JP2004257989A

JP2004257989A - Position detecting method and device

Info

Publication number: JP2004257989A
Application number: JP2003051748A
Authority: JP
Inventors: Yoshihiko Okayama; 喜彦岡山
Original assignee: Azbil Corp
Current assignee: Azbil Corp
Priority date: 2003-02-27
Filing date: 2003-02-27
Publication date: 2004-09-16
Anticipated expiration: 2023-02-27
Also published as: JP4085409B2

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position detecting method and its device capable of detecting a position with accuracy on the basis of the light intensity distribution on a light receiving face by Fresnel diffraction. <P>SOLUTION: The first rising part of the light intensity distribution on the light receiving face of a line sensor by the Fresnel diffraction of a monochromatic parallel light by an edge of a shielding matter, is approximated by a hyperbolic second function sech(x). The light receiving intensity by each light receiving cell of a line sensor is analyzed by using the hyperbolic second function to determine a position xo in the light receiving cell arrangement direction of the edge of the shielding matter. Simultaneously, a distance z between the shielding matter and the line sensor is determined by using the hyperbolic second function sech(x) on the basis of the light receiving intensity of the light receiving cell in determining the edge position xo, and the difference Δx between a position of the light receiving cell and the edge position xo. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【０００１】
【発明の属する技術分野】
本発明は、例えばロールから巻き戻されて一方向に高速に搬送される帯状体の縁部（エッジ）の幅方向における位置変位を高速度に、しかも高精度に検出することのできる位置検出方法および装置に関する。
【０００２】
【関連する背景技術】
フィルムやシート等の物品の縁部（エッジ）の位置を検出する位置検出装置として、物品（検査対象物）に向けて平行光を照射する投光部（光源）と、この投光部に対峙させて設けたＣＣＤ等の受光部（ラインセンサ）とを備えた光学式のものがある。この種の光学式の位置検出装置は、基本的には上記物品により遮られなかった平行光を受光部にて受光し、該受光部における平行光の受光領域と非受光領域（遮光領域）との境界を前記物品（検査対象物）の縁部（エッジ）の位置として検出するものである。
【０００３】
また最近ではレーザ光等の単色平行光を用い、物品（検査対象物）のエッジにおける上記単色平行光のフレネル回折に着目して前記ラインセンサ（受光部）の受光面上における光強度分布から上記物品（検査対象物）の縁部（エッジ）の位置を高精度に検出する装置も提唱されている（例えば特許文献１を参照）。
【０００４】
【特許文献１】
特開平８−２４７７２６号公報
【０００５】
【発明が解決しようとする課題】
ところで単色平行光のフレネル回折によるラインセンサ（受光部）の受光面上における光強度分布を利用して検査対象物のエッジの位置を検出する場合、予め上記光強度分布の特性を高精度に求めておくことが必要である。ちなみに上記フレネル回折による光強度分布は、図１１に示すようにエッジ位置近傍で急峻に立ち上がり、エッジ位置から離れるに従って振動しながら収束する。このような光強度分布の特性は、単色平行光の波長をλ［ｎｍ］、検査対象物のエッジから受光面までの距離をｚ［ｍｍ］、受光面上でのエッジ位置ｘ［μｍ］を［０］としたとき、∫を［ｘ＝０］から［（２／λｚ）^１／２・ｘ］までの積分を示す演算記号として
光強度＝（１／２）｛［１／２＋Ｓ（ｘ）］^２＋［１／２＋Ｃ（ｘ）］^２｝
Ｓ（ｘ）＝∫ｓｉｎ（π／２）・Ｕ^２ｄＵ
Ｃ（ｘ）＝∫ｃｏｓ（π／２）・Ｕ^２ｄＵ
として表される。但し、Ｕは仮の変数である。
【０００６】
また上式中の関数Ｓ（ｘ），Ｃ（ｘ）については、専ら数学公式集に示されるようにフレネル関数を用いて、ｘが大きいところでは
Ｓ（ｘ）’≒（１／２）−（１／πｘ）ｃｏｓ（πｘ^２／２）
Ｃ（ｘ）’≒（１／２）＋（１／πｘ）ｓｉｎ（πｘ^２／２）
としてそれぞれ近似することができる。従って基本的には上記近似式Ｓ（ｘ）’，Ｃ（ｘ）’を用いることにより、前記ラインセンサの各受光セルによる受光強度から前述したエッジ位置を計算することができる。
【０００７】
しかしながら実際に計算してみると、図１２に示すように関数Ｓ（ｘ），Ｃ（ｘ）とその近似式Ｓ（ｘ）’，Ｃ（ｘ）’とは、その立ち上がり以降の収束部分（２山目以降）において非常に良好に近似するものの、最初の立ち上がり部分（１山目）において大きなずれがあることが否めない。特にこの最初の立ち上がり部分の特性はエッジ検出において重要な役割を担うものであり、その特性のずれはエッジ位置の検出精度の低下の要因となる。
【０００８】
本発明はこのような事情を考慮してなされたもので、その目的は、フレネル回折による受光面上での光強度分布を、特に最初の立ち上がり部分の特性を高精度に近似し、これによって所定の光路内に侵入した遮蔽物のエッジ位置と受光面からエッジ位置までの距離とを高精度に検出することのできる位置検出方法および装置を提供することにある。
【０００９】
また本発明の別の目的は、複数の受光セルの配列ピッチが粗い安価なラインセンサを用いた場合であっても、エッジ位置と受光面からエッジ位置までの距離との高精度に、しかも簡易に検出することのできる位置検出方法および装置を提供するにある。
【００１０】
【課題を解決するための手段】
上述した目的を達成するべく本発明に係る位置検出方法は、一方向に所定のピッチで配列された複数の受光セルを備えたラインセンサ（受光部）と、このラインセンサに対峙して設けられて該ラインセンサの上記複数の受光セルに向けて単色平行光を投光する投光部と、前記ラインセンサの出力を解析して前記単色平行光の光路に存在する遮蔽物の前記受光セルの配設方向におけるエッジ位置を検出するエッジ検出部とを具備した位置検出装置に適用されるものであって、
特に前記エッジ検出部においては、前記遮蔽物による単色平行光のフレネル回折による前記ラインセンサの受光面上での光強度分布の最初の立ち上がり部分における光強度変化をハイパボリックセカンド関数ｓｅｃｈ（ｘ）により近似し、このハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて前記ラインセンサの各受光セルによる受光強度を解析して前記遮蔽物の前記受光セルの配列方向におけるエッジ位置を求めると共に、このエッジ位置と所定の受光強度が得られた受光セルの位置との差から前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて前記遮蔽物と前記ラインセンサとの間の距離を求めることをことを特徴としている。
【００１１】
即ち、本発明に係る位置検出方法は、単色平行光のフレネル回折による受光面上での光強度分布の最初の立ち上がり部分、特にその１山目の分布特性が、ａ，ｂ，ｃをそれぞれ係数として
ｙ＝ａ・ｓｅｃｈ（ｂｘ＋ｃ）
なるハイパボリックセカンド関数ｓｅｃｈ（ｘ）に極めて良好に近似することを見出してなされている。
【００１２】
そしてこのハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて前記ラインセンサの出力（光強度）を解析し、前記フレネル回折による受光面上での光強度分布において光強度（相対値）が［０．２５］となる位置ｘｏを前記遮蔽物の前記受光セルの配列方向におけるエッジ位置として検出し、更に前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて上記エッジ位置と所定の受光強度が得られる位置との関係から、具体的には上記エッジ位置と所定の受光強度が得られた受光セルの位置との差に基づいて前記エッジと前記ラインセンサの受光面との距離を求めることを特徴としている。
【００１３】
好ましくは前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いた前記ラインセンサの各受光セルによる受光強度の解析を、例えば予め規定された基準受光強度［０．２５］の近傍の該基準受光強度より大きい受光強度を得た受光セルおよび上記基準受光強度より小さい受光強度を得た受光セルをそれぞれ求め、これらの各受光セルの受光面において当該受光強度となる受光位置をハイパボリックセカンド関数ｓｅｃｈ（ｘ）の逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝に従って前記受光強度が［０．２５］となる位置からの相対位置をそれぞれ求め、これらの相対位置から補間により受光強度が［０．２５］となる位置ｘｏを求めるようにすれば良い。また前記遮蔽物と前記ラインセンサとの間の距離については、上述した受光セルの配列方向のエッジ位置を求める際に用いた受光強度が［０．２５］よりも大きい受光セルの位置ｘ２と受光強度が［０．２５］となるエッジ位置ｘｏとの差Δｘ、および上記位置ｘ２での受光強度とに基づいて前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）からフレネル回折の距離成分ｚを逆算して求めるようにすれば良い。
【００１４】
尚、前記遮蔽物と前記ラインセンサとの間の距離ｚについては、前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）の逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝を用いて近似した光強度分布において、その光強度が上記光強度［０．２５］から１山目のピーク位置の光強度である［１．３７］の範囲において予め任意に設定された、例えば［０．８］や［１．０］なる光強度となる位置ｘａとして求め、この位置Ｘａと前記エッジ位置ｘｏとの差Δｘに従ってハイパボリックセカンド関数ｓｅｃｈ（ｘ）から逆算するようにしても良い。
【００１５】
また本発明に係る位置検出装置は、一方向に所定のピッチで配列された複数の受光セルを備えたラインセンサと、このラインセンサに対峙して設けられて該ラインセンサの上記複数の受光セルに向けて単色平行光を投光する投光部と、前記遮蔽物による単色平行光のフレネル回折による前記ラインセンサの受光面上での光強度分布に従って前記ラインセンサの出力を解析して、前記単色平行光の光路に存在する遮蔽物の前記受光セルの配設方向におけるエッジの位置を検出するエッジ検出部とを備えたものであって、特に前記エッジ検出部として、
前記遮蔽物による単色平行光のフレネル回折による前記ラインセンサの受光面上での光強度分布の立ち上がり部分を近似したハイパボリックセカンド関数ｓｅｃｈ（ｘ）の逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝を用いて、前記ラインセンサの正規化出力から受光強度が［０．２５］となる前記受光セルの配設方向の位置ｘｏを求めるセル方向位置検出手段と、
上記逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝を用いて、前記受光セルの配列方向の複数の位置ｘａと各位置ｘａにおける受光強度とをそれぞれ求め、上記各位置Ｘａと前記光強度が［０．２５］となる前記受光セルの配列方向の位置ｘｏとの差Δｘに基づいて前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）から前記遮蔽物のエッジと前記ラインセンサとの間の距離ｚを算出する距離計算手段とを備えることを特徴としている。
【００１６】
具体的には上記セル方向位置検出手段は、前記ラインセンサの出力から予め規定された基準受光強度［０．２５］の近傍の該基準受光強度より大きい受光強度を得た受光セルと上記基準受光強度より小さい受光強度を得た受光セルとをそれぞれ特定する受光セル特定手段と、ハイパボリックセカンド関数ｓｅｃｈ（ｘ）の逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝により近似した光強度分布に従って前記受光セル特定手段にて特定した各受光セルの受光面において当該受光セルの受光強度となる受光位置をそれぞれ求める受光位置算出手段と、この受光位置算出手段でそれぞれ求められた受光位置から前記基準受光強度となる位置を前記遮蔽物のエッジ位置として検出する補間演算手段とにより構成される。
【００１７】
また距離計算手段は、前記ラインセンサの正規化出力からその受光強度が［０．２５］よりも大きくなる受光セル、および［０．２５］よりも小さくなる受光セルから受光強度が［０．２５］となるエッジ位置ｘｏを求め、受光強度が［０．２５］よりも大きい受光セルの位置ｘ２と受光強度が［０．２５］となるエッジ位置ｘｏとの差Δｘ、および上記位置ｘ２での受光強度とに基づいて前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）から距離ｚを算出するように構成される。
【００１８】
或いは前記距離計算手段は、前記逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝を用いて求められる予め設定された光強度Ａ（０．２５＜Ａ≦１．３７）となる前記受光セルの配列方向の位置ｘａと、前記セル方向位置検出手段にて求められたエッジ位置ｘｏとの差Δｘとに基づいて前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）から距離ｚを算出するように構成される。
【００１９】
このように構成された位置検出装置によれば、基準受光強度［０．２５］を挟む受光強度が得られた少なくとも受光セルにおいて当該受光セルの受光強度となる受光位置を、フレネル回折による光強度分布の最初の立ち上がり部分の特性を高精度に近似したハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いることでそれぞれ高精度に求めることができるので、これらの受光位置からラインセンサの受光面上におけるエッジの位置、つまり受光強度が［０．２５］となる位置を高精度に求めることができる。また同時に遮蔽物のエッジとラインセンサの受光面と間の距離を簡易に、しかも高精度に算出することが可能となる。
【００２０】
尚、上記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）の逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝については、これを級数展開したり、或いはＣＰＵに実装されている命令に従って演算することができるので、その演算処理速度（位置検出速度）を十分に高速化することができる。
尚、ラインセンサの出力の最初にピーク値をとる受光セルとその手前の受光セルをそれぞれ求め、これらの各受光セルの各受光強度から前述したハイパボリックセカンド関数ｓｅｃｈ（ｘ）の逆関数ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝に従ってエッジ位置を求めることも可能である。このようにしてエッジ位置を検出すれば、例えば検出対象物が半透明体からなり、検出対象物によって単色平行光を完全に遮光することができない場合であっても上記検出対象物の縁部（エッジ）の位置やラインセンサの受光面からの距離を高精度に検出することが可能となる。
【００２１】
【発明の実施の形態】
以下、図面を参照して本発明の一実施形態に係る位置検出方法および位置検出装置について説明する。
図１はこの実施形態に係る位置検出装置の概略構成図であり、基本的には図２に示すように一方向に所定のピッチＷで配列した複数の受光セル１ａを備えたラインセンサ（受光部）１と、このラインセンサ１の受光面に対峙して設けられて該ラインセンサ１の複数の受光セル１ａに向けて所定の光線束幅の単色平行光４を投光する投光部２とを備える。またマイクロコンピュータ等により実現される装置本体３は、前記ラインセンサ１の出力（各受光セル１ａの受光量）を解析することで前記単色平行光４の光路に位置付けられた、例えば帯状体からなる遮蔽物（検出対象物）７の前記受光セル１ａの配設方向におけるエッジ位置を高精度に検出する役割を担う。
【００２２】
尚、投光部２は、例えば図３にその概略構成を示すようにレーザダイオード（ＬＤ）からなる光源２ａが発した単色光（レーザ光）を反射するミラー（例えばアルミ蒸着により鏡面処理を施したプリズム）２ｂと、このミラー２ｂを介して導かれた単色光の光線束形状をスリット状に規定するアパーチャマスク（投光窓）２ｃと、このアパーチャマスク２ｃを介した光を平行光線束に変換して投射する投射レンズ（コリメータレンズ）２ｄとを備える。この投射レンズ２ｄと前記受光部１との間に検出対象物である遮蔽物７が位置付けられ、アパーチャマスク２ｃのスリットの長手方向に変位する上記遮蔽物７のエッジ位置が前記受光部１を介して検出される。
【００２３】
具体的にはアパーチャマスク２ｃは、その開口形状を矩形状のスリットとしたもので、前記光源２ａは上記スリットに向けて所定の拡がり角で単色光を射出するように設けられる。特に光源２ａとしてＬＤを用いた場合、このＬＤから楕円状の強度分布をもって射出するレーザ光は、アパーチャマスク２ｃに対して図中破線で示すように投射される。この際、上記レーザ光の長軸が、前記アパーチャマスク２ｃのスリットの長手方向となるように該ＬＤとアパーチャマスク２ｃとを光学的に配置することが、投光部２を小型化する上で好ましい。尚、ミラー（プリズム）２ｄは、ＬＤから発せられたレーザ光を略直角に反射させる光路を形成することで、ＬＤとアパーチャマスク２ｃ、ひいては投射レンズ２ｄとの光学的距離を維持しながら、投光部２の全体形状をコンパクト化する役割を担っている。尚、このような投光部２は、例えば前述したラインセンサ１と共に所定の隙間Ｌを形成したコの字状の筐体５に上記隙間を挟んで互いに対峙させて一体に組み込まれて、１つのセンシングユニットとして形成される。
【００２４】
このように構成された投光部２により、図４および図５にその光学系をそれぞれ模式的に示すように、上記アパーチャマスク２ｃおよび投射レンズ２ｄを通して平行光に変換されたスリット状の断面形状を有する平行光線束（単色平行光）４がラインセンサ（受光部）１に向けて投射される。この平行光線束の断面形状の大きさは、例えば長辺９ｍｍ×短辺３ｍｍであり、これに対して上記平衡光線束を受光するラインセンサ１の受光面の大きさは、例えば長辺８．７ｍｍ×短辺０．０８ｍｍである。即ち、それぞれの長辺の寸法は、ほぼ等しく設けられている。
【００２５】
ちなみに平行光線束の断面形状における短辺の寸法（３ｍｍ）をラインセンサ１の受光面の短辺寸法（０．０８ｍｍ）よりもかなり大きく設定しているのは、投光器と受光器との平行度の調整を容易化すると共に、投光器または受光器が傾いた場合においても、図５に示すようにアパーチャマスク２ｃのスリットの長辺側エッジ２ｈによるフレネル回折の影響を避ける為である。但し、このスリット状の平行光線束（単色平行光）４には、前述したアパーチャマスク２ｃを用いて光線束形状を整形した際、図４に示すようにアパーチャマスク２ｃのスリットの短辺側エッジ２ｅにおけるフレネル回折の影響により生じた非平行光線成分が含まれることが否めない。しかしこの非平行光線成分の影響については、後述するようにラインセンサ１の出力を正規化して補正するようにすれば良い。
【００２６】
ところで前記装置本体３は、前記ラインセンサ１の出力（各受光セル１ａの受光量）を取り込んで該ラインセンサ１の受光面上における光強度分布を求める入力バッファ３ａを備える。特に装置本体３は、その初期設定処理として予め前記投光部２から投光された所定の光線束幅の単色平行光の全てを前記ラインセンサ１にて受光し、このときの光強度分布に基づいて前記投光部２が投光する単色平行光の回折パターンを求めると共に、後述するようにこの回折パターンの逆数に従って前記各受光セル１ａの受光量に対する正規化パラメータを求める回折パターン検出手段３ｂを備える。この回折パターンは、上述したアパーチャマスク２ｃに形成されたスリットの短辺側エッジ２ｅにおけるフレネル回折の影響により生じた非平行光線成分に起因するものである。
【００２７】
更に装置本体３は、上記回折パターン検出手段３ｂにより求められた正規化パラメータに従って前記ラインセンサ１の出力を正規化する正規化手段３ｃと、この正規化手段３ｃにて正規化処理した前記ラインセンサ１の出力（正規化出力）に従って前記遮蔽物（検出対象物）７の端部（エッジ）の位置、具体的にはラインセンサ１における受光セル１ａの配列方向の位置を検出するエッジ検出部３ｂとを備える。
【００２８】
このエッジ検出部３ｄは、基本的には前記単色平行光の一部が遮蔽物（検出対象物）７にて遮られたとき、その端部（エッジ）においてフレネル回折が生じること、そしてフレネル回折を生じて前記ラインセンサ１の受光面に到達する光の強度が、前述した図１２に示したようにエッジ位置近傍で急峻に立ち上がり、エッジ位置から離れるに従って振動しながら収束する分布特性を持つことに着目し、ラインセンサ１の受光面上での光強度分布に従って前記遮蔽物７の端部（エッジ）の位置を高精度に検出するように構成される。
【００２９】
ちなみに上記エッジ位置は、単色平行光の一部が遮蔽物７により遮られたときの前記ラインセンサ１の受光面上での光強度分布が、光強度［０］から立ち上がって［１．０］に収束するものとすると、前述した特許文献１にも示されるように、その最初の立ち上がり部分（１山目）において光強度が［０．２５］となる位置として求められる。
【００３０】
また装置本体３は、前記ラインセンサ１の受光面上での光強度分布に従って上記フレネル回折を生じた遮蔽物７のエッジと上記ラインセンサ１の受光面との距離ｚを算出する距離検出手段（距離計算手段）３ｅを備える。この距離検出出段３ｅは、フレネル回折の影響を受けたラインセンサ１の受光面上での光強度分布が、特にその立ち上がり部分での光強度分布が前記単色平行光の波長λと上記距離ｚとに依存することから、この立ち上がり部分における前記ラインセンサ１の受光面の複数の位置でのそれぞれの受光強度に従って後述するように上記光強度分布の特性から前記距離ｚを計算するものとなっている。
【００３１】
さてこのように構成された位置検出装置において、この発明に係る位置検出方法および装置が特徴とするところは、前記装置本体（エッジ検出部）３においてラインセンサ１の出力から遮蔽物７のエッジの位置、具体的にはラインセンサ１における受光セル１ａの配列方向の位置ｘｏおよびラインセンサ１の受光面と上記遮蔽物７との距離ｚを検出するに際して、フレネル回折による光強度分布を近似したハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いてエッジ位置を算出する点にある。
【００３２】
即ち、フレネル回折による前記ラインセンサ１の受光面上での光強度分布を、特にその最初の立ち上がり部分（１山目）における光強度変化をハイパボリックセカンド関数ｓｅｃｈ（ｘ）により近似し、このハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて近似した光強度分布に従って前記ラインセンサ１の各受光セル１ａによる受光強度を解析して前記遮蔽物７のエッジ位置ｘｏと距離ｚとを求めるようにした点にある。
【００３３】
このフレネル回折による光強度分布のハイパボリックセカンド関数ｓｅｃｈ（ｘ）による近似について説明すると、前述したようにフレネル関数を用いた場合、光強度分布の最初の立ち上がり部分（１山目）における誤差が非常に大きいと言う問題がある。そこで光強度分布の最初の立ち上がり部分（１山目）だけに着目し、その山の形状（光強度の変化傾向）から２乗の有理関数、ハイパボリックコサイン関数、および指数関数を用いてそれぞれ近似することを試みた。
【００３４】
具体的には２乗の有理関数として
ｙ＝ａ／｛（ｘ＋ｂ）^２＋ｃ｝
ハイパボリックセカンド関数として
ｙ＝ａ・ｓｅｃｈ（ｂｘ＋ｃ）
そして指数関数として
ｙ＝ａ・ｅｘｐ｛−ｂ（ｘ＋ｃ）^２｝
なる３つの関数を考え、これらの各関数に示される係数ａ，ｂ，ｃにそれぞれ適当な値を代入しながらその特性曲線を求めたところ、図６に示すような計算結果が得られた。
【００３５】
ちなみに図６において特性Ａは光強度分布の理論値を示しており、また特性Ｂは上記２乗の有理関数における係数ａ，ｂ，ｃをそれぞれ［０．０５７］，［−０．３８］，［０．０４１７］としたときの光強度ｙの変化、特性Ｃは前記ハイパボリックセカンド関数における係数ａ，ｂ，ｃをそれぞれ［１．３７］，［６．２９］，［−２．４０］としたときの光強度ｙの変化、そして特性Ｄは前記指数関数における係数ａ，ｂ，ｃをそれぞれ［１．３７］，［１６．３０］，［−０．３８］としたときの光強度ｙの変化をそれぞれ示している。但し、これらの計算は、単色光の波長λを６７０ｎｍ、遮蔽物７のエッジからラインセンサ１の受光面迄の距離ｚを３００ｍｍとして行った。これらの計算結果に示されるように、ハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いれば、フレネル回折による光強度分布の、特に最初の立ち上がり部分（１山目）の特性を非常に高精度に近似し得ることが明らかとなった。
【００３６】
ちなみに前記ハイパボリックセカンド関数を前述したフレネル回折による光強度分布の式に当て嵌めて該光強度分の最初の立ち上がり部分（１山目）までを近似すると、そのハイパボリックセカンド関数ｓｅｃｈ（ｘ）は
光強度＝１．３７・ｓｅｃｈ｛１．９８（２／λｚ）^１／２ｘ−２．３９｝
として示される。そしてこの近似式は、３桁程度の精度で光強度分布の理論式に一致することが確認できた。但し、λは光の波長［ｎｍ］、ｚはエッジから受光面までの距離［ｍｍ］、ｘは受光面上でのエッジ位置を［０］とする座標［μｍ］であり、これらの実用的な単位の下で係数を設定している。
【００３７】
本発明はこのような知見に立脚し、フレネル回折による光強度分布を、特にその最初の立ち上がり部分を上述したハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて近似し、この光強度分布を近似したハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて前述したラインセンサ１の出力から遮蔽物７のエッジ位置を高精度に検出するようにしている。
【００３８】
この際、その計算処理を簡略化し、エッジ位置の検出処理速度の高速化を図るべく次のような工夫をしている。この計算処理のアルゴリズムについて説明すると、ハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて近似される光強度は、前述したように
光強度＝１．３７・ｓｅｃｈ｛１．９８（２／λｚ）^１／２ｘ−２．３９｝
として示される。そしてその逆関数を計算すると、
Ｙ＝（ｙ／１．３７），Ｘ＝１．９８（２／λｚ）^１／２ｘ
とおいて、
Ｘ＝２．３９−ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝
として表すことができる。
【００３９】
そこでエッジ検出部３ｄにおいては、例えば図７に示す手順に従い、先ずラインセンサ１における複数（ｍ個）の受光セル１ａから求められる正規化された各受光強度ｙ１，ｙ２，〜ｙｍから、互いに隣接して前述した基準光強度［０．２５］よりも大きい受光強度を得た受光セルＣｎと、上記基準光強度［０．２５］よりも小さい受光強度を得た受光セルＣｎ−１とをそれぞれ求める（ステップＳ１）。つまり複数の受光セル１ａ（Ｃ１，Ｃ２，〜Ｃｍ）間のそれぞれにおいて受光強度が［０．２５］となる、互いに隣接する２つの受光セルＣｎ，Ｃｎ−１を求める。そしてこれらの各受光セルＣｎ，Ｃｎ−１の受光強度ｙｎ，ｙｎ−１を上述した係数［１．３７］で除算してＸ−Ｙ座標上での光強度Ｙｎ，Ｙｎ−１に変換する（ステップＳ２）。
【００４０】
しかる後、これらの各受光セルＣｎ，Ｃｎ−１の受光強度Ｙｎ，Ｙｎ−１が得られる該受光セルＣｎ，Ｃｎ−１の受光面上での位置Ｘｎ，Ｘｎ−１を、前述した近似式に従って
Ｘｎ＝２．３９−ｌｎ｛［１＋（１−Ｙｎ^２）^１／２］／Ｙｎ｝
Ｘｎ−１＝２．３９−ｌｎ｛［１＋（１−Ｙｎ−１^２）^１／２］／Ｙｎ−１｝
としてそれぞれ逆変換によりＸ軸上の相対位置を計算し（受光位置算出手段；ステップＳ３）、これらの位置Ｘｎ，Ｘｎ−１から図８にその概念を示すように受光セルＣｎの位置と、受光強度が［０．２５］となるエッジ位置との差Δｘを
Δｘ＝Ｗ・［Ｘｎ／（Ｘｎ−Ｘｎ−１）］
なる補間演算により計算する（補間演算手段；ステップＳ４）。尚、上記差Δｘは、受光強度が［０．２５］となるエッジ位置ｘｏから受光セルＣｎの位置までの距離であるので、ラインセンサ１の受光面全体において１番目の受光セルＣ１から測ったときの絶対位置ｘは、ｎを光量Ｙ２を得た受光セル１ａのセル番号、受光セル１ａの配列ピッチをＷとしたとき
ｘ＝ｎ・Ｗ−Δｘ
となる。また上記逆変換において求められる相対位置Ｘｎ，Ｘｎ−１は、
Ｘ＝１．９８（２／λｚ）^１／２ｘ
として示されるように［１．９８（２／λｚ）^１／２］倍された値であるが、上記補間演算で比をとることにより実質的にこの項は削除される。
【００４１】
尚、この補間演算については前述した近似式を用いて実行しても良いが、上述した２つの受光セルＣｎ，Ｃｎ−１間での光強度の変化が直線的であると見なし得る場合には、単純な直線補間であっても良い。またここでは隣接する受光セル１ａ間で光強度が［０．２５］となる位置を見出し、その位置をセル境界とする２つの受光セルＣｎ，Ｃｎ−１を特定したが、単に上記位置を挟む２つ以上の受光セルを特定しても良い。但し、この場合には必ず前述した近似式を用いて補間演算を行うことで、その演算精度の低下を防止するようにすれば良い。また上述した逆変換については、例えば予めその計算値を記憶したテーブルを用いることで、その演算処理負担を大幅に軽減して瞬時に実行することが可能である。
【００４２】
一方、距離計算手段３ｅにおいては、図７に示すように前記受光セルＣｎ，Ｃｎ−１の受光面上での相対位置Ｘｎ，Ｘｎ−１と、受光強度が［０．２５］となる位置（エッジ位置）ｘｏと受光セルＣｎの位置との差Δｘ、また受光セルＣｎでの受光強度、および前記単色平行光の波長λとに基づいて、前記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）から遮蔽物７のエッジとラインセンサ１の受光面との距離、即ち、光路方向の距離ｚを求めている（ステップＳ５）。具体的にこの距離計算は、基本的には前述した１山目のフレネル回折を近似した前述した式
光強度Ａ（ｘ）＝１．３７・ｓｅｃｈ｛１．９８（２／λｚ）^１／２ｘ−２．３９｝
から距離ｚについて解き、
ｚ＝（２／λ）｛１．９８・ｘ／［ａｒｃｓｅｃｈ（Ａ（ｘ）／１．３７）＋２．３９］｝^２
として遮蔽物７のエッジとラインセンサ１の受光面との距離ｚを計算することによって行われる。
【００４３】
この場合、前述した受光セルの配列方向のエッジ位置を求める際に、光強度が［０．２５］よりも大きい強度が得られた受光セルＣｎの位置を利用して、この位置とエッジ位置との差Δｘから、
ｚ＝（２／λ）｛１．９８・Δｘ／［ａｒｃｓｅｃｈ（ｙｎ／１．３７）＋２．３９］｝^２
として計算すれば、遮蔽物７のエッジとラインセンサ１の受光面との距離ｚを簡単に求めることができる。特に上式中の分母の項は、前述した
Ｘｎ＝２．３９−ｌｎ｛［１＋（１−Ｙｎ^２）^１／２］／Ｙｎ｝
に相当するので、上述した演算を
ｚ＝（２／λ）｛１．９８・Δｘ／Ｘｎ｝^２
として更に簡単に計算することが可能となる。
【００４４】
具体的には図９（ａ）に示すようにｙ１，ｙ２を正規化された光強度［０．２５］を挟む２点の光量（ｙ２＞ｙ１）、ｎを光量ｙ２を得た受光セル１ａのセル番号、Ｗを受光セル間のピッチ、そして光波長をλとしたとき、
▲１▼ Ｙ１＝ｙ１／１．３７
▲２▼ Ｙ２＝ｙ２／１．３７
▲３▼ ｘ１＝２．３９−ｌｎ｛［１＋（１−Ｙ１^２）^１／２］／Ｙ１｝
▲４▼ ｘ２＝２．３９−ｌｎ｛［１＋（１−Ｙ２^２）^１／２］／Ｙ２｝
▲５▼ Δｘ２＝Ｗ［ｘ２／（ｘ２−ｘ１）］
▲６▼ ｘｏ＝Ｗ・ｎ−Δｘ２
▲７▼ ｚ＝（２／λ）（１．９８・Δｘ２／ｘ２）^２
として、ｘ方向（受光セル１ａの配列方向）およびｚ方向（光路方向）のエッジ位置を同時に求めることが可能となる。
【００４５】
ところで前記光強度が［０．２５］となる位置の前後の２点から距離ｚを計算したとき、その分解能が低くて誤差が大きくなる場合には、図９（ｂ）に示すように１山目のピークに至る前の、例えば［０．８］または［１．０］として予め設定された任意の光強度Ａが得られる位置ｘａを求め、この位置ｘａと前記光強度が［０．２５］となる位置ｘｏとの差Δｘを求め、この差Δｘに従って前記距離ｚを計算するようにしても良い。
【００４６】
例えば光強度が［１．０］となる位置ｘａを求める場合には、
１．０＝１．３７ｓｅｃｈ（Ｘ’−α）
Ｘ’−α＝ａｒｃｓｅｃｈ（１．０／１．３７）＝０．８３
となるので、光強度ｙが［１．０］となる位置ｘを原点とすると
ｙ＝１．３７ｓｅｃｈ（Ｘ’−０．８３）
を近似式として求めることができる。すると逆変換の式は
Ｙ＝ｙ／１．３７
とおいて、
Ｘ＝０．８３−ｌｎ｛［１＋（１−Ｙ^２）^１／２］／Ｙ｝
となるので、前述した計算を
▲１▼ Ｙ１＝ｙ１／１．３７
▲２▼ Ｙ２＝ｙ２／１．３７
▲３▼ ｘ１＝０．８３−ｌｎ｛［１＋（１−Ｙ１^２）^１／２］／Ｙ１｝
▲４▼ ｘ２＝０．８３−ｌｎ｛［１＋（１−Ｙ２^２）^１／２］／Ｙ２｝
▲５▼ Δｘ２＝Ｗ［ｘ２／（ｘ２−ｘ１）］
▲６▼ ｘａ＝Ｗ・ｎ−Δｘ２
▲７▼ ｚ＝（２／λ）｛１．９８・（ｘａ−ｘｏ）／［ａｒｃｓｅｃｈ（Ｙ２）＋２．３９］｝^２
として実行することが可能となる。但し、上記ｘｏは、光強度が［０．２５］となるエッジ位置である。
【００４７】
尚、予め設定された任意の光強度として［１．３７］なるフレネル回折の１山目のピーク位置ｘｐを求めれば、上式におけるハイパボリックセカンド関数の項が消えるので、距離ｚを
ｚ＝（２／λ）［１．９８・（ｘｐ−ｘｏ）／２．３９］^２
として簡単に計算することができる。
【００４８】
尚、一般的に光強度がＡ［０．２５＜Ａ≦１．３７］となる位置ｘａを求める場合には、ｙ１，ｙ２を正規化された光強度Ａを挟む２点の光量（ｙ２＞ｙ１）、ｎを光量ｙ２を得た受光セル１ａのセル番号、Ｗを受光セル１ａ間のピッチ、そして光波長をλとしたとき、
▲１▼ Ｙ１＝ｙ１／１．３７
▲２▼ Ｙ２＝ｙ２／１．３７
▲３▼ ｘ１＝ａｒｃｓｅｃｈ（Ａ／１．３７）−ｌｎ｛［１＋（１−Ｙ１^２）^１／２］／Ｙ１｝
▲４▼ ｘ２＝ａｒｃｓｅｃｈ（Ａ／１．３７）−ｌｎ｛［１＋（１−Ｙ２^２）^１／２］／Ｙ２｝
▲５▼ ｘａ＝Ｗ［ｎ−ｘ２／（ｘ２−ｘ１）］
なる計算を行えば良い。また光強度が［０．２５］となる前述したエッジ位置ｘｏを同様にして求め、その差Δｘを
Δｘ＝ｘａ−ｘｏ
として求めて、距離ｚを
ｚ＝（２／λ）｛１．９８・Δｘ／［ａｒｃｓｅｃｈ（Ｙ２）＋２．３９］｝^２
として算出するようにすれば良い。
【００４９】
かくして上述した如くして遮光物７のエッジ位置（受光セル１ａの配列方向の位置ｘおよび光路方向の位置ｚ）を検出する位置検出方法および装置によれば、フレネル回折による光強度分布を高精度に近似したハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いるので、ラインセンサ１の複数の受光セル１ａによる受光強度ｙからその光強度が［０．２５］となる位置Ｘ、つまり遮蔽物７のエッジ位置ｘおよびエッジまでの距離ｚをそれぞれ高精度に検出することができる。
【００５０】
また演算処理に用いた自然対数関数（ｌｎ関数）は、通常の浮動小数点演算（ＦＰＵ）機能を備えたマイクロプロセッサではその命令の中に含まれているが、このようなＦＰＵ機能を備えていないマイクロプロセッサであっても、例えば上記ハイパボリックセカンド関数ｓｅｃｈ（ｘ）、特にその逆関数ｌｎ（ｘ）については、例えば

として級数展開が可能であり、その収束も速いので計算が容易である。従ってエッジ位置の検出処理を簡単に、しかも高精度に行うことが可能となる等の効果が奏せられる。
【００５１】
またラインセンサ１の出力は、該ラインセンサ１における各受光セル１ａの配列ピッチＷとセル数によって変化する。ちなみに７μｍの配列ピッチで５０００セルを備えた分解能の高いイメージセンサを用いた場合には、例えば図１０（ａ）に示すように非常に緻密なセンサ出力が得られる。この点、８５μｍの配列ピッチで１０２セルを備えた汎用の安価なイメージセンサを用いた場合には、図１０（ｂ）に示すように粗いセンサ出力しか得ることができない。しかしセル数が少ない分だけセンサ出力の高速な読み出しが可能である。
【００５２】
しかしこのような分解能の低い安価なラインセンサ１を用いたとしても、前述したように本発明に係る位置検出方法および装置によれば、フレネル回折による光強度分布を高精度に近似したハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いるので受光セル１ａ間の受光強度の変化を高精度に補間することができる。従って分解能の低い安価なラインセンサ１を用いてセンサ出力の読み出し速度を十分に速くしながら、簡単な演算処理によってエッジ位置検出を高精度に行うことが可能となる等の実用上多大なる効果が奏せられる。
【００５３】
尚、本発明は上述した各実施形態に限定されるものではない。例えばラインセンサ１が備える受光セル１ａの数やその配列ピッチＷについては、その検出仕様に応じたものを用いれば十分である。またエッジ検出部３については、汎用のマイクロプロセッサを用いて実現すれば良く、前述した演算式をＲＯＭ化して与えるようにしても良い。その他、本発明はその要旨を逸脱しない範囲で種々変形して実施することができる。
【００５４】
【発明の効果】
以上説明したように本発明によれば、フレネル回折による受光強度分布をハイパボリックセカンド関数ｓｅｃｈ（ｘ）を用いて近似し、この近似式を用いてラインセンサの出力からセルの配列方向におけるエッジ位置とエッジと受光面との距離をそれぞれ計算するので、簡易にして高精度に、しかも高速度にエッジ位置を検出することができる。特に分解能の低い安価なラインセンサを用いた場合であっても、その計測精度を十分に高め得る等の実用上多大なる効果が奏せられる。
【図面の簡単な説明】
【図１】本発明の一実施形態に係る位置検出装置の基本的な構成を示す図。
【図２】ラインセンサにおける受光セルの配列を示す図。
【図３】投光部の概略構成を示す図。
【図４】投光部から射出される平行光線束の光学系を図３の矢視Ａ−Ａ方向からみて模式的に示す図。
【図５】投光部から射出される平行光線束の光学系を図３の矢視Ｂ−Ｂ方向からみて模式的に示す図。
【図６】フレネル回折による光強度分布の理論値と、関数を用いた近似特性とを対比して示す図。
【図７】本発明の一実施形態に係る一検出方法および装置におけるエッジ検出処理の手順の一例を示す図。
【図８】連接する２つの受光セルにおいて求められる受光強度と、これらの受光強度が得られた位置から求められるエッジ位置の関係を示す図。
【図９】エッジと趣向面との距離ｚを算出する上での演算処理の概念を示す図。
【図１０】ラインセンサの分解能の違いによるセンサ出力の例を示す図。
【図１１】フレネル回折による光強度分布特性を示す図。
【図１２】フレネル回折による光強度分布のフレネル関数を用いた近似における問題点を説明する為の図。
【符号の説明】
１ラインセンサ（受光部）
１ａ受光セル
２投光部
３装置本体
３ｂ回折パターン検出手段
３ｃ正規化手段
３ｄエッジ検出部
３ｅ距離検出部
７遮蔽物（検出対象物）[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention provides, for example, a position detecting method capable of detecting, at high speed and with high accuracy, a positional displacement in the width direction of an edge of a band-shaped body that is unwound from a roll and conveyed in one direction at high speed. And equipment.
[0002]
[Related background art]
As a position detecting device for detecting the position of an edge of an article such as a film or a sheet, a light projecting section (light source) that irradiates parallel light toward the article (test object) and faces the light projecting section There is an optical type including a light receiving unit (line sensor) such as a CCD provided in such a manner. This type of optical position detecting device basically receives parallel light that is not blocked by the article by a light receiving unit, and receives a parallel light receiving region and a non-light receiving region (light blocking region) in the light receiving unit. Is detected as the position of the edge of the article (inspection object).
[0003]
Recently, using monochromatic parallel light such as laser light and focusing on the Fresnel diffraction of the monochromatic parallel light at the edge of the article (object to be inspected), the light intensity distribution on the light receiving surface of the line sensor (light receiving section) is calculated as described above. A device that detects the position of an edge of an article (object to be inspected) with high accuracy has also been proposed (for example, see Patent Document 1).
[0004]
[Patent Document 1]
JP-A-8-247726
[0005]
[Problems to be solved by the invention]
By the way, when detecting the position of the edge of the inspection object using the light intensity distribution on the light receiving surface of the line sensor (light receiving unit) by Fresnel diffraction of monochromatic parallel light, the characteristics of the light intensity distribution are obtained in advance with high accuracy. It is necessary to keep. Incidentally, the light intensity distribution by the Fresnel diffraction rises sharply near the edge position as shown in FIG. 11, and converges while oscillating as the distance from the edge position increases. The characteristics of such a light intensity distribution include the wavelength of monochromatic parallel light as λ [nm], the distance from the edge of the inspection object to the light receiving surface z [mm], and the edge position x [μm] on the light receiving surface. When [0] is set, ∫ is changed from [x = 0] to [(2 / λz)^1/2• x] as an operation symbol indicating integration up to
Light intensity = (1/2) ｛[1/2 + S (x)]²+ [1/2 + C (x)]²｝
S (x) = ∫sin (π / 2) · U²dU
C (x) = ∫cos (π / 2) · U²dU
Is represented as Here, U is a temporary variable.
[0006]
For the functions S (x) and C (x) in the above equation, Fresnel functions are used exclusively as shown in a collection of mathematical formulas, and where x is large,
S (x) '≒ (1/2)-(1 / πx) cos (πx²/ 2)
C (x) '≒ (1/2) + (1 / πx) sin (πx²/ 2)
Respectively. Therefore, basically, by using the above approximate expressions S (x) 'and C (x)', the above-described edge position can be calculated from the light receiving intensity of each light receiving cell of the line sensor.
[0007]
However, when actually calculated, as shown in FIG. 12, the functions S (x) and C (x) and their approximate expressions S (x) ′ and C (x) ′ have a convergence portion ( Although it is very good approximation in the second mountain), it cannot be denied that there is a large deviation in the first rising portion (first mountain). In particular, the characteristic of the first rising portion plays an important role in edge detection, and the deviation of the characteristic causes a decrease in edge position detection accuracy.
[0008]
The present invention has been made in view of such circumstances, and has as its object to approximate the light intensity distribution on the light receiving surface by Fresnel diffraction, particularly the characteristics of the first rising portion with high accuracy, thereby obtaining a predetermined value. It is an object of the present invention to provide a position detecting method and apparatus capable of detecting the edge position of a shielding object that has entered the optical path and the distance from the light receiving surface to the edge position with high accuracy.
[0009]
Another object of the present invention is to provide a highly accurate and simple method for determining the edge position and the distance from the light receiving surface to the edge position even when using an inexpensive line sensor in which the arrangement pitch of a plurality of light receiving cells is coarse. Another object of the present invention is to provide a position detecting method and device capable of detecting a position.
[0010]
[Means for Solving the Problems]
In order to achieve the above-described object, a position detecting method according to the present invention includes a line sensor (light receiving unit) including a plurality of light receiving cells arranged at a predetermined pitch in one direction, and a line sensor (light receiving unit) provided facing the line sensor. A light projecting unit for projecting monochromatic parallel light toward the plurality of light receiving cells of the line sensor, and analyzing the output of the line sensor to detect the light receiving cell of a shield present in the optical path of the monochromatic parallel light. An edge detection unit that detects an edge position in the arrangement direction, and is applied to a position detection device,
In particular, in the edge detection unit, the light intensity change at the first rising portion of the light intensity distribution on the light receiving surface of the line sensor due to the Fresnel diffraction of the monochromatic parallel light by the shield is approximated by a hyperbolic second function sech (x). Using the hyperbolic second function sech (x), the light receiving intensity of each light receiving cell of the line sensor is analyzed to determine an edge position of the shield in the arrangement direction of the light receiving cells. The distance between the shield and the line sensor is obtained using the hyperbolic second function sech (x) from the difference between the position of the light receiving cell from which the light receiving intensity is obtained.
[0011]
That is, in the position detection method according to the present invention, the first rising portion of the light intensity distribution on the light receiving surface due to the Fresnel diffraction of the monochromatic parallel light, in particular, the distribution characteristic of the first peak has a, b, and c as coefficients, respectively. As
y = a · sech (bx + c)
It has been found that the approximation very well approximates the hyperbolic second function sech (x).
[0012]
The output (light intensity) of the line sensor is analyzed using the hyperbolic second function sech (x), and the light intensity (relative value) in the light intensity distribution on the light receiving surface by the Fresnel diffraction is [0.25]. Is detected as an edge position of the shielding object in the arrangement direction of the light receiving cells, and the relationship between the edge position and a position at which a predetermined light receiving intensity is obtained using the hyperbolic second function sech (x). Specifically, the distance between the edge and the light receiving surface of the line sensor is obtained based on the difference between the edge position and the position of the light receiving cell at which a predetermined light receiving intensity is obtained.
[0013]
Preferably, the analysis of the light receiving intensity of each light receiving cell of the line sensor using the hyperbolic second function sech (x) is performed by, for example, detecting a light receiving intensity larger than the reference light receiving intensity near a predetermined reference light receiving intensity [0.25]. The light receiving cell having the light receiving intensity and the light receiving cell having the light receiving intensity smaller than the reference light receiving intensity are obtained, and the light receiving position at which the light receiving intensity is obtained on the light receiving surface of each light receiving cell is obtained by inverting the hyperbolic second function sech (x). Function ln ｛[1+ (1-Y²)^1/2/ Y}, a relative position from the position where the received light intensity is [0.25] is obtained, and a position xo where the received light intensity is [0.25] is obtained by interpolation from these relative positions. good. Further, regarding the distance between the shielding object and the line sensor, the position x2 of the light receiving cell whose light receiving intensity used for obtaining the edge position in the arrangement direction of the light receiving cells described above is larger than [0.25]. The distance component z of Fresnel diffraction is calculated from the hyperbolic second function sech (x) based on the difference Δx from the edge position xo at which the intensity is [0.25] and the received light intensity at the position x2. You can do it.
[0014]
Note that the distance z between the shield and the line sensor is calculated as the inverse function ln ｛[1+ (1-Y) of the hyperbolic second function sech (x).²)^1/2/ Y}, the light intensity is arbitrarily set in advance in the range from the light intensity [0.25] to the light intensity at the peak position of the first peak [1.37]. For example, the position xa at which the light intensity becomes [0.8] or [1.0] is obtained, and the inverse calculation is performed from the hyperbolic second function sech (x) according to the difference Δx between the position Xa and the edge position xo. May be.
[0015]
Further, the position detecting device according to the present invention includes a line sensor including a plurality of light receiving cells arranged at a predetermined pitch in one direction, and the plurality of light receiving cells of the line sensor provided to face the line sensor. A light projecting unit for projecting monochromatic parallel light toward, and analyzing the output of the line sensor according to the light intensity distribution on the light receiving surface of the line sensor by Fresnel diffraction of the monochromatic parallel light by the shield, An edge detector for detecting the position of an edge in the direction in which the light-receiving cells of the shield present in the optical path of the monochromatic parallel light, and in particular, as the edge detector,
Inverse function ln ｛[1+ (1-Y) of the hyperbolic second function sech (x) approximating the rising portion of the light intensity distribution on the light receiving surface of the line sensor due to Fresnel diffraction of monochromatic parallel light by the shield.²)^1/2Cell direction position detecting means for obtaining a position xo in the disposition direction of the light receiving cell having a light receiving intensity of [0.25] from the normalized output of the line sensor using // Y｝,
The inverse function ln ｛[1+ (1-Y²)^1/2/ Y}, a plurality of positions xa in the arrangement direction of the light receiving cells and a light receiving intensity at each position xa are obtained, and the light receiving cells having the positions Xa and the light intensity of [0.25] are obtained. And a distance calculating means for calculating a distance z between the edge of the shielding object and the line sensor from the hyperbolic second function sech (x) based on a difference Δx from the position xo in the arrangement direction. I have.
[0016]
Specifically, the cell direction position detecting means comprises: a light receiving cell having a light receiving intensity greater than the reference light receiving intensity near a predetermined reference light receiving intensity [0.25] from the output of the line sensor; A light receiving cell specifying means for specifying light receiving cells each having a light receiving intensity smaller than the intensity, and an inverse function ln ｛[1+ (1-Y) of the hyperbolic second function sech (x).²)^1/2] / Y｝, a light receiving position calculating unit for respectively obtaining a light receiving position at which the light receiving intensity of the light receiving cell is determined on the light receiving surface of each light receiving cell specified by the light receiving cell specifying unit in accordance with the light intensity distribution approximated by Y / Means for detecting the position of the reference light receiving intensity from the light receiving positions obtained by the means as the edge position of the shield.
[0017]
In addition, the distance calculation means calculates the light receiving intensity from the light receiving cell whose light receiving intensity is larger than [0.25] and the light receiving cell whose light receiving intensity is smaller than [0.25] based on the normalized output of the line sensor. Is obtained, and the difference Δx between the position x2 of the light receiving cell having the received light intensity of greater than [0.25] and the edge position xo at which the received light intensity is [0.25] is obtained. The distance z is calculated from the hyperbolic second function sech (x) based on the received light intensity.
[0018]
Alternatively, the distance calculation means calculates the inverse function ln ｛[1+ (1-Y²)^1/2/ Y}, and a position xa in the arrangement direction of the light receiving cells at which a predetermined light intensity A (0.25 <A ≦ 1.37) is obtained, and a position xa obtained by the cell direction position detecting means. The distance z is calculated from the hyperbolic second function sech (x) based on the difference Δx from the edge position xo.
[0019]
According to the position detection device configured as described above, the light receiving position at which the light receiving intensity of the light receiving cell is obtained in at least the light receiving cells having the light receiving intensity sandwiching the reference light receiving intensity [0.25] is determined by the light intensity by Fresnel diffraction. By using the hyperbolic second function sech (x) that approximates the characteristics of the first rising portion of the distribution with high accuracy, the positions of the edges on the light receiving surface of the line sensor can be obtained from these light receiving positions. That is, the position where the received light intensity is [0.25] can be obtained with high accuracy. At the same time, the distance between the edge of the shield and the light receiving surface of the line sensor can be calculated easily and with high accuracy.
[0020]
The inverse function lnｌ [1+ (1-Y) of the hyperbolic second function sech (x) is used.²)^1/2] / Y} can be series-expanded, or can be operated according to an instruction implemented in the CPU, so that the operation processing speed (position detection speed) can be sufficiently increased.
A light receiving cell having a peak value at the beginning of the output of the line sensor and a light receiving cell in front of the light receiving cell are obtained, and an inverse function ln の [of the above-described hyperbolic second function sech (x) is obtained from each light receiving intensity of these light receiving cells. 1+ (1-Y²)^1/2] / Y}. If the edge position is detected in this manner, for example, even when the detection target is made of a translucent body and the monochromatic parallel light cannot be completely blocked by the detection target, the edge of the detection target ( The position of the edge) and the distance from the light receiving surface of the line sensor can be detected with high accuracy.
[0021]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, a position detection method and a position detection device according to an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a schematic configuration diagram of a position detecting device according to this embodiment. Basically, as shown in FIG. 2, a line sensor (light receiving device) including a plurality of light receiving cells 1a arranged at a predetermined pitch W in one direction. Unit) 1 and a light projecting unit 2 provided to face the light receiving surface of the line sensor 1 and projecting monochromatic parallel light 4 having a predetermined light beam width toward a plurality of light receiving cells 1a of the line sensor 1. And The apparatus body 3 realized by a microcomputer or the like is formed of, for example, a band-shaped body positioned in the optical path of the monochromatic parallel light 4 by analyzing the output of the line sensor 1 (the amount of light received by each light receiving cell 1a). It plays a role in detecting the edge position of the shield (detection target) 7 in the direction in which the light receiving cells 1a are arranged with high accuracy.
[0022]
The light projecting unit 2 is, for example, a mirror that reflects monochromatic light (laser light) emitted from a light source 2a composed of a laser diode (LD) as shown in FIG. Prism 2b), an aperture mask (light projecting window) 2c for defining the light beam shape of the monochromatic light guided through the mirror 2b into a slit shape, and converting the light passing through the aperture mask 2c into a parallel light beam. And a projection lens (collimator lens) 2d for converting and projecting. A shield 7 which is an object to be detected is positioned between the projection lens 2d and the light receiving unit 1, and the edge position of the shield 7 displaced in the longitudinal direction of the slit of the aperture mask 2c is interposed via the light receiving unit 1. Detected.
[0023]
More specifically, the aperture mask 2c has a rectangular slit opening, and the light source 2a is provided so as to emit monochromatic light toward the slit at a predetermined divergent angle. In particular, when an LD is used as the light source 2a, laser light emitted from the LD with an elliptical intensity distribution is projected onto the aperture mask 2c as shown by a broken line in the figure. At this time, optically arranging the LD and the aperture mask 2c so that the major axis of the laser light is in the longitudinal direction of the slit of the aperture mask 2c is necessary to reduce the size of the light projecting unit 2. preferable. The mirror (prism) 2d forms an optical path for reflecting the laser beam emitted from the LD at a substantially right angle, thereby maintaining the optical distance between the LD and the aperture mask 2c, and furthermore, the projection lens 2d while maintaining the optical distance. It plays a role of making the overall shape of the light unit 2 compact. In addition, such a light projecting unit 2 is integrated into the U-shaped casing 5 in which a predetermined gap L is formed together with the above-described line sensor 1 so as to face each other with the gap interposed therebetween. It is formed as one sensing unit.
[0024]
As shown schematically in FIGS. 4 and 5 by the light projecting unit 2 configured as above, a slit-shaped cross-sectional shape converted into parallel light through the aperture mask 2c and the projection lens 2d. Is projected toward the line sensor (light-receiving unit) 1. The size of the cross-sectional shape of the parallel light beam is, for example, 9 mm on the long side × 3 mm on the short side, whereas the size of the light receiving surface of the line sensor 1 that receives the balanced light beam is, for example, 8. 7 mm x 0.08 mm on the short side. That is, the lengths of the respective long sides are substantially equal.
[0025]
Incidentally, the dimension of the short side (3 mm) in the cross-sectional shape of the parallel light beam is set to be considerably larger than the short side dimension (0.08 mm) of the light receiving surface of the line sensor 1 because of the parallelism between the light emitter and the light receiver. This is to facilitate the adjustment of the above and to avoid the influence of Fresnel diffraction due to the long side edge 2h of the slit of the aperture mask 2c as shown in FIG. 5, even when the light projector or the light receiver is inclined. However, when the shape of the light beam is shaped using the above-described aperture mask 2c, the slit-like parallel light beam (monochromatic parallel light) 4 has a short side edge of the slit of the aperture mask 2c as shown in FIG. It cannot be denied that a non-parallel ray component generated by the influence of Fresnel diffraction in 2e is included. However, the influence of the non-parallel ray component may be corrected by normalizing the output of the line sensor 1 as described later.
[0026]
Incidentally, the apparatus main body 3 includes an input buffer 3a that takes in the output of the line sensor 1 (the amount of light received by each light receiving cell 1a) and obtains the light intensity distribution on the light receiving surface of the line sensor 1. In particular, the apparatus main body 3 receives, by the line sensor 1, all monochromatic parallel lights of a predetermined light beam width previously projected from the light projecting section 2 as its initial setting processing, and the light intensity distribution at this time is obtained. A diffraction pattern of the monochromatic parallel light projected by the light projecting unit 2 on the basis of the diffraction pattern, and a diffraction pattern detecting means 3b for determining a normalization parameter for the amount of light received by each of the light receiving cells 1a according to the reciprocal of the diffraction pattern as described later. Is provided. This diffraction pattern is caused by a non-parallel ray component generated by the influence of Fresnel diffraction at the short side edge 2e of the slit formed in the aperture mask 2c.
[0027]
Further, the apparatus main body 3 includes a normalizing means 3c for normalizing the output of the line sensor 1 according to the normalization parameter obtained by the diffraction pattern detecting means 3b, and the line sensor normalized by the normalizing means 3c. 1. An edge detector 3b that detects the position of the edge (edge) of the shielding object (detection target) 7 in accordance with the output (normalized output) of the light receiving cell 1a in the line sensor 1 in the arrangement direction. And
[0028]
Basically, when a part of the monochromatic parallel light is blocked by the blocking object (detection target) 7, the edge detection unit 3 d generates Fresnel diffraction at its end (edge). And the intensity of light reaching the light receiving surface of the line sensor 1 rises sharply near the edge position as shown in FIG. 12, and has a distribution characteristic of converging while oscillating as the distance from the edge position increases. , The position of the edge of the shield 7 is detected with high accuracy in accordance with the light intensity distribution on the light receiving surface of the line sensor 1.
[0029]
Incidentally, the edge position is such that the light intensity distribution on the light receiving surface of the line sensor 1 when a part of the monochromatic parallel light is blocked by the shield 7 rises from the light intensity [0] to [1.0]. As shown in the above-mentioned Patent Document 1, the light intensity is obtained as the position where the light intensity becomes [0.25] at the first rising portion (first mountain).
[0030]
Further, the apparatus body 3 calculates a distance z between the edge of the shield 7 that has caused the Fresnel diffraction and the light receiving surface of the line sensor 1 according to the light intensity distribution on the light receiving surface of the line sensor 1. (Distance calculating means) 3e. The distance detection output stage 3e is arranged such that the light intensity distribution on the light receiving surface of the line sensor 1 affected by Fresnel diffraction, especially the light intensity distribution at the rising portion, is equal to the wavelength λ of the monochromatic parallel light and the distance z. Therefore, the distance z is calculated from the characteristics of the light intensity distribution as described later in accordance with the respective light receiving intensities at a plurality of positions on the light receiving surface of the line sensor 1 at the rising portion. I have.
[0031]
The position detecting method and apparatus according to the present invention are characterized by the position detecting method and the apparatus according to the present invention. The apparatus main body (edge detecting unit) 3 detects the edge of the shield 7 from the output of the line sensor 1. When detecting the position, specifically the position xo of the light receiving cells 1a in the line sensor 1 in the arrangement direction and the distance z between the light receiving surface of the line sensor 1 and the shield 7, the hyperbolic approximation of the light intensity distribution by Fresnel diffraction. The point is that the edge position is calculated using the second function sech (x).
[0032]
That is, the light intensity distribution on the light receiving surface of the line sensor 1 due to Fresnel diffraction, in particular, the light intensity change at the first rising portion (first mountain) is approximated by a hyperbolic second function sech (x). The light receiving intensity of each light receiving cell 1a of the line sensor 1 is analyzed in accordance with the light intensity distribution approximated by using the function sech (x), and the edge position xo and the distance z of the shield 7 are obtained. .
[0033]
The approximation of the light intensity distribution by the Fresnel diffraction using the hyperbolic second function sech (x) will be described. When the Fresnel function is used as described above, the error at the first rising portion (first mountain) of the light intensity distribution is very small. There is a problem of being big. Therefore, focusing only on the first rising portion (first mountain) of the light intensity distribution, approximation is performed using a square rational function, a hyperbolic cosine function, and an exponential function from the shape of the mountain (change tendency of light intensity). Tried that.
[0034]
Specifically, as a squared rational function
y = a / ｛(x + b)²+ C｝
As a hyperbolic second function
y = a · sech (bx + c)
And as an exponential function
y = a · exp ｛−b (x + c)²｝
The following three functions were considered, and their characteristic curves were obtained while substituting appropriate values for the coefficients a, b, and c shown in these functions, and the calculation results as shown in FIG. 6 were obtained.
[0035]
In FIG. 6, the characteristic A indicates the theoretical value of the light intensity distribution, and the characteristic B indicates the coefficients a, b, and c in the squared rational function as [0.057], [−0.38], The change in the light intensity y when [0.0417] is set, and the characteristic C are the coefficients a, b, and c in the hyperbolic second function as [1.37], [6.29], and [-2.40], respectively. And the characteristic D is the light intensity y when the coefficients a, b, and c in the exponential function are [1.37], [16.30], and [−0.38], respectively. In each case. However, these calculations were performed with the wavelength λ of the monochromatic light being 670 nm and the distance z from the edge of the shield 7 to the light receiving surface of the line sensor 1 being 300 mm. As shown in these calculation results, if the hyperbolic second function sech (x) is used, the characteristics of the light intensity distribution due to Fresnel diffraction, particularly the characteristics of the first rising portion (first mountain) can be approximated with very high accuracy. It became clear.
[0036]
Incidentally, when the hyperbolic second function is applied to the above-described equation of the light intensity distribution by Fresnel diffraction to approximate the first rising portion (first mountain) of the light intensity, the hyperbolic second function sech (x) becomes
Light intensity = 1.37 · sech ｛1.98 (2 / λz)^1/2x-2.39｝
As shown. And it was confirmed that this approximation formula matched the theoretical formula of the light intensity distribution with an accuracy of about three digits. Here, λ is the light wavelength [nm], z is the distance [mm] from the edge to the light receiving surface, and x is the coordinate [μm] where the edge position on the light receiving surface is [0]. The coefficient is set under various units.
[0037]
Based on such knowledge, the present invention approximates a light intensity distribution by Fresnel diffraction, particularly a first rising portion thereof using the above-described hyperbolic second function sech (x), and hyperbolic second approximating the light intensity distribution. The edge position of the shield 7 is detected with high accuracy from the output of the line sensor 1 using the function sech (x).
[0038]
At this time, the following contrivance has been made in order to simplify the calculation process and increase the speed of the edge position detection process. The algorithm of this calculation processing will be described. The light intensity approximated using the hyperbolic second function sech (x) is, as described above,
Light intensity = 1.37 · sech ｛1.98 (2 / λz)^1/2x-2.39｝
As shown. And calculating its inverse function,
Y = (y / 1.37), X = 1.98 (2 / λz)^1/2x
And then
X = 2.39-ln ｛[1+ (1-Y²)^1/2] / Y｝
Can be expressed as
[0039]
Therefore, in the edge detection unit 3d, for example, according to the procedure shown in FIG. 7, first, the normalized light receiving intensities y1, y2, to ym obtained from the plurality (m) of the light receiving cells 1a in the line sensor 1 are adjacent to each other. The light receiving cell Cn that has obtained the light receiving intensity larger than the above-mentioned reference light intensity [0.25] and the light receiving cell Cn-1 that has obtained the light receiving intensity smaller than the above described reference light intensity [0.25] It is determined (step S1). That is, two light receiving cells Cn and Cn-1 adjacent to each other and having a light receiving intensity of [0.25] between the plurality of light receiving cells 1a (C1, C2 to Cm) are obtained. Then, the light receiving intensity yn, yn-1 of each of the light receiving cells Cn, Cn-1 is divided by the above-mentioned coefficient [1.37] to be converted into light intensity Yn, Yn-1 on the XY coordinate ( Step S2).
[0040]
Thereafter, the positions Xn and Xn-1 on the light receiving surface of the light receiving cells Cn and Cn-1 at which the light receiving intensities Yn and Yn-1 of the light receiving cells Cn and Cn-1 are obtained are calculated by the above-described approximate expression. According to
Xn = 2.39-ln ｛[1+ (1-Yn²)^1/2] / Yn｝
Xn-1 = 2.39-ln ｛[1+ (1-Yn-1²)^1/2] / Yn-1｝
The relative position on the X-axis is calculated by inverse transformation (light receiving position calculating means; step S3). From these positions Xn, Xn-1, the position of the light receiving cell Cn and the light receiving position are shown in FIG. The difference Δx from the edge position where the intensity is [0.25] is
Δx = W · [Xn / (Xn−Xn−1)]
(Interpolation calculation means; step S4). Since the difference Δx is a distance from the edge position xo at which the light receiving intensity becomes [0.25] to the position of the light receiving cell Cn, the difference Δx is measured from the first light receiving cell C1 on the entire light receiving surface of the line sensor 1. The absolute position x at this time is represented by n, where n is the cell number of the light receiving cell 1a that obtained the light amount Y2, and W is the arrangement pitch of the light receiving cells 1a.
x = nW-Δx
Becomes Further, the relative positions Xn and Xn-1 obtained in the above inverse transformation are
X = 1.98 (2 / λz)^1/2x
[1.98 (2 / λz) as shown as^1/2], But this term is substantially eliminated by taking the ratio in the above interpolation operation.
[0041]
Note that this interpolation operation may be performed using the above-described approximation formula. However, if the change in light intensity between the two light receiving cells Cn and Cn-1 can be considered to be linear, Alternatively, simple linear interpolation may be used. In this case, a position where the light intensity is [0.25] is found between the adjacent light receiving cells 1a, and two light receiving cells Cn and Cn-1 having the position as a cell boundary are specified. Two or more light receiving cells may be specified. However, in this case, it is sufficient to always perform the interpolation calculation using the above-described approximation formula so as to prevent the calculation accuracy from lowering. In addition, the above-described inverse conversion can be executed instantaneously by using a table in which the calculated values are stored in advance, thereby greatly reducing the calculation processing load.
[0042]
On the other hand, in the distance calculating means 3e, as shown in FIG. 7, the relative positions Xn and Xn-1 on the light receiving surface of the light receiving cells Cn and Cn-1 and the position where the light receiving intensity is [0.25] ( Based on the difference Δx between the edge position) xo and the position of the light receiving cell Cn, the light receiving intensity at the light receiving cell Cn, and the wavelength λ of the monochromatic parallel light, the hyperbolic second function sch (x) is used to calculate the The distance between the edge and the light receiving surface of the line sensor 1, that is, the distance z in the optical path direction is obtained (step S5). Specifically, this distance calculation is basically based on the above-described equation that approximates the Fresnel diffraction of the first mountain described above.
Light intensity A (x) = 1.37 · sech ｛1.98 (2 / λz)^1/2x-2.39｝
For a distance z from
z = (2 / λ) {1.98 × / [arcsech (A (x) /1.37) +2.39]}²
By calculating the distance z between the edge of the shield 7 and the light receiving surface of the line sensor 1.
[0043]
In this case, when the edge position in the arrangement direction of the light receiving cells described above is obtained, the position of the light receiving cell Cn at which the light intensity is greater than [0.25] is used to determine this position and the edge position. From the difference Δx of
z = (2 / λ) {1.98Δx / [arcsech (yn / 1.37) +2.39]}²
, The distance z between the edge of the shield 7 and the light receiving surface of the line sensor 1 can be easily obtained. In particular, the term of the denominator in the above equation is
Xn = 2.39-ln ｛[1+ (1-Yn²)^1/2] / Yn｝
, So the above calculation
z = (2 / λ) {1.98 · Δx / Xn}²
Can be calculated more easily.
[0044]
Specifically, as shown in FIG. 9 (a), y1 and y2 are the light receiving cells 1a that have obtained two points of light quantity (y2> y1) sandwiching the normalized light intensity [0.25], and n is light quantity y2. Cell number, W is the pitch between the light receiving cells, and the light wavelength is λ,
{Circle around (1)} Y1 = y1 / 1.37
{Circle around (2)} Y2 = y2 / 1.37
(3) x1 = 2.39-ln ＝ [1+ (1-Y1²)^1/2] / Y1｝
(4) x2 = 2.39-ln ｛[1+ (1-Y2²)^1/2] / Y2｝
(5) Δx2 = W [x2 / (x2-x1)]
(6) xo = Wn-Δx2
{Circle around (7)} z = (2 / λ) (1.98 · Δx2 / x2)²
As a result, it is possible to simultaneously determine the edge positions in the x direction (the arrangement direction of the light receiving cells 1a) and the z direction (the optical path direction).
[0045]
By the way, when the distance z is calculated from two points before and after the position where the light intensity becomes [0.25], if the resolution is low and the error is large, one peak is obtained as shown in FIG. Before reaching the eye peak, a position xa at which an arbitrary light intensity A preset as, for example, [0.8] or [1.0] is obtained is obtained, and the position xa and the light intensity are set to [0.25]. ], And the distance z may be calculated according to the difference Δx.
[0046]
For example, when finding the position xa where the light intensity is [1.0],
1.0 = 1.37sech (X '-[alpha])
X '-[alpha] = arcsech (1.0 / 1.37) = 0.83
Therefore, if the position x where the light intensity y becomes [1.0] is set as the origin,
y = 1.37s (X'-0.83)
Can be obtained as an approximate expression. Then the inverse transformation formula is
Y = y / 1.37
And then
X = 0.83-ln ｛[1+ (1-Y²)^1/2] / Y｝
So the above calculation
{Circle around (1)} Y1 = y1 / 1.37
{Circle around (2)} Y2 = y2 / 1.37
(3) x1 = 0.83-ln ＝ [1+ (1-Y1²)^1/2] / Y1｝
(4) x2 = 0.83-ln ｛[1+ (1-Y2²)^1/2] / Y2｝
(5) Δx2 = W [x2 / (x2-x1)]
(6) xa = Wn-Δx2
{7} z = (2 / λ) {1.98 · (xa−xo) / [arcsech (Y2) +2.39]}²
It can be executed as Here, xo is an edge position where the light intensity becomes [0.25].
[0047]
If the peak position xp of the first peak of Fresnel diffraction of [1.37] is obtained as an arbitrary predetermined light intensity, the term of the hyperbolic second function in the above equation disappears.
z = (2 / λ) [1.98 · (xp−xo) /2.39]²
Can be easily calculated as
[0048]
In general, when calculating the position xa where the light intensity is A [0.25 <A ≦ 1.37], the light amounts (y2>) of two points sandwiching the light intensity A in which y1 and y2 are normalized y1), n is the cell number of the light receiving cell 1a from which the light amount y2 is obtained, W is the pitch between the light receiving cells 1a, and the light wavelength is λ.
{Circle around (1)} Y1 = y1 / 1.37
{Circle around (2)} Y2 = y2 / 1.37
{Circle around (3)} x1 = arcsech (A / 1.37) -ln ｛[1+ (1-Y1²)^1/2] / Y1｝
{Circle around (4)} x2 = arcsech (A / 1.37) -ln ｛[1+ (1-Y2²)^1/2] / Y2｝
{Circle around (5)} xa = W [nx2 / (x2-x1)]
What kind of calculation should be performed. Further, the above-described edge position xo at which the light intensity becomes [0.25] is similarly obtained, and the difference Δx is calculated.
Δx = xa−xo
And the distance z is calculated as
z = (2 / λ) {1.98 · Δx / [arcsech (Y2) +2.39]}²
What is necessary is just to calculate.
[0049]
Thus, according to the position detecting method and apparatus for detecting the edge position (position x in the arrangement direction of the light receiving cells 1a and position z in the optical path direction) of the light shielding object 7 as described above, the light intensity distribution by Fresnel diffraction can be detected with high accuracy. Is used, the position X where the light intensity becomes [0.25] from the received light intensity y of the plurality of light receiving cells 1a of the line sensor 1, that is, the edge position x of the shield 7 And the distance z to the edge can be detected with high accuracy.
[0050]
The natural logarithmic function (In function) used in the arithmetic processing is included in the instructions of a microprocessor having a normal floating-point operation (FPU) function, but does not have such an FPU function. Even with a microprocessor, for example, for the hyperbolic second function sech (x), particularly its inverse function ln (x), for example,

The series expansion is possible, and the convergence is fast, so that the calculation is easy. Therefore, it is possible to obtain an effect that the detection processing of the edge position can be performed easily and with high accuracy.
[0051]
The output of the line sensor 1 changes according to the arrangement pitch W and the number of cells of each light receiving cell 1a in the line sensor 1. By the way, when an image sensor having 5000 cells at an arrangement pitch of 7 μm and having a high resolution is used, a very precise sensor output is obtained as shown in FIG. 10A, for example. In this regard, when a general-purpose inexpensive image sensor having an array pitch of 85 μm and including 102 cells is used, only a coarse sensor output can be obtained as shown in FIG. However, high-speed reading of sensor output is possible due to the small number of cells.
[0052]
However, even if such an inexpensive line sensor 1 having a low resolution is used, as described above, according to the position detection method and apparatus according to the present invention, the hyperbolic second function that approximates the light intensity distribution by Fresnel diffraction with high accuracy is used. Since sech (x) is used, it is possible to interpolate a change in the light receiving intensity between the light receiving cells 1a with high accuracy. Therefore, while the reading speed of the sensor output is sufficiently increased by using the inexpensive line sensor 1 having a low resolution, the edge position detection can be performed with high accuracy by simple arithmetic processing. Can be played.
[0053]
Note that the present invention is not limited to the above embodiments. For example, as for the number of light receiving cells 1a provided in the line sensor 1 and the arrangement pitch W thereof, it is sufficient to use one according to the detection specification. The edge detection unit 3 may be realized by using a general-purpose microprocessor, and the above-described arithmetic expression may be provided as a ROM. In addition, the present invention can be variously modified and implemented without departing from the gist thereof.
[0054]
【The invention's effect】
As described above, according to the present invention, the received light intensity distribution by Fresnel diffraction is approximated using the hyperbolic second function sech (x), and the edge position in the cell array direction is obtained from the output of the line sensor using this approximate expression. Since the distance between the edge and the light receiving surface is calculated, the edge position can be easily detected with high accuracy and at high speed. In particular, even when an inexpensive line sensor having a low resolution is used, a great effect in practical use can be obtained, such as a sufficiently high measurement accuracy.
[Brief description of the drawings]
FIG. 1 is a diagram showing a basic configuration of a position detection device according to an embodiment of the present invention.
FIG. 2 is a diagram showing an array of light receiving cells in a line sensor.
FIG. 3 is a diagram showing a schematic configuration of a light projecting unit.
FIG. 4 is a diagram schematically showing an optical system of a parallel light beam emitted from a light projecting unit when viewed from the direction of arrows AA in FIG. 3;
5 is a diagram schematically showing an optical system of a parallel light beam emitted from the light projecting unit when viewed from the direction of arrows BB in FIG. 3;
FIG. 6 is a diagram showing a comparison between a theoretical value of a light intensity distribution based on Fresnel diffraction and an approximate characteristic using a function.
FIG. 7 is a diagram showing an example of a procedure of an edge detection process in a detection method and device according to an embodiment of the present invention.
FIG. 8 is a diagram illustrating a relationship between light receiving intensity obtained in two connected light receiving cells and an edge position obtained from a position at which the light receiving intensity is obtained.
FIG. 9 is a diagram showing a concept of a calculation process for calculating a distance z between an edge and a desired surface.
FIG. 10 is a diagram illustrating an example of a sensor output depending on a difference in resolution of a line sensor.
FIG. 11 is a diagram showing light intensity distribution characteristics by Fresnel diffraction.
FIG. 12 is a diagram for explaining a problem in approximation of a light intensity distribution by Fresnel diffraction using a Fresnel function.
[Explanation of symbols]
1 Line sensor (light receiving unit)
1a Photocell
2 Floodlight
3 main unit
3b Diffraction pattern detection means
3c Normalization means
3d edge detector
3e Distance detector
7 Shield (object to be detected)

Claims

A line sensor having a plurality of light receiving cells arranged at a predetermined pitch in one direction; and a light projecting unit for projecting monochromatic parallel light toward the line sensor, and receiving light by each light receiving cell of the line sensor. In detecting the position of the shield present in the optical path of the monochromatic parallel light by analyzing the amount,
The light intensity change at the rising portion of the light intensity distribution on the light receiving surface of the line sensor due to the Fresnel diffraction of the monochromatic parallel light by the shield is approximated by the hyperbolic second function sech (x), and this hyperbolic second function sech (x) is The edge position in the arrangement direction of the light receiving cells of the shielding object is determined by analyzing the light receiving intensity of each light receiving cell of the line sensor using the edge position and the position of the light receiving cell at which the predetermined light receiving intensity is obtained. A distance between the shield and the line sensor in the optical path direction using the hyperbolic second function sech (x).

The edge position is a light receiving cell whose light receiving intensity is greater than [0.25] when the output of the line sensor is normalized to [1], and the light receiving intensity is smaller than [0.25]. The light receiving cells that have obtained the light receiving intensity are obtained, and the inverse function ln ｛[1+ (1-Y ² ) ^{1 of the} hyperbolic second function sech (x) is obtained from the position of each light receiving cell and the light receiving intensity at each light receiving cell. ^{/ 2} ] / Y}, the position at which the light receiving intensity is [0.25] is obtained as an edge position xo of the shielding object in the arrangement direction of the light receiving cells,
The distance between the shielding object and the line sensor in the optical path direction is determined by the difference Δx between the edge position xo and the position x2 of the light receiving cell having the light receiving intensity larger than [0.25], and 2. The position detection method according to claim 1, wherein the distance component z of Fresnel diffraction is calculated from the hyperbolic second function sech (x) based on the received light intensity at the position x2.

When the output of the line sensor is normalized to [1], the edge position is an array of the light receiving cells whose light intensity is [0.25] in a hyperbolic second function sech (x) approximating the light intensity distribution. Is obtained as the position xo in the direction,
The distance between the shielding object and the line sensor is a light intensity A (0.25 <A ≦ 1.37) set in advance in a hyperbolic second function sech (x) approximating the light intensity distribution. A position xa in the arrangement direction of the light receiving cells is obtained, and based on the difference Δx between the position and the position xo in the arrangement direction of the light receiving cells at which the light intensity is [0.25], the hyperbolic second function sech (x) is used. 2. The position detecting method according to claim 1, wherein the distance component z of the Fresnel diffraction is calculated by back calculation.

A line sensor having a plurality of light receiving cells arranged at a predetermined pitch in one direction, and a monochromatic parallel light projecting toward the plurality of light receiving cells of the line sensor provided opposite to the line sensor. The light projecting unit, analyzing the light intensity distribution on the light receiving surface of the line sensor by Fresnel diffraction of the monochromatic parallel light by the edge of the shield present in the optical path of the monochromatic parallel light, analyzing the output of the line sensor, A position detection device for obtaining an edge position of a shielding object,
Inverse function ln ｛[1+ (1−Y ² ) ^{1 of} the hyperbolic second function sech (x) approximating the rising portion of the light intensity distribution on the light receiving surface of the line sensor due to Fresnel diffraction of monochromatic parallel light by the shield. ^{/ 2} ] / Y}, a cell direction position detecting means for obtaining a position xo in the arrangement direction of the light receiving cells at which the light receiving intensity becomes [0.25] from the normalized output of the line sensor;
Using the inverse function ln {[1+ (1−Y ² ) ^1/2 ] / Y}, a plurality of positions xa in the arrangement direction of the light receiving cells and the light receiving intensity at each position xa are obtained. From the hyperbolic second function sech (x), the distance between the edge of the shield and the line sensor is determined based on the difference Δx between Xa and the position xo in the arrangement direction of the light receiving cells at which the light intensity is [0.25]. A distance calculating means for calculating a distance z of the position detecting device.

The distance calculation means calculates the light receiving intensity from the light receiving cell whose light receiving intensity is greater than [0.25] and the light receiving intensity whose light receiving intensity is smaller than [0.25] from the normalized output of the line sensor to [0.25]. Is obtained, and based on the difference Δx between the position x2 of the light receiving cell having the light receiving intensity larger than [0.25] and the edge position xo, and the light receiving intensity at the position x2. The position detecting device according to claim 4, wherein the distance z is calculated from the hyperbolic second function sech (x).

The distance calculating means includes a predetermined light intensity A (0.25 <A ≦ 1.37) obtained by using the inverse function ln {[1+ (1-Y ² ) ^1/2 ] / Y}. The distance z is calculated from the hyperbolic second function sech (x) based on the position xa in the arrangement direction of the light receiving cells and the difference Δx between the edge position xo obtained by the cell direction position detecting means. The position detecting device according to claim 4.