JP3582544B2 - Lens sheet, surface light source and display device - Google Patents

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である。つまり、これら光線の斜面ｆ２における反射角は、サイドローブ光を反射し得る角度範囲（式（９））をそれぞれ８／１０、６／１０、４／１０に分割する角度である。
【００４２】
このようにθ_{Ｒ，ｍａｘ}、θ_{Ｒ，ｐｅａｋ}、θ_{Ｒ，ｍｉｎ}を定めると、これらの光線が左斜面
ｆ１より出射するときの角度を底面ｆ３の法線、すなわち、面光源の出光面の法線ｎから測った値（サイドローブ出射角）Θ_{ｓｏ，ｍｉｎ}、Θ_{ｓｏ，ｐｅａｋ}、Θ_{ｓｏ，ｍａｘ}の具体的な値を頂角θ_ａ＝９０°の場合について計算すると、それぞれ５７．７°、７０．７°、８４．７°となる。
【００４３】
これに対して、図１５の曲線（Ａ）に見られるように、実測された頂角θ_ａ＝９０°の二等辺三角柱プリズムのサイドローブ光の最小角方向は、Θ_{ｓｏ，ｍｉｎ}＝５２°、光エネルギーが最大である方向（ピーク方向）は、Θ_{ｓｏ，ｐｅａｋ}＝６８°、そして、最大角方法は、Θ_{ｓｏ，ｍａｘ}＝８２°である。これらの値は、上記計算値のΘ_{ｓｏ，ｍｉｎ}、Θ_{ｓｏ，ｐｅａｋ}、Θ_{ｓｏ，ｍａｘ}とほぼ一致する。このことから、以下において光線Ｒ_{１，ｍａｘ}、Ｒ_{１，ｐｅａｋ}、Ｒ_{１，ｍｉｎ}は、それぞれ、光放出面の法線ｎから測った最小角方向、ピーク方向、最大角方向のサイドローブ光を近似するものとする。
【００４４】
次に、斜面ｆ１から光線Ｒ_{１，ｍａｘ}〜Ｒ_{１，ｍｉｎ}が透過する領域を特定し、その領域をサイドローブ光が生じない形状のプリズムに置き換えることについて記述する。このようにすることにより、頂角θ_ａの二等辺三角柱プリズムにおいて、高出力輝度特性を最大限活かした上で、サイドローブ光を消去することが可能となる。
【００４５】
まず、斜面ｆ１上で、サイドローブ光を放出する領域を特定する方法について、図８を用いて説明する。図８は、頂角がθ_ａ＝９０°である三角柱プリズムの主切断面を示している。光線Ｒ１１は、図７における最大輝度のサイドローブ光である光線Ｒ_{１，ｐｅａｋ}を表しており、そのサイドローブ出射角θ_ｓｏは、７０．７°である。
【００４６】
光線Ｒ１１は、光路Ｅ_１→Ｄ_１を経てプリズムに入射し、右斜面ｆ２上の点Ｃ_１で全反射された後に、左斜面ｆ１上にある点Ｐ_１からＡ_１方向へ出射する。いま、斜面Ｆ２上の反射点をＣ_１、Ｃ_２、・・・と漸次底面ｆ３の方向へ移動させると、光線は、Ｒ１１、Ｒ１２、・・・のように斜面ｆ１上を次第に底辺ｆ３の方向へ移動する。光線Ｒ_１ｃは、反射点が底辺ｆ３と斜面ｆ２が交わる点Ｂ_ｃと極限的に殆ど一致しており、Ｅ_ｃ→Ｂ_ｃ→Ｐ_ｃ→Ａ_ｃと進行する光線である。このように、光線Ｒ１１〜光線Ｒ_１ｃは、底面ｆ３からプリズムに入射し、斜面ｆ１よりサイドローブ光として出射する。
【００４７】
次に、斜辺ｆ１における出射点が、光線Ｒ_１ｃの出射点Ｐ_ｃより底辺ｆ３側の点Ｐ_３、Ｐ_４であるサイドローブ光として光線Ｒ１３、Ｒ１４が存在したと仮定する。これら光線を遡行していくと、これら光線の底面ｆ３に入射する角は、臨界角θ_ｃを超過しているために、もはや底面ｆ３の下方からプリズム内に入射せず、例えば光路Ｅ_３→Ｇ_３→Ｆ_３→Ｐ_３→Ａ_３の様に、斜面ｆ２から入射し、底面ｆ３で全反射するものでなければならない。しかしながら、通常の面光源を使用し、プリズムの底面ｆ３が面光源側を向くように設置した場合には、光線Ｒ１３、Ｒ１４に類する光線は、殆ど存在しない。従って、プリズムの斜面ｆ１において、点Ｐ_ｃとプリズムの頂角の間から、事実上ほとんどのサイドローブ光が出射することがわかる。
【００４８】
そこで、次に点Ｐ_ｃの位置を求める。上記までは、サイドローブ出射角がθ_{ｓｏ，ｐｅａｋ}であるＲ_{１，ｐｅａｋ}を例に取り上げたが、以下では、問題を一般化し、サイドローブ出射角がθ_ｓｏである光線Ｒ_１ｃについて考える。図９は、図８と同じ頂角がθ_ａである三角柱プリズムの主切断面ａｂｃと、その断面内を横切り、頂点ｃを通過している光線Ｒ_１ｃを示した図である。
【００４９】
光線Ｒ_１ｃが左斜面ｆ１に入射する角θ_ｓｉは、屈折の法則からθ_ｓｏを用いて、
θ_ｓｉ＝ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_ｓｏ） （１３）
となる。ただし、図７からΘ_{ｓｏ，ｍｉｎ}〜Θ_{ｓｏ，ｍａｘ}は、例外的に出光面の法線ｎ（プリズム底面ｆ３の法線に同じ）から測っているが、屈折の法則に用いる角θ_ｓｏは、出光面ｆ１の法線Ｎから測るため両者は、
θ_{ｓｏ，ｍｉｎ} ＝ Θ_{ｓｏ，ｍｉｎ} − θ_ｂ
θ_{ｓｏ，ｐｅａｋ} ＝ Θ_{ｓｏ，ｐｅａｋ} − θ_ｂ
θ_{ｓｏ，ｍａｘ} ＝ Θ_{ｓｏ，ｍａｘ} − θ_ｂ・・・・・・（１３ａ）
等の関係で結ばれる（ただし、θ_ｂは、三角形プリズム主切断面の底角である）。一方、三角形ａＰ_ｃｃにおいて、
角ａＰ_ｃｃ＝９０°− θ_ｓｉ （１４ａ）
角Ｐ_ｃｃａ＝９０°＋ θ_ｓｉ − θａ （１４ｂ）
である。
【００５０】
一般に、三辺の長さがＡ、Ｂ、Ｃである三角形のそれぞれの辺の対角をα、β、γとすれば、
（Ａ ＋ Ｂ）／（Ａ − Ｂ） ＝ （ｓｉｎα ＋ ｓｉｎβ）／（ｓｉｎα − ｓｉｎβ） ・・・・・ （１５）
が成り立つ。そこで、面ｃａ、ａＰ_ｃ、Ｐ_ｃｂの長さをそれぞれｘ、ｘ１、ｘ２とし、式（１５）に、式（１３）、（１４ａ）、（１４ｂ）を代入すれば、

従って、
ｘ１／ｘ２ ＝ １／（（ｓｉｎ（９０°ー θ_ｓｉ）／ｓｉｎ（９０°＋ θ_ｓｉ ー θ_ａ）） ー １） ・・・・・（１９ａ）
を得る。これより、頂角がθ_ａである二等辺三角柱プリズムの主切断面ａｂｃの面ｃａ及びａｂにおいて、
ａＰ_ｃ１／ｂＰ_ｃ１＝ｘ１／ｘ２ （２０）
又は、
ａＰ_ｃ２／ｃＰ_ｃ２＝ｘ１／ｘ２ （２１）
のとなる点Ｐ_ｃ１、Ｐ_ｃ２を求め、三角形Ｐ_ｃ１ａＰ_ｃ２をサイドローブ光を生じない、又は、サイドローブ光の光量を低減する形状のプリズムに置換すれば良いことになる。そのようにすることにより、出射角θ_ｓｏないしはそれ以上の角度のサイドローブ光の発生を抑制することが可能となる。
【００５１】
式（１９ａ）中のθ_ｓｉは、式（１３）に示されるようにθ_ｓｏに依存するため、上述のように定義される点Ｐ_ｃの位置は、サイドローブ光の出射角θ_ｓｏをθ_{ｓｏ，ｍｉｎ}≦θ_ｓｏ≦θ_{ｓｏ，ｍａｘ}のいずれに設定するかによって変化する。すなわち、（１９ａ）式をより厳密に記せば、
１／（ｃ０ − １） ≦ ｘ１／ｘ２ ≦ １／（ｄ０ − １） （２１ａ）
ただし、
ｃ０ ＝ ｃ１／ｃ２
ｄ０ ＝ ｄ１／ｄ２
ｃ１ ＝ ｓｉｎ（９０°− ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_{ｓｏ，ｍｉｎ}））
ｃ２ ＝ ｓｉｎ（９０°＋ ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_{ｓｏ，ｍｉｎ}） − θ_ａ）
ｄ１ ＝ ｓｉｎ（９０°− ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_{ｓｏ，ｍａｘ}））
ｄ２ ＝ ｓｉｎ（９０°＋ ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_{ｓｏ，ｍａｘ}） − θ_ａ）
となる。θ_ｓｏをθ_{ｓｏ，ｍａｘ}に近い値として点Ｐ_ｃの位置を求めた場合には、サイドローブ光の消去は完全なものとなる。その反面、図７又は式（１９ａ）から理解されるように、点Ｐ_ｃと頂角ａの間の距離ｘ１は、より長くなり、法線輝度に貢献する面の長さｘ２が短くなる。従って、法線輝度が低下するとともに、拡散角（主ローブの半値幅）も広がる。一般的には、これらの要求性能は、θ_ｓｏ＝θ_{ｓｏ，ｐｅａｋ}とすることにより程良くバランスする。
【００５２】
続いて、サイドローブ光が出射しない、又は、より低減されるプリズム形状を求める。図７又は図１５の曲線Ａから明らかであるように、特に頂角θａが９０°の三角柱プリズムにおいてサイドローブ光の強度が大きい。このサイドローブ光の強度は、頂角を次第に増大させると、一定の角度において急激に低下する。以下、この点について説明する。
【００５３】
図２６は、空気の屈折率ｎ０＝１、プリズムの屈折率ｎ１＝１．５のときに、頂角θ_ａ＝９０°のプリズムにおいて、強度がピークになるサイドローブ光Ｒ_{１，ｐｅａｋ}、すなわち、底面ｆ３に入射角４５．７°で入射する光線が、頂角θ_ａの増加とともにその経路をどのように変化させるかを示した図である。図２６から、頂角θ_ａが９０°から漸次増大すると、サイドローブ光の出射方向が次第に水平方向に傾いていくことが分かる。これは、図７において、Ｒ_{１，ｍｉｎ}〜Ｒ_{１，ｍａｘ}の出射光線が次第に反時計回りに回転していくことに相当している。図２６（Ｂ）に示すように、頂角θ_ａの増大の結果、出射光は隣接するプリズム（図中、左隣りのプリズム）の斜面に当たり、一部は反射され、光放出面の法線ｎ近傍の出力光線Ｒ_{１Ｒ，ｐｅａｋ}になる。また、残りの出射光は、透過、屈折して導光板又は光源側にフィードバックされる光線Ｒ_{１ｔ，ｐｅａｋ}となり、再利用される。このように、θ_ａの増大に伴い、サイドローブ光は次第に減少する。また、さらにθ_ａを増大させると、サイドローブ光は、図３において示したようにプリズム斜面において全反射し、導光板側にその全てがフィードバックされるために、完全に消失する。
【００５４】
次に、以上の過程を光線を追跡しながら説明する。図７において容易に分かるいうに、頂角θ_ａを９０°から増大させると、サイドローブ光Ｒ_{１，ｍｉｎ}〜_{Ｒ１，ｍａｘ}のうち、最も出射角の大きいＲ_{１，ｍａｘ}が、最初に隣接するプリズムの斜面に接するようになる。そこで、以下にサイドローブ光Ｒ_{１，ｍａｘ}に基づいて説明を進める。
図２４は、頂角θ_ａ＝９０°＋αである三角柱プリズムにおけるサイドローブ光の経路を示した図である。ここでαは、０°＜α＜９０°の関係を満たしており、θ_ａ＝９０°＋αとしたときに、図中の三角柱プリズムにおいて左斜面ｆ１から出射したサイドローブ光Ｒ_{１，ｍａｘ}（図中、点Ｄから点Ｅに向かう光線）が底面ｆ３（図中、辺ＪＩ）と平行となる角度である。このような角度関係が満たされれば、図２６からも分かるように隣接する単位プリズムの間の距離、または、Ｒ_{１，ｍａｘ}の出射点の位置の如何によらずサイドローブ光Ｒ_{１，ｍａｘ}は、必ず隣接する（左隣）のプリズム斜面に当たる。
【００５５】
また、頂角θ_ａが９０°＋αとなるのにともない、底面ｆ３と、斜面ｆ１又はｆ２とのなす角θ_ｂは、４５°−（α／２）となる。これは、三角形の内角の和が１８０°であること、二等辺三角形の両底角は相等しいこと、及び、底辺が（α／２）減少したぶん斜面ｆ２及びその法線が反時計回りに（α／２）回転することに注目すれば初等幾何学的に容易に求められる。その結果、左斜面ｆ１のＤ点におけるサイドローブ光Ｒ_{１，ｍａｘ}の入射角θ_{ｓｉ，ｍａｘ}は、図２４の三角形ＫＤＣの内角の和が１８０°であることから、

また、右斜面ｆ２での全反射角θ_{Ｒ，ｍａｘ}は、式（１２）より、

となる。
【００５６】
サイドローブ光Ｒ_{１，ｍａｘ}の斜面ｆ１における出射角θ_{ｓｏ，ｍａｘ}とθ_{Ｒ，ｍａｘ}は、点
Ｄにおいて屈折の法則により、以下のように関連づけられる。

従って、

となる。出射光線の方向（Ｄ→Ｅ）が底面ｆ３と平行であるということは、サイドローブ光Ｒ_{１，ｍａｘ}が底面ｆ３の法線（面光源出光面の法線）ｎと直交することを意味するから、図２４より、

となる。従って、式（２１ｅ）及び（２１ｆ）より、

【００５７】
式（２１ｇ）において両辺の正弦をとると、

を得る。
【００５８】
ここで、θ_ａ＝９０°＋αは三角形の頂角であり、０°＜θ_ａ＜１８０°であるから、
０°＜ α ＜ ９０°
∴ ４５°＜ （α／２） ＋ ４５°＜ ９０°
∴ １／√２ ＜ ｓｉｎ（（α／２） ＋ ４５°） ＜ １ （２１ｉ）
となり、（２１ｈ）式の右辺は、
（１／√２）（ｎ０／ｎ１） ＜ （ｎ０／ｎ１）ｓｉｎ（４５°＋ α／２） ＜ ｎ０／ｎ１ ・・・・・（２１ｊ）
となる。
【００５９】
従って、式（２１ｈ）及び（２１ｊ）より、
（ｎ０／ｎ１） ＞ ｓｉｎ（９０°ー θ_{Ｒ，ｍａｘ} ＋ （３／２）α） ＞ （１／√２）（ｎ０／ｎ１）・・・（２１ｋ）
となる（なお、式（２１ｋ）の不等号は、式（２１ｊ）における不等号とその向きを逆としている）。これに、式（２１ｃ）のθ_{Ｒ，ｍａｘ}を代入すると、
（ｎ０／ｎ１） ＞ ｓｉｎ（（６／１０）θ_ｃ ＋ （９／１０）α） ＞ （１／√２）（ｎ０／ｎ１）・・・（２１ｍ）
となる。
【００６０】
一方、式（２１ｍ）の正弦の中の角度は、元来図２４の斜面ｆ２の点Ｄにおける入射角θ_{Ｓｉ，ｍａｘ}であること、すなわち、

であることを考慮すれば、
０°＜ （６／１０）θ_ｃ＋（９／１０）α ＜ ９０° （２１ｐ）
となる。この区間において、逆正弦関数の主値は、１価の単調増加関数であることから式（２１ｍ）の逆正弦をとっても同じ不等号が成立し、
θ_ｃ ＞ （６／１０）θ_ｃ ＋ （９／１０）α ＞ ｓｉｎ^−１（（１／√２）（ｎ０／ｎ１））・・・（２１ｑ）
となる。ただし、臨界角の定義より、ｓｉｎ^−１（ｎ０／ｎ１）＝θ_ｃとしている。式（２１ｑ）をαについて解くと、

となり、図２４のような関係が成立するために頂角θ_{ａ，ｍａｘ}は、
θ_{ａ，ｍａｘ} ＝ ９０°＋ α

という条件を満たさなければならないことが分かる。
【００６１】
頂角θ_ａがさらに増加すると、順次サイドローブ光Ｒ_{１，ｐｅａｋ}、Ｒ_{１，ｍｉｎ}が底辺ｆ３と平行になり、サイドローブ光では無くなる。式（１１）、（１０）のθ_{Ｒ，ｐｅａｋ}、θ_{Ｒ，ｍｉｎ}を用いて上記と同様の計算を行うと、θ_{ａ，ｐｅａｋ}、θ_{ａ，ｍｉｎ}のそれぞれについて、

を得る。なお、ここでは、式（１０）、（１１）において、９０°を９０°＋αとして計算を行っている。
【００６２】
以上の結果をまとめると、頂角θ_ａ＝９０°のときは、プリズムの左斜面ｆ１から出射角θ_{ｓｏ，ｍｉｎ}≦θ≦θ_{ｓｏ，ｍａｘ}の範囲でサイドローブ光Ｒ_{１，ｍｉｎ}〜Ｒ_{１，ｐｅａｋ}〜Ｒ_{１，ｍａｘ}が全てそのまま出射される（図７）。頂角θ_ａを増加させると、出射サイドローブ光は、次第に反時計回りに傾き、はじめに左斜面の下方から出る光線が図２６（Ｂ）に示されるように隣接プリズムで偏向され始める。ただし、大部分の光は、そのまま出射する。頂角をθ_{ａ，ｍａｘ}まで変化させると、まずサイドローブ光のうち最大出射角のＲ_{１，ｍａｘ}が図２４に示すように斜面ｆ１から出射した後にプリズム底面ｆ３と平行になり、そして、図２６（ｃ）に示すように、出射光線が左斜面ｆ１における出射位置によらず隣接するプリズム斜面で反射及び透過して向きを変えサイドローブ光でなくなる。
【００６３】
さらに、θ_ａが増加して、θ_{ａ，ｐｅａｋ}に達すると、ピーク強度を与えるサイドローブ光Ｒ_{１，ｐｅａｋ}も左斜面ｆ１より出射した後に、底面ｆ３に平行となりサイドローブ光で無くなる。
最後に、θ_ａがθ_{ａ，ｍｉｎ}に達すると、最小出射角のサイドローブ光Ｒ_{１，ｍｉｎ}も同様にサイドローブ光でなくなり、全てのサイドローブ光Ｒ_{１，ｍｉｎ}〜Ｒ_{１，ｍａｘ}は、法線方向近傍に出射する反射光Ｒ_１Ｒと導光板（光源）側へフィードバックされる光線Ｒ_１ｔとに変換される。
【００６４】
θ_ａをθ_{ａ，ｍｉｎ}からなおいっそう増加させると、出射角の大きいサイドローブ光から順次左斜面ｆ２で全反射するようになる。そして、

となると、全サイドローブ光は、左斜面ｆ２において全反射され、底面ｆ３から導光板側へ戻る。図３は、ｎ０＝１．０、ｎ１＝１．５のとき式（２１ｖ）を満たす三角柱プリズムの例であり、頂角θ_ａ＝１４０°である。
【００６５】
次に、式（２１ｖ）の導出方法について説明する。
図１０は、頂角がθ_ａである三角柱プリズムの主切断面を示した図である。図中、光線Ｒ５は、光路Ｃ→Ｄ（全反射）→Ｅに沿ってプリズム内を進行し、斜面ｆ１よりＦ方向へ出射角θ_ｓｏで出射する光線である。
【００６６】
光線Ｒ５が斜面ｆ１及び斜面ｆ２にそれぞれ入射するときの角度をθ_ｓｉ及びθ_Ｒ１、また、点Ｃから点Ｄに進行する光線が底面ｆ３となす角度をθ_Ｒ２とすると、

なる関係が成り立つ。ここで、

が満たされれば、斜面ｆ１から出射し得る光線Ｒ５は、底面ｆ３から入射する光線ではなく、斜面ｆ２よりプリズム内に入射し、点Ｃにおいて全反射をする光線である。
【００６７】
逆に、

であれば、光線Ｒ５は、底面ｆ３よりプリズム内に入射した光線である。既に説明したように、斜面ｆ２よりプリズム内に入射する光線は、極く僅かである。従って、式（２２）及び（２５）を同時に満たすように、頂角θ_ａを定めることにより、底面ｆ３よりプリズムに入射し、その後にサイドローブ光となる光線の存在を防止することが可能となる。このような条件を満たすθ_ａは、式（２２）〜（２５）より、次式のように与えられる。

【００６８】
すなわち、頂角θ_ａが式（２１ｕ）のθ_{ａ，ｍｉｎ}からさらに増加して、式（２７）をも満たすようになると、サイドローブ光の出射が抑制されることは依然として同じであるが、抑制されたサイドローブ光は、全て斜面ｆ１、ｆ２において全反射され、導光板あるいは光源側にフィードバックされ、出力光として利用されなくなる。そのために、出力光の輝度（特に、光放出面の法線方向ｎの輝度）は低下する。その代わり、頂角が広くなった分だけ出力光の視野角（半値角）は広がり、また、導光板にフィードバックされた光は導光板内部を伝搬し、一部は再出力される。この結果、輝度の面分布はより均一となる。
【００６９】
故に、特に高い法線輝度と少ないサイドローブを求める場合は、

また、出力光の視野角の広さ、及び、法線輝度の高さよりもサイドローブ光の除去と光放出面内の輝度分布の均一化を求める場合は、

とすると良い。
【００７０】
図１７は、代表的な材料について、屈折率、臨界角、９０°頂角の場合における最大出射角θ_ｍａｘ、強度がピークの方向θ_ｐｅａｋ、及び、最小出射角θ_ｍｉｎのサイドローブを生じる各々の光線に対してこれを隣接斜面反射により抑止する緩斜面頂角θ_{ａ，ｍａｘ}、θ_{ａ，ｐｅａｋ}、θ_{ａ，ｍａｘ}及び両斜面ｆ１、ｆ２においてサイドローブ原因光が全反射されて出射を抑制する緩斜面頂角θ_Ｒｅｆを列挙した図である。ただし、空気の屈折率を１．００として計算を行っている。
【００７１】
図１１は、以上の説明に基づいて得られた五角柱プリズムの主切断面を示した図である。
プリズム上部の緩斜面ｆ４、ｆ５は、頂角がθ_ａ’（θ_ａ’＞θ_{ａ，ｍａｘ}）である二等辺三角形ａ’ｂ’ｃ’の斜辺の一部である。プリズム下部の急斜面ｆ１、ｆ２は、頂角がθ_ａ（θ_ａ≦θ_{ａ，ｍａｘ}）である二等辺三角形ａｂｃの斜辺の一部である。θ_ａ＜θ_{ａ，ｍａｘ}としたのは、θ_ａ≧θ_{ａ，ｍａｘ}とすると、サイドローブ光は減少するものの、プリズムを透過する光線（図２のＲ２、Ｒ３等）の屈折、収束が不十分となり、出射光の法線輝度の低下、拡散角の増大など、好ましくない結果を招くからである。
また、急斜面と緩斜面の長さの比は、後述の式（３６）を満たしている。なお、上記２つの斜面は、点Ｐ_ｃ１、Ｐ_ｃ２において階段状の段差を生じないように接続してある。
【００７２】
図１１に示すプリズムにおいて、底面ｆ３よりプリズムに入射した光線のうち、急斜面ｆ１、ｆ２を透過するものは、光放出面の法線方向へ効率よく収束するために、法線輝度は、向上する。また、例えば、緩斜面ｆ５において全反射し、緩斜面ｆ４へ進行する光線は、緩斜面ｆ４を出射した後に左隣のプリズム斜面（ｆ５）で一部反射して出光面の法線方向に進行し、残りは屈折して、底面ｆ３へフィードバックされるために、サイドローブ光の発生原因となることがない。このように、図１１に示す五角柱プリズムは、低サイドローブ特性と高法線輝度特性の両特性を合わせ持つプリズムである。
【００７３】
しかしながら、図１１に示すプリズムでは、図中の光線Ｒ６のように、底面ｆ３からプリズム内に入射した後に、急斜面ｆ２上の点Ｃにおいて全反射し、緩斜面ｆ４を透過してサイドローブ光となる光線が存在し得る。
つまり、光線Ｒ６は、点Ｃにおいて大きな角度で全反射した場合に、緩斜面上の点Ｄに小さい入射角で到達する。ここで、頂角θ_ａ’が十分に大きく取られておらず、斜面ｆ４の傾斜が急であれば、点Ｄへの光線Ｒ６の入射角θ_ｓｉは、臨界角θ_ｃ未満となり、光線Ｒ６は、斜面ｆ４を透過する。実際に計算すると、例えば、点Ｂにおける光線Ｒ６の入射角θ_ｉｎ＝４８．９°、緩斜面の頂角θ_ａ’＝１２０°と仮定した場合に、入射角θ_ｓｉは３１°となり、光線Ｒ６は、射角θ_ｓｏ＝５０°で出射する。この出射光路Ｒ６は、左上方へ進行するものであり、すでに議論したように、その大部分は、左隣りのプリズムで反射することなく、そのままサイドローブ光となる。
【００７４】
このようなサイドローブ光は、以下のようにして求められる条件により防ぐことが可能である。すなわち、図１１に示した経路によりプリズムに入射する光線を全て急斜面ｆ４、ｆ５において全反射させ、底面ｆ３へフィードバックするようにすればよいのである。
図１２は、頂角がθ_ａ（＜θ_{ａ，ｍａｘ}）である二等辺三角柱プリズムの主切断面
ＡＢＣを示した図である。図中、光線Ｒ７は、右斜面ｆ２において全反射した後に、左斜面ｆ１上の点Ｅに入射角θ_ｓｉ（＜θ_ｃ）で到達し、サイドローブ光としてプリズムから出射する光線である。
【００７５】
ここで、斜面ｆ１を点Ｅを中心に時計方向へ角度Δθだけ回転させると考える。これは、斜面ｆ１の傾斜をΔθだけ減少させることに相当する。逆にθ_ｓｉは、Δθだけ増大する。Δθが、θ_ｓｉ＋Δθ≧θ_ｃ、すなわち、

であれば、θ_ｓｉは、臨界角θ_ｃより大きくなる。その結果、光線Ｒ７は、斜面ｆ１において全反射し、サイドローブ光となることを防ぐことが可能となる。
【００７６】
図１３は、上述の考察をもとに形状を決定した五角柱プリズムの主切断面を示した図である。五角形Ａ’Ｐ_ｃ１ＢＣＰ_ｃ２は、頂角θ_ａの三角形ＡＢＣにおいて、右斜辺ＣＡ（左斜辺ＡＢ）の一部分である辺Ｐ_ｃ２Ａ（辺Ｐ_ｃ１Ａ）を半時時計回り（時計回り）に式（２８）を満たす角度Δθだけ回転させ、２辺Ｐ_ｃ１Ａ、Ｐ_ｃ２Ａが交わる点を新たに点Ａ’としたものである。従って、五角形Ａ’Ｐ_ｃ１ＢＣＰ_ｃ２において、面Ｐ_ｃ２Ａ’（ｆ５）及びＰ_ｃ１Ａ’（ｆ４）は、緩斜面であり、面ＣＰ_ｃ２（ｆ２）及びＰ_ｃ１Ｂ（ｆ１）は、急斜面である。
【００７７】
ここで、角ＡＢＣの角度（底角）をθ_ｂとすると、頂角θ_ａ’とθ_ｂの関係は
、二等辺三角形の両底辺が等しいことを考慮すると、

となる。従って、

である。さらに、式（１３）と式（２８）より、

が導かれる。θ_ｓｏは、Θ_{ｓｏ，ｍｉｎ}〜Θ_{ｓｏ，ｍａｘ}と式（１３ａ）の関係にあることから、出射するサイドローブ光の出射角がθ_{ｓｏ，ｍｉｎ}〜θ_{ｓｏ，ｍａｘ}の範囲を有することを考慮すると、Θ_{ｓｏ，ｍｉｎ}−θ_ｂ≦θ_ｓｏ≦Θ_{ｓｏ，ｍａｘ}−θ_ｂとなるから、図１３に示す
五角柱プリズムは、

より好ましくは、

なる条件を満たすことにより、底面ｆ３より入射し、図１３の経路を進行する光線がサイドローブ光となることを防止するようになる。しかしながら、θ_ａ’が大きすぎると、視野角が不必要に拡がり、法線輝度が低下して好ましくない。従って、

とすることが好ましい。図１７に、θ_{ａ，ｐｅｒｆｅｃｔ}の例を示す。ただし、急斜面の頂角は、θ_ａ＝９０°、屈折率は、ｎ０＝１、ｎ１＝１．５とする。
【００７８】
次に、上述のような五角柱プリズムにおける緩斜面の長さｘ１’と急斜面の長さｘ２の比を求める。
図１４は、五角柱プリズムの主切断面を示した図である。主切断面ＡＢＰ_ｃ１
Ｃ’Ｐ_ｃ２は、頂角θ_ａの二等辺三角形ＡＢＣの臨界点Ｐ_ｃ１、Ｐ_ｃ２よりも上部を頂角
θ_ａ’（θ_ａ’＞θ_ａ）の二等辺三角形Ｐ_ｃ１Ｃ’Ｐ_ｃ２に置き換えた形状を有している。図中のＰ_ｃ１Ｃ（Ｐ_ｃ２Ｃ）は、式（１９ａ）中のｘ１に相当する。また、Ｐ_ｃ１Ｃ’（Ｐ_ｃ２Ｃ’）＝ｘ１’とする。
【００７９】
図から明らかなように、
Ｐ_ｃ１Ｃ’’＝ Ｐ_ｃ２Ｃ’’＝ ｘ１ｓｉｎ（θ_ａ／２） （３３）
であり、また同時に、
Ｐ_ｃ１Ｃ’’＝ Ｐ_ｃ２Ｃ’’＝ ｘ１’ｓｉｎ（θ_ａ’／２） （３４）
である。従って、式（３３）及び式（３４）より
ｘ１’＝ （ｓｉｎ（θ_ａ／２）／ｓｉｎ（θ_ａ’／２））・ｘ１ （３５）
となる。
【００８０】
ここで、式（１９ａ）と式（３５）を比較すると、次式を得ることができる。

ただし、
ｋ０ ＝ ｋ１／ｋ２
ｋ１ ＝ ｓｉｎ（９０°− ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_ｓｏ））
ｋ２ ＝ ｓｉｎ（９０°＋ ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎθ_ｓｏ） − θ_ａ）
ｅ ＝ ｓｉｎ（θ_ａ／２）／ｓｉｎ（θ_ａ’／２）
式（３１）のときと同様に、θ_ｓｏは、（Θ_{ｓｏ，ｍｉｎ}−θ_ｂ）〜（Θ_{ｓｏ，ｍａｘ}−θ_ｂ）
の範囲を有することを考慮すれば、

ただし、
ｃ０ ＝ ｃ１／ｃ２
ｄ０ ＝ ｄ１／ｄ２
ｃ１ ＝ ｓｉｎ（９０°− ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎ（Θ_{ｓｏ，ｍｉｎ} ー θ_ｂ）））
ｃ２ ＝ ｓｉｎ（９０°＋ ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎ（Θ_{ｓｏ，ｍｉｎ} ー θ_ｂ）） − θ_ａ）
ｄ１ ＝ ｓｉｎ（９０°− ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎ（Θ_{ｓｏ，ｍａｘ} ー θ_ｂ）））
ｄ２ ＝ ｓｉｎ（９０°＋ ｓｉｎ^−１（（ｎ０／ｎ１）ｓｉｎ（Θ_{ｓｏ，ｍａｘ} ー θ_ｂ）） − θ_ａ）
ｅ ＝ ｓｉｎ（θ_ａ／２）／ｓｉｎ（θ_ａ’／２）
を得る。
【００８１】
図１８は、急斜面の頂角θ_ａ＝９０°、臨界角θ_ｃ＝４１．８°（プリズムの
屈折率ｎ０＝１．５、空気の屈折率ｎ１＝１．０）、である場合について、緩斜面の頂角θ_ａ’及び緩斜面と急斜面の長さの比ｘ１’／ｘ２を算出した結果を示している。なお、除去すべきサイドローブ光の出射角は、それぞれ、出光面法線ｎから測ってΘ_{ｓｏ，ｍａｘ}＝８４．７°、Θ_{ｓｏ，ｐｅａｋ}＝７０．７°、Θ_{ｓｏ，ｍｉｎ}＝５７．７°としてある。
【００８２】
最後に、頂角θ_ａと臨界角θ_ｃの関係が、θ_ａ≦２θ_ｃのである場合について
、本発明に係る単位五角形プリズムの形状が満たすべき条件について、図６を用いて説明する。この場合は、点Ｄにおける光線の入射角θ_ｓｉは、点Ｃにおける光線の入射角θ_Ｒが僅かにθ_ｃを超過した時点で、臨界角未満になる。従って、θ
_Ｒ＝θ_ｃとなる光線Ｒ１２を用いて図８及び図９において説明した計算を行い、
臨界点Ｐ_ｃを求める。その他の計算等は、上述したのと同様に行う。
【００８３】
【実施例】
（レンズシートの実施例）
以下、図面などを参照しながら、実施例をあげて、さらに詳しく説明する。
図１９は、本発明によるレンズシートの実施例を、比較例とともに示した図である。なお、図１９（Ａ）、（Ｂ）、（Ｃ）、（Ｄ）の配置は、図２、図３、図４及び図５に対応する。
また、これらのレンズシートは、いずれも厚さ５０μｍの透明な２軸延伸ＰＥＴ（ポリエチレンテレフタレート）シートの表面に、紫外線で架橋硬化させた屈折率１．５０のウレタンアクリレート樹脂を用いて成形されたものである。
【００８４】
比較例１
図１９（Ａ）に示すように、頂角９０°の３角形プリズム線型配列レンズシート１０５を、後述するバックライト上に積層したもの。プリズムの繰り返し周期は５０μｍ、主断面内で頂角を挟む２辺の長さは各々３６μｍである。
【００８５】
比較例２
図１９（Ｂ）に示すように、頂角１０８°（θ_{ａ，ｍｉｎ}＜θ_ａ＜θ_{ａ，Ｒｅｆ}）の３
角形プリズム線型配列レンズシート１０６を、後述するバックライト上に積層したもの。プリズムの繰り返し周期は５０μｍ、主断面内で頂角を挟む２辺の長さは各々２７μｍである。
【００８６】
実施例
図１９（Ｃ）に示すように、基部側の辺が頂角９０°、頂部側の辺が頂角１０８°の５角形プリズム線型配列のレンズシート１を、後述するバックライト上に、単位五角形プリズムが観察側に向くように積層したもの。プリズムの繰り返し周期は５０μｍ、主断面内における急斜面の辺長（図１のＬ_１）は１８μｍ、緩斜面の辺長（図１のＬ_２）は１６μｍである。
【００８７】
比較例３
図１９（Ｄ）に示すように、基部側の辺が頂角９０°、頂部側の辺が頂角１０８°の実施例と同様の５角形プリズム線型配列レンズシート１Ｂを、後述するバックライト上に、単位五角形プリズムが光源側に向くように積層したもの。
【００８８】
バックライトは、９．４インチの画面で、厚さ４ｍｍの導光板１０１であって、表面にサンドブラストＰＥＴシートからなる光等方性拡散層１０２、裏面に白色インキ印刷による散点パターン状の光拡散反射層１０３を形成したもの用いて、長辺２灯式の約φ３ｃｍの冷陰極管（消費電力４ワット）からなる光源１０４を使用した。
この輝度測定は、レンズシート１０５，１０６，１，１Ｂの裏面にバックライトをおき、各レンズシートの正面から３０ｃｍの位置に輝度計〔トプコンＢＭ−８（２°）〕を用いて行なった。なお、バックライトの導光板上に何も載せない場合及び導光板上に光等方性拡散層のみを載せた場合の法線輝度は、各々７７０〔ｃｄ／ｃｍ^２〕、９６８〔ｃｄ／ｃｍ^２〕であった。
【００８９】
図１５，図１６は、上記実施例及び比較例１〜比較例３のレンズシートの輝度測定を行なった結果を示す線図である。
比較例１は、図１５の（Ａ）に示すように、法線輝度が高いがサイドローブが大きく発生していた。法線輝度の値は１２４４〔ｃｄ／ｃｍ^２〕、半値角は６６°であり、サイドローブ／主ローブ（法線輝度）の輝度比は０．２３であった。
比較例２は、図１５の（Ｂ）に示すように、サイドローブが殆どなくなっていたが、法線輝度は１０４５〔ｃｄ／ｃｍ^２〕と比較例１と比べ１６％程度低下していた。半値角は７４°であり、比較例１と比べ視野角が広がったが、サイドローブは、サイドローブ／主ローブの輝度比＝０．００（図１５のグラフからの読み取り値）と大幅に低下した。
実施例は、図１５の（Ｃ）に示すように、法線輝度が１１４５〔ｃｄ／ｃｍ^２〕、半値角が７０°、サイドローブ／主ローブの輝度比が０．１４であり、法線
輝度の低下は少なく、視野角も広く、しかも、サイドローブも小さかった。
比較例３は、図１６に示すように、法線輝度が４３５〔ｃｄ／ｃｍ^２〕と低く、しかも、サイドローブ／主ローブの輝度比＝１．３４と主ローブよりも大きなサイドローブが発生していた。また、半値角も１２５°と大きく（ただし、サイドローブピーク輝度の１／２以上を有する角度範囲として評価）、実用上不要な角度範囲にまで光を放射している。
【００９０】
（エッジライト型の面光源の実施例）
図２０は、本発明による面光源の第１実施例（エッジライト型）を示す斜視図である。第１実施例の面光源は、エッジライト型のバックライト４０の導光板４１の上面に、光等方拡散性層２０及び本発明のレンズシート１が配置されている。このバックライト４０は、導光板４１の下面に、散点パターンの光拡散反射層４２が形成されており、導光板４１の側端面の両側には、それぞれ線光源４３，反射膜４４，照明カバー４５が設けられている。エッジライト型の面光源は、薄型で光放出面が発熱しにくい利点がある。
【００９１】
（直下型の面光源の実施例）
図２１は、本発明による面光源の第２実施例（直下型）を示した断面図である。第２実施例の面光源は、ケース３１内に、蛍光灯などの線光源３２が設けられた直下型のバックライト３０の開口側に、光等方拡散性層２０及び本発明のレンズシート１を配置したものである。また、ケース３１の光源側内面は、光拡散反射面に加工されている。
【００９２】
（表示装置の実施例）
図２０，図２１に示した面光源は、公知の透過型の液晶表示素子の背面に配置することによって、液晶表示装置として使用することができる。また、透過型の液晶表示素子の他に、エレクトロクロミック表示素子などの背面光源を必要とする素子に適用することができる。
【００９３】
（レンズシートの他の実施例）
図２２は、本発明によるレンズシートの他の実施例を示した図である。
図１９（Ｃ）の実施例では、５角柱プリズムの単位五角形プリズム１０を１次元的に配置した例で説明したが、図２２に示すように、緩斜面の４角錐台の上に、急斜面の４角錐が連設された単位五角形プリズム１０’を２次元的に配置したものであっても、同様の効果が得られる。
【００９４】
また、前記各実施例では、斜面の左右の長さが等しい例で説明したが、ラップトップ形のパソコンの表示装置に使用するような場合には、単位五角形プリズムが特定の方向に傾いていてもよい。即ち、両底角が等しくない左右非対称な形状でもよい。さらに、必要に応じ、特開平６−３２４２０５号公報等に開示されているような高さが光りの波長以上の微小突起部からなる微小凹凸を形成し、導光板との光学密着を防止することもできる。
【００９５】
【発明の効果】
以上詳しく説明したように、本発明によれば、単位五角形プリズムが出光側に凸状に形成されており、１方向又は直交する２方向の断面形状が５角形であるので、基部側のレンズの急斜面によって、光放出面の法線方向の輝度を高めて、視野角を規制し、頂部側のレンズの緩斜面によって、サイドローブの発生を抑制し、高法線輝度を実現できるので、法線近傍の所定角度に集光した明るい面発光が可能となった。
【図面の簡単な説明】
【図１】本発明によるレンズシートの単位五角形プリズムを作用を説明する模式図。
【図２】三角形プリズム線形配列レンズシート（頂角９０°）の単位レンズ部内に入射した光線を示した図。
【図３】三角形プリズム線形配列レンズシート（頂角１４０°）の単位レンズ部内に入射した光線を示した図。
【図４】本発明による五角形プリズム線形配列レンズシートの単位レンズ部内に入射した光線を示した図。
【図５】五角形プリズム線形配列レンズシートのレンズ部を入光側に向けて配置した場合の光線を示した図。
【図６】頂角θ_ａの三角柱プリズムにおいて、サイドローブ光の発生原因について説明した図。
【図７】頂角θ_ａの三角柱プリズムにおいて、最小角方向、ピーク方向、最大角方向のサイドローブ光の軌跡を示した図。
【図８】頂角θ_ａの三角柱プリズムにおいて、光線が入射する領域とサイドローブ光を放出する領域の関係を示した図。
【図９】頂角θ_ａの三角柱プリズムにおいて、サイドローブ光を放出する領域の長さｘ１と、放出しない領域の長さｘ２の関係を示した図。
【図１０】頂角θ_ａの三角柱プリズムにおいて、底面ｆ３より入射し、斜面ｆ１より出射角θｓｏで出射するサイドローブ光の軌跡を示した図。
【図１１】式（１９ａ）及び（２７）を満たす五角柱プリズムにおいて、サイドローブ光となる光線の軌跡を示した図。
【図１２】頂角θ_ａの三角柱プリズムにおいて、斜面ｆ２において全反射し、斜面ｆ１に到達した光線の斜面ｆ１への入射角θ_ｓｉと斜面ｆ１の傾きの関係を示した図。
【図１３】式（３１）を満たす五角柱プリズムの主切断面形状を説明した図。
【図１４】主切断面は、頂角θ_ａの二等辺三角形ＡＢＣの臨界点Ｐ_ｃ１、Ｐ_ｃ２よりも上部を頂角θ_ａ’（θ_ａ’＞θ_ａ）の二等辺三角形Ｐ_ｃ１Ｃ’Ｐ_ｃ２に置き換えた形状を有している五角柱プリズムの主切断面を示した図。
【図１５】比較例１（Ａ）、比較例２（Ｂ）及び実施例（Ｃ）のレンズシートの輝度測定を行なった結果を示す線図である。
【図１６】比較例３のレンズシートの輝度測定を行なった結果を示す線図である。
【図１７】代表的な材料について、屈折率、臨界角、９０°頂角の場合における最大出射角θ_ｍａｘ、強度がピークの方向θ_ｐｅａｋ、及び、最小出射角θ_ｍｉｎのサイドローブを生じる各々の光線に対してこれを隣接斜面反射により抑止する緩斜面頂角θ_{ａ，ｍａｘ}、θ_{ａ，ｐｅａｋ}、θ_{ａ，ｍａｘ}及び両斜面ｆ１、ｆ２においてサイドローブ原因光が全反射されて出射を抑制する緩斜面頂角θ_Ｒｅｆを列挙した図である。
【図１８】急斜面の頂角θ_ａ＝９０°、臨界角θ_ｃ＝４１．８°（プリズムの屈折率ｎ０＝１．５、空気の屈折率ｎ１＝１．０）、である場合について、緩斜面の頂角θ_ａ’及び緩斜面と急斜面の長さの比ｘ１’／ｘ２を算出した結果を示した図である。
【図１９】本発明によるレンズシートを設置したエッジライト型面光源の実施例を、比較例とともに示した図である。
【図２０】本発明による面光源の第１実施例（エッジライト型）を示す斜視図である。
【図２１】本発明による面光源の第２実施例（直下型）を示した断面図である。
【図２２】本発明によるレンズシートの他の実施例を示した図である。
【図２３】エッジライト型の面光源の従来例を示す図である。
【図２４】頂角θ_ａ＝９０°＋αである三角柱プリズムにおけるサイドローブ光の経路を示した図である。
【図２５】頂角θ_ａ＝９０°＋αである三角柱プリズムにおけるサイドローブ光の経路を示した図２４とは異なる図である。
【図２６】空気の屈折率ｎ０＝１、プリズムの屈折率ｎ１＝１．５のときに、三角柱プリズムの頂角と強度がピークになるサイドローブ光Ｒ_{１，ｐｅａｋ}の経路との関係を示した図である。
【符号の説明】
１、１’、１Ｂ レンズシート
１０、１０’ 単位五角形プリズム
３１ ケース
３２、４３ 線光源
４０ バックライト
４１、１０１ 導光板
４２、１０３ 光拡散反射層
４４ 反射膜
４５ 照明カバー
１０２ 光等方拡散層
１０５、１０６ レンズシート[0001]
[Industrial applications]
The present invention relates to a lens sheet in which a unit lens unit is arranged so as to be convex on the light output side, a surface light source using the lens sheet, and a transmission type display device using the surface light source as a backlight. .
[0002]
[Prior art]
As a liquid crystal display device, a device using a direct-type or edge-light type diffusion surface light source is known (JP-A-5-173134, JP-A-2-257188, JP-A-4-107201, JP-A-6-18707). No. JP-A-6-67178).
[0003]
FIG. 23 is a diagram showing a conventional example of an edge light type surface light source.
The surface light source 100A has a specification disclosed in Japanese Patent Application Laid-Open No. 5-173134, Japanese Utility Model Application Laid-Open No. 4-107201, etc., and the light isotropically diffusing layer 102 is formed on one surface of the translucent substrate 101. Further, an isosceles triangular prism prism linear array lens sheet 105 having an apex angle α of 90 degrees is laminated. Further, a reflective layer 103 is formed on the other surface, and a point-like or linear light source 104 is arranged on the side surface.
The surface light source 100B has a specification disclosed in JP-A-6-18707, JP-A-6-67178, etc., and has a vertex angle α of 110 degrees instead of the lens sheet 105 of the surface light source 100A. It is a stack of isosceles triangular prism prism linear array lens sheets 106.
[0004]
[Problems to be solved by the invention]
In the former surface light source 100A, the light isotropically diffused by the isotropic light diffusing layer 102 is deflected by the prism action of the lens sheet 105, so that the light energy is concentrated near the normal direction of the light emitting surface, and the energy is reduced. The use efficiency is high, and high luminance can be achieved with low power consumption. However, as shown by a curve (A) in FIG. 15, a phenomenon (a side lobe in the angular distribution of transmitted light intensity) in which some light deviates from a predetermined angle range near the normal direction occurs (A-1). ), There is a problem that the light emitted in the oblique direction becomes unnecessary light (stray light, noise light) for nearby workers.
[0005]
As shown by the curve (B) in FIG. 15, the latter surface light source 100B has no or small side lobes, but has a normal luminance (meaning luminance in the normal direction of the light emitting surface, the same applies hereinafter) of 25%. However, there is a problem that it is reduced to the extent.
[0006]
An object of the present invention is to provide a lens sheet, a surface light source, and a display device that can eliminate unnecessary light in oblique directions without lowering normal luminance.
[0007]
[Means for Solving the Problems]
In order to solve the above problem, the invention of claim 1 arranges a large number of one-dimensional or two-dimensional unit pentagonal prisms formed on the light-emitting side of the light-transmitting substrate on the light-emitting side. A lens sheet having a lens array layer, wherein the main cut surface of the unit pentagonal prism has a vertex angle θ_aAnd two steep slopes in contact with the light-transmitting substrate,_aAnd two gentle slopes that are not in contact with the light-transmitting base material, the apex angle θ when the refractive index of the unit pentagonal prism is n1, and the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0._a, Θ_a'But,
θ_a<90 ° + (10/9) sin^-1((1 / √2) (n0 / n1))-(6/9) sin^-1(N0 / n1)
And,
θ_a′ ≧ θ_a
It is characterized by being.
[0008]
According to a second aspect of the present invention, in the lens sheet according to the first aspect, the apex angle θ_a’Range is
θ_a′ ≧ 60 ° + (4/3) sin^-1(N0 / n1)
It is characterized by being.
[0009]
The invention according to claim 3 is a lens sheet having a lens array layer in which a large number of unit pentagonal prisms convexly formed on the light emitting side are arranged one-dimensionally or two-dimensionally on the light emitting side surface of the light-transmitting substrate. And the main cut surface shape of the unit pentagonal prism has an apex angle θ_aAnd two steep slopes in contact with the light-transmitting substrate,_a', Two gentle slopes not in contact with the translucent base material, the refractive index of the unit pentagonal prism is n1, the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0, and the side emitted from the two steep slopes The maximum emission angle of the lobe light measured from the normal to the bottom of the prism is Θ_{so, max}, Minimum emission angle Θ_{so, min}, The base angle of the steep prism_bAnd the vertical angle θ_a, Θ_a'But,
θ_a<90 ° + (10/9) sin^-1((1 / √2) (n0 / n1))-(6/9) sin^-1(N0 / n1)
And,
θ_a+ 2 sin^-1(N0 / n1)-EQ1 ≥ θ_a′ ≧ θ_a+ 2 sin^-1(N0 / n1)-EQ2
However,
EQ1 = 2sin^-1((N0 / n1) sin (Θ_{so, min}  − Θ_b))
EQ2 = 2sin^-1((N0 / n1) sin (Θ_{so, max}  − Θ_b))
It is characterized by being.
[0010]
According to a fourth aspect of the present invention, in the lens sheet according to the first or second aspect, the maximum emission angle of the side lobe light emitted from the two steep slopes of the unit pentagonal prism including the steep slope measured from the normal line of the bottom surface of the prism. Θ_{so, max}, Minimum emission angle Θ_{so, min}, The base angle of the steep prism_bAnd the length x1 'of the gentle slope and the length x2 of the steep slope are
e / (c0-1) ≤x1 '/ x2≤e / (d0-1)
However,
c0 = c1 / c2
d0 = d1 / d2
c1 = sin (90 ° −sin^-1((N0 / n1) sin (Θ_{so, min}  − Θ_b)))
c2 = sin (90 ° + sin^-1((N0 / n1) sin (Θ_{so, min}  − Θ_b)) − Θ_a)
d1 = sin (90 ° −sin^-1((N0 / n1) sin (Θ_{so, max}  − Θ_b)))
d2 = sin (90 ° + sin^-1((N0 / n1) sin (Θ_{so, max}  − Θ_b)) − Θ_a)
e = sin (θ_a/ 2) / sin (θ_a'/ 2)
It is characterized by having the following relationship.
[0011]
According to a fifth aspect of the present invention, there is provided a light guide comprising a light-transmitting flat plate or a rectangular parallelepiped cavity, a light reflection layer provided at least partially on a back surface of the light guide, and at least one of side end faces of the light guide. 5. The lens sheet according to claim 1, wherein the light source is a point-like or linear light source provided adjacent to or above the surface, and the lens sheet is disposed on the front surface side of the light guide. Or a light isotropic diffusive layer laminated inside, wherein the surface of the lens sheet is a diffused light emission surface.
[0012]
The invention according to claim 6, wherein one or more point-like or linear light sources, a light source housing that surrounds the light sources, has one surface as an opening, and the inner surface on the opening side as a light reflecting surface, A lens sheet, comprising: the lens sheet according to claim 1, which is disposed on an opening side of the storage unit; and a light isotropically diffusing layer laminated outside or inside the lens sheet. Is characterized in that the surface of the surface becomes a diffused light emission surface.
[0013]
A seventh aspect of the present invention is characterized by including a transmission type display element and the surface light source according to the fifth or sixth aspect provided on the back surface of the display element.
[0014]
[Action]
FIG. 1 is a schematic diagram illustrating the operation of a unit pentagonal prism of a lens sheet according to the present invention.
In the lens sheet 1 of the present invention, the unit pentagonal prism 10 is formed in a convex shape on the light emission side, and has a pentagonal cross section (main cut surface) in one direction or two orthogonal directions. The unit pentagonal prism 10 may be one in which a large number of one-dimensionally arranged pentagonal prisms are arranged such that the pentagonal prisms are parallel to each other in the ridge direction, or a pentagonal prism in which four-sided pyramids are stacked on a four-sided pyramid. They may be arranged two-dimensionally in an array.
[0015]
The unit pentagonal prism 10 has an angle formed by two surfaces (steep slopes) 12 and 13 on the base side (side in contact with the light-transmissive substrate) (this is a virtual extension line of the two surfaces 12 and 13 as shown in the drawing). Of the angles formed by the pentagonal prism) θ_aIs the angle (ie, apex angle) θ between the two surfaces (slowly inclined surfaces) 14 and 15 on the top side (the side not in contact with the translucent substrate)._a’(Θ_a’> Θ_a). Therefore, the angle between the steep slopes 12 and 13 and the gentle slopes 14 and 15 and the bottom surface 11 is θ₁, Θ₂Then θ₂<Θ₁Holds. Here, the steep slopes 12 and 13 are parts that fulfill the function of increasing luminance, and the gentle slopes 14 and 15 are parts that fulfill the function of suppressing side lobes.
[0016]
Hereinafter, in order to show the operation of the lens sheet according to the present invention, first, the behavior of an incident light beam in a unit triangular prism having apical angles of 90 ° and 140 ° will be described. Next, the behavior of the incident light beam in the unit pentagonal prism according to the present invention will be described, and it will be described that the unit pentagonal prism having an appropriate shape achieves the improvement of luminance and the prevention of generation of side lobe light. Furthermore, in order to exhibit such a function, the conditions that the unit pentagonal prism must satisfy (the angle θ in FIG. 1)._a’And θ_aThe procedure to derive the conditions that should be satisfied and the ratio of the length of the steep slope to the gentle slope) will be described.
[0017]
FIG. 2 shows the structure of a unit prism of an isosceles triangular prism linear array lens sheet having an apex angle of 90 °, and light rays incident on the unit prism when the lens sheet is arranged on a light guide plate of an edge light type surface light source. FIG.
[0018]
For simplicity, the trajectory of the light ray is calculated and obtained under the following assumptions.
1) The refractive index of air was n0 = 1.0, and the refractive index of the prism was n1 = 1.5.
2) The angle of incidence of the light ray R1 on the bottom surface of the prism was 45.7 ° counterclockwise.
3) The incident angles of the light rays R2 and R3 on the bottom surface of the prism were both 22.8 ° clockwise or counterclockwise.
4) One unit prism was taken out of the linear array lens sheet and simulated.
5) Considering the main cut surface of the columnar prism, it was assumed that the incident light was within the main cut surface.
6) The behavior of the light beam was examined with the prism bottom surface as the diffused light incident direction (downward in the figure).
[0019]
Also, on each outer peripheral surface of the unit prism, the trajectory of the light beam reflected or refracted is
(A) the law of reflection (θ = θ ′ when the incident angle θ and the reflection angle θ ′),
(B) The law of refraction (the refractive index n1 in the medium 1, the angle between the light beam and the normal to the interface between the mediums 1 and 2 is θ₁, The refractive index n2 of the medium 2 and the angle between the emitted light beam and its normal line are θ₂Where n1 sin θ₁= N2 sin θ₂)
Determined based on
[0020]
In FIG. 2, as light rays to be traced, R1, R2, and R3, which are three typical light rays among the reflected light rays having an angular distribution, which are reflected by the light diffusion / reflection layer on the back surface of the light guide plate and enter the prism, are used. I have chosen. Among them, the light ray R2 represents, among the diffused light rays that enter the prism, those that enter from the left, are deflected in the normal direction of the light emitting surface, and emit. The light ray R3 is representative of the diffuse light rays that enter the prism and that are incident from the right, deflected in the normal direction of the light emitting surface, and emitted.
[0021]
The light ray R1 is a light ray that causes side lobe light. Particularly, in the case of a lens sheet having a remarkable apex angle of 90 ° of side lobe light, the main factor of the side lobe is that the light enters the inclined surface of the unit prism at an angle larger than the critical angle, is totally reflected, and is horizontally reflected. Is a light beam that is deflected in the horizontal direction and is further deflected in the horizontal direction by the opposite slope. Ray R1 is representative of such a ray. The light ray R1 should be selected one by one for each of the right and left. However, the unit prism is symmetrical to the left and right, and in order to avoid complicating the drawing, only one light ray R1 is represented from the right.
[0022]
As can be seen in FIG.₂→ H₂→ I₂Follow along. So
As a result, when the light beam R2 exits the unit prism, it is deflected in a direction close to the normal line n of the light emitting surface (the angle between the light line R2 and the normal line n is 3.8 ° counterclockwise), It can be seen that this contributes to increasing the normal luminance of the sheet. Similarly, the ray R3 is also deflected in the process of passing through the unit prism in a direction close to the normal to the light emitting surface (the angle formed with the normal n is 3.8 ° clockwise), and the normal to the lens sheet. This contributes to an increase in luminance.
[0023]
On the other hand, the ray R1 is A₂→ B₂Through the prism, and C on the right slope f2₂At the point, the incident angle of 73.5 ° is more than the critical angle of 41.8 °, so that the light is totally reflected. As a result, it is deflected to near the horizontal in the left direction, and the point D on the left slope f1 is₂Reach Then, when it comes out into the air, it is further deflected horizontally and E₂Leads to.
At this time, the angle between the light ray R1 (emitted light) and the normal line n of the light emission surface of the surface light source is 70.7 °, and the light ray R1 has a viewing angle (light emission angle) used in a normal display device. It can be seen that it deviates from the normal of the surface by about ± 45 ° at the maximum) and becomes side lobe light. Here, the emission direction of the light ray R1 will be compared with the emission direction of the actually measured side lobe light.
[0024]
FIG. 15 is a diagram showing the results of measuring the luminance of transmitted light as a function of angle in various types of prism linear array sheets. The measurement is performed by placing a light diffusion transmission sheet on the surface of an edge light type surface light source, and placing the above-described triangular prism linear array sheet on the surface so that the prism surface faces outward (opposite to the light guide plate side). ing. In the figure, the curve (A) drawn by a solid line is a measurement result for a triangular prism linear array sheet having a vertex angle of 90 °, and particularly (A-1) shows the luminance of the side lobe light. As can be seen from FIG. 15, the emission angle 70.7 ° of the light ray R1 substantially coincides with the actually measured angle 68 ° between the peak direction of the side lobe light and the normal to the light emitting surface.
[0025]
FIG. 3 shows the structure of a unit prism of a triangular prism linear array lens sheet having an apex angle of 140 ° and the trajectory of light rays entering the unit prism when the lens sheet is arranged on a light guide plate of an edge light type surface light source. FIG.
In FIG. 2, the light beam R1 which has been the side lobe light is changed to a point C on the right slope f2 of the unit prism.₁At the point D on the bottom surface f3.₁, Point E on left slope f1₁But total reflection, F₁→ G₁And return to the bottom side. Therefore, no side lobe light is generated in this unit prism. This agrees with the result of measuring the luminance of the transmitted light of the lens sheet by an experiment (see FIG. 15, broken line (B)). However, in an actual surface light source, there are various types of light rays other than the light rays R1, so that some side lobe light is generated.
[0026]
On the other hand, the light rays R2 and R3 are both deflected in a direction close to the normal line n of the light emitting surface, as in the case of FIG. In addition, since the figure is symmetrical, only the light ray R3 is shown in the figure. The angle formed by the ray R3 and the normal n is 12.5 °, which is slightly larger than 3.8 ° when the apex angle is 90 °. This means that in the unit prism having the apex angle of 140 °, the luminance in the normal direction slightly decreases and the viewing angle increases. This is also consistent with the tendency of the experimental results (see FIG. 15).
[0027]
FIG. 4 shows the structure of the unit prism of the pentagonal prism linear array lens sheet according to the present invention and the trajectory of light rays incident on the unit prism when the lens sheet is arranged on the light guide plate of the edge light type surface light source. FIG.
[0028]
In the illustrated unit pentagonal prism, the steep slopes (f1, f2) below the prism have the same shape as a unit triangular prism having a vertex angle of 90 °. Therefore, ray R1 is A₀→ B₀And enters the prism through the point C on the slope f2.₀And is deflected to near the left horizontal line. Next, the ray R1 is reflected at a point D on the slope f4 above the prism.₀To reach. Here, since the slopes f4 and f5 on the upper part of the prism have the same shape as the triangular prism with the apex angle of 140 °, the incident angle of the light ray R1 on the slope f4 is 50 ° larger than the critical angle. For this reason, the ray R1 is₀At the point E on the bottom surface f3.₀And F₀Is fed back to the light guide plate. Therefore, the light ray R1 does not become the side lobe light.
[0029]
The above calculation result also agrees well with the actually measured data (see FIG. 15, data when the apex angle of the gentle slope shown in the curve (C) is 108 °). In the experiment, since various light beams not simulated in FIG. 3 are irradiated from the surface light source to the prism, the side lobe light has not completely disappeared. However, compared to the side lobe light measured in the prism with the 90 ° apex angle, its brightness is greatly reduced. (The side lobe luminance in FIG. 15C is 58% of the side lobe luminance in FIG. 15A.)
[0030]
In FIG. 4, the light beam R1 is totally reflected twice in the prism, and is fed back to the light guide plate via the bottom surface f3. The number of times of total reflection is smaller than that in the case of the unit triangular prism having the apex angle of 140 ° shown in FIG. 3 (three times). Further, the optical path length in which the ray R1 travels in the prism is shorter in the case of FIG. 4 than in the case of FIG. Therefore, in the unit pentagonal prism, the rate of attenuation of the light beam before being fed back to the light guide plate is small, and after being fed back to the light guide plate, the light beam is diffusely reflected on the back surface of the light guide plate and again enters the prism as output light. The proportion is large.
[0031]
In FIG. 4, as a result of refraction in the prism, the light ray R3 is deflected, converged, and emitted 3.8 degrees from the normal line n of the light emitting surface. This is smaller than 12.5 ° shown in FIG. 3, indicating that the pentagonal prism according to the present invention converges output light more densely in the normal direction.
[0032]
The simulations in FIGS. 2 to 4 are all performed in a case where the prism surface faces the light emission surface side (the side opposite to the light guide plate). On the other hand, FIG. 5 is a simulation in a case where the prism surface faces the incident surface side (light guide plate side).
[0033]
In the figure, a ray R1 has an optical path A₃→ B₃→ C₃→ D₃→ E₃Finally, since the feedback is made to the light guide plate, it does not cause side lobe light.
However, when this light ray is slightly shifted to the left and enters the prism, that is, in the case of the light ray R1 ', the optical path is F₃→ G₃→ H₃→ I₃The light exits from the bottom surface f3 of the prism at an angle of 64.0 ° with respect to the normal n of the light emitting surface. Therefore, the light ray R1 'is a cause of the generation of the side lobe light.
Further, the ray R2 and the ray R2 'which is slightly shifted to the right and enter the prism are emitted from the bottom surface f3 at angles of 35.5 ° and 49.4 ° with the normal line n of the light emitting surface. Although the illustration corresponding to the ray R3 is omitted, it shows the same behavior as the ray R2.
[0034]
As described above, when the pentagonal prism according to the present invention is used with the prism surface directed toward the light guide plate, the normal luminance is reduced as compared with the case where the prism surface is directed toward the light emission direction, and the side lobe is reduced. Light is generated. Note that the same tendency is obtained in the actually measured data (see FIG. 16).
[0035]
From the above simulations, in the case of the edge light type surface light source using the light guide plate, the pentagonal prism linear array lens sheet according to the present invention can turn the prism surface toward the light emitting surface side (the opposite side to the light guide plate). It can be seen that this is preferable for increasing the normal luminance.
Further, even in the case of a direct type surface light source, in the case where the diffused light is incident on the prism through the light transmitting diffusion sheet, the prism surface is changed to the light emitting surface by the same operation mechanism as in FIGS. It turns out that it is preferable to face the side (the side opposite to the light guide plate) in order to increase the normal luminance and reduce the side lobe to obtain a necessary and sufficient viewing angle.
[0036]
Next, generation of side lobe light will be considered in more detail with reference to FIG. FIG. 6 shows a main cut surface (a unit prism represented by an isosceles triangle PQJ) of an isosceles triangular prism having an apex angle of θa. In the following, unless otherwise specified, the apex angle θ_aAnd the critical angle θ at the prism / air interface_cIs
θ_a> 2θ_c                                          (1)
Have the following relationship. However,
θ_c= Sin^-1(N0 / n1) (2)
It is.
[0037]
The rays R11, R12, and R13 are rays that enter the prism from the bottom surface f3 and are totally reflected at a point C on the right slope f2. Note that the angle of incidence with respect to the slope f2 is the critical angle θ_cSince the smaller light rays are refracted in the direction of the normal line n of the light emitting surface and pass through the slope f2 and do not contribute to the side lobe light, the description is omitted.
[0038]
Ray R11 is incident angle θ at point C._c11Is the critical angle θ_cAfter being totally reflected at the point C, the incident angle θ is changed to a point D on the slope f1._d11Has reached. Here, from the condition of equation (1),
θ_d11= Θ_a− Θ_c11> Θ_c                              (3)
It is. Therefore, the light ray R11 is also totally reflected at the point D. Thereafter, since the light ray R11 is fed back from the bottom surface f3 to the light guide plate side, the light ray R11 does not become side lobe light.
[0039]
On the other hand, the ray R12 has an incident angle θ at the point C._c12But,
θ_c12= Θ_a− Θ_c                                      (4)
Is a ray of light. The ray R12 enters the slope f1 at the point I after being totally reflected at the point C. The incident angle θ at this time_d12Is
θ_d12= Θ_a− Θ_c12= Θ_c                              (5)
It is. Therefore, after reaching the point I, the ray R12 travels along the slope f1 to the point J and is fed back to the bottom side (light guide plate) from the point J, so that the ray R12 does not become a sidelobe light like the ray R11.
[0040]
Ray R13 has an incident angle θ at point C_c13But
θ_c13> Θ_a− Θ_c                                      (6)
Therefore, the incident angle θ at the point M on the slope f1_d13Is
θ_d13<Θ_c                                            (7)
It is. As a result, the light ray R13 is emitted from the inclined surface f1 at a large angle with respect to the normal line n (an angle close to the left horizontal direction in the figure) and becomes a side lobe light. From this, it is understood that the light beam that is totally reflected at the point C and that passes through the inside of the angle ICQ and reaches the slope f1 is a sidelobe light. here,
Angle ICQ = 90 °-(θ_a− Θ_c) (8)
Because
θ_c13= (Θ_a− Θ_c) + K (90 ° − (θ_a− Θ_c))
However, 0 <k <1, (9)
Is led.
[0041]
FIG. 7 shows that the same apex angle as in FIG._a3 shows the main cut surface of the triangular prism. Ray R in the figure_{1, max}, R_{1, peak}, R_{1, min}Respectively enter the prism from the bottom surface f3, and the respective incident angles θ on the inclined surface f2._{R, max}, Θ_{R, peak}, Θ_{R, min}Is a ray totally reflected so as to satisfy the expression (9). In particular,

It is. That is, the reflection angles of these light rays on the inclined surface f2 are angles that divide the angle range in which the side lobe light can be reflected (formula (9)) into 8/10, 6/10, and 4/10, respectively.
[0042]
Thus θ_{R, max}, Θ_{R, peak}, Θ_{R, min}Defines that these rays are on the left slope
Value measured from the normal to the bottom surface f3, that is, the normal n of the light emitting surface of the surface light source (sidelobe emission angle) Θ_{so, min}, Θ_{so, peak}, Θ_{so, max}The specific value of_aCalculating for the case of = 90 ° yields 57.7 °, 70.7 °, and 84.7 °, respectively.
[0043]
On the other hand, as can be seen from the curve (A) in FIG._a= 90 °, the minimum angle direction of the side lobe light of the isosceles triangular prism is Θ_{so, min}= 52 °, the direction in which the light energy is maximum (peak direction) is Θ_{so, peak}= 68 ° and the maximum angle method is Θ_{so, max}= 82 °. These values are Θ of the above calculated values._{so, min}, Θ_{so, peak}, Θ_{so, max}And almost match. From this, in the following the ray R_{1, max}, R_{1, peak}, R_{1, min}Respectively approximate the side lobe light in the minimum angle direction, the peak direction, and the maximum angle direction measured from the normal line n of the light emitting surface.
[0044]
Next, a ray R from the slope f1_{1, max}~ R_{1, min}The following describes how to specify a region through which the light passes, and replace that region with a prism having a shape that does not generate side lobe light. By doing so, the apex angle θ_aIn the isosceles triangular prism, it is possible to eliminate the side lobe light while maximizing the high output luminance characteristics.
[0045]
First, a method of specifying a region that emits side lobe light on the slope f1 will be described with reference to FIG. FIG. 8 shows that the apex angle is θ._a9 shows the main cut surface of the triangular prism with 90 = 90 °. The light beam R11 is a light beam R, which is the side lobe light having the maximum brightness in FIG._{1, peak}And the side lobe emission angle θ_soIs 70.7 °.
[0046]
Light ray R11 is transmitted through optical path E₁→ D₁And enters the prism via a point C on the right slope f2.₁After being totally reflected at point P on the left slope f1₁From A₁Emits in the direction. Now, let the reflection point on the slope F2 be C₁, C₂,... Gradually move in the direction of the bottom surface f3, and the light beam gradually moves on the inclined surface f1 in the direction of the base f3 as indicated by R11, R12,. Ray R_1cIs the point B where the reflection point intersects the base f3 and the slope f2_cIs almost the same as E_c→ B_c→ P_c→ A_cIt is a light ray that travels. Thus, the light rays R11 to R_1cEnters the prism from the bottom surface f3 and exits from the inclined surface f1 as side lobe light.
[0047]
Next, the emission point on the hypotenuse f1 is the ray R_1cExit point P of_cPoint P on the lower f3 side₃, P₄It is assumed that light rays R13 and R14 exist as side lobe light. As these rays travel backward, the angle of incidence of these rays on the bottom surface f3 becomes the critical angle θ._cAnd no longer enters the prism from below the bottom surface f3, for example, the optical path E₃→ G₃→ F₃→ P₃→ A₃, The light must be incident from the inclined surface f2 and totally reflected by the bottom surface f3. However, when an ordinary surface light source is used and the prism is installed such that the bottom surface f3 of the prism faces the surface light source, there are almost no light rays similar to the light rays R13 and R14. Therefore, on the slope f1 of the prism, the point P_cIt can be seen that virtually all of the side lobe light is emitted from between the prism and the vertex angle.
[0048]
Then, the point P_cFind the position of Until the above, the sidelobe emission angle is θ_{so, peak}R that is_{1, peak}In the following, the problem is generalized, and the sidelobe emission angle becomes θ_soRay R_1cthink about. FIG. 9 shows that the same apex angle as in FIG._aAnd the ray R passing through the vertex c, crossing the main section plane abc of the triangular prism and the cross section thereof._1cFIG.
[0049]
Ray R_1cIs the angle θ at which the light enters the left slope f1._siIs θ from the law of refraction_soUsing,
θ_si= Sin^-1((N0 / n1) sin θ_so) (13)
It becomes. However, from FIG._{so, min}~ Θ_{so, max}Is exceptionally measured from the normal line n of the light exit surface (same as the normal line of the prism bottom surface f3), but the angle θ used for the law of refraction is_soAre measured from the normal line N of the light emitting surface f1.
θ_{so, min}  = Θ_{so, min}  − Θ_b
θ_{so, peak}= Θ_{so, peak}− Θ_b
θ_{so, max}  = Θ_{so, max}  − Θ_b... (13a)
(However, θ_bIs the base angle of the main cut surface of the triangular prism). On the other hand, the triangle aP_cIn c,
Angle aP_cc = 90 ° -θ_si                              (14a)
Angle P_cca = 90 ° + θ_si  − Θa (14b)
It is.
[0050]
In general, assuming that the diagonal of each side of a triangle having three sides A, B, and C is α, β, and γ,
(A + B) / (A−B) = (sinα + sinβ) / (sinα−sinβ) (15)
Holds. Then, surfaces ca, aP_c, P_cIf the lengths of b are x, x1, and x2, and substituting equations (13), (14a), and (14b) into equation (15),

Therefore,
x1 / x2 = 1 / ((sin (90 ° -θ_si) / Sin (90 ° + θ)_si  ー θ_a)) ー 1) ・ ・ ・ ・ ・ (19a)
Get. From this, the apex angle is θ_aIn the planes ca and ab of the main cutting plane abc of the isosceles triangular prism,
aP_c1/ BP_c1= X1 / x2 (20)
Or
aP_c2/ CP_c2= X1 / x2 (21)
The point P_c1, P_c2And find the triangle P_c1aP_c2Can be replaced by a prism having a shape that does not generate side lobe light or reduces the amount of side lobe light. By doing so, the emission angle θ_soOr, it is possible to suppress the generation of the side lobe light at an angle larger than that.
[0051]
Θ in equation (19a)_siIs θ as shown in equation (13)._so, The point P defined as above_cIs the emission angle θ of the side lobe light._soTo θ_{so, min}≤θ_so≤θ_{so, max}It changes depending on which of the settings is made. That is, if equation (19a) is more strictly described,
1 / (c0-1) ≤x1 / x2≤1 / (d0-1) (21a)
However,
c0 = c1 / c2
d0 = d1 / d2
c1 = sin (90 ° −sin^-1((N0 / n1) sin θ_{so, min}))
c2 = sin (90 ° + sin^-1((N0 / n1) sin θ_{so, min}) − Θ_a)
d1 = sin (90 ° −sin^-1((N0 / n1) sin θ_{so, max}))
d2 = sin (90 ° + sin^-1((N0 / n1) sin θ_{so, max}) − Θ_a)
It becomes. θ_soTo θ_{so, max}Point P as a value close to_cIs obtained, the erasing of the side lobe light is completed. On the other hand, as understood from FIG. 7 or equation (19a), the point P_cThe distance x1 between the angle x and the apex angle a is longer, and the length x2 of the surface contributing to the normal luminance is shorter. Accordingly, the normal angle luminance is reduced and the diffusion angle (half-width of the main lobe) is also increased. Generally, these required performances are θ_so= Θ_{so, peak}By doing so, the balance is moderate.
[0052]
Subsequently, a prism shape from which side lobe light is not emitted or which is further reduced is determined. As is clear from the curve A in FIG. 7 or FIG. 15, the intensity of the side lobe light is particularly large in a triangular prism having a vertical angle θa of 90 °. The intensity of the side lobe light rapidly decreases at a certain angle when the vertex angle is gradually increased. Hereinafter, this point will be described.
[0053]
FIG. 26 shows the apex angle θ when the refractive index of air n0 = 1 and the refractive index of the prism n1 = 1.5._a= 90 °, the side lobe light R at which the intensity peaks_{1, peak}That is, a light ray incident on the bottom surface f3 at an incident angle of 45.7 ° has an apex angle θ_aFIG. 7 is a diagram showing how the route is changed with an increase in the number. From FIG. 26, the apex angle θ_aIs gradually increased from 90 °, the emission direction of the side lobe light gradually inclines in the horizontal direction. This is shown in FIG._{1, min}~ R_{1, max}Corresponds to the fact that the outgoing light beam gradually rotates counterclockwise. As shown in FIG. 26B, the apex angle θ_aAs a result, the output light impinges on the slope of the adjacent prism (the prism adjacent to the left in the figure), is partially reflected, and the output light R near the normal line n of the light emission surface._{1R, peak}become. Further, the remaining outgoing light is transmitted and refracted, and the light ray R fed back to the light guide plate or the light source side._{1t, peak}And is reused. Thus, θ_a, The side lobe light gradually decreases. In addition, θ_aIs increased, the side lobe light is totally reflected at the prism slope as shown in FIG. 3 and completely disappears because all of it is fed back to the light guide plate side.
[0054]
Next, the above process will be described while tracing light rays. As can be easily understood from FIG._aIs increased from 90 °, the side lobe light R_{1, min}~_{R1, max}Of which R has the largest emission angle_{1, max}Will first come into contact with the slope of the adjacent prism. Therefore, the side lobe light R_{1, max}The explanation will proceed based on.
FIG. 24 shows the vertical angle θ._aFIG. 9 is a diagram illustrating a path of side lobe light in a triangular prism with = 90 ° + α. Here, α satisfies the relationship of 0 ° <α <90 °, and θ_a= 90 ° + α, the side lobe light R emitted from the left slope f1 in the triangular prism shown in FIG._{1, max}This is the angle at which (the light beam going from point D to point E in the figure) is parallel to the bottom surface f3 (side JI in the figure). If such an angular relationship is satisfied, as can be seen from FIG. 26, the distance between adjacent unit prisms, or R_{1, max}Regardless of the position of the exit point of_{1, max}Always hits the adjacent (left adjacent) prism slope.
[0055]
Also, the apex angle θ_aBecomes 90 ° + α, the angle θ formed between the bottom surface f3 and the slope f1 or f2._bIs 45 ° − (α / 2). This is because the sum of the interior angles of the triangle is 180 °, the two base angles of the isosceles triangle are the same, and the slope f2 whose base is reduced by (α / 2) and its normal are counterclockwise. If attention is paid to (α / 2) rotation, it can be easily obtained in elementary geometric form. As a result, the side lobe light R at the point D on the left slope f1 is obtained._{1, max}Incident angle θ_{si, max}Since the sum of the interior angles of the triangle KDC in FIG. 24 is 180 °,

Also, the total reflection angle θ on the right slope f2_{R, max}Is, from equation (12),

It becomes.
[0056]
Side lobe light R_{1, max}Output angle θ on the slope f1_{so, max}And θ_{R, max}Is a point
In D, according to the law of refraction, it is related as follows.

Therefore,

It becomes. The fact that the direction (D → E) of the emitted light beam is parallel to the bottom surface f3 means that the side lobe light R_{1, max}Means that is perpendicular to the normal line n of the bottom surface f3 (the normal line of the light emitting surface of the surface light source).

It becomes. Therefore, from equations (21e) and (21f),

[0057]
Taking the sine of both sides in equation (21g),

Get.
[0058]
Where θ_a= 90 ° + α is the apex angle of the triangle, 0 ° <θ_a<180 °,
0 ° <α <90 °
∴ 45 ° <(α / 2) + 45 ° <90 °
√ 1 / √2 <sin ((α / 2) + 45 °) <1 (21i)
And the right side of equation (21h) is
(1 / √2) (n0 / n1) <(n0 / n1) sin (45 ° + α / 2) <n0 / n1 (21j)
It becomes.
[0059]
Therefore, from equations (21h) and (21j),
(N0 / n1)> sin (90 ° -θ)_{R, max}+ (3/2) α)> (1 / √2) (n0 / n1) (21k)
(Note that the inequality sign in equation (21k) is opposite to the inequality sign in equation (21j)). In addition, θ in equation (21c)_{R, max}Substituting
(N0 / n1)> sin ((6/10) θ_c+ (9/10) α)> (1 / √2) (n0 / n1) (21 m)
It becomes.
[0060]
On the other hand, the angle in the sine of the equation (21m) is originally the incident angle θ at the point D on the slope f2 in FIG._{Si, max}That is,

Considering that
0 ° <(6/10) θ_c+ (9/10) α <90 ° (21p)
It becomes. In this section, since the main value of the inverse sine function is a monovalent monotonically increasing function, the same inequality holds even if the inverse sine of equation (21m) is taken,
θ_c> (6/10) θ_c+ (9/10) α> sin^-1((1 / √2) (n0 / n1)) (21q)
It becomes. However, from the definition of the critical angle, sin^-1(N0 / n1) = θ_cAnd Solving equation (21q) for α yields

24, and the apex angle θ_{a, max}Is
θ_{a, max}= 90 ° + α

It must be understood that the condition must be satisfied.
[0061]
Apex angle θ_aFurther increases, the side lobe light R_{1, peak}, R_{1, min}Becomes parallel to the base f3, and is no longer side lobe light. Θ in equations (11) and (10)_{R, peak}, Θ_{R, min}When the same calculation as above is performed using_{a, peak}, Θ_{a, min}For each of the

Get. Here, in the equations (10) and (11), the calculation is performed by setting 90 ° to 90 ° + α.
[0062]
Summarizing the above results, the apex angle θ_a= 90 °, the exit angle θ from the left slope f1 of the prism_{so, min}≤θ≤θ_{so, max}Side lobe light R in the range_{1, min}~ R_{1, peak}~ R_{1, max}Are all emitted as they are (FIG. 7). Apex angle θ_aWhen is increased, the outgoing side lobe light gradually tilts counterclockwise, and firstly, the light beam emitted from below the left slope starts to be deflected by the adjacent prism as shown in FIG. 26 (B). However, most of the light is emitted as it is. The vertical angle is θ_{a, max}To the maximum emission angle R of the side lobe light._{1, max}After being emitted from the slope f1 as shown in FIG. 24, it becomes parallel to the prism bottom surface f3, and as shown in FIG. The light is reflected and transmitted to change its direction and is no longer side lobe light.
[0063]
Furthermore, θ_aIncreases, θ_{a, peak}, The side lobe light R giving the peak intensity_{1, peak}After being emitted from the left slope f1, the light also becomes parallel to the bottom face f3 and disappears as side lobe light.
Finally, θ_aIs θ_{a, min}, The side lobe light R having the minimum emission angle_{1, min}Is no longer the side lobe light, and all the side lobe light R_{1, min}~ R_{1, max}Is the reflected light R emitted near the normal direction._1RAnd light ray R fed back to the light guide plate (light source) side_1tIs converted to
[0064]
θ_aTo θ_{a, min}When it is further increased, the side lobe light having the larger emission angle is sequentially totally reflected on the left slope f2. And

Then, all the side lobe lights are totally reflected on the left slope f2 and return from the bottom face f3 to the light guide plate side. FIG. 3 shows an example of a triangular prism that satisfies the equation (21v) when n0 = 1.0 and n1 = 1.5, and has an apex angle θ._a= 140 °.
[0065]
Next, a method for deriving Expression (21v) will be described.
FIG. 10 shows that the apex angle is θ._aFIG. 4 is a diagram showing a main cut surface of a triangular prism which is a triangular prism. In the figure, a ray R5 travels in the prism along an optical path C → D (total reflection) → E, and an emission angle θ from a slope f1 in the F direction._soIt is a light beam emitted at.
[0066]
The angle at which the ray R5 enters the slope f1 and the slope f2 is θ_siAnd θ_R1The angle formed by the ray traveling from point C to point D with the bottom surface f3 is θ_R2Then

The following relationship holds. here,

Is satisfied, the light ray R5 that can be emitted from the inclined surface f1 is not a light beam incident from the bottom surface f3 but a light beam that enters the prism from the inclined surface f2 and undergoes total reflection at the point C.
[0067]
vice versa,

If, the ray R5 is a ray that has entered the prism from the bottom surface f3. As described above, the number of light rays entering the prism from the slope f2 is extremely small. Accordingly, the apex angle θ is set so as to simultaneously satisfy the equations (22) and (25)._aBy defining the above, it is possible to prevent the existence of a light beam that enters the prism from the bottom surface f3 and subsequently becomes side lobe light. Θ satisfying such conditions_aIs given by the following equation from equations (22) to (25).

[0068]
That is, the apex angle θ_aIs θ in equation (21u)._{a, min}When the value further satisfies Expression (27), the emission of the side lobe light is still suppressed, but the suppressed side lobe light is totally reflected on the slopes f1 and f2. Then, the light is fed back to the light guide plate or the light source, and is not used as output light. Therefore, the luminance of the output light (particularly, the luminance in the normal direction n of the light emitting surface) decreases. Instead, the viewing angle (half-value angle) of the output light increases as the vertex angle increases, and the light fed back to the light guide plate propagates inside the light guide plate, and a part of the light is output again. As a result, the surface distribution of luminance becomes more uniform.
[0069]
Therefore, especially when high normal luminance and low side lobes are required,

In addition, when it is desired to remove the side lobe light and make the luminance distribution uniform in the light emission surface rather than the width of the viewing angle of the output light and the height of the normal luminance,

It is good to
[0070]
FIG. 17 shows the refractive index, the critical angle, and the maximum exit angle θ at 90 ° apex angle for typical materials._max, The intensity is the peak direction θ_peak, And the minimum emission angle θ_minGentle slope apex angle θ that suppresses each ray that produces side lobes by adjacent slope reflection_{a, max}, Θ_{a, peak}, Θ_{a, max}And the gentle slope apex angle θ that suppresses the emission by totally reflecting the side lobe cause light on both slopes f1 and f2._RefFIG. However, the calculation is performed with the refractive index of air being 1.00.
[0071]
FIG. 11 is a diagram showing a main cut surface of the pentagonal prism obtained based on the above description.
The gentle slopes f4 and f5 above the prism have an apex angle of θ._a’(Θ_a’> Θ_{a, max}) Is a part of the hypotenuse of an isosceles triangle a′b′c ′. The steep slopes f1 and f2 below the prism have an apex angle of θ._a(Θ_a≤θ_{a, max}) Is a part of the hypotenuse of the isosceles triangle abc. θ_a<Θ_{a, max}The reason is that θ_a≧ θ_{a, max}Then, although the side lobe light is reduced, the refraction and convergence of the light (R2, R3, etc. in FIG. 2) transmitted through the prism become insufficient, and it is preferable to reduce the normal luminance of the emitted light and increase the diffusion angle. Because it has no consequences.
The ratio between the length of the steep slope and the length of the gentle slope satisfies Expression (36) described later. The two slopes are at point P_c1, P_c2Are connected so as not to generate a step-like step.
[0072]
In the prism shown in FIG. 11, among the light rays incident on the prism from the bottom surface f3, those that pass through the steeply inclined surfaces f1 and f2 are efficiently converged in the normal direction of the light emitting surface, so that the normal luminance is improved. . Further, for example, a light ray totally reflected on the gentle slope f5 and traveling to the gentle slope f4 is partially reflected by the prism slope (f5) on the left side after exiting the gentle slope f4, and travels in the normal direction of the light emitting surface. However, the rest is refracted and fed back to the bottom surface f3, so that it does not cause the generation of side lobe light. As described above, the pentagonal prism shown in FIG. 11 is a prism having both low side lobe characteristics and high normal line luminance characteristics.
[0073]
However, in the prism shown in FIG. 11, after entering the prism from the bottom surface f3 like the ray R6 in the figure, it is totally reflected at the point C on the steep slope f2, passes through the gentle slope f4, and becomes side lobe light. There may be more light rays.
That is, when the light ray R6 is totally reflected at a large angle at the point C, it reaches the point D on the gentle slope at a small incident angle. Where the apex angle θ_aIs not sufficiently large and the slope f4 has a steep slope, the incident angle θ of the ray R6 to the point D_siIs the critical angle θ_cAnd the ray R6 passes through the slope f4. When actually calculated, for example, the incident angle θ of the ray R6 at the point B_in= 48.9 °, apex angle θ of gentle slope_a′ = 120 °, the incident angle θ_siIs 31 ° and the ray R6 has an angle of incidence θ_so= 50 °. The exit light path R6 travels to the upper left, and as described above, most of the exit light path R6 becomes the side lobe light without being reflected by the prism on the left.
[0074]
Such side lobe light can be prevented by the conditions required as follows. That is, all rays incident on the prism along the path shown in FIG. 11 may be totally reflected on the steep slopes f4 and f5 and fed back to the bottom face f3.
FIG. 12 shows that the apex angle is θ_a(<Θ_{a, max}) Is the main cut surface of the isosceles triangular prism
It is the figure which showed ABC. In the figure, the ray R7 is totally reflected on the right slope f2, and then enters the point E on the left slope f1 at an incident angle θ._si(<Θ_c) And emitted from the prism as side lobe light.
[0075]
Here, it is assumed that the slope f1 is rotated clockwise about the point E by the angle Δθ. This corresponds to reducing the inclination of the slope f1 by Δθ. Conversely, θ_siIncreases by Δθ. Δθ is θ_si+ Δθ ≧ θ_cThat is,

Then θ_siIs the critical angle θ_cBe larger. As a result, it is possible to prevent the light ray R7 from being totally reflected on the slope f1 and becoming a side lobe light.
[0076]
FIG. 13 is a diagram showing a main cut surface of a pentagonal prism whose shape is determined based on the above consideration. Pentagon A'P_c1BCP_c2Is the vertical angle θ_aOf the triangle ABC, the side P which is a part of the right hypotenuse CA (left hypotenuse AB)_c2A (side P_c1A) is rotated clockwise (clockwise) by an angle Δθ that satisfies Expression (28) half an hour, and the two sides P_c1A, P_c2The point at which A intersects is newly designated as point A '. Therefore, the pentagon A'P_c1BCP_c2At the plane P_c2A '(f5) and P_c1A ′ (f4) is a gentle slope, and the surface CP_c2(F2) and P_c1B (f1) is a steep slope.
[0077]
Here, the angle (base angle) of the angle ABC is θ_bThen the apex angle θ_a’And θ_bThe relationship is
, Considering that both bases of an isosceles triangle are equal,

It becomes. Therefore,

It is. Further, from Expressions (13) and (28),

Is led. θ_soIs Θ_{so, min}~ Θ_{so, max}And Equation (13a), the emission angle of the emitted side lobe light is θ_{so, min}~ Θ_{so, max}Considering that it has a range of Θ_{so, min}−θ_b≤θ_so≤Θ_{so, max}−θ_bAs shown in FIG.
The pentagonal prism is

More preferably,

By satisfying the following condition, it is possible to prevent the light beam entering from the bottom surface f3 and traveling along the path in FIG. 13 from becoming the side lobe light. However, θ_aIs too large, the viewing angle unnecessarily widens and the normal luminance decreases, which is not preferable. Therefore,

It is preferable that FIG._{a, perfect}Here is an example. However, the apex angle of the steep slope is θ_a= 90 ° and the refractive indexes n0 = 1 and n1 = 1.5.
[0078]
Next, the ratio between the length x1 'of the gentle slope and the length x2 of the steep slope in the pentagonal prism as described above is determined.
FIG. 14 is a diagram showing a main cut surface of the pentagonal prism. Main cutting plane ABP_c1
C'P_c2Is the vertical angle θ_aCritical point P of the isosceles triangle ABC of_c1, P_c2Apex above
θ_a’(Θ_a’> Θ_a) Isosceles triangle P_c1C'P_c2It has the shape replaced with. P in the figure_c1C (P_c2C) corresponds to x1 in the equation (19a). Also, P_c1C '(P_c2C ′) = x1 ′.
[0079]
As is clear from the figure,
P_c1C '' = P_c2C ″ = x1sin (θ_a/ 2) (33)
And at the same time,
P_c1C '' = P_c2C ″ = x1′sin (θ_a'/ 2) (34)
It is. Therefore, from Equations (33) and (34),
x1 ′ = (sin (θ_a/ 2) / sin (θ_a'/ 2)) x1 (35)
It becomes.
[0080]
Here, by comparing the expression (19a) and the expression (35), the following expression can be obtained.

However,
k0 = k1 / k2
k1 = sin (90 ° −sin^-1((N0 / n1) sin θ_so))
k2 = sin (90 ° + sin^-1((N0 / n1) sin θ_so) − Θ_a)
e = sin (θ_a/ 2) / sin (θ_a'/ 2)
As in equation (31), θ_soIs (Θ_{so, min}−θ_b) ~ (Θ_{so, max}−θ_b)
Considering that it has a range of

However,
c0 = c1 / c2
d0 = d1 / d2
c1 = sin (90 ° −sin^-1((N0 / n1) sin (Θ_{so, min}  ー θ_b)))
c2 = sin (90 ° + sin^-1((N0 / n1) sin (Θ_{so, min}  ー θ_b)) − Θ_a)
d1 = sin (90 ° −sin^-1((N0 / n1) sin (Θ_{so, max}  ー θ_b)))
d2 = sin (90 ° + sin^-1((N0 / n1) sin (Θ_{so, max}  ー θ_b)) − Θ_a)
e = sin (θ_a/ 2) / sin (θ_a'/ 2)
Get.
[0081]
FIG. 18 shows the vertical angle θ of the steep slope._a= 90 °, critical angle θ_c= 41.8 ° (of the prism
The refractive index n0 = 1.5 and the refractive index of air n1 = 1.0)._aAnd the ratio x1 '/ x2 of the length of the gentle slope and the steep slope are calculated. Note that the emission angles of the side lobe lights to be removed are each measured from the light output surface normal n._{so, max}= 84.7 °, Θ_{so, peak}= 70.7 °, Θ_{so, min}= 57.7 °.
[0082]
Finally, the apex angle θ_aAnd critical angle θ_cIs θ_a≤2θ_cAbout when
The conditions that the shape of the unit pentagonal prism according to the present invention should satisfy will be described with reference to FIG. In this case, the incident angle θ of the light beam at the point D_siIs the incident angle θ of the ray at point C_RIs slightly θ_cIs exceeded, the angle becomes less than the critical angle. Therefore, θ
_R= Θ_cThe calculation described in FIGS. 8 and 9 is performed using the ray R12
Critical point P_cAsk for. Other calculations and the like are performed in the same manner as described above.
[0083]
【Example】
(Example of lens sheet)
Hereinafter, an example will be described in more detail with reference to the drawings and the like.
FIG. 19 is a diagram showing an example of a lens sheet according to the present invention together with a comparative example. The arrangements in FIGS. 19A, 19B, 19C, and 19D correspond to FIGS. 2, 3, 4, and 5, respectively.
Each of these lens sheets was formed on the surface of a transparent biaxially stretched PET (polyethylene terephthalate) sheet having a thickness of 50 μm using a urethane acrylate resin having a refractive index of 1.50 cross-linked and cured by ultraviolet rays. Things.
[0084]
Comparative Example 1
As shown in FIG. 19A, a prism prism linear array lens sheet 105 having a vertical angle of 90 ° is laminated on a backlight described later. The repetition period of the prism is 50 μm, and the length of two sides sandwiching the apex angle in the main section is 36 μm.
[0085]
Comparative Example 2
As shown in FIG. 19B, the apex angle is 108 ° (θ_{a, min}<Θ_a<Θ_{a, Ref}3)
A prism prism linear array lens sheet 106 laminated on a backlight described later. The repetition period of the prism is 50 μm, and the lengths of two sides sandwiching the apex angle in the main cross section are each 27 μm.
[0086]
Example
As shown in FIG. 19C, a lens sheet 1 of a pentagonal prism linear array having a base side of 90 ° apex angle and a top side of 108 ° apex angle is placed on a backlight, which will be described later, as a unit pentagon. The prisms are stacked so that the prism faces the observation side. The repetition cycle of the prism is 50 μm, and the side length of the steep slope in the main section (L in FIG. 1).₁) Is 18 μm and the side length of the gentle slope (L in FIG. 1)₂) Is 16 μm.
[0087]
Comparative Example 3
As shown in FIG. 19 (D), a pentagonal prism linear array lens sheet 1B similar to the embodiment in which the base side has a vertex angle of 90 ° and the vertex side has a vertex angle of 108 ° is mounted on a backlight described later. And the unit pentagonal prism is stacked so that it faces the light source side.
[0088]
The backlight is a light guide plate 101 having a screen of 9.4 inches and a thickness of 4 mm, a light isotropic diffusion layer 102 made of a sandblasted PET sheet on the front surface, and a scattered pattern light by white ink printing on the back surface. A light source 104 composed of a cold-cathode tube (power consumption: 4 watts) having a diameter of about 3 cm and having a long side and two lamps was used.
This luminance measurement was performed using a luminance meter [Topcon BM-8 (2 °)] at a position 30 cm from the front of each lens sheet with a backlight placed on the back surface of the lens sheets 105, 106, 1, and 1B. In addition, when nothing is placed on the light guide plate of the backlight and when only the light isotropic diffusion layer is placed on the light guide plate, the normal luminance is 770 [cd / cm].²], 968 [cd / cm²〕Met.
[0089]
FIGS. 15 and 16 are diagrams showing the results of measurement of the luminance of the lens sheets of the above-described example and Comparative Examples 1 to 3. FIG.
In Comparative Example 1, as shown in FIG. 15A, the normal luminance was high, but the side lobe was large. The value of the normal luminance is 1244 [cd / cm²The half-value angle was 66 °, and the luminance ratio of side lobe / main lobe (normal luminance) was 0.23.
In Comparative Example 2, as shown in FIG. 15B, the side lobe was almost completely eliminated, but the normal luminance was 1045 [cd / cm].²] And about 16% as compared with Comparative Example 1. The half value angle was 74 °, and the viewing angle was wider than that of Comparative Example 1. However, the side lobe was significantly reduced to a luminance ratio of side lobe / main lobe = 0.00 (read value from the graph in FIG. 15). did.
In this embodiment, as shown in FIG. 15C, the normal luminance is 1145 [cd / cm].²], The half value angle is 70 °, the luminance ratio of the side lobe / main lobe is 0.14, and the normal line
The decrease in luminance was small, the viewing angle was wide, and the side lobe was small.
In Comparative Example 3, as shown in FIG. 16, the normal luminance was 435 [cd / cm²], And the side lobe / main lobe had a luminance ratio of 1.34, which was larger than the main lobe. Further, the half value angle is as large as 125 ° (evaluated as an angle range having half or more of the side lobe peak luminance), and light is emitted to an angle range that is not practically necessary.
[0090]
(Example of edge light type surface light source)
FIG. 20 is a perspective view showing a first embodiment (edge light type) of the surface light source according to the present invention. In the surface light source of the first embodiment, the light isotropic diffusion layer 20 and the lens sheet 1 of the present invention are disposed on the upper surface of the light guide plate 41 of the edge light type backlight 40. In the backlight 40, a light diffusion / reflection layer 42 having a scattered pattern is formed on the lower surface of a light guide plate 41. On both sides of a side end surface of the light guide plate 41, a line light source 43, a reflection film 44, and a lighting cover are provided. 45 are provided. The edge light type surface light source has an advantage that it is thin and the light emission surface does not easily generate heat.
[0091]
(Example of a direct type surface light source)
FIG. 21 is a sectional view showing a second embodiment (direct type) of the surface light source according to the present invention. The surface light source according to the second embodiment includes a light isotropically diffusing layer 20 and a lens sheet 1 according to the present invention, which are provided inside a case 31 on the opening side of a direct-type backlight 30 provided with a linear light source 32 such as a fluorescent lamp. Is arranged. The light source side inner surface of the case 31 is processed into a light diffusion / reflection surface.
[0092]
(Example of display device)
The surface light source shown in FIGS. 20 and 21 can be used as a liquid crystal display device by disposing it on the back of a known transmission type liquid crystal display element. Further, in addition to a transmissive liquid crystal display element, the present invention can be applied to an element requiring a back light source, such as an electrochromic display element.
[0093]
(Other Examples of Lens Sheet)
FIG. 22 is a view showing another embodiment of the lens sheet according to the present invention.
In the embodiment of FIG. 19 (C), an example in which the unit pentagonal prisms 10 of the pentagonal prism are arranged one-dimensionally has been described. However, as shown in FIG. The same effect can be obtained even when the unit pentagonal prism 10 'in which the four pyramids are continuously arranged is two-dimensionally arranged.
[0094]
Further, in each of the above embodiments, the example in which the left and right lengths of the slope are equal has been described. However, in the case of using the display device of a laptop personal computer, the unit pentagonal prism is inclined in a specific direction. Is also good. In other words, a left-right asymmetric shape in which both base angles are not equal may be used. Further, if necessary, as described in Japanese Unexamined Patent Publication No. Hei 6-324205, the height of the minute projections and projections having a height equal to or greater than the wavelength of light is formed to prevent optical adhesion to the light guide plate. Can also.
[0095]
【The invention's effect】
As described in detail above, according to the present invention, since the unit pentagonal prism is formed in a convex shape on the light emission side and the cross-sectional shape in one direction or two orthogonal directions is pentagonal, The steep slope enhances the brightness in the normal direction of the light emitting surface, restricts the viewing angle, and the gentle slope of the top lens suppresses the occurrence of side lobes and achieves high normal brightness. Bright surface light emission condensed at a predetermined angle in the vicinity became possible.
[Brief description of the drawings]
FIG. 1 is a schematic diagram illustrating the operation of a unit pentagonal prism of a lens sheet according to the present invention.
FIG. 2 is a diagram showing light rays incident into a unit lens portion of a triangular prism linear array lens sheet (vertical angle 90 °).
FIG. 3 is a diagram illustrating light rays incident into a unit lens section of a triangular prism linear array lens sheet (vertical angle 140 °).
FIG. 4 is a diagram illustrating light rays incident into a unit lens unit of a pentagonal prism linear array lens sheet according to the present invention.
FIG. 5 is a diagram illustrating light rays when the lens unit of the pentagonal prism linear array lens sheet is arranged so as to face the light incident side.
FIG. 6: Apex angle θ_aFIG. 4 is a diagram for explaining a cause of generation of side lobe light in the triangular prism of FIG.
FIG. 7: apex angle θ_aFIG. 5 is a diagram showing the trajectories of side lobe light in the minimum angle direction, the peak direction, and the maximum angle direction in the triangular prism of FIG.
FIG. 8: Vertical angle θ_aFIG. 5 is a diagram showing a relationship between a region where a light beam enters and a region where side lobe light is emitted in the triangular prism of FIG.
FIG. 9: Apex angle θ_aFIG. 7 is a diagram showing a relationship between a length x1 of a region emitting side lobe light and a length x2 of a region not emitting the side lobe light in the triangular prism of FIG.
FIG. 10: Apex angle θ_aFIG. 6 is a diagram showing a trajectory of side lobe light that enters from a bottom surface f3 and exits from an inclined surface f1 at an emission angle θso in the triangular prism of FIG.
FIG. 11 is a diagram showing a trajectory of a light beam serving as side lobe light in a pentagonal prism satisfying Expressions (19a) and (27).
FIG. 12: Apex angle θ_aIncident on the inclined surface f1 of the light ray totally reflected on the inclined surface f2 and reaching the inclined surface f1_siFIG. 7 is a diagram showing a relationship between the slope and the inclination of the slope f1.
FIG. 13 is a diagram illustrating a main cut surface shape of a pentagonal prism that satisfies Expression (31).
FIG. 14 is a diagram showing a main cutting plane having a vertical angle θ._aCritical point P of the isosceles triangle ABC of_c1, P_c2Apex angle θ above_a’(Θ_a’> Θ_a) Isosceles triangle P_c1C'P_c2The figure which showed the main cut surface of the pentagonal prism which has the shape replaced by FIG.
FIG. 15 is a diagram showing the results of measuring the luminance of the lens sheets of Comparative Example 1 (A), Comparative Example 2 (B) and Example (C).
FIG. 16 is a diagram showing the result of measurement of the luminance of the lens sheet of Comparative Example 3.
FIG. 17 shows a refractive index, a critical angle, and a maximum exit angle θ in the case of a 90 ° apex angle for typical materials._max, The intensity is the peak direction θ_peak, And the minimum emission angle θ_minGentle slope apex angle θ that suppresses each ray that produces side lobes by adjacent slope reflection_{a, max}, Θ_{a, peak}, Θ_{a, max}And the gentle slope apex angle θ that suppresses the emission by totally reflecting the side lobe cause light on both slopes f1 and f2._RefFIG.
FIG. 18: Apex angle θ of steep slope_a= 90 °, critical angle θ_c= 41.8 ° (refractive index of the prism n0 = 1.5, refractive index of the air n1 = 1.0), the apex angle θ of the gentle slope_aAnd the result of calculating the ratio x1 '/ x2 of the length of the gentle slope and the steep slope.
FIG. 19 is a diagram showing an example of an edge light type surface light source provided with a lens sheet according to the present invention, together with a comparative example.
FIG. 20 is a perspective view showing a first embodiment (edge light type) of the surface light source according to the present invention.
FIG. 21 is a sectional view showing a second embodiment (direct type) of the surface light source according to the present invention.
FIG. 22 is a view showing another embodiment of the lens sheet according to the present invention.
FIG. 23 is a diagram showing a conventional example of an edge light type surface light source.
FIG. 24: Apex angle θ_aFIG. 9 is a diagram illustrating a path of side lobe light in a triangular prism with = 90 ° + α.
FIG. 25: Apex angle θ_aFIG. 25 is a diagram different from FIG. 24, illustrating a path of side lobe light in the triangular prism with = 90 ° + α.
FIG. 26 shows the side lobe light R at which the apex angle and the intensity of the triangular prism are peaked when the refractive index of air n0 = 1 and the refractive index of the prism n1 = 1.5._{1, peak}FIG. 6 is a diagram showing a relationship with a route.
[Explanation of symbols]
1, 1 ', 1B lens sheet
10, 10 'unit pentagonal prism
31 cases
32, 43 line light source
40 backlight
41, 101 light guide plate
42,103 Light diffuse reflection layer
44 Reflective film
45 Lighting cover
102 Light isotropic diffusion layer
105, 106 Lens sheet

Claims (7)

A lens sheet having a lens array layer in which a large number of unit pentagonal prisms formed in a convex shape on the light emitting side are one-dimensionally or two-dimensionally arranged on a light emitting side surface of a light transmitting base material,
The main cut surface shape of the unit pentagonal prism,
Two steep in contact with the translucent base apex angle of theta _a,
Having two gentle slopes not in contact with the translucent substrate having an apex angle of θ _a ′,
When the refractive index of the unit pentagonal prism is n1 and the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0, the apex angles θ _a and θ _a ′ are
θ _a <90 ° + (10/9) sin ⁻¹ ((1 / √2) (n0 / n1)) − (6/9) sin ⁻¹ (n0 / n1)
And,
θ _a '≧ θ _a
A lens sheet, characterized in that: The lens sheet according to claim 1,
The range of the apex angle θ _a ′ is
θ _a ′ ≧ 60 ° + (4/3) sin ⁻¹ (n0 / n1)
A lens sheet, characterized in that: A lens sheet having a lens array layer in which a large number of unit pentagonal prisms formed in a convex shape on the light emitting side are arranged one-dimensionally or two-dimensionally on the light emitting side surface of the light transmitting substrate,
The main cut surface shape of the unit pentagonal prism,
Two steep in contact with the translucent base apex angle of theta _a,
Having two gentle slopes not in contact with the translucent substrate having an apex angle of θ _a ′,
The refractive index of the unit pentagonal prism is n1, the refractive index of the surrounding atmosphere of the unit pentagonal prism is n0, and the maximum emission angle of the side lobe light emitted from the two steep slopes measured from the normal to the prism bottom is Θ _{so, max} , minimum emission angle Θ _{so, min} , and apex angles θ _a , θ _a ′ when the base angle of the steep prism surface is θ _b ,
θ _a <90 ° + (10/9) sin ⁻¹ ((1 / √2) (n0 / n1)) − (6/9) sin ⁻¹ (n0 / n1)
And,
^{_{θ a + 2sin -1 (n0 /}} n1) - EQ1 ≧ θ a '≧ θ a + 2sin -1 (n0 / n1) - EQ2
However,
^{EQ1 = 2sin -1 ((n0 /} n1) sin (Θ so, min - θ b))
^{EQ2 = 2sin -1 ((n0 /} n1) sin (Θ so, max - θ b))
A lens sheet, characterized in that: The lens sheet according to claim 1 or 2,
The maximum outgoing angle of the side lobe light emitted from the two steeply inclined surfaces of the unit pentagonal prism including the steeply inclined surface measured from the normal to the bottom surface of the prism is ｓ _{so, max} , the minimum outgoing angle Θ _{so, min} , and the base angle of the steep prismatic surface Is θ _b ,
The length x1 ′ of the gentle slope and the length x2 of the steep slope are:
e / (c0-1) ≤x1 '/ x2≤e / (d0-1)
However,
c0 = c1 / c2
d0 = d1 / d2
^{c1 = sin (90 ° - sin} -1 ((n0 / n1) sin (Θ so, min - θ b)))
^{c2 = sin (90 ° + sin} -1 ((n0 / n1) sin (Θ so, min - θ b)) - θ a)
^{d1 = sin (90 ° - sin} -1 ((n0 / n1) sin (Θ so, max - θ b)))
^{d2 = sin (90 ° + sin} -1 ((n0 / n1) sin (Θ so, max - θ b)) - θ a)
_{e = sin (θ a / 2} ) / sin (θ a '/ 2)
A lens sheet having the following relationship: A light guide made of a translucent flat plate or a rectangular parallelepiped cavity,
A light reflection layer provided at least partially on the back surface of the light guide,
A point-like or linear light source provided adjacent to at least one or more of the side end surfaces of the light guide,
The lens sheet according to any one of claims 1 to 4, wherein the lens sheet is arranged on a surface side of the light guide.
Including a light isotropic diffusive layer laminated on the outside or inside of the lens sheet,
A surface light source, wherein a surface of the lens sheet is a diffused light emission surface. One or more point or linear light sources;
A light source storage part surrounding the light source, and having one surface as an opening, and an inner surface on the opening side as a light reflecting surface;
The lens sheet according to claim 1, wherein the lens sheet is arranged on an opening side of the light source storage unit.
Including a light isotropic diffusive layer laminated on the outside or inside of the lens sheet,
A surface light source, wherein a surface of the lens sheet is a diffused light emission surface. A transmissive display element,
A display device, comprising: the surface light source according to claim 5 provided on a back surface of the display element.

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