OBJECTIVE, USE OF AN OBJECTIVE, MEASUREMENT SYSTEM COMPRISING AN OBJECTIVE AND USE OF A BI-ASPHERICAL PLASTIC LENS IN AN OBJECTIVE

Abstract

The invention relates to a hybrid objective having a fixed focal length, which has five lenses. The objective is suitable for use in a LIDAR measurement system. Moreover, the use of a bi-aspherical plastic lens for correcting the curvature of the image field and/or astigmatism and/or distortion of an imaging objective is proposed.

Claims

1. A lens with a fixed focal length F and a field of view of more than 45° with respect to the optical axis, with at least a first surface, a second surface, a third surface, a fourth surface, a fifth surface, a sixth surface, a seventh surface, an eighth surface, a ninth surface, and a tenth surface being successively arranged in the beam path, wherein the first surface and the second surface belong to a first lens element with a first focal length f.sub.1, the third surface and the fourth surface belong to a second lens element with a second focal length f.sub.2, the fifth surface and the sixth surface belong to a third lens element with a third focal length f.sub.3 and a refractive index of greater than 1.7, the seventh surface and the eighth surface belong to a fourth lens element with a fourth focal length f.sub.4, the ninth surface and the tenth surface belong to a fifth lens element with a fifth focal length f.sub.5, the first lens element is formed as a meniscus with a negative refractive power D.sub.1=1/f.sub.1<0, a diaphragm is arranged between the second lens element and the third lens element, the third lens element has a positive refractive power D.sub.3=1/f.sub.3>0, the sum D.sub.3+D.sub.4+D.sub.5 of the refractive power D.sub.3=1/f.sub.3 of the third lens element and the refractive power D.sub.4=1/f.sub.4 of the fourth lens element and the refractive power D.sub.5=1/f.sub.5 of the fifth lens element is positive, the ninth surface is formed to be aspherical and has a near-axis convex region and a peripheral concave region, at least one of the seventh surface, eighth surface, and tenth surface is formed to be aspherical, and where $.Math.\frac{1}{f_2}+\frac{1}{f_4}+\frac{1}{f_5}.Math.\le \frac{0.15}{F}$ applies.

2. The lens as claimed in claim 1, wherein the first lens element consists of a first glass, and/or the second lens element consists of a first plastic, and/or the third lens element consists of a second glass, and/or the fourth lens element consists of a second plastic, and/or the fifth lens element consists of a third plastic.

3. The lens as claimed in claim 1, wherein the fifth lens element consists of a third plastic. The lens as claimed in claim 1, wherein the Abbe number of the third lens element is less than 35 and the Abbe numbers of the second, fourth, and fifth lens elements are all either between 50 and 65 or between 18 and 32.

4. The lens as claimed in claim 1, wherein the first lens element and/or the second lens element have at least one aspherical surface and/or in that the seventh surface, eighth surface, ninth surface, and tenth surface are all formed to be aspherical.

5. The lens as claimed in claim 1, wherein at least one of the eighth surface and tenth surface and/or at least three of the third surface, seventh surface, eighth surface, and tenth surface each have at least one point of inflection.

6. The lens as claimed in claim 1, wherein the tenth surface is formed to be concave and without convex regions and/or in that a first derivative dz/dy of the z-coordinate of the tenth surface with respect to a y-direction in a plane x=0 has at least one point of inflection.

7. The lens as claimed in claim 1, wherein the fifth surface is formed as a flat surface and/or a diaphragm is arranged on the fifth surface.

8. The lens as claimed in claim 1, wherein it has a focal length F of between 2 mm and 5 mm and/or in that the focal length f.sub.1 of the first lens element is between 0.7-times and 1.3-times the focal length f.sub.2 of the second lens element and/or in that the sum of the center thicknesses of the glass lens elements is greater than the sum of the center thicknesses of the plastic lens elements and/or in that the lens has an overall length and an image circle diameter, the overall length being between two-times and five-times the image circle diameter.

9. The lens as claimed in claim 1, wherein it is formed to be approximately telecentric on the image side, the image-side telecentricity error being less than 10°.

10. The lens as claimed in claim 1, wherein the lens has a lens speed of at least 1:1.3.

11. The lens as claimed in claim 1, wherein the lens comprises a bandpass filter for separating the signal light from the light source from ambient light, in particular from daylight, or is operable together with a bandpass filter arranged outside the lens.

12. The use of a lens as claimed in claim 1 fora measurement system for at least detecting a time-of-flight of at least one-light beam.

13. A measurement system, comprising at least one lens as claimed in claim 1, at least one light source, and at least one matrix sensor, wherein the light source is a laser beam source or an LED and in that the light source is operated in a pulsed manner and in that the pulse length is between 1 ns and 1 ms.

14. The measurement system as claimed in claim 1, wherein the matrix sensor is a SPAD array and/or in that the light source is a VCSEL array or an LED array.

15. The use of a plastic bi-aspheric lens element for correcting field curvature and/or astigmatism and/or distortion a constitutent part of a lens as claimed in claim 1, wherein the plastic bi-aspheric lens element has a light entry surface with a near-axis convex region and a peripheral concave region and a light exit surface of the plastic lens element is formed to be concave and without points of inflection, and a first derivative dz/dy of the z coordinate of the light exit surface with respect to a y-direction in a plane x=0 has at least one point of inflection between the optical axis and the edge of the light exit surface.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0082] The present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only, and thus, are not limitive of the present invention, and wherein:

[0083] FIG. 1 shows a first exemplary embodiment.

[0084] FIG. 2 shows the beam path of the first exemplary embodiment.

[0085] FIG. 3 shows the astigmatism of the first exemplary embodiment.

[0086] FIG. 4 shows the f-tan theta distortion of the first exemplary embodiment.

[0087] FIG. 5 shows the f-theta distortion of the first exemplary embodiment.

[0088] FIG. 6 shows a second exemplary embodiment.

[0089] FIG. 7 shows the astigmatism of the second exemplary embodiment.

[0090] FIG. 8 shows the f-tan theta distortion of the second exemplary embodiment.

[0091] FIG. 9 shows the f-theta distortion of the second exemplary embodiment.

[0092] FIG. 10 shows a plastic bi-aspheric lens element according to the invention.

[0093] FIG. 11 shows the light exit surface of the plastic bi-aspheric lens element.

[0094] FIG. 12 shows the first derivative of the light exit surface.

[0095] FIG. 13 shows the second derivative of the light exit surface.

[0096] FIG. 14 shows the third derivative of the light exit surface.

[0097] FIG. 15 shows the light exit surface of a further plastic lens element.

[0098] FIG. 16 shows the first derivative of the light exit surface.

[0099] FIG. 17 shows the second derivative of the light exit surface.

[0100] FIG. 18 shows the light exit surface of a further plastic lens element.

[0101] FIG. 19 shows the first derivative of the light exit surface.

[0102] FIG. 20 shows the second derivative of the light exit surface.

[0103] FIG. 21 shows the light exit surface of a further plastic lens element.

[0104] FIG. 22 shows the first derivative of the light exit surface.

[0105] FIG. 23 shows the second derivative of the light exit surface.

[0106] FIG. 24 shows a third exemplary embodiment.

[0107] FIG. 25 shows the astigmatism of the third exemplary embodiment.

[0108] FIG. 26 shows the f-tan theta distortion of the third exemplary embodiment.

[0109] FIG. 27 shows the f-theta distortion of the third exemplary embodiment.

[0110] FIG. 28 shows a fourth exemplary embodiment.

[0111] FIG. 29 shows the astigmatism of the fourth exemplary embodiment.

[0112] FIG. 30 shows the f-tan theta distortion of the fourth exemplary embodiment.

[0113] FIG. 31 shows the f-theta distortion of the fourth exemplary embodiment.

[0114] FIG. 32 shows a measurement system according to the invention.

DETAILED DESCRIPTION

[0115] The invention will be explained below with reference to exemplary embodiments.

[0116] FIG. 1 shows a first exemplary embodiment. Shown is a lens 1 with a fixed focal length F, with a first surface 6, a second surface 7, a third surface 9, a fourth surface 10, a fifth surface 12, a sixth surface 13, a seventh surface 17, an eighth surface 18, a ninth surface 20, and a tenth surface 21 being successively arranged in the beam path. The lens has an optical axis 3. The optical axis is in the z-direction. In the figures, the image plane is on the right, that is to say in the z-direction, while the object plane is located to the left of the lens. The lens comprises a first lens element 5, a second lens element 8, a third lens element 11, a fourth lens element 16, and a fifth lens element 19. The lens elements are successively arranged in the z-direction in the order mentioned.

[0117] The first lens element is a negative refractive power spherical meniscus lens element, that is to say it has two opposing spherical optical surfaces.

[0118] The third lens element 11 has a positive refractive power.

[0119] The second lens element 8 is made of a first plastic. The second lens element 8 is in the form of a diverging bi-aspheric lens. The third lens element 11 is made of a second glass. The third lens element 11 is a converging spherical lens.

[0120] The fourth lens element 16 is in the form of a converging bi-aspheric lens. It is made from a second plastic. In this case, the second plastic is the same as the first plastic.

[0121] The fifth lens element 19 is designed as shown in FIG. 10, FIG. 11, FIG. 12, FIG. 13, and FIG. 14 and explained further below.

[0122] In addition, a filter 30 which separates the signal light from the ambient light can optionally be provided in front of the matrix sensor 33.

[0123] FIG. 2 shows the beam path of the first exemplary embodiment. In this figure and the further figures, the hatching of the lens elements has been omitted in order to be able to show the light rays 4, which represent the beam path 2, better. A diaphragm 15 is arranged between the second lens element 8 and the third lens element 11. The diaphragm plane 14 is located on the fifth surface 12, which is in the form of a flat surface. An image sensor for recording an image or a matrix sensor for detecting the time-of-flight of a light beam is arranged in the image plane 33.

[0124] The optical design in the variant without filter is implemented according to table 1 below:

TABLE-US-00001 TABLE 1 Radius of Thickness/ curvature distance Radius No. Type Comment KR in mm in mm Material in mm 1 STANDARD Object ∞ ∞ Air 2 STANDARD Surface 1 19.770000 1.132000 Glass 1 8.970777 (n = 1.5168) 3 STANDARD Surface 2 4.982000 4.616000 Air 4.900000 4 ASPHERE Surface 3 −322.400000 1.061000 Polymer 1 4.185478 (n = 1.5300) 5 ASPHERE Surface 4 7.544000 2.200000 Air 3.282936 6 STANDARD Diaphragm ∞ 0.000000 Air 2.701642 7 STANDARD Surface 5 ∞ 7.268000 Glass 2 2.901642 (n = 1.9037) 8 STANDARD Surface 6 −7.848000 0.228900 Air 5.319136 9 ASPHERE Surface 7 7.989000 5.179000 Polymer 2 5.963481 (n = 1.5300) 10 ASPHERE Surface 8 15.860000 1.308000 Air 5.715791 11 ASPHERE Surface 9 6.849000 1.508000 Polymer 3 4.921023 (n = 1.5300) 12 ASPHERE Surface 10 40.000000 3.300000 Air 4.662680 13 STANDARD Image ∞ 0.000000 5.000000

[0125] The first column provides an index, which is numbered from the object side. The “standard” type designates a flat or spherically curved surface. The “ASPHERE” type designates an aspherical surface. An interface or lens element surface can be understood to be a surface. Attention is drawn to the fact that the object plane (No. 1), a diaphragm (No. 6), and the image plane (No. 13) are also numbered in the first column. The lens element surfaces specified in the description and in the set of claims are given as a comment.

[0126] The radius of curvature KR column indicates the radius of curvature of the respective surface. In the case of an aspherical surface, this should be understood to mean the paraxial radius of curvature. In the table, the sign of a radius of curvature is positive if the shape of a surface is convex toward the object side, and the sign is negative if the shape of a surface is convex toward the image side. The specification ∞ in the radius of curvature column means that this relates to a flat surface. The distance between the i-th surface and the (i+1)-th surface on the optical axis is specified in the “thickness/distance” column. The specification ∞ in this column in No. 1 means that the object distance is infinite, that is to say a lens focused at infinity. For rows 2, 4, 7, 9, and 11, this column gives the center thickness of the first, second, third, fourth, and fifth lens element, respectively. In the material column, the material between the respective surfaces is specified with the respective refractive index n. In this case, the specified refractive index n refers to the sodium D line commonly used. The radius column indicates the outer radius of the respective surface. In the case of the diaphragm (No. 6), this is the aperture. In the case of the lens element surfaces, this is the maximum usable distance of the light rays from the optical axis. In the equation below, this corresponds to the maximum value h for the respective surface.

[0127] The coefficients of the aspherical surfaces for the respective index from column 1 of table 1 are given in the two subsequent tables, table 2 and table 3, below.

TABLE-US-00002 TABLE 2 No. C.sub.2 in mm−1 C.sub.4 in mm−3 C.sub.6 in mm−5 C.sub.8 in mm−7 4 0  1.8929E−03 −1.3862E−04 5.6479E−06 5 0  3.8511E−03 −1.1177E−07 0.0000E00  9 0 −1.9215E−04  1.1981E−05 −9.0353E−07  10 0 −1.4834E−03  2.1040E−05 2.4410E−06 11 0 −1.9231E−03 −7.9651E−05 1.8942E−06 12 0  1.9405E−03 −4.5728E−04 4.7035E−05

TABLE-US-00003 TABLE 3 No. C.sub.10 in mm−9 C.sub.12 in mm−11 C.sub.14 in mm−13 C.sub.16 in mm−15 4 −2.9882E−07  7.5065E−09 0.0000E00 0.0000E00 5 0.0000E00 0.0000E00 0.0000E00 0.0000E00 9  4.9619E−08 −2.1430E−09  5.1996E−11 −5.9086E−13 10 −1.8093E−07  3.5743E−09 −1.2977E−11 −1.5515E−13 11 0.0000E00 0.0000E00 0.0000E00 0.0000E00 12 −2.4843E−06  4.3636E−08  1.4519E−09 −4.8891E−11

[0128] In the numerical values of the aspherical data, “E−n” (n: integer) means “x10−n” and “E+n” means “x10+n”. Furthermore, the aspherical surface coefficients are the coefficients C.sub.m with m=2, . . . , 16 in an aspherical expression that is represented by the following equation:

[00003]$\mathrm{Zd}=\frac{h^2}{\mathrm{KR}+\sqrt{{\mathrm{KR}}^2-\left(1+k\right)h^2}}+{.Math.}_{m=2}^{16}{C}_m.Math.h^m,$

where

[0129] Zd is the depth of an aspherical surface (i.e., the length of a perpendicular from a point on the aspherical surface at a height h to a plane touching the apex of the aspherical surface and perpendicular to an optical axis), h is the height (i.e., a length from the optical axis to the point on the aspherical surface), KR is the paraxial radius of curvature, and C.sub.m are the aspherical surface coefficients (m=2, . . . , 16) given below. Unspecified aspherical surface coefficients, here all with an odd index, are to be assumed to be zero. The coordinate h is to be entered in millimeters, just as the radius of curvature; the result Zd is obtained in millimeters. The coefficient k is the conicity coefficient. The statements made in this paragraph also apply to all other following exemplary embodiments.

[0130] The conicity coefficient k is zero for all surfaces in the present first exemplary embodiment.

[0131] The focal length of the first lens element is f.sub.1=−13.45 mm, that of the second lens element is f.sub.2=−14.08 mm. The focal length of the third lens element is f.sub.3=8.94 mm, that of the fourth lens element is f.sub.4=25.11 mm and that of the fifth lens element is f.sub.5=15.56 mm. The lens has a focal length F of 3.46 mm.

[0132] In a modification of this exemplary embodiment, the lens is focused at a finite object distance. This can be implemented by changing the image distance. To this end, the distance in line No. 12 can be increased accordingly.

[0133] In a further modification, not shown, the lens can be used as a projection lens. To this end, a light source is arranged in plane 33 instead of the sensor. Then a scene located in front of the lens in the negative z direction, identified as −z direction in FIG. 1, can be illuminated.

[0134] FIG. 3 shows the astigmatism of the first exemplary embodiment. All astigmatism diagrams show the focal position on the horizontal axis and the angle of incidence on the vertical axis. The designation “sagittal” designates the sagittal image and the designation “tangential” designates the tangential image, which can also be designated as a meridional image.

[0135] FIG. 4 shows the f-tan theta distortion of the first exemplary embodiment. All distortion diagrams show the distortion in % on the horizontal axis and the angle of incidence on the vertical axis.

[0136] FIG. 5 shows the f-theta distortion of the first exemplary embodiment.

[0137] FIG. 6 shows a second exemplary embodiment. This is described in the following paragraphs. In the second embodiment, a bi-aspheric lens from FIG. 15, FIG. 16, and FIG. 17 is used as the fifth lens element 19. Corresponding to the explanations given under the first exemplary embodiment, the optical design of the second exemplary embodiment is implemented according to table 4 below:

TABLE-US-00004 TABLE 4 Radius of Thickness/ curvature distance Radius No. Type Comment KR in mm in mm Material in mm 1 STANDARD Object ∞ ∞ Air 2 STANDARD Surface 1 20.924016 1.570690 Glass 1 9.504763 (n = 1.5168) 3 STANDARD Surface 2 4.904248 4.490025 Air 4.808687 4 ASPHERE Surface 3 26.365451 1.040302 Polymer 1 3.986409 (n = 1.5300) 5 ASPHERE Surface 4 6.865847 2.271235 Air 3.075385 6 STANDARD Diaphragm ∞ 0.068453 Air 2.615000 7 STANDARD Surface 5 493.296366 6.836047 Glass 2 2.709185 (n = 1.9037) 8 STANDARD Surface 6 −7.808490 0.200000 Air 4.982316 9 ASPHERE Surface 7 8.080616 5.129109 Polymer 2 5.681749 (n = 1.5300) 10 ASPHERE Surface 8 18.165906 1.396368 Air 5.451244 11 ASPHERE Surface 9 6.328728 1.794420 Polymer 3 4.654312 (n = 1.5300) 12 ASPHERE Surface 10 26.365451 2.680000 Air 4.297779 13 STANDARD Image ∞ 0.000000 5.000000 ∞

[0138] The coefficients of the aspherical surfaces (surfaces of the asphere type with the index in column 1 specified in table 4 above) given in the following tables, table 5 and table 6, were used:

TABLE-US-00005 TABLE 5 No. C.sub.2 in mm−1 C.sub.4 in mm−3 C.sub.6 in mm−5 C.sub.8 in mm−7 4 0  2.0640E−03 −1.8390E−04  7.5156E−06 5 0  4.1140E−03 −6.2569E−05 0.0000E00 9 0 −3.2401E−04  2.8561E−05 −2.8433E−06 10 0 −2.2771E−03  1.2112E−04 −7.6327E−06 11 0 −2.4015E−03 −8.7228E−05  2.5882E−06 12 0  1.3413E−03 −3.0440E−04  3.2103E−05

TABLE-US-00006 TABLE 6 No. C.sub.10 in mm−9 C.sub.12 in mm−11 C.sub.14 in mm−13 C.sub.16 in mm−15 4 −3.2934E−07  7.6917E−09 0.0000E00 0.0000E00 5 0.0000E00 0.0000E00 0.0000E00 0.0000E00 9  1.7810E−07 −7.0211E−09  1.5061E−10 −1.3976E−12 10  4.4701E−07 −1.8247E−08  4.0458E−10 −3.7038E−12 11 0.0000E00 0.0000E00 0.0000E00 0.0000E00 12 −2.6772E−06  1.8024E−07 −7.1280E−09  1.2002E−10

[0139] Unspecified aspherical surface coefficients, here all with an odd index, are to be assumed to be zero. The conicity coefficients k of all surfaces are likewise equal to zero in this example.

[0140] The focal length of the first lens element is f.sub.1=−13.03 mm, that of the second lens element is f.sub.2=−18.08 mm. The focal length of the third lens element is f.sub.3=8.81 mm, that of the fourth lens element is f.sub.4=23.69 mm and that of the fifth lens element is f.sub.5=15.45 mm. The lens has a focal length F of 3.51 mm.

[0141] In a modification of this exemplary embodiment, the lens is focused at a finite object distance. This can be implemented by changing the image distance. To this end, the distance in line No. 12 can be increased accordingly.

[0142] In a further modification, not shown, the lens can be used as a projection lens. To this end, a light source is arranged in plane 33 instead of the sensor. Then a scene located in front of the lens in the negative z-direction can be illuminated.

[0143] The design wavelength of the first and second exemplary embodiment is 940 nm. Modifications of the exemplary embodiments can also be used at other wavelengths listed in the description.

[0144] FIG. 7 shows the astigmatism of the second exemplary embodiment. FIG. 8 shows the f-tan theta distortion of the second exemplary embodiment. A high level of distortion toward the edge of the image is intended in this case. FIG. 9 shows the f-theta distortion of the second exemplary embodiment.

[0145] FIG. 10 shows a plastic bi-aspheric lens element according to the invention. A light entry surface 20 of the plastic bi-aspheric lens element 19 is equipped with a near-axis convex region 22 and a peripheral concave area 23. The light exit surface 21 of the plastic lens element is concave and without points of inflection. The optical axis 3 runs in the z-direction. This lens element shown here is used as the fifth lens element 19 of the first exemplary embodiment and is designed with the parameters given in table 1, table 2, and table 3.

[0146] FIG. 11 shows the light exit surface of the plastic bi-aspheric lens element. The light exit surface of the lens element shown in FIG. 10, the right-hand lens element surface 21 in the illustration in FIG. 10, is shown as a function z(y). The z and y values are each given in mm. The value y=0 corresponds to the optical axis. The function is shown in a sectional plane x=0, which runs through the optical axis.

[0147] FIG. 12 shows the first derivative of the light exit surface. The first derivative z′(y)=dz(y)/dy of the function z(y) shown in FIG. 11 is shown. y is also specified in mm here. The first derivative has a first point of inflection 24, a second point of inflection 25, and a third point of inflection 26. These points of inflection are each visible twice in the illustration because the derivative is shown from the negative to the positive edge of the lens element. If only the range y≥0 is considered, then each point of inflection is present only once. This corresponds to the statement that there are three points of inflection between the optical axis at y=0 and the edge of the lens element, here at y=4.6 mm.

[0148] FIG. 13 shows the second derivative of the light exit surface. The curvature is shown as z″(y)=d.sup.2z(y)/dy.sup.2 of the function z(y) shown in FIG. 11. The coordinate y is likewise specified in mm here, z″ in 1/mm.

[0149] In this example, there is a local maximum as the first extremal value 27 of the curvature, and it is also the global maximum. This local maximum is arranged at a distance from the edge of the light exit surface. There is lower curvature at the lens element edge in comparison with this global maximum.

[0150] A local minimum as a second extremal value 28 is present between the global maximum 27 of the curvature and the closest local maximum as a third extremal value 29. The second maximum 29 is arranged at a distance from the optical axis. As a result, three points of inflection of the first derivative dz(y)/dy are present between the optical axis and the edge. The curvature is non-negative, that is to say ≥0, everywhere. A further local minimum of the curvature can be seen on the optical axis, that is to say at the point y=0, with there being no point of inflection of the first derivative z′ at this point. FIG. 14 shows the third derivative of the light exit surface. The third derivative z″“(y) of the function shown in FIG. 11 has a respective zero crossing at each point of inflection of the first derivative z′ shown in FIG. 12, this being a sufficient criterion for the presence of the aforementioned points of inflection 24, 25, and 26 of the first derivative.

[0151] FIG. 15, FIG. 16, and FIG. 17 show another plastic bi-aspheric lens element suitable for the use according to the invention. This lens element shown here is used as the fifth lens element of the second exemplary embodiment and is designed with the parameters given in table 4, table 5, and table 6. FIG. 15 shows the light exit surface. FIG. 16 shows the first derivative of the light exit surface. In this case, there are two points of inflection 24, 25 between the optical axis and the lens element edge. FIG. 17 shows the second derivative of the light exit surface. A global maximum 27 of the curvature is provided at the edge of the light exit surface and a local maximum 29 of the curvature is at a distance from the edge. A local minimum 28 of the curvature is arranged between the local maximum and the global maximum situated at the edge.

[0152] FIG. 18, FIG. 19, and FIG. 20 show another plastic bi-aspheric lens element suitable for the use according to the invention. This lens element shown here is used to correct the field curvature in the third exemplary embodiment and is designed with the parameters given as surface 10 in line no. 10 of table 7, table 8, and table 9. In this case, there are two points of inflection 24, 25 of the first derivative z′ between the optical axis and the lens element edge.

[0153] FIG. 21, FIG. 22, and FIG. 23 show another plastic bi-aspheric lens element suitable for the use according to the invention. This lens element shown here is used to correct the field curvature in the third exemplary embodiment and is designed with the parameters given as surface 10 in line no. 10 of table 10, table 11, and table 12. In this case, there are two points of inflection 24, 25 of the first derivative z′ between the optical axis and the lens element edge.

[0154] FIG. 24 shows a third exemplary embodiment. Shown is the use of the further plastic bi-aspheric lens element 19 from FIG. 18, FIG. 19, and FIG. 20 for correcting the field curvature of an imaging lens with four lens elements. The lens elements are indicated in the figure as first lens element 5, second lens element 8, third lens element 11, and corrective lens element 19 with the light entry surface 20 and the light exit surface 21 of the corrective lens element. Corresponding to the explanations given under the first exemplary embodiment, the optical design of this third exemplary embodiment is implemented according to table 7 below:

TABLE-US-00007 TABLE 7 Radius of Thickness/ curvature distance Radius No. Type Comment KR in mm in mm Material in mm 1 Standard Object ∞ ∞ Air 2 Asphere Surface 1 −6.230944   5.701835 Polymer 1 12.416714 (n = 1.5300) 3 Asphere Surface 2 −8.896737   1.577207 Air 10.200998 4 Standard Diaphragm ∞ 0.100000 Air 8.835525 5 Asphere Surface 3 9.246630 5.998586 Polymer 2 11.594786 (n = 1.5300) 6 Asphere Surface 4 9.519479 7.127095 Air 12.406077 7 Standard Surface 5 18.050311  8.511258 Glass 1 12.744462 (n = 1.8467) 8 Standard Surface 6 ∞ 0.234272 Air 11.478141 9 Asphere Surface 9 9.856429 3.999862 Polymer 3 9.088801 (n = 1.5300) 10 Asphere Surface 10 15.549429  6.050000 Air 7.605896 11 Standard Image ∞ 0.000000 7.500000

[0155] The coefficients of the aspherical surfaces (surfaces of the asphere type with the index in column 1 specified in table 7 above) given in the following tables, table 8 and table 9, were used:

TABLE-US-00008 TABLE 8 No. k C.sub.2 in mm−1 C.sub.4 in mm−3 C.sub.6 in mm−5 C.sub.8 in mm−7 2 −2.560057 0 5.3091E−05 1.9890E−06 −3.0424E−08 3 −0.969566 0 2.7298E−04 3.4469E−06 −1.2549E−07 5 −1.104189 0 −2.6562E−04  3.4788E−06 −4.9384E−08 6 −4.302363 0 −3.0131E−04  5.9167E−06 −1.1209E−07 9 −1.608437 0 1.2814E−04 5.7453E−06 −4.7252E−07 10 −6.018323 0 6.8157E−04 −1.3795E−05   8.8297E−07

TABLE-US-00009 TABLE 9 No. C.sub.10 in mm−9 C.sub.12 in mm−11 C.sub.14 in mm−13 C.sub.16 in mm−15 2 2.4762E−10 −1.2391E−12 3.6987E−15 −5.1645E−18 3 2.5971E−09 −3.1175E−11 1.9796E−13 −5.0661E−16 5 4.8536E−10 −2.7529E−12 6.7391E−15 −4.4890E−18 6 1.3620E−09 −9.9515E−12 3.8787E−14 −6.2599E−17 9 1.5230E−08 −3.0286E−10 2.9497E−12 −1.0681E−14 10 −3.8027E−08   7.6878E−10 −7.8042E−12   3.4208E−14
Unspecified aspherical surface coefficients, here all with an odd index, are to be assumed to be zero.

[0156] The focal length of the first lens element is f.sub.1=−149.85 mm, that of the second lens element is f.sub.2=17.67 mm. The focal length of the third lens element is f.sub.3=22.08 mm, that of the corrective lens element is f.sub.5=41.43 mm. The lens has a focal length F of 13.01 mm.

[0157] In a modification of this exemplary embodiment, the lens is focused at a finite object distance. This can be implemented by changing the image distance. To this end, the distance in line No. 10 can be increased accordingly.

[0158] In a further modification, not shown, the lens can be used as a projection lens. To this end, a light source is arranged in plane 33 instead of the sensor. Then a scene located in front of the lens in the negative z-direction can be illuminated.

[0159] The design wavelength of this exemplary embodiment is 905 nm. Modifications of the exemplary embodiments can also be used at other wavelengths listed in the description.

[0160] FIG. 25 shows the astigmatism of the third exemplary embodiment. FIG. 26 shows the f-tan theta distortion of the third exemplary embodiment. FIG. 27 shows the f-theta distortion of the third exemplary embodiment.

[0161] FIG. 28 shows a fourth exemplary embodiment. The use of a further plastic bi-aspheric lens element from FIG. 21, FIG. 22, and FIG. 23 is shown. The lens elements are indicated in the figure as first lens element 5, second lens element 8, third lens element 11, and corrective lens element 19 with the light entry surface 20 and the light exit surface 21 of the corrective lens element. Corresponding to the explanations given under the first exemplary embodiment, the optical design of this fourth exemplary embodiment is implemented according to table 10 below:

TABLE-US-00010 TABLE 10 Radius of Thickness/ curvature distance Radius No. Type Comment KR in mm in mm Material in mm 1 Standard Object ∞ ∞ Air 2 Asphere Surface 1 −6.188174  6.000000 Polymer 1 12.782538 (n = 1.5300) 3 Asphere Surface 2 −8.350660  0.663085 Air 10.534452 4 Standard Diaphragm ∞ 0.100000 Air 8.770000 5 Asphere Surface 3  9.327281 6.000000 Polymer 2 11.954788 (n = 1.5300) 6 Asphere Surface 4 10.451651 6.213997 Air 12.610611 7 Standard Surface 5 97.655164 7.000000 Glass 1 13.059946 (n = 1.8467) 8 Standard Surface 6 −33.034230   0.100000 Air 12.981984 9 Asphere Surface 9 10.465107 6.000000 Polymer 3 10.250292 (n = 1.5300) 10 Asphere Surface 10 24.825405 5.643037 Air 8.490759 11 Standard Image ∞ 0.000000 8.000000

[0162] The coefficients of the aspherical surfaces (surfaces of the asphere type with the index in column 1 specified in table 7 above) given in table 11 and table 12 below, were used:

TABLE-US-00011 TABLE 11 No. k C.sub.2 in mm−1 C.sub.4 in mm−3 C.sub.6 in mm−5 C.sub.8 in mm−7 2 −2.753519 0 3.2627E−05  1.4596E−06 −1.3738E−08  3 −1.279765 0 3.1220E−04 −1.0671E−06 1.1099E−08 5 −1.242730 0 −1.9211E−04   1.5774E−06 −1.3278E−08  6 −8.448702 0 −1.5813E−04   4.9644E−07 1.9398E−09 9 −8.196975 0 7.5321E−04 −1.7029E−05 2.9885E−07 10 −20.000000 0 3.7068E−04 −6.5538E−06 1.8875E−07

TABLE-US-00012 TABLE 12 No. C.sub.10 in mm−9 C.sub.12 in mm−11 C.sub.14 in mm−13 C.sub.16 in mm−15 2  5.7568E−11 −9.5057E−14  0.0000E00 0.0000E00 3 −7.0163E−11 2.9540E−13 0.0000E00 0.0000E00 5  7.5324E−11 −2.7316E−13  0.0000E00 0.0000E00 6 −5.6079E−11 3.3197E−13 −9.2673E−16 0.0000E00 9 −3.3110E−09 1.3902E−11 0.0000E00 0.0000E00 10 −4.2876E−09 3.3680E−11 0.0000E00 0.0000E00

[0163] Unspecified aspherical surface coefficients, here all with an odd index, are to be assumed to be zero.

[0164] The focal length of the first lens element is f.sub.1=−966.18 mm, that of the second lens element is f.sub.2=17.84 mm. The focal length of the third lens element is f.sub.3=30.94 mm, that of the corrective lens element is f.sub.5=30.26 mm. The lens has a focal length F of 12.64 mm.

[0165] In a modification of this exemplary embodiment, the lens is focused at a finite object distance. This can be implemented by changing the image distance. To this end, the distance in line No. 10 can be increased accordingly.

[0166] In a further modification, not shown, the lens can be used as a projection lens. To this end, a light source is arranged in plane 33 instead of the sensor. Then a scene located in front of the lens in the negative z-direction can be illuminated.

[0167] The design wavelength of this exemplary embodiment is 905 nm. Modifications of the exemplary embodiments can also be used at other wavelengths listed in the description.

[0168] FIG. 29 shows the astigmatism of the fourth exemplary embodiment. FIG. 30 shows the f-tan theta distortion of the fourth exemplary embodiment. FIG. 30 shows the f-tan theta distortion of the fourth exemplary embodiment.

[0169] FIG. 32 shows a measurement system according to the invention. The measurement system 31 comprises a transmitter lens 34, a receiver lens 35, a light source 32, and a matrix sensor 33. The light source illuminates one or more objects 36 with a transmitter light 37. The matrix sensor detects the time-of-flight of the reflected light 38.

[0170] The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are to be included within the scope of the following claims.