KR101789383B1 - Off-axis optic device - Google Patents

Off-axis optic device Download PDF

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KR101789383B1
KR101789383B1 KR1020150163795A KR20150163795A KR101789383B1 KR 101789383 B1 KR101789383 B1 KR 101789383B1 KR 1020150163795 A KR1020150163795 A KR 1020150163795A KR 20150163795 A KR20150163795 A KR 20150163795A KR 101789383 B1 KR101789383 B1 KR 101789383B1
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mirror
optical system
distance
curved surface
autonomous
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KR20170059625A (en
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박수종
장승혁
김건희
김상혁
전민우
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경희대학교 산학협력단
재단법인 다차원 스마트 아이티 융합시스템 연구단
한국기초과학지원연구원
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/02—Catoptric systems, e.g. image erecting and reversing system
    • G02B17/06—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror
    • G02B17/0605—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using two curved mirrors
    • G02B17/0615—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using two curved mirrors off-axis or unobscured systems in wich all of the mirrors share a common axis of rotational symmetry

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Abstract

The present invention is based on the finding that an optical design corresponding to a ratio of effective focal length to effective aperture is determined in the absence of linear astigmatism and a non-axial reflection An optical system device is disclosed.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to a non-

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a non-axis reflection optical system device, and more particularly, to a non-axis reflection optical system in which a non-axis reflection optical system, in which a non-axis reflection relation is formed based on optical design values corresponding to ratios of effective focal lengths (Entrance Pupil Diameter) ≪ / RTI >

The space telescope mounted on the satellite should be of a structure that can withstand impacts when launching the satellite, and may be a refractive optical telescope or a reflective optical telescope (eg, a Cassegrain-based reflective telescope).

Refractive optical telescopes, on the other hand, have excellent optical performance, but they may not be suitable for space telescopes because of the limited material and size of the lenses.

In addition, since the spherical mirror, which is a convex mirror, is placed in front of the main reflecting mirror, the reflecting optical system telescope, which is most widely used as a space telescope, can be diffracted and scattered by the sub- And there may be a constraint on fixing the sub-radius.

As a new alternative to this, non-reflecting optical system devices (e. G., Stocked Cassegrain telescopes) may be suitable as space telescopes.

In addition, since the non-axial reflection optical system device is free from thermal radiation noise due to a minor radius, it can be used as an infrared telescope, and when the reflector is made of aluminum material, the reflector can be firmly fixed and can be used as a military infrared telescope.

In addition, since the non-axial reflection optical system device has no scattered light due to the sub-diameter, it can be suitable as an astronomical telescope for astronomical research. For example, an astronomical telescope may be suitable as a coronagraph telescope used in solar observations and may be suitable as a coronagraph telescope used to find extraterrestrial planets.

Further, in the case where a small-size reflector can be manufactured in a large quantity, the non-axis reflective optical system can be suitable as a small-sized telescope for an amateur because the structure of the lens barrel becomes simple and can be spread at a low unit price.

Therefore, the non-axis reflection optical system apparatus can be widely used in various fields mentioned above or applications thereof.

However, in the non-axial reflection optical system device, linear astigmatism may occur due to the fact that the central axis of the optical system does not coincide with the central axis of the visual field, and may be caused by the distance of the central axis or the non- Coma aberration may exist.

Previously, linear astigmatism was eliminated through numerical optimization using lens design software such as Zemax and CodeV, but linear astigmatism was only partially removed and could not be removed completely.

Further, conventionally, coma aberration is removed through a relational expression or an equation, but there is a difficulty in calculating an optimized parameter.

In the prior art (US7274513), two confocal reflector systems were constructed as confocal. However, as a result of the hermetically induced aberration, the linear astigmatism among the optical aberrations represented by the higher order term can be eliminated There was a problem.

Korean Patent Publication No. 20070115739 (Dec. 2007), "Information Lens Having Improved Non- Korean Patent No. 0504388 (June, 2005), "Non-Aspherical Multifocal Optical Lens" Korean Unexamined Patent Publication No. 20120054754 (May 31, 2012), "Optical Lens Containing Non-Aspheric Areas" U.S. Patent No. 7274513 (Sep. 25, 2007), "Off-axis projection optics and extreme ultraviolet lithography apparatus employing the same"

The present invention provides a non-axial reflective optical system device in which a non-axial alignment relationship is established based on an optical design value corresponding to a ratio of effective focal length to effective aperture.

Further, the present invention provides a non-axial reflecting optical system device in which coma aberration is efficiently removed based on autonomous curved surface shape parameters for a reflecting mirror.

In addition, the present invention provides a non-retroreflective optical system device having optical performance superior to that of a non-retroreflective telescope having a same effective aperture ratio from the optical design of a non-retroreflective telescope with a coma aberration-free effective focal length to a effective aperture ratio of 2 .

 In a non-axial reflective optical system according to an embodiment of the present invention, an optical design value corresponding to a ratio of an effective focal length to an effective aperture is determined in a state in which linear astigmatism is removed, and based on the optical design, -axis) arrangement relationship.

When the effective aperture diameter is D and the ratio of the effective focal length to the effective aperture diameter is 2, the optical design value is the effective focal length of 2D, from the second and the distance d 1 is 4D up to the mirror, wherein the distance d 2 is 4.82842D up to the top from the second mirror, the incidence angle i on the object surface 1 is 30 ° of light incident to the first mirror, wherein And an incident angle i 2 of a ray incident on the second mirror in the first mirror is 13.4495 °.

Also, in the non-shore reflecting optical system according to the embodiment of the present invention, at least one of coma aberration, astigmatism, and curvature of field is removed based on autonomous curved surface shape parameters of the first mirror and the second mirror And the aberration is removed.

The autonomic curved surface shape parameter may be characterized by being determined by [Expression 3] and [Expression 4].

[Equation 3]

Z M1 = k [2.0412 × 10 -3 and (x / k) 2 + 1.5309 × 10 -3 and (y / k) 2 + 3.5572 × 10 -6 and (x / k) 2 (y / k) + 2.6963 × 10 -6 and (y / k) 3 + 5.0571 × 10 -8 and (x / k) 4 + 7.5766 × 10 -8 and (x / k) 2 (y / k) 2 + 3.0727 × 10 -8 and (y / k) 4 + 2.9754 × 10 -10 and (x / k) 4 (y / k) + 4.1891 × 10 -10 and (x / k) 2 (y / k) 3 + 1.4090 × 10 -10 and (y / k) 5 - 1.4605 × 10 -11 and (x / k) 6 - 6.1711 × 10 -12 and (x / k) 4 (y / k) 2 + 2.6243 × 10 -12 and (x / k) 2 (y / k) 4 + 6.5926 × 10 -13 and (y / k) 6 + 1.8594 × 10 -13 and (x / k) 6 (y / k) - 2.8353 × 10 -13 and (x / k) 4 (y / k) 3 - 1.5301 × 10 -13 and (x / k) 2 (y / k) 5 - 8.8929 × 10 -15 and (y / k) 7 + 1.9815 × 10 -14 and (x / k ) 8 + 1.9898 × 10 -14 and (x / k) 6 (y / k) 2 + 1.0456 × 10 -14 and (x / k) 4 (y / k) 4 + 2.8057 × 10 -16 and (x / k) 2 (y / k) 6 + 4.1329 × 10 -16 and (y / k) 8 + 1.3180 × 10 -16 and (x / k) 8 (y / k) + 2.9654 × 10 -16 and (x / k) 6 (y / k) 3 - 2.1533 × 10 -16 and (x / k) 4 (y / k) 5 + 9.0877 × 10 -17 and (x / k) 2 (y / k) 7 + 4.8722 × 10-18 and (y / k) 9 - 7.9424 × 10 -18 and (x / k) 10 - 8.2722 × 10 -18 and (x / k) 8 (y / k) 2 - 7.6216 × 10 -18 Pa ( x / k) 6 (y / k) 4 - 1.2784 × 10 -18 and (x / k) 4 (y / k) 6 + 8.2116 × 10 -19 and (x / k) 2 (y / k) 8 - 7.8028 × 10 -20 and (y / k) 10 ]

 [Equation 4]

Z M2 = k [1.8176 × 10 -3 and (x / k) 2 + 1.7193 × 10 -3 and (y / k) 2 - 2.5759 × 10 -7 and (x / k) 2 (y / k) - 2.4328 × 10 -7 and (y / k) 3 + 6.7443 × 10 -9 and (x / k) 4 + 1.2961 × 10 -8 and (x / k) 2 (y / k) 2 + 6.2515 × 10 -9 and (y / k) 4 - 3.6149 × 10 -12 and (x / k) 4 (y / k) - 6.7564 × 10 -12 and (x / k) 2 (y / k) 3 - 2.5391 × 10 -12 and (y / k) 5 + 2.0621 × 10 -13 and (x / k) 6 + 4.9951 × 10 -13 and (x / k) 4 (y / k) 2 + 3.6649 × 10 -13 and (x / k) 2 (y / k) 4 + 5.4035 × 10 -14 and (y / k) 6 - 3.0463 × 10 -16 and (x / k) 6 (y / k) - 4.1040 × 10 -16 and (x / k) 4 (y / k) 3 - 3.2806 × 10 -16 and (x / k) 2 (y / k) 5 - 2.1804 × 10 -16 and (y / k) 7 - 3.9709 × 10 -17 and (x / k ) 8 - 1.4260 × 10 -16 and (x / k) 6 (y / k) 2 - 1.5951 × 10 -16 and (x / k) 4 (y / k) 4 - 6.1253 × 10 -17 and (x / k) 2 (y / k) 6 + 4.5582 × 10 -19 and (y / k) 8 + 6.4526 × 10 -20 and (x / k) 8 (y / k) + 1.1905 × 10 -19 and (x / k) 6 (y / k) 3 + 3.6559 × 10 -20 and (x / k) 4 (y / k) 5 + 3.7553 × 10 -20 and (x / k) 2 (y / k) 7 + 1.7630 × 10-20 and (y / k) 9 + 3.7932 × 10 -21 and (x / k) 10 + 2.0048 × 10 -20 and (x / k) 8 (y / k) 2 + 3.2896 × 10 -20 Pa ( x / k) 6 (y / k) 4 + 82.3294 × 10 -20 and (x / k) 4 (y / k) 6 + 6.5446 × 10 -21 and (x / k) 2 (y / k) 8 - 9.4191 × 10 -23 and (y / k) 10 wherein Z M1 is an autonomous curved surface parameter for the first mirror, Z M2 is an autonomous curved surface parameter for the second mirror, x is an autonomic curved surface along an axis parallel to the sagittal plane, Y is the distance from the autocurved surface along the axis parallel to the tangential plane, k is D / 50 mm,

The first mirror and the second mirror may be free-form surface mirrors.

The present invention can provide a non-axial reflecting optical system device in which a non-axial alignment relationship is established based on optical design values corresponding to the ratio of the effective focal length to the effective aperture.

Further, the present invention can provide a non-axial reflecting optical system device that efficiently removes coma aberration based on the autonomous curved surface shape parameter for the reflecting mirror.

In addition, the present invention can provide superior optical performance to a coaxial non-retroreflective telescope having the same effective aperture ratio from an optical design of a non-retroreflective telescope with a coma aberration effective focal distance to a ratio of two effective aperture ratios.

1 is an example showing an optical path of a non-axis reflective optical system device.
Fig. 2 is an example showing a top surface tilting and a linear astigmatism on a convex curvature surface.
Fig. 3 shows an example of a section of a non-axial reflecting optical system device in which linear astigmatism is removed.
4A shows an example of a beam spot change according to a focus shift in a non-axial reflective optical system device in which the linear astigmatism of FIG. 3 is removed.
Fig. 4B is an example showing the change of the comb spot according to the focus shift in the axial optical system device.
FIG. 5 illustrates a non-axis reflective optical system according to an embodiment of the present invention.

The terminology used herein is for the purpose of illustrating embodiments and is not intended to be limiting of the present invention. In the present specification, the singular form includes plural forms unless otherwise specified in the specification. It is noted that the terms "comprises" and / or "comprising" used in the specification are intended to be inclusive in a manner similar to the components, steps, operations, and / Or additions.

Unless defined otherwise, all terms (including technical and scientific terms) used herein may be used in a sense commonly understood by one of ordinary skill in the art to which this invention belongs. Also, commonly used predefined terms are not ideally or excessively interpreted unless explicitly defined otherwise.

In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. The terminology used herein is a term used for appropriately expressing an embodiment of the present invention, which may vary depending on the user, the intent of the operator, or the practice of the field to which the present invention belongs. Therefore, the definitions of these terms should be based on the contents throughout this specification.

FIG. 1 shows an example of an optical path of a non-axial reflecting optical system, and FIG. 2 shows an example of a top surface tilting and a linear astigmatism on a non-axis-curvilinear surface.

In an optical system, the aberration can be represented by a polynomial expression for a path difference (OPL) between a ray (main ray) passing through the center of the reflector and a ray (peripheral ray) passing around the periphery.

Referring to FIG. 1, in the non-axial reflection optical system, the mirror MIRROR has no axisymmetry unlike the axisymmetric optical system.

Also, in an axisymmetric optical system, the OPL has a low order in the third order while in the non-axial optical system, the OPL has a second order in the low order as in Equation (1).

[Equation 1]

Figure 112015113805301-pat00001

here,

Figure 112015113805301-pat00002
Represents an optical path from the object surface to the reflector,
Figure 112015113805301-pat00003
Represents an optical path from the reflector to the upper surface,
Figure 112015113805301-pat00004
And
Figure 112015113805301-pat00005
X denotes a distance from an autocurved surface along an axis parallel to the sagittal plane, and y denotes a distance from the surface of the object to the reflector at the object surface in the ideal reflector, A i (i = 1, 2, 3) represents the coefficient of each polynomial, and O (4) represents the fourth order polynomial over.

In the oracular reflective orphan academy device, the second term of OPL (

Figure 112015113805301-pat00006
) Represents the linear astigmatism caused by the inclination of the upper surface and the center axis and the central axis of the visual field do not coincide with each other.

Further, in the non-axial reflecting optical system apparatus,

Figure 112015113805301-pat00007
Represents the coma aberration that occurs as the distance of the central axis or the light rays for the object are not collected.

Referring to FIG. 2, linear astigmatism is the most fatal aberration in the reflector of the non-axial reflecting optical system device because it is lower in one order than a normal sidelel aberration, and must be removed in order to observe the field of view.

Here, the linear astigmatism can be eliminated by satisfying the following expression (2) in the non-axial reflecting optical system consisting of two reflecting mirrors sharing the focal point.

[Equation 2]

Figure 112015113805301-pat00008

Here, R is the central curvature of the bottom edge including the reflecting mirror, I is the distance between the focal point and the reflecting mirror,

Figure 112015113805301-pat00009
Is the incident angle of the central ray, m is the principal angle, and s is the sub-diameter.

FIG. 3 shows an example of a section of a non-axial reflecting optical system device in which linear astigmatism is removed, FIG. 4A shows an example of a beam spot variation according to focus shift in the non- And Fig. 4B is an example showing a beam spot change according to the focus shift in the axial optical system device.

Referring to FIGS. 4A and 4B, the non-axis reflective optical system apparatus can maintain the optical performance equivalent to that of the axial optical system by eliminating the linear astigmatism. Hereinafter, a non-axis reflective optical system according to an embodiment of the present invention will be described in detail with reference to FIG.

FIG. 5 illustrates a non-axis reflective optical system according to an embodiment of the present invention.

Referring to Fig. 5, the non-axis reflective optical system includes a first mirror M1 and a second mirror M2.

The first mirror M1 may be a concave mirror and the second mirror M2 may be a convex mirror. The first mirror M1 and the second mirror M2 may be free-form surface mirrors.

The non-axial reflective optical system device determines the optical design values corresponding to the ratio of the effective focal length to the effective aperture in the absence of linear astigmatism, and establishes an off-axis positional relationship based on the optical design values do.

Here, the effective aperture means the diameter of the first mirror M1, and the ratio of the effective focal length to the effective aperture means that the transfer ratio of the brightness from the object surface to the mirror surface is relatively expressed.

According to one aspect of the present invention, the non-axial reflecting optical system device may further include an additional mirror as well as the first mirror M1 and the second mirror M2, and the additional mirror may include a first mirror M1 and a second mirror M2 ) In the case of the above-described arrangement.

When the effective aperture diameter is D and the ratio of the effective focal length to the effective aperture is 2, the optical design value is the effective focal distance of 2D and the distance d 1 from the first mirror to the second mirror is 4D, up to a distance d 2 is 4.82842D, and the angle of incidence on the object surface 1 i of 30 ° of light incident on the first mirror, characterized in that a first of the light beams incident on the mirror in the second mirror incidence angle i 2 is a 13.4495 ° .

For example, when the effective aperture D is 50 mm, the optical design value is 200 mm, the effective focal distance of 100 mm, and the distance d 1 from the first mirror M 1 to the second mirror M 2 is 200 mm. From the second mirror M 2 the distance from the top surface to the 241.421mm d 2, and the incident angle i 1 is 30 ° of the light that is incident from the object plane to the first mirror (M1), the first incident on the mirror (M1) to the second mirror (M2) light And the incident angle i 2 of the incident light is 13.4495 °.

According to the embodiment, since the optical design values corresponding to the ratio 2 of the effective focal length to the effective aperture are determined as described above, the optical design values corresponding to the various effective focal lengths to the effective aperture ratios are determined , Various reservoir arrangement relationships can be formed.

According to the embodiment, the non-axial reflecting optical system device is configured to measure coma aberration, astigmatism, and curvature of image field based on autonomous curved surface parameters for the first mirror M1 and the second mirror M2. May be removed.

The autonomous curved surface shape parameter can be determined by [Expression 3] and [Expression 4].

[Equation 3]

Z M1 = k [2.0412 × 10 -3 and (x / k) 2 + 1.5309 × 10 -3 and (y / k) 2 + 3.5572 × 10 -6 and (x / k) 2 (y / k) + 2.6963 × 10 -6 and (y / k) 3 + 5.0571 × 10 -8 and (x / k) 4 + 7.5766 × 10 -8 and (x / k) 2 (y / k) 2 + 3.0727 × 10 -8 and (y / k) 4 + 2.9754 × 10 -10 and (x / k) 4 (y / k) + 4.1891 × 10 -10 and (x / k) 2 (y / k) 3 + 1.4090 × 10 -10 and (y / k) 5 - 1.4605 × 10 -11 and (x / k) 6 - 6.1711 × 10 -12 and (x / k) 4 (y / k) 2 + 2.6243 × 10 -12 and (x / k) 2 (y / k) 4 + 6.5926 × 10 -13 and (y / k) 6 + 1.8594 × 10 -13 and (x / k) 6 (y / k) - 2.8353 × 10 -13 and (x / k) 4 (y / k) 3 - 1.5301 × 10 -13 and (x / k) 2 (y / k) 5 - 8.8929 × 10 -15 and (y / k) 7 + 1.9815 × 10 -14 and (x / k ) 8 + 1.9898 × 10 -14 and (x / k) 6 (y / k) 2 + 1.0456 × 10 -14 and (x / k) 4 (y / k) 4 + 2.8057 × 10 -16 and (x / k) 2 (y / k) 6 + 4.1329 × 10 -16 and (y / k) 8 + 1.3180 × 10 -16 and (x / k) 8 (y / k) + 2.9654 × 10 -16 and (x / k) 6 (y / k) 3 - 2.1533 × 10 -16 and (x / k) 4 (y / k) 5 + 9.0877 × 10 -17 and (x / k) 2 (y / k) 7 + 4.8722 × 10-18 and (y / k) 9 - 7.9424 × 10 -18 and (x / k) 10 - 8.2722 × 10 -18 and (x / k) 8 (y / k) 2 - 7.6216 × 10 -18 Pa ( x / k) 6 (y / k) 4 - 1.2784 × 10 -18 and (x / k) 4 (y / k) 6 + 8.2116 × 10 -19 and (x / k) 2 (y / k) 8 - 7.8028 × 10 -20 and (y / k) 10 ]

[Equation 4]

Z M2 = k [1.8176 × 10 -3 and (x / k) 2 + 1.7193 × 10 -3 and (y / k) 2 - 2.5759 × 10 -7 and (x / k) 2 (y / k) - 2.4328 × 10 -7 and (y / k) 3 + 6.7443 × 10 -9 and (x / k) 4 + 1.2961 × 10 -8 and (x / k) 2 (y / k) 2 + 6.2515 × 10 -9 and (y / k) 4 - 3.6149 × 10 -12 and (x / k) 4 (y / k) - 6.7564 × 10 -12 and (x / k) 2 (y / k) 3 - 2.5391 × 10 -12 and (y / k) 5 + 2.0621 × 10 -13 and (x / k) 6 + 4.9951 × 10 -13 and (x / k) 4 (y / k) 2 + 3.6649 × 10 -13 and (x / k) 2 (y / k) 4 + 5.4035 × 10 -14 and (y / k) 6 - 3.0463 × 10 -16 and (x / k) 6 (y / k) - 4.1040 × 10 -16 and (x / k) 4 (y / k) 3 - 3.2806 × 10 -16 and (x / k) 2 (y / k) 5 - 2.1804 × 10 -16 and (y / k) 7 - 3.9709 × 10 -17 and (x / k ) 8 - 1.4260 × 10 -16 and (x / k) 6 (y / k) 2 - 1.5951 × 10 -16 and (x / k) 4 (y / k) 4 - 6.1253 × 10 -17 and (x / k) 2 (y / k) 6 + 4.5582 × 10 -19 and (y / k) 8 + 6.4526 × 10 -20 and (x / k) 8 (y / k) + 1.1905 × 10 -19 and (x / k) 6 (y / k) 3 + 3.6559 × 10 -20 and (x / k) 4 (y / k) 5 + 3.7553 × 10 -20 and (x / k) 2 (y / k) 7 + 1.7630 × 10-20 and (y / k) 9 + 3.7932 × 10 -21 and (x / k) 10 + 2.0048 × 10 -20 and (x / k) 8 (y / k) 2 + 3.2896 × 10 -20 Pa ( x / k) 6 (y / k) 4 + 82.3294 × 10 -20 and (x / k) 4 (y / k) 6 + 6.5446 × 10 -21 and (x / k) 2 (y / k) 8 - 9.4191 × 10 -23 and (y / k) 10 ]

Here, Z M1 is the distance, y from the autonomous curved surface parameters, Z M2 is autonomous surface along parallel axes in the autonomous form surface shape parameter, x is the sagittal (sagittal) plane of the second mirror to the first mirror The distance from the autocurved surface along the axis parallel to the tangential plane, k, is D / 50 mm.

More specifically, Z M1 may be a height from a position (vertex) at which the center ray of the first mirror comes in contact, and Z M2 may be a height from a position where the center ray of the second mirror comes in contact.

The autonomous curved surface shape parameter can be expressed by [Equation 5] and can be expressed by [Table 1]. [Equation 3] and [Equation 4] are summarized.

[Equation 5]

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

[Table 1]

Figure 112015113805301-pat00010

Figure 112015113805301-pat00011

In Equation 5, a is a polynomial coefficient, x and y are indices, and coefficients not shown in Table 1 are all zero.

The non-axis reflective optical system according to an exemplary embodiment of the present invention can be used as a space telescope, an infrared telescope, an astronomical telescope, an amateur miniature telescope, and various telescopes using the same.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

M1: First mirror
M2: second mirror
D: Effective aperture of the first mirror
d 1 : the distance from the first mirror to the second mirror
d 2 : a distance from the second mirror to the upper surface
i 1 : the angle of incidence of the ray incident on the first mirror from the object plane
i 2 : the angle of incidence of the light incident from the first mirror to the second mirror
Z: autonomous curved surface shape parameter

Claims (4)

An optical design value corresponding to a ratio of the effective focal length to the effective aperture is determined with linear astigmatism removed, and a non-axial reflection optical system device having an off-axis positional relationship based on the optical design value As a result,
When the effective aperture diameter is D and the effective focal length to effective aperture ratio is 2, the optical design value is the effective focal distance of 2D and the distance d 1 from the first mirror to the second mirror is 4D, A distance d 2 from the second mirror to the image plane is 4.82842 D, an incident angle i 1 of the light beam incident on the first mirror on the object plane is 30 °, an incident angle and i 2 is 13.4495 °. The method according to claim 1,
Wherein at least one of coma aberration, astigmatism, and curvature of field is eliminated based on autonomous curved surface shape parameters of the first mirror and the second mirror. 3. The method of claim 2,
Wherein the autonomic curved surface shape parameter is determined by [Expression 3] and [Expression 4].
[Equation 3]
Z M1 = k [2.0412 × 10 -3 and (x / k) 2 + 1.5309 × 10 -3 and (y / k) 2 + 3.5572 × 10 -6 and (x / k) 2 (y / k) + 2.6963 × 10 -6 and (y / k) 3 + 5.0571 × 10 -8 and (x / k) 4 + 7.5766 × 10 -8 and (x / k) 2 (y / k) 2 + 3.0727 × 10 -8 and (y / k) 4 + 2.9754 × 10 -10 and (x / k) 4 (y / k) + 4.1891 × 10 -10 and (x / k) 2 (y / k) 3 + 1.4090 × 10 -10 and (y / k) 5 - 1.4605 × 10 -11 and (x / k) 6 - 6.1711 × 10 -12 and (x / k) 4 (y / k) 2 + 2.6243 × 10 -12 and (x / k) 2 (y / k) 4 + 6.5926 × 10 -13 and (y / k) 6 + 1.8594 × 10 -13 and (x / k) 6 (y / k) - 2.8353 × 10 -13 and (x / k) 4 (y / k) 3 - 1.5301 × 10 -13 and (x / k) 2 (y / k) 5 - 8.8929 × 10 -15 and (y / k) 7 + 1.9815 × 10 -14 and (x / k ) 8 + 1.9898 × 10 -14 and (x / k) 6 (y / k) 2 + 1.0456 × 10 -14 and (x / k) 4 (y / k) 4 + 2.8057 × 10 -16 and (x / k) 2 (y / k) 6 + 4.1329 × 10 -16 and (y / k) 8 + 1.3180 × 10 -16 and (x / k) 8 (y / k) + 2.9654 × 10 -16 and (x / k) 6 (y / k) 3 - 2.1533 × 10 -16 and (x / k) 4 (y / k) 5 + 9.0877 × 10 -17 and (x / k) 2 (y / k) 7 + 4.8722 × 10-18 and (y / k) 9 - 7.9424 × 10 -18 and (x / k) 10 - 8.2722 × 10 -18 and (x / k) 8 (y / k) 2 - 7.6216 × 10 -18 Pa ( x / k) 6 (y / k) 4 - 1.2784 × 10 -18 and (x / k) 4 (y / k) 6 + 8.2116 × 10 -19 and (x / k) 2 (y / k) 8 - 7.8028 × 10 -20 and (y / k) 10 ]
[Equation 4]
Z M2 = k [1.8176 × 10 -3 and (x / k) 2 + 1.7193 × 10 -3 and (y / k) 2 - 2.5759 × 10 -7 and (x / k) 2 (y / k) - 2.4328 × 10 -7 and (y / k) 3 + 6.7443 × 10 -9 and (x / k) 4 + 1.2961 × 10 -8 and (x / k) 2 (y / k) 2 + 6.2515 × 10 -9 and (y / k) 4 - 3.6149 × 10 -12 and (x / k) 4 (y / k) - 6.7564 × 10 -12 and (x / k) 2 (y / k) 3 - 2.5391 × 10 -12 and (y / k) 5 + 2.0621 × 10 -13 and (x / k) 6 + 4.9951 × 10 -13 and (x / k) 4 (y / k) 2 + 3.6649 × 10 -13 and (x / k) 2 (y / k) 4 + 5.4035 × 10 -14 and (y / k) 6 - 3.0463 × 10 -16 and (x / k) 6 (y / k) - 4.1040 × 10 -16 and (x / k) 4 (y / k) 3 - 3.2806 × 10 -16 and (x / k) 2 (y / k) 5 - 2.1804 × 10 -16 and (y / k) 7 - 3.9709 × 10 -17 and (x / k ) 8 - 1.4260 × 10 -16 and (x / k) 6 (y / k) 2 - 1.5951 × 10 -16 and (x / k) 4 (y / k) 4 - 6.1253 × 10 -17 and (x / k) 2 (y / k) 6 + 4.5582 × 10 -19 and (y / k) 8 + 6.4526 × 10 -20 and (x / k) 8 (y / k) + 1.1905 × 10 -19 and (x / k) 6 (y / k) 3 + 3.6559 × 10 -20 and (x / k) 4 (y / k) 5 + 3.7553 × 10 -20 and (x / k) 2 (y / k) 7 + 1.7630 × 10-20 and (y / k) 9 + 3.7932 × 10 -21 and (x / k) 10 + 2.0048 × 10 -20 and (x / k) 8 (y / k) 2 + 3.2896 × 10 -20 Pa ( x / k) 6 (y / k) 4 + 82.3294 × 10 -20 and (x / k) 4 (y / k) 6 + 6.5446 × 10 -21 and (x / k) 2 (y / k) 8 - 9.4191 × 10 -23 and (y / k) 10 ]
Wherein Z M1 is an autonomous curved surface parameter for the first mirror, Z M2 is an autonomous curved surface parameter for the second mirror, x is a distance from an autocurved surface along an axis parallel to the sagittal plane, y Is the distance from the autocurved surface along the axis parallel to the tangential plane, k is D / 50 mm) The method according to claim 1,
Wherein the first mirror and the second mirror are free-form surface mirrors.
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CN108227195B (en) * 2017-12-29 2020-05-19 南京信息工程大学 Off-axis two-mirror free-form surface optical system
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