JP4201218B2 - Computer generated hologram - Google Patents

Description

となる。
【００１６】
ここで、今後の議論を分かりやすくするため、ホログラム面でのＡ_HOLO（ｘ，ｙ）を"HoloAmp" 、ホログラム面でのφ_HOLO（ｘ，ｙ）を"HoloPha" 、再生像面でのＡ_IMG （ｕ，ｖ）を"ImgAmp" 、再生像面でのφ_IMG （ｕ，ｖ）を"ImgPha"で表現する。
【００１７】
本発明においては、まず、このＧｅｒｃｈｂｅｒｇ−Ｓａｘｔｏｎ反復計算法を利用して、背後からホログラム面に垂直に平行光で照明した場合に所定の観察域へのみ光を回折する計算機ホログラムを得ることを考える。図１は、このためのフローチャートであり、ステップ▲１▼で、ホログラム面領域ｘ₀ ≦ｘ≦ｘ₁ ，ｙ₀ ≦ｙ≦ｙ₁ で、ホログラムの振幅HoloAmp を１に、ホログラムの位相HoloPha をランダムな値に初期化して、ステップ▲２▼で、その初期化した値に上記式（３）のフーリエ変換を施す。ステップ▲３▼で、フーリエ変換で得られた再生像面での振幅ImgAmpが所定の領域、例えばｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ 内で略一定値になり、その所定領域外で略０になったと判断された場合は、ステップ▲１▼で初期化した振幅と位相が所望の計算機ホログラムとなる。ステップ▲３▼でこのような条件が満足されないと判断された場合は、ステップ▲４▼で束縛条件が付与される。具体的には、上記の所定領域内では再生像面での振幅ImgAmpは１にされ、その外では０にされ、再生像面での位相ImgPhaはそのままに維持される。そのような束縛条件が付与された後、ステップ▲５▼で、上記式（４）のフーリエ逆変換が施される。そのフーリエ逆変換で得られたホログラム面での値は、ステップ▲６▼で束縛条件が付与され、振幅HoloAmp は１にされ、位相HoloPha は多値化（元の関数をデジタルな階段状の関数に近似（量子化））される。なお、位相HoloPha が連続的な値を持ってもよい場合は、この多値化は必ずしも必要ない。そして、ステップ▲２▼でその値にフーリエ変換が施され、ステップ▲３▼で、フーリエ変換で得られた再生像面での振幅ImgAmpが所定の領域、例えばｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ 内で略一定値になり、その所定領域外で略０になったと判断された場合は、ステップ▲６▼で束縛条件が付与された振幅と位相が所望の計算機ホログラムとなる。ステップ▲３▼でこのような条件が満足されないと判断された場合は、ステップ▲４▼→▲５▼→▲６▼→▲２▼→▲３▼のループがステップ▲３▼の条件が満足されるまで（収束するまで）繰り返され、最終的な所望の計算機ホログラムが得られる。
【００１８】
ここで、ステップ▲３▼で、再生像面で振幅ImgAmpが略所定の値に収束したと判断する評価関数としては、例えば次のようなものを用いる。

ただし、ｕ，ｖに関するΣ（和）は、ｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ 内のホログラムのセルにおける値の和を取ることを意味し、〈Ａ_IMG （ｕ，ｖ）〉はそのセル内における理想的な振幅である。この（評価関数）が例えば０．０１以下になることをもって収束したと判断する。
【００１９】
この他、計算ループの反復の前回の振幅の値と今回の値の差を用いた次のような評価関数を用いることもできる。

ここで、Ａ_{IMG i-1} （ｕ，ｖ）は前回の振幅の値、Ａ_{IMG i} （ｕ，ｖ）は今回の振幅の値である。
【００２０】
ところで、上記のようにして得られた計算機ホログラムは位相HoloPha のみが分布している位相板であるが、この計算機ホログラムは、背後からホログラム面に垂直に平行光で照明した場合に所定の観察域（上記のｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ 内）へのみ光を回折する計算機ホログラムである。しかし、図９のような液晶表示素子４０の反射拡散板３１とするには、背後から斜めに入射した光を所定の前方の観察域へ回折するものでなければならない（透過型から反射型へ変更する操作については後述）。
【００２１】
そこで、本発明においては、背後からホログラム面に斜めに入射した平行光を所定の観察域に回折するホログラムとするために、図１の手順中、上記の所定の観察域（ｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ 内）の代わりに、それから位置がシフトした別の領域（ｕ₀ ’≦ｕ≦ｕ₁ ’，ｖ₀ ’≦ｖ≦ｖ₁ ’の範囲とする。）を用いて、計算機ホログラムを設計する。すなわち、図１のフローで計算機ホログラムを求める場合に、再生像面で振幅ImgAmpを略一定にする領域を、ｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ でなく、それからシフトしたｕ₀ ’≦ｕ≦ｕ₁ ’，ｖ₀ ’≦ｖ≦ｖ₁ ’の範囲に指定し、その領域外で略０になっるようにする。このシフトした範囲ｕ₀ ’≦ｕ≦ｕ₁ ’，ｖ₀ ’≦ｖ≦ｖ₁ ’の決め方としては、得られた計算機ホログラムのホログラム面に垂直でなく斜めに平行光を入射させた場合に（得られた計算機ホログラムは垂直に平行光を入射させるものとして設計されている。）、設計のときの回折範囲（ｕ₀ ’≦ｕ≦ｕ₁ ’，ｖ₀ ’≦ｖ≦ｖ₁ ’）と異なる所定の観察域（ｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ 内）へのみ光を回折するように設定する。
【００２２】
この点をもう少し詳しく説明する。図２（ａ）は図１のフローで求められた、垂直に平行な照明光３’が入射の場合に再生像面２のｕ₀ ’≦ｕ≦ｕ₁ ’，ｖ₀ ’≦ｖ≦ｖ₁ ’の範囲にのみ光を回折する計算機ホログラム１を示す。この回折範囲は、図示のように、計算機ホログラム１に対して斜め前方になる。図はｕ方向のみを示してあるが、ｖ方向についても同様である。計算機ホログラム１の位相HoloPha の分布を回折格子であるとすると、計算機ホログラム１による回折は、回折格子の基本式、
ｓｉｎθ_d −ｓｉｎθ_i ＝ｍλ／ｄ ・・・（７）
で表される。ここで、ｍは回折次数、ｄは回折格子のピッチ、λは波長、θ_i は入射角、θ_d は回折角である。設計条件から、θ_i ＝０、α₀ ’≦θ_d ≦α₁ ’である。ただし、α₀ ’は入射位置から再生像面２のｕ₀ ’の位置へ回折する角度、α₁ ’はｕ₁ ’の位置へ回折する角度である。
【００２３】
このような計算機ホログラム１に入射角θで斜めに平行な照明光３が入射する場合を図２（ｂ）に示す。回折の式（７）から、この場合は、θ_i ＝θとなり、図の場合を正とすると、回折角θ_d の範囲α₀ ≦θ_d ≦α₁ はα₀ ’≦θ_d ≦α₁ ’より小さい方にシフトすることになり、図２（ｂ）に示すように、再生像面２での回折範囲ｕ₀ ≦ｕ≦ｕ₁ （ｕ₀ は入射位置から回折角α₀ で回折光が再生像面２へ入射する位置、ｕ₁ は回折角α₁ で入射する位置）を計算機ホログラム１の略正面方向にすることが可能である。ｖ方向についても同様である。
【００２４】
以上のように、本発明による計算機ホログラムは、背後からホログラム面に垂直に平行光を入射させた場合に前方の所定の観察域（ｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ ）から位置がシフトした前方の別の領域（ｕ₀ ’≦ｕ≦ｕ₁ ’，ｖ₀ ’≦ｖ≦ｖ₁ ’）へ回折する計算機ホログラムであって、その背後からホログラム面に斜めに平行光を入射させた場合に前方の所定の観察域（ｕ₀ ≦ｕ≦ｕ₁ ，ｖ₀ ≦ｖ≦ｖ₁ ）へ回折する計算機ホログラムである。
【００２５】
このようにして求めた位相分布φ（ｘ，ｙ）から、実際のホログラムの深さ分布を求めるが、これは反射型と透過型で異なる。位相分布φ（ｘ，ｙ）を、反射型の場合は次の式（８ａ）に基づいて、透過型の場合は次の式（８ｂ）に基づいて、計算機ホログラムの深さＤ（ｘ，ｙ）に変換する。
【００２６】
Ｄ（ｘ，ｙ）＝λφ（ｘ，ｙ）／（４π） ・・・（８ａ）
Ｄ（ｘ，ｙ）＝λφ（ｘ，ｙ）／｛２π（ｎ₁ −ｎ₀ ）｝ ・・・（８ｂ）
ここで、λは使用中心波長、ｎ₁ ，ｎ₀ は透過型ホログラムを構成する２つの材質の屈折率である。
【００２７】
反射型の場合、図３（ａ）に断面図を示すように、基板１０の表面に上記式（８ａ）で求めたＤ（ｘ，ｙ）の深さのレリーフパターン１１を形成し、そのレリーフパターン１１上にアルミニウム等の反射層１２を設けることによって本発明の計算機ホログラム１が得られる。透過型の場合、図３（ｂ）に断面図を示すように、上記式（８ｂ）で求めたＤ（ｘ，ｙ）の深さのレリーフパターン１１を形成することによって本発明の計算機ホログラム１が得られる。図４にこの計算機ホログラム１の平面図を示す。この計算機ホログラム１は縦横Ｎ×Ｍ（図４の場合は１６×１６）の碁盤の目状に配置された縦横寸法がΔの微小なセル１３の集合体からなり、各セル１３がそれぞれ式（８ａ）もしくは（８ｂ）で与えられる深さＤ（ｘ，ｙ）を有している。
【００２８】
図５に以上のようにして得られた本発明に基づく計算機ホログラム１の作用を反射型について模式的に示す。図中、符号２が再生像面であり、前方から入射角θで入射する所定波長の照明光３は計算機ホログラム１で回折光４として前方へ回折され、再生像面２中の所定の反射域５へ達し、その領域外にはほとんど達しないものである。したがって、このような計算機ホログラム１を例えば図９に示した反射型液晶表示装置の反射拡散板３１として用いることにより、液晶表示素子４０の表示側から入射する照明光３２をその前方の所定の観察域へのみ拡散反射させ、明所で自発光型のバックライトを使用することなしに明るい表示が可能なものとなる。
【００２９】
また、このような計算機ホログラム１は、図１０に示したように、反射型液晶表示装置の液晶層４５と背面基板４２’の間に反射板として配置してもよい。この場合は、計算機ホログラム１の反射層１２が光反射性電極４４’を兼ねることになる。
【００３０】
次に、具体的な１つの実施例を説明する。図５の計算機ホログラム１としては縦横１６×１６の碁盤の目状のセルに量子化し、再生像面２も同様に縦横１６×１６の碁盤の目状のセルに量子化し、再生像面２の反射域５をその縦横１６×１６の横方向の中央の８×縦方向の上の８とする場合の、図１のリープを３６０回回した結果得られたホログラム面の位相分布HoloPha と、垂直及び斜めに平行光を照明したときの再生像面２での振幅分布ImgAmpの例をそれぞれ図６、図７、図８に示す。ただし、図６においては、位相を−π〜＋πの間で１６段階に量子化をしている。
【００３１】
この例から明らかなように、本発明に基づいて計算機ホログラムを構成すると、斜めに前方から入射する照明光をその前方の所定の観察域へのみ拡散反射させることができ、明るい表示等が可能になる。なお、この実施例は、本発明の計算機ホログラム１が具体的に演算可能であることを示すための例にすぎず、実際の計算機ホログラム１を構成するには、セルの数をケタ違いに増加させて演算する。
【００３２】
以上、本発明による計算機ホログラムを原理と実施例に基づいて説明してきたが、これらの限定されず種々の変形が可能である。また、本発明の計算機ホログラムは、反射型液晶表示装置用の反射板以外にも、例えば表示用の反射板等に用いることが可能である。また、本発明の計算機ホログラムは反射板だけでなく、反射層１２を設けないで透過型として透過板として構成してもよい。
【００３３】
【発明の効果】
以上の説明から明らかなように、本発明の計算機ホログラムによると、２次元的にアレー状に配置された微小なセルの集合体からなる計算機ホログラムであって、前記セルは反射光若しくは透過光に対して各々独自の位相を与える光路長を有しており、該位相の分布が斜めから所定の入射角で入射する光束を所定の観察域内に実質的に回折し、その観察域外には実質的には回折しないような位相分布であり、かつ、垂直に入射する光束を前記の所定の観察域の位置がシフトした別の領域内に実質的に回折し、その別の領域外には実質的には回折しないような位相分布を有しているので、この計算機ホログラムを例えば反射型液晶表示装置の反射板として用いることにより、液晶表示素子の表示側から斜めに入射する照明光をその前方の所定の観察域へのみ拡散反射させ、明所で自発光型のバックライトを使用することなしに明るい表示が可能なものを構成することができる。
【図面の簡単な説明】
【図１】本発明の計算機ホログラム反射板を構成する計算機ホログラムを得るためのフローチャートである。
【図２】図１のフローで求められた計算機ホログラムの垂直照明と斜め照明の場合の回折範囲を対比して示す図である。
【図３】本発明の計算機ホログラムの構成を示す断面図である。
【図４】本発明による計算機ホログラムの平面図である。
【図５】本発明による計算機ホログラムの作用を模式的に示す図である。
【図６】具体的な１実施例のホログラム面の位相分布を示す図である。
【図７】具体的な１実施例の垂直照明のときの再生像面での振幅分布を示す図である。
【図８】具体的な１実施例の斜め照明のときの再生像面での振幅分布を示す図である。
【図９】反射型液晶表示装置の構成を示す断面図である。
【図１０】本発明に基づく計算機ホログラム反射板を適用した別の反射型液晶表示装置の構成を示す断面図である。
【符号の説明】
１…計算機ホログラム
２…再生像面
３…斜め照明光
３’…垂直照明光
４…回折光
５…反射域
１０…基板
１１…レリーフパターン
１２…反射層
１３…セル
３１…反射拡散板
３２…照明光
４０…液晶表示素子
４１、４２…ガラス基板
４２’…背面基板
４３…透明表示電極
４４…透明対向電極
４４’…反射性電極
４５…液晶層
４６、４７…偏光板[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a computer generated hologram. For example, the present invention relates to a computer generated hologram that can be brightly displayed by being arranged on the back surface of a reflective liquid crystal display device.
[0002]
[Prior art]
Conventionally, as shown in FIG. 9, the reflective liquid crystal display device has a reflection diffusion plate 31 made of a metal plate such as matted aluminum disposed on the side opposite to the observation side of the liquid crystal display element 40. Illumination light 32 incident from the display side of the liquid crystal display element 40 is diffusely reflected forward by the reflection diffusion plate 31 disposed on the back surface thereof, and display is possible without using a self-luminous backlight in a bright place. It is. Here, the liquid crystal display element 40 includes, for example, a twisted nematic liquid crystal layer 45 sandwiched between two glass substrates 41 and 42, and a uniform transparent counter electrode is formed on the inner surface of one glass substrate 42. 44, and a transparent display electrode 43 and a black matrix (not shown) are provided on the inner surface of the other glass substrate 41 independently for each pixel. In the case of a color display device, a transparent display electrode 43, a color filter, and a black matrix are provided on the inner surface of the other glass substrate 41 independently for each of the liquid crystal cells R, G, and B. Further, an alignment layer (not shown) is provided on the liquid crystal layer 45 side of the electrodes 43 and 44, and further, a polarizing plate 46 is provided on the outer surface of the observation side glass substrate 41, and the glass substrate 42 on the opposite side to the observation side. Polarizing plates 47 are respectively attached to the outer surfaces, and for example, their transmission axes are arranged so as to be orthogonal to each other. By controlling the voltage applied between the transparent display electrode and the transparent counter electrode of the liquid crystal display element 40 and changing its transmission state, it is possible to selectively display numbers, characters, symbols, pictures, etc. It is.
[0003]
Such a reflective liquid crystal display device does not require a backlight, and thus has an advantage of low power consumption. However, since it is displayed by external light, it is difficult to see the display. Further, even under illumination light, in the regular reflection direction where the reflection intensity is strongest, there is a problem that the contrast is remarkably lowered due to surface reflection in the liquid crystal display device.
[0004]
In order to solve such a problem, WO96 / 37805 or the like proposes a reflector using a combination of a transmission volume hologram and a reflective layer. This reflector can be said to have a high diffraction efficiency in a specific wavelength region since the diffraction efficiency can achieve 100% at a predetermined wavelength when photographing using a volume hologram photosensitive material.
[0005]
[Problems to be solved by the invention]
However, in such a method using a volume hologram, an expensive volume hologram photosensitive material must be used, and hologram imaging by two-beam interference must be performed. I could not say.
[0006]
Further, the volume hologram has a characteristic that only a specific wavelength called wavelength selectivity is strongly diffracted, and there is a problem that the display is colored.
[0007]
The present invention has been made in view of such problems of the prior art, and an object of the present invention is to calculate a reflector or transmission plate that diffracts light incident at a predetermined incident angle into a predetermined limited range. It is to be realized by a hologram, and it is to provide a computer generated hologram that does not need to use an expensive hologram photosensitive material, does not need to perform hologram photographing, and is easy to manufacture.
[0008]
[Means for Solving the Problems]
The computer generated hologram of the present invention that achieves the above object is a computer generated hologram composed of a collection of minute cells arranged two-dimensionally in an array, each cell being unique to reflected light or transmitted light. It has an optical path length that gives a phase, and the phase distribution diffracts a light beam incident from a slant at a predetermined incident angle into a predetermined observation area and does not substantially diffract outside the observation area. A phase distribution and a vertically incident light beam is substantially diffracted into another area where the position of the predetermined observation area is shifted, and is not substantially diffracted outside the other area. It has a characteristic phase distribution.
[0009]
In this case, the cells are preferably arranged in a grid pattern vertically and horizontally.
Specifically, for example, the computer generated hologram of the present invention can be configured by providing an uneven relief pattern on the surface of a substrate and providing a reflective layer thereon.
[0010]
The computer generated hologram of the present invention can be arranged as a reflector on the back surface of a reflective liquid crystal display device, for example. Moreover, it can arrange | position as a reflecting plate between the liquid crystal layer of a reflection type liquid crystal display device, and a back substrate.
[0011]
In the present invention, a computer generated hologram comprising a collection of minute cells arranged two-dimensionally in an array, each cell having an optical path length that gives a unique phase to reflected or transmitted light. The phase distribution is such that the light flux incident at a predetermined incident angle from an oblique angle is substantially diffracted within a predetermined observation area, and is not substantially diffracted outside the observation area; and The phase distribution is such that the vertically incident light beam is substantially diffracted into another area where the position of the predetermined observation area is shifted, and is not substantially diffracted outside the other area. Therefore, by using this computer generated hologram as a reflection plate of a reflective liquid crystal display device, for example, the illumination light incident obliquely from the display side of the liquid crystal display element is diffused and reflected only to a predetermined observation area in front of it. With a self-luminous type No bright display can use the light can be configured capable.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
The principle and embodiment of the computer generated hologram according to the present invention will be described below.
Now, when a certain hologram is considered and the reproduction distance from it is sufficiently larger than the size of the hologram, and illuminating with parallel light perpendicular to the hologram surface, the diffracted light obtained on the reproduction image surface is (Fraunhofer diffraction) expressed by Fourier transform of the amplitude distribution and phase distribution at.
[0013]
Therefore, conventionally, in order to give a predetermined diffracted light to the reproduced image plane, a computer generated hologram that is arranged on the hologram plane while alternately repeating Fourier transform and inverse Fourier transform while applying a constraint condition between the hologram plane and the reproduced image plane. Is known as the Gerchberg-Saxton iterative calculation method (for example, the 22nd Winter Seminar text sponsored by the Optical Society of Japan (Applied Physics Society) “From holograms to diffractive optical elements—from basic theory to industrial applications— Pp. 36-39).
[0014]
Here, when the light distribution on the hologram surface is h (x, y) and the light distribution on the reproduced image surface is f (u, v),
h (x, y) = A _HOLO (x, y) exp (iφ _HOLO (x, y)) (1)
f (u, v) = A _IMG (u, v) exp (iφ _IMG (u, v)) (2)
Can be written. Here, A _HOLO (x, y) is the amplitude distribution on the hologram surface, φ _HOLO (x, y) is the phase distribution on the hologram surface, A _IMG (u, v) is the amplitude distribution on the reproduced image surface, φ _IMG (u, v) is a phase distribution on the reproduced image plane.
[0015]
The above Fourier transform and inverse Fourier transform are

It becomes.
[0016]
Here, in order to make the future discussion easier to understand, A _HOLO (x, y) on the hologram surface is “HoloAmp”, φ _HOLO (x, y) on the hologram surface is “HoloPha”, and A _HOLO (x, y) is A on the reproduced image surface. _IMG (u, v) is expressed as “ImgAmp”, and φ _IMG (u, v) in the reproduced image plane is expressed as “ImgPha”.
[0017]
In the present invention, first, it is considered to obtain a computer generated hologram that diffracts light only to a predetermined observation area when illuminated with parallel light perpendicularly to the hologram surface from behind using this Gerchberg-Saxton iterative calculation method. . FIG. 1 is a flowchart for this purpose. In step {circle around (1)}, hologram surface area x ₀ ≦ x ≦ x ₁ , y ₀ ≦ y ≦ y ₁ , hologram amplitude HoloAmp is set to 1, and hologram phase HoloPha is set. Initializing to a random value, in step (2), the initialized value is subjected to the Fourier transform of the above equation (3). In step {circle around (3)}, the amplitude ImgAmp on the reproduced image plane obtained by Fourier transform becomes a substantially constant value within a predetermined region, for example, u ₀ ≦ u ≦ u ₁ , v ₀ ≦ v ≦ v ₁ . If it is determined that the value has become substantially 0 outside the area, the amplitude and phase initialized in step (1) become the desired computer generated hologram. If it is determined in step (3) that such a condition is not satisfied, a binding condition is given in step (4). Specifically, the amplitude ImgAmp on the reproduced image plane is set to 1 within the predetermined area, and is set to 0 outside the predetermined area, and the phase ImgPha on the reproduced image plane is maintained as it is. After such constraint conditions are given, the inverse Fourier transform of the above equation (4) is performed in step (5). The value on the hologram surface obtained by the inverse Fourier transform is given a constraint condition in step (6), the amplitude HoloAmp is set to 1, and the phase HoloPha is multivalued (the original function is converted into a digital step-like function). Is approximated (quantized). If the phase HoloPha may have a continuous value, this multi-leveling is not necessarily required. In step {circle around (2)}, the value is subjected to Fourier transformation. In step {circle around (3)}, the amplitude ImgAmp on the reproduced image plane obtained by the Fourier transformation is a predetermined region, for example u ₀ ≦ u ≦ u ₁ , v If it is determined that the value is substantially constant within ₀ ≦ v ≦ v ₁ and is substantially 0 outside the predetermined region, the amplitude and phase to which the constraint condition is applied in step (6) are the desired computer hologram. Become. If it is determined in step (3) that these conditions are not satisfied, the loop of step (4) → (5) → (6) → (2) → (3) satisfies the condition of step (3). Until it is done (until it converges) to obtain the final desired computer generated hologram.
[0018]
Here, for example, the following is used as an evaluation function for determining that the amplitude ImgAmp has converged to a substantially predetermined value on the reproduced image plane in step (3).

However, Σ (sum) with respect to u and v means to take the sum of values in the hologram cell within u ₀ ≦ u ≦ u ₁ and v ₀ ≦ v ≦ v ₁ , and <A _IMG (u, v )> Is the ideal amplitude in the cell. When this (evaluation function) is, for example, 0.01 or less, it is determined that convergence has occurred.
[0019]
In addition, the following evaluation function using the difference between the previous amplitude value of the iteration of the calculation loop and the current value can also be used.

Here, A _{IMG i-1} (u, v) is the previous amplitude value, and A _{IMG i} (u, v) is the current amplitude value.
[0020]
By the way, the computer generated hologram obtained as described above is a phase plate in which only the phase HoloPha is distributed. This computer generated hologram has a predetermined observation area when illuminated with parallel light perpendicularly to the hologram surface from behind. This is a computer generated hologram that diffracts light only (within the above u ₀ ≦ u ≦ u ₁ , v ₀ ≦ v ≦ v ₁ ). However, in order to obtain the reflection diffusion plate 31 of the liquid crystal display element 40 as shown in FIG. 9, it is necessary to diffract light incident obliquely from the back into a predetermined front observation area (from transmission type to reflection type). The operation to change will be described later).
[0021]
Therefore, in the present invention, in order to obtain a hologram that diffracts parallel light incident obliquely on the hologram surface from the back into a predetermined observation region, the predetermined observation region (u ₀ ≦ u ≦ instead of _{u 1, v 0 ≦ v ≦} v _1), then the position is in the range of another region shifted _{(u 0 '≦ u ≦ u} 1', v 0 '≦ v ≦ v 1'.) Is used to design a computer generated hologram. That is, when the computer generated hologram is obtained by the flow of FIG. 1, the region in which the amplitude ImgAmp is made substantially constant on the reproduced image plane is not u ₀ ≦ u ≦ u ₁ , v ₀ ≦ v ≦ v ₁ , but shifted from u _It is specified in the range of ₀ ′ ≦ u ≦ u ₁ ′, v ₀ ′ ≦ v ≦ v ₁ ′, and becomes substantially 0 outside the area. The shifted ranges u ₀ ′ ≦ u ≦ u ₁ ′, v ₀ ′ ≦ v ≦ v ₁ ′ are determined when parallel light is incident obliquely, not perpendicularly to the hologram surface of the obtained computer generated hologram. (The obtained computer generated hologram is designed to allow parallel light to enter vertically.) Diffraction range at the time of design (u ₀ ′ ≦ u ≦ u ₁ ′, v ₀ ′ ≦ v ≦ v ₁ ′) Is set so that light is diffracted only into a predetermined observation region (within u ₀ ≦ u ≦ u ₁ , v ₀ ≦ v ≦ v ₁ ).
[0022]
This point will be explained in more detail. FIG. 2A shows a case where u ₀ ′ ≦ u ≦ u ₁ ′, v ₀ ′ ≦ v ≦ v of the reproduced image plane 2 when the vertically parallel illumination light 3 ′ obtained in the flow of FIG. A computer generated hologram 1 that diffracts light only in the range of ₁ 'is shown. This diffraction range is obliquely forward with respect to the computer generated hologram 1 as shown in the figure. Although the figure shows only the u direction, the same applies to the v direction. If the distribution of the phase HoloPha of the computer generated hologram 1 is a diffraction grating, the diffraction by the computer generated hologram 1 is the basic equation of the diffraction grating,
sin θ _d −sin θ _i = mλ / d (7)
It is represented by Here, m is the diffraction order, d is the pitch of the diffraction grating, λ is the wavelength, θ _i is the incident angle, and θ _d is the diffraction angle. From design conditions, θ _i = 0 and α ₀ ′ ≦ θ _d ≦ α ₁ ′. However, α ₀ ′ is an angle diffracting from the incident position to the position u ₀ ′ of the reproduced image plane 2, and α ₁ ′ is an angle diffracting to the position u ₁ ′.
[0023]
FIG. 2B shows a case where illumination light 3 that is obliquely parallel with an incident angle θ is incident on such a computer generated hologram 1. From the diffraction equation (7), θ _i = θ in this case, and assuming that the case in the figure is positive, the range α ₀ ≦ θ _d ≦ α ₁ of the diffraction angle θ _d is α ₀ ′ ≦ θ _d ≦ α _1. 2 ′, the diffraction range u ₀ ≦ u ≦ u ₁ on the reproduced image plane 2 (u ₀ is the diffracted light at the diffraction angle α ₀ from the incident position, as shown in FIG. 2B). Can be made to be substantially in the front direction of the computer generated hologram 1 at a position where is incident on the reproduced image plane 2 and u ₁ is an incident position at the diffraction angle α ₁ . The same applies to the v direction.
[0024]
As described above, the computer generated hologram according to the present invention has a predetermined observation area in the front (u ₀ ≦ u ≦ u ₁ , v ₀ ≦ v ≦ v ₁ ) when parallel light is incident perpendicularly to the hologram surface from behind. Is a computer generated hologram that diffracts to another region (u ₀ ′ ≦ u ≦ u ₁ ′, v ₀ ′ ≦ v ≦ v ₁ ′) whose position is shifted from the front, and is parallel to the hologram surface obliquely from behind Is a computer generated hologram that diffracts to a predetermined observation area (u ₀ ≦ u ≦ u ₁ , v ₀ ≦ v ≦ v ₁ ).
[0025]
The actual depth distribution of the hologram is obtained from the thus obtained phase distribution φ (x, y), which is different between the reflection type and the transmission type. The phase distribution φ (x, y) is calculated based on the following equation (8a) in the case of the reflection type, and based on the following equation (8b) in the case of the transmission type. ).
[0026]
D (x, y) = λφ (x, y) / (4π) (8a)
D (x, y) = λφ (x, y) / {2π (n ₁ −n ₀ )} (8b)
Here, λ is a use center wavelength, and n ₁ and n ₀ are refractive indexes of two materials constituting the transmission hologram.
[0027]
In the case of the reflection type, as shown in the sectional view of FIG. 3A, a relief pattern 11 having a depth of D (x, y) obtained by the above equation (8a) is formed on the surface of the substrate 10, and the relief is formed. By providing a reflective layer 12 such as aluminum on the pattern 11, the computer generated hologram 1 of the present invention is obtained. In the case of the transmission type, as shown in a cross-sectional view in FIG. 3B, the computer generated hologram 1 of the present invention is formed by forming a relief pattern 11 having a depth of D (x, y) obtained by the above equation (8b). Is obtained. FIG. 4 shows a plan view of the computer generated hologram 1. This computer generated hologram 1 is made up of an assembly of small cells 13 having a vertical and horizontal dimension of Δ arranged in a grid pattern of N × M in the vertical and horizontal directions (16 × 16 in the case of FIG. 4). It has a depth D (x, y) given by 8a) or (8b).
[0028]
FIG. 5 schematically shows the operation of the computer generated hologram 1 based on the present invention obtained as described above for the reflection type. In the figure, reference numeral 2 denotes a reproduction image plane. Illumination light 3 having a predetermined wavelength incident from the front at an incident angle θ is diffracted forward as diffracted light 4 by the computer generated hologram 1, and a predetermined reflection area in the reproduction image plane 2. It reaches 5 and hardly reaches outside the area. Therefore, by using such a computer generated hologram 1 as, for example, the reflection diffusion plate 31 of the reflection type liquid crystal display device shown in FIG. 9, the illumination light 32 incident from the display side of the liquid crystal display element 40 can be observed in a predetermined direction in front thereof. Bright reflection is possible without using a self-luminous backlight in a bright place.
[0029]
Further, as shown in FIG. 10, such a computer generated hologram 1 may be arranged as a reflector between the liquid crystal layer 45 of the reflective liquid crystal display device and the back substrate 42 ′. In this case, the reflection layer 12 of the computer generated hologram 1 also serves as the light reflective electrode 44 ′.
[0030]
Next, one specific example will be described. The computer generated hologram 1 shown in FIG. 5 is quantized into 16 × 16 grid cells in the horizontal and vertical directions, and the reproduced image plane 2 is similarly quantized into 16 × 16 grid cells in the vertical and horizontal directions. The phase distribution HoloPha of the hologram surface obtained as a result of rotating the leap of FIG. 1 360 times when the reflection area 5 is 8 × 8 in the center of the horizontal direction of 16 × 16 in the vertical direction, Examples of the amplitude distribution ImgAmp on the reproduced image plane 2 when the parallel light is illuminated obliquely are shown in FIGS. 6, 7, and 8, respectively. However, in FIG. 6, the phase is quantized in 16 steps between −π to + π.
[0031]
As is apparent from this example, when a computer generated hologram is constructed based on the present invention, illumination light incident obliquely from the front can be diffusely reflected only to a predetermined observation area in front of the computer hologram, thereby enabling bright display and the like. Become. Note that this embodiment is merely an example to show that the computer generated hologram 1 of the present invention can be specifically calculated, and in order to construct an actual computer generated hologram 1, the number of cells is increased by a number of digits. Let's calculate.
[0032]
As mentioned above, although the computer generated hologram according to the present invention has been described based on the principle and the embodiment, these are not limited and various modifications are possible. Further, the computer generated hologram of the present invention can be used, for example, as a reflection plate for display in addition to the reflection plate for a reflective liquid crystal display device. Further, the computer generated hologram of the present invention may be configured as a transmission plate as a transmission type without providing the reflection layer 12 as well as the reflection plate.
[0033]
【The invention's effect】
As is apparent from the above description, according to the computer generated hologram of the present invention, a computer generated hologram composed of a collection of minute cells arranged two-dimensionally in an array, the cell being used as reflected light or transmitted light. Each has an optical path length that gives a unique phase, and the phase distribution substantially diffracts a light beam incident at an angle of incidence from an oblique angle within a predetermined observation area, and is substantially outside the observation area. The phase distribution is such that it does not diffract, and the vertically incident light beam is substantially diffracted into another area where the position of the predetermined observation area is shifted, and is substantially outside the other area. Therefore, by using this computer generated hologram as a reflector of a reflective liquid crystal display device, for example, illumination light incident obliquely from the display side of the liquid crystal display element Predetermined Was observed diffuse reflections into observation zone, it is possible to configure one capable of bright display without the use of the backlight of the self-luminous in the light.
[Brief description of the drawings]
FIG. 1 is a flowchart for obtaining a computer generated hologram constituting a computer generated hologram reflector of the present invention.
FIG. 2 is a diagram showing a comparison of diffraction ranges in the case of vertical illumination and oblique illumination of a computer generated hologram obtained in the flow of FIG.
FIG. 3 is a cross-sectional view showing a configuration of a computer generated hologram according to the present invention.
FIG. 4 is a plan view of a computer generated hologram according to the present invention.
FIG. 5 is a diagram schematically showing the operation of a computer generated hologram according to the present invention.
FIG. 6 is a diagram showing a phase distribution of a hologram surface in a specific example.
FIG. 7 is a diagram illustrating an amplitude distribution on a reproduced image plane in the case of vertical illumination according to a specific example.
FIG. 8 is a diagram illustrating an amplitude distribution on a reproduced image plane when oblique illumination is performed according to a specific embodiment;
FIG. 9 is a cross-sectional view illustrating a configuration of a reflective liquid crystal display device.
FIG. 10 is a cross-sectional view showing a configuration of another reflective liquid crystal display device to which a computer generated hologram reflecting plate according to the present invention is applied.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Computer hologram 2 ... Reproduction image surface 3 ... Diagonal illumination light 3 '... Vertical illumination light 4 ... Diffraction light 5 ... Reflection area 10 ... Substrate 11 ... Relief pattern 12 ... Reflection layer 13 ... Cell 31 ... Reflection diffuser plate 32 ... Illumination Light 40 ... Liquid crystal display elements 41, 42 ... Glass substrate 42 '... Back substrate 43 ... Transparent display electrode 44 ... Transparent counter electrode 44' ... Reflective electrode 45 ... Liquid crystal layer 46, 47 ... Polarizing plate

Claims (5)

A computer generated hologram comprising a collection of minute cells arranged two-dimensionally in an array, each cell having an optical path length that gives a unique phase to reflected or transmitted light, The phase distribution is such that a light beam incident at an angle of incidence from an oblique angle is substantially diffracted within a predetermined observation area, and is not substantially diffracted outside the observation area, and is incident vertically. The phase distribution is such that the light beam is substantially diffracted into another region where the position of the predetermined observation area is shifted, and is not substantially diffracted outside the other region. Computer hologram to do. 2. The computer generated hologram according to claim 1, wherein the cells are arranged vertically and horizontally in a grid pattern. 3. The computer generated hologram according to claim 1, wherein a relief pattern having an unevenness is provided on the surface of the substrate, and a reflective layer is provided thereon. The computer generated hologram according to any one of claims 1 to 3, wherein the computer-generated hologram is arranged as a reflector on a back surface of the reflective liquid crystal display device. 5. The computer generated hologram according to claim 1, wherein the computer-generated hologram is arranged as a reflecting plate between a liquid crystal layer of the reflective liquid crystal display device and a rear substrate.

Images