JP3735842B2 - Computer-readable recording medium storing a program for driving an eye optical system simulation apparatus - Google Patents

Description

【００３１】
ここで、ｐ(ｕ,ｖ,ｕ−μ,ｖ−ν)は各点(ｕ,ｖ)から(ｕ−μ,ｖ−ν)離れた点におけるPSFの値である。また、ａはPSFの広がり半径である。この式を用い、網膜上の全ての点において光強度を求めることにより、回旋網膜像の静止画像を得ることができる。図１１は実施例１の方法によって得られた回旋網膜像の静止画像の例を示す図である。この例は右目遠用0.00D加入2.00Dの眼鏡用累進レンズ(HOYALUX GP；ホーヤ株式会社の商品名)の近用部分を通して、卓面にある印刷物を333mmの距離で見た場合の回旋網膜像である。視野は左右50°、上下38.5°である。右上隅の円形は中心視線のレンズ通過点位置を示すための表示である。この通過点位置は、図では識別できないが、円形内に赤色の点で示される。この円形はレンズの輪郭を表し、円形内の中心に付された点はレンズの幾何中心を示し、幾何中心の上下の○印は遠用測定点(上)及び近用測定点(下)を示す。Ｒ文字を裏にしたマークは右レンズであることを示す。図１１の例は中心視線のレンズ通過点が近用測定点(下の○)上にある場合の例である。左右におけるボケと歪みが如実に再現されていることがわかる。
【００３２】
この実施例によれば、累進多焦点レンズ等のレンズ系を通して見たときに知覚されるボケや歪みを近似的に再現した画像が得られる。即ち、健常裸眼であれば視野全体が鮮明に知覚されるが、老眼者が累進多焦点レンズを装用した場合には、視野の一部のみが鮮明に見え、他の部分はボケや歪みをともなって見える。この実施例によれば、そのような老眼者が知覚するであろう像を画像として再現できる。従って、得られた画像を表示装置に表示すれば、老眼でもない設計者自身が自ら設計した累進多焦点レンズの見え味を装用者の立場に立って確認することができるという、最も望ましい評価が可能になる。
【００３３】
ところで、この実施例において、計算処理等に最も時間を要する工程がPSF取得工程である。特に、レンズ系が累進多焦点レンズである場合には、全ての視線方向におけるPSFが異なるため、全ての画素に対してPSFを求める必要がある。例えば、800×600の画像で、PSFを求めるときに追跡する光線の本数を400(決して多くない)に設定すると、全体に192,000,000回光線追跡計算を行うことになる。光学系の面の複雑さや面数にもよるが、コンピュータの計算能力が秒間3,000本と仮定すると、64,000秒、つまり17時間46分40秒になる。これは、まだ畳み込み演算などの必要時間を考慮に入れていない場合の計算時間である。
【００３４】
そこで考えたのは、すべての物体点に対して光線追跡するのではなく、標本点だけに光線追跡を行い、その他の点についてはスプライン補間で求める方法である。空間上任意点Ａは、直交座標(ｘ,ｙ,ｚ)で表現しても良いが、眼鏡の場合眼からの距離が重要なので、回旋点からの距離の逆数Ｄ1と方位角の正接ψ,ζで表した方が適切である。つまり、
【００３５】
【数２】

である。点Ａから発する任意光線、即ち仮入射瞳平面上任意点(ｙp,ｚp)を通過する光線を追跡して得られる光線データ(網膜上の交点に対応する入射光線のｔｋm,ｃｆm、光路長など)は、Ｄ1,ψ,ζ,ｙp,ｚpの関数である。即ち、ｔｋm＝Ｆt（Ｄ1,ψ,ζ,ｙp,ｚp）、ｃｋm＝Ｆc(Ｄ1,ψ,ζ,ｙp,ｚp）、ｐｋm＝Ｆp（Ｄ1,ψ,ζ,ｙp,ｚp）で表現することができる。色収差を考える場合は更に波長次元を追加するとよい。各変数Ｄ1,ψ,ζ,ｙp,ｚpそれぞれの所定範囲内に適当な数、位置に標本点を設け、その5次元格子上のすべての標本点に対して、あらかじめ光線追跡を行って光線データを求めれば、所定範囲内(5次元ボックス)任意点についての光線データをスプライン補間によって求めることができる。
【００３６】
次にスプライン補間演算の高速化を検討する。一次元スプライン補間は、
【数３】

で表される。ここで、ｉは各次元の節点番号、Ｃiはその係数、ｎは標本点数である。ＮI(ｘ)はｉ番節点に対応する基底関数であり、階数Ｍの場合、ｉ番節点とｉ＋Ｍ番節点との間の範囲でゼロでない値を持ち、隣接節点間はｍ-1次多項式で表される(基底関数の局部性）。言い換えると、ｘの定義域内の点任意ａにおいては、多くてＭ個のゼロでないＮI(ｘ)しか存在しない。従って、補間式は一見ｎ項あるように見えるが、ｘ＝ａにおいては実質Ｍ項であり、Ｍ回の掛け算とＭ回の足し算でＦ(ａ)が得られる。五次元スプライン補間は、
【００３７】
【数４】

で表される。ここで、ｉ,ｊ,ｋ,ｌ,ｍは各次元の節点番号であり、それぞれ標本点数だけ変化する。つまり、項の数は各次元の標本点数の積になるわけである。しかし、上述の基底関数の局部性により、ある一点については、ゼロでない項の数は、各次元の階数の積である。各次元のスプライン階数が4の場合、項の数は45＝1024である。つまり一回の補間演算では、足し算1024回、掛け算1024×5＝5120回行うことになる。一般的には、ｎｊ次元のＭ階スプライン補間演算に必要な掛け算の回数は、ｎｊ×Ｍnjであり、次元数が大きくなるにつれて急激に計算負担が増える。ところが、上式を、
【００３８】
【数５】

に書き直すと、若干減らすことができる。これは、1次元の補間のネスト構造であり、次元の順番は自由に変えることができる。掛け算と足し算はともに4＋4×（4＋4×（4＋4×4）））＝1364回であり、ほぼ1/3の計算時間で済む。一般的には、ｎｊ次元のＭ階スプライン補間演算に必要な掛け算の回数は、
【００３９】
【数６】

である。このような方策を採りいれても、まだ計算量が大きく、実用的でない。一般的に、多次元スプライン補間の演算時間を上記の方法より更に短縮することは困難であろう。しかし、PSFを求める場合は、その特殊な事情ゆえに、もっと短縮する方法がある。物体上一点(Ｄ0,ψ0,ζ0)のPSFを求めるためには、入射瞳面(ｙp,ｚp平面)上多数(例えば400)の点と結ぶ光線データが必要である。400回五次元スプライン補間の三次元の変数は同じ値を入れることになる。もし、その400回の補間を二次元スプライン補間で行えば、計算時間の大幅短縮が可能である。五次元スプライン補間式を次のように書きかえる。
【００４０】
【数７】

【００４１】
この式は、五次元スプライン空間のうち、三次元の変数が確定した場合の二次元空間を求める方法を表している。ここで、この二次元スプラインを点(Ｄ0,ψ0,ζ0)の縮退空間といい、ｃl,mは縮退スプラインの係数である。もちろん縮退スプラインの節点、基底関数はすべて五次元スプラインと同一である。ｃl,mの数は標本点数の積で、ｙp,ｚp両次元それぞれ9点の標本点を設定する場合、81個である。各係数を求めるには、式のように三次元スプライン補間を用いる。そして、得られたｃl,mを用いて、ｙp-ｚp面上任意一点の光線データを二次元スプライン補間計算することができる。従って、81回の三次元補間と400回の二次元補間計算を行うだけで、点ｃにおけるPSFを得ることができる。掛け算の回数は、81×｛4／（4-1）｝（43-1)＋400×｛4／（4-1）｝（42-1)＝14804回であり、1光線あたり約37回である。400回の五次元補間より、計算量の削減効果は顕著である。上記の方法を活用すると、光線追跡の1／10の時間で光線データが得られる。図１３に、以上説明したPSF取得の概略手順を纏めてPSF取得方法二として示した。
【００４２】
次に、PSFのパラメータ化を検討する。上述の通り、光線データを光線追跡の代わりにスプライン補間法で計算することによって、10倍の計算速度を実現した。それにしても、1コマ当たりの処理時間でいうと、64000秒(17時間46分40秒)が6400秒(1時間46分40秒)に短縮しただけである。実用的には1コマ当たりの処理時間を数分にしたいのである。現状の方法では、PSFを取得するための計算がもっとも時間がかかるので、それを短縮するのが一番効果的である。
【００４３】
厳密にある物体点(Ｄ0,ψ0,ζ0)のPSFを取得するには、多数の光線を追跡または補間し、その光線密度を求めなければならない。しかも得られたPSFは画素単位の離散関数であり、密度も画素当たりの光線数の形になる。光線が集中している場合(焦点が合っている)は、少数の画素に多量の光線数が入り、連続関数に近いが、広範囲に散らばる(焦点が合わない)場合、単位画素に入る光線数が少なく、誤差が大きい。それをカバーするためにはますます多量の光線が必要となる。そこで、PSFをあらかじめ連続関数に仮定し、そのパラメータを光線追跡のデータを用いて当てはめるようにすれば、上記のジレンマから脱出することができる。そして、すべての物体点においてのパラメータを求める必要がなく、標本点を定めて、スプライン補間(三次元)で求めることができる。
【００４４】
さて、分布関数をどんな関数にすればよいのかの点について検討すると、ほとんどのPSFは山の形になっているから、二次元正規分布が適切であろと考えられる。つまり、
【００４５】
【数８】

【００４６】
ここで、μ,νはそれぞれtk、cf方向の主光線からの偏移量、σμ,σν,ρは正規分布のパラメータである。これらのパラメータは下記の性質を持っている。−1＜ρ＜1、σμ＞0、σν＞0、楕円
【数９】

の全ての点(μ,ν)において、
【数１０】

である。そしてその等確立楕円内の積分は、
【数１１】

図１４のように、等確率楕円は、外接長方形の形σμ／σνとρによって形が決められ、半径数ｃによって大きさが決められる。楕円の方程式を極座標に書き換えると、ｃ＝１のときの楕円は、
【数１２】

となる。それを整理すると、
【数１３】

となる。ここで、
【数１４】

である。このように、Ａ＞Ｂが確実に成立するので、γの最大値と最小値、つまり楕円の長短軸の長さは、
【数１５】

長短軸の角度はαとα＋π／2とである。これらは非点ボケ方向や程度を評価するための重要な量である。
【００４７】
このように、二次元正規分布関数は、広がりの程度(σμ,σν)と非点ボケの程度(等確率楕円長短軸比）、角度(長軸の角度)を表すことができる。もちろんPSFの光学系の状態による無限に近い変化を忠実に表すことはできないが、PSFを表現する簡略関数として有効であろう。
【００４８】
二次元正規分布関数のパラメータσμ,σν,ρを、光線データから求める方法を考えると、(μ,ν)平面に散布する多数の光線の交点(各交点が入射瞳上の各分割点に対応)の統計値を求めて、σμ,σν,ρにあてる方法を自然に浮かぶ。つまり、
【数１６】

である。ここで、Ｎは光線数で、(μi,νi)は交点座標である。σμ0,σν0,ρはあくまで分布の統計量であり、近似正規分布のパラメータとしては、多くの場合適当ではない。図１４はその例を示している。左側の山はその交点密度を示し、右側の山はσμ0,σν0,ρをパラメータとした正規分布を示している。
【００４９】
図１５のように、σμ0,σν0,ρを直接適用した正規分布を採用した場合、主軸方向および長短軸比は実際の分布に即しているが、広がりの程度が実際の分布とかなりかけ離れている。従って、適当な比例係数ｋを定め、σμ＝ｋσμ0、σν＝ｋσν0を適用すれば、実際の分布にかなり近い近似が得られると考えられる。問題は如何にｋを決めるかということになるが、これについては、等確率楕円内部の確率Ｐ(ｃ)と半係数ｃの関係曲線にヒントを得ることができよう。パラメータがσμ＝ｋσμ0，σν＝ｋσν0，ρに変更した場合の正規分布のＰ(ｃ)曲線はＰk(ｃ)＝１−ｅｘｐ(−ｃ2／2ｋ2)である。
それを実際分布のＰr(ｃ)曲線に近づけるようにｋを決めればよい。
【００５０】
図１６は、図１５の例のＰ(ｃ),Ｐk(ｃ),Ｐr(ｃ)の曲線をプロットしたものである。PSF分布の近似を求める場合、特に中心部分が重要である。従って、ｃが小さい時のＰr(ｃ)曲線になるべく近いＰk(ｃ)が望ましい。統計値σμ0，σν0，ρをそのまま適用した場合の曲線Ｐ(ｃ)は、実際の分布Ｐr(ｃ)とは離れており、近似分布関数としては不適である。一方ｋ＝0.65のσμ＝ｋσμ0,σν＝ｋσν0,ρを適用した正規分布の曲線Ｐk(ｃ)は中心付近にＰr(ｃ)曲線と一致する部分が多く、実際の分布に近い近似であることが伺える。図１７はσμ＝ｋσμ0,σν＝ｋσν0,ρを正規分布と実際の分布との比較である。
【００５１】
この実施例では、ｋの値を決めるに当たって、以下の方法を採っている。まず、Ｐr(ｃ)曲線とＰk(ｃ)曲線の交わる点Ａの確率Ｐ0の値を決める。中心付近重視ということで、ここではＰ0＝0.1とする。Ｐ(ｃ)曲線上Ｐ(ｃ)＝Ｐ0の点では、
【数１７】

である。Ｐr（ｃ）曲線Ａ点のｃ＝Ｃr であれば、ｋ＝Ｃr／Ｃ0となる。
【００５２】
他の方法も(例えばＰr(ｃ)とＰk(ｃ)との差を中心付近で最小にするなど)考えられるが、上記の方法がもっとも簡単である。このように、物体空間上任意一点(Ｄ0,ψ0,ζ0）のPSF分布関数を、パラメータσμ,σν,ρをもつ二次元正規分布関数で近似することができる。もちろんシミュレーションの過程に遭遇するすべての物体点に対してσμ,σν,ρを求める必要がなく、標本点でのσμ,σν,ρだけをあらかじめ求めておいて、それを用いて任意物体点においてのσμ,σν,ρをスプライン補間で求めることができる。それによって、計算時間を大幅に節約できる。
【００５３】
PSF分布関数をパラメータ化することによって、1コマ当たりの処理時間を1時間46分40秒から2〜10分程度に短縮することに成功した。処理時間に幅があるのは、ボケの程度によって処理時間が変わるからである。図１８に、以上説明したPSF取得の概略手順を纏めてPSF取得方法三として示した。
【００５４】
次に上述の実施例で示したシミュレーションを行なうための装置について簡単に説明する。図１９は実施例のシミュレーションを行なうための装置の概略構成を示すブロック図である。図１９に示したように、この装置は、プロセッサ６１、読取専用メモリ(ROM)６２、メインメモリ６３、グラフィック制御回路６４、表示装置６５、マウス６６、キーボード６７、ハードディスク装置(HDD)６８、フロッピー（登録商標）ディスク装置(FDD)６９、プリンタ７０、磁気テープ装置７１等から構成されている。これらの要素は、データバス７２によって結合されている。
【００５５】
プロセッサ６１は、装置全体を統括的に制御する。読取専用メモリ６２には立ち上げ時に必要なプログラムが格納される。メインメモリ６３にはシミュレーションを行なうためのシミュレーションプログラムが格納される。グラフィック制御回路６４はビデオメモリを含み、得られた画像データを表示信号に変換して表示装置６５に表示する。マウス６６は表示装置上の各種のアイコン、メニュー等を選択するポインティングデバイスである。ハードディスク装置６８はシステムプログラム、シミュレーションプログラム等が格納され、電源投入後にメインメモリ６３にローディングされる。また、シミュレーションデータを一時的に格納する。
【００５６】
フロッピー（登録商標）ディスク装置６９は原画像データ等の必要なデータをフロッピー（登録商標）６９ａを通じて入力したり、必要に応じてフロッピー（登録商標）６９ａにセービングする。プリンタ装置７０は回旋網膜像等をプリントアウトするのに用いられる。磁気テープ装置７１は必要に応じてシミュレーションデータを磁気テープにセービングするのに使用する。なお、以上のべた基本構成を有する装置としては、高性能のパーソナルコンピュータや一般の汎用コンピュータを用いて構成することができる。
【発明の効果】
【００５７】
以上詳述したように、本発明にかかる眼光学系のシミュレーション装置を駆動するためのプログラムを記録したコンピュータ読み取り可能な記録媒体は、
眼の前に配置されたレンズ系を通して外界を観察したときの見え方をシミュレーションする眼光学系のシミュレーション装置を駆動するためのプログラムを記録したコンピュータ読み取り可能な記録媒体であって、前記プログラムは、以下の手順を有する。
ａ．コンピュータに、仮想三次元空間内にコンピュータグラフィックスによる仮想物体を作成して配置し、この仮想物体が、特定の位置に回旋中心点を置き且つ特定の中心視線方向を持つ眼に入る特定視野角の画像を原画像として作成するとともに、前記原画像の各画素の代表する物体点位置と眼の回旋中心点との距離である物体点距離を求める原画像作成手順。
ｂ．前記眼の前に配置するレンズ系上に前記中心視線通過点を設定し、視野中心物体点から出射して前記中心視線通過点を通過し、前記回旋中心点に向かう光線を光線追跡法で求め、この求めたレンズ系の出射光線方向を中心視線とする視野をレンズ系通過後視野と定義したとき、このレンズ系通過後視野における前記原画像の各画素の対応する物体点への視線の方向及びレンズ系通過点を光線追跡法で求め、前記レンズ系による歪みを含めた画像を作成する歪み原画像作成手順。
ｃ．前記眼の光学系として調節対応眼球モデルを導入し、前記原画像の各画素に対し、前記原画像作成手段によって得られた物体点距離と、前記歪み原画像作成手段によって得られた物体点から出射する主光線のレンズ系通過点における度数に合わせて前記眼球モデルの調節状態を設定し、前記レンズ系とその主光線方向に合わせて回旋した眼球モデルとの合成光学系において、前記物体点から出射する光による前記調節対応眼球モデルの網膜上の輝度分布を表すＰＳＦ（ＰｏｉｎｔＳｐｒｅａｄ Ｆｕｎｃｔｉｏｎ：点広がり関数）を求めるＰＳＦ取得手順。
ｄ．前記歪み原画像作成手段によって作成されたレンズ系による歪みを含めた画像と前記ＰＳＦ取得手段によって得られた各画素のＰＳＦとの畳み込み演算（ｃｏｎｖｏｌｕｔｉｏｎ）を行ない、前記仮想三次元空間に配置した仮想物体を特定の位置及び視線方向の眼で前記レンズ系の特定位置を通して見た場合の回旋網膜像を作成する畳み込み手順。
この眼光学系のシミュレーション装置を駆動するためのプログラムを記録したコンピュータ読み取り可能な記録媒体を用いることにより、コンピュータによって、累進多焦点レンズ等のレンズ系を装用した場合における揺れ、歪み、ボケ等を伴う見え方をもシミュレーションを行うことができる。
【図面の簡単な説明】
【００６５】
【図１】回旋網膜像作成の流れを示す図である。
【図２】回旋網膜像の座標系を示す図である。
【図３】レンズ系を装用した場合の回旋網膜像の座標系を示す図である。
【図４】Navarro模型眼の光学パラメータ（非調節状態）を示す図である。
【図５】Navarro模型眼の水晶体レンズの調節力依存式を示す図である。
【図６】PSFの説明図である。
【図７】光線追跡と入射瞳との関係を示す図である。
【図８】入射瞳の分割法を示す図である。
【図９】網膜位置と入射角度を示す図である。
【図１０】PSF取得方法一を示す図である。
【図１１】回旋網膜像の静止画像の例を示す図である。
【図１２】回旋網膜像の動画像作成の流れを示す図である。
【図１３】PSF取得方法二を示す図である。
【図１４】等確立楕円を示す図である。
【図１５】光線密度分布及びσμ0、σν0、ρによる近似正規分布を示す図である。
【図１６】Ｐ(ｃ)、Ｐk(ｃ)、Ｐr(ｃ)の曲線を示す図である。
【図１７】光線密度分布及びｋσμ0、ｋσν0、ρによる近似正規分布を示す図である。
【図１８】PSF取得方法三を示す図である。
【図１９】本発明にかかる眼光学系のシミュレーション方法を実施するための装置の構成を示すブロック図である。[0001]
BACKGROUND OF THE INVENTION
  The present invention simulates the appearance when the outside world is observed through a lens system arranged in front of the eyes.Computer-readable recording medium storing a program for driving an eye optical system simulation apparatusAbout.
[0002]
[Prior art]
  As a disclosure of an eye optical system simulation method and apparatus for simulating the appearance when the external environment is observed through a lens system arranged in front of the eye, such as when wearing eyeglasses, There is an apparatus described in Japanese Patent Application Laid-Open No. 8-266473.
[0003]
The apparatus described in the above publication simulates a scene image in a range that can be overlooked by turning the human eye with a spectacle lens worn by performing PSF calculation or the like. As a result, it has become possible to simulate a wide-angle scene accompanied by the rotation of the human eye when wearing optical lenses such as eyeglasses.
[0004]
[Problems to be solved by the invention]
By the way, in particular, when a progressive multifocal lens is worn, there may be a case where an unpleasant sensation such as shaking, distortion, or blur is felt instead of performing a bifocal function. Therefore, in designing a progressive multifocal lens, it is required to suppress discomfort as much as possible while realizing a bifocal function. For this purpose, it is most desirable for the designer himself to know in advance what kind of vibration, distortion, blur, etc. the designed lens is accompanied by. The above-described conventional eye optical system simulation method is very useful for a certain purpose because it can simulate a wide-angle scene accompanied by rotation of the human eye when wearing an optical lens such as eyeglasses. However, the distortion, blur, etc. that the wearer would feel are not simulated in a manner that is close to reality, taking into consideration even human perception. Therefore, when the wearer wears the designed lens, it is not always sufficient for the purpose of the designer knowing in advance what kind of distortion, blur, etc. the wearer actually feels. It was not a thing. Moreover, it was impossible to deal with the shaking that seems to be the most problematic when actually worn.
[0005]
The image of the outside world that humans recognize (perceive) through the eyes is considered not to be an optical image itself formed on the retina of the eye according to the optical principle. That is, the distribution of photoreceptors (cones and rods) on the retina has a high density near the fovea and a low periphery. Therefore, if the optical image formed on the retina itself is perceived, even if the optical image is ideally formed, only the center is clear and the periphery is blurred. Should be perceived as. However, a healthy eye can be clearly seen anywhere in the field of view. This is because the action of perception is not a simple action of detecting the optical image projected on the retina as it is, but is based on the result of complicated processing by the neural information processing system after the retina. Because it is.
[0006]
According to the research of the present inventors, such a perceptual effect cannot be directly simulated, but based on a certain assumption found by the present inventors, the result of the perceptual effect is approximately reproduced by image processing. It was clarified that it was possible.
[0007]
The present invention has been made based on the above-described background, and enables simulation of appearance accompanied by shaking, distortion, blur, etc. when a lens system such as a progressive multifocal lens is worn.Computer-readable recording medium storing a program for driving an eye optical system simulation apparatusThe purpose is to provide.
[0008]
[Means for Solving the Problems]
According to a first aspect of the present invention, there is provided a program for driving an eye optical system simulation device for simulating appearance when an external environment is observed through a lens system disposed in front of an eye.Computer-readable recording medium recordingThe program has the following procedure.
a. A virtual object created by computer graphics is created and arranged in a virtual three-dimensional space, and this virtual object is an image of a specific viewing angle that enters the eye with a rotation center point at a specific position and a specific central line-of-sight direction. An original image creation procedure for creating an original image and obtaining an object point distance that is a distance between an object point position represented by each pixel of the original image and a rotation center point of the eye.
b. The central line-of-sight passing point is set on a lens system arranged in front of the eye, and a light ray that is emitted from the visual field center object point, passes through the central line-of-sight passing point, and goes to the rotation center point is obtained by a ray tracing method. When the field of view in which the direction of the emitted light of the lens system is the central line of sight is defined as the field of view after passing through the lens system, the direction of the line of sight toward the corresponding object point of each pixel of the original image in the field of view after passing through the lens system And a distortion original image creating procedure for obtaining a lens system passing point by a ray tracing method and creating an image including distortion caused by the lens system.
c. Introducing an accommodation-compatible eyeball model as the optical system of the eye, for each pixel of the original image, from the object point distance obtained by the original image creation means and the object point obtained by the distortion original image creation means In the combined optical system of the lens system and the eyeball model rotated in accordance with the principal ray direction, the adjustment state of the eyeball model is set according to the power at the lens system passing point of the emitted principal ray. A PSF acquisition procedure for obtaining a PSF (Point Spread Function) representing the luminance distribution on the retina of the accommodation-compatible eyeball model by the emitted light.
d. A virtual convolution operation is performed on the image including distortion generated by the distortion original image creation means and the PSF of each pixel obtained by the PSF acquisition means, and arranged in the virtual three-dimensional space. A convolution procedure for creating a rotated retinal image when an object is viewed through a specific position of the lens system with an eye in a specific position and line of sight.
[0009]
  The second invention is related to the first invention.Computer-readable recording medium storing a program for driving an eye optical system simulation apparatusIn the PSF acquisition procedure, all the data of rays that are emitted from the object point represented by each corresponding pixel and pass through each point set by dividing the entrance pupil of the eyeball model are obtained by the ray tracing method. As a light spot distribution density on the retina of the eyeball model or as a diffraction integration based on wave opticsFeatures.
[0010]
  The third invention relates to the first invention.Computer-readable recording medium storing a program for driving an eye optical system simulation apparatusIn the PSF acquisition procedure, a finite number of object sample points are set in the three-dimensional object space in advance, and a finite number of pass sample points are selected on the entrance pupil plane, and the object sample point and the pass point sample are selected. Ray ray data by all combinations with points is obtained by ray tracing method, spline interpolation coefficient data is created, emitted from the object point represented by each pixel of the original image, and passes through each point obtained by equally dividing the entrance pupil. It is a procedure for obtaining ray data by the spline interpolation method using the previously prepared spline interpolation coefficient data, and obtaining PSF as a spot distribution density of rays on the retina or as a diffraction integration method based on wave optics.Features.
[0011]
  The fourth invention relates to the first invention.Computer-readable recording medium storing a program for driving an eye optical system simulation apparatusIn the PSF acquisition procedure, the PSF is approximated by a certain function and expressed by its parameters, a finite number of object sample points are selected in advance in the three-dimensional object space, and PSFs and approximate function parameters of all the object sample points are obtained. The spline interpolation coefficient data is created, and the PSF parameter for each pixel of the original image is obtained by the spline interpolation method using the previously prepared spline interpolation coefficient data.Features.
DETAILED DESCRIPTION OF THE INVENTION
[0012]
(Example 1) FIG. 1 is a diagram showing the flow of creating a rotated retinal image in the simulation method of an eye optical system according to Example 1 of the present invention, FIG. 2 is a diagram showing a coordinate system of the rotated retinal image, and FIG. FIG. 4 is a diagram showing the optical parameters (non-adjusted state) of the Navarro model eye, and FIG. 5 is an equation showing the dependence of the lens lens on the adjustment force of the Navarro model eye. FIG. 6 is an explanatory diagram of PSF, FIG. 7 is a diagram showing a relationship between ray tracing and an entrance pupil, FIG. 8 is a diagram showing a method of dividing an entrance pupil, and FIG. 9 is a diagram showing a retinal position and an entrance angle. . Hereinafter, a simulation method for an eye optical system according to Example 1 of the present invention will be described with reference to these drawings.
[0013]
  The eye optical system simulation method according to this embodiment is a method for obtaining a still image of a rotating retinal image when a three-dimensional object image created by computer graphics is viewed through a lens. Note that the convoluted retinal image is an approximated image perceived by the eye by performing image processing in consideration of optical action on the three-dimensional object image based on certain assumptions found by the present inventors. It is a reproduced image. In other words, the convoluted retinal image is not an optical image projected on the retina surface of the eye, but is defined as an image obtained by connecting the images captured by the fovea by rotating the eyeball with respect to all object points in the field of view. The
[0014]
  The eye optical system simulation method according to the first embodiment is roughly divided into (1) original image creation step, (2) distortion original image creation step, (3) PSF acquisition step, and (4) convolution step. .
[0015]
  (1) Original image creation process This process creates and places a virtual object by computer graphics in a virtual three-dimensional space, and this virtual object places a rotation center point at a specific position and a specific center line-of-sight direction. In this step, an image having a specific viewing angle that enters the eye having an eye is created as an original image, and an object point distance that is a distance between the object point position represented by each pixel of the original image and the rotation center point of the eye is obtained. This will be described below.
[0016]
  Creation of virtual object image that is the basis of the original image First, a virtual three-dimensional object is created and arranged in a virtual three-dimensional space by a known computer graphics technique. For example, an image is created in which desks, chairs, furniture, etc. are arranged in the room, or flower beds, trees, signs, etc. are arranged in the outdoors.
[0017]
  Creation of the original image The created virtual object creates an image of a specific viewing angle that enters the eye with the rotation center point at a specific position and a specific center line-of-sight direction as the original image. That is, as shown in FIG. 2, a visual field pyramid A1A2A3A4 is set as the specific visual field. The center A of the visual field pyramid A1A2A3A4 is the center of the visual field. A line connecting A and the rotation center O is a central line of sight, which is the x axis, and O is the origin. Then, the rotational retinal coordinates of an arbitrary point P (x, y, z), which is an arbitrary object point in the visual field pyramid, are set as Ψ = tan β = y / x and ζ = tan γ = z / x. Here, β and γ are azimuth angles of P (x, y, z). If each object point in the field of view is represented in this coordinate system, an arbitrary straight line in the space appears as a straight line on the rotated retinal image. An image representing each object point in this coordinate system is defined as an original image. Further, each object point distance is obtained from the coordinate value of P (x, y, z).
[0018]
  (2) Distortion original image creation step This step sets the central line-of-sight passing point on the lens system arranged in front of the eye, exits from the visual field center object point, passes through the central line-of-sight passing point, the center of rotation The ray tracing to the point is obtained by the ray tracing method, and when the field of view having the centered line of sight as the obtained ray direction of the lens system is defined as the field of view after passing through the lens system, each pixel of the original image in the field of view after passing through the lens system is defined. In this step, the direction of the line of sight to the corresponding object point and the lens system passing point are obtained by the ray tracing method, and an image including distortion due to the lens system is created.
[0019]
  That is, as shown in FIG. 3, the lens L is arranged at a position close to O between the origins O and A in FIG. The light beam emitted from the object point in the viewing quadrangular pyramid is refracted by the lens L and reaches the point O. Therefore, in order to gaze at point A, the eyeball must be directed in the OB direction. A visual field pyramid representing a visual field is also B1B2B3B4 (a visual field after passing through the lens system). The rotated retinal image at that time must take a coordinate system with the x ′ axis as the line of sight (center line of sight). This is obtained by ray tracing in consideration of the frequency of each point on the lens, and an image based on the object point coordinates thus obtained is used as a distortion original image.
[0020]
  As described above, when the lens is passed, the relative positional relationship is changed unlike the case where the coordinates on the rotated retinal image of each point in the field of view are naked eyes. This is a cause of distortion of the spectacle lens. The OB direction varies depending on the lens use position. Especially in the case of progressive lenses, the change is severe. Other light rays in the field of view also change the angle at which they enter the eye, especially in the case of a progressive lens, and the change is uneven, so it is perceived as shaking or distortion.
[0021]
  (3) PSF acquisition process This process introduces an accommodation-compatible eyeball model as the optical system of the eye, and for each pixel of the original image, the object point distance obtained in the original image creation process and the distortion original image creation process In the combined optical system of the lens system and the eyeball model rotated according to the principal ray direction, the adjustment state of the eyeball model is set according to the power at the lens system passing point of the principal ray emitted from the obtained object point. This is a step of obtaining a PSF (Point Spread Function) representing a luminance distribution on the retina of an eyeball model that can be adjusted by light rays emitted from an object point.
[0022]
  (1) Introduction of an adjustment-compatible eyeball model Since an image obtained by forming an original distortion image on the retina through the optical system of the eye is a rotated retinal image, it is necessary to introduce a model of the optical system of the eye. In this case, since the eye has an adjusting action according to the object distance, it must be taken into consideration. In this example, an adjustment-dependent eyeball model by R. Navarro et al., Which is an eyeball model that also takes account of accommodation action, was used. In Navarro's model, not only paraxial values, but also spherical aberration and chromatic aberration are adjusted to the actual measured values of the eye. With a simple four-surface configuration, three of them are quadratic aspherical surfaces. The crystalline lens does not have a refractive index distribution structure, and the tracking calculation is simple. The radius of curvature, thickness, and asphericity change in proportion to the logarithm of the adjustment power. FIG. 4 shows optical parameters when Navarro's accommodation-dependent eye model is unadjusted. In addition, FIG. 5 shows a parameter dependency equation depending on adjustment. An aspherical surface is represented by y2 + z2 + (1 + Q) x2-2Rx = 0. Q is the asphericity.
[0023]
  (2) PSF calculation
a. Meaning of PSF In general, an optical image by an optical system is obtained by obtaining a PSF of the optical system and performing a convolution operation with the actual image. As shown in FIG. 6, this PSF is a function that represents a collective state of points (spots) where a light beam emitted from one point of a real object is focused on the imaging plane, and is expressed as the number of spots per unit area. Can be represented. In the case of a perfect optical system, the PSF gathers all spots at the image point, and its distribution is a vertical straight line, but usually has a shape similar to a broadened Gaussian distribution. Since an object is considered to be composed of points, an image can be obtained by convolution of the luminance distribution of the object and PSF.
[0024]
b. PSF calculation method
FIG. 7 is a diagram showing the relationship between the tracking ray and the entrance pupil in the optical system for obtaining the PSF when the object point P is viewed through the Q point on the lens. The light beam from the object point P is refracted at the lens surface Q point, the emission direction changes, and reaches the rotation point O. It appears to the eye that the object point P is on the extended line of the exit light direction QO. Thus, when viewing P, first, the optical axis of the eyeball is rotated in the QO direction, and the degree of adjustment is determined according to the distance of P and the refractive power of the Q point. At this point, the optical system is solidified and PSF can be obtained.
[0025]
  As described above, PSF is the density of spots on the imaging plane of light rays emitted from an object point and passing through the centers of a number of regions obtained by equally dividing the entrance pupil. Strictly speaking, the position of the entrance pupil is the object side conjugate point of the pupil. However, the pupil position changes with rotation, and the position of the conjugate point varies depending on the adjustment state. On the other hand, the position of the center of rotation is fixed, and the distance from the conjugate point of the pupil is very small compared to the object distance. Therefore, in the case of the naked eye, the position of the entrance pupil can be considered as the center of rotation. When wearing spectacles, the entrance pupil of the entire optical system is a conjugate point to the spectacle lens at the center of rotation, but in the case of a progressive lens, the power varies depending on the passing point, and its position changes slightly. Since the amount of change is also small compared to the object distance, the position of the entrance pupil is at the point O ′ on the extension line of PQ, and it can be assumed that PO = PO ′.
[0026]
  In order to obtain an accurate PSF, it is important to divide the entrance pupil into a large number of small regions having a uniform distribution. As shown in FIG. 8, there are two types of division methods, lattice division and annular division. The grid division provides good uniformity, but because there are wasted corners, only about 70% of the planned rays can be traced. On the other hand, in zone division, a book beam can be traced by individual zones, and the uniformity of spots can be improved by adjusting the phase angle of the zones. In this embodiment, the annular zone division method is adopted.
[0027]
  In this way, PSF is obtained by tracking a large number of light rays that are emitted from an object point and pass through a uniform division point of the entrance pupil, and count the spots on the retina surface. However, this PSF is a function of the retinal position (ym, zm), and cannot be directly subjected to a convolution calculation with a convoluted retinal image having the tangent (Ψ, ζ) of the convolution angle as coordinates. Therefore, it is necessary to determine the angle of the incident light beam corresponding to the retina position. In most cases (ym, zm) is close to the optical axis, so the paraxial optics formula can be applied. That is, as shown in FIG. 9, the deflection angles (βm, γm) of the incident light beam corresponding to (ym, zm) from the optical axis are tan βm = ym / f, tan γm = zm / f. Here, f is the focal length of the eyeball. Strictly speaking, the relational expression between the incident angle and the retinal position changes depending on the object distance and the eye adjustment state. However, in the case of the eye, the object distance is very long compared to the focal distance, and can be regarded as an infinite distance.
[0028]
  Considering the case where the arbitrary object point P in FIG. 7 is viewed, the angle from the gaze line corresponding to the retinal position (ym, zm) is further deviated from the direction angle (β, γ) of P by (βm, γm). It is a thing. It should be noted here that the angle is not generally (β + βm, γ + γm), and it is necessary to obtain it using the law of listing rotation. In this way, PSF (ym, zm) on the retina obtained by ray tracing can be converted to PSF (Ψ, ζ) on the incident ray angle coordinate, and convolution with the luminance distribution of the object becomes possible. It was. FIG. 10 summarizes the outline of the PSF acquisition procedure described above and shows it as a PSF acquisition method.
[0029]
  (4) Convolution process This process performs a convolution operation between the original distortion image including distortion caused by the lens system created in the original distortion image creation process and the PSF of each pixel obtained in the PSF acquisition process, thereby creating a virtual three-dimensional space. This is a step of creating a convoluted retinal image when the virtual object placed in is viewed through a specific position of the lens system with eyes in a specific position and line-of-sight direction. The convolution operation is performed as follows, for example. If the light intensity distribution of the ideal image on the image plane is f (μ, ν) and the PSF at the point (μ, ν) is p (x, μ, u, v), the point at the point (μ, ν) on the retina The light intensity is represented by the following formula.
[0030]
[Expression 1]

[0031]
  Here, p (u, v, u−μ, v−ν) is the value of PSF at a point separated from each point (u, v) by (u−μ, v−ν). Moreover, a is the spreading radius of PSF. By using this equation and obtaining the light intensity at all points on the retina, a still image of a convoluted retinal image can be obtained. FIG. 11 is a diagram illustrating an example of a still image of a rotated retinal image obtained by the method of the first embodiment. This example shows a rotating retinal image of a printed matter on a table viewed at a distance of 333 mm through the near-field part of a progressive lens for eyeglasses (HOYALUX GP; trade name of Hoya Co., Ltd.) with 0.00D for 2.00D for the right eye. It is. The field of view is 50 ° left and right and 38.5 ° up and down. The circle in the upper right corner is a display for indicating the lens passing point position of the central line of sight. This passing point position is not identified in the figure, but is indicated by a red dot in a circle. This circle represents the outline of the lens, and the point attached to the center of the circle indicates the geometric center of the lens, and the circles above and below the geometric center indicate the distance measurement point (top) and the near measurement point (bottom). Show. The mark with the R letter on the back indicates the right lens. The example of FIG. 11 is an example in the case where the lens passing point of the central line of sight is on the near measurement point (lower circle). It can be seen that the blur and distortion on the left and right are reproduced as is.
[0032]
  According to this embodiment, an image that approximately reproduces blur and distortion perceived when viewed through a lens system such as a progressive multifocal lens can be obtained. In other words, the entire visual field is clearly perceived if the naked eye is healthy, but when a presbyopic eye wears a progressive multifocal lens, only a part of the visual field appears clear, and the other part is blurred or distorted. Looks. According to this embodiment, an image that such a presbyopic person would perceive can be reproduced as an image. Therefore, if the obtained image is displayed on the display device, the most desirable evaluation is that the appearance of the progressive multifocal lens designed by the designer himself who is not presbyopia can be confirmed from the viewpoint of the wearer. It becomes possible.
[0033]
  By the way, in this embodiment, the process that takes the most time for the calculation process or the like is the PSF acquisition process. In particular, when the lens system is a progressive multifocal lens, the PSFs in all line-of-sight directions are different, so it is necessary to obtain PSFs for all pixels. For example, in an image of 800 × 600, if the number of rays to be traced when obtaining PSF is set to 400 (never more), the ray tracing calculation is performed 192,000,000 times in total. Depending on the complexity and number of faces of the optical system, assuming that the computing power of the computer is 3,000 per second, it is 64,000 seconds, or 17 hours 46 minutes and 40 seconds. This is the calculation time when the necessary time for the convolution operation is not yet taken into consideration.
[0034]
  In view of this, the ray tracing is not performed for all the object points, but the ray tracing is performed only for the sample points, and the other points are obtained by spline interpolation. The arbitrary point A in space may be expressed by Cartesian coordinates (x, y, z), but in the case of glasses, since the distance from the eye is important, the reciprocal D1 of the distance from the turning point and the tangent ψ, It is more appropriate to express by ζ. That means
[0035]
[Expression 2]

It is. Ray data obtained by tracking an arbitrary ray emitted from the point A, that is, a ray passing through an arbitrary point (yp, zp) on the provisional entrance pupil plane (tkm, cfm of incident ray corresponding to the intersection on the retina, optical path length, etc. ) Is a function of D1, ψ, ζ, yp, zp. That is, tkm = Ft (D1, ψ, ζ, yp, zp), ckm = Fc (D1, ψ, ζ, yp, zp), pkm = Fp (D1, ψ, ζ, yp, zp) Can do. When considering chromatic aberration, it is better to add a wavelength dimension. Sample points are provided at an appropriate number and position within a predetermined range of each variable D1, ψ, ζ, yp, zp, and ray tracing is performed in advance for all the sample points on the five-dimensional grid. , The ray data for an arbitrary point within a predetermined range (5-dimensional box) can be obtained by spline interpolation.
[0036]
  Next, we will consider speeding up spline interpolation. One-dimensional spline interpolation is
[Equation 3]

It is represented by Here, i is the node number of each dimension, Ci is its coefficient, and n is the number of sample points. NI (x) is a basis function corresponding to the i-th node. In the case of rank M, NI (x) has a non-zero value in the range between the i-th node and the i + M-th node, and the adjacent node is expressed by an m-1 order polynomial. Expressed (locality of basis functions). In other words, there are at most M non-zero NI (x) at any point a in the domain of x. Therefore, although the interpolation equation seems to have n terms at first glance, when x = a, it is substantially M terms, and F (a) is obtained by M multiplications and M additions. Five-dimensional spline interpolation is
[0037]
[Expression 4]

It is represented by Here, i, j, k, l, and m are node numbers in each dimension, and change by the number of sample points. In other words, the number of terms is the product of the number of sample points in each dimension. However, due to the locality of the basis functions described above, for a certain point, the number of non-zero terms is the product of the rank of each dimension. If the spline rank in each dimension is 4, the number of terms is 45 = 1024. In other words, in one interpolation calculation, the addition is performed 1024 times, and multiplication is performed 1024 × 5 = 5120 times. In general, the number of multiplications required for the nj-dimensional M-order spline interpolation calculation is nj × Mnj, and the calculation load increases rapidly as the number of dimensions increases. However, the above equation
[0038]
[Equation 5]

If you rewrite it, you can reduce it slightly. This is a one-dimensional interpolation nested structure, and the order of dimensions can be freely changed. Multiplication and addition are both 4 + 4 x (4 + 4 x (4 + 4 x 4)) = 1364 times, which requires almost 1/3 of the calculation time. In general, the number of multiplications required for nj-dimensional M-order spline interpolation is
[0039]
[Formula 6]

It is. Even if such a measure is adopted, the calculation amount is still large and not practical. In general, it will be difficult to further reduce the computation time of multidimensional spline interpolation than the above method. However, there is a way to shorten PSF because of its special circumstances. In order to obtain the PSF of one point (D0, ψ0, ζ0) on the object, light ray data connected to a large number (for example, 400) on the entrance pupil plane (yp, zp plane) is necessary. The 3D variable of 400 times 5D spline interpolation will have the same value. If the 400 interpolations are performed by two-dimensional spline interpolation, the calculation time can be greatly reduced. The five-dimensional spline interpolation formula can be rewritten as follows.
[0040]
[Expression 7]

[0041]
  This expression represents a method for obtaining a two-dimensional space in a five-dimensional spline space when a three-dimensional variable is determined. Here, this two-dimensional spline is called a degenerate space of the point (D0, ψ0, ζ0), and cl, m is a coefficient of the degenerate spline. Of course, the nodes and basis functions of the degenerate spline are all the same as the five-dimensional spline. The number of cl, m is the product of the number of sample points, and is 81 when nine sample points are set for both yp and zp dimensions. To obtain each coefficient, three-dimensional spline interpolation is used as in the equation. Then, using the obtained cl, m, two-dimensional spline interpolation calculation can be performed on light data at an arbitrary point on the yp-zp plane. Therefore, the PSF at the point c can be obtained only by performing 81 three-dimensional interpolations and 400 two-dimensional interpolation calculations. The number of multiplications is 81 x {4 / (4-1)} (43-1) + 400 x {4 / (4-1)} (42-1) = 14804 times, approximately 37 times per beam is there. Compared with 400 five-dimensional interpolation, the effect of reducing the amount of calculation is remarkable. Using the above method, ray data can be obtained in 1/10 of the ray tracing time. FIG. 13 collectively shows the PSF acquisition method 2 described above as a general PSF acquisition procedure.
[0042]
  Next, we will consider the parameterization of PSF. As described above, the calculation speed of 10 times was realized by calculating the ray data by the spline interpolation method instead of ray tracing. Even so, in terms of processing time per frame, 64000 seconds (17 hours 46 minutes 40 seconds) was only shortened to 6400 seconds (1 hour 46 minutes 40 seconds). In practice, we want to reduce the processing time per frame to a few minutes. In the current method, the calculation for obtaining the PSF takes the most time, so it is most effective to shorten it.
[0043]
  In order to obtain the PSF of a certain object point (D0, ψ0, ζ0), it is necessary to track or interpolate a large number of rays and obtain the ray density. Moreover, the obtained PSF is a discrete function in units of pixels, and the density is in the form of the number of rays per pixel. When rays are concentrated (in focus), a small number of pixels contain a large number of rays and are close to a continuous function, but when scattered widely (not in focus), the number of rays entering a unit pixel There are few and the error is large. Increasing amounts of light are needed to cover it. Therefore, if the PSF is assumed to be a continuous function in advance and its parameters are applied using ray tracing data, it is possible to escape from the above dilemma. Then, it is not necessary to obtain parameters for all object points, and sample points can be determined and obtained by spline interpolation (three-dimensional).
[0044]
  Now, considering what kind of function the distribution function should be, most PSFs have a mountain shape, so it seems that a two-dimensional normal distribution is appropriate. That means
[0045]
[Equation 8]

[0046]
  Here, μ and ν are deviation amounts from principal rays in the tk and cf directions, respectively, and σμ, σν, and ρ are parameters of a normal distribution. These parameters have the following properties: −1 <ρ <1, σμ> 0, σν> 0, ellipse
[Equation 9]

At all points (μ, ν)
[Expression 10]

It is. And the integral within that established ellipse is
## EQU11 ##

As shown in FIG. 14, the equal probability ellipse is determined by the circumscribed rectangles σμ / σν and ρ, and the size is determined by the radius number c. Rewriting the ellipse equation to polar coordinates, the ellipse when c = 1 is
[Expression 12]

It becomes. Organizing it,
[Formula 13]

It becomes. here,
[Expression 14]

It is. Thus, since A> B is certainly established, the maximum and minimum values of γ, that is, the length of the major and minor axes of the ellipse are
[Expression 15]

The major and minor axis angles are α and α + π / 2. These are important quantities for evaluating the direction and degree of astigmatic blur.
[0047]
  As described above, the two-dimensional normal distribution function can express the extent of spread (σμ, σν), the degree of astigmatism blur (equal probability elliptic long / short axis ratio), and the angle (major axis angle). Of course, near-infinite change due to the state of the PSF optical system cannot be faithfully expressed, but it will be effective as a simplified function to express PSF.
[0048]
  Considering the method of obtaining the parameters σμ, σν, ρ of the two-dimensional normal distribution function from the ray data, the intersection of many rays scattered on the (μ, ν) plane (each intersection corresponds to each division point on the entrance pupil) ) Statistical values, and the method of assigning to σμ, σν, ρ naturally appears. That means
[Expression 16]

It is. Here, N is the number of rays, and (μi, νi) is the intersection coordinates. σμ0, σν0, and ρ are distribution statistics, and are not appropriate as parameters of the approximate normal distribution in many cases. FIG. 14 shows an example. The mountain on the left shows the intersection density, and the mountain on the right shows a normal distribution with σμ0, σν0, ρ as parameters.
[0049]
  As shown in FIG. 15, when a normal distribution to which σμ0, σν0, and ρ is directly applied is adopted, the principal axis direction and the major / minor axis ratio are in accordance with the actual distribution, but the extent of the spread is considerably different from the actual distribution. Yes. Therefore, if an appropriate proportionality coefficient k is determined and σμ = kσμ0 and σν = kσν0 are applied, it is considered that an approximation very close to the actual distribution can be obtained. The problem is how to determine k, and for this, a hint can be obtained on the relationship curve between the probability P (c) and the half coefficient c inside the equiprobability ellipse. The P (c) curve of the normal distribution when the parameters are changed to σμ = kσμ0, σν = kσν0, and ρ is Pk (c) = 1−exp (−c2 / 2k2).
What is necessary is just to determine k so that it may approach the Pr (c) curve of the actual distribution.
[0050]
  FIG. 16 is a plot of P (c), Pk (c), and Pr (c) curves of the example of FIG. The center part is particularly important when obtaining an approximation of the PSF distribution. Therefore, Pk (c) as close as possible to the Pr (c) curve when c is small is desirable. The curve P (c) when the statistical values σμ0, σν0, and ρ are applied as they are is far from the actual distribution Pr (c) and is not suitable as an approximate distribution function. On the other hand, the normal distribution curve Pk (c) applying σμ = kσμ0, σν = kσν0, ρ with k = 0.65 has many portions that coincide with the Pr (c) curve near the center and is an approximation close to the actual distribution. I can ask. FIG. 17 is a comparison of σμ = kσμ0, σν = kσν0, ρ with a normal distribution and an actual distribution.
[0051]
  In this embodiment, the following method is used to determine the value of k. First, the value of the probability P0 of the point A where the Pr (c) curve and the Pk (c) curve intersect is determined. In this case, P0 = 0.1 because of emphasis on the vicinity of the center. At the point P (c) = P0 on the P (c) curve,
[Expression 17]

It is. If c = Cr of the Pr (c) curve A point, k = Cr / C0.
[0052]
  Other methods are conceivable (for example, the difference between Pr (c) and Pk (c) is minimized near the center), but the above method is the simplest. Thus, the PSF distribution function at an arbitrary point (D0, ψ0, ζ0) in the object space can be approximated by a two-dimensional normal distribution function having parameters σμ, σν, ρ. Of course, it is not necessary to obtain σμ, σν, ρ for all object points encountered in the simulation process, and only σμ, σν, ρ at the sample points are obtained in advance and used for any object point. Σμ, σν, and ρ can be obtained by spline interpolation. Thereby, the calculation time can be greatly saved.
[0053]
  By parameterizing the PSF distribution function, we succeeded in reducing the processing time per frame from 1 hour 46 minutes 40 seconds to 2-10 minutes. The reason why the processing time varies is that the processing time varies depending on the degree of blur. FIG. 18 shows the PSF acquisition method 3 as a summary of the above-described outline of the PSF acquisition.
[0054]
  Next, an apparatus for performing the simulation shown in the above embodiment will be briefly described. FIG. 19 is a block diagram showing a schematic configuration of an apparatus for performing the simulation of the embodiment. As shown in FIG. 19, this apparatus includes a processor 61, a read-only memory (ROM) 62, a main memory 63, a graphic control circuit 64, a display device 65, a mouse 66, a keyboard 67, a hard disk device (HDD) 68, a floppy disk. (Registered trademark) disk device (FDD) 69, printer 70, magnetic tape device 71, and the like. These elements are coupled by a data bus 72.
[0055]
  The processor 61 comprehensively controls the entire apparatus. The read-only memory 62 stores a program necessary for startup. The main memory 63 stores a simulation program for performing a simulation. The graphic control circuit 64 includes a video memory, converts the obtained image data into a display signal, and displays it on the display device 65. The mouse 66 is a pointing device that selects various icons, menus, and the like on the display device. The hard disk device 68 stores a system program, a simulation program, and the like, and is loaded into the main memory 63 after the power is turned on. In addition, simulation data is temporarily stored.
[0056]
  The floppy (registered trademark) disk device 69 inputs necessary data such as original image data through the floppy (registered trademark) 69 a or saves it to the floppy (registered trademark) 69 a as necessary. The printer device 70 is used to print out a rotated retinal image or the like. The magnetic tape device 71 is used to save simulation data to a magnetic tape as necessary. The apparatus having the above basic configuration can be configured using a high-performance personal computer or a general-purpose computer.
【The invention's effect】
[0057]
As described in detail above, the present invention is applied.Computer-readable recording medium storing a program for driving an eye optical system simulation apparatusIs
    Simulate the appearance of the outside world through a lens system placed in front of the eyesComputer-readable recording medium storing a program for driving an eye optical system simulation apparatusThe program has the following procedure.
a. Create and place a virtual object by computer graphics in a virtual three-dimensional space on the computer, and this virtual object places the center of rotation at a specific position and enters a eye with a specific central line-of-sight direction The original image creation procedure for creating the original image and obtaining the object point distance which is the distance between the object point position represented by each pixel of the original image and the center of rotation of the eye.
b. The central line-of-sight passing point is set on a lens system arranged in front of the eye, and a light ray that is emitted from the visual field center object point, passes through the central line-of-sight passing point, and goes to the rotation center point is obtained by a ray tracing method. When the field of view in which the direction of the emitted light of the lens system is the central line of sight is defined as the field of view after passing through the lens system, the direction of the line of sight toward the corresponding object point of each pixel of the original image in the field of view after passing through the lens system And a distortion original image creating procedure for obtaining a lens system passing point by a ray tracing method and creating an image including distortion caused by the lens system.
c. Introducing an accommodation-compatible eyeball model as the optical system of the eye, for each pixel of the original image, from the object point distance obtained by the original image creation means and the object point obtained by the distortion original image creation means In the combined optical system of the lens system and the eyeball model rotated in accordance with the principal ray direction, the adjustment state of the eyeball model is set according to the power at the lens system passing point of the emitted principal ray. A PSF acquisition procedure for obtaining a PSF (Point Spread Function) representing the luminance distribution on the retina of the accommodation-compatible eyeball model by the emitted light.
d. A virtual convolution operation is performed on the image including distortion generated by the distortion original image creation means and the PSF of each pixel obtained by the PSF acquisition means, and arranged in the virtual three-dimensional space. A convolution procedure for creating a rotated retinal image when an object is viewed through a specific position of the lens system with an eye in a specific position and line of sight.
Computer-readable recording medium storing a program for driving the eye optical system simulation apparatusBy using the computer, it is possible to simulate the appearance accompanied by shaking, distortion, blur, etc. when a lens system such as a progressive multifocal lens is worn by a computer.
[Brief description of the drawings]
[0065]
FIG. 1 is a diagram showing a flow of creating a rotated retinal image.
FIG. 2 is a diagram showing a coordinate system of a rotated retinal image.
FIG. 3 is a diagram illustrating a coordinate system of a rotated retinal image when a lens system is worn.
FIG. 4 is a diagram showing optical parameters (non-adjusted state) of a Navarro model eye.
FIG. 5 is a diagram showing an accommodation dependency formula of a lens lens of a Navarro model eye.
FIG. 6 is an explanatory diagram of PSF.
FIG. 7 is a diagram illustrating a relationship between ray tracing and an entrance pupil.
FIG. 8 is a diagram illustrating a method of dividing an entrance pupil.
FIG. 9 is a diagram showing a retina position and an incident angle.
FIG. 10 is a diagram illustrating a PSF acquisition method.
FIG. 11 is a diagram illustrating an example of a still image of a rotated retinal image.
FIG. 12 is a diagram illustrating a flow of creating a moving image of a rotated retinal image.
FIG. 13 is a diagram showing a PSF acquisition method 2;
FIG. 14 is a diagram showing an equally established ellipse.
FIG. 15 is a diagram showing a light density distribution and an approximate normal distribution by σμ0, σν0, and ρ.
FIG. 16 is a diagram showing curves of P (c), Pk (c), and Pr (c).
FIG. 17 is a diagram showing a ray density distribution and an approximate normal distribution based on kσμ0, kσν0, and ρ.
FIG. 18 is a diagram showing PSF acquisition method 3;
FIG. 19 is a block diagram showing the configuration of an apparatus for carrying out the eye optical system simulation method according to the present invention.

Claims (4)

A computer-readable recording medium that records a program for driving a simulation device of an eye optical system that simulates appearance when observing the outside through a lens system disposed in front of the eye, A computer-readable recording medium storing a program for driving a simulation apparatus for an eye optical system, characterized by having the following procedure.
a. A virtual object created by computer graphics is created and arranged in a virtual three-dimensional space, and this virtual object is an image of a specific viewing angle that enters the eye with a rotation center point at a specific position and a specific central line-of-sight direction. An original image creation procedure for creating an original image and obtaining an object point distance that is a distance between an object point position represented by each pixel of the original image and a rotation center point of the eye.
b. The central line-of-sight passing point is set on a lens system arranged in front of the eye, and a light ray that is emitted from the visual field center object point, passes through the central line-of-sight passing point, and goes to the rotation center point is obtained by a ray tracing method. When the field of view in which the direction of the emitted light of the lens system is the central line of sight is defined as the field of view after passing through the lens system, the direction of the line of sight toward the corresponding object point of each pixel of the original image in the field of view after passing through the lens system And a distortion original image creating procedure for obtaining a lens system passing point by a ray tracing method and creating an image including distortion caused by the lens system.
c. Introducing an accommodation-compatible eyeball model as the optical system of the eye, for each pixel of the original image, from the object point distance obtained by the original image creation means and the object point obtained by the distortion original image creation means In the combined optical system of the lens system and the eyeball model rotated in accordance with the principal ray direction, the adjustment state of the eyeball model is set according to the power at the lens system passing point of the emitted principal ray. A PSF acquisition procedure for obtaining a PSF (Point Spread Function) representing the luminance distribution on the retina of the accommodation-compatible eyeball model by the emitted light.
d. A virtual convolution operation is performed on the image including distortion generated by the distortion original image creation means and the PSF of each pixel obtained by the PSF acquisition means, and arranged in the virtual three-dimensional space. A convolution procedure for creating a rotated retinal image when an object is viewed through a specific position of the lens system with an eye in a specific position and line of sight. In the computer-readable recording medium which recorded the program for driving the simulation apparatus of the eye optical system of Claim 1,
The PSF acquisition procedure is to obtain all the data of light rays emitted from an object point represented by each corresponding pixel and passing through each point set by equally dividing the entrance pupil of the eyeball model, and the PSF is calculated by the ray tracing method. A computer-readable recording medium storing a program for driving an eye optical system simulation apparatus, characterized in that the procedure is to obtain a light spot distribution density on the retina of an eyeball model or as a diffraction integration based on wave optics . In the computer-readable recording medium which recorded the program for driving the simulation apparatus of the eye optical system of Claim 1,
The PSF acquisition procedure sets a finite number of object sample points in the three-dimensional object space in advance, selects a finite number of pass sample points on the entrance pupil plane, and sets the object sample point and the pass point sample points. Ray data obtained by all combinations is obtained by the ray tracing method, spline interpolation coefficient data is created, emitted from the object point represented by each pixel of the original image, and ray data passing through each point obtained by equally dividing the entrance pupil. calculated by the spline interpolation method using a spline interpolation coefficient data to which the previously prepared, the PSF as a spot distribution density of epiretinal rays, or ocular optical system, which is a procedure for obtaining a diffraction integral method based on wave optics A computer-readable recording medium on which a program for driving a simulation apparatus is recorded . In the computer-readable recording medium which recorded the program for driving the simulation apparatus of the eye optical system of Claim 1,
In the PSF acquisition procedure, the PSF is approximated by a certain function and expressed by its parameters, a finite number of object sample points are selected in advance in the three-dimensional object space, the PSFs at all the object sample points and their approximate function parameters are obtained, and the spline is obtained. Driving a simulation apparatus for an eye optical system , wherein interpolation coefficient data is created, and a PSF parameter for each pixel of the original image is obtained by a spline interpolation method using the spline interpolation coefficient data prepared in advance. A computer-readable recording medium on which a program for recording is recorded .

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