Patent ID: 12210211

DETAILED DESCRIPTION

An identification module includes an imaging lens system, a first panel and a second panel. The imaging lens system includes four lens elements. The four lens elements are, in order from an object side to an image side, a first lens element, a second lens element, a third lens element and a fourth lens element. Each of the four lens elements of the imaging lens system has an object-side surface facing toward the object side and an image-side surface facing toward the image side. The first panel is disposed on the object side of the imaging lens system, and more specifically, the first panel is located between the first lens element of the imaging lens system and an imaged object (which is also on the object side of the first lens element of the imaging lens system). The second panel is disposed on the image side of the imaging lens system, and more specifically, the second panel is located between the fourth lens element and an image surface of the imaging lens system (which is also on the image side of the fourth lens element of the imaging lens system).

The first lens element has negative refractive power. Therefore, it is favorable for the imaging lens system to have a wider detection range so as to improve the accuracy of image identification. The object-side surface of the first lens element can be convex in a paraxial region thereof, and the image-side surface of the first lens element can be concave in a paraxial region thereof. Therefore, it is favorable for preventing total reflection by obtaining a sufficiently large incident angle of light on the lens surfaces so as to allow light with a large view angle can converge on the image surface. The object-side surface of the first lens element can be convex in a paraxial region thereof, and the object-side surface of the first lens element can have a convex-to-concave-to-convex shape change in order from the paraxial region thereof to an off-axis region thereof. Therefore, it is favorable for controlling the required space for the first lens element in the imaging lens system so as to better arrange space among the lens elements, thereby preventing the imaging lens system from being overly large. The object-side surface of the first lens element can have at least one inflection point. Therefore, it is favorable for correcting off-axis aberrations and the miniaturization of the imaging lens system.

The fourth lens element has positive refractive power. Therefore, it is favorable for effectively controlling an incident angle of light on the image surface so as to provide sufficient light on the image surface, thereby increasing illuminance on the peripheral region of the image surface for a better result of the peripheral image identification. The object-side surface of the fourth lens element can be convex in a paraxial region thereof. Therefore, it is favorable for balancing the curvatures of the object-side surface and the image-side surface of the fourth lens element so as to prevent any single lens surface from having an overly large curvature, thereby reducing aberrations. The image-side surface of the fourth lens element can be convex in a paraxial region thereof. Therefore, it is favorable for controlling the back focal length of the imaging lens system so as to provide sufficient space for accommodating additional optical components. At least one of the object-side surface and the image-side surface of the fourth lens element can have at least one inflection point. Therefore, it is favorable for correcting distortion and astigmatism.

According to the present disclosure, at least one lens element of the imaging lens system can have at least one lens surface having at least one inflection point. Therefore, it is favorable for correcting field curvature and reducing the total track length of the imaging lens system so as to obtain a compact configuration. Please refer toFIG.29, which shows a schematic view of an inflection point P on the object-side surface111of the first lens element110according to the 1st embodiment of the present disclosure. The inflection point P on the object-side surface of the first lens element inFIG.29is only exemplary. The other lens surfaces of the four lens elements may also have one or more inflection points.

When a central thickness of the first lens element is CT1, and a central thickness of the second lens element is CT2, the following condition is satisfied: 1.20<CT1/CT2<15.0. Therefore, it is favorable for increasing the mechanical strength of the imaging lens system against harsh environmental conditions. Moreover, the following condition can also be satisfied: 1.50<CT1/CT2<5.0. Moreover, the following condition can also be satisfied: 2.35<CT1/CT2<7.50.

When a focal length of the first lens element is f1, and a focal length of the second lens element is f2, the following condition is satisfied: |f1|<|f2|. Therefore, it is favorable for the first lens element to control the light path, and for the second lens element to correct aberrations generated by the first lens element, such that the first lens element and the second lens element are configured as being complementary.

When an axial distance between the object-side surface of the first lens element and the image surface is TL, and a focal length of the imaging lens system is f, the following condition can be satisfied: 5.50<TL/f<16.0. Therefore, it is favorable for balancing the total length and controlling the field of view of the imaging lens system so as to provide a retro-focus lens configuration, thereby making the imaging lens system applicable to various applications. Moreover, the following condition can also be satisfied: 5.50<TL/f<14.0. Moreover, the following condition can also be satisfied: 8.50<TL/f<12.0. Please refer toFIG.30, which shows a schematic view of TL according to the 1st embodiment of the present disclosure.

When an axial distance between the imaged object and the object-side surface of the first lens element is OL, a central thickness of the first panel is CTf, an axial distance between the image-side surface of the fourth lens element and the image surface is BL, and a central thickness of the second panel is CTr, the following condition can be satisfied: (OL−CTf)/(BL−CTr)<1.80. Therefore, it is favorable for balancing space between the object side and the image side of the imaging lens system so as to achieve an efficient space arrangement of the imaging lens system. Please refer toFIG.30, which shows a schematic view of CTf, OL, BL and CTr according to the 1st embodiment of the present disclosure, wherein the optical window150is the first panel, and the cover glass160is the second panel, but the present disclosure is not limited thereto. In other configurations, the second panel is, for example, a filter.

When the focal length of the imaging lens system is f, and an entrance pupil diameter of the imaging lens system is EPD, the following condition can be satisfied: f/EPD<1.90. Therefore, it is favorable for providing accurate identification under low-light conditions, such that the imaging lens system can be flexible in various environmental settings. Moreover, the following condition can also be satisfied: 0.50<f/EPD<1.70. Moreover, the following condition can also be satisfied: 0.80<f/EPD<1.50.

When the central thickness of the first panel is CTf, and an axial distance between the object-side surface of the first lens element and the image-side surface of the fourth lens element is TD, the following condition can be satisfied: 0.25<CTf/TD<1.50. Therefore, it is favorable for providing the panel on the object side of the imaging lens system with sufficient structural strength to withstand a high amount of compressions by external forces, thereby providing better product utilization. Moreover, the following condition can also be satisfied: 0.35<CTf/TD<0.70. Please refer toFIG.30, which shows a schematic view of CTf and TD according to the 1st embodiment of the present disclosure.

When a curvature radius of the object-side surface of the fourth lens element is R7, and a curvature radius of the image-side surface of the fourth lens element is R8, the following condition can be satisfied: −1.0<(R7+R8)/(R7−R8). Therefore, it is favorable for obtaining a proper curvature of the image-side surface of the fourth lens element so as to control an incident angle of light on the image surface with a proper back focal length. Moreover, the following condition can also be satisfied: −1.0<(R7+R8)/(R7−R8)<5.0. Moreover, the following condition can also be satisfied: −0.50<(R7+R8)/(R7−R8)<0.50.

When the focal length of the first lens element is f1, and a focal length of the third lens element is f3, the following condition can be satisfied: |f1|<|f3|. Therefore, it is favorable for having stronger refractive power on the object side of the imaging lens system so as to achieve compactness.

When the focal length of the first lens element is f1, and the focal length of the second lens element is f2, the following condition can be satisfied: |f1/f2|<0.50. Therefore, it is favorable for correcting aberrations of the first lens element by the second lens element as a correction lens so as to improve image quality. Moreover, the following condition can also be satisfied: |f1/f2|<0.30.

When a maximum value among Abbe numbers of all lens elements of the imaging lens system is Vmax, and a minimum value among Abbe numbers of all lens elements of the imaging lens system is Vmin, the following condition can be satisfied: 0≤Vmax−Vmin<10.0. Therefore, it is favorable for obtaining highly similar materials for the lens elements so as to improve manufacturing planning and cost managements. Moreover, the following condition can also be satisfied: 0≤Vmax−Vmin<5.0.

When a maximum effective radius of the image-side surface of the first lens element is Y12, and a curvature radius of the image-side surface of the first lens element is R2, the following condition can be satisfied: 1.50<Y12/R2<5.50. Therefore, it is favorable for controlling the curvature distribution of the image-side surface of the first lens element so as to receive images and correct aberrations with a large angle of view. Please refer toFIG.29, which shows a schematic view of Y12 according to the 1st embodiment of the present disclosure.

When the focal length of the second lens element is f2, and a focal length of the fourth lens element is f4, the following condition can be satisfied: |f4/f2|<0.50. Therefore, it is favorable for controlling the light path on the image side of the imaging lens system for various applications. Moreover, the following condition can also be satisfied: |f4/f2|<0.30.

According to the present disclosure, the imaging lens system further includes an aperture stop. When an axial distance between the aperture stop and the image surface is SL, and the axial distance between the object-side surface of the first lens element and the image surface is TL, the following condition can be satisfied: 0.25<SL/TL<0.60. Therefore, it is favorable for controlling the position of the aperture stop while balancing between the field of view and the total track length of the imaging lens system. Moreover, the following condition can also be satisfied: 0.35<SL/TL<0.50. Please refer toFIG.30, which shows a schematic view of SL and TL according to the 1st embodiment of the present disclosure.

According to the present disclosure, an axial distance between the first panel and the first lens element can be smaller than 0.90 mm. Therefore, it is favorable for keeping the electronic device in a compact size so as to be applicable to a wide range of applications. Moreover, the axial distance between the first panel and the first lens element can be smaller than 0.55 mm.

When the focal length of the second lens element is f2, and the focal length of the fourth lens element is f4, the following condition can be satisfied: |f4|<|f2|. Therefore, it is favorable for balancing the refractive power distribution of the imaging lens system by the fourth lens element.

When the axial distance between the object-side surface of the first lens element and the image surface is TL, the following condition can be satisfied: TL<4.50 [mm]. Therefore, it is favorable for controlling the total length of the imaging lens system so as to achieve compactness. Moreover, the following condition can also be satisfied: TL<4.0 [mm].

When the focal length of the imaging lens system is f, the entrance pupil diameter of the imaging lens system is EPD, and an incident angle of a chief ray at a maximum field of view on the object-side surface of the first lens element relative to an optical axis (i.e., half of the maximum field of view of the imaging lens system) is HFOV, the following condition can be satisfied: 0<f/[EPD×tan(HFOV)]<1.0. Therefore, it is favorable for enhancing the light-gathering ability and the imaging range of the imaging lens system. Moreover, the following condition can also be satisfied: 0.30<f/[EPD×tan(HFOV)]<0.90. Please refer toFIG.29, which shows a schematic view of HFOV according to the 1st embodiment of the present disclosure, wherein there is a chief ray CR at a maximum field of view of incidence on the object-side surface111of the first lens element110, and the angle between the chief ray CR and the optical axis is HFOV.

When the axial distance between the object-side surface of the first lens element and the image surface is TL, and a maximum image height of the imaging lens system (half of a diagonal length of an effective photosensitive area of an image sensor) is ImgH, the following condition can be satisfied: 5.0<TL/ImgH<10.0. Therefore, it is favorable for controlling the dimensions of the imaging lens system so as to properly balance the view angle and the image height. Moreover, the following condition can also be satisfied: 5.0<TL/ImgH<8.0. Moreover, the following condition can also be satisfied: 5.0<TL/ImgH<7.0.

According to the present disclosure, the imaging lens system can be operated within a wavelength range of 480 nanometers (nm) to 590 nm. Therefore, it is favorable for obtaining desirable identification results by being operated within a narrower wavelength range of visible light so as to be applicable to various applications. However, the imaging lens system of the present disclosure is not limited to be operated within the aforementioned wavelength range. In other aspects, the imaging lens system can be operated within other wavelength range of visible light or infrared light.

According to the present disclosure, each of the four lens elements of the imaging lens system can have an Abbe number larger than 50.0. Therefore, it is favorable for satisfying the requirements for identification applications while reducing manufacturing costs and increasing manufacturing feasibility.

When a vertical distance between a non-axial convex critical point on the object-side surface of the first lens element and the optical axis is Y11cx, and a vertical distance between a non-axial concave critical point on the object-side surface of the first lens element and the optical axis is Y11ca, the following condition can be satisfied: 1.10<Y11cx/Y11ca<3.20. Therefore, it is favorable for correcting aberrations at different fields of view and reducing the total track length of the imaging lens system. Moreover, the following condition can also be satisfied: 1.30<Y11cx/Y11ca<2.20. Please refer toFIG.29, which shows a schematic view of Y11cx, Y11 ca and critical points C on the object-side surface111of the first lens element110according to the 1st embodiment of the present disclosure. The critical points C on the object-side surface of the first lens element inFIG.29is only exemplary. The other lens surfaces of the four lens elements may also have one or more critical points.

When the focal length of the imaging lens system is f, the focal length of the first lens element is f1, the focal length of the second lens element is f2, and the focal length of the third lens element is f3, the following condition can be satisfied: 0<|f/f1|−|f/f21−|f/f3|. Therefore, it is favorable for providing the first lens element with sufficient power, and correcting aberrations by the second lens element and third lens elements so as to improve image quality.

When the maximum image height of the imaging lens system is ImgH, and the focal length of the imaging lens system is f, the following condition can be satisfied: 1.20<ImgH/f<3.0. Therefore, it is favorable for providing a retro-focus lens configuration so as to achieve a wider imaging range and capture more image information, thereby improving image identifications.

According to the present disclosure, an axial distance between the first lens element and the second lens element T12can be a maximum among axial distances between each of all adjacent lens elements of the imaging lens system.

That is, the axial distance between the first lens element and the second lens element T12can be larger than or equal to an axial distance between the second lens element and the third lens element T23, and an axial distance between the third lens element and the fourth lens element T34. Therefore, it is favorable for providing sufficient space on the object side of the imaging lens system so as to retrieve light with a large field of view, thereby reducing aberrations.

According to the present disclosure, the central thickness of the first lens element CT1 can be a maximum among central thickness of all lens elements of the imaging lens system. That is, the central thickness of the first lens element CT1 can be larger than or equal to the central thickness of the second lens element CT2, a central thickness of the third lens element CT3, and a central thickness of the fourth lens element CT4. Therefore, it is favorable for balancing among the thicknesses of the lens elements with different dimensions so as to improve the lens molding quality and the assembling yield rate.

When the focal length of the third lens element is f3, and the focal length of the fourth lens element is f4, the following condition can be satisfied: |f4|<|f3|. Therefore, it is favorable for balancing the refractive power distribution on the image side of the imaging lens system so as to provide good image quality.

When a displacement in parallel with the optical axis from an axial vertex to a maximum effective radius position on the image-side surface of the first lens element is SAG12, and the curvature radius of the image-side surface of the first lens element is R2, the following condition can be satisfied: 1.20<SAG12/R2<5.50. Therefore, it is favorable for retrieving light at a large field of view so as to achieve a large imaging area and effectively reduce the total length of the imaging lens system. Please refer toFIG.29, which shows a schematic view of SAG12 according to the 1st embodiment of the present disclosure. When the direction from the axial vertex of one surface to the maximum effective radius position of the same surface is facing towards the image side of the imaging lens system, the value of displacement is positive; when the direction from the axial vertex of the surface to the maximum effective radius position of the same surface is facing towards the object side of the imaging lens system, the value of displacement is negative.

When a maximum effective radius of the object-side surface of the first lens element is Y11, and a maximum effective radius of the image-side surface of the fourth lens element is Y42, the following condition can be satisfied: 3.0<Y11/Y42<6.0. Therefore, it is favorable for balancing the aperture diameters on the object side and image side of the imaging lens system so as to obtain a large field of view and a proper light receiving area. Moreover, the following condition can also be satisfied: 3.30<Y11/Y42<4.30. Please refer toFIG.29, which shows a schematic view of Y11 and Y42 according to the 1st embodiment of the present disclosure.

When a maximum value among all axial distances between each of all adjacent lens elements of the imaging lens system is ATmax, and a minimum value among central thicknesses of all lens elements of the imaging lens system is CTmin, the following condition can be satisfied: 3.0<ATmax/CTmin<5.0. Therefore, it is favorable for balancing between the total length of the imaging lens system and the thicknesses of the lens elements so as to improve space utilization.

According to the present disclosure, the aforementioned features and conditions can be utilized in numerous combinations so as to achieve corresponding effects.

According to the present disclosure, the lens elements of the imaging lens system can be made of either glass or plastic material. When the lens elements are made of glass material, the refractive power distribution of the imaging lens system may be more flexible. The glass lens element can either be made by grinding or molding. When the lens elements are made of plastic material, the manufacturing cost can be effectively reduced. Furthermore, surfaces of each lens element can be arranged to be aspheric, which allows more control variables for eliminating aberrations thereof, the required number of the lens elements can be reduced, and the total track length of the imaging lens system can be effectively shortened. The aspheric surfaces may be formed by plastic injection molding or glass molding.

According to the present disclosure, when a lens surface is aspheric, it means that the lens surface has an aspheric shape throughout its optically effective area, or a portion(s) thereof.

According to the present disclosure, one or more of the lens elements' material may optionally include an additive which alters the lens elements' transmittance in a specific range of wavelength for a reduction in unwanted stray light or colour deviation. For example, the additive may optionally filter out light in the wavelength range of 600 nm to 800 nm to reduce excessive red light and/or near infrared light; or may optionally filter out light in the wavelength range of 350 nm to 450 nm to reduce excessive blue light and/or near ultraviolet light from interfering the final image. The additive may be homogeneously mixed with a plastic material to be used in manufacturing a mixed-material lens element by injection molding.

According to the present disclosure, each of an object-side surface and an image-side surface has a paraxial region and an off-axis region. The paraxial region refers to the region of the surface where light rays travel close to the optical axis, and the off-axis region refers to the region of the surface away from the paraxial region. Particularly, unless otherwise stated, when the lens element has a convex surface, it indicates that the surface is convex in the paraxial region thereof; when the lens element has a concave surface, it indicates that the surface is concave in the paraxial region thereof. Moreover, when a region of refractive power or focus of a lens element is not defined, it indicates that the region of refractive power or focus of the lens element is in the paraxial region thereof.

According to the present disclosure, when the parameters (e.g., refractive index and focal length) of the imaging lens system, the identification module and the electronic device are not specifically defined, these parameters may be determined according to the operating wavelength range.

According to the present disclosure, an inflection point is a point on the surface of the lens element at which the surface changes from concave to convex, or vice versa. A critical point is a non-axial point of the lens surface where its tangent is perpendicular to the optical axis.

According to the present disclosure, an image surface of the imaging lens system, based on the corresponding image sensor, can be flat or curved, especially a curved surface being concave facing towards the object side of the imaging lens system.

According to the present disclosure, an image correction unit, such as a field flattener, can be optionally disposed between the lens element closest to the image side of the imaging lens system and the image surface for correction of aberrations such as field curvature. The optical properties of the image correction unit, such as curvature, thickness, index of refraction, position and surface shape (convex or concave surface with spherical, aspheric, diffractive or Fresnel types), can be adjusted according to the design of an image capturing unit. In general, a preferable image correction unit is, for example, a thin transparent element having a concave object-side surface and a planar image-side surface, and the thin transparent element is disposed near the image surface.

According to the present disclosure, the imaging lens system can include at least one stop, such as an aperture stop, a glare stop or a field stop. Said glare stop or said field stop is set for eliminating the stray light and thereby improving image quality thereof.

According to the present disclosure, an aperture stop can be configured as a front stop or a middle stop. A front stop disposed between an imaged object and the first lens element can provide a longer distance between an exit pupil of the imaging lens system and the image surface to produce a telecentric effect, and thereby improves the image-sensing efficiency of an image sensor (for example, CCD or CMOS). A middle stop disposed between the first lens element and the image surface is favorable for enlarging the viewing angle of the imaging lens system and thereby provides a wider field of view for the same.

According to the present disclosure, the imaging lens system can include an aperture control unit. The aperture control unit may be a mechanical component or a light modulator, which can control the size and shape of the aperture through electricity or electrical signals. The mechanical component can include a movable member, such as a blade assembly or a light baffle. The light modulator can include a shielding element, such as a filter, an electrochromic material or a liquid-crystal layer. The aperture control unit controls the amount of incident light or exposure time to enhance the capability of image quality adjustment. In addition, the aperture control unit can be the aperture stop of the present disclosure, which changes the f-number to obtain different image effects, such as the depth of field or lens speed.

According to the above description of the present disclosure, the following specific embodiments are provided for further explanation.

1st Embodiment

FIG.1is a schematic view of an identification module according to the 1st embodiment of the present disclosure.FIG.2is a partially enlarged view ofFIG.1.FIG.3shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 1st embodiment. InFIG.1andFIG.2, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window150, a cover glass160and an image sensor180. The imaging lens system includes, in order from an object side to an image side, a first lens element110, a second lens element120, an aperture stop100, a third lens element130, a stop101, a fourth lens element140and an image surface170. The imaging lens system includes four lens elements (110,120,130and140) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element110with negative refractive power has an object-side surface111being convex in a paraxial region thereof and an image-side surface112being concave in a paraxial region thereof. The first lens element110is made of plastic material and has the object-side surface111and the image-side surface112being both aspheric. The object-side surface111of the first lens element110has two inflection points. The image-side surface112of the first lens element110has two inflection points. The object-side surface111of the first lens element110has at least one convex critical point and at least one concave critical point in an off-axis region thereof.

The second lens element120with positive refractive power has an object-side surface121being convex in a paraxial region thereof and an image-side surface122being concave in a paraxial region thereof. The second lens element120is made of plastic material and has the object-side surface121and the image-side surface122being both aspheric. The object-side surface121of the second lens element120has three inflection points.

The third lens element130with positive refractive power has an object-side surface131being convex in a paraxial region thereof and an image-side surface132being concave in a paraxial region thereof. The third lens element130is made of plastic material and has the object-side surface131and the image-side surface132being both aspheric. The image-side surface132of the third lens element130has two inflection points.

The fourth lens element140with positive refractive power has an object-side surface141being convex in a paraxial region thereof and an image-side surface142being convex in a paraxial region thereof. The fourth lens element140is made of plastic material and has the object-side surface141and the image-side surface142being both aspheric. The object-side surface141of the fourth lens element140has one inflection point.

The optical window150is a light-permeable substrate and located between the imaged object O and the first lens element110(i.e., the object side of the first lens element110), and will not affect the focal length of the imaging lens system. The cover glass160is a glass panel and located between the fourth lens element140and the image surface170(i.e., the image side of the fourth lens element140), and will not affect the focal length of the imaging lens system. The image sensor180is disposed on or near the image surface170of the imaging lens system.

The equation of the aspheric surface profiles of the aforementioned lens elements of the 1st embodiment is expressed as follows:

X⁡(Y)=(Y2/R)/(1+s⁢q⁢r⁢t⁡(1-(1+k)×(Y/R)2))+∑i⁢(Ai)×(Yi),

where,X is the relative distance between a point on the aspheric surface spaced at a distance Y from an optical axis and the tangential plane at the aspheric surface vertex on the optical axis;Y is the vertical distance from the point on the aspheric surface to the optical axis;R is the curvature radius;k is the conic coefficient; andAi is the i-th aspheric coefficient, and in the embodiments, i may be, but is not limited to, 4, 6, 8, 10, 12, 14 and 16.

In the imaging lens system of the image capturing unit according to the 1st embodiment, when a focal length of the imaging lens system is f, an f-number of the imaging lens system in a working distance (in this embodiment, the working distance includes a central thickness of the optical window150) is Fno(work), an f-number of the imaging lens system for imaged object at an infinite distance is Fno(inf.), and an incident angle of a chief ray at a maximum field of view on the object-side surface111of the first lens element110relative to the optical axis is HFOV, these parameters have the following values: f=0.36 millimeters (mm), Fno(work)=1.41, Fno(inf.)=1.37, HFOV=60.4 degrees (deg.).

When a central thickness of the first lens element110is CT1, and a central thickness of the second lens element120is CT2, the following condition is satisfied: CT1/CT2=3.87.

When a maximum value among all axial distances between each of all adjacent lens elements of the imaging lens system is ATmax, and a minimum value among central thicknesses of all lens elements of the imaging lens system is CTmin, the following condition is satisfied: ATmax/CTmin=3.30. In this embodiment, an axial distance between two adjacent lens elements is an air gap in a paraxial region between the two adjacent lens elements. ATmax is equal to an axial distance between the first lens element110and the second lens element120, and CTmin is equal to the central thickness of the second lens element120.

When a curvature radius of the object-side surface141of the fourth lens element140is R7, and a curvature radius of the image-side surface142of the fourth lens element140is R8, the following condition is satisfied: (R7+R8)/(R7−R8)=−0.23.

When a focal length of the first lens element110is f1, and a focal length of the second lens element120is f2, the following condition is satisfied: |f1/f2|=0.14.

When the focal length of the second lens element120is f2, and a focal length of the fourth lens element140is f4, the following condition is satisfied: |f4/f2|=0.11.

When the focal length of the imaging lens system is f, the focal length of the first lens element110is f1, the focal length of the second lens element120is f2, and a focal length of the third lens element130is f3, the following condition is satisfied: |f/f1|−|f/f2|−|f/f3|=0.33.

When the focal length of the imaging lens system is f, and an entrance pupil diameter of the imaging lens system is EPD, the following condition is satisfied: f/EPD=1.37.

When the central thickness of the optical window150is CTf, and an axial distance between the object-side surface111of the first lens element110and the image-side surface142of the fourth lens element140is TD, the following condition is satisfied: CTf/TD=0.50.

When an axial distance between the imaged object O and the object-side surface111of the first lens element110is OL, the central thickness of the optical window150is CTf, an axial distance between the image-side surface142of the fourth lens element140and the image surface170is BL, and a central thickness of the cover glass160is CTr, the following condition is satisfied: (OL−CTf)/(BL−CTr)=0.90.

When an axial distance between the aperture stop100and the image surface170is SL, and an axial distance between the object-side surface111of the first lens element110and the image surface170is TL, the following condition is satisfied: SL/TL=0.42.

When the axial distance between the object-side surface111of the first lens element110and the image surface170is TL, and the focal length of the imaging lens system is f, the following condition is satisfied: TL/f=10.17.

When a maximum image height of the imaging lens system is ImgH, and the focal length of the imaging lens system is f, the following condition is satisfied: ImgH/f=1.60.

When the axial distance between the object-side surface111of the first lens element110and the image surface170is TL, the following condition is satisfied: TL=3.69 [mm].

When the axial distance between the object-side surface111of the first lens element110and the image surface170is TL, and the maximum image height of the imaging lens system is ImgH, the following condition is satisfied: TL/ImgH=6.36.

When a maximum effective radius of the image-side surface112of the first lens element110is Y12, and a curvature radius of the image-side surface112of the first lens element110is R2, the following condition is satisfied: Y12/R2=2.26.

When a displacement in parallel with the optical axis from an axial vertex to a maximum effective radius position on the image-side surface112of the first lens element110is SAG12, and the curvature radius of the image-side surface112of the first lens element110is R2, the following condition is satisfied: SAG12/R2=1.62.

When a maximum value among Abbe numbers of all lens elements of the imaging lens system is Vmax, and a minimum value among Abbe numbers of all lens elements of the imaging lens system is Vmin, the following condition is satisfied: Vmax−Vmin=0. In this embodiment, the Abbe numbers of the first through fourth lens elements (110,120,130and140) are the same, so Vmax=Vmin.

When the focal length of the imaging lens system is f, the entrance pupil diameter of the imaging lens system is EPD, and the incident angle of the chief ray at the maximum field of view on the object-side surface111of the first lens element110relative to the optical axis is HFOV, the following condition is satisfied: f/[EPD×tan(HFOV)]=0.78.

When a vertical distance between the non-axial convex critical point on the object-side surface111of the first lens element110and the optical axis is Y11cx, and a vertical distance between the non-axial concave critical point on the object-side surface111of the first lens element110and the optical axis is Y11ca, the following condition is satisfied: Y11cx/Y11ca=1.95.

When a maximum effective radius of the object-side surface111of the first lens element110is Y11, and a maximum effective radius of the image-side surface142of the fourth lens element140is Y42, the following condition is satisfied: Y11/Y42=3.88.

The detailed optical data of the 1st embodiment are shown in Table 1 and the aspheric surface data are shown in Table 2 below.

TABLE 11st Embodimentf = 0.36 mm, Fno(work) = 1.41, Fno(inf.) = 1.37, HFOV = 60.4 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.5123Lens 12.975(ASP)0.861Plastic1.54856.0−0.8540.362(ASP)0.7345Lens 21.410(ASP)0.222Plastic1.54856.06.0462.321(ASP)0.3397Ape. StopPlano−0.0298Lens 32.796(ASP)0.270Plastic1.54856.010.3695.324(ASP)0.07310StopPlano−0.01511Lens 40.520(ASP)0.517Plastic1.54856.00.6712−0.827(ASP)0.30013Cover GlassPlano0.145Glass1.52064.2—14Plano0.27115ImagePlano—Note:Reference wavelength is 525 nm. The working distance is the axial distance (2.012 mm) between the imaged object O (Surface 0) and the object-side surface 111 (Surface 3). An effective radius of the stop 101 (Surface 10) is 0.400 mm.

TABLE 2Aspheric CoefficientsSurface #3456k =−7.5615E−02−9.9014E−01−8.0158E+007.6369E+00A4 =−3.5499E−01−2.2609E+00−2.7080E+00−1.5749E+00A6 =2.8955E−014.5614E+001.4535E+013.4354E+01A8 =−1.2466E−01−1.7090E+01−4.6580E+00−4.7998E+01A10 =3.0717E−028.5975E+01−2.3345E+02−1.3153E+03A12 =−4.1130E−03−1.9869E+027.8209E+021.4188E+04A14 =2.5076E−041.9695E+02−8.0514E+02−3.6655E+04A16 =−3.5065E−06−6.9868E+01——Surface #891112k =4.7699E+017.5880E+00−3.1065E−01−3.5020E−01A4 =4.4002E−01−8.9169E+00−7.7521E+001.7289E+00A6 =1.3943E+012.0323E+029.2786E+01−1.8428E+01A8 =−1.2654E+02−3.7936E+03−9.7450E+021.8622E+02A10 =1.1422E+034.9201E+046.5932E+03−1.1973E+03A12 =−4.8404E+03−3.8255E+05−2.7399E+044.2000E+03A14 =6.4928E+031.6023E+066.2224E+04−7.7161E+03A16 =—−2.7040E+06−5.8669E+045.8027E+03

In Table 1, the curvature radius, the thickness and the focal length are shown in millimeters (mm). Surface numbers 0-15 represent the surfaces sequentially arranged from the object side to the image side along the optical axis. In Table 2, k represents the conic coefficient of the equation of the aspheric surface profiles. A4-A16 represent the aspheric coefficients ranging from the 4th order to the 16th order. The tables presented below for each embodiment are the corresponding schematic parameter and aberration curves, and the definitions of the tables are the same as Table 1 and Table 2 of the 1st embodiment. Therefore, an explanation in this regard will not be provided again.

2nd Embodiment

FIG.4is a schematic view of an identification module according to the 2nd embodiment of the present disclosure.FIG.5is a partially enlarged view ofFIG.4.FIG.6shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 2nd embodiment. InFIG.4andFIG.5, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window250, a cover glass260and an image sensor280. The imaging lens system includes, in order from an object side to an image side, a first lens element210, a second lens element220, an aperture stop200, a third lens element230, a stop201, a fourth lens element240and an image surface270. The imaging lens system includes four lens elements (210,220,230and240) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element210with negative refractive power has an object-side surface211being convex in a paraxial region thereof and an image-side surface212being concave in a paraxial region thereof. The first lens element210is made of plastic material and has the object-side surface211and the image-side surface212being both aspheric. The object-side surface211of the first lens element210has two inflection points. The image-side surface212of the first lens element210has two inflection points. The object-side surface211of the first lens element210has at least one convex critical point and at least one concave critical point in an off-axis region thereof.

The second lens element220with positive refractive power has an object-side surface221being convex in a paraxial region thereof and an image-side surface222being concave in a paraxial region thereof. The second lens element220is made of plastic material and has the object-side surface221and the image-side surface222being both aspheric. The object-side surface221of the second lens element220has one inflection point.

The third lens element230with positive refractive power has an object-side surface231being convex in a paraxial region thereof and an image-side surface232being convex in a paraxial region thereof. The third lens element230is made of plastic material and has the object-side surface231and the image-side surface232being both aspheric. The image-side surface232of the third lens element230has one inflection point.

The fourth lens element240with positive refractive power has an object-side surface241being convex in a paraxial region thereof and an image-side surface242being convex in a paraxial region thereof. The fourth lens element240is made of plastic material and has the object-side surface241and the image-side surface242being both aspheric. The object-side surface241of the fourth lens element240has one inflection point.

The optical window250is a light-permeable substrate and located between the imaged object O and the first lens element210(i.e., the object side of the first lens element210), and will not affect the focal length of the imaging lens system. The cover glass260is a glass panel and located between the fourth lens element240and the image surface270(i.e., the image side of the fourth lens element240), and will not affect the focal length of the imaging lens system. The image sensor280is disposed on or near the image surface270of the imaging lens system.

The detailed optical data of the 2nd embodiment are shown in Table 3 and the aspheric surface data are shown in Table 4 below.

TABLE 32nd Embodimentf = 0.35 mm, Fno(work) = 1.38, Fno(inf.) = 1.34, HFOV = 59.7 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.5113Lens 12.964(ASP)0.851Plastic1.54856.0−0.8340.353(ASP)0.7525Lens 21.593(ASP)0.205Plastic1.54856.08.8562.264(ASP)0.3137Ape. StopPlano−0.0218Lens 32.850(ASP)0.289Plastic1.54856.04.479−16.895(ASP)0.05910StopPlano−0.00611Lens 40.567(ASP)0.531Plastic1.54856.00.7212−0.861(ASP)0.30013Cover GlassPlano0.145Glass1.52064.2—14Plano0.27115ImagePlanoNote:Reference wavelength is 525 nm. The working distance is the axial distance (2.011 mm) between the imaged object O (Surface 0) and the object-side surface 211 (Surface 3). An effective radius of the stop 201 (Surface 10) is 0.400 mm.

TABLE 4Aspheric CoefficientsSurface #3456k =−2.4632E−01−1.0000E+00−1.5610E+010.0000E+00A4 =−3.5476E−01−2.2911E+00−2.9412E+00−1.7385E+00A6 =2.8937E−014.5667E+001.4187E+013.3417E+01A8 =−1.2460E−01−1.7053E+01−2.6595E+00−2.1047E+01A10 =3.0732E−028.5964E+01−2.3326E+02−1.3828E+03A12 =−4.1114E−03−1.9870E+027.8209E+021.4188E+04A14 =2.5072E−041.9695E+02−8.0514E+02−3.6655E+04A16 =−3.5636E−06−6.9868E+01——Surface #891112k =0.0000E+000.0000E+00−3.1172E−013.0098E−01A4 =8.7863E−01−8.1284E+00−7.0331E+001.8012E+00A6 =1.5183E+011.9943E+029.0184E+01−1.7831E+01A8 =−1.3192E+02−3.7871E+03−9.6440E+021.8493E+02A10 =1.2198E+034.9236E+046.5849E+03−1.1931E+03A12 =−4.8404E+03−3.8255E+05−2.7399E+044.2005E+03A14 =6.4928E+031.6023E+066.2224E+04−7.7161E+03A16 =—−2.7040E+06−5.8669E+045.8027E+03

In the 2nd embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 2nd embodiment, so an explanation in this regard will not be provided again.

Moreover, these parameters can be calculated from Table 3 and Table 4 as the following values and satisfy the following conditions:

2nd Embodimentf [mm]0.35(OL − CTf)/(BL − CTr)0.89Fno (work)1.38SL/TL0.43Fno (inf.)1.34TL/f10.41HFOV [deg.]59.7ImgH/f1.64CT1/CT24.15TL [mm]3.69ATmax/CTmin3.67TL/ImgH6.36(R7 + R8)/(R7 − R8)−0.21Y12/R22.31|f1/f2|0.09SAG12/R21.66|f4/f2|0.08Vmax − Vmin0|f/f1| − |f/f2| − |f/f3|0.31f/[EPD × tan (HFOV)]0.78f/EPD1.34Y11cx/Y11ca1.97CTf/TD0.50Y11/Y423.85

3rd Embodiment

FIG.7is a schematic view of an identification module according to the 3rd embodiment of the present disclosure.FIG.8is a partially enlarged view ofFIG.7.FIG.9shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 3rd embodiment. InFIG.7andFIG.8, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window350, a cover glass360and an image sensor380. The imaging lens system includes, in order from an object side to an image side, a first lens element310, a second lens element320, an aperture stop300, a third lens element330, a stop301, a fourth lens element340and an image surface370. The imaging lens system includes four lens elements (310,320,330and340) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element310with negative refractive power has an object-side surface311being convex in a paraxial region thereof and an image-side surface312being concave in a paraxial region thereof. The first lens element310is made of plastic material and has the object-side surface311and the image-side surface312being both aspheric. The object-side surface311of the first lens element310has two inflection points. The image-side surface312of the first lens element310has two inflection points.

The second lens element320with positive refractive power has an object-side surface321being convex in a paraxial region thereof and an image-side surface322being convex in a paraxial region thereof. The second lens element320is made of plastic material and has the object-side surface321and the image-side surface322being both aspheric. The object-side surface321of the second lens element320has one inflection point. The image-side surface322of the second lens element320has one inflection point.

The third lens element330with positive refractive power has an object-side surface331being convex in a paraxial region thereof and an image-side surface332being convex in a paraxial region thereof. The third lens element330is made of plastic material and has the object-side surface331and the image-side surface332being both aspheric. The image-side surface332of the third lens element330has one inflection point.

The fourth lens element340with positive refractive power has an object-side surface341being convex in a paraxial region thereof and an image-side surface342being convex in a paraxial region thereof. The fourth lens element340is made of plastic material and has the object-side surface341and the image-side surface342being both aspheric. The object-side surface341of the fourth lens element340has two inflection points.

The optical window350is a light-permeable substrate and located between the imaged object O and the first lens element310(i.e., the object side of the first lens element310), and will not affect the focal length of the imaging lens system. The cover glass360is a glass panel and located between the fourth lens element340and the image surface370(i.e., the image side of the fourth lens element340), and will not affect the focal length of the imaging lens system. The image sensor380is disposed on or near the image surface370of the imaging lens system.

The detailed optical data of the 3rd embodiment are shown in Table 5 and the aspheric surface data are shown in Table 6 below.

TABLE 53rd Embodimentf = 0.38 mm, Fno(work) = 1.42, Fno(inf.) = 1.38, HFOV = 64.1 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.0993Lens 10.806(ASP)0.809Plastic1.53855.9−0.9740.206(ASP)1.0045Lens 212.013(ASP)0.210Plastic1.54856.010.856−11.682(ASP)0.2767Ape. StopPlano−0.0198Lens 33.272(ASP)0.295Plastic1.54856.01.929−1.501(ASP)0.06610StopPlano0.01211Lens 40.886(ASP)0.520Plastic1.54856.00.8812−0.834(ASP)0.30013Cover GlassPlano0.210Glass1.52064.2—14Plano0.21815ImagePlano—Note:Reference wavelength is 525 nm. The working distance is the axial distance (1.599 mm) between the imaged object O (Surface 0) and the object-side surface 311 (Surface 3). An effective radius of the stop 301 (Surface 10) is 0.430 mm.

TABLE 6Aspheric CoefficientsSurface #3456k =−1.0000E+00−1.0000E+000.0000E+000.0000E+00A4 =−7.1010E−01−7.1658E+00−2.5274E+00−1.0043E+00A6 =4.5784E−016.0799E+011.6545E+011.8231E+01A8 =−1.7508E−01−4.0241E+02−4.7196E+013.4024E+02A10 =4.2210E−021.5021E+033.8518E+01−6.3125E+03A12 =−6.3312E−03−2.9641E+032.4543E+014.3577E+04A14 =5.4835E−042.8882E+03—−9.7108E+04A16 =−2.1283E−05−1.0928E+03——Surface #891112k =0.0000E+00−1.9971E+01−4.5571E−01−2.7608E−01A4 =1.0773E+00−2.4786E+00−2.6405E+008.5451E−01A6=6.7775E+003.2120E+001.5718E+01−1.0325E+01A8 =−4.7767E+015.1290E+02−9.8604E+011.0064E+02A10 =1.0749E+03−7.3955E+033.4439E+02−6.6266E+02A12 =−4.6925E+034.6490E+04−4.7994E+022.3749E+03A14 =—−9.6249E+041.2446E+02−4.3735E+03A16 =———3.2816E+03

In the 3rd embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 3rd embodiment, so an explanation in this regard will not be provided again.

Moreover, these parameters can be calculated from Table 5 and Table 6 as the following values and satisfy the following conditions:

3rd Embodimentf [mm]0.38(OL − CTf)/(BL − CTr)0.19Fno (work)1.42SL/TL0.41Fno (inf.)1.38TL/f10.14HFOV [deg.]64.1ImgH/f1.51CT1/CT23.85TL [mm]3.90ATmax/CTmin4.78TL/ImgH6.73(R7 + R8)/(R7 − R8)0.03Y12/R23.66|f1/f2|0.09SAG12/R24.07|f4/f2|0.08Vmax − Vmin0.1|f/f1| − |f/f2| − |f/f3|0.16f/[EPD × tan (HFOV)]0.67f/EPD1.38Y11cx/Y11ca—CTf/TD0.47Y11/Y423.77

4th Embodiment

FIG.10is a schematic view of an identification module according to the 4th embodiment of the present disclosure.FIG.11is a partially enlarged view ofFIG.10.FIG.12shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 4th embodiment. InFIG.10andFIG.11, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window450, a cover glass460and an image sensor480. The imaging lens system includes, in order from an object side to an image side, a first lens element410, a second lens element420, an aperture stop400, a third lens element430, a stop401, a fourth lens element440and an image surface470. The imaging lens system includes four lens elements (410,420,430and440) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element410with negative refractive power has an object-side surface411being convex in a paraxial region thereof and an image-side surface412being concave in a paraxial region thereof. The first lens element410is made of plastic material and has the object-side surface411and the image-side surface412being both aspheric. The object-side surface411of the first lens element410has two inflection points. The image-side surface412of the first lens element410has two inflection points.

The second lens element420with positive refractive power has an object-side surface421being concave in a paraxial region thereof and an image-side surface422being convex in a paraxial region thereof. The second lens element420is made of plastic material and has the object-side surface421and the image-side surface422being both aspheric. The object-side surface421of the second lens element420has two inflection points. The image-side surface422of the second lens element420has one inflection point.

The third lens element430with positive refractive power has an object-side surface431being convex in a paraxial region thereof and an image-side surface432being convex in a paraxial region thereof. The third lens element430is made of plastic material and has the object-side surface431and the image-side surface432being both aspheric. The image-side surface432of the third lens element430has one inflection point.

The fourth lens element440with positive refractive power has an object-side surface441being convex in a paraxial region thereof and an image-side surface442being convex in a paraxial region thereof. The fourth lens element440is made of plastic material and has the object-side surface441and the image-side surface442being both aspheric. The object-side surface441of the fourth lens element440has two inflection points.

The optical window450is a light-permeable substrate and located between the imaged object O and the first lens element410(i.e., the object side of the first lens element410), and will not affect the focal length of the imaging lens system. The cover glass460is a glass panel and located between the fourth lens element440and the image surface470(i.e., the image side of the fourth lens element440), and will not affect the focal length of the imaging lens system. The image sensor480is disposed on or near the image surface470of the imaging lens system.

The detailed optical data of the 4th embodiment are shown in Table 7 and the aspheric surface data are shown in Table 8 below.

TABLE 74th Embodimentf = 0.38 mm, Fno(work) = 1.42, Fno(inf.) = 1.37, HFOV = 62.3 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.1003Lens 10.789(ASP)0.793Plastic1.53855.9−0.9940.206(ASP)0.9765Lens 2−4.243(ASP)0.210Plastic1.54856.015.316−2.867(ASP)0.2987Ape. StopPlano0.0138Lens 31.568(ASP)0.309Plastic1.54856.02.379−7.020(ASP)0.07310StopPlano−0.01311Lens 40.701(ASP)0.514Plastic1.54856.00.8112−0.888(ASP)0.30013Cover GlassPlano0.210Glass1.52064.2—14Plano0.21715ImagePlano—Note:Reference wavelength is 525 nm. The working distance is the axial distance (1.600 mm) between the imaged object O (Surface 0) and the object-side surface 411 (Surface 3). An effective radius of the stop 401 (Surface 10) is 0.475 mm.

TABLE 8Aspheric CoefficientsSurface #3456k =−1.0000E+00−1.0000E+001.2908E+010.0000E+00A4 =−6.6691E−01−5.7225E+00−2.7807E+00−1.0284E+00A6 =3.9285E−014.0347E+011.1078E+01−4.4899E+00A8 =−1.2988E−01−2.6066E+02−9.0704E+004.2219E+02A10 =2.4114E−029.7612E+02−1.6746E+01−4.7977E+03A12 =−2.0823E−03−1.9615E+032.2700E+012.4592E+04A14 =6.9331E−061.9725E+03—−4.2388E+04A16 =7.8490E−06−7.7985E+02——Surface #891112k =−1.9279E+004.0016E+01−1.0433E+001.4762E−01A4 =−7.3903E−01−5.2994E+00−4.9462E+001.1745E+00A6 =2.3421E+014.4008E+013.5206E+01−1.0600E+01A8 =−2.5161E+02−1.2204E+02−1.6614E+027.4480E+01A10 =1.7697E+03−5.2678E+024.3339E+02−2.9439E+02A12 =−4.5973E+035.2746E+03−5.3776E+025.5759E+02A14 =—−8.5277E+032.2659E+02−4.1030E+02

In the 4th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 4th embodiment, so an explanation in this regard will not be provided again.

Moreover, these parameters can be calculated from Table 7 and Table 8 as the following values and satisfy the following conditions:

4th Embodimentf [mm]0.38(OL − CTf)/(BL − CTr)0.19Fno (work)1.42SL/TL0.42Fno (inf.)1.37TL/f10.19HFOV [deg.]62.3ImgH/f1.52CT1/CT23.78TL [mm]3.90ATmax/CTmin4.65TL/ImgH6.72(R7 + R8)/(R7 − R8)−0.12Y12/R23.63|f1/f2|0.06SAG12/R23.90|f4/f2|0.05Vmax − Vmin0.1|f/f1| − |f/f2| − |f/f3|0.20f/[EPD × tan (HFOV)]0.72f/EPD1.37Y11cx/Y11ca—CTf/TD0.47Y11/Y423.60

5th Embodiment

FIG.13is a schematic view of an identification module according to the 5th embodiment of the present disclosure.FIG.14is a partially enlarged view ofFIG.13.FIG.15shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 5th embodiment. InFIG.13andFIG.14, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window550, a cover glass560and an image sensor580. The imaging lens system includes, in order from an object side to an image side, a first lens element510, a second lens element520, an aperture stop500, a third lens element530, a stop501, a fourth lens element540and an image surface570. The imaging lens system includes four lens elements (510,520,530and540) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element510with negative refractive power has an object-side surface511being convex in a paraxial region thereof and an image-side surface512being concave in a paraxial region thereof. The first lens element510is made of plastic material and has the object-side surface511and the image-side surface512being both aspheric. The object-side surface511of the first lens element510has two inflection points. The image-side surface512of the first lens element510has one inflection point.

The second lens element520with negative refractive power has an object-side surface521being concave in a paraxial region thereof and an image-side surface522being convex in a paraxial region thereof. The second lens element520is made of plastic material and has the object-side surface521and the image-side surface522being both aspheric. The object-side surface521of the second lens element520has two inflection points. The image-side surface522of the second lens element520has one inflection point.

The third lens element530with positive refractive power has an object-side surface531being convex in a paraxial region thereof and an image-side surface532being convex in a paraxial region thereof. The third lens element530is made of plastic material and has the object-side surface531and the image-side surface532being both aspheric. The image-side surface532of the third lens element530has one inflection point.

The fourth lens element540with positive refractive power has an object-side surface541being convex in a paraxial region thereof and an image-side surface542being convex in a paraxial region thereof. The fourth lens element540is made of plastic material and has the object-side surface541and the image-side surface542being both aspheric. The object-side surface541of the fourth lens element540has one inflection point.

The optical window550is a light-permeable substrate and located between the imaged object O and the first lens element510(i.e., the object side of the first lens element510), and will not affect the focal length of the imaging lens system. The cover glass560is a glass panel and located between the fourth lens element540and the image surface570(i.e., the image side of the fourth lens element540), and will not affect the focal length of the imaging lens system. The image sensor580is disposed on or near the image surface570of the imaging lens system.

The detailed optical data of the 5th embodiment are shown in Table 9 and the aspheric surface data are shown in Table 10 below.

TABLE 95th Embodimentf = 0.38 mm, Fno(work) = 1.41, Fno(inf.) = 1.36, HFOV = 62.7 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.0983Lens 10.872(ASP)0.808Plastic1.53855.9−1.0340.229(ASP)0.9825Lens 2−1.298(ASP)0.210Plastic1.54856.0−5.916−2.293(ASP)0.2707Ape. StopPlano−0.0408Lens 30.977(ASP)0.306Plastic1.54856.01.739−28.421(ASP)0.08710StopPlano0.03411Lens 40.731(ASP)0.517Plastic1.54856.00.8112−0.842(ASP)0.30013Cover GlassPlano0.210Glass1.52064.2—14Plano0.21815ImagePlano—Note:Reference wavelength is 525 nm. The working distance is the axial distance (1.598 mm) between the imaged object O (Surface 0) and the object-side surface 511 (Surface 3). An effective radius of the stop 501 (Surface 10) is 0.455 mm.

TABLE 10Aspheric CoefficientsSurface #3456k =−1.0000E+00−1.0000E+000.0000E+000.0000E+00A4 =−5.8079E−01−3.6336E+00−3.8565E+00−2.6447E+00A6 =3.4199E−011.3790E+013.2752E+014.3307E+01A8 =−1.2047E−01−7.2959E+01−1.0978E+02−1.8621E+02A10 =2.6841E−022.4425E+021.8404E+021.9396E+02A12 =−3.6955E−03−4.3479E+02−1.2864E+025.2436E+03A14 =2.8889E−043.8523E+02—−1.5422E+04A16 =−9.5373E−06−1.3441E+02——Surface #891112k =2.7911E+000.0000E+00−1.0000E+000.0000E+00A4 =−1.9999E+00−3.9808E+00−3.2081E+001.1945E+00A6 =2.2029E+012.2378E+011.4196E+01−7.4495E+00A8 =−1.6596E+025.8115E+01−5.6957E+014.1097E+01A10 =1.1270E+03−1.6273E+031.8505E+02−1.2863E+02A12 =−3.1487E+031.0570E+04−3.8416E+021.8953E+02A14 =—−1.8076E+043.4631E+02−1.1358E+02

In the 5th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 5th embodiment, so an explanation in this regard will not be provided again.

Moreover, these parameters can be calculated from Table 9 and Table 10 as the following values and satisfy the following conditions:

5th Embodimentf [mm]0.38(OL − CTf)/(BL − CTr)0.19Fno (work)1.41SL/TL0.42Fno (inf.)1.36TL/f10.39HFOV [deg.]62.7ImgH/f1.54CT1/CT23.85TL [mm]3.90ATmax/CTmin4.68TL/ImgH6.73(R7 + R8)/(R7 − R8)−0.07Y12/R23.36|f1/f2|0.17SAG12/R23.29|f4/f2|0.14Vmax − Vmin0.1|f/f1| − |f/f2| − |f/f3|0.08f/[EPD × tan (HFOV)]0.70f/EPD1.36Y11cx/Y11ca—CTf/TD0.47Y11/Y423.60

6th Embodiment

FIG.16is a schematic view of an identification module according to the 6th embodiment of the present disclosure.FIG.17is a partially enlarged view ofFIG.16.FIG.18shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 6th embodiment. InFIG.16andFIG.17, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window650, a cover glass660and an image sensor680. The imaging lens system includes, in order from an object side to an image side, a first lens element610, a second lens element620, an aperture stop600, a third lens element630, a stop601, a fourth lens element640and an image surface670. The imaging lens system includes four lens elements (610,620,630and640) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element610with negative refractive power has an object-side surface611being convex in a paraxial region thereof and an image-side surface612being concave in a paraxial region thereof. The first lens element610is made of plastic material and has the object-side surface611and the image-side surface612being both aspheric. The object-side surface611of the first lens element610has two inflection points. The image-side surface612of the first lens element610has one inflection point. The object-side surface611of the first lens element610has at least one convex critical point and at least one concave critical point in an off-axis region thereof.

The second lens element620with positive refractive power has an object-side surface621being convex in a paraxial region thereof and an image-side surface622being concave in a paraxial region thereof. The second lens element620is made of plastic material and has the object-side surface621and the image-side surface622being both aspheric. The object-side surface621of the second lens element620has three inflection points.

The third lens element630with positive refractive power has an object-side surface631being convex in a paraxial region thereof and an image-side surface632being convex in a paraxial region thereof. The third lens element630is made of plastic material and has the object-side surface631and the image-side surface632being both aspheric. The image-side surface632of the third lens element630has one inflection point.

The fourth lens element640with positive refractive power has an object-side surface641being convex in a paraxial region thereof and an image-side surface642being convex in a paraxial region thereof. The fourth lens element640is made of plastic material and has the object-side surface641and the image-side surface642being both aspheric. The object-side surface641of the fourth lens element640has one inflection point.

The optical window650is a light-permeable substrate and located between the imaged object O and the first lens element610(i.e., the object side of the first lens element610), and will not affect the focal length of the imaging lens system. The cover glass660is a glass panel and located between the fourth lens element640and the image surface670(i.e., the image side of the fourth lens element640), and will not affect the focal length of the imaging lens system. The image sensor680is disposed on or near the image surface670of the imaging lens system.

The detailed optical data of the 6th embodiment are shown in Table 11 and the aspheric surface data are shown in Table 12 below.

TABLE 116th Embodimentf = 0.35 mm, Fno(work) = 1.38, Fno(inf.) = 1.34, HFOV = 58.6 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.5103Lens 13.142(ASP)0.866Plastic1.54856.0−0.8540.365(ASP)0.7585Lens 22.160(ASP)0.209Plastic1.57237.47.2364.365(ASP)0.3027Ape. StopPlano−0.0198Lens 34.887(ASP)0.285Plastic1.54856.04.509−4.864(ASP)0.07010StopPlano−0.01611Lens 40.591(ASP)0.522Plastic1.54856.00.7312−0.847(ASP)0.30013Cover GlassPlano0.145Glass1.52064.2—14Plano0.26815ImagePlano—Note:Reference wavelength is 525 nm. The working distance is the axial distance (2.010 mm) between the imaged object O (Surface 0) and the object-side surface 611 (Surface 3). An effective radius of the stop 601 (Surface 10) is 0.395 mm.

TABLE 12Aspheric CoefficientsSurface #3456k =−1.9583E−01−9.9450E−011.8639E+005.7217E+01A4 =−3.3330E−01−2.3095E+00−3.4291E+00−1.7041E+00A6 =2.6868E−016.1740E+002.1228E+013.6669E+01A8 =−1.1307E−01−2.7456E+01−3.7151E+012.7261E+01A10 =2.6970E−021.1973E+02−1.3277E+02−2.6129E+03A12 =−3.3941E−03−2.5594E+025.8767E+022.4738E+04A14 =1.7598E−042.4480E+02−6.3456E+02−6.4476E+04A16 =−2.7449E−07−8.5287E+01——Surface #891112k =−1.7048E+019.9000E+01−3.4625E−015.2768E−01A4 =9.5519E−01−7.0206E+00−6.1076E+001.8459E+00A6 =2.0661E+011.8408E+027.6537E+01−1.6878E+01A8 =−2.2311E+02−3.6802E+03−8.0568E+021.7683E+02A10 =2.1224E+034.9831E+045.3540E+03−1.1663E+03A12 =−9.6686E+03−3.9846E+05−2.1547E+044.1843E+03A14 =1.7095E+041.7039E+064.7214E+04−7.7606E+03A16 =—−2.9215E+06−4.2953E+045.8441E+03

In the 6th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 6th embodiment, so an explanation in this regard will not be provided again.

Moreover, these parameters can be calculated from Table 11 and Table 12 as the following values and satisfy the following conditions:

6th Embodimentf [mm]0.35(OL − CTf)/(BL − CTr)0.90Fno (work)1.38SL/TL0.42Fno (inf.)1.34TL/f10.41HFOV [deg.]58.6ImgH/f1.55CT1/CT24.15TL [mm]3.69ATmax/CTmin3.64TL/ImgH6.70(R7 + R8)/(R7 − R8)−0.18Y12/R22.13|f1/f2|0.12SAG12/R21.54|f4/f2|0.10Vmax − Vmin18.5|f/f1| − |f/f2| − |f/f3|0.29f/[EPD × tan (HFOV)]0.82f/EPD1.34Y11cx/Y11ca1.95CTf/TD0.50Y11/Y423.85

7th Embodiment

FIG.19is a schematic view of an identification module according to the 7th embodiment of the present disclosure.FIG.20is a partially enlarged view ofFIG.19.FIG.21shows, in order from left to right, spherical aberration curves, astigmatic field curves and a distortion curve of the image capturing unit according to the 7th embodiment. InFIG.19andFIG.20, the identification module includes the imaging lens system (its reference numeral is omitted) of the present disclosure, an optical window750, a cover glass760and an image sensor780. The imaging lens system includes, in order from an object side to an image side, a first lens element710, a second lens element720, an aperture stop700, a third lens element730, a stop701, a fourth lens element740and an image surface770. The imaging lens system includes four lens elements (710,720,730and740) with no additional lens element disposed between each of the adjacent four lens elements.

The first lens element710with negative refractive power has an object-side surface711being convex in a paraxial region thereof and an image-side surface712being concave in a paraxial region thereof. The first lens element710is made of plastic material and has the object-side surface711and the image-side surface712being both aspheric. The object-side surface711of the first lens element710has two inflection points. The image-side surface712of the first lens element710has three inflection points. The object-side surface711of the first lens element710has at least one convex critical point and at least one concave critical point in an off-axis region thereof.

The second lens element720with positive refractive power has an object-side surface721being concave in a paraxial region thereof and an image-side surface722being convex in a paraxial region thereof. The second lens element720is made of plastic material and has the object-side surface721and the image-side surface722being both aspheric. The object-side surface721of the second lens element720has two inflection points. The image-side surface722of the second lens element720has one inflection point.

The third lens element730with positive refractive power has an object-side surface731being convex in a paraxial region thereof and an image-side surface732being convex in a paraxial region thereof. The third lens element730is made of plastic material and has the object-side surface731and the image-side surface732being both aspheric. The image-side surface732of the third lens element730has one inflection point.

The fourth lens element740with positive refractive power has an object-side surface741being convex in a paraxial region thereof and an image-side surface742being convex in a paraxial region thereof. The fourth lens element740is made of plastic material and has the object-side surface741and the image-side surface742being both aspheric. The object-side surface741of the fourth lens element740has two inflection points. The image-side surface742of the fourth lens element740has one inflection point.

The optical window750is a light-permeable substrate and located between the imaged object O and the first lens element710(i.e., the object side of the first lens element710), and will not affect the focal length of the imaging lens system. The cover glass760is a glass panel and located between the fourth lens element740and the image surface770(i.e., the image side of the fourth lens element740), and will not affect the focal length of the imaging lens system. The image sensor780is disposed on or near the image surface770of the imaging lens system.

The detailed optical data of the 7th embodiment are shown in Table 13 and the aspheric surface data are shown in Table 14 below.

TABLE 137th Embodimentf = 0.35 mm, Fno(work) = 1.36, Fno(inf.) = 1.32, HFOV = 60.2 deg.Surface #Curvature RadiusThicknessMaterialIndexAbbe #Focal Length0ObjectPlano0.0001Optical WindowPlano1.500—1.52064.2—2Plano0.5233Lens 10.834(ASP)0.464Plastic1.53855.9−1.1140.280(ASP)0.9555Lens 2−4.837(ASP)0.224Plastic1.54856.014.016−3.016(ASP)0.3157Ape. StopPlano−0.0078Lens 36.358(ASP)0.255Plastic1.54856.02.669−1.861(ASP)0.04710StopPlano0.00911Lens 40.810(ASP)0.523Plastic1.54856.00.7612−0.669(ASP)0.30013Cover GlassPlano0.145Glass1.52064.2—14Plano0.24715ImagePlano—Note:Reference wavelength is 525 nm. The working distance is the axial distance (2.023 mm) between the imaged object O (Surface 0) and the object-side surface 711 (Surface 3). An effective radius of the stop 701 (Surface 10) is 0.390 mm.

TABLE 14Aspheric CoefficientsSurface #3456k =−1.0000E+00−1.0000E+000.0000E+000.0000E+00A4 =−1.5120E+00−3.6890E+00−5.2868E+00−7.2318E+00A6 =1.8619E+00−8.3761E−014.0167E+011.5824E+02A8 =−1.3707E+003.0868E+01−1.1558E+02−1.7664E+03A10 =6.4843E−01−8.4443E+011.2203E+011.4694E+04A12 =−1.9812E−011.1594E+027.9599E+02−8.3943E+04A14=3.7781E−02−8.9738E+01−1.9129E+033.0705E+05A16 =−4.0814E−033.7135E+011.4446E+03−5.0104E+05A18 =1.9025E−04−6.3720E+00——Surface #891112k =0.0000E+001.3901E+01−8.3036E+00−2.8791E−01A4 =7.8086E−01−7.4505E−01−1.9964E+005.4660E+00A6 =2.0753E+019.1144E+017.1667E+01−1.1701E+02A8 =1.0091E+03−3.3947E+03−1.3660E+031.7291E+03A10 =−3.9119E+046.5236E+041.4379E+04−1.5895E+04A12 =5.5079E+05−6.3256E+05−8.6829E+049.1146E+04A14 =−3.5005E+063.0369E+062.9598E+05−3.2582E+05A16 =8.4437E+06−5.6447E+06−5.2497E+057.0353E+05A18 =——3.7373E+05−8.4064E+05A20 =———4.2965E+05

In the 7th embodiment, the equation of the aspheric surface profiles of the aforementioned lens elements is the same as the equation of the 1st embodiment. Also, the definitions of these parameters shown in the following table are the same as those stated in the 1st embodiment with corresponding values for the 7th embodiment, so an explanation in this regard will not be provided again.

Moreover, these parameters can be calculated from Table 13 and Table 14 as the following values and satisfy the following conditions:

7th Embodimentf [mm]0.35(OL − CTf)/(BL − CTr)0.96Fno (work)1.36SL/TL0.44Fno (inf.)1.32TL/f9.92HFOV [deg.]60.2ImgH/f1.65CT1/CT22.07TL [mm]3.48ATmax/CTmin4.26TL/ImgH5.99(R7 + R8)/(R7 − R8)0.10Y12/R23.70|f1/f2|0.08SAG12/R22.42|f4/f2|0.05Vmax − Vmin0.1|f/f1| − |f/f2| − |f/f3|0.16f/[EPD × tan (HFOV)]0.76f/EPD1.32Y11cx/Y11ca1.82CTf/TD0.54Y11/Y423.62

8th Embodiment

FIG.22is a perspective view of an image capturing unit according to the 8th embodiment of the present disclosure. In this embodiment, an image capturing unit10is a camera module including a lens unit11, a driving device12, an image sensor13and an image stabilizer14. The lens unit11includes the imaging lens system disclosed in the 1st embodiment, a barrel and a holder member (their reference numerals are omitted) for holding the imaging lens system. The imaging light converges in the lens unit11of the image capturing unit10to generate an image with the driving device12utilized for image focusing on the image sensor13, and the generated image is then digitally transmitted to other electronic component for further processing.

The driving device12can have auto focusing functionality, and different driving configurations can be obtained through the usages of voice coil motors (VCM), micro electro-mechanical systems (MEMS), piezoelectric systems, or shape memory alloy materials. The driving device12is favorable for obtaining a better imaging position of the lens unit11, so that a clear image of the imaged object can be captured by the lens unit11with different object distances. The image sensor13(for example, CCD or CMOS), which can feature high photosensitivity and low noise, is disposed on the image surface of the imaging lens system to provide higher image quality.

The image stabilizer14, such as an accelerometer, a gyro sensor and a Hall Effect sensor, is configured to work with the driving device12to provide optical image stabilization (OIS). The driving device12working with the image stabilizer14is favorable for compensating for pan and tilt of the lens unit11to reduce blurring associated with motion during exposure. In some cases, the compensation can be provided by electronic image stabilization (EIS) with image processing software, thereby improving image quality while in motion or low-light conditions.

9th Embodiment

FIG.23is one perspective view of an electronic device according to the 9th embodiment of the present disclosure.FIG.24is another perspective view of the electronic device inFIG.23.FIG.25is a block diagram of the electronic device inFIG.23.

In this embodiment, an electronic device20is a smartphone including the image capturing unit10disclosed in the 8th embodiment, an image capturing unit10a, an image capturing unit10b, an image capturing unit10c, a flash module21, a focus assist module22, an image signal processor23, a user interface24and an image software processor25. The image capturing unit10cis located on the same side as the user interface24, and the image capturing unit10, the image capturing unit10aand the image capturing unit10bare located on the opposite side. The image capturing unit10, the image capturing unit10aand the image capturing unit10ball face the same direction. Furthermore, the image capturing unit10a, the image capturing unit10band the image capturing unit10call have a configuration similar to that of the image capturing unit10. In detail, each of the image capturing unit10a, the image capturing unit10band the image capturing unit10cincludes a lens unit, a driving device, an image sensor and an image stabilizer, and the lens unit includes a lens assembly, a barrel and a holder member for holding the lens assembly.

In this embodiment, the image capturing unit10ais a telephoto image capturing unit and the image capturing unit10bis an ultra-wide-angle image capturing unit. The image capturing unit10has a field of view ranging between that of the image capturing unit10aand the image capturing unit10b. The image capturing units10,10a,10bhave different fields of view, such that the electronic device20has various magnification ratios so as to meet the requirement of optical zoom functionality. In this embodiment, the electronic device20includes multiple image capturing units10,10a,10band10c, but the present disclosure is not limited to the number and arrangement of image capturing units.

When a user captures images of an object26, the light rays converge in the image capturing unit10, the image capturing unit10aor the image capturing unit10bto generate an image(s), and the flash module21is activated for light supplement. The focus assist module22detects the object distance of the imaged object26to achieve fast auto focusing. The image signal processor23is configured to optimize the captured image to improve image quality. The light beam emitted from the focus assist module22can be either conventional infrared or laser. In addition, the electronic device20can capture images of the object26via the image capturing unit10c. The user interface24can be a touch screen or a physical button. The user is able to interact with the user interface24and the image software processor25having multiple functions to capture images and complete image processing. The image processed by the image software processor25can be displayed on the user interface24.

The smartphone in this embodiment is only exemplary for showing the image capturing unit10of the present disclosure installed in an electronic device, and the present disclosure is not limited thereto. The image capturing unit10can be optionally applied to optical systems with a movable focus. Furthermore, the imaging lens system of the image capturing unit10features good capability in aberration corrections and high image quality, and can be applied to 3D (three-dimensional) image capturing applications, in products such as digital cameras, mobile devices, digital tablets, smart televisions, network surveillance devices, dashboard cameras, vehicle backup cameras, multi-camera devices, image recognition systems, motion sensing input devices, wearable devices and other electronic imaging devices. In addition, the imaging lens system of the present disclosure can not only be applied to the image capturing applications as described above, but also be applied to image identification applications.

10th Embodiment

FIG.26is a perspective view of an electronic device according to the 10th embodiment of the present disclosure.FIG.27is a schematic view of the electronic device inFIG.26identifying a fingerprint.

In this embodiment, an electronic device20bis a smartphone having a biometric identification function. The electronic device20bincludes an image capturing unit10dand an identification module30b. The image capturing unit10dis a front-facing camera of the electronic device20bfor taking selfies, and the image capturing unit10dincludes the imaging lens system of the present disclosure and an image sensor.

The identification module30bhas a fingerprint identification function, which includes the imaging lens system of the present disclosure, an image sensor and a panel (optical window)15b. The panel15bis disposed between the imaged object O and the imaging lens system, and the panel15bcan be a display module. The display module includes a display layer151band a display substrate, and the display module can provide protection to the screen and thus minimize the use of additional components. Light rays can travel through the display layer151binto the imaging lens system of the identification module30bfor wider applications. The display layer151bhas a touch-screen function, such that there is no need of additional input devices, and it's favorable for making the operation more intuitive. Furthermore, the display layer151bmay be an OLED display layer or an active-matrix organic light-emitting diode (AMOLED) display layer, such that the display layer151bcan be a light source for illuminating the imaged object O, thereby saving additional light sources.

In this embodiment, the imaging lens system and the display module of the identification module30band the image capturing unit10dall face the same direction so as to use the display module as a light source for the imaging lens system of the identification module30b, but the present disclosure is not limited thereto. In some configurations, the image capturing unit and the display module of the identification module may be located on opposite sides of the electronic device. In addition, in this embodiment, each of the image capturing unit10dand the identification module30bincludes the imaging lens system of the present disclosure, but the present disclosure is not limited thereto. For example, in some configurations, only one of the image capturing unit10dand the identification module30bincludes the imaging lens system of the present disclosure.

The electronic device of the present disclosure is not limited to the above configuration.FIG.28is a schematic view of an electronic device according to another embodiment of the present disclosure identifying a fingerprint. In this embodiment, the electronic device includes an identification module30c. The identification module30chas a fingerprint identification function and includes the imaging lens system of the present disclosure, an image sensor, a light source S and a panel (optical window)15c. The panel15cis disposed between the imaged object O and the imaging lens system, and the panel15ccan be a glass substrate. The light source S is disposed on one side of the imaging lens system for illuminating the imaged object O. Light rays from the imaged object O can travel through the panel15cinto the imaging lens system of the identification module30c. In this embodiment, the identification module30cincludes the imaging lens system disclosed in the 1st embodiment, but the present disclosure is not limited thereto.

According to the present disclosure, the imaging lens system of the identification module features good capability in aberration corrections and high image quality, and the identification module can be applied to smartphones for under-display fingerprint identification, but the present disclosure is not limited thereto. For example, the identification module can be applied to other biometric identification applications such as iris and face identifications.

The foregoing description, for the purpose of explanation, has been described with reference to specific embodiments. It is to be noted that TABLES 1-14 show different data of the different embodiments; however, the data of the different embodiments are obtained from experiments. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, to thereby enable others skilled in the art to best utilize the disclosure and various embodiments with various modifications as are suited to the particular use contemplated. The embodiments depicted above and the appended drawings are exemplary and are not intended to be exhaustive or to limit the scope of the present disclosure to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings.