JP2010048672A - Position-measuring system and imaging device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position-measuring system, etc. which expand the range of the position of an object (light source 100), wherefrom significant detection information is obtained, and enable measurement of the position of the object, over a wide range. <P>SOLUTION: The system includes a lens 210 which transmits light from the light source 100 and forms a ring-shaped light concentration area, a light-receiving element 220, which detects the light concentration area formed by the lens 210 and an operating device 300 which measures the position of the light source 100, based on the detection information of the light concentration area detected by the light-receiving element 220. The lens 210 is characterized by that a third-order field curvature aberration coefficient in the first plane counted from the light source 100 side being positive and that the third-order field curvature aberration coefficient in the second plane is negative. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a position measurement system that measures the position of a light source by detecting a light ring image formed by spherical aberration of a lens with light from the light source.

  As a technique for measuring the three-dimensional position of an object, there are techniques disclosed in Patent Documents 1 and 2. The position measurement system described in Patent Document 1 measures the position of a light source (point light source) as an object by using spherical aberration of a lens. In this technique, for example, light from a light source such as an LED is converted into an optical ring image (light concentration region) by spherical aberration of a lens. The light ring image is detected by a CCD sensor, and the light source position is measured based on the detected information (the diameter and detection position of the light ring) of the light ring image.

JP 2004-212328 A

In this type of position measurement system, if the detection information of the detected image is significant, the position of the object can be measured based on the detection information. Therefore, the wider the range of the position of the object (light source) from which significant detection information can be obtained, the higher the practicality because the position of the object can be measured over a wide range.
An object of the present invention is to provide a position measurement system or the like that can expand the range of the position of an object (light source) from which significant detection information can be obtained and can measure the position of the object over a wide range.

According to the first aspect of the present invention, a lens that transmits light from a light source to form a ring-shaped light concentration region, a light receiving element that detects the light concentration region formed by the lens, and a light detection element that detects the light concentration region And a calculation device that measures the position of the light source based on the detected information on the light concentration region, and the lens has a positive third-order field curvature aberration coefficient on the first surface counted from the light source side. And a third-order field curvature aberration coefficient on the second surface is negative.
The invention according to claim 2 is the position measurement system according to claim 1, wherein the first surface has a negative power and the second surface has a positive power. .
In the invention according to claim 3, the lens has a refractive index of 1.8 to 2.0, and a curvature radius r1 of the first surface and a curvature radius r2 of the second surface are:
15 ≧ r1 / r2 ≧ 5
The position measurement system according to claim 1, wherein:
The invention according to claim 4 is the position measurement system according to claim 1, wherein the lens has a center thickness larger than a radius of curvature of the second surface.
In the invention according to claim 5, the material of the lens is SNPH2 Ohara, and the curvature radius r1 of the first surface and the curvature radius r2 of the second surface are:
r1 / r2 = 5.37
The position measurement system according to claim 1, wherein the relationship is satisfied.
According to a sixth aspect of the invention, the lens has a focal length of 200.0000 mm, a diameter of the first surface is 3.1268 mm, a radius of curvature of the first surface is −29.5500 mm, 6. The position measurement system according to claim 5, wherein a diameter of the second surface is 7.3837 mm, a radius of curvature of the second surface is −5.5000 mm, and a center thickness is 5.68 mm. It is.
The invention according to claim 7 is a lens that transmits light from a light source to form a ring-shaped light concentration region, and detects the light concentration region formed by the lens, and the obtained light concentration region A light-receiving element that outputs detection information to an arithmetic unit that measures the position of the light source, and the lens has a positive third-order field curvature aberration coefficient on the first surface counted from the light source side. An imaging apparatus characterized in that the third-order field curvature aberration coefficient on the second surface is negative.
The invention according to claim 8 is the imaging apparatus according to claim 7, wherein the first surface has a negative power and the second surface has a positive power.
In the invention according to claim 9, the lens has a refractive index of 1.8 to 2.0, and a curvature radius r1 of the first surface and a curvature radius r2 of the second surface are:
15 ≧ r1 / r2 ≧ 5
The imaging apparatus according to claim 7, wherein:
The invention according to claim 10 is the imaging apparatus according to any one of claims 7 to 9, wherein the lens has a center thickness larger than a radius of curvature of the second surface.

According to the first aspect of the present invention, it is possible to obtain a ring-shaped light concentration region with respect to a light source located in a wider range of view angle and to calculate the position of the light source than in the case where the configuration of the present invention is not used. it can.
According to the second aspect of the present invention, it is possible to calculate the position of the light source in a wider range of angle of view by reducing the field curvature aberration of the lens.
According to the invention of claim 3, it is possible to realize a system capable of calculating the position of the light source in the range of half angle of view of 30 ° or more.
According to the fourth aspect of the present invention, a better light concentration region can be obtained as compared with the case where the configuration of the present invention is not used.
According to the invention of claim 5, it is possible to realize a system capable of reducing the material cost of the lens and calculating the position of the light source in a range of a half angle of view of 30 ° or more.
According to the sixth aspect of the present invention, it is possible to realize a system capable of calculating the position of the light source in a wide field angle range by using a lens having a size suitable for the camera of the position measurement system.
According to the invention of claim 7, compared to the case where the configuration of the present invention is not used, a ring-shaped light concentration region used for calculating the position of the light source with respect to the light source located in a wider range of angle of view. Can be obtained.
According to the invention of claim 8, by reducing the field curvature aberration of the lens, it is possible to obtain a ring-shaped light concentration region with respect to the light source in a wider field angle range.
According to the ninth aspect of the present invention, a ring-shaped light concentration region can be obtained with respect to a light source in a range of a half angle of view of 30 ° or more.
According to the tenth aspect of the present invention, a better light concentration region can be obtained as compared with the case where the configuration of the present invention is not used.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
<System configuration>
FIG. 1 is a diagram showing an overall configuration of a position measurement system to which the present embodiment is applied.
As shown in FIG. 1, the position measurement system according to the present embodiment includes a light source 100 that is an imaging target, a camera 200 that is an imaging device that captures the light source 100, and an image captured by the camera 200. And an arithmetic device 300 for calculating a three-dimensional position. The camera 200 includes a lens 210 that collects light from the light source, and a light receiving element 220 that detects light transmitted through the lens 210.

  The light source 100 is composed of, for example, an LED (Light Emitting Diode). In the present embodiment, the wavelength of light emitted from the light source 100 is not particularly limited, and a wavelength to be used corresponding to the sensitivity of the light receiving element 220 may be appropriately determined. For example, an infrared LED having a peak wavelength of 880 nm is used.

  The lens 210 has a surface on the light source 100 side as a first surface and a surface on the light receiving element 220 side as a second surface. That is, the light emitted from the light source 100 enters the lens 210 from the first surface of the lens 210 and reaches the light receiving element 220 through the second surface. At this time, the light rays are refracted on the first surface and the second surface, respectively. In the lens 210 of this embodiment, the first surface has a negative power and the second surface has a positive power. Further, the second surface is a spherical surface, and in order to obtain a better light concentration region, the center thickness CT of the lens 210 is assumed to be larger than the radius of curvature of the second surface. A more detailed configuration of the lens 210 will be described later.

  The light receiving element 220 is configured by a two-dimensional CCD (Charge Coupled Device), a CMOS (Complementary Metal Oxide Semiconductor), or the like having sensitivity to the wavelength of light emitted from the light source 100. For example, as described above, when the light source 100 is an infrared LED having a peak wavelength of 880 nm, a CCD having sensitivity to infrared light near 880 nm is used as the light receiving element 220. In the present embodiment, a ring-shaped light concentration region is formed on the light receiving surface of the light receiving element 220 by being refracted and condensed on the first surface and the second surface of the lens 210. The ring shape of the light concentration region is circular, elliptical, or a shape close to these, and the position, shape, size, etc., on the light receiving surface of the light receiving element 220 change according to the position of the light source 100 with respect to the camera 200. To do.

  The arithmetic device 300 is realized by a computer such as a personal computer, for example. As described above, the position, shape, size, and the like of the light concentration region formed on the light receiving surface of the light receiving element 220 change according to the position of the light source 100 with respect to the camera 200. Using this, the arithmetic unit 300 calculates the position (coordinates) of the light source 100 with respect to the camera 200 based on the position, shape, size, etc. of the light concentration area obtained in the light receiving element 220. Further, when the present embodiment is applied to a target three-dimensional position measurement system described later, the arithmetic device 300 further determines the three-axis angle of the target on which the light source 100 is provided based on the obtained position of the light source 100. The calculation is also performed.

<Description of light concentration area>
The ring-shaped light concentration region formed on the light receiving surface of the light receiving element 220 by the light beam transmitted through the lens 210 will be described in detail.
FIG. 2 is a diagram for explaining the shape of the light concentration region formed on the light receiving surface of the light receiving element 220 by the lens 210.
As described above, the lens 210 of the present embodiment has a negative power on the first surface. However, for the sake of simplicity, in the example shown in FIG. explain. Even if a simplified model in which the lens 210 is a hemispherical lens is used, the mechanism for forming a ring-shaped light concentration region is the same. The light source 100 is assumed to be on the optical axis of the lens 210.

  In FIG. 2, the light emitted from the light source 100 is incident on the first surface of the lens 210 as indicated by the locus of the light beam. At this time, the light is refracted according to Snell's law. Next, the light reaches the spherical second surface and is refracted. The light is condensed on the optical axis by refraction at the second surface, but is not condensed at one point due to the large spherical aberration of the lens 210, but is concentrated in a certain range on the optical axis. Lighted. When the light beam is traced with reference to FIG. 2, the light beam that has passed through the lens region close to the optical axis is condensed on the optical axis far from the lens, but the light beam that has passed through the lens region far from the optical axis is light close to the lens. It turns out that it condenses on an axis | shaft.

  More specifically, when the light receiving surface of the light receiving element 220 is installed at a position on the optical axis as shown in FIG. 2 and the light path and the light reaching the light receiving surface are observed, The position of the light on the light receiving surface gradually moves away from the optical axis as the trajectory of the lens moves away from the optical axis of the lens 210. However, when the locus of the light beam is further away from the optical axis of the lens 210, the effect of refraction by the lens 210 increases, and conversely, it begins to approach the optical axis. That is, as the trajectory of the light beam passing through the lens 210 moves away from the optical axis, the light on the light receiving surface of the light receiving element 220 first moves away from the optical axis, then turns back and begins to approach the optical axis. It passes through the axis and spreads to the opposite side.

  Considering such a relationship in the two-dimensional plane of the light receiving surface of the light receiving element 220, the return position of the light reaching the light receiving surface is a circle centered on the optical axis. At the turn-back position, the light concentration region has a high light density. Therefore, a ring-shaped light concentration region 221 as shown in FIG. 2 is formed. The light concentration region 221 is a perfect circle when the light source 100 is on the optical axis of the lens 210. The diameter of the ring decreases as the light source 100 moves away from the lens 210, and the diameter of the ring increases as the light source 100 approaches the lens 210. Further, when the light source 100 moves in a direction perpendicular to the optical axis of the lens 210, the entire light concentration region 221 moves in a direction opposite to the moving direction of the light source 100. Accordingly, by formulating the relationship between the position of the light source 100 and the shape and coordinates of the light concentration region 221, the position (coordinates) of the light source 100 can be obtained from information on the shape and coordinates of the light concentration region 221.

FIG. 3 is a schematic diagram showing the relationship between the three-dimensional coordinates of the light source 100 and the light concentration region 221.
Assuming that the three-dimensional coordinates of the light source 100 are (x, y, z), x, y, z are approximately expressed as the following Expression 1-3.

x = L × cos (θ) (Formula 1)
y = L × sin (θ) × cos (s) (Formula 2)
z = L × sin (θ) × cos (s) (Formula 3)

Here, θ is an angle formed by a line segment connecting the point where the optical axis passes (optical axis point) and the light source 100 on the first surface of the lens 210 and the optical axis. In the light receiving surface of the light receiving element 220, s is an angle formed by a line segment connecting the optical axis point and the center of the light concentration region 221 and a vertical line with respect to the optical axis point.

The ring diameter D of the light concentration region 221 is approximately expressed by the following equation 4 from the distance L from the optical axis point on the first surface of the lens 210 to the light source 100 and the lens characteristic values a and b. The

D = a / L + b (Formula 4)

The lens characteristic values a and b are values obtained from the curvature and refractive index of the lens. Therefore, the distance L to the light source 100 is obtained by substituting the diameter of the image of the light concentration area 221 obtained on the light receiving surface of the light receiving element 220 (that is, the photographed image of the camera 200) into Equation 4, and obtaining the obtained L Is substituted into the above Equations 1 to 3 to obtain the three-dimensional coordinates of the light source 100.

<Lens configuration>
Next, the configuration of the lens 210 of the present embodiment will be described.
In the description of the light concentration region 221 described above, the lens 210 has been described as a hemispherical lens having a first surface as a plane for simplicity. However, if the lens 210 of the camera 200 is actually composed of a hemispherical lens, the image of the light concentration region 221 is reduced to a dot shape at a half angle of view of about 25 °. Therefore, it is difficult to obtain the distance of the light source 100 based on the diameter of the image. As will be described in detail later, the position measurement system to which the present embodiment is applied corresponds to the widest possible field angle, and is more practical if the position of the light source 100 can be measured over a wide range.

  Therefore, in order to realize position measurement with a wider angle of view, the lens 210 used in the present embodiment is configured such that the positive and negative field curvature aberration coefficients of the first surface and the second surface are reversed. Specifically, the first surface has a curvature of field aberration coefficient that is positive, and the second surface has a curvature of field aberration coefficient that is negative. In this way, the field curvature aberration of the entire lens 210 is improved, so that the image in the light concentration region 221 is prevented from being reduced even if the half angle of view is increased to some extent.

  As a specific configuration for realizing this, the first surface of the lens 210 has a gentle negative power and the second surface has a positive power. However, since the spherical aberration of the lens 210 contributes to the ring-shaped image of the light concentration region 221, the rough shape of the entire lens 210 is a shape close to a hemispherical lens.

More specifically, when the radius of curvature r1 of the first surface is reduced, the field curvature aberration of the entire lens system is improved, but at the same time, coma and astigmatism increase, and the optical ring image The shape will be damaged. On the other hand, if the curvature radius r1 is excessively increased, the correction of the field curvature is insufficient, and as described above, the diameter of the ring image in the light concentration region 221 decreases rapidly as the angle of view increases. To enable position measurement with a half angle of view of 30 ° or more using a sensor with a general sensitivity and a lens material with a refractive index of 1.8 to 2.0 corresponding to a light source wavelength that is relatively easily available. Is

15 ≧ r1 / r2 ≧ 5

It is necessary to satisfy the conditions. If the refractive index of the lens 210 is high, higher performance can be obtained. However, since a lens material having a high refractive index is expensive and causes an increase in cost, it is practical to configure the lens 210 in the above range. .

FIG. 4 is a diagram for explaining the behavior of light rays from the outside of the optical axis that enter the lens 210 of the present embodiment.
The light beam emitted from the light source 100 is refracted on the first surface of the lens 210 that satisfies the above conditions, and is refracted again on the second surface. At this time, if the chief ray incident on the center of the stop from other than the optical axis coincides with the normal line of the second surface, the chief ray does not refract on the second surface and goes straight. In addition, the peripheral ray (marginal ray) is projected on the second surface as an ellipse centered on the principal ray by refraction at the first surface, so that it passes through the elliptical stop from the light source on the optical axis. It behaves in the same way as a light beam incident on the lens 210. In the present embodiment, the principal ray does not completely coincide with the normal line of the second surface, and does not travel straight on the second surface, but behaves substantially equal to the above. Therefore, by arranging the sensor closer to the lens 210 than the focal plane of light from infinity, an elliptical light ring image can be obtained.

FIG. 5 is a chart showing an example of design parameters of specific lenses 210 used in the present embodiment.
Referring to the item of the lens 210 in FIG. 5, the curvature radius r1 of the first surface (front) is −29.5500 mm, the curvature radius r2 of the second surface (back) is −5.5000 mm, and the center thickness CT (THICKNESS). ) Is 5.6800 mm. Therefore, r1 / r2≈5.37, which satisfies the above condition of 15 ≧ r1 / r2 ≧ 5. The center thickness CT satisfies CT> r2.

  The light emitted from the light source 100 enters the first surface after passing through a diaphragm (a diaphragm 230 shown in FIG. 4) provided close to the first surface of the lens 210. As described above, since the principal ray is hardly refracted on the second surface, the magnification of the lens 210 is substantially determined by the refraction on the first surface. Then, the third-order field curvature aberration coefficient becomes positive due to the negative power on the first surface, and acts in the direction to cancel the negative field curvature aberration coefficient generated on the second surface.

FIG. 6 is a chart showing third-order aberration coefficients generated on each surface of the optical system of the present embodiment including the lens 210 shown in FIG.
In FIG. 6, surface 1 is the light source 100, surface 2 is the diaphragm 230, surface 3 is the first surface of the lens 210, surface 4 is the second surface of the lens 210, and surface 5 is the light receiving surface of the light receiving element 220 (sum of aberrations). Indicates. In FIG. 6, the PETZVAL value indicates the degree of field curvature. As illustrated, the PETZVAL value is a positive value on the surface 3 (first surface), and the negative value on the surface 4 (second surface) is decreased (see the value of the surface 5).

7 to 9 are diagrams showing the results of simulating the shape and contrast of the image formed on the light receiving surface of the light receiving element 220 according to this embodiment. FIG. 10 and FIG. 11 are diagrams showing simulation results performed using a hemispherical lens for comparison with the present embodiment.
7 and 10 are images of the light concentration region 221 when the light source 100 is on the optical axis of the lens 210. FIG. 8 and 11 are images of the light concentration region 221 when the light source 100 is at a position (half angle of view: 24.22 °) deviated from the optical axis of the lens 210. FIG. FIG. 9 is an image of the light concentration region 221 when the light source 100 is at a position deviated from the optical axis of the lens 210 (half angle of view: 40.36 °).

  Comparing these figures, when the light source 100 is on the optical axis of the lens 210 (FIGS. 7 and 10), the image of the light concentration region 221 forms a circular ring. However, when the light source 100 is at a position with a half angle of view of 24.22 °, the image of the light concentration region 221 forms a substantially circular ring in this embodiment (FIG. 8), but a hemispherical lens is used. In the case (FIG. 11), the image of the light concentration region 221 does not form a ring. Therefore, it is difficult to perform a calculation for obtaining the distance to the light source 100 based on the size of the ring.

  In the present embodiment, even when the light source 100 is at a position with a half angle of view of 40.36 ° (FIG. 9), the image of the light concentration region 221 maintains a ring shape despite the shape of an ellipse. Based on this, it is possible to calculate the distance to the light source 100. Considering that the distance to the light source 100 can be obtained over a range of an angle of view of 80 ° or more (twice or more when using a hemispherical lens), the position measurement system using the lens 210 of this embodiment is very It can be said that the utility is high.

FIG. 12 is an aberration diagram of a specific example of the lens 210 used in the present embodiment. FIG. 13 is an aberration diagram of the hemispherical lens presented for comparison with the present embodiment.
Comparing FIG. 12 and FIG. 13, it can be seen that when the lens 210 of this embodiment is used, the field curvature aberration is greatly improved.

<Application example>
Next, an application example of the position measurement system configured as described above will be described.
FIG. 14 is a diagram illustrating an example of the overall configuration of a position measurement system in a fixed space to which the present embodiment is applied.
In the example shown in FIG. 14, cameras 200 are respectively installed at four corners of a fixed space (such as a room) partitioned into rectangular parallelepipeds. When the lens 210 of the camera 200 has the characteristics shown in FIG. 7 to FIG. 9, the effective angle of view (which can calculate the position of the light source 100) is 80 ° or more. It corresponds to the whole. However, in consideration of a case where there is a shield in the space and the light source 100 cannot be imaged, a plurality of cameras 200 may be appropriately installed as shown in FIG. Each camera 200 is connected to the arithmetic device 300, and outputs detection information of the light concentration area 221 detected by the light receiving element 220 to the arithmetic device 300.

  When the target 110 provided with the light source 100 is placed in this space, the camera 200 images the light source 100 and, based on the obtained information such as the position and size of the ring-shaped light concentration region 221, The position of the target 110 is detected. The target 110 may be fixed at a specific position in the space, or may be carried by a person or moved by hand.

  In general, when the relative positional relationship of six points arranged in a three-dimensional space is known in advance, an object formed by six points from an image obtained by photographing these points with a camera. It is possible to calculate a position (hereinafter referred to as a three-dimensional position) and an angle (roll angle, pitch angle and yaw angle: hereinafter referred to as a three-axis angle) of an object in a three-dimensional space. Therefore, six light sources 100 are provided at predetermined positions on the surface of the target 110, the light sources 100 are photographed by the camera 200, and the positional relationship of the six light sources 100 is obtained, whereby the space of the target 110 is obtained. It is possible to realize a system capable of calculating the orientation in the interior.

  In the above embodiment, the light source 100 is a light emitting point constituted by an LED, but the present invention is not limited to this. For example, a retroreflecting plate may be provided instead of the LED as the light source 100, light may be emitted from an illumination device provided near the camera 200, and reflected light from the retroreflecting plate may be photographed by the camera 200.

It is a figure showing the whole position measuring system composition to which this embodiment is applied. It is a figure explaining the shape of the light concentration area | region formed on the light-receiving surface of a light receiving element with the lens of this embodiment. It is the schematic which shows the relationship between the three-dimensional coordinate of the light source in this embodiment, and a light concentration area | region. It is a figure explaining the behavior of the light ray from the optical axis which injects into the lens of this embodiment. It is a graph which shows the example of the design parameter of the concrete lens used for this embodiment. 6 is a chart showing third-order aberration coefficients generated on each surface of the optical system of the present embodiment including the lens shown in FIG. 5. It is a figure which shows the result of having simulated the shape and contrast of the image formed in the light-receiving surface of a light receiving element by this embodiment, and is a figure which shows the image of the light concentration area | region when a light source exists on the optical axis of a lens. It is a figure which shows the result of having simulated the shape and contrast of the image formed in the light-receiving surface of a light receiving element by this embodiment, and exists in the position (half angle of view: 24.22 degrees) where the light source shifted | deviated from the optical axis of the lens. It is a figure which shows the image of the light concentration area | region in a case. It is a figure which shows the result of having simulated the shape and contrast of the image formed in the light-receiving surface of a light receiving element by this embodiment, and exists in the position (half angle of view: 40.36 degrees) where the light source shifted | deviated from the optical axis of the lens. It is a figure which shows the image of the light concentration area | region in a case. It is a figure which shows the result of having simulated the shape and contrast of the image formed in the light-receiving surface of a light receiving element using a hemispherical lens, and is a figure which shows the image of the light concentration area | region when a light source exists on the optical axis of a lens. . It is a figure which shows the result of having simulated the shape and contrast of the image formed in the light-receiving surface of a light receiving element using a hemispherical lens, and the light source is in the position (half angle of view: 24.22 degrees) off from the optical axis of the lens. It is a figure which shows the image of the light concentration area | region in a certain case. It is an aberration diagram in a specific example of a lens used in the present embodiment. It is an aberration diagram of a hemispherical lens. It is a figure which shows the example of whole structure of the position measurement system in the fixed space where this embodiment is applied.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 ... Light source, 200 ... Camera, 210 ... Lens, 220 ... Light receiving element, 221 ... Light concentration area | region, 300 ... Arithmetic unit

Claims (10)

A lens that transmits light from the light source and forms a ring-shaped light concentration region;
A light receiving element for detecting the light concentration region formed by the lens;
An arithmetic unit that measures the position of the light source based on detection information of the light concentration area detected by the light receiving element;
The lens has a third-order field curvature aberration coefficient on the first surface counted from the light source side is positive and a third-order field curvature aberration coefficient on the second surface is negative. system.   The position measurement system according to claim 1, wherein the first surface has negative power and the second surface has positive power. The lens has a refractive index of 1.8 to 2.0, and a curvature radius r1 of the first surface and a curvature radius r2 of the second surface are:
15 ≧ r1 / r2 ≧ 5
The position measurement system according to claim 1, wherein:   4. The position measurement system according to claim 1, wherein the lens has a center thickness larger than a radius of curvature of the second surface. 5. The lens is
The material is SNPH2 Ohara,
The radius of curvature r1 of the first surface and the radius of curvature r2 of the second surface are:
r1 / r2 = 5.37
The position measurement system according to claim 1, wherein the relationship is satisfied. The lens is
The focal length is 200.0000 mm;
The aperture of the first surface is 3.1268 mm;
The radius of curvature of the first surface is −29.5500 mm;
The aperture of the second surface is 7.3837 mm;
The radius of curvature of the second surface is −5.5000 mm;
6. The position measuring system according to claim 5, wherein the center thickness is 5.6800 mm. A lens that transmits light from the light source and forms a ring-shaped light concentration region;
A light receiving element that detects the light concentration area formed by the lens and outputs the obtained detection information of the light concentration area to an arithmetic device that measures the position of the light source;
The lens is characterized in that the third-order field curvature aberration coefficient on the first surface counted from the light source side is positive, and the third-order field curvature aberration coefficient on the second surface is negative. .   The imaging device according to claim 7, wherein the first surface has a negative power and the second surface has a positive power. The lens has a refractive index of 1.8 to 2.0, and a curvature radius r1 of the first surface and a curvature radius r2 of the second surface are:
15 ≧ r1 / r2 ≧ 5
The imaging apparatus according to claim 7, wherein:   The imaging apparatus according to claim 7, wherein the lens has a center thickness larger than a radius of curvature of the second surface.

Images