CN115755359A - Off-axis three-mirror optical system - Google Patents
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- CN115755359A CN115755359A CN202211360670.5A CN202211360670A CN115755359A CN 115755359 A CN115755359 A CN 115755359A CN 202211360670 A CN202211360670 A CN 202211360670A CN 115755359 A CN115755359 A CN 115755359A
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Abstract
The invention relates to an off-axis three-mirror optical system. The first reflector is used for reflecting light rays from an object space to form first reflected light; the second reflecting mirror is arranged on the reflection light path of the first reflecting mirror and is used for reflecting the first reflection light to form second reflection light; the third reflector is arranged on the reflection light path of the second reflector and used for reflecting the second reflection light to form third reflection light which is emitted to the second reflector, the second reflector is also used for reflecting the third reflection light to form fourth reflection light, and the fourth reflection light is imaged at the image surface. By the special design, the folding of the light path is realized on the premise of not increasing the number of elements, and the volume of the off-axis three-mirror optical system is favorably reduced.
Description
Technical Field
The invention relates to the technical field of optical systems, in particular to an off-axis three-mirror optical system.
Background
With the development of ultra-precision machining technology, the description of the surface of an element in an optical system is not limited to spherical and aspherical surfaces, but gradually develops to a free-form surface without rotational symmetry. The application of the free-form surface enables more design freedom degrees of optical design, and the optical design provides more possibilities for improving the imaging quality of an optical system and realizing the volume compression of the optical system.
High resolution and small volume have been the pursuit of goals in the design of aerospace cameras. When the size of the detector pixel is determined, the focal length of the optical system determines the ground resolution of the aerial camera. In order to improve the resolving power to the ground, it is necessary to design an optical system having a long focal length, but in order to reduce the size of the camera, the length of each direction of the optical system is required to be as small as possible. Therefore, there is a certain contradiction between a long focal length and a small volume.
The off-axis three-mirror optical imaging system in the related art, although having a longer focal length, lacks the necessary folding of the optical path in its optical structure, thereby rendering the optical imaging system bulky.
Disclosure of Invention
Based on this, the embodiment of the application provides an off-axis three-mirror optical system, so as to be beneficial to further reducing the volume of the optical system under the condition of ensuring a long focal length, and further being beneficial to realizing a compact off-axis three-mirror optical imaging system.
The application provides an off-axis three-mirror optical system. The off-axis three-mirror optical system comprises a first reflector, a second reflector and a third reflector. The first reflector is used for reflecting light rays from an object space to form first reflected light. The second reflecting mirror is arranged on the reflection light path of the first reflecting mirror and used for reflecting the first reflection light to form second reflection light. The third reflector is arranged on the reflection light path of the second reflector and used for reflecting the second reflection light to form third reflection light which is shot to the second reflector. The second mirror is further configured to reflect the third reflected light to form fourth reflected light, and the fourth reflected light is imaged at an image plane.
In this application, the light beam incident to the off-axis three-mirror optical system is reflected twice by the second reflecting mirror, so that the light beam is reflected four times by the three-mirror. Through the special design, the folding of the light path is realized on the premise of not increasing the number of elements, the reduction of the volume of the off-axis three-mirror optical system is facilitated under the condition of ensuring a long focal length, and the difficulty of installation and alignment is reduced. In addition, under the condition of the same quantity of the three reflectors, the light rays are reflected for four times, namely, one reflector is added, so that the reduction of focal power borne by each reflector is facilitated, the reduction of curvature radius of a mirror surface is facilitated, and the processing difficulty of the optical element is reduced.
Further, the off-axis three-mirror optical system further comprises an aperture stop, and the aperture stop is arranged on the first reflector or the third reflector.
Alternatively, in some embodiments, the aperture stop of the off-axis three-mirror optical system is disposed between the object and the first mirror and is located on the optical path of the light rays from the object.
In some embodiments, the reflective surfaces of the first mirror, the second mirror, and the third mirror are one of spherical, aspherical, and free-form surfaces.
In some embodiments, the reflective surfaces of the first mirror, the second mirror, and the third mirror are free-form surfaces, and define a first three-dimensional rectangular coordinate system (x) in space 1 ，y 1 ，z 1 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a second three-dimensional rectangular coordinate system (x) based on said first mirror 2 ，y 2 ，z 2 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a third three-dimensional rectangular coordinate system (x) based on said second reflector 3 ，y 3 ，z 3 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a fourth three-dimensional rectangular coordinate system (x) based on said third mirror 4 ，y 4 ，z 4 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a fifth three-dimensional rectangular coordinate system (x) based on the image plane 5 ，y 5 ，z 5 )；
The second three-dimensional rectangular coordinate system (x) 2 ，y 2 ，z 2 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -3.606058mm, 441.699735mm), z 2 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 Rotating the shaft in the positive direction counterclockwise by 10.156621 degrees;
the third rectangular coordinate system (x) 3 ，y 3 ，z 3 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has coordinates of (0 mm, -236.197739mm, 72.477861mm), z 3 Positive axial direction with respect to a first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 Rotating the shaft in the positive direction counterclockwise by 7.664499 degrees;
the fourth three-dimensional rectangular coordinate system (x) 4 ，y 4 ，z 4 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -257.371562mm, 456.080600mm), z 4 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 Rotating the shaft in the positive direction counterclockwise by 0.621483 degrees;
the fifth three-dimensional rectangular coordinate system (x) 5 ，y 5 ，z 5 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -127.405735mm, 471.826343mm), z 5 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 The positive axial direction rotates counterclockwise 18.815418 degrees.
In some embodiments, the reflective surface of the first mirror is about x 2 y 2 The reflecting surface of the second reflector is related to x 3 y 3 The reflecting surface of the third reflector is related to x 4 y 4 6 th order polynomial free-form surface.
In some embodiments, the x 2 y 2 The equation for the 4 th order polynomial of (1) is:
wherein c is the base curvature of the first reflector, k is the conic coefficient of the first reflector, c = -4.212955E-04, k = -4.422194E +00, A 3 ＝-4.820757E-03，A 4 ＝-3.074835E-05，A 6 ＝-1.966639E-06，A 8 ＝6.349666E-08，A 10 ＝4.290582E-08，A 11 ＝4.429853E-11，A 13 ＝8.264656E-11，A 15 ＝3.376195E-11。
In some embodiments, the x 3 y 3 The equation for the 6 th order polynomial of (c) is:
wherein c is the base curvature of the second reflector, k is the conic coefficient of the second reflector, c = -3.662751E-04, k = -4.032E +01, A 3 ＝1.154211E-01，A 4 ＝-9.521947E-05，A 6 ＝3.071521E-05，A 8 ＝1.054537E-07，A 10 ＝-1.547028E-08，A 11 ＝5.999201E-10，A 13 ＝1.136090E-09，A 15 ＝2.627475E-10，A 17 ＝-4.642604E-13，A 1g ＝-2.663330E-12，A 21 ＝0.000000E+00，A 22 ＝-7.562139E-16，A 24 ＝-1.412069E-15，A 26 ＝4.622521E-15，A 28 ＝-4.318231E-16。
In some embodiments, the x 4 y 4 Polynomial of degree 6 the equation of (1) is:
wherein c is the base curvature of the third reflector, k is the conic coefficient of the third reflector, c =3.055129E-04, k = -4.786315E +01, A = 3 ＝2.174659E-01，A 4 ＝-4.667853E-05，A 6 ＝7.647619E-05，A 8 ＝2.750348E-07，A 10 ＝9.428285E-08，A 11 ＝5.071565E-10，A 13 ＝1.019023E-09，A 15 ＝5.371274E-10，A 17 ＝-2.049697E-13，A 19 ＝-1.267790E-12，A 21 ＝-5.818602E-13，A 22 ＝6.683527E-16，A 24 ＝2.869677E-15，A 26 ＝8.119148E-15，A 28 ＝-4.726691E-16。
In some embodiments, the off-axis three-mirror optical system has a field angle of 4 ° x 3 °.
In some embodiments, the material of the first mirror, the second mirror, and the third mirror comprises gold, silver, silicon carbide, microcrystalline, or an aluminum alloy.
Drawings
FIG. 1 is a schematic structural diagram of an off-axis three-mirror optical system according to an embodiment of the present disclosure;
FIG. 2 is a graph of MTF for an off-axis three-mirror optical system according to an embodiment of the present application;
FIG. 3 is an RMS wave aberration diagram of an off-axis three-mirror optical system according to an embodiment of the present application.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, embodiments accompanying figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are not to be considered limiting of the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood according to specific situations by those of ordinary skill in the art.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
It will be understood that when an element is referred to as being "secured to" or "disposed on" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and the like as used herein are for illustrative purposes only and do not denote a unique embodiment.
Off-axis reflective optical systems are becoming the focus of optical system design research. The main reason is that the off-axis reflective optical system has no central blocking, high light energy utilization rate and can work in a wider wave band range. In addition, the common off-axis reflective optical system adopts a reflection mode, so that the light path is effectively folded, and the size of the system can be shortened.
High resolution and small volume have been the pursuit of goals in the design of aerospace cameras. When the size of the detector pixel is determined, the focal length of the optical system determines the ground resolution of the aerial camera. With the demand for ground resolution becoming higher and higher, the required focal length of the optical system becomes longer and longer, which makes the size of the existing off-axis reflective optical system unable to meet the requirement of small volume well. Therefore, it is highly desirable to design a compact off-axis three-mirror optical imaging system with a long focal length.
Based on this, the present application proposes an off-axis three-mirror optical system 1. As shown in fig. 1 to 3, the off-axis three-mirror optical system 1 includes a first mirror 100, a second mirror 200, and a third mirror 300. The first reflector 100 is configured to reflect light from an object to form a first reflected light a. Second reflecting mirror 200 is disposed on the reflected light path of first reflecting mirror 100 to reflect first reflected light a to form second reflected light B. The third reflecting mirror 300 is disposed on the reflecting light path of the second reflecting mirror 200, and reflects the second reflected light B to form a third reflected light C directed to the second reflecting mirror 200. The second mirror 200 is also used to reflect the third reflected light C to form fourth reflected light D, and the fourth reflected light D is imaged at the image plane 400.
In this application, first speculum 100, second speculum 200 and third speculum 300 form the quartic reflection to the light path respectively to can realize that the light path is further folded under the condition that does not additionally increase the speculum, and then realize long focus, small compact off-axis three anti-optical system. Specifically, the optical path of the off-axis three-mirror optical system 1 during operation is as follows: in this system, light from an object point at infinity is incident on the first mirror 100 at an angle. The first reflected light a is formed by reflection by the first mirror 100. The first reflected light a passes through the second reflecting mirror 200 for the first time and is reflected by the second reflecting mirror 200 to form a second reflected light B. The second reflected light B is reflected by the third reflecting mirror 300 to form third reflected light C. The incident angle of the second reflected light B on the third reflecting mirror 300 is small, and the exit angle of the reflected third reflected light C is also small, so that the second reflected light B passes through the second reflecting mirror 200 for the second time after being reflected by the third reflecting mirror 300. At this time, the third reflected light C is reflected by the second reflecting mirror 200 for the second time to form fourth reflected light D. It will be readily understood that the second reflected light B may also be considered to be reflected by the third mirror 300 to the fourth mirror, except that the fourth mirror has the same surface type parameters and position coordinates as the second mirror 200. Finally, the fourth reflected light D is imaged at image plane 400 between the first mirror 100 and the third mirror 300. The image plane 400 refers to the location where the imaging plane is located. For example, a photosensitive element such as an image sensor or the like may be disposed at the image plane 400.
In this application, the light beam incident on the off-axis three-mirror optical system 1 is reflected by the second mirror 200 twice, so that the light beam is reflected by the three-mirror four times. By the special design, the folding of the light path is realized on the premise of not increasing the number of elements, and the reduction of the volume of the off-axis three-mirror optical system 1 is facilitated under the condition of ensuring a long focal length. In addition, under the condition of the same quantity of the three reflectors, the light rays are reflected for four times, namely, one reflector is added, so that the reduction of focal power borne by each reflector is facilitated, the reduction of curvature radius of a mirror surface is facilitated, and the processing difficulty of the optical element is reduced.
Further, the off-axis three-mirror optical system 1 further includes an aperture stop (not shown). The aperture stop refers to a perforated screen and a frame of various imaging elements (such as lenses, mirrors and the like) capable of limiting an imaging beam in an optical system. The position of the aperture stop of the off-axis three-mirror optical system 1 can be flexibly set. For example, an aperture stop may be provided on the first mirror 100. Alternatively, an aperture stop may be provided on the third mirror 300.
Alternatively, in some embodiments, the aperture stop may also be disposed between the object and the first mirror 100 and located on the optical path of the light from the object. The aperture stop is arranged in front of the off-axis three-mirror optical system 1, i.e. in the light path before the light rays enter the first mirror 100. Because the aperture diaphragm is an independent optical element and is not connected with each reflector, the aperture diaphragm can be freely moved and adjusted in space, so that the adjustable freedom degree of the off-axis three-mirror optical system 1 is further improved, the optical performance of the off-axis three-mirror optical system 1 is further improved, and the imaging quality is further improved.
In some embodiments, the materials of first mirror 100, second mirror 200, and third mirror 30 include gold, silver, silicon carbide, microcrystalline, or an aluminum alloy. The personnel in the field can flexibly select according to the processing cost, the material processing difficulty, the use scene and the like.
In some embodiments, the reflective surface of the first reflector 100 is one of spherical, aspherical, and free-form. The spherical first reflecting mirror 100 is simple to process and easy to inspect, thereby being beneficial to reducing the production cost. The aspheric surface is an even term with an increased polar diameter on the basis of a spherical quadric surface substrate, and the aspheric surface is still a rotational symmetric surface. The aspheric surface is more complex than the spherical surface, but the first reflecting mirror 100 with the aspheric surface is beneficial to better correcting aberration and further beneficial to improving the imaging quality. A free-form surface is an optical curved surface without rotational symmetry. Compared with an aspheric surface, the free-form surface has higher degree of freedom, and the emergent trend of the light can be better controlled according to requirements. The first reflector 100 with a free-form surface is beneficial to better correcting aberration, and further beneficial to improving imaging quality.
It will be readily appreciated that the reflective surface types of second mirror 200 and third mirror 300 may also be flexibly selected. Specifically, in some embodiments, the reflective surface of second mirror 200 is one of spherical, aspherical, and free-form. In some embodiments, the reflective surface of the third reflector 300 is one of spherical, aspherical, and free-form.
In a specific embodiment, the reflective surfaces of the first mirror 100, the second mirror 200, and the third mirror 300 are all free-form surfaces. The arrangement is such that the degree of freedom of the off-axis three-mirror optical system 1 is large, so that the parameters of each mirror can be flexibly set to achieve a high level of imaging quality.
In some embodiments, a first three-dimensional rectangular coordinate system (x) is defined in space 1 ，y 1 ，z 1 ) The first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) I.e. a global coordinate system, i.e. an absolute coordinate system, of the entire space.
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) A second three-dimensional rectangular coordinate system (x) is defined based on the first reflector 100 2 ，y 2 ，z 2 ) That is, the second three-dimensional rectangular coordinate system (x) 2 ，y 2 ，z 2 ) The spatial coordinate system established on the basis of the first mirror 100 is a local coordinate system.
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) A third three-dimensional rectangular coordinate system (x) is defined on the basis of the second reflector 200 3 ，y 3 ，z 3 ) That is, the third three-dimensional rectangular coordinate system (x) 3 ，y 3 ，z 3 ) The spatial coordinate system established for second mirror 200 is a local coordinate system.
In space relative to theFirst three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) A fourth three-dimensional rectangular coordinate system (x) is defined based on the third reflector 300 4 ，y 4 ，z 4 ) That is, the fourth three-dimensional rectangular coordinate system (x) 4 ，y 4 ，z 4 ) The spatial coordinate system established on the basis of the third mirror 300 is a local coordinate system.
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a fifth three-dimensional rectangular coordinate system (x) based on the image plane 400 5 ，y 5 ，z 5 ) That is, the fifth three-dimensional rectangular coordinate system (x) 5 ，y 5 ，z 5 ) The spatial coordinate system established based on the image plane 400 is a local coordinate system.
Thus, there is a relative relationship between the local coordinate system of each mirror, and the local coordinate system and the global coordinate system at the image plane 400. That is, when describing the coordinates of each mirror, the coordinates may be described in terms of a local coordinate system in which the mirror is located, and finally the coordinates may be converted into coordinates in an absolute coordinate system through a relative relationship of the coordinate system. The arrangement is beneficial to simplifying the expression of the curved surface of each reflector, and is convenient for determining the polynomial high-order expression coefficient of each reflector.
The specific relationship between the coordinate system established by each mirror itself and the coordinate system established by 400 itself at the image plane and the absolute coordinate system of the whole space is as follows:
as shown in fig. 1, a second three-dimensional rectangular coordinate system (x) 2 ，y 2 ，z 2 ) Is in a first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -3.606058mm, 441.699735mm), z 2 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 The positive axial direction rotates counterclockwise 10.156621 degrees.
Third three-dimensional rectangular coordinate system (x) 3 ，y 3 ，z 3 ) In the first three-dimensionalRectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has coordinates of (0 mm, -236.197739mm, 72.477861mm), z 3 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 The positive axial direction rotates counterclockwise 7.664499 degrees (not shown).
Fourth three-dimensional rectangular coordinate system (x) 4 ，y 4 ，z 4 ) Is in a first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -257.371562mm, 456.080600mm), z 4 Positive axial direction with respect to a first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 The positive axial direction rotates counterclockwise 0.621483 degrees.
Fifth three-dimensional rectangular coordinate system (x) 5 ，y 5 ，z 5 ) Is in a first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -127.405735mm, 471.826343mm), z 5 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 The positive axis rotates counterclockwise 18.815418 degrees.
Through the relative relation of the coordinate systems, the coordinate values of the first reflecting mirror 100, the second reflecting mirror 200, the third reflecting mirror 300 and the image plane 400 in different coordinate systems can be converted, so that the expression of the curved surface is simplified, and the determination of the expression coefficient of the curved surface is facilitated.
Furthermore, the reflecting surfaces of the three reflectors are free-form surfaces and adopt XY polynomial free-form surfaces. Specifically, the formula of the XY polynomial is:
wherein z is the rise of the curved surface and c is the base of the curved surfaceBottom curvature, k is the coefficient of the quadric surface, A j Is the coefficient of the polynomial term.
The number of terms of the polynomial can reach infinite terms, but in the optimization process, if the number of terms of the xy polynomial is increased without limit, huge burden is caused on ray tracing, so that the optimization time is too long, and the efficiency of determining the coefficient of the free-form surface is not improved. Thus, in some embodiments, the reflective surface of first mirror 100 is about x 2 y 2 The 4 th order polynomial free-form surface of second reflecting mirror 200 is defined with respect to x 3 y 3 Of the third mirror 300 is a polynomial free-form surface of degree 6 with respect to x 4 y 4 6 th order polynomial free-form surface.
Since each mirror of the off-axis three-mirror optical system 1 of the present embodiment is symmetrical with respect to the yz plane, only the even term of x can be retained. Specifically, x of the reflection surface of the first mirror 100 2 y 2 The equation for the fourth order polynomial of (a) is:
in this embodiment, x of the reflection surface of the first mirror 100 2 y 2 Base curvature c, conic coefficient k, and coefficients A of the terms in the polynomial j See table 1 for values of (a). It will be appreciated that the base curvature c, the conic coefficient k and the individual coefficients A j The values of (A) are also not limited to those described in Table 1, and can be adjusted by those skilled in the art according to actual needs.
TABLE 1 x of the reflecting surface of the first mirror 2 y 2 Values of coefficients in the polynomial
| Curvature of the base c | -4.212955E-04 |
| Coefficient of quadric surface k | -4.422194E+00 |
| A 3 | -4.820757E-03 |
| A 4 | -3.074835E-05 |
| A 6 | -1.966639E-06 |
| A 8 | 6.349666E-08 |
| A 10 | 4.290582E-08 |
| A 11 | 4.429853E-11 |
| A 13 | 8.264656E-11 |
| A 15 | 3.376195E-11 |
In some embodiments, x of second mirror 200 3 y 3 The equation for the 6 th order polynomial of (c) is:
the true bookIn the embodiment, x of the reflecting surface of second mirror 200 3 y 3 Base curvature c, conic coefficient k, and coefficients A in the polynomial j See table 2 for values of (d). It will be appreciated that the base curvature c, the conic coefficient k and the individual coefficients A j The values of (c) are also not limited to those shown in table 2, and can be adjusted by those skilled in the art according to actual needs.
TABLE 2 reflection of the second mirror x 3 y 3 Values of coefficients in the polynomial
| Curvature of the substrate c | -3.662751E-04 |
| Coefficient of quadric surface k | -4.032032E+01 |
| A 3 | 1.154211E-01 |
| A 4 | -9.521947E-05 |
| A 6 | 3.071521E-05 |
| A 8 | 1.054537E-07 |
| A 10 | -1.547028E-08 |
| A 11 | 5.999201E-10 |
| A 13 | 1.136090E-09 |
| A 15 | 2.627475E-10 |
| A 17 | -4.642604E-13 |
| A 19 | -2.663330E-12 |
| A 21 | 0.000000E+00 |
| A 22 | -7.562139E-16 |
| A 24 | -1.412069E-15 |
| A 26 | 4.622521E-15 |
| A 28 | -4.318231E-16 |
In some embodiments, x of third mirror 300 4 y 4 The equation for the 6 th order polynomial of (c) is:
in this embodiment, x of the reflection surface of the third reflector 300 4 y 4 Base curvature c, conic coefficient k, and coefficients A of the terms in the polynomial j See table 3 for values of (d). It will be appreciated that the base curvature c, the conic coefficient k and the individual coefficients A j The values of (c) are also not limited to those shown in table 3, and can be adjusted by those skilled in the art according to actual needs.
TABLE 3 reflection surface x of the second mirror 3 y 3 Values of coefficients in the polynomial
Further, the field of view of the off-axis three-mirror optical system 1 using a free-form surface is 4 ° × 3 °.
Further, the off-axis three-mirror optical system 1 has an F-number of 15, a focal length of 2m, and an entrance pupil diameter of 133mm.
As shown in fig. 2, the MTF graph of the off-axis three-mirror optical system 1 using the free-form surface is shown. As can be seen from the graph, the off-axis three-mirror optical system 1 has better imaging quality.
As shown in fig. 3, the RMS wave aberration diagram of the off-axis three-mirror optical system 1 using a free-form surface is shown. As can be seen from the RMS wave aberration diagram, the average wave aberration of the system is 0.014964 lambda, and the standard deviation of the wave aberration is 0.0022383, which indicates that the designed off-axis three-mirror optical system 1 has better imaging quality.
Therefore, compared with a common off-axis three-reflector optical system, the off-axis three-reflector optical system adopts a three-reflector four-refraction structure, realizes optical path folding under the condition of not increasing the number of system elements, and is beneficial to reducing the volume of the optical system. In addition, under the condition of the same quantity of the reflectors, the focal power of the optical system can be born by more reflecting surfaces, so that the reduction of the curvature radius of the mirror surface is facilitated, and the processing difficulty is reduced.
The technical features of the embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments are not described, however, as long as there is no contradiction between the combinations of the technical features, the combinations should be considered as the scope of the description in the present specification.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that various changes and modifications can be made by those skilled in the art without departing from the spirit of the invention, and these changes and modifications are all within the scope of the invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. An off-axis three-mirror optical system, comprising:
the first reflector is used for reflecting light rays from an object side to form first reflected light;
the second reflector is arranged on the reflection light path of the first reflector and used for reflecting the first reflection light to form second reflection light; and
and the third reflector is arranged on the reflection light path of the second reflector and used for reflecting the second reflection light to form third reflection light which is shot to the second reflector, the second reflector is also used for reflecting the third reflection light to form fourth reflection light, and the fourth reflection light is imaged at the image surface.
2. An off-axis three-mirror optical system according to claim 1, further comprising an aperture stop disposed on the first mirror or the third mirror;
or the aperture diaphragm is arranged between the object space and the first reflecting mirror and is positioned on a light path of light rays from the object space.
3. An off-axis three-mirror optical system according to claim 1, wherein the reflecting surfaces of the first mirror, the second mirror, and the third mirror are one of spherical, aspherical, and free-form surfaces.
4. An off-axis three-mirror optical system according to claim 1, wherein a first three-dimensional rectangular coordinate system (x) is defined in space 1 ，y 1 ，z 1 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a second three-dimensional rectangular coordinate system (x) based on said first mirror 2 ，y 2 ，z 2 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a third three-dimensional rectangular coordinate system (x) based on said second reflector 3 ，y 3 ，z 3 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a fourth three-dimensional rectangular coordinate system (x) based on said third mirror 4 ，y 4 ，z 4 )；
In space with respect to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Defining a fifth three-dimensional rectangular coordinate system (x) based on the image plane 5 ，y 5 ，z 5 )；
Wherein the second three-dimensional rectangular coordinate system (x) 2 ，y 2 ，z 2 ) In said first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -3.606058mm, 441.699735mm), z 2 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 Clockwise and anticlockwise rotationRotating 10.156621 degrees;
the third rectangular coordinate system (x) 3 ，y 3 ，z 3 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has coordinates of (0 mm, -236.197739mm, 72.477861mm), z 3 Positive axial direction with respect to a first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 Rotating the shaft in the positive direction counterclockwise by 7.664499 degrees;
the fourth three-dimensional rectangular coordinate system (x) 4 ，y 4 ，z 4 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -257.371562mm, 456.080600mm), z 4 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 Rotating the shaft in the positive direction counterclockwise by 0.621483 degrees;
the fifth three-dimensional rectangular coordinate system (x) 5 ，y 5 ，z 5 ) Is in the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Has the coordinates of (0 mm, -127.405735mm, 471.826343mm), z 5 Positive axial direction relative to the first three-dimensional rectangular coordinate system (x) 1 ，y 1 ，z 1 ) Z of (a) 1 The positive axial direction rotates counterclockwise 18.815418 degrees.
5. An off-axis three-mirror optical system according to claim 4, wherein the reflective surface of the first mirror is about x 2 y 2 The reflecting surface of the second reflector is related to x 3 y 3 The reflecting surface of the third reflector is related to x 4 y 4 6 th order polynomial free-form surface.
6. An off-axis three-mirror optical system according to claim 5, wherein x is 2 y 2 The equation for the 4 th order polynomial of (1) is:
wherein c is the base curvature of the first reflector, k is the conic coefficient of the first reflector, c = -4.212955E-04, k = -4.422194E +00, A 3 ＝-4.820757E-03，A 4 ＝-3.074835E-05，a 6 ＝-1.966639E-06，A 8 ＝6.349666E-08，A 10 ＝4.290582E-08，A 11 ＝4.429853E-11，A 13 ＝8.264656E-11，a 15 ＝3.376195E-11。
7. An off-axis three-mirror optical system according to claim 6, wherein x is 3 y 3 The equation for the 6 th order polynomial of (c) is:
wherein c is the base curvature of the second reflector, k is the conic coefficient of the second reflector, c = -3.662751E-04, k = -4.032E +01, A 3 ＝1.154211E-01，A 4 ＝-9.521947E-05，A 6 ＝3.071521E-05，A 8 ＝1.054537E-07，A 10 ＝-1.547028E-08，A 11 ＝5.999201E-10，A 13 ＝1.136090E-09，A 15 ＝2.627475E-10，A 17 ＝-4.642604E-13，A 19 ＝-2.663330E-12，A 21 ＝0.000000E+00，A 22 ＝-7.562139E-16，A 24 ＝-1.412069E-15，A 26 ＝4.622521E-15，A 28 ＝-4.318231E-16。
8. An off-axis three-mirror optical system according to claim 7, wherein x is 4 y 4 The equation for the 6 th order polynomial of (c) is:
wherein c is the base curvature of the third reflector, k is the conic coefficient of the third reflector, c =3.055129E-04, k = -4.786315E +01, A = 3 ＝2.174659E-01，A 4 ＝-4.667853E-05，A 6 ＝7.647619E-05，A 8 ＝2.750348E-07，A 10 ＝9.428285E-08，A 11 ＝5.071565E-10，A 13 ＝1.019023E-09，A 15 ＝5.371274E-10，A 17 ＝-2.049697E-13，A 19 ＝-1.267790E-12，A 21 ＝-5.818602E-13，A 22 ＝6.683527E-16，A 24 ＝2.869677E-15，A 26 ＝8.119148E-15，A 28 ＝-4.726691E-16。
9. An off-axis three-mirror optical system according to claim 8, having a field angle of 4 ° x 3 °.
10. An off-axis three-mirror optical system according to claim 1, wherein the material of the first, second and third mirrors comprises gold, silver, silicon carbide, microcrystalline or aluminum alloy.
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| CN202211360670.5A CN115755359A (en) | 2022-11-02 | 2022-11-02 | Off-axis three-mirror optical system |
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| CN202211360670.5A CN115755359A (en) | 2022-11-02 | 2022-11-02 | Off-axis three-mirror optical system |
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| CN115755359A true CN115755359A (en) | 2023-03-07 |
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