CN101598849B - Optical imaging system and manufacturing method thereof - Google Patents

Abstract

The invention discloses an optical imaging system which comprises a secondary lens, a main lens, a correction lens group and an image field correction lens which are sequentially arranged. Four items of spherical aberration, coma aberration, astigmatism and image field curvature in monochromatic aberration are considered to be eliminated according to a third-order aberration theory. The main lens is a paraboloid; the secondary lens is a hyperboloid, and the conical coefficient of the hyperboloid of the secondary lens is determined according to the refractive index of the material of the secondary lens. Optimized by a computer, the image quality and the view field of the double reflection optical imaging system are obviously improved, and in the sights of a geometric spot diagram (SPOT), a modulation transfer function (MTF) and encircled energy (EE), the image quality of the optical imaging system basically reaches a diffraction limit.

Description

Optical imaging system and manufacturing approach thereof

Technical field

The invention belongs to optical field, relate to a kind of optical imaging system, relate in particular to a kind of two anti-correction up lens optical system, in addition, the invention still further relates to the manufacturing approach of this optical system.

Background technology

Traditional two anti-form object lens have Pascal Greggory system (as shown in Figure 1), card match Green system (as shown in Figure 2) and R-C system.

Wherein the characteristics of Pascal Greggory system are, primary mirror is parabolic, and secondary mirror is an ellipsoid, and the paraboloidal focus of primary mirror overlaps with a focus of secondary mirror ellipsoid, images in the another one focus of secondary mirror, picture point in the middle of system exists, and tube length is bigger;

The primary mirror of card match Green system is parabolic, and secondary mirror is a hyperboloid, and the primary mirror parabolic focus overlaps with the bi-curved virtual focus of secondary mirror, images on the another one focus of secondary mirror, because there is not middle picture point, tube length is shorter;

The R-C system is the improvement to card match Green system; In order to increase the visual field, primary mirror is changed near paraboloidal hyperboloid, secondary mirror still is a hyperboloid; But two minute surface focuses do not overlap; Under the prerequisite of control picture element, carry out computer optimization, obtain final aspheric surface and spacing parameter, its tube length is suitable with card match Green system.

RC system (two anti-system) commonly used is according to third-order aberration theory design, preceding two of only having considered five kinds of monochromatic aberrations, i.e. spherical aberration and coma.In its design result, main, secondary mirror all is an aspheric surface, and wherein primary mirror is that secondary mirror is a hyperboloid near paraboloidal hyperboloid, and the check of the two must cooperatively interact and could accomplish, and this has brought great difficulty to inspection during manufacture.In addition, secondary mirror is a hyperboloid, and its circular cone COEFFICIENT K is many between-1～-6, because of its result of computer optimization normally, so have uncertainty, causes secondary mirror can't carry out independent check.To one of improvement of RC system is to add the correcting lens group, but can not change the relative position of primary and secondary minute surface focus like this, is very limited with index aspect the increase visual field improving picture element.

Summary of the invention

Technical matters to be solved by this invention is: a kind of two reflective imaging system that can effectively improve picture element and visual field is provided.

In addition, the present invention also provides a kind of manufacturing approach of above-mentioned two reflective imaging systems.

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

A kind of optical imaging system comprises the secondary mirror, primary mirror, correcting lens group, the field corrector that are arranged in order; According to third-order aberration theory, consider to eliminate four of spherical aberration in the monochromatic aberration, coma, astigmatism and filed curvatures, said primary mirror be a parabola; Secondary mirror is a hyperboloid, and the bi-curved circular cone coefficient of secondary mirror is confirmed according to secondary mirror material refractive index.

As a kind of preferred version of the present invention, the bi-curved circular cone coefficient of said secondary mirror is more than or equal to the opposite number-0.5 of secondary mirror material refractive index square, smaller or equal to opposite number+0.5 of secondary mirror material refractive index square.Preferably, the bi-curved circular cone coefficient of said secondary mirror is the opposite number of secondary mirror material refractive index square.

As a kind of preferred version of the present invention, the bi-curved circular cone coefficient of said secondary mirror is confirmed according to secondary mirror material refractive index and check light beam wavelength; The circular cone coefficient $k=-n_{\mathrm{\λ}}^2,$ Wherein k is the circular cone coefficient, and λ is the wavelength of check light beam, n _λBe illustrated in the refractive index under the wavelength X.

As a kind of preferred version of the present invention, a side of said secondary mirror is a hyperboloid, and opposite side is the plane reflection face.

As a kind of preferred version of the present invention, said primary mirror does not overlap with the focus of secondary mirror; If when the focus of primary mirror secondary mirror overlapped, secondary mirror was L apart from the distance of primary mirror, the primary mirror focal length is f ', and then the distance of secondary mirror and primary mirror is greater than L+0.06*f ', smaller or equal to L+0.10*f '.

As a kind of preferred version of the present invention, said primary mirror, secondary mirror, no focal power correcting lens group and image field correcting lens are quartz material.

The manufacturing approach of above-mentioned optical imaging system comprises the steps:

The step of processing primary mirror: the parabola that primary mirror is processed into setting;

The step of processing secondary mirror: secondary mirror is processed into hyperboloid, and this bi-curved circular cone coefficient is confirmed according to secondary mirror material refractive index and check light beam wavelength.

As a kind of preferred version of the present invention; The bi-curved circular cone coefficient of said secondary mirror is more than or equal to the opposite number-0.5 of secondary mirror material refractive index square, smaller or equal to opposite number+0.5 of secondary mirror material refractive index square; Preferably, the bi-curved circular cone coefficient of said secondary mirror is the opposite number of secondary mirror material refractive index square.

As a kind of preferred version of the present invention, in the step of said processing secondary mirror, a side of secondary mirror is a hyperboloid, and opposite side is the plane reflection face; Work in-process is processed into the plane reflection face of secondary mirror the plane and plates reflectance coating, and its hyperboloid of while does not temporarily plate any film and is; After also qualified, again hyperboloid plated reflectance coating, and then debug and total inspection with primary mirror through the check of independent face type.

As a kind of preferred version of the present invention, said method comprises the step of eliminating spherical aberration, coma, astigmatism, four monochromatic aberrations of the curvature of field.

Beneficial effect of the present invention is: the two reflective imaging systems of the present invention are through computer optimization; Its picture element and visual field have obtained comparatively significantly improving; From how much point range figures (SPOT), modulation transfer function MTF and encircled power EE, its picture element has reached diffraction limit basically.

Description of drawings

Fig. 1 is the structural representation of Pascal Greggory Gregory system in the prior art.

Fig. 2 is the structural representation of card match Green Cassegrain system in the prior art.

Fig. 3 is the structural representation of optical system of the present invention.

Fig. 4 is the structural representation of optical system secondary mirror.

Fig. 5 is the structural representation of optical system Aberration Analysis.

Embodiment

Specify the preferred embodiments of the present invention below in conjunction with accompanying drawing.

See also Fig. 3, the present invention has disclosed a kind of optical imaging system, comprises the secondary mirror 1, primary mirror 2, correcting lens group 3, field corrector 4, the focal plane 5 that are arranged in order.Said primary mirror 2 is parabolic; Secondary mirror 1 is a hyperboloid, and secondary mirror 1 bi-curved circular cone coefficient is confirmed according to secondary mirror material refractive index and check light beam wavelength.In the present embodiment, the bi-curved circular cone coefficient of said secondary mirror is the opposite number of secondary mirror material refractive index square.

See also Fig. 4, a side of said secondary mirror 1 is a hyperboloid 11, and opposite side is a plane reflection face 12.In the aspheric single dioptric imaging of hyperbolic type, use the special secondary mirror of this kind 1, when being placed on the focus of its far-end to pointolite, the light beam of dispersing can pass through aspheric surface and get into medium and become directional light.As shown in Figure 4, the left surface of lens is a hyperboloid 11, and right flank is a plane reflection face 12.Utilize this characteristic, can carry out this aspheric aberrationless point (need not bucking-out system) independence test.This surperficial circular cone coefficient is the negative value of square getting of material refractive index, this with the actual COEFFICIENT K of using at identical interval, therefore consider the secondary mirror of this surface as two anti-systems designed, with convenient processing separately, check.

Among the present invention, said primary mirror 2 does not overlap with the focus of secondary mirror 1.If when the focus of primary mirror 2 secondary mirrors 1 overlapped, secondary mirror was L apart from the distance of primary mirror, the primary mirror focal length is f ', then among the present invention the distance of secondary mirror 1 and primary mirror 2 greater than L+0.06*f ', smaller or equal to L+0.10*f '.The focus of primary and secondary mirror overlaps and forms images for the axle glazed thread is very favorable, because this meets the principle of geometrical optics fully, but under the situation of big visual field; For off-axis ray, picture element meeting rapid deterioration, therefore in the present invention; Theoretical according to aberration design, consider secondary mirror is moved certain distance to the direction away from primary mirror, at first introduce negative aberration; With all kinds of aberrations of compensation subsequent optical face, the aberration correction of doing like this off-axis ray provides favourable starting condition.Practical design result shows that such interval is chosen, and comparatively significantly effect has been played in the improvement of photographs of off-axis ray.

In addition, said primary mirror, secondary mirror, no focal power correcting lens group and image field correcting lens are quartz material.

Below introduce the manufacturing approach of optical imaging system of the present invention, in this method, primary mirror is processed into the parabola of setting; Secondary mirror is processed into hyperboloid, and this bi-curved circular cone coefficient is confirmed according to secondary mirror material refractive index and check light beam wavelength.In the present embodiment, the bi-curved circular cone coefficient of said secondary mirror is the opposite number of secondary mirror material refractive index square.

In the step of said processing secondary mirror, a side of secondary mirror is a hyperboloid, and opposite side is the plane reflection face; Work in-process is processed into the plane reflection face of secondary mirror the plane and plates reflectance coating, and its hyperboloid of while does not temporarily plate any film and is; After through the check of independent face type, again hyperboloid is plated reflectance coating, and then debug and total inspection with primary mirror.

See also Fig. 5, this manufacturing approach comprises the step of eliminating spherical aberration, coma, astigmatism, four monochromatic aberrations of the curvature of field, specifically comprises correcting lens group elimination monochromatic aberration step, reaches field corrector elimination monochromatic aberration step.Monochromatic aberration one in the third-order aberration theory has five types, is respectively spherical aberration, coma, astigmatism, filed curvature and distortion, uses S respectively ₁, S ₂, S ₃, S ₄And S ₅Represent.

The concrete grammar of correcting lens group elimination monochromatic aberration step is following:

$\left.\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=h_1{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^4{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+h_2{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^4{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+h_3{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_3,\\ {\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=y_1{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+J{W}_1+{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^3{y}_1{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+y_2{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+{\mathrm{JW}}_2+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^3{y}_2{K}_2+y_3{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_3+{\mathrm{JW}}_3,\\ {\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">S</figure-callout>}}_3=\frac{{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^2}{h_1}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+2J\frac{y_1}{h_1}{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_1+J^2\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}{\mathrm{\&Phi;}}_1+{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{y}_1^2{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\\ +\frac{y_2^2}{h_2}{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+2J\frac{y_2}{h_2}{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_2+J^2\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}{\mathrm{\&Phi;}}_2+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{y}_2^2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+\frac{y_3^2}{h_3}{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_3+2J\frac{y_3}{h_3}{\mathrm{<figure-callout\; id="3"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_3,\\ {\mathrm{<figure-callout\; id="4"\; label="S"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">S</figure-callout>}}_4=\frac{{\mathrm{\&Pi;}}_1}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}+\frac{{\mathrm{\&Pi;}}_2}{h_2}\end{array}\right\}---\left(1\right)$

Wherein, P, W, Φ, ∏, K are intermediate variable, are used for substituting recurrent polynomial expression; J is normalized Laplace invariant, and to simplify expression formula, h is an axle glazed thread height on the whole; Y is a chief ray height on the whole, and index number is represented the sequence number of optical surface, index number 1 expression primary mirror information; Index number 2 expression secondary mirror information, index number 3 expressions the 3rd mirror information;

Wherein:

h ₁＝l ₁u ₁＝l′ ₁u′ ₁， h ₂＝l ₂u ₂＝l′ ₂u′ ₂， h ₃＝l ₃u ₃＝l′ ₃u′ ₃

y ₁＝l _p1u _p1＝l′ _p1u′ _p1， y ₂＝l _p2u _p2＝l′ _p2u′ _p2， y ₃＝l _p3u _p3＝l′ _p3u′ _p3；

Wherein, l representes object distance, and u representes light subtended angle, l _pFor going into interpupillary distance, u _pBe the entrance pupil subtended angle, the sequence number rule is ditto said, upper right footmark ' expression picture side, no upper right corner target is represented object space;

For two catoptrons:

${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1={\left(\frac{\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}{\mathrm{\&Delta;}\frac{1}{n_1}}\right)}^2\mathrm{\&Delta;}\frac{u_1}{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1},$ ${\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2={\left(\frac{\mathrm{\&Delta;}{u}_2}{\mathrm{\&Delta;}\frac{1}{n_2}}\right)}^2\mathrm{\&Delta;}\frac{u_2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2},$

${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=-\frac{\mathrm{\&Delta;}{u}_1}{\mathrm{\&Delta;}\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1}}\mathrm{\&Delta;}\frac{u_1}{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1},$ ${\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_2=-\frac{\mathrm{\&Delta;}{u}_2}{\mathrm{\&Delta;}\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}}\mathrm{\&Delta;}\frac{u_2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}$

${\mathrm{\&Phi;}}_1=\mathrm{\&Delta;}\frac{u_1}{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1},$ ${\mathrm{\&Phi;}}_2=\mathrm{\&Delta;}\frac{u_2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2},$

${\mathrm{\&Pi;}}_1=\frac{\mathrm{\&Delta;}{n}_1{u}_1}{n_1{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1^{\&prime;}},$ ${\mathrm{\&Pi;}}_2=\frac{\mathrm{\&Delta;}{n}_2{u}_2}{n_1{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^{\&prime;}},$

${\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_1=-\frac{{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">e</figure-callout>}}_1^2}{r_{01}^3}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_1,$ ${\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_2=-\frac{{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">e</figure-callout>}}_2^2}{r_{02}^3}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2,;$

Wherein, r ₀Be the radius-of-curvature on aspheric surface summit, e representes the excentricity of quafric curve, and v is an Abbe number; N is the material refractive index; The sequence number rule is ditto said;

For no focal power correcting lens group:

u ₂′＝u ₃＝u ₃′；

In the formula;

representes focal power; The sequence number rule is ditto said; First lens in the subscript 31 expression lens combination, and the like.

The optical imaging system structural parameters are constructed as follows: wherein f representes focal length, and j representes Laplace invariant, 1) when object is positioned at infinity,

l ₁→∞，u ₁＝0，h ₁＝l ₁u ₁＝l′ ₁u′ ₁＝１，

n ₁＝n′ ₂＝n ₃＝n′ ₃＝1， n′ ₁＝n ₂＝-1， h ₂＝l ₂u ₂＝l′ ₂u′ ₂，

h ₃＝l ₃u ₃＝l′ ₃u′ ₃， u′ ₂＝u ₃＝u′ ₃＝1， f′＝1，

2) when the light field is on primary mirror,

l _p1＝0， u _p1＝-1， j＝1

y ₃＝l _p1u _p1＝l′ _p1u′ _p1＝-l _p1，

y ₂＝l _p2u _p2＝l′ _p2u′ _p2，

y ₃＝l _p3u _p3＝l′ _p3u′ _p3，

Introduce new parameter, the ratio of obstruction α and secondary mirror magnification β,

${\mathrm{\&alpha;}}_2=\frac{l_2}{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\&prime;}}=\frac{{2l}_2}{r_{01}}\&ap;\frac{h_2}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}={\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2,$ ${\mathrm{\&alpha;}}_3=\frac{h_3}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}={\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_3,$ $\mathrm{\&beta;}=\frac{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^{\&prime;}}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}=\frac{u_2}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2^{\&prime;}}={\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2,$

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\&prime;}=\frac{l_2}{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}=\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}=\frac{1}{\mathrm{\&beta;}},$ $r_{01}=\frac{2}{\mathrm{\&beta;}},$

By paraxial formula

$\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^{\&prime;}-n_2}{r_{02}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^{\&prime;}}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^{\&prime;}}-\frac{n_2}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2},$ $\frac{2}{r_{02}}=\frac{1}{l_2}(\frac{1}{\mathrm{\&beta;}}+1)=\frac{2}{{\mathrm{\&alpha;}}_2{r}_{01}}\left(\frac{1+\mathrm{\&beta;}}{\mathrm{\&beta;}}\right),$

Draw

$r_{02}=\frac{{\mathrm{\&alpha;}}_2\mathrm{\&beta;}}{\mathrm{\&beta;}+1}{r}_{01},$ $r_{02}=\frac{2{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}+1},---\left(2\right)$

Find the solution the height of chief ray on each face, draw

$\left.\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=0,\\ {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=-\frac{1-{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}},\\ {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_3=\frac{\mathrm{\&beta;}({\mathrm{\&alpha;}}_2-{\mathrm{\&alpha;}}_3)-{\mathrm{\&alpha;}}_3(1-{\mathrm{\&alpha;}}_2)}{{\mathrm{\&alpha;}}_2\mathrm{\&beta;}}\end{array}\right\}---\left(3\right)$

Thus, to the aspheric parameter value of double mirror:

$\left.\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1=-\frac{{\mathrm{\&beta;}}^3}{4},& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2=\frac{{(1-\mathrm{\&beta;})}^2(1+\mathrm{\&beta;})}{4},\\ {\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=-\frac{{\mathrm{\&beta;}}^2}{2},& {\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_2=-\frac{1-{\mathrm{\&beta;}}^2}{2},\\ {\mathrm{\&Pi;}}_1=\mathrm{\&beta;},& {\mathrm{\&Pi;}}_2=-(1+\mathrm{\&beta;}),\\ {\mathrm{\&Phi;}}_1=-\mathrm{\&beta;},& {\mathrm{\&Phi;}}_2=\frac{1+\mathrm{\&beta;}}{{\mathrm{\&alpha;}}_2},\\ {\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_1=\frac{{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">e</figure-callout>}}_1^2{\mathrm{\&beta;}}^3}{4},& {\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_2=-\frac{{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">e</figure-callout>}}_2^2{(1+\mathrm{\&beta;})}^3}{4{\mathrm{\&alpha;}}_2^3},\end{array}\right\}---\left(4\right)$

Here α representes that secondary mirror leaves the distance of first focus, has also shown the screening hurdle ratio of secondary mirror with primary mirror, and β representes the magnification of secondary mirror;

In above-mentioned expression formula substitution (1), make the S in (1) ₁=S ₂=S ₃=S ₄=0, promptly eliminate spherical aberration, coma, astigmatism and filed curvature, obtain the initial value of the structural parameters of optical system.

The concrete grammar of field corrector elimination monochromatic aberration step is following:

Symbol definition is ditto said; Emerging

representes focal power, and the sequence number rule is ditto said.

To the optical system structure parameter of double mirror aspheric surface and field corrector composition, under the condition of ruleization:

1) object is positioned at infinity (by shown in Figure 1)

l ₁→∞，u ₁＝0， h ₁＝l ₁u ₁＝l′ ₁u′ ₁＝1，

n ₁＝n′ ₂＝n ₃＝n′ ₃＝1， n′ ₁＝n ₂＝-1， h ₂＝l ₂u ₂＝l′ ₂u′ ₂，

h ₃＝l ₃u ₃＝l′ ₃u′ ₃， u′ ₂＝u ₃＝u′ ₃＝1， f′＝1，

2) light field on primary mirror (like Fig. 1)

l _p1＝0， u _p1＝-1， j＝1

y ₁＝l _p1u _p1＝l′ _p1u′ _p1＝-l _p1，

y ₂＝l _p2u _p2＝l′ _p2u′ _p2，

y ₃＝l _p3u _p3＝l′ _p3u′ _p3，

Introduce new parameter, α 2 is the secondary mirror the ratio of obstruction, α 3 field corrector the ratio of obstruction, and β 2 is the secondary mirror magnification, and β 3 is the field corrector magnification, and β=β 2 β 3 are the combination magnification of secondary mirror and field corrector:

${\mathrm{\&alpha;}}_2=\frac{h_2}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}={\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2,$ ${\mathrm{\&alpha;}}_3=\frac{h_3}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}={\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_3,$

${\mathrm{\&beta;}}_2=\frac{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^{\&prime;}}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}=\frac{u_2}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2^{\&prime;}},$ ${\mathrm{\&beta;}}_3=\frac{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_3^{\&prime;}}{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_3}=\frac{u_3}{{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_3^{\&prime;}}={\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_3={\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2^{\&prime;},$ $\mathrm{\&beta;}={\mathrm{\&beta;}}_2{\mathrm{\&beta;}}_3=\frac{u_2}{{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_3^{\&prime;}}={\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2$

$\frac{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\&prime;}}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}=\frac{l_2}{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}=\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">u</figure-callout>}}_2}=\frac{1}{\mathrm{\&beta;}},$ ${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\&prime;}=\frac{1}{\mathrm{\&beta;}},$ $r_{01}=\frac{2}{\mathrm{\&beta;}},$

By paraxial formula

$\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^{\&prime;}-n_2}{r_{02}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^{\&prime;}}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^{\&prime;}}-\frac{n_2}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2},$ $\frac{2}{r_{02}}=\frac{1}{l_2}(\frac{1}{{\mathrm{\&beta;}}_2}+1)=\frac{2}{{\mathrm{\&alpha;}}_2{r}_{01}}\left(\frac{1+{\mathrm{\&beta;}}_2}{{\mathrm{\&beta;}}_2}\right),$

Draw

$r_{02}=\frac{2{\mathrm{\&alpha;}}_2}{(1+{\mathrm{\&beta;}}_2){\mathrm{\&beta;}}_3}=\frac{2{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}+{\mathrm{\&beta;}}_3},---\left(6\right)$

Find the solution the height of chief ray on each face, draw

$\left.\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=0,\\ {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=-\frac{1-{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}},\\ {\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">y</figure-callout>}}_3=\frac{{\mathrm{\&beta;}}_2({\mathrm{\&alpha;}}_2-{\mathrm{\&alpha;}}_3)-{\mathrm{\&alpha;}}_3(1-{\mathrm{\&alpha;}}_2)}{{\mathrm{\&alpha;}}_2\mathrm{\&beta;}}\end{array}\right\}---\left(7\right)$

Thus, to the aspheric parameter value of double mirror:

${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_1=-\frac{{\mathrm{\&beta;}}_2^3{\mathrm{\&beta;}}_3^3}{4},$ ${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=-\frac{{\mathrm{\&beta;}}^2}{2},$

${\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">P</figure-callout>}}_2=\frac{{\mathrm{\&beta;}}_3^3{(1-{\mathrm{\&beta;}}_2)}^2(1+{\mathrm{\&beta;}}_2)}{4},$ ${\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">W</figure-callout>}}_2=-\frac{{\mathrm{\&beta;}}_3^2(1-{\mathrm{\&beta;}}_2^2)}{2},$

Φ ₁＝-β， ∏ ₁＝β，

Φ ₂＝β ₃(1+β ₂)， ∏ ₂＝-β ₃(1+β ₂)，

${\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_1=\frac{{\mathrm{\&beta;}}^3{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">e</figure-callout>}}_1^2}{4},$

${\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">K</figure-callout>}}_2=-\frac{{\mathrm{\&beta;}}_3^3{(1+{\mathrm{\&beta;}}_2)}^3{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">e</figure-callout>}}_2^2}{4{\mathrm{\&alpha;}}_2^3},$

$\frac{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_3^{\&prime;}}{f^{\&prime;}}=\frac{h_3}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008100387019E00021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1},$ l′ ₃＝α ₃

In above-mentioned expression formula substitution formula (5), make the S in the formula (5) ₁=S ₂=S ₃=S ₄=0, promptly eliminate spherical aberration, coma, astigmatism and filed curvature, can obtain the initial value of the structural parameters of optical system.

Obtain the structural parameters of corresponding form through above-mentioned steps, then the structural parameters with two kinds of forms merge and adjustment, draw the structural parameters initial value of system.

The two reflective imaging systems of the present invention are through computer optimization, and its picture element and visual field have obtained comparatively significantly improving, and from how much point range figures (SPOT), modulation transfer function MTF and encircled power EE, its picture element has reached diffraction limit basically.

Above embodiment is the unrestricted technical scheme of the present invention in order to explanation only.Do not break away from any modification or the local replacement of spirit and scope of the invention, all should be encompassed in the middle of the claim scope of the present invention.

Claims (10)

1. an optical imaging system comprises the secondary mirror, primary mirror, correcting lens group, the field corrector that are arranged in order; It is characterized in that: said primary mirror is for parabolic; Secondary mirror is a hyperboloid, and the bi-curved circular cone coefficient of secondary mirror is confirmed according to secondary mirror material refractive index; Wherein, the bi-curved circular cone coefficient of said secondary mirror is more than or equal to the opposite number-0.5 of secondary mirror material refractive index square, smaller or equal to opposite number+0.5 of secondary mirror material refractive index square.

2. optical imaging system according to claim 1 is characterized in that: a side of said secondary mirror is a hyperboloid, and opposite side is the plane reflection face.

3. optical imaging system according to claim 1 is characterized in that: said primary mirror does not overlap with the focus of secondary mirror; If when the focus of primary mirror secondary mirror overlapped, secondary mirror was L apart from the distance of primary mirror, the primary mirror focal length is f ', and then the distance of secondary mirror and primary mirror is greater than L+0.06*f ', smaller or equal to L+0.10*f '.

4. optical imaging system according to claim 1 is characterized in that: said primary mirror, secondary mirror, correcting lens group and image field correcting lens are quartz material.

5. the manufacturing approach of any said optical imaging system of claim 1 to 4 is characterized in that: comprise the steps:

The step of processing primary mirror: the parabola that primary mirror is processed into setting;

The step of processing secondary mirror: secondary mirror is processed into hyperboloid, and the bi-curved circular cone coefficient of said secondary mirror is confirmed according to secondary mirror material refractive index; Wherein, the bi-curved circular cone coefficient of said secondary mirror is more than or equal to the opposite number-0.5 of secondary mirror material refractive index square, smaller or equal to opposite number+0.5 of secondary mirror material refractive index square.

6. manufacturing approach according to claim 5 is characterized in that: in the step of said processing secondary mirror, a side of secondary mirror is a hyperboloid, and opposite side is the plane reflection face; Work in-process is processed into the plane reflection face of secondary mirror the plane and plates reflectance coating, and its hyperboloid of while does not temporarily plate any film and is; After through the check of independent face type, again hyperboloid is plated reflectance coating, and then debug and total inspection with primary mirror.

7. according to claim 4 or 5 described manufacturing approaches, it is characterized in that: said method comprises the step of eliminating spherical aberration, coma, astigmatism, four monochromatic aberrations of the curvature of field.

8. manufacturing approach according to claim 7 is characterized in that: the step of eliminating monochromatic aberration comprises the step of correcting lens group elimination monochromatic aberration; Concrete grammar is following:

Monochromatic aberration one in the third-order aberration theory has five types, is respectively spherical aberration, coma, astigmatism, filed curvature and distortion, uses S respectively for its preceding four ₁, S ₂, S ₃And S ₄Represent as follows;

$\left.\begin{array}{c}{S}_1=h_1{P}_1+h_1^4{K}_1+h_2{P}_2+h_2^4{K}_2+h_3{P}_3,\\ S_2=y_1{P}_1+{\mathrm{JW}}_1+h_1^3{y}_1{K}_1+y_2{P}_2+{\mathrm{JW}}_2+h_2^3{y}_2{K}_2+y_3{P}_3+{\mathrm{JW}}_3,\\ S_3=\frac{y_1^2}{h_1}{P}_1+2J\frac{y_1}{h_1}{W}_1+J^2\frac{1}{h_1}{\mathrm{\&Phi;}}_1+h_1^2{y}_1^2{K}_1\\ +\frac{y_2^2}{h_2}{P}_2+2J\frac{y_2}{h_2}{W}_2+J^2\frac{1}{h_2}{\mathrm{\&Phi;}}_2+h_2^2{y}_2^2{K}_2+\frac{y_3^2}{h_3}{P}_3+2J\frac{y_3}{h_3}{W}_3,\\ S_4=\frac{{\mathrm{\&Pi;}}_1}{h_1}+\frac{{\mathrm{\&Pi;}}_2}{h_2}\end{array}\right\}---\left(1\right)$

Wherein, P, W, Φ, ∏, K are intermediate variable, are used for substituting recurrent polynomial expression; J is normalized Laplace invariant, and to simplify expression formula, h is an axle glazed thread height on the whole; Y is a chief ray height on the whole, and index number is represented the sequence number of optical surface, index number 1 expression primary mirror information; Index number 2 expression secondary mirror information, index number 3 expressions the 3rd mirror information;

Wherein:

h ₁＝l ₁u ₁＝l′ ₁u′ ₁，h ₂＝l ₂u ₂＝l′ ₂u′ ₂，h ₃＝l ₃u ₃＝l′ ₃u′ ₃

y ₁＝l _p1u _p1＝l′ _p1u′ _p1，y ₂＝l _p2u _p2＝l′ _p2u′ _p2，y ₃＝l _p3u _p3＝l′ _p3u′ _p3；

Wherein, l representes object distance, and u representes light subtended angle, l _pFor going into interpupillary distance, u _pBe the entrance pupil subtended angle, the sequence number rule is ditto said, upper right footmark ' expression picture side, no upper right corner target is represented object space;

For two catoptrons:

$P_1={\left(\frac{\mathrm{\&Delta;}{u}_1}{\mathrm{\&Delta;}\frac{1}{n_1}}\right)}^2\mathrm{\&Delta;}\frac{u_1}{n_1},$ $P_2={\left(\frac{\mathrm{\&Delta;}{u}_2}{\mathrm{\&Delta;}\frac{1}{n_2}}\right)}^2\mathrm{\&Delta;}\frac{u_2}{n_2},$

$W_1=-\frac{\mathrm{\&Delta;}{u}_1}{\mathrm{\&Delta;}\frac{1}{n_1}}\mathrm{\&Delta;}\frac{u_1}{n_1},$ $W_2=-\frac{\mathrm{\&Delta;}{u}_2}{\mathrm{\&Delta;}\frac{1}{n_2}}\mathrm{\&Delta;}\frac{u_2}{n_2}$

${\mathrm{\&Phi;}}_1=\mathrm{\&Delta;}\frac{u_1}{n_1},$ ${\mathrm{\&Phi;}}_2=\mathrm{\&Delta;}\frac{u_2}{n_2},$

${\mathrm{\&Pi;}}_1=\frac{\mathrm{\&Delta;}{n}_1{u}_1}{n_1{n}_1^{\&prime;}},$ ${\mathrm{\&Pi;}}_2=\frac{\mathrm{\&Delta;}{n}_2{u}_2}{n_1{n}_2^{\&prime;}},$

$K_1=-\frac{r_1^2}{r_{01}^3}\mathrm{\&Delta;}{n}_1,$ $K_2=-\frac{e_2^2}{r_{02}^3}\mathrm{\&Delta;}{n}_2,;$

Wherein, r ₀Be the radius-of-curvature on aspheric surface summit, e representes the excentricity of quafric curve, and v is an Abbe number; N is the material refractive index; The sequence number rule is ditto said;

For no focal power correcting lens group:

u′ ₂＝u ₃＝u′ ₃；

In the formula;

representes focal power; The sequence number rule is ditto said; First lens in the subscript 31 expression lens combination, and the like;

The optical imaging system structural parameters are constructed as follows: wherein f representes focal length, and j representes the Laplace invariant,

1) when object is positioned at infinity,

l ₁→∞，u ₁＝0，h ₁＝l ₁u ₁＝l′ ₁u′ ₁＝1，

n ₁＝n′ ₂＝n ₃＝n′ ₃＝1，n′ ₁＝n ₂＝-1，h ₂＝l ₂u ₂＝l′ ₂u′ ₂，

h ₃＝l ₃u ₃＝l′ ₃u′ ₃，u′ ₂＝u ₃＝u′ ₃＝1，f′＝1，

2) when the light field is on primary mirror,

l _p1＝0，u _p1＝-1，j＝1

y ₁＝l _p1u _p1＝l′ _p1u′ _p1＝-l _p1，

y ₂＝l _p2u _p2＝l′ _p2u′ _p2，

y ₃＝l _p3u _p3＝l′ _p3u′ _p3，

Introduce new parameter, the ratio of obstruction α and secondary mirror magnification β,

${\mathrm{\&alpha;}}_2=\frac{l_2}{f_1^{\&prime;}}=\frac{{2l}_2}{r_{01}}\&ap;\frac{h_2}{h_1}=h_2,$ ${\mathrm{\&alpha;}}_3=\frac{h_3}{h_1}=h_3,$ $\mathrm{\&beta;}=\frac{l_2^{\&prime;}}{l_2}=\frac{u_2}{u_2^{\&prime;}}=u_2,$

$f_1^{\&prime;}=\frac{l_2}{h_2}=\frac{1}{u_2}=\frac{1}{\mathrm{\&beta;}},$ $r_{01}=\frac{2}{\mathrm{\&beta;}},$

By paraxial formula

$\frac{n_2^{\&prime;}-n_2}{r_{02}}=\frac{n_2^{\&prime;}}{l_2^{\&prime;}}-\frac{n_2}{l_2},$ $\frac{2}{r_{02}}=\frac{1}{l_2}(\frac{1}{\mathrm{\&beta;}}+1)=\frac{2}{{\mathrm{\&alpha;}}_2{r}_{02}}\left(\frac{1+\mathrm{\&beta;}}{\mathrm{\&beta;}}\right),$

Draw

$r_{02}=\frac{{\mathrm{\&alpha;}}_2\mathrm{\&beta;}}{\mathrm{\&beta;}+1}{r}_{01},$ $r_{02}=\frac{2{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}+1},---\left(2\right)$

Find the solution the height of chief ray on each face, draw

$\left.\begin{array}{c}{y}_1=0\\ y_2=-\frac{1-{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}},\\ y_3=\frac{\mathrm{\&beta;}({\mathrm{\&alpha;}}_2-{\mathrm{\&alpha;}}_3)-{\mathrm{\&alpha;}}_3(1-{\mathrm{\&alpha;}}_2)}{{\mathrm{\&alpha;}}_2\mathrm{\&beta;}}\end{array}\right\}---\left(3\right)$

Thus, to the aspheric parameter value of double mirror:

$\left.\begin{array}{cc}{P}_1=-\frac{{\mathrm{\&beta;}}^3}{4},& P_2=\frac{{(1-\mathrm{\&beta;})}^2(1+\mathrm{\&beta;})}{4},\\ W_1=-\frac{{\mathrm{\&beta;}}^2}{2},& W_2=-\frac{1-{\mathrm{\&beta;}}^2}{2},\\ {\mathrm{\&Pi;}}_1=\mathrm{\&beta;},& {\mathrm{\&Pi;}}_2=-(1+\mathrm{\&beta;}),\\ {\mathrm{\&Phi;}}_1=-\mathrm{\&beta;},& {\mathrm{\&Phi;}}_2=\frac{1+\mathrm{\&beta;}}{{\mathrm{\&alpha;}}_2},\\ K_1=\frac{e_1^2{\mathrm{\&beta;}}^3}{4},& K_2=-\frac{e_2^2{(1+\mathrm{\&beta;})}^3}{4{\mathrm{\&alpha;}}_2^3},\end{array}\right\}---\left(4\right)$

Here α representes that secondary mirror leaves the distance of first focus, has also shown the screening hurdle ratio of secondary mirror with primary mirror, and β representes the magnification of secondary mirror;

In above-mentioned expression formula substitution (1), make the S in (1) ₁=S ₂=S ₃=S ₄=0, promptly eliminate spherical aberration, coma, astigmatism and filed curvature, obtain the initial value of the structural parameters of optical system.

9. manufacturing approach according to claim 8 is characterized in that: the step of eliminating monochromatic aberration comprises the step of field corrector elimination monochromatic aberration; Concrete grammar is following:

Monochromatic aberration one in the third-order aberration theory has five types, is respectively spherical aberration, coma, astigmatism, filed curvature and distortion, uses S respectively for its preceding four ₁, S ₂, S ₃And S ₄Represent;

Symbol definition is ditto said; Emerging representes focal power, and the sequence number rule is ditto said;

To the optical system structure parameter of double mirror aspheric surface and field corrector composition, under the condition of ruleization:

1) object is positioned at infinity

l ₁→∞，u ₁＝0，h ₁＝l ₁u ₁＝l′ ₁u′ ₁＝1，

n ₁＝n′ ₂＝n ₃＝n′ ₃＝1，n′ ₁＝n ₂＝-1，h ₂＝l ₂u ₂＝l′ ₂u′ ₂，

h ₃＝l ₃u ₃＝l′ ₃u′ ₃，u′ ₂＝u ₃＝u′ ₃＝1，f′＝1，

2) the light field is on primary mirror

l _p1＝0，u _p1＝-1，j＝1

y ₁＝l _p1u _p1＝l′ _p1u′ _p1＝-l _p1，

y ₂＝l _p2u _p2＝l′ _p2u′ _p2，

y ₃＝l _p3u _p3＝l′ _p3u′ _p3，

Introduce new parameter, α 2 is the secondary mirror the ratio of obstruction, α 3 field corrector the ratio of obstruction, and β 2 is the secondary mirror magnification, and β 3 is the field corrector magnification, and β=β 2 β 3 are the combination magnification of secondary mirror and field corrector:

${\mathrm{\&alpha;}}_2=\frac{h_2}{h_1}=h_2,$ ${\mathrm{\&alpha;}}_3=\frac{h_3}{h_1}=h_3,$

${\mathrm{\&beta;}}_2=\frac{l_2^{\&prime;}}{l_2}=\frac{u_2}{u_2^{\&prime;}},$ ${\mathrm{\&beta;}}_3=\frac{l_3^{\&prime;}}{l_3}=\frac{u_3}{u_3^{\&prime;}}=u_3=u_2^{\&prime;},$ $\mathrm{\&beta;}={\mathrm{\&beta;}}_2{\mathrm{\&beta;}}_3=\frac{u_2}{u_3^{\&prime;}}=u_2$

$\frac{f_1^{\&prime;}}{h_1}=\frac{l_2}{h_2}=\frac{1}{u_2}=\frac{1}{\mathrm{\&beta;}},$ $f_1^{\&prime;}=\frac{1}{\mathrm{\&beta;}},$ $r_{01}=\frac{2}{\mathrm{\&beta;}},$

By paraxial formula

$\frac{n_2^{\&prime;}-n_2}{r_{02}}=\frac{n_2^{\&prime;}}{l_2^{\&prime;}}-\frac{n_2}{l_2},$ $\frac{2}{r_{02}}=\frac{1}{l_2}(\frac{1}{{\mathrm{\&beta;}}_2}+1)=\frac{2}{{\mathrm{\&alpha;}}_2{r}_{01}}\left(\frac{1+{\mathrm{\&beta;}}_2}{{\mathrm{\&beta;}}_2}\right),$

Draw

$r_{02}=\frac{2{\mathrm{\&alpha;}}_2}{(1+{\mathrm{\&beta;}}_2){\mathrm{\&beta;}}_3}=\frac{2{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}+{\mathrm{\&beta;}}_3},---\left(6\right)$

Find the solution the height of chief ray on each face, draw

$\left.\begin{array}{c}{y}_1=0,\\ y_2=-\frac{1-{\mathrm{\&alpha;}}_2}{\mathrm{\&beta;}},\\ y_3=\frac{{\mathrm{\&beta;}}_2({\mathrm{\&alpha;}}_2-{\mathrm{\&alpha;}}_3)-{\mathrm{\&alpha;}}_3(1-{\mathrm{\&alpha;}}_2)}{{\mathrm{\&alpha;}}_2\mathrm{\&beta;}}\end{array}\right\}---\left(7\right)$

Thus, to the aspheric parameter value of double mirror:

$P_1=-\frac{{\mathrm{\&beta;}}_2^3{\mathrm{\&beta;}}_3^3}{4},$ $W_1=-\frac{{\mathrm{\&beta;}}^2}{2},$

$P_2=\frac{{\mathrm{\&beta;}}_3^3{(1-{\mathrm{\&beta;}}_2)}^2(1+{\mathrm{\&beta;}}_2)}{4},$ $W_2=-\frac{{\mathrm{\&beta;}}_3^2(1-{\mathrm{\&beta;}}_2^2)}{2},$

Φ ₁＝-β，∏ ₁＝β，

Φ ₂＝β ₃(1+β ₂)，∏ ₂＝-β ₃( ₁+β ₂)，

$K_1=\frac{{\mathrm{\&beta;}}^3{e}_1^2}{4},$

$K_2=-\frac{{\mathrm{\&beta;}}_3^3{(1+{\mathrm{\&beta;}}_2)}^3{e}_2^2}{4{\mathrm{\&beta;}}_2^3},$

$\frac{l_3^{\&prime;}}{f^{\&prime;}}=\frac{h_3}{h_1},$ l′ ₃＝α ₃

In above-mentioned expression formula substitution formula (5), make the S in the formula (5) ₁=S ₂=S ₃=S ₄=0, promptly eliminate spherical aberration, coma, astigmatism and filed curvature, can obtain the initial value of the structural parameters of optical system.

10. manufacturing approach according to claim 9 is characterized in that: the step of eliminating monochromatic aberration comprises the step of correcting lens group elimination monochromatic aberration, reaches the step that field corrector is eliminated monochromatic aberration; Obtain the structural parameters of corresponding form through above-mentioned steps, then the structural parameters with two kinds of forms merge and adjustment, draw the structural parameters initial value of system.

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