CN103197419B - Simulation method of Golay structure multiple-mirror-face telescope system - Google Patents

Abstract

The invention relates to a simulation method of a Golay structure multiple-mirror-face telescope system. The simulation method comprises the following steps: (1) all subsidiary mirrors are divided into a plurality of Golay3 structure triple-subsidiary-mirror groups and a coordinate system is set up: (2) on the basis of a reflection-type or back-turning-type full aperture optical system, an 'empty object' stands for the coordinate system, a 'reflection face' stands for a subsidiary mirror, and a Golay structure spherical surface reflection mirror model is set up; (3) an executable program is set up through program design, a document which can be read by a corresponding optical design software is generated, the document is executed and simulation is achieved; and (4) component parameters are changed, the third step is repeated, relevant program codes are modified and the Golay structure multiple-mirror-face telescope system under a condition that errors exist is simulated. The simulation method of the Golay structure multiple-mirror-face telescope system is simple in principle, convenient to operate, rapid and convenient to conduct data analysis, and beneficial to evaluation of imaging quality of the Golay structure multiple-mirror-face telescope system and influence, on the imaging quality, of the errors and has guidance value for system manufacturing.

Description

The emulation mode of Golay structure multi mirror telescope system

Technical field

The invention belongs to space remote sensing field, particularly a kind of emulation mode of high-resolution optical remote sensing system.

Background technology

Resolution needed for space telescope system is higher, then its bore need manufacture and design larger.Along with the development of Space Cause, the bore of space telescope is designed to be increasing.But constantly being increased by the bore of space telescope makes the weight of whole space telescope system, volume, manufacture and detection difficulty all sharply increase, to manufacture and launch cost significantly increases, when bore greatly to a certain extent time, current technology cannot manufacture.Sparse aperture imaging system is for solving heavy caliber, the telescopical manufacturing issue of fine angular resolution and a kind of New Scheme of proposing, this space telescope system synthesizes an optical imaging system with multiple small-bore system comparatively easily manufactured carry out alternative full aperture imaging system by certain way is arranged together, there is the resolving power identical with full aperture imaging system, but its weight is lighter, cost is lower, has boundless development prospect.

Actual available sparse aperture imaging system adopts the reflective or refraction-reflection type structure be made up of multiple catoptron mostly, embody rule has 2 kinds of forms, be respectively multi mirror telescope system (Multiple-mirrortelescopes, and many telescopes telescopic system (Multiple-telescope telescopes, MTT) two types MMT).Multi mirror telescope system also claims common secondary mirror telescopic system, is on the basis of an autocollimator, use multiple less sub-mirror to replace the catoptron that original monoblock is large, and the circumscribed circle diameter of this little mirror equals the bore of original primary mirror.Many telescopes telescopic system be by multiple small-bore sub-telescope regularly permutation and combination become a bigbore imaging system, by the telescopical imaging beam of each height of coherence stack, obtain whole system imaging.The arrangement architecture of sparse aperture sub-aperture mainly contains the various structures such as annular, Golay and three arms, and to be wherein considered to nonredundancy higher for Golay structure, adopts the system performance of the sparse aperture imaging system of Golay structure better.

Golay structure is a kind of nonredundancy structure proposed by Golay in 1971, and the number of sub-mirror is the multiple of 3.If the number M=3N of sub-mirror, wherein N is natural number, is called GolayM structure according to the number of sub-mirror.For Golay3 structure, 3 sub-vertex points are equal to the distance of full aperture reflective mirror central shaft, and sub-vertex point is 120 degree to the vertical line angle each other of central shaft, and three sub-mirrors exist a circumscribed circle, and circumscribed circle bore equals the bore of full aperture reflective mirror.GolayM structure can be regarded as and be made up of N number of Golay3 structure, and each Golay3 structure has different circumscribed circles, and they have rotated different angles around central shaft.

At present, domesticly mainly based on perfect optical system model, study sparse aperture imaging system, do not consider the curvature of optical surface, there are differences when this kind of result of study and actual use, the multi mirror telescope systematic research in conjunction with actual service factor is even more important.Simultaneously, due in the processes such as manufacture and installation, in multi mirror telescope system, its ideal position may be departed from the position of each sub-mirror, therefore the radius-of-curvature of optical surface also can produce error, in the sparse aperture imaging system of many telescope configurations, its ideal position also may be departed from the telescopical position of each son, and these errors all likely have an impact to the picture element of system imaging.There is not yet the open report conducted a research for the multi mirror telescope system with above-mentioned impact both at home and abroad at present.

Summary of the invention

For the emulation mode of prior art middle high-resolution remote optical sensing system, the invention provides a kind of emulation mode of Golay structure multi mirror telescope system.

Technical scheme of the present invention is:

The emulation mode of Golay structure multi mirror telescope system, concrete steps are as follows:

Step one, all sub-mirrors are divided into the sub-mirror group of N number of Golay3 structure three.The sub-mirror group of so-called Golay3 structure three refers to the combination that three sub-mirrors that can form Golay3 structure are formed, it is made up of three sub-mirrors, every sub-vertex point is equal to the distance of primary mirror central shaft, sub-vertex point is 120 degree to the vertical line angle each other of central shaft, there is a circumscribed circle in three sub-mirrors, the mirror mirror region at circumscribed circle place is a spherical crown, the summit of this spherical crown is the summit of the sub-mirror group of this Golay3 structure three, defining this external diameter of a circle is the bore of this group, claims the straight line vertical with primary mirror through summit to be the central shaft of this group.As N=1,2,3 ... Deng time, emulate Golay3, Golay6, Golay9 respectively ... the structure multi mirror telescope systems such as GolayM, M=3N.

Then in Golay structure multi mirror telescope system, coordinate system is set up.Concrete steps are:

Step (1) sets up XYZ coordinate system, and getting the catoptron summit that need be designed to Golay structure is initial point, and mirror center axle and optical axis are taken as Z axis, positive dirction is along the direction of propagation of 0 degree of visual field chief ray, X-axis, Y-axis and Z axis are mutually vertical, form right-handed coordinate system.

Step (2) sets up U in the sub-mirror group of each Golay3 structure three _iv _iw _icoordinate system, W _iaxle overlaps with Z axis, and the summit of one of them sub-mirror is at U _iw _iin plane, U _iaxle, V _iaxle, W _iaxle is mutually orthogonal, becomes right-handed coordinate system, wherein 1≤i≤N.U _iv _iw _icoordinate system can rotate ψ by XYZ coordinate system around Z axis _iangle obtains, corner ψ _idetermined by system architecture.Work as ψ _iwhen=0, U _iv _iw _icoordinate system and XYZ coordinate system overlap.

Step (3) is by U _iv _iw _icoordinate system rotates 0 °, 120 ° ,-120 ° respectively around Wi axle, and ξ set up by three sub-mirrors of Golay3 structure three sub-mirror group _ijη _ijζ _ijcoordinate system, wherein j=1,2,3.For same i value, at each ξ _ijη _ijζ _ijin coordinate system, sub-vertex point coordinate value is all the same with inclination angle.

Step 2, designed containing in the full aperture reflective formula of spherical reflector or refraction-reflection type telescopic system basis, according to the required spherical reflector parameter being designed to Golay structure, set up Golay structure spherical reflector model.Concrete steps are as follows:

Step (1) adds the element that a type is " empty object ", represents XYZ coordinate system.

Step (2) adds the element that N number of type is " empty object ", represents U respectively _iv _iw _icoordinate system, they are relative to XYZ coordinate system, and initial point is (0,0,0), and the corner around Z axis is ψ _i.

Step (3) represents U each _iv _iw _iadd three " empty object " type elements after the element of coordinate system respectively, represent ξ _ijη _ijζ _ijcoordinate system.Relative to U _iv _iw _icoordinate system, ξ _ijη _ijζ _ijthe initial point of coordinate system is (0,0,0), when j gets 1, and 2, when 3, they are around W _icorner be respectively 0 °, 120 ° ,-120 °.

Step (4) represents ξ each _ijη _ijζ _ijadd " reflecting surface " element respectively after " empty object " element of coordinate system, represent sub-mirror, relative to ξ _ijη _ijζ _ijcoordinate system, the apex coordinate of " reflecting surface " element is:

b _ix＝Rsin(β _i)、b _iy＝0、b _iz＝R-Rcos(β _i) (1)

${\mathrm{\β}}_i=\arcsin \left(\frac{D_i}{2R}\right)-\arcsin \left(\frac{d}{2R}\right)---\left(2\right)$

Wherein D _ifor the bore of the sub-mirror group of Golay3 structure three, R is the radius-of-curvature of catoptron, and d is sub-aperture of mirror.

The central shaft of each element is around ξ _ij, η _ij, ζ _ijthe rotation angle of axle is respectively

θ _ix=0 _i、θ _iy=β _i、θ _iz=0 (3)

Step (5) is due to U ₁v ₁w ₁coordinate system, XYZ coordinate system and ξ ₁₁η ₁₁ζ ₁₁coordinate system overlaps, U _iv _iw _icoordinate system and ξ _i1η _i1ζ _i1coordinate system overlaps, and counter element also overlaps, and merging these elements is an element.

Step 3, according to full aperture reflective formula or refraction-reflection type telescopic system parameter and Golay structure spherical reflector model, according to optical design software file layout, by program design, set up executable program, generate the file that can be read by corresponding optical design software.Perform this file, realize the emulation to Golay structure multi mirror telescope system.

The parameters such as step 4, the coordinate passing through amendment " reflecting surface " type element, inclination angle and radius-of-curvature, return step 3, and revise related program code, emulate sub-mirror site error, droop error and radius-of-curvature error, error amount equals parameter value knots modification.When knots modification 0, the sub-mirror of analogue system is without site error, droop error and radius-of-curvature error.

The technical scheme that the present invention emulates Golay structure multi mirror telescope systems approach has the following advantages:

(1) principle is simple, easy to operate.The present invention establishes and organizes coordinate system more, utilizes the rotation relationship between coordinate system, determines position and the inclination angle of each sub-mirror.Belong to the sub-mirror of same Golay3 structure three sub-mirror group, the parameter representing their " reflecting surface " element is completely the same.The parameter value such as position, inclination angle, radius-of-curvature changing element introduces error, and error amount is parameter value knots modification.Adopt program design to generate the file that can be read by optical design software, realize emulation, when systematic parameter changes, only need update routine code, simple to operate.

(2) data are analyzed convenient.The present invention sets up the file of corresponding optical design software, emulation multi mirror telescope system, and software has the power analyzing optical system, provides convenient for analyzing multi mirror telescope mass of system.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the emulation mode of Golay structure multi mirror telescope system of the present invention;

Fig. 2 is that a sub-mirror of Golay3 structure is at ξ _1jη _1jζ _1jthe location drawing in coordinate system;

Fig. 3 is Golay3 structure multiple mirror telescope primary mirror simulation result schematic diagram, and 1 is primary mirror, and 2,3,4 is three sub-mirrors;

Fig. 4 is Golay3 structure multi mirror telescope system emulation result schematic diagram, and 5 is secondary mirror, and 6 is image planes;

Fig. 5 is when the sub-mirror 2 that in Golay3 structure primary mirror, j=1 is corresponding is along ζ ₁₁when axle positive dirction moves 2mm, the distribution situation schematic diagram of emulation resulting bottle mirror on primary mirror;

Fig. 6 is when the sub-mirror 2 that in Golay3 structure primary mirror, j=1 is corresponding is around ξ ₁₁when axle rotates 30 degree, the distribution situation schematic diagram of emulation resulting bottle mirror on primary mirror;

Fig. 7 is when sub-mirror 2 radius-of-curvature that j=1 in Golay3 structure primary mirror is corresponding becomes-26.5636mm, the distribution situation schematic diagram of emulation resulting bottle mirror on primary mirror;

Fig. 8 is Golay6 plane structure chart;

Fig. 9 is Golay6 structure multiple mirror telescope primary mirror simulation result schematic diagram, and 1 is primary mirror, and 2,3,4,7,8,9 is six sub-mirrors;

Figure 10 is Golay6 structure multi mirror telescope system emulation result schematic diagram, and 5 is secondary mirror, and 6 is image planes;

Figure 11 is when the sub-mirror 2 that in Golay6 structure primary mirror, i=j=1 is corresponding is along ζ ₁₁when axle positive dirction moves 2mm, the distribution situation schematic diagram of emulation resulting bottle mirror on primary mirror;

Figure 12 is when the sub-mirror 2 that in Golay6 structure primary mirror, i=j=1 is corresponding is around ξ ₁₁when axle rotates 30 degree, the distribution situation schematic diagram of emulation resulting bottle mirror on primary mirror;

Figure 13 is when sub-mirror 2 radius-of-curvature that i=j=1 in Golay6 structure primary mirror is corresponding becomes-16.5636mm, the distribution situation schematic diagram of emulation resulting bottle mirror on primary mirror.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail:

Multi mirror telescope system belongs to the surface structure of more complicated, face type not ready-made in existing optical design software.Conventional optical design software has ZEMAX, CODE V etc., and they are for design and analysis optical system, as design and analysis camera lens, illuminator etc.ZEMAX optical design software can operative norm sequence optical element ray tracing, Non-sequential component parasitic light follow the trail of and physical optics beam propagation.It can also simulate ray by the propagation of optical element as camera lens (comprising aspheric surface and gradient-index lens), catoptron, diffraction optical element etc.ZEMAX optical design software also can the effect of analog element surface optics film, and can produce various standard analysis chart.It comprises abundant camera lens storehouse.Its physical optics transfer function can be used for the problem must considering diffraction, as holographic in laser beam propagation and single-mode fiber optically-coupled.ZEMAX optical design software has powerful optimization tool external member, can be used for camera lens Automatic Optimal adjustment parameter to improve performance to greatest extent reducing aberration, and has abundant tolerance properties.Therefore, ZEMAX optical design software comprises optical module, Optical system module.

CODE V is another kind widely used optical design and analysis software in the world, can the various symmetry of analysis optimization or asymmetric, conventional or unconventional complicated optical system, as the element with three dimension eccentric and/or inclination, system can adopt special optical to look like the face type of diffraction grating, holography or binary optical face, complicated aspheric surface and user oneself definition.Software has non-sequential face ray tracing function, and element capability design and analysis roof prism, corner reflector, light pipe, optical fiber, resonator cavity etc. to special light path is powerful.CODEV has optimization to imaging optical system and free space photon device, the function such as analysis and Tolerance assignment.Therefore, CODE V optical design software also comprises optical module, Optical system module.

For sake of convenience, the catoptron that described need are designed to Golay structure is taken as primary mirror, becomes the method for Golay structure identical therewith other mirror design.

Embodiment 1

The emulation mode of the Golay structure multi mirror telescope system of the present embodiment is the emulation for Golay3 structure multi mirror telescope system, and as shown in Figure 1, concrete steps are as follows for flow process:

1. according to the feature of Golay structure, all sub-mirrors are divided into the sub-mirror group of N number of Golay3 structure three, set up XYZ coordinate system, U _iv _iw _icoordinate system, ξ _ijη _ijζ _ijcoordinate system, respectively corresponding full aperture reflective mirror, Golay3 structure three sub-mirror group and sub-mirror, wherein 1≤i≤N, j=1,2,3.The initial point of three class coordinate systems overlaps, Z axis, W _iaxle, ζ _ijaxle overlaps.

See Fig. 4, described Golay3 structure three sub-mirror group refers to the combination that three sub-mirrors that can form Golay3 structure are formed, it is made up of three sub-mirrors, every sub-vertex point is equal to the distance of primary mirror central shaft, every sub-vertex point is 120 degree to the vertical line angle each other of central shaft, there is a circumscribed circle in three sub-mirrors, the mirror mirror region at circumscribed circle place is spherical crown shape, the summit of this spherical crown is the summit of the sub-mirror group of this Golay3 structure three, define the bore that this external diameter of a circle is the sub-mirror group of this Golay3 structure three, will through the summit of this Golay3 structure three sub-mirror group and the straight line vertical with primary mirror is called the central shaft of the sub-mirror group of this Golay3 structure three.As N=1,2,3 ... Deng time, emulate Golay3, Golay6, Golay9 respectively ... the structure multi mirror telescope systems such as GolayM, M=3N.

Golay3 structure has three sub-mirrors 2,3,4, and system only has N=1 the sub-mirror group of Golay3 structure three, now the bore D of the sub-mirror group of Golay3 structure three ₁equal primary mirror bore D.Set up XYZ coordinate system, primary mirror 1 summit is initial point, and primary mirror 1 central shaft and optical axis are taken as Z axis, and positive dirction is along the direction of propagation of 0 degree of visual field chief ray, and X-axis, Y-axis and Z axis are mutually vertical, form right-handed coordinate system.Then U is set up ₁v ₁w ₁coordinate system, W ₁axle is consistent with Z axis, makes the summit of sub-mirror 2 at U ₁w ₁in plane, U ₁axle, V ₁axle, W ₁axle is mutually orthogonal, becomes right-handed coordinate system.By U ₁v ₁w ₁coordinate system is around W ₁axle rotates 0 °, 120 ° ,-120 ° respectively, obtains ξ _1jη _1jζ _1jcoordinate system, corresponds respectively to three sub-mirrors, wherein j=1,2,3, as shown in Figure 2.In Fig. 2, P and C point is respectively summit and the centre of sphere of primary mirror 1, and the summit of sub-mirror is S _1j, T _1j, M _1jfor sub-mirror and ξ _1jζ _1jthe intersection point in face, N _1jfor line segment T _1jm _1jmid point.

2. designed two anti-system structure parameters are as shown in table 1, and light hurdle is arranged on primary mirror 1, and wavelength X is 0.55 μm, and primary mirror 1 is sphere, bore D=50mm, radius of curvature R=-126.5636mm, and secondary mirror 5 is oblate ellipsoids.

The anti-system structure parameter of table 1 two

Then, Golay3 structure spherical reflector model is set up, so that primary mirror is converted to sparse aperture structure.Increase by 1,1,3 " empty object " elements respectively, represent XYZ, U ₁v ₁w ₁, ξ _1jη _1jζ _1jcoordinate system, then represent ξ each _1jη _1jζ _1j1 " reflecting surface " element is increased respectively after " empty object " element of coordinate system, and parameters.Get sub-aperture of mirror d=7.5mm, according to formula (1) ~ (3), obtain b _1x=-17.6038mm, b _1y=0mm, b _1z=-1.2302mm, θ _1x=0 °, θ _1y=7.9928 °, θ _1z=0 °.

Then, merging coincidence element is an element, and the parameter of the element obtained thus is as shown in table 2.

Table 2Golay3 primary mirror component parameters

3. according to above parameter, according to optical design software file layout, by program design, set up executable program, generate the file that can be read by corresponding optical design software.Primary mirror 1 adopts the simulation result of Golay3 structure as shown in Figure 3, and Golay3 structure multi mirror telescope system emulation result as shown in Figure 4.

4. by amendment " reflecting surface " component parameters, introduce error, emulation has the system of error.When sub-mirror 2 corresponding to j=1 is respectively along ζ ₁₁axle positive dirction moves 2mm, around ξ ₁₁axle rotates 30 degree, when radius-of-curvature becomes-26.5636mm, 3. emulates the sub-mirror 2,3,4 that the obtains distribution situation on primary mirror 1 respectively as shown in Fig. 5,6,7 by step.

Embodiment 2

The emulation mode of the Golay structure multi mirror telescope system of the present embodiment is the emulation for Golay6 structure multi mirror telescope system, and concrete steps are as follows:

1. Golay6 structure has N=2 the sub-mirror group of Golay3 structure three, and as shown in Figure 8, wherein P represents the center of gravity of equilateral Δ ABE to planar structure, the center S of three sub-mirrors 7,8,9 ₂₁, S ₂₂, S ₂₃be in the mid point on each bar limit of Δ ABE, the center S of another three sub-mirrors 2,3,4 ₁₁, S ₁₂, S ₁₃meet | AS ₁₁|=| BS ₁₂|=| ES ₁₃|, all equal 1/4 of the length of side.Sub-mirror S ₁₁, S ₁₂, S ₁₃form a sub-mirror group of Golay3 structure three, in figure, solid line circle is their circumscribed circle, and its diameter is set to D ₁, equal the bore D of primary mirror.Sub-mirror S ₂₁, S ₂₂, S ₂₃form the sub-mirror group of another Golay3 structure three, in figure, broken circle is its circumscribed circle, and diameter is set to D ₂.With reference to the method for similar embodiment 1, set up XYZ, U _iv _iw _i, ξ _ijη _ijζ _ijcoordinate system, wherein 1≤i≤2, j=1,2,3.

2. the systems compliant that the two anti-systems obtained by optical design and table 1 are provided, primary mirror 1 is sphere, bore D=50mm, radius of curvature R=-126.5636mm.

Then, Golay6 structure spherical reflector model is set up.Increase by 1,2,6 " empty object " type elements respectively, represent XYZ, U _iv _iw _i, ξ _ijη _ijζ _ijcoordinate system coordinate system, then represent ξ each _ijη _ijζ _ij1 " reflecting surface " element is increased respectively after " empty object " element of coordinate system, and parameters.Analysis chart 8 can obtain, U ₁v ₁w ₁, U ₂v ₂w ₂coordinate system is ψ relative to the rotation angle of XYZ coordinate system ₁=0, ψ ₂==40.8934 °.Get the bore d=5mm of sub-mirror, each sub-mirror can be tried to achieve at corresponding ξ according to formula (1) ~ (3) _1jη _1jζ _1jand ξ _2jη _2jζ _2jthe position of coordinate system, b _1x=-20.0789mm, b _1y=0mm, b _1z=-1.6029mm, b _2x=-15.2059mm, b _2y=0mm, b _2z=-0.9168mm, θ _1x=θ _2x=0 °, θ _1y=9.1284 °, θ _2y=6.9004 °, θ _1z=θ _2z=0 °.

Then, merging coincidence element is an element, and the component parameters obtained thus is as shown in table 3.

Table 3Golay6 primary mirror component parameters

3. according to above parameter, according to optical design software file layout, by program design, set up executable program, generate the file that can be read by corresponding optical design software.Primary mirror 1 adopts the simulation result of Golay6 structure as shown in Figure 9, and Golay6 structure multi mirror telescope system emulation result as shown in Figure 10.

4. by amendment " reflecting surface " type component parameters, error is introduced, emulation has the system of error.When sub-mirror 2 corresponding to i=j=1 is respectively along ζ ₁₁axle positive dirction moves 2mm, around ξ ₁₁when axle rotation 30 degree, radius-of-curvature become-16.5636mm, 3. emulate by step the sub-mirror 2,3,4,7,8,9 obtained and distribute respectively as shown in Figure 11,12,13.

Claims (3)

1. The emulation mode of 1.Golay structure multi mirror telescope system, specifically comprises the steps:

   (1) according to Golay structure feature, all sub-mirrors are divided into the sub-mirror group of N number of Golay3 structure three, on full aperture reflective mirror, Golay3 structure three sub-mirror group and sub-mirror, set up XYZ coordinate system, U respectively _iv _iw _icoordinate system and ξ _ijη _ijζ _ijcoordinate system, wherein 1≤i≤N, j=1,2,3, the initial point of three class coordinate systems overlaps, wherein, Z axis, W _iaxle and ζ _ijaxle overlaps;

   (2) in the reflective or refraction-reflection type full-aperture optical system-based containing spherical reflector designed, according to the required spherical reflector parameter being designed to Golay structure, Golay structure spherical reflector model is set up;

   (3) according to full aperture reflective formula or refraction-reflection type telescopic system parameter and Golay structure spherical reflector model, according to optical design software file layout, pass through program design, set up executable program, the file that generation can be read by corresponding optical design software, perform this file, realize the emulation to Golay structure multi mirror telescope system;

   (4) that revises " reflecting surface " element comprises coordinate, inclination angle and radius-of-curvature parameter, return step (3), amendment related program code, emulate Golay structure multi mirror telescope system when sub-mirror has site error, droop error and a radius-of-curvature error respectively, error amount equals parameter value knots modification; When knots modification 0, the sub-mirror of analogue system is without site error, droop error and radius-of-curvature error.
2. 2. the emulation mode of Golay structure multi mirror telescope system according to claim 1, is characterized in that: set up Golay structure spherical reflector model concrete steps in described step (2) as follows:

   A () adds an empty object elements, represent XYZ coordinate system;

   B () adds N number of empty object elements, represent U _iv _iw _icoordinate system, each elements relative is (0,0,0) in the coordinate of XYZ coordinate system, and the corner around Z axis is ψ _i, ψ _idetermined by adopted Golay structure;

   C () is representing U _iv _iw _iadd three empty object elements after the element of coordinate system respectively, represent ξ _ijη _ijζ _ijcoordinate system, relative to U _iv _iw _icoordinate system, their coordinate figure is (0,0,0), when j gets 1,2, three coordinate systems when 3 are around W _icorner be respectively 0 °, 120 ° ,-120 °;

   D () represents ξ each _ijη _ijζ _ijadd a reflective surface element after the element of coordinate system respectively, represent sub-mirror, arrange component parameters, if representative sub-mirror belongs to the sub-mirror group of same Golay3 structure three, in free from error situation, component parameters is identical;

   E () merges coincidence element.
3. 3. the emulation mode of Golay structure multi mirror telescope system according to claim 1 and 2, is characterized in that: the catoptron needing to be designed to Golay structure described in step (2) is any one catoptron in system.