CN104635336A - Design method for unblocked two-reflector off-axis three-mirror optical system - Google Patents

Abstract

The invention relates to a design method for an unblocked two-reflector off-axis three-mirror optical system and belongs to the field of optical design. The off-axis three-mirror optical system is formed by a main mirror, a secondary mirror and a tertiary mirror; a main mirror and a tertiary mirror in a conventional off-axis three-reflection optical system are improved into aspherical reflectors; the unblocked two-reflector off-axis three-mirror optical system is invented. Compared with the prior art, the design method disclosed by the invention is simple and easy to operate and the designed optical system is low in processing and adjusting difficulty.

Description

A kind of explicit two catoptrons are from axle three reflecting optical system method for designing

Technical field

The invention belongs to optical design arts, particularly a kind of method of designing optical system.

Background technology

Refraction type and the restriction of catadioptric due to refractive material performance and the impact of wide spectral range aberration, or eliminate second order spectrum by the structure of complexity, make it apply and be subject to certain restrictions.And reflective optical system does not produce aberration, it is comparatively large that aperture can be done, and be easy to lightweight.Two reflecting system structures are simple, but variable is few, can not meet the requirement of Large visual angle, object lens of large relative aperture.And three anti-systems have 3 radiuses, 2 intervals and 3 asphericity coefficients totally 8 parameters, add the degree of freedom of system optimization.Except meeting the system performances such as focal length, spherical aberration, coma, astigmatism and the curvature of field and picture element requirement, enough variablees are also had to carry out the optimal design of system layout and structure.But three-mirror reflection system is when visual field is larger, central obscuration can be caused excessive, impact enters the gross energy of system, also reduces the resolution of optical system simultaneously.Adopt and there is not central obscuration from the Three mirror optical system of axle form, and can optimized variable many, effectively improve system imaging quality while improving optical system visual field size.Usual off-axis three-mirror anastigmat is made up of primary mirror, secondary mirror and three mirrors, due to introduce with from axle, the performance of system is subject to processing with the restriction of alignment error level very large, to processing with the tolerance such as to debug also strict especially.

In order to overcome above-mentioned difficulties, the primary mirror in traditional off-axis three-mirror anastigmat and three mirrors are improved to one piece of non-spherical reflector by the present invention, have invented a kind of explicit two catoptrons from axle three reflecting optical system.

Summary of the invention

Technical matters to be solved by this invention: for shortcomings and deficiencies of the prior art, the invention provides a kind of explicit two catoptrons from axle three reflecting optical system method for designing, this method for designing is simple, the optical system processing of design and resetting difficulty low.

The present invention is design like this: a kind of explicit two catoptrons, from axle three reflecting optical system method for designing, is characterized in that: comprise the steps,

The initial structure parameter of step one, three-mirror reflection optical system calculates,

Three-mirror reflection optical system is made up of primary mirror M1, secondary mirror M2, three mirror M3, after light, arrives image planes successively through primary mirror M1, secondary mirror M2, three mirror M3; The radius-of-curvature on described primary mirror M1, secondary mirror M2, three mirror M3 summits is respectively R1, R2, R3, and the asphericity coefficient of primary mirror M1, secondary mirror M2, three mirror M3 is respectively the spacing of primary mirror M1, secondary mirror M2, three mirror M3 and image planes is respectively d ₁, d ₂,-l ₃'; The feature of two catoptron three reflecting optical systems is that primary mirror M1 is identical with three mirror M3 and overlap, and namely requires R1=R3, d ₁=-d ₂;

The imaging character of three reflecting optical systems is by structural parameters α ₁, α ₂, β ₁, β ₂determine; Described α ₁for secondary mirror is to the ratio of obstruction of primary mirror: α ₁=l ₂/ f ₁' ≈ h ₂/ h ₁; Described α ₂be the ratio of obstruction of three mirrors to secondary mirror: α ₂=l ₃/ l ₂' ≈ h ₃/ h ₂; Described β ₁, β ₂be respectively the magnification of secondary mirror and three mirrors;

By total focal distance f '=1 normalized, can obtain:

d ₁＝α ₂(1-α ₁) ²+α ₁(1-α ₂) ²；

$d_2=\frac{{\mathrm{\α}}_1(1-{\mathrm{\α}}_2)}{{\mathrm{\β}}_2};$

By α ₁, α ₂as initial known quantity, can obtain according to flat field condition:

${\mathrm{\β}}_1=\frac{1-{\mathrm{\α}}_1}{d_1{\mathrm{\β}}_2};$

${\mathrm{\β}}_2=\frac{1-\frac{{\mathrm{\α}}_2{(1-{\mathrm{\α}}_1)}^2}{d_1}}{{\mathrm{\α}}_2-1};$

Utilize Gaussian optics theoretical, the formula of three-mirror reflection optical system structure parameter can be obtained:

$R_1=\frac{2}{{\mathrm{\β}}_1{\mathrm{\β}}_2}{f}^{\′};$

$R_2=\frac{{2\mathrm{\α}}_1}{{\mathrm{\β}}_2(1+{\mathrm{\β}}_1)}{f}^{\′};$

$R_3=\frac{{2\mathrm{\α}}_1{\mathrm{\α}}_2}{1+{\mathrm{\β}}_2}{f}^{\′};$

d ₁＝[α ₂(1-α ₁) ²+α ₁(1-α ₂) ²]f′；

$d_2=\frac{{\mathrm{\α}}_1(1-{\mathrm{\α}}_2)}{{\mathrm{\β}}_2}{f}^{\′};$

l ₃′＝α ₁α ₂f′；

In formula, total focal length that described f ' is system; Determine three-mirror reflection optical system initial structure parameter thus;

Restriction R ₁=R ₃, obtain:

${\mathrm{\α}}_2=-\frac{{2\mathrm{\α}}_1^2-{4\mathrm{\α}}_1+1}{{\mathrm{\α}}_1};$

According to above formula, provide a α ₁just α can be obtained ₂, by α ₁and α ₂substitute in above-mentioned three-mirror reflection optical system structure parameter equation, just can obtain the entire infrastructure parameter of two catoptron three-mirror reflection optical systems;

The three grades of spherical aberrations, the coma that make two catoptron three-mirror reflection optical systems are zero, can obtain the asphericity coefficient of two catoptrons by primary spherical aberration coefficient S _i=0:

$e_1^2=1+\frac{1}{{\mathrm{\β}}_1^3{\mathrm{\β}}_2^3}[{\mathrm{\α}}_1{\mathrm{\α}}_2(1+{\mathrm{\β}}_2){(1-{\mathrm{\β}}_2)}^2-{\mathrm{\α}}_1{\mathrm{\β}}_2^3(1+{\mathrm{\β}}_1){(1-{\mathrm{\β}}_1)}^2+e_2^2{\mathrm{\α}}_1{\mathrm{\β}}_2^3{(1+{\mathrm{\β}}_1)}^3-e_1^2{\mathrm{\α}}_1{\mathrm{\α}}_2{(1+{\mathrm{\β}}_2)}^3];$

By elementary coma coefficient S _iI=0:

$\begin{array}{c}{e}_2^2({\mathrm{\α}}_1-1){\mathrm{\β}}_2^3{(1+{\mathrm{\β}}_1)}^3-e_1^2[{\mathrm{\α}}_2({\mathrm{\α}}_1-1)+{\mathrm{\β}}_1(1-{\mathrm{\α}}_2)]{(1+{\mathrm{\β}}_2)}^3\\ =({\mathrm{\α}}_1-1){\mathrm{\β}}_2^3(1+{\mathrm{\β}}_1){(1-{\mathrm{\β}}_1)}^2-[{\mathrm{\α}}_2({\mathrm{\α}}_1-1)+{\mathrm{\β}}_1(1-{\mathrm{\α}}_2)](1+{\mathrm{\β}}_2){(1-{\mathrm{\β}}_2)}^2-{2\mathrm{\β}}_1{\mathrm{\β}}_2\end{array};$

By α ₁, α ₂, β ₁, β ₂bring the asphericity coefficient can obtaining two mirror surfaces in above-mentioned formula into so far, the structural parameters R of system ₁(R ₃), R ₂, d ₁(-d ₂), all determine;

Step 2, the initial structure parameter calculating acquisition in step one is input in Zemax optical design software; Be placed in by diaphragm on first surface, getting optical aperture is that the system non-stop layer of making blocks, and carries out Optical System Design optimization, can be met explicit two catoptrons of requirement from axle three reflecting optical system from axle amount.

By above-mentioned design proposal, the present invention can bring following beneficial effect:

The present invention proposes a kind of explicit two catoptrons from axle three reflecting optical system method for designing, primary mirror in traditional off-axis three-mirror anastigmat and three mirrors are improved to one piece of non-spherical reflector by the method, because primary mirror and three mirrors share one piece of catoptron, compare common off-axial three-reflective system, reduce processing and resetting difficulty.Derived the initial optical parameter calculation formula of two catoptron three-reflection optical systems, drawn the solving equation group being applicable to this optical system, method for designing is simple.

Accompanying drawing explanation

Illustrate that the invention will be further described with embodiment below in conjunction with accompanying drawing:

Fig. 1 is the initial configuration schematic diagram of a kind of explicit two catoptrons of the present invention from two catoptron three reflecting optical systems of axle three reflecting optical system method for designing.

Fig. 2 is a kind of explicit two catoptrons of the present invention from two catoptrons of axle three reflecting optical system method for designing from the structural representation of axle three reflecting optical system.

Embodiment

Explicit two catoptrons are from an axle three reflecting optical system method for designing as shown in the figure, it is characterized in that, condition needed for the method and performing step as follows:

Required condition: initial structure parameter computation model, Zemax optical design software;

Performing step:

The initial structure parameter of step 1, three-mirror reflection optical system calculates.

Three-mirror reflection optical system is made up of primary mirror, secondary mirror and three mirrors, after light, successively through primary mirror M1, secondary mirror M2 and three mirror M3, finally arrives image planes.The radius-of-curvature on primary mirror M1, secondary mirror M2 and three mirror M3 summits is respectively R1, R2, R3; The asphericity coefficient of M1, M2 and M3 is respectively d ₁, d ₂,-l ₃' be respectively the spacing of primary mirror and secondary mirror, secondary mirror and three mirrors and three mirrors and image planes.As shown in Figure 1, this system features is that primary mirror is identical with three mirrors and overlap to the initial configuration of two catoptron three-reflection optical systems, namely requires R1=R3, d ₁=-d ₂.

The imaging character of three-mirror reflection optical system is by structural parameters α ₁, α ₂, β ₁and β ₂determine.α ₁=l ₂/ f ₁' ≈ h ₂/ h ₁for secondary mirror is to the ratio of obstruction of primary mirror; α ₂=l ₃/ l ₂' ≈ h ₃/ h ₂be the ratio of obstruction of three mirrors to secondary mirror; β ₁and β ₂be respectively the magnification of secondary mirror and three mirrors.

Consider from the general structure of instrument, wish that lens barrel is better shorter, by total focal distance f '=1 normalized, can obtain

d ₁＝α ₂(1-α ₁) ²+α ₁(1-α ₂) ²(1)

$d_2=\frac{{\mathrm{\α}}_1(1-{\mathrm{\α}}_2)}{{\mathrm{\β}}_2}---\left(2\right)$

In order to the relation making the condition of given related structure aspect and system overall length require is more clear, by α ₁, α ₂as initial known quantity, can obtain according to flat field condition:

${\mathrm{\β}}_1=\frac{1-{\mathrm{\α}}_1}{d_1{\mathrm{\β}}_2}---\left(3\right)$

${\mathrm{\β}}_2=\frac{1-\frac{{\mathrm{\α}}_2{(1-{\mathrm{\α}}_1)}^2}{d_1}}{{\mathrm{\α}}_2-1}---\left(4\right)$

Utilize Gaussian optics theoretical, the formula that three-mirror reflection penetrates formula system structure parameter can be obtained:

$R_1=\frac{2}{{\mathrm{\β}}_1{\mathrm{\β}}_2}{f}^{\′}---\left(5\right)$

$R_2=\frac{{2\mathrm{\α}}_1}{{\mathrm{\β}}_2(1+{\mathrm{\β}}_1)}{f}^{\′}---\left(6\right)$

$R_3=\frac{{2\mathrm{\α}}_1{\mathrm{\α}}_2}{1+{\mathrm{\β}}_2}{f}^{\′}---\left(7\right)$

d ₁＝[α ₂(1-α ₁) ²+α ₁(1-α ₂) ²]f′ (8)

$d_2=\frac{{\mathrm{\α}}_1(1-{\mathrm{\α}}_2)}{{\mathrm{\β}}_2}{f}^{\′}---\left(9\right)$

l ₃′＝α ₁α ₂f′ (10)

In formula, total focal length that f ' is system.Thus, initial profile structural parameters are determined.Also R will be limited ₁=R ₃primary mirror just can be made identical with the radius-of-curvature of three mirrors, obtain:

${\mathrm{\α}}_2=-\frac{{2\mathrm{\α}}_1^2-{4\mathrm{\α}}_1+1}{{\mathrm{\α}}_1}---\left(11\right)$

According to above formula, provide a α ₁just α can be obtained ₂, by α ₁and α ₂substitute into said system structural parameters formula (3) ~ (10), just can obtain all the other entire infrastructure parameters of two catoptron Three mirror optical system.

The three grades of spherical aberrations, the coma that make system are zero, can obtain the asphericity coefficient of two catoptrons accordingly by primary spherical aberration coefficient S _i=0:

$e_1^2=1+\frac{1}{{\mathrm{\β}}_1^3{\mathrm{\β}}_2^3}[{\mathrm{\α}}_1{\mathrm{\α}}_2(1+{\mathrm{\β}}_2){(1-{\mathrm{\β}}_2)}^2-{\mathrm{\α}}_1{\mathrm{\β}}_2^3(1+{\mathrm{\β}}_1){(1-{\mathrm{\β}}_1)}^2+e_2^2{\mathrm{\α}}_1{\mathrm{\β}}_2^3{(1+{\mathrm{\β}}_1)}^3-e_1^2{\mathrm{\α}}_1{\mathrm{\α}}_2{(1+{\mathrm{\β}}_2)}^3]---\left(12\right)$

By elementary coma coefficient S _iI=0,

$\begin{array}{c}{e}_2^2({\mathrm{\α}}_1-1){\mathrm{\β}}_2^3{(1+{\mathrm{\β}}_1)}^3-e_1^2[{\mathrm{\α}}_2({\mathrm{\α}}_1-1)+{\mathrm{\β}}_1(1-{\mathrm{\α}}_2)]{(1+{\mathrm{\β}}_2)}^3\\ =({\mathrm{\α}}_1-1){\mathrm{\β}}_2^3(1+{\mathrm{\β}}_1){(1-{\mathrm{\β}}_1)}^2-[{\mathrm{\α}}_2({\mathrm{\α}}_1-1)+{\mathrm{\β}}_1(1-{\mathrm{\α}}_2)](1+{\mathrm{\β}}_2){(1-{\mathrm{\β}}_2)}^2-{2\mathrm{\β}}_1{\mathrm{\β}}_2\end{array}---\left(13\right)$

By α ₁, α ₂, β ₁, β ₂bring into (12), (13) can obtain the asphericity coefficient of two mirror surfaces so far, the structural parameters R of system ₁(R ₃), R ₂, d ₁(-d ₂), all determine.

Method is asked according to above-mentioned initial structure parameter, devise focal distance f=1000mm, F number is 10,2w=2 ° × 0.4 °, visual field (rectangular field), two catoptron Three mirror optical system of service band 0.4 ~ 0.7 μm, ccd detector pixel dimension a=10 μm (Nyquist frequency f N=1/2a=50lp/mm).Consider the rationality of system architecture, get α ₁=0.49, then α ₂=0.9792, β ₁=-50, β ₂=-0.04, the initial structure parameter obtaining system is as shown in table 1.Visible primary mirror, secondary mirror are hyperboloid.

The coaxial initial structure parameter of table 1

Step 2, Optical System Design optimization

By in these parameters input optical design software ZEMAX, obtain coaxial optical system structural drawing and modulation transfer function (MTF), system stop on primary mirror, without intermediate image.

The optical system axis outward flange view field imaging poor quality of the initial configuration solved, need carry out initial optimization.For ensureing the rationality of system architecture, keeping each interval constant in optimizing process, being optimized for variable with each radius surface and asphericity coefficient, obtaining the coaxial system that image quality increases.Diaphragm is placed on first surface, and get from axle amount 230mm, the system non-stop layer of making blocks, now can not using from axle amount as optimized variable, otherwise system can progressively be tending towards coaxial.The tilt quantity of primary mirror and secondary mirror is set to variable, formed as shown in Figure 2 from axle two catoptron Three mirror optical system, structural parameters are as shown in table 2.

Table 2 is from the structural parameters after axle optimization

Performance of Optical System curve, MTF reacts optical system to the transmission capacity of incident beam spatial frequency composition, and can find out under Nyquist frequency, in full filed, full band range, the MTF of system is close to diffraction limit.Point range figure reflects geometrical ray and incides intensity in image planes, and point spread function and energy distribution reflect light spot energy intensity, and as can be seen from point range figure, point spread function and energy profile, energy comparison is concentrated, good imaging quality.

Achieve a kind of explicit two catoptrons by above step to design from axle three reflecting optical system.

The present invention proposes a kind of explicit two catoptrons from axle three reflecting optical system method for designing, primary mirror in traditional off-axis three-mirror anastigmat and three mirrors are improved to one piece of non-spherical reflector by the method, because primary mirror and three mirrors share one piece of catoptron, compare common off-axial three-reflective system, reduce processing and resetting difficulty.Derived the initial optical parameter calculation formula of two catoptron three-reflection optical systems, drawn the solving equation group being applicable to this optical system, method for designing is simple.

Claims (1)

1. explicit two catoptrons are from an axle three reflecting optical system method for designing, it is characterized in that: comprise the steps,

The initial structure parameter of step one, three-mirror reflection optical system calculates,

Three-mirror reflection optical system is made up of primary mirror M1, secondary mirror M2, three mirror M3, after light, arrives image planes successively through primary mirror M1, secondary mirror M2, three mirror M3; The radius-of-curvature on described primary mirror M1, secondary mirror M2, three mirror M3 summits is respectively R1, R2, R3, and the asphericity coefficient of primary mirror M1, secondary mirror M2, three mirror M3 is respectively the spacing of primary mirror M1, secondary mirror M2, three mirror M3 and image planes is respectively the feature of two catoptron three reflecting optical systems is that primary mirror M1 is identical with three mirror M3 and overlap, and namely requires R1=R3, d ₁=-d ₂;

The imaging character of three reflecting optical systems is by structural parameters α ₁, α ₂, β ₁, β ₂determine; Described α ₁for secondary mirror is to the ratio of obstruction of primary mirror: α ₁=l ₂/ f ₁' ≈ h ₂/ h ₁; Described α ₂be the ratio of obstruction of three mirrors to secondary mirror: α ₂=l ₃/ l ₂' ≈ h ₃/ h ₂; Described β ₁, β ₂be respectively the magnification of secondary mirror and three mirrors;

By total focal distance f '=1 normalized, can obtain:

d ₁＝α ₂(1-α ₁) ²+α ₁(1-α ₂) ²；

$d_2=\frac{{\mathrm{\α}}_1(1-{\mathrm{\α}}_2)}{{\mathrm{\β}}_2};$

By α ₁, α ₂as initial known quantity, can obtain according to flat field condition:

${\mathrm{\β}}_1=\frac{1-{\mathrm{\α}}_1}{d_1{\mathrm{\β}}_2};$

${\mathrm{\β}}_2=\frac{1-\frac{{\mathrm{\α}}_2{(1-{\mathrm{\α}}_1)}^2}{d_1}}{{\mathrm{\α}}_2-1};$

Utilize Gaussian optics theoretical, the formula of three-mirror reflection optical system structure parameter can be obtained:

$R_1=\frac{2}{{\mathrm{\β}}_1{\mathrm{\β}}_2}{f}^{\′};$

$R_2=\frac{2{\mathrm{\α}}_1}{{\mathrm{\β}}_2(1+{\mathrm{\β}}_1)}{f}^{\′};$

$R_3=\frac{2{\mathrm{\α}}_1{\mathrm{\α}}_2}{1+{\mathrm{\β}}_2}{f}^{\′};$

d ₁＝[α ₂(1-α ₁) ²+α ₁(1-α ₂) ²]f′；

$d_2=\frac{{\mathrm{\α}}_1(1-{\mathrm{\α}}_2)}{{\mathrm{\β}}_2}{f}^{\′};$

l ₃′＝α ₁α ₂f′；

In formula, total focal length that described f ' is system; Determine three-mirror reflection optical system initial structure parameter thus;

Restriction R ₁=R ₃, obtain:

${\mathrm{\α}}_2=-\frac{2{\mathrm{\α}}_1^2-4{\mathrm{\α}}_1+1}{{\mathrm{\α}}_1};$

According to above formula, provide a α ₁just α can be obtained ₂, by α ₁and α ₂substitute in above-mentioned three-mirror reflection optical system structure parameter equation, just can obtain the entire infrastructure parameter of two catoptron three-mirror reflection optical systems;

The three grades of spherical aberrations, the coma that make two catoptron three-mirror reflection optical systems are zero, can obtain the asphericity coefficient of two catoptrons by primary spherical aberration coefficient S _i=0:

$e_1^2=1+\frac{1}{{\mathrm{\β}}_1^3{\mathrm{\β}}_2^3}[{\mathrm{\α}}_1{\mathrm{\α}}_2(1+{\mathrm{\β}}_2){(1-{\mathrm{\β}}_2)}^2-{\mathrm{\α}}_1{\mathrm{\β}}_2^3(1+{\mathrm{\β}}_1){(1-{\mathrm{\β}}_1)}^2+e_2^2{\mathrm{\α}}_1{\mathrm{\β}}_2^3{(1+{\mathrm{\β}}_1)}^3-e_1^2{\mathrm{\α}}_1{\mathrm{\α}}_2{(1+{\mathrm{\β}}_2)}^3];$

By elementary coma coefficient S _iI=0:

$\begin{array}{c}{e}_2^2({\mathrm{\α}}_1-1){\mathrm{\β}}_2^3{(1+{\mathrm{\β}}_1)}^3-e_1^2[{\mathrm{\α}}_2({\mathrm{\α}}_1-1)+{\mathrm{\β}}_1(1-{\mathrm{\α}}_2)]{(1+{\mathrm{\β}}_2)}^3\\ =({\mathrm{\α}}_1-1){\mathrm{\β}}_2^3(1+{\mathrm{\β}}_1){(1-{\mathrm{\β}}_1)}^2-[{\mathrm{\α}}_2({\mathrm{\α}}_1-1)+{\mathrm{\β}}_1(1-{\mathrm{\α}}_2)](1+{\mathrm{\β}}_2){(1-{\mathrm{\β}}_2)}^2-2{\mathrm{\β}}_1{\mathrm{\β}}_2\end{array};$

By α ₁, α ₂, β ₁, β ₂bring the asphericity coefficient can obtaining two mirror surfaces in above-mentioned formula into so far, the structural parameters R of system ₁(R ₃), R ₂, d ₁(-d ₂), all determine;

Step 2, the initial structure parameter calculating acquisition in step one is input in Zemax optical design software; Be placed in by diaphragm on first surface, getting optical aperture is that the system non-stop layer of making blocks, and carries out Optical System Design optimization, can be met explicit two catoptrons of requirement from axle three reflecting optical system from axle amount.