JPH0572477A - Afocal optical device - Google Patents
Afocal optical deviceInfo
- Publication number
- JPH0572477A JPH0572477A JP3235050A JP23505091A JPH0572477A JP H0572477 A JPH0572477 A JP H0572477A JP 3235050 A JP3235050 A JP 3235050A JP 23505091 A JP23505091 A JP 23505091A JP H0572477 A JPH0572477 A JP H0572477A
- Authority
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- Prior art keywords
- mirror
- equation
- order aspherical
- optical axis
- angle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Abstract
Description
【0001】[0001]
【産業上の利用分野】この発明は望遠鏡やビ−ム整形光
学系などに用いられるアフォ−カル光学装置に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an afocal optical device used in a telescope, a beam shaping optical system and the like.
【0002】[0002]
【従来の技術】放物面からなる反射面を有する主鏡と副
鏡とをカセグレン配置にすると、軸上無収差の非焦点系
(アフォ−カル系)が得られる。しかしながら、光軸に
対して所定の角度で傾斜した画角においては収差が存在
する。この収差を軸外収差という。2. Description of the Related Art When a primary mirror and a secondary mirror having a reflecting surface formed of a parabolic surface are arranged in a Cassegrain arrangement, an axially non-afocal system (afocal system) can be obtained. However, there is aberration at an angle of view inclined at a predetermined angle with respect to the optical axis. This aberration is called off-axis aberration.
【0003】従来、アフォ−カル系の光学装置において
は、軸外収差を補正するということがほとんど行われて
いなかった。図3(a)は従来のアフォ−カル光学系に
おける画角と軸外収差との関係を示す。この図から分か
るように、軸外収差は画角が大きくなればなる程、大き
くなる。そのため、その光学系が軸外での使用を要求さ
れる場合、高い光学性能が得られないということがあっ
た。Conventionally, correction of off-axis aberrations has hardly been performed in afocal optical devices. FIG. 3A shows the relationship between the angle of view and the off-axis aberration in the conventional afocal optical system. As can be seen from this figure, the off-axis aberration increases as the angle of view increases. Therefore, when the optical system is required to be used off-axis, high optical performance may not be obtained.
【0004】[0004]
【発明が解決しようとする課題】このように、従来のア
フォ−カル光学装置は、画角が大きくなればなる程、収
差も大きくなるので、軸外で使用する場合の光学性能が
低下するということがあった。As described above, in the conventional afocal optical device, the larger the angle of view is, the larger the aberration is. Therefore, the optical performance when used off-axis is deteriorated. There was something.
【0005】この発明は上記事情にもとづきなされたも
ので、その目的とするところは、使用画角が大きくなっ
ても、その使用画角の範囲全体にわたって良好な収差特
性が得られるようにしたアフォ−カル光学装置を提供す
ることにある。The present invention has been made in view of the above circumstances. An object of the present invention is to provide an afocal lens capable of obtaining a good aberration characteristic over the entire range of the use angle of view even if the use angle of view becomes large. -To provide a Cull optical device.
【0006】[0006]
【課題を解決するための手段】上記課題を解決するため
にこの発明は、中心部に光線が通る通孔が形成された凹
状反射面を有する主鏡と、上記通孔に対向して配置され
た凸状反射面を有する副鏡とから構成され、上記主鏡と
副鏡との反射面は回転放物面を基本とし、下記式によっ
て定められる高次非球面からなるとともに、光軸に対し
て傾いた所定の範囲内の画角における軸外収差が所定値
以下となるよう、下記式中におけるk、An のパラメ−
タのうち、少なくともkが最適化されることを特徴とす
るアフォ−カル光学装置にある。SUMMARY OF THE INVENTION In order to solve the above problems, the present invention is directed to a main mirror having a concave reflecting surface having a through hole through which a light beam passes in a central portion, and a main mirror disposed opposite to the above through hole. And a secondary mirror having a convex reflecting surface, the reflecting surfaces of the primary and secondary mirrors are basically paraboloids of revolution, consisting of higher-order aspherical surfaces defined by the following formula, and with respect to the optical axis: The parameters of k and A n in the following equations are set so that the off-axis aberrations within a predetermined angle of view within a predetermined range are below a predetermined value.
In the afocal optical device, at least k is optimized.
【0007】[0007]
【数2】 ただし、Xは光軸方向に沿う座標、hは光軸と直交する
方向の座標、kは円錐定数、An は高次非球面係数、c
は中心曲率である。[Equation 2] Here, X is a coordinate along the optical axis direction, h is a coordinate in a direction orthogonal to the optical axis, k is a conical constant, A n is a high-order aspherical surface coefficient, and c is
Is the central curvature.
【0008】[0008]
【作用】上記構成によれば、使用される所定の範囲内の
画角における軸外収差を所定値以下とすることができる
から、その画角内における光学性能を向上させることが
できる。According to the above construction, since the off-axis aberration in the field angle within the predetermined range to be used can be set to the predetermined value or less, the optical performance within the field angle can be improved.
【0009】[0009]
【実施例】以下、この発明の一実施例を図面を参照して
説明する。図1はアフォ−カル光学装置を示し、同図中
1は主鏡である。この主鏡1には、中心部に光線Lが入
射する通孔2が穿設されているとともに、通過側の一側
面は回転放物面を基本とする高次非球面からなる凹状反
射面3に形成されている。DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 shows an afocal optical device, in which 1 is a primary mirror. The main mirror 1 is provided with a through hole 2 through which a light ray L is incident at the center thereof, and one side surface on the passing side is a concave reflecting surface 3 which is a high-order aspherical surface based on a paraboloid of revolution. Is formed in.
【0010】上記主鏡1の凹状反射面3と対向する部位
には、副鏡4が光学中心を上記主鏡1の光学中心と同一
光軸O上に位置させて配置されている。この副鏡4の上
記凹状反射面3と対向する面は、回転放物面を基本とす
る高次非球面からなる凸状反射面5に形成されていて、
この凸状反射面5と上記凹状反射面3とは焦点Fを共有
して配置されている。したがって、上記主鏡1の通孔2
から光線Lが光軸Oと平行に入射すれば、その光線Lは
副鏡4の凸状反射面5で拡大方向に反射して主鏡1の凹
状反射面3に入射し、この凹状反射面3で上記光軸Oと
平行に反射する。光線Lが光軸Oに対して所定の傾斜角
度で上記通孔2から入射すれば、主鏡1の凹状反射面3
で反射した光線Lは図1の鎖線で示すように光軸Oに対
して傾斜し、角度rの画角が生じることになる。At a portion of the main mirror 1 facing the concave reflecting surface 3, a sub mirror 4 is arranged with its optical center on the same optical axis O as the optical center of the main mirror 1. The surface of the sub-mirror 4 facing the concave reflecting surface 3 is formed as a convex reflecting surface 5 composed of a high-order aspherical surface based on a paraboloid of revolution,
The convex reflecting surface 5 and the concave reflecting surface 3 are arranged so as to share a focal point F. Therefore, the through hole 2 of the primary mirror 1
When the light ray L is incident parallel to the optical axis O, the light ray L is reflected by the convex reflecting surface 5 of the secondary mirror 4 in the expanding direction and is incident on the concave reflecting surface 3 of the primary mirror 1. At 3, the light is reflected parallel to the optical axis O. When the light ray L is incident on the optical axis O at a predetermined inclination angle through the through hole 2, the concave reflecting surface 3 of the primary mirror 1 is formed.
The light ray L reflected by is inclined with respect to the optical axis O as shown by the chain line in FIG. 1, and an angle of view of the angle r is generated.
【0011】上記凹状反射面3と凸状反射面5とは、図
2に示すように光軸O方向に沿う座標をX、光軸Oと直
交する方向の座標をhとすると、次式による高次非球面
に設定されている。The concave reflecting surface 3 and the convex reflecting surface 5 are given by the following equations, where X is the coordinate along the optical axis O direction and h is the coordinate orthogonal to the optical axis O as shown in FIG. It is set to a high-order aspherical surface.
【0012】[0012]
【数3】 [Equation 3]
【0013】上記(1)式において、kは円錐定数、A
は4次非球面係数、Bは6次非球面係数、Cは8次非球
面係数、Dは10次非球面係数、cは中心曲率である。
そして、上記各反射面3、5の形状を設定するにあたっ
ては、円錐定数k、および4〜10次の非球面係数A〜
Dの各パラメ−タを下記[表1]に示す例1〜例5のよ
うにした。つまり、各例において、4〜10次の非球面
係数A〜Dは選択的に使用し、円錐定数は各例の全てに
必ず使用した。なお、(1)式は(2)式から導出され
る。In the above equation (1), k is a conic constant, A
Is a fourth-order aspherical coefficient, B is a sixth-order aspherical coefficient, C is an eighth-order aspherical coefficient, D is a tenth-order aspherical coefficient, and c is a central curvature.
When setting the shapes of the reflecting surfaces 3 and 5, the conical constant k and the aspherical coefficients A to 4th to 10th orders are set.
Each parameter of D was set as in Examples 1 to 5 shown in [Table 1] below. That is, in each example, the fourth to tenth order aspherical coefficients A to D were selectively used, and the conic constant was always used in all of the examples. The expression (1) is derived from the expression (2).
【0014】[0014]
【数4】 [Equation 4]
【0015】すなわち、(1)式はl(エル)=5の場
合を示している。ただし、(1)式における係数Aは
(2)式における係数A2 、同じく(1)式における係
数Bは(2)式における係数A3 、同じく(1)式にお
ける係数Cは(2)式における係数A4 、同じく(1)
式における係数Dは(2)式における係数A5 となって
いる。なお、この実施例において、(1)式中にA1 h
2 の項がないのは、この2次項が(1)式中のThat is, the equation (1) shows the case where l (ell) = 5. However, (1) the coefficients A are (2) Factor A 2, also (1) factor in the equation B is (2) the coefficient in the equation A 3 in formula, also (1) coefficient C (2) in the equation in the equation Coefficient A 4 in the same manner (1)
The coefficient D in the equation is the coefficient A 5 in the equation (2). In this example, in the formula (1), A 1 h
2 The fact that there is no term of is that this quadratic term in equation (1)
【0016】[0016]
【数5】 の項により、現わされることによる。また、l(エル)
は6以上であってもよいこと無論である。[Equation 5] By being expressed by the section. Also, l
Of course, it may be 6 or more.
【0017】[0017]
【表1】 [Table 1]
【0018】下記[表2]は[表1]に示される例1〜
5の円錐定数kおよび高次非球面係数A〜Dのパラメ−
タの使用形態において、これらパラメ−タを最適化した
値を示す。The following [Table 2] shows Examples 1 to 1 shown in [Table 1].
Parameters of the conic constant k of 5 and the higher-order aspherical coefficients A to D
The optimized values of these parameters are shown in the usage pattern of the data.
【0019】[0019]
【表2】 [Table 2]
【0020】図3(b)は[表2]の例3にもとづく最
適化によって主鏡1と副鏡4との反射面3、5を高次非
球面化して収差配分した場合の画角と波面収差との関係
を示し、使用画角0と、最大使用画角(この場合は1mr
ad)とでの波面収差がほぼ等しくなるよう設定した。つ
まり、光軸O上の収差を許し、光軸O外の収差を低減す
ることで、従来に比べて使用最大画角における最大収差
を十分に小さくし、使用画角全体にわたって良好な収差
特性となるようにした。それによって、使用画角全体に
わたって波面収差を所定値以下にできるから、画角が0
から1mradの範囲内で所定値以上の光学精度で使用する
ことができる。FIG. 3B shows an angle of view when the reflecting surfaces 3 and 5 of the primary mirror 1 and the secondary mirror 4 are made higher-order aspherical surfaces and aberrations are distributed by optimization based on Example 3 in [Table 2]. It shows the relationship with the wavefront aberration, and the field angle 0 and the maximum field angle (1mr in this case)
Ad) and wavefront aberration are set to be almost equal. That is, by allowing the aberrations on the optical axis O and reducing the aberrations outside the optical axis O, the maximum aberration at the maximum use angle of view can be made sufficiently small compared to the conventional one, and good aberration characteristics can be obtained over the entire use angle of view. I tried to be. As a result, the wavefront aberration can be reduced to a predetermined value or less over the entire field of view, so that the field of view is 0
It can be used with an optical accuracy of a predetermined value or more within the range of 1 to 1 mrad.
【0021】なお、図3(a)、(b)は光線Lの波長
λが780nm の場合の画角と、波面収差との関係を示し、
最大使用画角が1mradのときに、従来は図3(a)のよ
うに波面収差が約λ/11(RMS)であったものが、反射
面3、5をこの発明にもとづいて高次非球面化すると、
図3(b)に示すように最大使用画角1mradにおいて、
波面収差を約λ/22.7(RAS) に改善することができたこ
とを示している。この発明は上記一実施例に限定され
ず、たとえば光線Lの光路中に補正レンズを配置し、軸
外収差をさらに小さくするようにしてもよい。3A and 3B show the relationship between the angle of view and the wavefront aberration when the wavelength λ of the light beam L is 780 nm.
When the maximum usable angle of view is 1 mrad, the wavefront aberration is about λ / 11 (RMS) as shown in FIG. 3A, but the reflecting surfaces 3 and 5 have a higher order non-degree according to the present invention. When sphered,
As shown in Fig. 3 (b), at the maximum usable angle of view of 1 mrad,
It shows that the wavefront aberration could be improved to about λ / 22.7 (RAS). The present invention is not limited to the above-mentioned embodiment, and for example, a correction lens may be arranged in the optical path of the light ray L to further reduce the off-axis aberration.
【0022】[0022]
【発明の効果】以上述べたようにこの発明は、アフォ−
カル光学系を構成する主鏡と副鏡の反射面を高次非球面
化するに際して、円錐定数と高次非球面係数のうち、少
なくとも上記円錐定数を最適化するようにした。As described above, the present invention is an after-effect.
At the time of making the reflecting surfaces of the primary mirror and the secondary mirror constituting the Cull optical system higher-order aspherical surfaces, at least the above-mentioned conical constants of the conical constants and the higher-order aspherical surface coefficients are optimized.
【0023】そのため、軸外での使用が要求される場
合、使用される最大画角における収差を従来に比べて小
さくし、使用画角内全体における収差を所定値以下に平
均化することができるから、使用画角全体にわたって光
学的性能の向上が計れる。Therefore, when use outside the axis is required, the aberration at the maximum field angle used can be made smaller than in the prior art, and the aberration within the entire field angle used can be averaged below a predetermined value. Therefore, the optical performance can be improved over the entire field of view.
【図1】この発明の一実施例の全体構成図。FIG. 1 is an overall configuration diagram of an embodiment of the present invention.
【図2】同じく反射面形状を設定する式におけるXとh
との関係の説明図。2] Similarly, X and h in the equation for setting the reflection surface shape
Explanatory diagram of the relationship with.
【図3】(a)は軸外収差を補正しない従来の反射面の
画角と収差との関係を示すグラフ、(b)は軸外収差を
補正した場合の反射面の画角と収差との関係を示すグラ
フ。FIG. 3A is a graph showing the relationship between the angle of view and aberration of a conventional reflecting surface that does not correct off-axis aberration, and FIG. 3B shows the angle of view and aberration of the reflecting surface when correcting off-axis aberration. The graph which shows the relationship of.
1…主鏡、2…通孔、3…凹状反射面、4…副鏡、5…
凸状反射面。1 ... Primary mirror, 2 ... Through hole, 3 ... Concave reflecting surface, 4 ... Secondary mirror, 5 ...
Convex reflective surface.
Claims (2)
状反射面を有する主鏡と、上記通孔に対向して配置され
た凸状反射面を有する副鏡とから構成され、上記主鏡と
副鏡との反射面は回転放物面を基本とし、下記式によっ
て定められる高次非球面からなるとともに、光軸に対し
て傾いた所定の範囲内の画角における軸外収差が所定値
以下となるよう、下記式中におけるk、An のパラメ−
タのうち、少なくともkが最適化されることを特徴とす
るアフォ−カル光学装置。 【数1】 ただし、Xは上記光軸方向に沿う座標、hは上記光軸と
直交する方向の座標、kは円錐定数、An は高次非球面
係数、cは中心曲率である。1. A main mirror having a concave reflecting surface in which a through hole for passing a light beam is formed in a central portion, and a secondary mirror having a convex reflecting surface arranged facing the through hole. The reflecting surfaces of the primary and secondary mirrors are basically paraboloids of revolution, and consist of higher-order aspherical surfaces defined by the following formula, and off-axis aberrations at an angle of view within a predetermined range tilted with respect to the optical axis are The parameters of k and A n in the following equation are set so that they are below a predetermined value.
Afocal optical device, wherein at least k is optimized. [Equation 1] Here, X is a coordinate along the optical axis direction, h is a coordinate in a direction orthogonal to the optical axis, k is a conic constant, A n is a high-order aspherical surface coefficient, and c is a central curvature.
ける収差がほぼ等しく設定されることを特徴とする請求
項1記載のアフォ−カル光学装置。2. The afocal optical device according to claim 1, wherein the aberrations at the view angle of 0 and at the maximum usable view angle are set to be substantially equal.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP3235050A JPH0572477A (en) | 1991-09-13 | 1991-09-13 | Afocal optical device |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP3235050A JPH0572477A (en) | 1991-09-13 | 1991-09-13 | Afocal optical device |
Publications (1)
Publication Number | Publication Date |
---|---|
JPH0572477A true JPH0572477A (en) | 1993-03-26 |
Family
ID=16980347
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP3235050A Pending JPH0572477A (en) | 1991-09-13 | 1991-09-13 | Afocal optical device |
Country Status (1)
Country | Link |
---|---|
JP (1) | JPH0572477A (en) |
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