. Preferably, the following relation may be satisfied: 0.01≤|R 1 /R 2 |≤0.4.

A curvature radius of the object-side surface of the fourth lens element is R 9 . A curvature radius of the image-side surface of the fourth lens element is R 10 . The following condition is satisfied: −200<(R 7 −R 8 )/(R 7 +R 8 )<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 IN 12 . The following condition is satisfied: 0<IN 12 /f≤0.25. Preferably, the following relation may be satisfied: 0.01≤IN 12 /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 IN 23 . The following condition is satisfied: 0<IN 23 /f≤0.25. Preferably, the following relation may be satisfied: 0.01≤IN 23 /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 IN 34 . The following condition is satisfied: 0<IN 34 /f≤0.25. Preferably, the following relation may be satisfied: 0.001≤IN 34 /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 TP 1 and TP 2 , respectively. The following condition is satisfied: 1≤(TP 1 +IN 12 )/TP 2 ≤10. Hereby, the sensitivity of 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 TP 3 and TP 4 , respectively, and a distance between the aforementioned two lens elements on the optical axis is IN 34 . The following condition is satisfied: 0.2≤(TP 4 +IN 34 )/TP 4 ≤3. Hereby, the sensitivity of 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 IN 23 . A total sum of distances from the first lens element to the fourth lens element on the optical axis is ΣTP. The following condition is satisfied: 0.01≤IN 23 /(TP 2 +IN 23 +TP 3 )≤0.5. Preferably, the following relation may be satisfied: 0.05≤IN 23 /(TP 2 +IN 23 +TP 3 )≤0.4. Hereby, the aberration generated when the incident light is travelling inside the optical system can be corrected 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 paralleling 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 InRS 41 (InRS 41 is positive if the horizontal displacement is toward the image-side surface, or InRS 41 is negative if the horizontal displacement is toward the object-side surface). A distance paralleling 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 InRS 42 . A central thickness of the fourth lens element 140 on the optical axis is TP 4 . The following conditions are satisfied: −1 mm≤InRS 41 ≤1 mm, −1 mm≤InRS 42 ≤1 mm, 1 mm≤|InRS 41 |+|InRS 42 |≤2 mm, 0.01≤|InRS 41 |/TP 4 ≤10 and 0.01≤|InRS 42 /TP 4 ≤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 paralleling 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 SGI 411 . A distance paralleling 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 SGI 421 . The following conditions are satisfied: 0<SGI 411 /(SGI 411 +TP 4 )≤0.9 and 0<SGI 421 /(SGI 421 +TP 4 )≤0.9. Preferably, the following relations may be satisfied: 0.01<SGI 411 /(SGI 411 +TP 4 )≤0.7 and 0.01<SGI 421 /(SGI 421 +TP 4 )≤0.7.

A distance paralleling 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 SGI 412 . A distance paralleling 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 SGI 422 . The following conditions are satisfied: 0<SGI 412 /(SGI 412 +TP 4 )≤0.9 and 0<SGI 422 /(SGI 422 +TP 4 )≤0.9. Preferably, the following relations may be satisfied: 0.1≤SGI 412 /(SGI 412 +TP 4 )≤0.8 and 0.1≤SGI 422 /(SGI 422 +TP 4 )≤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 HIF 411 . 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 HIF 421 . The following conditions are satisfied: 0.01≤HIF 411 /HOI≤0.9 and 0.01≤HIF 421 /HOI≤0.9. Preferably, the following relations may be satisfied: 0.09≤HIF 411 /HOI≤0.5 and 0.09≤HIF 421 /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 HIF 412 . 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 HIF 422 . The following conditions are satisfied: 0.01≤HIF 412 /HOI≤0.9 and 0.01≤HIF 422 /HOI≤0.9. Preferably, the following relations may be satisfied: 0.09≤HIF 412 /HOI≤0.8 and 0.09≤HIF 422 /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 HIF 413 . 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 HIF 423 . The following conditions are satisfied: 0.001 mm≤|HIF 413 |≤5 mm and 0.001 mm≤|HIF 423 |≤5 mm. Preferably, the following relations may be satisfied: 0.1 mm≤|HIF 423 |≤3.5 mm and 0.1 mm≤|HIF 413 |≤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 HIF 414 . 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 HIF 424 . The following conditions are satisfied: 0.001 mm|HIF 414 |≤5 mm and 0.001 mm≤|HIF 424 |≤5 mm. Preferably, the following relations may be satisfied: 0.1 mm≤|HIF 424 |≤3.5 mm and 0.1 mm≤|HIF 414 |≤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 equation for the aforementioned aspheric surface is:

z=ch 2 /[1+[1−( k+ 1) c 2 h 2 ] 0.5 ]+ A 4 h 4 +A 6 h 6 +A 8 h 8 +A 10 h 10 +A 12 h 12 +A 14 h 14 +A 16 h 16 +A 18 h 18 +A 20 h 20 + . . .   (1),

where z is a 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 A 4 , A 6 , A 8 , A 10 , A 12 , A 14 , A 16 , A 18 , and A 20 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 as well as the weight of the lens element can be reduced effectively. If lens elements are made of glass, the heat effect can be controlled and the room for adjustment of 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, which provides more control variables, such that the number of lens elements used can be reduced in contrast to traditional glass lens element, and the aberration can be reduced too. 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 adjacent to the optical axis is convex. If the lens element has a concave surface, the surface of the lens element adjacent to the optical axis is concave.

Besides, 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.

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 applications.

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 and enables the movement of the lens elements. 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 frequency the optical system is out of focus owing to the vibration of the lens during photo or video shooting.

At least one lens element among the first lens element, the second lens element, the third lens element and the fourth lens element of the optical image capturing system of the present disclosure may be a light filtering element which has a wavelength less than 500 nm according to the actual requirements. The light filtering element may be made by coating film on at least one surface of the lens element with the specific filtration function or the lens element per se is designed with the material which is able to filter the short wavelength.

The image plane of the optical image capturing system of the present disclosure may be a plane or a curved surface, depending on the design requirement. When the image plane is a curved surface (e.g. a spherical surface with curvature radius), the incident angle required such that the rays are focused on the image plane can be reduced. As such, the length of the optical image capturing system (TTL) can be minimized, and the relative illumination may be improved as well.

According to the above embodiments, the specific embodiments with figures are presented in detail as below.

The First Embodiment

Please refer to FIG. 1A to FIG. 1C . FIG. 1A is a schematic view of the optical image capturing system according to the first embodiment of the present invention. FIG. 1B shows the 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 invention. FIG. 1C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the entrance pupil and incident at the position of 0.7 HOI on the image plane, according to the first embodiment of the present invention. As shown in FIG. 1A , in the order from an object side to an image side, the optical image capturing system includes an aperture stop 100 , 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 , and both of the object-side surface 112 and the image-side surface 114 are aspheric and have an inflection point. The length of outline curve of the maximum effective half diameter of the object-side surface of the first lens element is denoted as ARS 11 . The length of outline curve of the maximum effective half diameter of the image-side surface of the first lens element is denoted as ARS 12 . The length of outline curve of ½ entrance pupil diameter (HEP) of the object-side surface of the first lens element is denoted as ARE 11 , and the length of outline curve of ½ entrance pupil diameter (HEP) of the image-side surface of the first lens element is denoted as ARE 12 . The thickness of the first lens element on the optical axis is TP 1 .

A distance paralleling 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 SGI 111 . A distance paralleling 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 SGI 121 . The following conditions are satisfied: SGI 111 =0.2008 mm, SGI 121 =0.0113 mm, |SGI 111 |/(|SGI 111 |+TP 1 )=0.3018 and |SGI 121 |/(|SGI 121 |+TP 1 )=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 HIF 111 . 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 HIF 121 . The following conditions are satisfied: HIF 111 =0.7488 mm, HIF 121 =0.4451 mm, HIF 111 /HOI=0.2552 and HIF 121 /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 of the object-side surface of the second lens element is denoted as ARS 21 , and the length of outline curve of the maximum effective half diameter of the image-side surface of the second lens element is denoted as ARS 22 . The length of outline curve of ½ entrance pupil diameter (HEP) of the object-side surface of the second lens element is denoted as ARE 21 , and the length of outline curve of ½ entrance pupil diameter (HEP) of the image-side surface of the second lens element is denoted as ARE 22 . The thickness of the second lens element on the optical axis is TP 2 .

A distance paralleling 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 SGI 211 . A distance paralleling 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 SGI 221 . The following conditions are satisfied: SGI 211 =−0.1791 mm and |SGI 211 |/(|SGI 211 |+TP 2 )=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 HIF 211 . 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 HIF 221 . The following conditions are satisfied: HIF 211 =0.8147 mm and HIF 211 /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 ARS 31 , 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 ARS 32 . The length of outline curve of a ½ entrance pupil diameter (HEP) of the object-side surface of the third lens element is denoted as ARE 31 , and the length of outline curve of the ½ entrance pupil diameter (HEP) of the image-side surface of the third lens element is denoted as ARE 32 . The central thickness of the third lens element on the optical axis is TP 3 .

A distance paralleling 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 SGI 311 . A distance paralleling 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 SGI 321 . The following relationship are satisfied: SGI 321 =−0.1647 mm; |SGI 321 |/(|SGI 321 |+TP 3 )≤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 HIF 311 . 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 HIF 321 . The following conditions are satisfied: HIF 321 =0.7269 mm and HIF 321 /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 thereof has two inflection points while the image-side surface 144 thereof has an inflection point. The length of the maximum effective half diameter outline curve of the object-side surface of the fourth lens element is denoted as ARS 41 , and the length of the maximum effective half diameter outline curve of the image-side surface of the fourth lens element is denoted as ARS 42 . The length of ½ entrance pupil diameter (HEP) outline curve of the object-side surface of the fourth lens element is denoted as ARE 41 , and the length of the ½ entrance pupil diameter (HEP) outline curve of the image-side surface of the fourth lens element is denoted as ARE 42 . The central thickness of the fourth lens element on the optical axis is TP 4 .

A distance paralleling 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 SGI 411 . A distance paralleling 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 SGI 421 . The following conditions are satisfied: SGI 411 =0.0137 mm, SGI 421 =−0.0922 mm, |SGI 411 |/(|SGI 411 |+TP 4 )=0.0155 and |SGI 421 |/(|SGI 421 +TP 4 )=0.0956.

A distance paralleling an 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 SGI 412 . The following conditions are satisfied: SGI 412 =−0.1518 mm and |SGI 412 |/(|SGI 412 |+TP 4 )=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 HIF 411 . 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 HIF 421 . The following conditions are satisfied: HIF 411 =0.2890 mm, HIF 421 =0.5794 mm, HIF 411 /HOI=0.0985 and HIF 421 /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 second nearest to the optical axis and the optical axis is denoted by HIF 412 . The following conditions are satisfied: HIF 412 =1.3328 mm and HIF 412 /HOI=0.4543.

The IR-bandstop filter 170 is made of glass material and is disposed between the fourth lens element 140 and the image plane 180 without affecting the focal length of the optical image capturing system.

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 f 1 and a focal length of the fourth lens element 140 is f 4 . The following conditions are satisfied: f 1 =3.2736 mm, |f/f|=1.0501, f 4 =−8.3381 mm and |f 1 /f 4 |=0.3926.

In the optical image capturing system of the first embodiment, a focal length of the second lens element 120 is f 2 and a focal length of the third lens element 130 is f 3 . The following conditions are satisfied: |f 2 |+f 3 |=10.0976 mm, |f 1 |+f 4 =11.6116 mm and |f 2 |+|f 3 |<|f 1 |+|f 4 |.

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 powers 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 powers is NPR. In the optical image capturing system of the first embodiment, a sum of the PPR of all lens elements with positive refractive powers is ΣPPR=|f/f 1 |+|f/f 2 |=1.95585. A sum of the NPR of all lens elements with negative refractive powers is ΣNPR=f/f 3 +|f/f 4 |=0.95770, ΣPPR/ΣNPR=2.04224. The following conditions are also satisfied: |f/f 1 |=1.05009, |f/f 2 |=0.90576, |f/f 3 |=0.54543 and |f/f 4 |=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 conditions 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 conditions are satisfied: ΣTP=2.4437 mm and ΣTP/InTL=0.76793. Therefore, both contrast ratio for the image formation in the optical image capturing system and yield rate of the manufacturing process of the lens element can be balanced, 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 R 1 . A curvature radius of the image-side surface 114 of the first lens element is R 2 . The following condition is satisfied: |R 1 /R 2 |=0.1853. Hereby, the first lens element has a suitable magnitude of the positive refractive power, so as to prevent the spherical aberration from increasing 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 R 7 . A curvature radius of the image-side surface 144 of the fourth lens element is R 8 . The following condition is satisfied: (R 7 −R 8 )/(R 7 +R 8 )=0.2756. As such, the astigmatism generated by the optical image capturing system can be corrected.

In the optical image capturing system of the first embodiment, the focal lengths for the first lens element 110 and the second lens element 120 are respectively f 1 and f 2 . The sum of the focal lengths for all lens elements having positive refractive power is ΣPP, which satisfies the following conditions: ΣPP=f 1 +f 2 =7.0688 mm and f 1 /(f 1 +f 2 )≤0.4631. Therefore, the positive refractive power of the first lens element 110 may be distributed to other lens elements with positive refractive power appropriately, so as to suppress noticeable aberrations generated when the incident light is tracing along the optical system.

In the optical image capturing system of the first embodiment, the focal lengths for the third lens element 130 and the fourth lens element 140 are respectively f 3 and f 4 . The sum of the focal lengths for all lens elements having negative refractive power is ΣNP, which satisfies the following conditions: ΣNP=f 3 +f 4 =−14.6405 mm and f 4 /(f 2 +f 4 )=0.5695. Therefore, the negative refractive power of the fourth lens element may be distributed to other lens elements with negative refractive power appropriately, so as to suppress noticeable aberrations generated when the incident light is tracing along the optical system.

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 IN 12 . The following conditions are satisfied: IN 12 =0.3817 mm and IN 12 /f=0.11105. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance of the optical system is 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 IN 23 . The following conditions are satisfied: IN 23 =0.0704 mm and IN 23 /f=0.02048. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance of the optical system is 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 IN 34 . The following conditions are satisfied: IN 34 =0.2863 mm and IN 34 /f=0.08330. Hereby, the chromatic aberration of the lens elements can be improved, such that the performance of the optical system is 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 TP 1 and TP 2 , respectively. The following conditions are satisfied: TP 1 =0.46442 mm, TP 2 =0.39686 mm, TP 1 /TP 2 =1.17023 and (TP 1 +IN 12 )/TP 2 =2.13213. Hereby, the sensitivity of the optical image capturing system can be controlled, and the performance thereof 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 TP 3 and TP 4 , respectively. The separation distance between the third lens element 130 and the fourth lens element 140 on the optical axis is IN 34 . The following conditions are satisfied: TP 3 =0.70989 mm, TP 4 =0.87253 mm, TP 3 /TP 4 =0.81359 and (TP 4 +IN 34 )/TP 3 =1.63248. Hereby, the sensitivity of the optical image capturing system can be controlled, and the performance thereof can be increased.

In the optical image capturing system of the first embodiment, the following relations are satisfied: IN 23 /(TP 2 +IN 23 +TP 3 )=0.05980. Hereby, the aberration generated when the incident light is travelling inside the optical system can be corrected 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 first embodiment, a distance paralleling 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 InRS 41 . A distance paralleling 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 InRS 42 . A central thickness of the fourth lens element 140 is TP 4 . The following conditions are satisfied: InRS 41 =−0.23761 mm, InRS 42 =−0.20206 mm, |InRS 41 |+|InRS 42 |=0.43967 mm, |InRS 41 |/TP 4 =0.27232 and |InRS 42 |/TP 4 =0.23158. Hereby, it is favorable to the manufacturing and forming of the lens element, while maintaining the minimization for the optical image capturing system.

In the optical image capturing system of the first embodiment, a distance perpendicular to the optical axis between a critical point C 41 on the object-side surface 142 of the fourth lens element and the optical axis is HVT 41 . A distance perpendicular to the optical axis between a critical point C 42 on the image-side surface 144 of the fourth lens element and the optical axis is HVT 42 . The following conditions are satisfied: HVT 41 =0.5695 mm, HVT 42 =1.3556 mm and HVT 41 /HVT 42 =0.4201. With this configuration, the off-axis aberration could be corrected effectively.

In the optical image capturing system of the first embodiment, the following condition is satisfied: HVT 42 /HOI=0.4620. As such, the aberration at the surrounding field of view of the optical image capturing system may be corrected effectively.

In the optical image capturing system of the first embodiment, the following condition is satisfied: HVT 42 /HOS=0.3063. As such, the aberration at the surrounding field of view of the optical image capturing system may be corrected effectively.

In the optical image capturing system of the first embodiment, the Abbe number of the first lens element is NA 1 . The Abbe number of the second lens element is NA 2 . The Abbe number of the third lens element is NA 3 . The Abbe number of the fourth lens element is NA 4 . The following conditions are satisfied: |NA 1 −NA 2 |=0 and NA 3 /NA 2 =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 conditions are satisfied: |TDT|=0.4% and |ODT|=2.5%.

In the optical image capturing system of the first embodiment, the transverse aberration of the longest operation wavelength of a positive direction tangential fan passing through the edge of the aperture and incident at the position of 0.7 field of view on the image plane is denoted as PLTA, which is 0.001 mm (pixel size is 1.12 μm). The transverse aberration of the shortest operation wavelength of a positive direction tangential fan passing through the edge of the aperture and incident at the position of 0.7 field of view on the image plane is denoted as PSTA, which is 0.004 mm (pixel size is 1.12 μm). The transverse aberration of the longest operation wavelength of the negative direction tangential fan passing through the edge of the aperture and incident at the position of 0.7 field of view on the image plane is denoted as NLTA, which is 0.003 mm (pixel size is 1.12 μm). The transverse aberration of the shortest operation wavelength of the negative direction tangential fan passing through the edge of the aperture and incident at the position of 0.7 field of view on the image plane is denoted as NSTA, which is −0.003 mm (pixel size is 1.12 m). The transverse aberration of the longest operation wavelength of the sagittal fan passing through the edge of the aperture and incident at the position of 0.7 field of view on the image plane is denoted as SLTA, which is 0.003 mm (pixel size is 1.12 μm). The transverse aberration of the shortest operation wavelength of the sagittal fan passing through the edge of the aperture and incident at the position of 0.7 field of view on the image plane is denoted as SSTA, which is 0.004 mm (pixel size is 1.12 μm).

Table 1 and Table 2 below should be incorporated into the reference of the present embodiment.

The values pertaining to the length of the outline curves are obtainable from the data in Table 1 and Table 2:

Table 1 is the detailed structural data to the first embodiment in FIG. 1A , wherein the unit for the curvature radius, the central thickness, the distance, and the focal length is millimeters (mm). Surfaces 0-11 illustrate the surfaces from the object side to the image plane in the optical image capturing system. Table 2 shows the aspheric coefficients of the first embodiment, wherein k is the conic coefficient in the aspheric surface equation, and A 1 -A 20 are respectively the first to the twentieth order aspheric surface coefficients. Besides, the tables in the following embodiments correspond to the schematic view and the aberration graphs, respectively, and definitions of parameters in these tables are similar to those in the Table 1 and the Table 2, so the repetitive details will not be given here.

Second Embodiment

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 invention. FIG. 2B shows the longitudinal spherical aberration curves, astigmatic field curves, and an optical distortion grid of the optical image capturing system of the second embodiment, in the order from left to right. FIG. 2C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the aperture stop and incident at the position of 0.7 HOI on the image plane, according to optical image capturing system of the second embodiment. As shown in FIG. 2A , in the order from an object side to an image side, the optical image capturing system includes a first lens element 210 , an aperture stop 200 , 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 negative refractive power and is made of plastic material. The first lens element 210 has a convex object-side surface 212 and a concave image-side surface 214 , and both object-side surface 212 and image-side surface 214 are aspheric.

The second lens element 220 has negative refractive power and is made of plastic material. The second lens element 220 has a convex object-side surface 222 and a concave image-side surface 224 , and both object-side surface 222 and image-side surface 224 are aspheric.

The third lens element 230 has positive refractive power and is made of plastic material. The third lens element 230 has a convex object-side surface 232 and a convex image-side surface 234 , and both object-side surface 232 and image-side surface 234 are aspheric.

The fourth lens element 240 has positive refractive power and is made of plastic material. The fourth lens element 240 has a convex object-side surface 242 and a convex image-side surface 244 , and both object-side surface 242 and image-side surface 244 are aspheric. The image-side surface 244 thereof has an inflection point.

The IR-bandstop filter 270 is made of glass material and is disposed between the fourth lens element 240 and the image plane 280 , without affecting the focal length of the optical image capturing system.

Table 3 and Table 4 below should be incorporated into the reference of the present embodiment

In the second embodiment, the presentation of the aspheric surface equation is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are similar to those in the first embodiment, so the repetitive details will not be given here.

The following values for the conditional expressions can be obtained from the data in Table 3 and Table 4.

The following values for the conditional expressions can be obtained from the data in Table 3 and Table 4.

Values Related to Inflection Point of Second Embodiment

(Primary Reference Wavelength = 555 nm)

HIF421

0.3136

HIF421/HOI

0.1036

SGI421

−0.0004

|SGI421 |/(|SGI421 | + TP4)

0.0002

The values pertaining to the length of the outline curves are obtainable from the data in Table 3 and Table 4:

Third Embodiment

Please refer to FIG. 3A to FIG. 3C . FIG. 3A is a schematic view of the optical image capturing system according to the third embodiment of the present invention. FIG. 3B shows the 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 invention. FIG. 3C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the aperture stop and incident at the position of 0.7 HOI on the image plane, according to the third embodiment of the present invention. As shown in FIG. 3A , in the order from an object side to an image side, the optical image capturing system includes a first lens element 310 , an aperture stop 300 , 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 negative refractive power and is made of plastic material. The first lens element 310 has a convex object-side surface 312 and a concave image-side surface 314 , and both object-side surface 312 and image-side surface 314 are aspheric. The object-side surface 312 has an inflection point.

The second lens element 320 has positive refractive power and is made of plastic material. The second lens element 320 has a convex object-side surface 322 and a concave image-side surface 324 , and both object-side surface 322 and image-side surface 324 are aspheric.

The third lens element 330 has positive refractive power and is made of plastic material. The third lens element 330 has a convex object-side surface 332 and a convex image-side surface 334 , and both object-side surface 332 and image-side surface 334 are aspheric.

The fourth lens element 340 has positive refractive power and is made of plastic material. The fourth lens element 340 has a concave object-side surface 342 and a convex image-side surface 344 ; both object-side surface 342 and image-side surface 344 are aspheric and have an inflection point.

The IR-bandstop filter 370 is made of glass material and is disposed between the fourth lens element 340 and the image plane 380 , without affecting the focal length of the optical image capturing system.

Table 5 and Table 6 below should be incorporated into the reference of the present embodiment.

In the third embodiment, the presentation of the aspheric surface equation is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are similar to those in the first embodiment, so the repetitive details will not be given here.

The following values for the conditional expressions can be obtained from the data in Table 5 and Table 6.

The following values for the conditional expressions can be obtained from the data in Table 5 and Table 6.

The values pertaining to the length of the outline curves are obtainable from the data in Table 5 and Table 6:

Fourth Embodiment

Please refer to FIG. 4A to FIG. 4C . FIG. 4A is a schematic view of the optical image capturing system according to the fourth embodiment of the present invention. FIG. 4B shows the 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 invention. FIG. 4C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the aperture stop and incident at the position of 0.7 HOI on the image plane, according to the fourth embodiment of the present invention. As shown in FIG. 4A , in the order from an object side to an image side, the optical image capturing system includes a first lens element 410 , an aperture stop 400 , 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 negative refractive power and is made of plastic material. The first lens element 410 has a convex object-side surface 412 and a concave image-side surface 414 , and both object-side surface 412 and image-side surface 414 are aspheric. The object-side surface 412 has an inflection point.

The second lens element 420 has negative refractive power and is made of plastic material. The second lens element 420 has a convex object-side surface 422 and a planar image-side surface 424 , and both object-side surface 422 and image-side surface 424 are aspheric. The image-side surface 424 thereof has an inflection point.

The third lens element 430 has positive refractive power and is made of plastic material. The third lens element 430 has a convex object-side surface 432 and a convex image-side surface 434 , and both object-side surface 432 and image-side surface 434 are aspheric. The image-side surface 434 thereof has an inflection point.

The fourth lens element 440 has positive refractive power and is made of plastic material. The fourth lens element 440 has a convex object-side surface 442 and a convex image-side surface 444 ; both object-side surface 442 and image-side surface 444 are aspheric and have an inflection point.

The IR-bandstop filter 470 is made of glass material and is disposed between the fourth lens element 440 and the image plane 480 , without affecting the focal length of the optical image capturing system.

Table 7 and Table 8 below should be incorporated into the reference of the present embodiment.

In the fourth embodiment, the form of the aspheric surface equation is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are similar to those in the first embodiment, so the repetitive details will not be given here.

The following values for the conditional expressions can be obtained from the data in Table 7 and Table 8.

The following values for the conditional expressions can be obtained from the data in Table 7 and Table 8.

The values pertaining to the length of the outline curves are obtainable from the data in Table 7 and Table 8:

Fifth Embodiment

Please refer to FIG. 5A to FIG. 5C . FIG. 5A is a schematic view of the optical image capturing system according to the fifth embodiment of the present invention. FIG. 5 B shows the 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 invention. FIG. 5C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the aperture stop and incident at the position of 0.7 HOI on the image plane, according to the optical image capturing system of the fifth embodiment. As shown in FIG. 5A , in the order from an object side to an image side, the optical image capturing system includes a first lens element 510 , an aperture stop 500 , 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 negative refractive power and is made of plastic material. The first lens element 510 has a convex object-side surface 512 and a concave image-side surface 514 , and both object-side surface 512 and image-side surface 514 are aspheric. The object-side surface 512 has an inflection point.

The second lens element 520 has negative refractive power and is made of plastic material. The second lens element 520 has a convex object-side surface 522 and a concave image-side surface 524 , and both object-side surface 522 and image-side surface 524 are aspheric.

The third lens element 530 has positive refractive power and is made of plastic material. The third lens element 530 has a convex object-side surface 532 and a convex image-side surface 534 , and both object-side surface 532 and image-side surface 534 are aspheric.

The fourth lens element 540 has positive refractive power and is made of plastic material. The fourth lens element 540 has a convex object-side surface 542 and a convex image-side surface 544 . Both object-side surface 542 and image-side surface 544 are aspheric, and the image-side surface 544 has an inflection point.

The IR-bandstop filter 570 is made of glass material and is disposed between the fourth lens element 540 and the image plane 580 , without affecting the focal length of the optical image capturing system.

Table 9 and Table 10 below should be incorporated into the reference of the present embodiment.

In the fifth embodiment, the form of the aspheric surface equation is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are similar to those in the first embodiment, so the repetitive details will not be given here.

The following values for the conditional expressions can be obtained from the data in Table 9 and Table 10:

The following values for the conditional expressions can be obtained from the data in Table 9 and Table 10.

The values pertaining to the length of the outline curves are obtainable from the data in Table 9 and Table 10:

Sixth Embodiment

Please refer to FIG. 6A to FIG. 6C . FIG. 6A is a schematic view of the optical image capturing system according to the sixth embodiment of the present invention. FIG. 6B shows the 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 invention. FIG. 6C is a transverse aberration diagram of the longest operation wavelength and the shortest operation wavelength for tangential fan and sagittal fan, wherein the longest operation wavelength and the shortest operation wavelength pass through an edge of the aperture stop and incident at the position of 0.7 HOI on the image plane, according to the optical image capturing system of the sixth embodiment. As shown in FIG. 6A , in the 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 negative refractive power and is made of plastic material. The first lens element 610 has a convex object-side surface 612 and a concave image-side surface 614 , and both object-side surface 612 and image-side surface 614 are aspheric. The object-side surface 612 has an inflection point.

The second lens element 620 has negative refractive power and is made of plastic material. The second lens element 620 has a convex object-side surface 622 and a concave image-side surface 624 , and both object-side surface 622 and image-side surface 624 are aspheric. The object-side surface 622 thereof has two inflection points.

The third lens element 630 has positive refractive power and is made of plastic material. The third lens element 630 has a convex object-side surface 632 and a convex image-side surface 634 , and both object-side surface 632 and image-side surface 634 are aspheric.

The fourth lens element 640 has positive refractive power and 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 object-side surface 642 and image-side surface 644 are aspheric.

The IR-bandstop filter 670 is made of glass material and is disposed between the fourth lens element 640 and the image plane 680 , without affecting the focal length of the optical image capturing system.

Table 11 and Table 12 below should be incorporated into the reference of the present embodiment.

In the sixth embodiment, the form of the aspheric surface equation is similar to that in the first embodiment. Besides, the definitions of parameters in following tables are similar to those in the first embodiment, so the repetitive details will not be given here.

The following values for the conditional expressions can be obtained from the data in Table 11 and Table 12:

The following values for the conditional expressions can be obtained from the data in Table 11 and Table 12:

The values pertaining to the length of the outline curves are obtainable from the data in Table 11 and Table 12:

Although the present invention is disclosed by the aforementioned embodiments, those embodiments do not serve to limit the scope of the present invention. A person skilled in the art could perform various alterations and modifications to the present invention, without departing from the spirit and the scope of the present invention. Hence, the scope of the present invention should be defined by the following appended claims.

Despite the fact that the present invention is specifically presented and illustrated with reference to the exemplary embodiments thereof, it should be apparent to a person skilled in the art that, various modifications could be performed to the forms and details of the present invention, without departing from the scope and spirit of the present invention defined in the claims and their equivalence.