KR102023875B1 - Off-axis optic device in which linear astigmatism is removed - Google Patents

Abstract

The present invention provides an off-axis reflective optical system device with removed linear astigmatism. According to an embodiment of the present invention, the off-axis reflective optical system device determines an optical design value corresponding to a ratio of an effective aperture to an effective focal length while linear astigmatism is removed, and forms an off-axis arrangement relation based on the optical design value. If the effective aperture is D and the ratio of the effective aperture to the effective focal length is 3.3, the optical design value has the effective focal length of 3.3D. The distance d_1 from a common focus of a first and a second mirror to the first mirror is 4.16D. The distance d_2 from a common focus of the second mirror and a third mirror to the third mirror is 5.208D. The distance d_3 from the third mirror to an image surface is 2.753D. The incident angle i_1 of a beam entering the first mirror from an object surface is 16°. The incident angle i_2 of a beam entering the second mirror from the first mirror is 22°. The incident angle i_3 of a beam entering the third mirror from the second mirror is 11.3755°.

Description

OFF-AXIS OPTIC DEVICE IN WHICH LINEAR ASTIGMATISM IS REMOVED}

The present invention relates to a non-reflective optical system device in which linear astigmatism has been removed, and more particularly, based on an optical design value corresponding to a ratio of effective focal length to effective Pupil Diameter from which coma aberration has been removed. It relates to a non-axis reflective optical system device is formed.

Optical systems used in satellites and space telescopes are limited in size and weight and must withstand vibration environments. For this reason, a reflective optical system using a reflector is used more than a refractive optical system using a lens.

However, in the general on-axis optical system, the diffraction and scattering of incident light are caused by the secondary diameter and its support, and the diffraction and scattering of the incident light can be a big factor that degrades the final imaging performance. .

On the other hand, the refractive optical telescope has excellent optical performance, but there is a limitation in the material and size of the lens, it may not be suitable for the space telescope.

In addition, since the reflection optics telescope most widely used as a space telescope is a convex mirror located in front of the main reflector, incident light by the secondary and secondary support can be diffracted and scattered, and constraints may be generated to create a clear image. In addition, constraints may occur in fixing the secondary diameter.

As a new alternative to this, the off-axis reflection optics device (eg, off-axis casein telescope) may be suitable as a space telescope.

In addition, the non-axis reflection optical system device may be suitable as an infrared telescope because there is no thermal radiation noise due to the secondary diameter, and when the reflector is made of aluminum, it can be firmly fixed to the reflector and may be suitable as a military infrared telescope.

In addition, the non-axis reflection optical system device may be suitable as an astronomical telescope for astronomy research because there is no scattered light due to the secondary diameter.

For example, an astronomical telescope may be suitable as a coronagraph telescope used to observe the sun, or as a coronagraph telescope used to find alien planets.

In addition, when a small reflector can be manufactured in large quantities, the non-axis reflecting optical system device can be suitable as an amateur miniature telescope because the structure of the barrel is simplified and can be supplied at low cost.

Therefore, the non-axis reflective optical system device may be widely used in the above-mentioned various fields or fields to which the same is applied.

In addition, the existing non-axis reflection optical system may cause linear astigmatism because the central axis of the optical system and the central axis of the field of vision do not coincide with each other, and the coma generated when the distance of the central axis or the light beams for the object are not collected. There may be aberrations.

This aberration can greatly affect final image performance degradation. Conventional non-reflective optical systems can reduce linear astigmatism through the optimization process using optical design programs, but cannot eliminate it completely.

Existing inventions (US Patent No.7274513 and Korean Patent Registration No. 10-1789383) use confocals to analytically remove linear astigmatism appearing in non-reflective optics and use this to determine the focal length A non-reflective optical system using two reflectors with an F-ratio of 2 was designed. Here, the confocal point means that the focal points of two optical elements overlap one point, and may represent a focal point shared by two optical elements.

However, the non-reflective optical system using two reflecting mirrors has a disadvantage in that the secondary diameter is much larger than the main diameter.

On the other hand, even the optical system exhibiting the same performance has the advantage that the size can be reduced if the number of the reflector is increased.

Therefore, a non-axis reflective optics device may be proposed that adds a reflector to reduce the size of each reflector and the overall system while eliminating linear astigmatism.

Korean Registered Patent No. 10-1789383, "Axial Reflective Optical System Device" Korea Patent Registration No. 10-1812584, "Earth observation optical system" Korean Laid-Open Patent Publication No. 10-2017-0121976, "Coude-type stockpile telescope and its alignment method" Korean Patent No. 10-0674959, "Non-axis projection optical system and extreme ultraviolet lithography apparatus using the same" US Patent No. 7274513, "off-axis projection optics and extreme ultraviolet lithography apparatus employing the same"

It is an object of the present invention to provide a non-axis reflection optical system device in which a non-axis arrangement relationship is formed based on an optical design value corresponding to the ratio of the effective focal length to the effective aperture.

An object of the present invention is to provide a non-axis reflective optical system device in which coma aberration is efficiently removed based on an autonomic curved shape parameter with respect to a reflector.

The present invention provides an optical axis reflecting optical system having an optical performance superior to that of a common axis axis reflecting telescope having the same effective aperture ratio from the optical design of an effective focal length to which the effective aperture distance without effective aberration is 3.3. The purpose can be provided.

The present invention can be aimed at providing a non-reflective optical system device that reduces the size of each reflector and the entire system using three reflectors in the non-reflective optical system device.

According to an embodiment of the present invention, in the non-axis reflection optical system device, an optical design value corresponding to the ratio of the effective focal length to the effective aperture is determined in a state where linear astigmatism is removed, and the stockpile is based on the optical design value. (off-axis) arrangement relationship is formed, and when the effective aperture is D and the ratio of the effective focal length to the effective aperture is 3.3, the optical design value has the effective focal length of 3.3D, and the first mirror the distance from the third to the mirror and from the second distance from the second to the first mirror from the shared focus (common focus) of the mirror ₁ d is 4.16D, the shared focus (common focus) of the second mirror and the third mirror d ₂ is 5.208D, the distance from the third mirror to the upper surface d ₃ is 2.753D, the incidence angle i ₁ of the light beam incident from the object plane to the first mirror is 16 °, and the first mirror at the first mirror is 2 The incident angle i ₂ of the light beam incident on the mirror is 22 °, and the incident angle i ₃ of the light beam incident on the third mirror is 11.3755 °.

According to an embodiment of the present invention, at least one of coma aberration, astigmatism, or top curvature is based on an autonomic curved shape parameter for at least one of the first mirror, the second mirror, or the third mirror. It may be characterized in that it is removed.

According to an embodiment of the present invention, the autonomic curve shape parameter for the first mirror may be determined by Equation 3.

[Equation 3]

_{Z M1 = k [-4.161198 Х 10} -4 · (x / k) 2 - 3.845047 Х 10 -4 · (y / k) 2 + 9.641603 Х 10 -8 · (x / k) 2 (y / k) + 5.573436 Х 10 ^-10 (y / k) ³ + 1.010284 Х 10 ^-10 (x / k) ⁴ + 1.776302 Х 10 ^-10 (x / k) ² (y / k) ² + 1.006174 Х 10 ^{-10 · (y / k) 4 -} 1.548852 Х 10 -13 · (x / k) 4 (y / k) - 3.211816 Х 10 -13 · (x / k) 2 (y / k) 3 - 8.606285 Х 10 -14 ^{· (y / k) 5 -} 1.818727 Х 10 -15 · (x / k) 6 - 1.040144 Х 10 -15 · (x / k) 4 (y / k) 2 - 1.296413 Х 10 -15 · (x / k ) ² (y / k) ⁴ + 1.557898 Х 10 ^-15 (y / k) ⁶ + 2.013918 Х 10 ^-17 (x / k) ⁶ (y / k) + 4.582719 Х 10 ^{-17 ) 4 (y / k) 3} + 2.978542 Х 10 -17 · (x / k) 2 (y / k) 5 - 1.386084 Х 10 -18 · (y / k) 7 + 2.495899 Х 10 -19 · (x / k) ⁸ + 6.754 432 Х 10 ^-20 (x / k) ⁶ (y / k) ² + 4.564714 Х 10 ^-19 (x / k) ⁴ (y / k) ⁴ + 2.408273 Х 10 ^-19 (x ^{/ k) 2 (y / k} ) 6 - 2.212558 Х 10 -19 · (y / k) 8 - 1.330036 Х 10 -21 · (x / k) 8 (y / k) - 3.469298 Х 10 -21 · (x ^{/ k) 6 (y / k} ) 3 - 5.065371 Х 10 -21 · (x / k) 4 (y / k) 5 - 1.606291 Х 10 -21 · (x / k) 2 (y / k) 7 + 3.926423 ^{Х 10 -23 · (y / k} ) 9 - 1.245 ^{698 Х 10 -23 · (x /} k) 10 + 7.462334 Х 10 -24 · (x / k) 8 (y / k) 2 - 3.519848 Х 10 -23 · (x / k) 6 (y / k) 4 ^{- 3.147035 Х 10 -23 · (x} / k) 4 (y / k) 6 - 1.501654 Х 10 -23 · (x / k) 2 (y / k) 8 + 1.174413 Х 10 -23 · (y / k) ¹⁰ ]

(Where Z _M1 is an autonomic surface shape parameter for the first mirror, x is the distance from the autonomic surface along the axis parallel to the sagittal plane, y is from the autonomic surface along the axis parallel to the tangential plane) Distance, k is D / 150mm)

According to an embodiment of the present invention, the autonomic curve shape parameter for the second mirror may be determined by Equation 4.

 [Equation 4]

_{Z M2 = k [-1.378580 Х 10} -3 · (x / k) 2 - 1.185124 Х 10 -3 · (y / k) 2 + 3.290996 Х 10 -7 · (x / k) 2 (y / k) - ^{8.034641 Х 10 -7 · (y /} k) 3 - 2.671748 Х 10 -9 · (x / k) 4 - 4.978006 Х 10 -9 · (x / k) 2 (y / k) 2 - 2.012845 Х 10 -9 ^{· (y / k) 4 -} 2.356142 Х 10 -13 · (x / k) 4 (y / k) - 6.601985 Х 10 -12 · (x / k) 2 (y / k) 3 - 6.872502 Х 10 -12 ^{· (y / k) 5 +} 1.476119 Х 10 -13 · (x / k) 6 - 1.182993 Х 10 -13 · (x / k) 4 (y / k) 2 - 3.134349 Х 10 -13 · (x / k ^{) 2 (y / k) 4} - 2.488053 Х 10 -13 · (y / k) 6 - 2.525948 Х 10 -16 · (x / k) 6 (y / k) - 4.882015 Х 10 -15 · (x / k ^{) 4 (y / k) 3} - 5.524294 Х 10 -15 · (x / k) 2 (y / k) 5 - 5.328826 Х 10 -16 · (y / k) 7 - 1.233799 Х 10 -16 · (x / k) ⁸ + 2.437263 Х 10 ^-17 (x / k) ⁶ (y / k) ² + 1.917 720 Х 10 ^-16 (x / k) ⁴ (y / k) ⁴ + 2.788647 Х 10 ^-16 / k) ² (y / k) ⁶ + 1.506545 Х 10 ^-16 (y / k) ⁸ + 5.539970 Х 10 ^-20 (x / k) ⁸ (y / k) + 2.063952 Х 10 ^-18 / k) ⁶ (y / k) ³ + 3.426432 Х 10 ^-18 (x / k) ⁴ (y / k) ⁵ + 2.094280 Х 10 ^-18 (x / k) ² (y / k) ⁷ + 8.833037 Х 10 ^-20 (y / k) ⁹ + 2.932082 ^{Х 10 -20 · (x / k} ) 10 - 6.612407 Х 10 -22 · (x / k) 8 (y / k) 2 - 4.586598 Х 10 -20 · (x / k) 6 (y / k) 4 - ^{1.014695 Х 10 -19 · (x /} k) 4 (y / k) 6 - 9.517335 Х 10 -20 · (x / k) 2 (y / k) 8 - 3.388727 Х 10 -20 · (y / k) 10 ]

(Where Z _M2 is an autonomic surface shape parameter for the second mirror, x is the distance from the autonomic surface along the axis parallel to the sagittal plane, y is from the autonomic surface along the axis parallel to the tangent plane) Distance, k is D / 150mm)

According to an embodiment of the present invention, the autonomic curve shape parameter for the third mirror may be determined by Equation 5.

 [Equation 5]

_{Z M3 = k [-9.431401 Х 10} -4 · (x / k) 2 - 9.064491 Х 10 -4 · (y / k) 2 + 1.131963 Х 10 -7 · (x / k) 2 (y / k) - ^{3.088910 Х 10 -8 · (y /} k) 3 - 9.863945 Х 10 -10 · (x / k) 4 - 2.009904 Х 10 -9 · (x / k) 2 (y / k) 2 - 8.828431 Х 10 -10 ^{· (y / k) 4 +} 5.119344 Х 10 -13 · (x / k) 4 (y / k) + 2.919386 Х 10 -13 · (x / k) 2 (y / k) 3 - 4.598343 Х 10 -14 ^{· (y / k) 5 -} 7.559752 Х 10 -16 · (x / k) 6 - 4.678887 Х 10 -15 · (x / k) 4 (y / k) 2 - 5.209513 Х 10 -15 · (x / k ^{) 2 (y / k) 4} - 1.129971 Х 10 -15 · (y / k) 6 - 4.581130 Х 10 -17 · (x / k) 6 (y / k) - 2.778866 Х 10 -19 · (x / k ^{) 4 (y / k) 3} - 1.500174 Х 10 -18 · (x / k) 2 (y / k) 5 - 1.263548 Х 10 -17 · (y / k) 7 - 2.237052 Х 10 -19 · (x / ^{k) 8 - 6.129264 Х 10 -19} · (x / k) 6 (y / k) 2 - 9.465954 Х 10 -20 · (x / k) 4 (y / k) 4 - 2.451029 Х 10 -19 · (x ^{/ k) 2 (y / k} ) 6 - 6.147891 Х 10 -20 · (y / k) 8 + 3.266634 Х 10 -21 · (x / k) 8 (y / k) + 3.788574 Х 10 -21 · (x ^{/ k) 6 (y / k} ) 3 - 2.837298 Х 10 -21 · (x / k) 4 (y / k) 5 + 1.493862 Х 10 -21 · (x / k) 2 (y / k) 7 + 5.993513 ^{Х 10 -22 · (y / k} ) 9 + 9.64317 ^{3 Х 10 -24 · (x /} k) 10 + 5.941310 Х 10 -23 · (x / k) 8 (y / k) 2 - 1.268172 Х 10 -23 · (x / k) 6 (y / k) 4 + 2.686726 Х 10 ^-23 (x / k) ⁴ (y / k) ⁶ + 7.936686 Х 10 ^-25 (x / k) ² (y / k) ⁸ + 1.261056 Х 10 ^-24 (y / k) ¹⁰ ]

(Where Z _M3 is an autonomic surface shape parameter for the third mirror, x is the distance from the autonomic surface along an axis parallel to the sagittal plane, y is from the autonomic surface along the axis parallel to the tangent plane) Distance, k is D / 150mm)

According to an embodiment of the present invention, the first to third mirrors may be characterized in that they are freeform surface mirrors.

In the present invention, a non-axis arrangement relationship can be formed based on an optical design value corresponding to the ratio of the effective focal length to the effective aperture.

According to the present invention, coma aberration can be efficiently removed based on the autonomic curved shape parameter for the reflector.

The present invention can provide better optical performance than common axis non-reflective telescopes having the same effective aperture ratio from the optical design of the non-axis reflector with a ratio of effective focal length to effective aperture without coma aberration of 3.3.

The present invention can reduce the size of each reflector and the overall system by using three reflectors in the non-axis reflective optics device.

The present invention can reduce the cost of manufacturing a reflector by reducing the size of each reflector and the entire system using three reflectors.

1 is a view for explaining an optical path of a non-axis reflective optical system device.
FIG. 2 is a diagram for explaining image tilt and linear astigmatism on a non-axis autonomic curve.
3A is a view for explaining a cross section of a non-axis reflection optical system device from which linear astigmatism has been removed according to an embodiment of the present invention.
FIG. 3B is a view for explaining an optical axis beam transmitted by a non-axis reflection optical system device in which linear astigmatism has been removed according to an embodiment of the present invention.

Hereinafter, various embodiments of the present disclosure will be described with reference to the accompanying drawings.

The examples and terms used therein are not intended to limit the techniques described in this document to specific embodiments, but should be understood to include various modifications, equivalents, and / or alternatives to the examples.

In the following description of the various embodiments, when it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted.

In addition, terms to be described below are terms defined in consideration of functions in various embodiments, and may vary according to a user's or operator's intention or custom. Therefore, the definition should be made based on the contents throughout the specification.

In connection with the description of the drawings, similar reference numerals may be used for similar components.

Singular expressions may include plural expressions unless the context clearly indicates otherwise.

In this document, expressions such as "A or B" or "at least one of A and / or B" may include all possible combinations of items listed together.

Expressions such as "first," "second," "first," or "second," etc. may modify the components, regardless of order or importance, to distinguish one component from another. Used only and do not limit the components.

When any (eg first) component is said to be "connected (functionally or communicatively)" or "connected" to another (eg second) component, the other component is said other It may be directly connected to the component or may be connected through another component (for example, the third component).

In this specification, "configured to" is modified to have the ability to "suitable," "to," "to," depending on the context, for example, hardware or software. Can be used interchangeably with "made to", "doing", or "designed to".

In some situations, the expression “device configured to” may mean that the device “can” together with other devices or components.

For example, the phrase “processor configured (or configured to) perform A, B, and C” may be implemented by executing a dedicated processor (eg, an embedded processor) to perform its operation, or one or more software programs stored in a memory device. It may mean a general purpose processor (eg, a CPU or an application processor) capable of performing the corresponding operations.

In addition, the term 'or' means inclusive or 'inclusive or' rather than 'exclusive or'.

In other words, unless stated otherwise or unclear from the context, the expression 'x uses a or b' means any one of natural inclusive permutations.

The terms '.. unit' and '.. group' used below mean a unit for processing at least one function or operation, which may be implemented by hardware or software, or a combination of hardware and software.

1 is a view for explaining an optical path of a non-axis reflective optical system device.

Referring to FIG. 1, the mirror MIRROR in the non-axis reflective optical system does not have axis symmetry unlike the axisymmetric optical system. For example, the mirror may also be referred to as a reflector.

For example, in an optical system, the aberration may be expressed on a polynomial equation for an optical path length (OPL) of a light ray (main ray) passing through the center of the reflector and a light ray passing around the periphery (peripheral ray). For example, light rays may also be referred to as optical axis beams.

In addition, in the axisymmetric optical system device, the OPL has a low order third term, while in the non-axis reflective optical system device, the OPL may have a second degree as shown in Equation 1 below.

[Equation 1]

은 물체면에서 반사경까지의 광경로를 나타낼 수 있고,

는 반사경으로부터 상면까지의 광경로를 나타낼 수 있으며,

는 각각 이상적인 반사경에서의 물체면에서의 반사경까지의 광경로를 나타낼 수 있고,

는 반사경으로부터 상면까지의 광경로를 나타낼 수 있으며, x는 새지털(sagittal) 면에서 나란한 축을 따르는 자율곡면으로부터의 거리를 나타낼 수 있고, y는 탄젠셜(tangential) 면에서 나란한 축을 따르는 자율곡면으로부터의 거리를 나타낼 수 있으며, A_i(i=1,2,3)는 각 다항식의 계수를 나타낼 수 있고, O(4)는 4차 다항식 이상을 나타낼 수 있다.According to [Equation 1],

Represents the light path from the object plane to the reflector,

Represents the light path from the reflector to the top surface,

Can each represent the optical path from the ideal reflector to the reflector at the object plane,

Can represent the optical path from the reflector to the top surface, x can represent the distance from the autonomic surface along the axis parallel to the sagittal plane, and y from the autonomic surface along the axis parallel to the tangent plane. A _i (i = 1,2,3) may represent the coefficient of each polynomial, and O (4) may represent more than a fourth order polynomial.

은 비축 반사 광학계 장치에서 상면의 기울어짐 및 중심축과 시야의 중심축이 일치하지 않아 발생되는 선형 비점수차(linear astigmatism)를 나타낼 수 있다.OPL

In the non-axis reflective optical system, linear astigmatism may be generated due to the inclination of the image plane and the central axis and the central axis of the field of view.

은 비축 반사 광학계 장치에서 중심축의 거리 또는 물체에 대한 광선이 모아지지 않음에 따라 발생되는 코마 수차(coma aberration)를 나타낼 수 있다.Also, OPL

In the non-axis reflective optical system, the coma aberration may be generated as the distance of the central axis or the light beam for the object is not collected.

FIG. 2 is a diagram for explaining image tilt and linear astigmatism on a non-axis autonomic curve.

Referring to FIG. 2, the linear astigmatism may be the most lethal aberration in the reflector of the off-axis reflection optics device because the first order is lower than the general siedel aberration. Therefore, linear astigmatism must be eliminated to ensure visibility.

For example, linear astigmatism can be eliminated by satisfying Equation 2 below in a non-axis reflective optical system device in which reflecting mirrors sharing a focal point.

[Equation 2]

는 중심 광선의 입사각을 나타낼 수 있고, m은 주경을 나타낼 수 있으며, s는 부경을 나타낼 수 있다.According to Equation 2, R may represent the center radius of curvature of the parent diameter including the reflector, l may represent the distance between the focus and the reflector,

May represent an angle of incidence of the center ray, m may represent a principal diameter, and s may represent a minor diameter.

For example, the reflector may include a major diameter and a minor diameter.

3A is a view for explaining a cross section of a non-axis reflection optical system device from which linear astigmatism has been removed according to an embodiment of the present invention.

Referring to FIG. 3A, the non-axis reflection optical system device may include a first mirror M1, a second mirror M2, and a third mirror M3. For example, the reflector may include a first mirror M1, a second mirror M2, and a third mirror M3.

The first mirror M1 may be a concave mirror, the second mirror M2 may be a convex mirror, and the third mirror M3 may be a concave mirror.

In addition, the first mirror M1, the second mirror M2, and the third mirror M3 may be freeform surface mirrors.

In the non-axis reflective optical system, an optical design value corresponding to the ratio of the effective focal length to the effective aperture is determined in a state where linear astigmatism is removed, and an off-axis arrangement relationship is formed based on the optical design value. Can be.

According to one embodiment of the invention the effective aperture reaches the surface of the first mirror M1 and means the diameter of the bundle of light parallel to the optical axis, and the ratio of the effective focal length to the effective aperture is from the object plane to the mirror surface. It means relatively representing the transmission ratio of the reached brightness.

According to one aspect of the present invention, the non-axis reflective optical system device may further include an additional mirror as well as the first mirror M1, the second mirror M2, and the third mirror M3.

In addition, the additional mirror may be provided corresponding to the non-axis arrangement relationship of the first mirror M1, the second mirror M2, and the third mirror M3.

According to an embodiment of the present invention, when the effective aperture is D and the ratio of the effective focal length to the effective aperture is 3.3, the optical design value may have an effective focal length of 3.3D.

Further, the distance d ₁ from the common focus of the first mirror and the second mirror to the first mirror is 4.16D, and the distance d from the shared focus of the second mirror and the third mirror to the third mirror d. ₂ is 5.208D, and the distance d ₃ from the third mirror to the top surface may be 2.753D.

In addition, the incident angle i ₁ of the light beam incident from the object plane to the first mirror is 16 °, the incident angle i ₂ of the light beam incident from the first mirror to the second mirror is 22 °, and is incident from the second mirror to the third mirror. The angle of incidence i ₃ of the light beam to be may be 11.3755 °.

For example, the optical design value has an effective focal length of 500 mm when the effective aperture D is 150 mm, the distance d ₁ from the shared focus of the first mirror and the second mirror to the first mirror is 625 mm, and the second mirror The distance d ₂ from the co-focus of the third mirror to the third mirror may be 781.1917 mm, and the distance d ₃ from the third mirror to the top surface may be 413.5042 mm.

In addition, the optical design value is that the incidence angle i ₁ of the light beam incident from the object plane to the first mirror is 16 degrees, the incidence angle i ₂ of the light beam incident from the first mirror to the second mirror is 22 degrees, and the third mirror to the third The incident angle i ₃ of the light beam incident on the mirror may be 11.3755 °.

In addition, the field of view in the optical design may be 5.51 ° x 4.13 °.

In other words, when the aperture of the non-axis reflection optical system device increases or decreases according to the optical design value, the entire size can be adjusted at the same ratio.

Therefore, the non-axis reflection optical system device according to the present invention can secure a sufficient space for the filter wheel to be mounted in front of the sensor when astronomical observation.

According to one embodiment of the present invention, in the non-axis reflective optics device, an optical design value corresponding to the ratio 3.3 of the effective focal length to the effective aperture may be determined as described above.

Thus, optical design values corresponding to various effective focal lengths to effective aperture ratios can be determined, and various non-axis arrangement relationships can be formed.

According to an embodiment of the present invention, the non-axis reflective optical system device may have a coma aberration, based on autonomic curved shape parameters for the first mirror M1, the second mirror M2, and the third mirror M3. At least one of astigmatism and a curvature of image field may be removed.

In the present invention, a non-axis arrangement relationship can be formed based on an optical design value corresponding to the ratio of the effective focal length to the effective aperture.

In addition, the present invention can efficiently remove coma aberration based on the autonomic curved shape parameter for the reflector.

In one example, the non-axis reflective optical system device may determine the autonomic curved shape parameter for the first mirror M1 by [Equation 3].

[Equation 3]

_{Z M1 = k [-4.161198 Х 10} -4 · (x / k) 2 - 3.845047 Х 10 -4 · (y / k) 2 + 9.641603 Х 10 -8 · (x / k) 2 (y / k) + 5.573436 Х 10 ^-10 (y / k) ³ + 1.010284 Х 10 ^-10 (x / k) ⁴ + 1.776302 Х 10 ^-10 (x / k) ² (y / k) ² + 1.006174 Х 10 ^{-10 · (y / k) 4 -} 1.548852 Х 10 -13 · (x / k) 4 (y / k) - 3.211816 Х 10 -13 · (x / k) 2 (y / k) 3 - 8.606285 Х 10 -14 ^{· (y / k) 5 -} 1.818727 Х 10 -15 · (x / k) 6 - 1.040144 Х 10 -15 · (x / k) 4 (y / k) 2 - 1.296413 Х 10 -15 · (x / k ^{) 2 (y / k) 4} + 1.557898 Х 10 -15 · (y / k) 6 + 2.013918 Х 10 -17 · (x / k) 6 (y / k) + 4.582719 Х 10 -17 · (x / k ^{) 4 (y / k) 3} + 2.978542 Х 10 -17 · (x / k) 2 (y / k) 5 - 1.386084 Х 10 -18 · (y / k) 7 + 2.495899 Х 10 -19 · (x / k) ⁸ + 6.754 432 Х 10 ^-20 (x / k) ⁶ (y / k) ² + 4.564714 Х 10 ^-19 (x / k) ⁴ (y / k) ⁴ + 2.408273 Х 10 ^{-19 / k) 2 (y / k} ) 6 - 2.212558 Х 10 -19 · (y / k) 8 - 1.330036 Х 10 -21 · (x / k) 8 (y / k) - 3.469298 Х 10 -21 · (x ^{/ k) 6 (y / k} ) 3 - 5.065371 Х 10 -21 · (x / k) 4 (y / k) 5 - 1.606291 Х 10 -21 · (x / k) 2 (y / k) 7 + 3.926423 ^{Х 10 -23 · (y / k} ) 9 - 1.245 ^{698 Х 10 -23 · (x /} k) 10 + 7.462334 Х 10 -24 · (x / k) 8 (y / k) 2 - 3.519848 Х 10 -23 · (x / k) 6 (y / k) 4 ^{- 3.147035 Х 10 -23 · (x} / k) 4 (y / k) 6 - 1.501654 Х 10 -23 · (x / k) 2 (y / k) 8 + 1.174413 Х 10 -23 · (y / k) ¹⁰ ]

In one example, the non-axis reflection optical system device may determine the autonomic curved shape parameter for the second mirror M2 by [Equation 4].

[Equation 4]

_{Z M2 = k [-1.378580 Х 10} -3 · (x / k) 2 - 1.185124 Х 10 -3 · (y / k) 2 + 3.290996 Х 10 -7 · (x / k) 2 (y / k) - ^{8.034641 Х 10 -7 · (y /} k) 3 - 2.671748 Х 10 -9 · (x / k) 4 - 4.978006 Х 10 -9 · (x / k) 2 (y / k) 2 - 2.012845 Х 10 -9 ^{· (y / k) 4 -} 2.356142 Х 10 -13 · (x / k) 4 (y / k) - 6.601985 Х 10 -12 · (x / k) 2 (y / k) 3 - 6.872502 Х 10 -12 ^{· (y / k) 5 +} 1.476119 Х 10 -13 · (x / k) 6 - 1.182993 Х 10 -13 · (x / k) 4 (y / k) 2 - 3.134349 Х 10 -13 · (x / k ^{) 2 (y / k) 4} - 2.488053 Х 10 -13 · (y / k) 6 - 2.525948 Х 10 -16 · (x / k) 6 (y / k) - 4.882015 Х 10 -15 · (x / k ^{) 4 (y / k) 3} - 5.524294 Х 10 -15 · (x / k) 2 (y / k) 5 - 5.328826 Х 10 -16 · (y / k) 7 - 1.233799 Х 10 -16 · (x / k) ⁸ + 2.437263 Х 10 ^-17 (x / k) ⁶ (y / k) ² + 1.917 720 Х 10 ^-16 (x / k) ⁴ (y / k) ⁴ + 2.788647 Х 10 ^{-16 / k) 2 (y / k} ) 6 + 1.506545 Х 10 -16 · (y / k) 8 + 5.539970 Х 10 -20 · (x / k) 8 (y / k) + 2.063952 Х 10 -18 · (x / k) ⁶ (y / k) ³ + 3.426432 Х 10 ^-18 (x / k) ⁴ (y / k) ⁵ + 2.094280 Х 10 ^-18 (x / k) ² (y / k) ⁷ + 8.833037 Х 10 ^-20 (y / k) ⁹ + 2.932082 ^{Х 10 -20 · (x / k} ) 10 - 6.612407 Х 10 -22 · (x / k) 8 (y / k) 2 - 4.586598 Х 10 -20 · (x / k) 6 (y / k) 4 - ^{1.014695 Х 10 -19 · (x /} k) 4 (y / k) 6 - 9.517335 Х 10 -20 · (x / k) 2 (y / k) 8 - 3.388727 Х 10 -20 · (y / k) 10 ]

According to one embodiment of the present invention, the non-axis reflective optical system device may determine the autonomic curved shape parameter for the third mirror M3 by [Equation 5].

[Equation 5]

_{Z M3 = k [-9.431401 Х 10} -4 · (x / k) 2 - 9.064491 Х 10 -4 · (y / k) 2 + 1.131963 Х 10 -7 · (x / k) 2 (y / k) - ^{3.088910 Х 10 -8 · (y /} k) 3 - 9.863945 Х 10 -10 · (x / k) 4 - 2.009904 Х 10 -9 · (x / k) 2 (y / k) 2 - 8.828431 Х 10 -10 ^{· (y / k) 4 +} 5.119344 Х 10 -13 · (x / k) 4 (y / k) + 2.919386 Х 10 -13 · (x / k) 2 (y / k) 3 - 4.598343 Х 10 -14 ^{· (y / k) 5 -} 7.559752 Х 10 -16 · (x / k) 6 - 4.678887 Х 10 -15 · (x / k) 4 (y / k) 2 - 5.209513 Х 10 -15 · (x / k ^{) 2 (y / k) 4} - 1.129971 Х 10 -15 · (y / k) 6 - 4.581130 Х 10 -17 · (x / k) 6 (y / k) - 2.778866 Х 10 -19 · (x / k ^{) 4 (y / k) 3} - 1.500174 Х 10 -18 · (x / k) 2 (y / k) 5 - 1.263548 Х 10 -17 · (y / k) 7 - 2.237052 Х 10 -19 · (x / ^{k) 8 - 6.129264 Х 10 -19} · (x / k) 6 (y / k) 2 - 9.465954 Х 10 -20 · (x / k) 4 (y / k) 4 - 2.451029 Х 10 -19 · (x ^{/ k) 2 (y / k} ) 6 - 6.147891 Х 10 -20 · (y / k) 8 + 3.266634 Х 10 -21 · (x / k) 8 (y / k) + 3.788574 Х 10 -21 · (x ^{/ k) 6 (y / k} ) 3 - 2.837298 Х 10 -21 · (x / k) 4 (y / k) 5 + 1.493862 Х 10 -21 · (x / k) 2 (y / k) 7 + 5.993513 Х 10 ^-22 (y / k) ⁹ + 9.64317 ^{3 Х 10 -24 · (x /} k) 10 + 5.941310 Х 10 -23 · (x / k) 8 (y / k) 2 - 1.268172 Х 10 -23 · (x / k) 6 (y / k) 4 + 2.686726 Х 10 ^-23 (x / k) ⁴ (y / k) ⁶ + 7.936686 Х 10 ^-25 (x / k) ² (y / k) ⁸ + 1.261056 Х 10 ^-24 (y / k) ¹⁰ ]

In Equations 3 to 5, Z _M1 may be a height from a position where the center ray of the first mirror touches, Z _M2 may be a height from a position where the center ray of the second mirror touches, Z _M3 may be a height from the position where the center ray of the third mirror touches.

In addition, in [Equation 3] to [Equation 5], x is the distance from the autonomic surface along the axis parallel to the sagittal plane, y is the distance from the autonomous surface along the axis parallel to the tangent plane, k may be D / 150 mm.

If Equation 3, Equation 4, and Equation 5 are summarized, the autonomic curve shape parameter may be represented by Equation 6.

[Equation 6]

Z (x, y) = a ₀ x + a ₁ y + a ₂ x ² + a ₃ xy + a ₄ y ² + a ₅ x ³ + a ₆ x ² y + a ₇ xy ² + a ₈ y ³ + … + a ₆₄ y ¹⁰

According to Equation 6, Z may represent an autonomic surface shape parameter, x may represent a distance from the autonomic surface along an axis parallel to the sagittal plane, and y may be from an autonomic surface along an axis parallel to the tangent plane. It can represent the distance of.

 In addition, Equation 3, Equation 4, and Equation 5 may be summarized as Table 1 below.

TABLE 1

In Equation 6, a is a coefficient of the polynomial, x and y are indices, and all coefficients not shown in Table 1 may be zero.

FIG. 3B is a view for explaining an optical axis beam transmitted by a non-axis reflection optical system device in which linear astigmatism has been removed according to an embodiment of the present invention.

3B may illustrate light transmitted in an optical structure of a non-axis reflecting telescope.

Referring to FIG. 3B, the non-axis reflection optical system device may include a first mirror M1, a second mirror M2, and a third mirror M3.

The non-axis reflective optical system device receives an optical axis beam from an object plane at the first mirror M1 and transmits the optical axis beam to the second mirror M2, and the second mirror M2 transmits the optical axis beam to the third mirror M3. The third mirror M3 may transmit the optical axis beam to the upper surface.

The present invention can provide better optical performance than common axis non-reflective telescopes having the same effective aperture ratio from the optical design of the non-axis reflector with a ratio of effective focal length to effective aperture without coma aberration of 3.3.

In addition, the present invention can reduce the size of each reflector and the entire system by using three reflectors in the non-axis reflective optics device.

In addition, the present invention can reduce the cost of manufacturing non-reflective reflectors by using the three reflectors to reduce the size of each reflector and the entire system.

In addition, although the non-reflective optical system of Korean Patent No. 10-1789383 uses two reflectors, the non-reflective optical system device of the present invention has a difference of using three reflectors.

The method according to the embodiment may be embodied in the form of program instructions that can be executed by various computer means and recorded in a computer readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination.

The program instructions recorded on the media may be those specially designed and constructed for the purposes of the embodiments, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, such as floppy disks. Magneto-optical media, and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like.

Examples of program instructions include not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

Although the embodiments have been described by the limited embodiments and the drawings as described above, various modifications and variations are possible to those skilled in the art from the above description. For example, the described techniques may be performed in a different order than the described method, and / or components of the described systems, structures, devices, circuits, etc. may be combined or combined in a different form than the described method, or other components. Or even if replaced or substituted by equivalents, an appropriate result can be achieved.

Therefore, other implementations, other embodiments, and equivalents to the claims are within the scope of the claims that follow.

M1: first mirror M2: second mirror
M3: third mirror D: effective aperture of the first mirror
d ₁ : distance from the first mirror to the second mirror
d ₂ : distance from the second mirror to the third mirror
d ₃ : distance from the third mirror to the upper surface
i ₁ : the incident angle of light rays incident from the object plane into the first mirror
i ₂ : incident angle of light incident from the first mirror to the second mirror
i ₃ : Incident angle of light rays incident from the second mirror to the third mirror
Z _M1 : Autonomous surface shape parameter for the first mirror
Z _M2 : Autonomic Surface Shape Parameter for Second Mirror
Z _M3 : Autonomic Surface Shape Parameters for Third Mirror

Claims (6)

The optical design value corresponding to the ratio of the effective focal length to the effective aperture is determined in a state in which the linear astigmatism is removed, and an off-axis arrangement relationship is formed based on the optical design value. In
When the effective aperture is D and the ratio of the effective focal length to the effective aperture is 3.3, the optical design value has the effective focal length of 3.3D and the common focus of the first mirror and the second mirror is common. from said first and the distance from the mirror to d ₁ is 4.16D, and the second distance from the third mirror and from the mirror to the shared focus (common focus) of the third mirror is 5.208D d _2, the third The distance d ₃ from the mirror to the upper surface is 2.753D, the incident angle i ₁ of the light beam incident from the object plane to the first mirror is 16 °, and the incident angle i ₂ of the light beam incident from the first mirror to the second mirror is 2 °. Is 22 °, and the incident angle i ₃ of the light beam incident from the second mirror to the third mirror is 11.3755 °.
Non-axis reflective optics device with linear astigmatism removed.
The method of claim 1,
At least one of coma aberration, astigmatism, or top curvature is removed based on an autonomic curved shape parameter for at least one of the first mirror, the second mirror, or the third mirror.
Non-axis reflective optics device with linear astigmatism removed.
The method of claim 2,
Autonomic surface shape parameter for the first mirror is characterized in that determined by [Equation 3]
Non-axis reflective optics device with linear astigmatism removed.
[Equation 3]
_{Z M1 = k [-4.161198 Х 10} -4 · (x / k) 2 - 3.845047 Х 10 -4 · (y / k) 2 + 9.641603 Х 10 -8 · (x / k) 2 (y / k) + 5.573436 Х 10 ^-10 (y / k) ³ + 1.010284 Х 10 ^-10 (x / k) ⁴ + 1.776302 Х 10 ^-10 (x / k) ² (y / k) ² + 1.006174 Х 10 ^{-10 · (y / k) 4 -} 1.548852 Х 10 -13 · (x / k) 4 (y / k) - 3.211816 Х 10 -13 · (x / k) 2 (y / k) 3 - 8.606285 Х 10 -14 ^{· (y / k) 5 -} 1.818727 Х 10 -15 · (x / k) 6 - 1.040144 Х 10 -15 · (x / k) 4 (y / k) 2 - 1.296413 Х 10 -15 · (x / k ) ² (y / k) ⁴ + 1.557898 Х 10 ^-15 (y / k) ⁶ + 2.013918 Х 10 ^-17 (x / k) ⁶ (y / k) + 4.582719 Х 10 ^{-17 ) 4 (y / k) 3} + 2.978542 Х 10 -17 · (x / k) 2 (y / k) 5 - 1.386084 Х 10 -18 · (y / k) 7 + 2.495899 Х 10 -19 · (x / ^{k) 8 + 6.754432 Х 10 -20} · (x / k) 6 (y / k) 2 + 4.564714 Х 10 -19 · (x / k) 4 (y / k) 4 + 2.408273 Х 10 -19 · (x ^{/ k) 2 (y / k} ) 6 - 2.212558 Х 10 -19 · (y / k) 8 - 1.330036 Х 10 -21 · (x / k) 8 (y / k) - 3.469298 Х 10 -21 · (x ^{/ k) 6 (y / k} ) 3 - 5.065371 Х 10 -21 · (x / k) 4 (y / k) 5 - 1.606291 Х 10 -21 · (x / k) 2 (y / k) 7 + 3.926423 ^{Х 10 -23 · (y / k} ) 9 - 1.245 ^{698 Х 10 -23 · (x /} k) 10 + 7.462334 Х 10 -24 · (x / k) 8 (y / k) 2 - 3.519848 Х 10 -23 · (x / k) 6 (y / k) 4 ^{- 3.147035 Х 10 -23 · (x} / k) 4 (y / k) 6 - 1.501654 Х 10 -23 · (x / k) 2 (y / k) 8 + 1.174413 Х 10 -23 · (y / k) ¹⁰ ]
(Where Z _M1 is an autonomic surface shape parameter for the first mirror, x is the distance from the autonomic surface along the axis parallel to the sagittal plane, y is from the autonomic surface along the axis parallel to the tangential plane) Distance, k is D / 150mm)
The method of claim 3,
The autonomic surface shape parameter for the second mirror is determined by Equation 4
Non-axis reflective optics device with linear astigmatism removed.
[Equation 4]
_{Z M2 = k [-1.378580 Х 10} -3 · (x / k) 2 - 1.185124 Х 10 -3 · (y / k) 2 + 3.290996 Х 10 -7 · (x / k) 2 (y / k) - ^{8.034641 Х 10 -7 · (y /} k) 3 - 2.671748 Х 10 -9 · (x / k) 4 - 4.978006 Х 10 -9 · (x / k) 2 (y / k) 2 - 2.012845 Х 10 -9 ^{· (y / k) 4 -} 2.356142 Х 10 -13 · (x / k) 4 (y / k) - 6.601985 Х 10 -12 · (x / k) 2 (y / k) 3 - 6.872502 Х 10 -12 ^{· (y / k) 5 +} 1.476119 Х 10 -13 · (x / k) 6 - 1.182993 Х 10 -13 · (x / k) 4 (y / k) 2 - 3.134349 Х 10 -13 · (x / k ^{) 2 (y / k) 4} - 2.488053 Х 10 -13 · (y / k) 6 - 2.525948 Х 10 -16 · (x / k) 6 (y / k) - 4.882015 Х 10 -15 · (x / k ^{) 4 (y / k) 3} - 5.524294 Х 10 -15 · (x / k) 2 (y / k) 5 - 5.328826 Х 10 -16 · (y / k) 7 - 1.233799 Х 10 -16 · (x / k) ⁸ + 2.437263 Х 10 ^-17 (x / k) ⁶ (y / k) ² + 1.917 720 Х 10 ^-16 (x / k) ⁴ (y / k) ⁴ + 2.788647 Х 10 ^-16 / k) ² (y / k) ⁶ + 1.506545 Х 10 ^-16 (y / k) ⁸ + 5.539970 Х 10 ^-20 (x / k) ⁸ (y / k) + 2.063952 Х 10 ^{-18 / k) 6 (y / k} ) 3 + 3.426432 Х 10 -18 · (x / k) 4 (y / k) 5 + 2.094280 Х 10 -18 · (x / k) 2 (y / k) 7 + 8.833037 Х 10 ^-20 (y / k) ⁹ + 2.932082 ^{Х 10 -20 · (x / k} ) 10 - 6.612407 Х 10 -22 · (x / k) 8 (y / k) 2 - 4.586598 Х 10 -20 · (x / k) 6 (y / k) 4 - ^{1.014695 Х 10 -19 · (x /} k) 4 (y / k) 6 - 9.517335 Х 10 -20 · (x / k) 2 (y / k) 8 - 3.388727 Х 10 -20 · (y / k) 10 ]
(Where Z _M2 is an autonomic surface shape parameter for the second mirror, x is the distance from the autonomic surface along the axis parallel to the sagittal plane, y is from the autonomic surface along the axis parallel to the tangent plane) Distance, k is D / 150mm)
The method of claim 4, wherein
The autonomic surface shape parameter for the third mirror is characterized by [Equation 5]
Non-axis reflective optics device with linear astigmatism removed.
[Equation 5]
_{Z M3 = k [-9.431401 Х 10} -4 · (x / k) 2 - 9.064491 Х 10 -4 · (y / k) 2 + 1.131963 Х 10 -7 · (x / k) 2 (y / k) - ^{3.088910 Х 10 -8 · (y /} k) 3 - 9.863945 Х 10 -10 · (x / k) 4 - 2.009904 Х 10 -9 · (x / k) 2 (y / k) 2 - 8.828431 Х 10 -10 ^{· (y / k) 4 +} 5.119344 Х 10 -13 · (x / k) 4 (y / k) + 2.919386 Х 10 -13 · (x / k) 2 (y / k) 3 - 4.598343 Х 10 -14 ^{· (y / k) 5 -} 7.559752 Х 10 -16 · (x / k) 6 - 4.678887 Х 10 -15 · (x / k) 4 (y / k) 2 - 5.209513 Х 10 -15 · (x / k ^{) 2 (y / k) 4} - 1.129971 Х 10 -15 · (y / k) 6 - 4.581130 Х 10 -17 · (x / k) 6 (y / k) - 2.778866 Х 10 -19 · (x / k ^{) 4 (y / k) 3} - 1.500174 Х 10 -18 · (x / k) 2 (y / k) 5 - 1.263548 Х 10 -17 · (y / k) 7 - 2.237052 Х 10 -19 · (x / ^{k) 8 - 6.129264 Х 10 -19} · (x / k) 6 (y / k) 2 - 9.465954 Х 10 -20 · (x / k) 4 (y / k) 4 - 2.451029 Х 10 -19 · (x ^{/ k) 2 (y / k} ) 6 - 6.147891 Х 10 -20 · (y / k) 8 + 3.266634 Х 10 -21 · (x / k) 8 (y / k) + 3.788574 Х 10 -21 · (x ^{/ k) 6 (y / k} ) 3 - 2.837298 Х 10 -21 · (x / k) 4 (y / k) 5 + 1.493862 Х 10 -21 · (x / k) 2 (y / k) 7 + 5.993513 Х 10 ^-22 (y / k) ⁹ + 9.64317 ^{3 Х 10 -24 · (x /} k) 10 + 5.941310 Х 10 -23 · (x / k) 8 (y / k) 2 - 1.268172 Х 10 -23 · (x / k) 6 (y / k) 4 + 2.686726 Х 10 ^-23 (x / k) ⁴ (y / k) ⁶ + 7.936686 Х 10 ^-25 (x / k) ² (y / k) ⁸ + 1.261056 Х 10 ^-24 (y / k) ¹⁰ ]
(Where Z _M3 is an autonomic surface shape parameter for the third mirror, x is the distance from the autonomic surface along the axis parallel to the sagittal plane, y is from the autonomic surface along the axis parallel to the tangential plane) Distance, k is D / 150mm)
The method of claim 1,
The first to third mirrors are freeform surface mirrors.
Non-axis reflective optics device with linear astigmatism removed.

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