JPS63298113A - Structure of image forming optical system of optical range detector - Google Patents

Structure of image forming optical system of optical range detector

Info

Publication number
JPS63298113A
JPS63298113A JP13419887A JP13419887A JPS63298113A JP S63298113 A JPS63298113 A JP S63298113A JP 13419887 A JP13419887 A JP 13419887A JP 13419887 A JP13419887 A JP 13419887A JP S63298113 A JPS63298113 A JP S63298113A
Authority
JP
Japan
Prior art keywords
image
optical system
rotationally symmetrical
mirror
axis
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP13419887A
Other languages
Japanese (ja)
Inventor
Masanori Idesawa
正徳 出澤
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
RIKEN Institute of Physical and Chemical Research
Original Assignee
RIKEN Institute of Physical and Chemical Research
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by RIKEN Institute of Physical and Chemical Research filed Critical RIKEN Institute of Physical and Chemical Research
Priority to JP13419887A priority Critical patent/JPS63298113A/en
Publication of JPS63298113A publication Critical patent/JPS63298113A/en
Pending legal-status Critical Current

Links

Abstract

PURPOSE:To enhance an SN ratio in detection, by arranging a mirror, which has suitable rotary symmetrical surfaces on the side of an image in an image forming optical system, and condensing the image of a bright spot on a body, on which an annular image is formed when the mirror is not provided, at a position, which is close to the axis of the optical system. CONSTITUTION:A rotary symmetric (cylindrical or conical) mirror Ms is arranged in an image forming optical system. The radius of an annular image L is made small. Even if the radius of the annular image I is made small, the amount of movement of the image with respect to the change in a range on an image position detecting element P is not changed. Therefore, range detecting sensitivity is not decreased, but can be increased so that the amount of the detected light is approximately proportional to the inverse ratio of the radius. Thus an SN ratio can be enhanced. In another example, the light, which is associated with image formation, is bent in the direction of a rotary symmetrical axis As. The image is formed at a position close to the rotary symmetrical axis As.

Description

【発明の詳細な説明】 (産業上の利用分野) 本発明は光ビームの投射方向への距離を非接触で検出す
る光学的距離検出装置の結像光学系の構成に係わり、特
に3次元形状計測機器等のプローブとして使用するのに
好適な高精度かつ高安定な距離検出特性を有する光学的
距離検出装置の結像光学系の構成に関する。
Detailed Description of the Invention (Industrial Application Field) The present invention relates to the configuration of an imaging optical system of an optical distance detection device that detects the distance in the projection direction of a light beam in a non-contact manner. The present invention relates to the configuration of an imaging optical system of an optical distance detecting device having highly accurate and highly stable distance detecting characteristics suitable for use as a probe for measuring instruments and the like.

(従来の技術) 撮像レンズと物体との間に円筒鏡を配置し、光軸方向に
光ビームを投射することにより物体上に輝点を生成し、
円筒鏡で反射された後に撮像レンズへ入射して生成され
る輝点の半径方向像位置を検出して3角測量の原理に基
づいて光ビーム投射方向の距離情報を検出する型の光学
的距離検出装置が考案されている。また、撮像光学系の
幅を狭く保つために、撮像系の像側に回転対称ミラーを
配置した構造のものが考案されている。さらに、撮像光
学系の結像のために回転対称ミラーを用いた距離検出装
置の構成を考案した。
(Prior art) A cylindrical mirror is placed between an imaging lens and an object, and a bright spot is generated on the object by projecting a light beam in the optical axis direction.
A type of optical distance that detects the radial image position of a bright spot generated by entering the imaging lens after being reflected by a cylindrical mirror, and detects distance information in the direction of light beam projection based on the principle of triangulation. A detection device has been devised. Furthermore, in order to keep the width of the imaging optical system narrow, a structure in which a rotationally symmetrical mirror is arranged on the image side of the imaging system has been devised. Furthermore, we devised a configuration of a distance detection device that uses a rotationally symmetrical mirror for image formation in the imaging optical system.

第4a図から第5b図に従来の光学的距離検出装置を示
す。第4a図および第4b図に結像レンズLと対象物○
との間に回転対称ミラーMRを配置した光学的距離検出
器の構成を、第5a図および第5b図には回転対称結像
ミラーMLを用いた光学的距離検出器の構成を示した。
A conventional optical distance detection device is shown in FIGS. 4a to 5b. Figures 4a and 4b show the imaging lens L and the object ○.
5a and 5b show the configuration of an optical distance detector using a rotationally symmetrical imaging mirror ML.

いずれの構成においても、光ビームB投射方向(対称軸
方向)の距iは、観測面上に配置された像位置検出素子
Pで光ビームBを投射して物体0表面上に生成された輝
点Tの像位置■を検出して得られる。観測面上に得られ
る輝点の像Iは、それぞれ第4b図 −および第5b図
に示されているように円環状となる。輝点の生成される
距離により円環状像Iの半径が異なったものとなるので
、図に示すように像の移動方向(半径方向)に1次元像
位置検出素子Pを配置して像の半径方向位置を検出する
ように構成されている。
In either configuration, the distance i in the light beam B projection direction (symmetry axis direction) is the brightness generated on the surface of the object 0 by projecting the light beam B by the image position detection element P arranged on the observation surface. It is obtained by detecting the image position (■) of point T. The image I of the bright spot obtained on the observation surface has an annular shape as shown in FIGS. 4b and 5b, respectively. Since the radius of the annular image I differs depending on the distance at which the bright spot is generated, a one-dimensional image position detecting element P is arranged in the moving direction (radial direction) of the image as shown in the figure. The device is configured to detect directional position.

(発明が解決しようとする問題点) 第4b図および第5b図からも分かるように、1次元像
位置検出素子P上には、円環状像形成にかかわる光のご
く一部しか投射されず、多くの光は、像位置検出に有効
に利用されていないため、しばしば、検出信号のS/N
比の低下が生じ、検出精度を向上させる上で不利となっ
ている。
(Problems to be Solved by the Invention) As can be seen from FIGS. 4b and 5b, only a small portion of the light involved in forming an annular image is projected onto the one-dimensional image position detection element P. Since much light is not effectively used for image position detection, the S/N of the detection signal is often
This results in a decrease in the ratio, which is disadvantageous in improving detection accuracy.

(問題を解決するための手段) 上記の問題を解決し、検出光量を増大し、位置信号検出
のS/N比を向上させるために本発明では、回転対称内
面鏡によりその対称軸上にある点光源の像は、半径方向
に対しては、その対称軸上で収束するという性質を利用
して、等価的に回転対称内面鏡の対称軸に近接して結像
させ、それを1次元像゛位置検出素子で検出するように
したことを特徴とする。
(Means for Solving the Problems) In order to solve the above problems, increase the amount of detected light, and improve the S/N ratio of position signal detection, the present invention uses a rotationally symmetric internal mirror that is located on the axis of symmetry. Taking advantage of the property that the image of a point light source converges on its axis of symmetry in the radial direction, it is equivalently formed close to the axis of symmetry of a rotationally symmetric internal mirror, and then converted into a one-dimensional image.゛It is characterized by detecting with a position detection element.

(作用) 結像光学系の像側に適当な回転対称面を有するミラーを
配置することにより、それなしでは円環状に結像される
物体上の輝点の像を光学系の光軸に近接した位置に収束
させることができ、光軸上あるいはその近傍に像位置検
出素子を配置すれば、従来法では1次元像位置検出素子
の間に投射され、有効に用いられなかった光をも有効使
用可能となり、信号検出のS/N比を高められる。また
、更に光を囲んで外向きに配置された平面鏡により、光
軸に近接した信号に生成されるべき像は、反射され、鏡
の反対側光軸に近接した位置と対称な位置に像が形成さ
れるので、像位置検出素子を複数個配置する場合には、
それが容易となる。
(Function) By arranging a mirror with a suitable rotationally symmetrical surface on the image side of the imaging optical system, the image of a bright spot on an object, which would otherwise be imaged in an annular shape, can be brought close to the optical axis of the optical system. By arranging the image position detection element on or near the optical axis, the light that was projected between the one-dimensional image position detection elements and was not used effectively in the conventional method can be effectively focused. This makes it possible to increase the S/N ratio of signal detection. Further, by a plane mirror placed outward surrounding the light, the image to be generated in the signal close to the optical axis is reflected, and an image is formed at a position symmetrical to the position close to the optical axis on the opposite side of the mirror. Therefore, when arranging multiple image position detection elements,
It becomes easier.

(発明の効果) 本発明によれば、従来の方式では、円環状の像となり、
像位置検出素子の間に投射され有効に検出できなかった
光をも、有効に像位置検出素子上に集光することができ
るので像位置検出信号のS/N比を高めることができる
。特に、回転対称面ミラーによる結像系を用いる場合に
は、等価的な結像位置を完全に光軸上に一致させること
もできるため、その効果は著しい。
(Effects of the Invention) According to the present invention, in the conventional method, an annular image is obtained,
Even light that is projected between the image position detection elements and cannot be effectively detected can be effectively focused on the image position detection elements, so that the S/N ratio of the image position detection signal can be increased. In particular, when an imaging system using a rotationally symmetrical mirror is used, the equivalent imaging position can be completely aligned on the optical axis, so the effect is remarkable.

(実施例) 像位置検出にかかわる光量を増大させるには、結像位置
が対称軸に近接した状態メし、円環状像の半径が小さく
なるように構成することが有効である。このような回転
対称ミラーを用いた光学系では対称軸上の点より発射さ
れた光は、回転対称ミラーで反射された後に必ず対称軸
上へと収束されるという性質がある。従って、輝点の結
像位置が対称軸上に一致するようにし、像位置検出素子
を対称軸上に配置すれば、結像にかかわる光を総て像位
置検出に利用できるはずである。また、結像位置ができ
るだけ対称軸に近接するようにし、円環状像の半径が小
さくなるようにした方が、像位置検出器に入射する光量
の割合を大きくでき、像位置検出のS/N比を向上させ
る上で有利となる。本発明は、以上のような性質を利用
したものであり、具体的には、以下のように実現できる
(Embodiment) In order to increase the amount of light involved in image position detection, it is effective to configure the image forming position to be close to the axis of symmetry and to make the radius of the annular image small. In an optical system using such a rotationally symmetrical mirror, light emitted from a point on the axis of symmetry always converges onto the axis of symmetry after being reflected by the rotationally symmetrical mirror. Therefore, if the imaging position of the bright spot is made to coincide with the axis of symmetry and the image position detection element is arranged on the axis of symmetry, all the light related to imaging should be able to be used for image position detection. Also, by making the image formation position as close to the axis of symmetry as possible and making the radius of the annular image small, the ratio of the amount of light incident on the image position detector can be increased, and the S/N of image position detection can be increased. This is advantageous in improving the ratio. The present invention utilizes the properties described above, and specifically can be realized as follows.

第1a図および第1b図は本発明に基づき、結像光学系
に回転対称(円筒あるいは円錐)ミラーMSを配置して
円環状像りの半径が小さくなるように構成した光学的距
離検出器の一実施例である。
Figures 1a and 1b show an optical distance detector according to the present invention, which is configured by arranging a rotationally symmetric (cylindrical or conical) mirror MS in the imaging optical system so that the radius of the annular image becomes small. This is an example.

円環状像■の半径が小さくなっても、距離変化に対する
像位置検出素子P上での像の移動量は変化しない。従っ
て、距離検出感度の低下は来たさずに、検出光量がほぼ
半径の逆比に比例するように増大でき、S/N比を高め
られる。
Even if the radius of the annular image (2) becomes smaller, the amount of movement of the image on the image position detection element P with respect to a change in distance does not change. Therefore, the amount of detected light can be increased almost in proportion to the inverse ratio of the radius without reducing the distance detection sensitivity, and the S/N ratio can be increased.

第2a図および第2b図は、本発明に基づき、結像光学
系に回転対称プリズム(円錐レンズ)Lsを導入して構
成した光学的距離検出器の一実施例である。回転対称プ
リズムL、により、結像にかかわる光は、回転対称軸A
、力方向と屈曲され、回転対称軸Asに近接した位置に
結像されるように構成されている。適当な回転対称プリ
ズムL。
2a and 2b show an embodiment of an optical distance detector constructed by introducing a rotationally symmetrical prism (conical lens) Ls into an imaging optical system based on the present invention. Due to the rotationally symmetrical prism L, the light involved in imaging is directed along the rotationally symmetrical axis A.
, is bent in the force direction, and is configured to be imaged at a position close to the axis of rotational symmetry As. A suitable rotationally symmetrical prism L.

を適当な配置にすると、結像位置を回転対称軸に一致さ
せることも可能となる。その場合、円環状像Iの半径は
極限的に0となり、距離は、回転対称軸A、上の像■の
回転対称軸A、力方向位置を検出することにより確定で
きる。第2図には、結像位置が回転対称軸よりやや外れ
た位置となる場合の構成例が示しである。
By arranging them appropriately, it becomes possible to align the imaging position with the axis of rotational symmetry. In that case, the radius of the annular image I becomes zero in the limit, and the distance can be determined by detecting the rotational symmetry axis A, the rotational symmetry axis A of the upper image II, and the position in the force direction. FIG. 2 shows an example of a configuration in which the imaging position is slightly off from the axis of rotational symmetry.

第3a図および第3b図には、本発明に基づき、回転対
称プリズムL、と平面鏡Mとを撮像光学系に導入して構
成した光学的距離検出器の一実施例を示した。この構成
で鏡Mを配置しないと輝点の像は、回転対称軸A、上に
IVとして結像される構成となっている。像位置検出素
子Pを回転対称軸上に一致させて配置することは必ずし
も容易とは言えないので、平面鏡Mを配置し、これらの
平面鏡に対し、対称軸と鏡像の関係にある位置に結像す
るようにし、1次元像位置検出素子Pをそれぞれの鏡に
対応した結像位置に配置して構成した実施例である。こ
れにより、1次元像位置検出素子Pを仮想的に対称軸上
に配置したのと等価な効果が得られる。この構成では、
4枚の平面鏡Mが配置され、それぞれにおいては、輝点
からそれぞれに対応した異なった方向へ発射されている
光を結像するので、それぞれに対応した結像位置に配置
される1次元像位置検出素子Pの受光光量を別々に検出
し、それらの差から対称物表面の傾斜に関する情報の収
得にも利用できる可能性も生ずる。
3a and 3b show an embodiment of an optical distance detector constructed by introducing a rotationally symmetrical prism L and a plane mirror M into an imaging optical system based on the present invention. If the mirror M is not arranged in this configuration, the image of the bright spot will be formed on the rotational symmetry axis A as IV. Since it is not necessarily easy to arrange the image position detection element P so that it coincides with the axis of rotational symmetry, plane mirrors M are arranged and the image is formed at a position that is in a mirror image relationship with the axis of symmetry with respect to these plane mirrors. This is an embodiment in which a one-dimensional image position detection element P is arranged at an image forming position corresponding to each mirror. This provides an effect equivalent to arranging the one-dimensional image position detection element P virtually on the axis of symmetry. In this configuration,
Four plane mirrors M are arranged, and each one images the light emitted from the bright spot in different directions corresponding to each one, so the one-dimensional image position is placed at the corresponding imaging position. There is also a possibility that the amount of light received by the detection element P can be detected separately and the difference between them can be used to obtain information regarding the inclination of the surface of the object.

第3図の構成では、輝点の仮想的結像位置を対称軸上に
一致させない場合でも、実際の結像位置を、結像の条件
は変化させずに、対称軸より離れた位置に移動させるこ
とができるので、1次元像移動検出素子や光学系の配置
の上で空間的な自由度が増すことも大きな長所の一つと
言える。
In the configuration shown in Figure 3, even if the virtual imaging position of the bright spot does not coincide with the axis of symmetry, the actual imaging position can be moved to a position away from the axis of symmetry without changing the imaging conditions. One of the great advantages is that the degree of spatial freedom is increased in the arrangement of the one-dimensional image movement detection element and the optical system.

【図面の簡単な説明】[Brief explanation of the drawing]

第1a図および第1b図は、本発明に基づき、回転対称
ミラーを用い像の結像半径を縮小した構成例の側面光学
図および像位置検出素子部分の軸方向平面図、 第2a図および第2b図は、本発明に基づき、回転対称
プリズム(円筒レンズ)により像の結像半径を縮小する
構成例の側面光学図および像位置検出素子部分の軸方向
平面図、 第3a図および第3b図は、本発明に基づき、更に平面
鏡を配置し、本来、対称軸上に結像すべき像を対称軸上
より外れるようにした構成の一例を示す側面光学図およ
び像位置検出素子部分の軸方向平面図、 第4(a)図および第4(b)図はそれぞれ回転対称ミ
ラーと撮像レンズとを組み合わせた光学的距離検出器の
構成例の側面光学図および像位置検出素子部分の軸方向
平面図、および 第5(a)図および第5(b)図はそれぞれ回転対称結
像ミラーを用いた光学的距離検出器の構成例の側面光学
図および像位置検出素子部分の軸方向平面図。 (符号の説明) L・・・・・・撮像レンズ、 Mi・・・・・・回転対
称ミラー、B・・・・・・光ビーム、 T・・・・・・
輝点、0・・・・・・物体、   P・・・・・・像位
置検出素子、■・・・・・・像、    A、・・・・
・・対称軸、ML・・・・・・回転対称結像ミラー、M
S・・・・・・回転対称ミラー、 L、・・・・・・回転対称プリズム(円錐レンズ)、M
・・・・・・平面ミラー、  工、・・・・・・仮想像
、Pv・・・・・・仮想像位置検出素子。
1a and 1b are a side optical view and an axial plan view of the image position detection element portion of a configuration example in which a rotationally symmetrical mirror is used to reduce the imaging radius of the image according to the present invention, and FIGS. 2a and 1b are 2b is a side optical view of a configuration example in which the imaging radius of an image is reduced by a rotationally symmetrical prism (cylindrical lens) according to the present invention, and an axial plan view of the image position detection element portion; FIGS. 3a and 3b; FIG. 1 is a side optical view showing an example of a configuration in which a plane mirror is further arranged based on the present invention so that an image that should originally be formed on the axis of symmetry is deviated from the axis of symmetry, and an axial direction of the image position detection element portion A plan view, FIG. 4(a), and FIG. 4(b) are a side optical view of a configuration example of an optical distance detector that combines a rotationally symmetrical mirror and an imaging lens, and an axial plane of an image position detection element portion, respectively. 5(a) and 5(b) are a side optical view and an axial plan view of an image position detecting element portion, respectively, of a configuration example of an optical distance detector using a rotationally symmetrical imaging mirror. (Explanation of symbols) L...Imaging lens, Mi...Rotationally symmetrical mirror, B...Light beam, T...
Bright spot, 0...Object, P...Image position detection element, ■...Image, A,...
...Axis of symmetry, ML...Rotationally symmetrical imaging mirror, M
S...Rotationally symmetrical mirror, L...Rotationally symmetrical prism (conical lens), M
...Flat mirror, ...Virtual image, Pv...Virtual image position detection element.

Claims (4)

【特許請求の範囲】[Claims] (1)光ビームを光学系回転対称軸方向に投射して対称
物表面に生成された輝点を回転対称結像光学系によって
観測面上へ投影結像し、この観測面上における輝点像の
位置から前記対称物表面までの距離情報を取得する型の
光学的距離検出装置において、前記回転対称結像光学系
の像側に、前記観測面上における輝点像を回転対称軸方
向へ縮小する縮小光学系が設けられていることを特徴と
する光学的距離検出装置の結像光学系の構成。
(1) A light beam is projected in the direction of the rotationally symmetrical axis of the optical system, and a bright spot generated on the surface of the object is projected and imaged onto an observation surface by a rotationally symmetrical imaging optical system, and a bright spot image is formed on this observation surface. In an optical distance detection device of the type that acquires distance information from a position to the surface of the object, on the image side of the rotationally symmetrical imaging optical system, a bright spot image on the observation surface is reduced in the direction of the rotationally symmetrical axis. 1. A configuration of an imaging optical system of an optical distance detection device, characterized in that a reduction optical system is provided.
(2)前記縮小光学系は、前記輝点像を前記回転対称軸
上へ近接または一致させる回転対称面ミラーであること
を特徴とする特許請求の範囲第(1)項記載の光学的距
離検出装置の結像光学系の構成。
(2) The optical distance detection according to claim 1, wherein the reduction optical system is a rotationally symmetrical mirror that brings the bright spot image closer to or coincides with the rotationally symmetrical axis. Configuration of the imaging optical system of the device.
(3)前記縮小光学系は、前記輝点像を、前記回転対称
軸に近接させるか一致させる回転対称プリズムであるこ
とを特徴とする特許請求の範囲第(1)項記載の光学的
距離検出装置の結像光学系の構成。
(3) The optical distance detection according to claim 1, wherein the reduction optical system is a rotationally symmetrical prism that brings the bright spot image close to or coincides with the rotationally symmetrical axis. Configuration of the imaging optical system of the device.
(4)前記縮小光学系が、回転対称面ミラーあるいは回
転対称プリズムと、このミラーの反射像あるいは回転対
称プリズム通過後の像を向かい合わせて配置された像位
置検出素子上に反射する外向きの平面鏡とからなること
を特徴とする特許請求の範囲第(1)項記載の光学的距
離検出装置の結像光学系の構成。
(4) The reduction optical system includes a rotationally symmetrical plane mirror or a rotationally symmetrical prism, and an outwardly directed image that reflects the reflected image of this mirror or the image after passing through the rotationally symmetrical prism onto an image position detection element that is arranged facing each other. The configuration of an imaging optical system of an optical distance detecting device according to claim 1, characterized in that the imaging optical system comprises a plane mirror.
JP13419887A 1987-05-29 1987-05-29 Structure of image forming optical system of optical range detector Pending JPS63298113A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP13419887A JPS63298113A (en) 1987-05-29 1987-05-29 Structure of image forming optical system of optical range detector

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP13419887A JPS63298113A (en) 1987-05-29 1987-05-29 Structure of image forming optical system of optical range detector

Publications (1)

Publication Number Publication Date
JPS63298113A true JPS63298113A (en) 1988-12-05

Family

ID=15122724

Family Applications (1)

Application Number Title Priority Date Filing Date
JP13419887A Pending JPS63298113A (en) 1987-05-29 1987-05-29 Structure of image forming optical system of optical range detector

Country Status (1)

Country Link
JP (1) JPS63298113A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0413917A (en) * 1990-05-08 1992-01-17 Hamamatsu Photonics Kk Distance detector
JP2008275453A (en) * 2007-04-27 2008-11-13 Mitsutoyo Corp Optical displacement measuring apparatus

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5722506A (en) * 1980-07-16 1982-02-05 Muroran Kogyo Daigaku Optical noncontact type detector
JPS6126812A (en) * 1984-07-17 1986-02-06 Rikagaku Kenkyusho Detecting device for distance
JPS61231408A (en) * 1985-04-05 1986-10-15 Nippon Kogaku Kk <Nikon> Optical non-contact position measuring apparatus
JPS6266110A (en) * 1985-09-19 1987-03-25 Rikagaku Kenkyusho Optical distance detecting device

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5722506A (en) * 1980-07-16 1982-02-05 Muroran Kogyo Daigaku Optical noncontact type detector
JPS6126812A (en) * 1984-07-17 1986-02-06 Rikagaku Kenkyusho Detecting device for distance
JPS61231408A (en) * 1985-04-05 1986-10-15 Nippon Kogaku Kk <Nikon> Optical non-contact position measuring apparatus
JPS6266110A (en) * 1985-09-19 1987-03-25 Rikagaku Kenkyusho Optical distance detecting device

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0413917A (en) * 1990-05-08 1992-01-17 Hamamatsu Photonics Kk Distance detector
JP2008275453A (en) * 2007-04-27 2008-11-13 Mitsutoyo Corp Optical displacement measuring apparatus

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