Method for aligning annular spliced sub-mirrors based on laser tracker

Abstract

The invention discloses an annular spliced sub-mirror alignment method based on a laser tracker, which comprises the following steps of: firstly, designing fixed points on a reference sub-mirror and a sub-mirror to be measured, and measuring the coordinates of the fixed points in a global coordinate system through the laser tracker; then, determining conversion parameters of the local coordinate system of the sub-mirror relative to the global coordinate system by using least square fitting; then, calculating the relationship between the local coordinate systems of the two sub-mirrors, and extracting the out-of-plane and in-plane degrees of freedom of the to-be-measured sub-mirror relative to the reference sub-mirror; and finally, through the calculated angle and position relation, the actuator is utilized to adjust the sub-mirror so as to realize high-quality optical imaging. The method can be applied to alignment of the sub-mirrors of the annular spliced telescope, which is crucial for realizing co-phase adjustment of the annular spliced telescope. And the out-of-plane degree of freedom of the sub-mirror can be measured, and the in-plane degree of freedom of the sub-mirror can also be measured, which is of great significance to the in-plane degree of freedom adjustment of the aspheric primary mirror.

Description

Technical Field

[0001] The invention relates to the technical field of annular splicing mirror sub-mirror alignment, in particular to an annular splicing sub-mirror alignment method based on a laser tracker. Background Art

[0002] The alignment of sub-mirrors is an important prerequisite for achieving confocality and common phase in spliced ​​mirror telescopes. High-precision sub-mirror alignment has two important meanings: first, it helps detect and adjust the sub-mirror's out-of-plane degrees of freedom, thereby connecting with the subsequent optical common phase measurement system; second, it helps compensate for the influence of sub-mirror processing errors and overall surface errors.

[0003] At present, the alignment of the sub-mirrors of the spliced ​​mirror telescope generally uses three-dimensional measuring instruments. For example, the Keck telescope uses an electronic theodolite to locate the sub-mirrors, with a positioning accuracy of ±0.25mm. The GTC telescope uses a theodolite and a total station to locate the sub-mirrors, with a positioning accuracy of ±0.1mm. Among the three-dimensional coordinate measuring instruments that can achieve the above measurement accuracy, the laser tracker can also meet the requirements, and it has been widely used in the positioning and alignment of telescope optical elements. However, the application of laser trackers in spliced ​​telescopes is relatively small. This is mainly because most spliced ​​telescopes use closely arranged hexagonal sub-mirrors. There is no space around the sub-mirrors to place reflectors, resulting in the laser tracker being unable to complete the alignment between the sub-mirrors due to the lack of a reference. For example, the TMT telescope under construction has a main mirror made of hexagonal sub-mirrors, and there is no extra space to place reflectors. Therefore, the laser tracker is only used to align other optical elements except the main mirror, and the main mirror is not aligned. Another GMT telescope under construction has a main mirror made up of circular sub-mirrors. There are gaps around the sub-mirrors to place reflectors, so the project team plans to use a laser tracker to complete the alignment of the sub-mirrors, with an expected position accuracy of 120μm and an angle accuracy of 30.96".

[0004] At present, the Chinese solar physics community is actively promoting the 8-meter aperture CGST (Chinese Giant Solar Telescope) project. Its main mirror adopts a unique ring-sector-shaped sub-mirror splicing method. There is space for placing reflectors on the inner and outer circles of the sub-mirrors, which makes it possible to align the sub-mirrors using a laser tracker. Based on this, we propose a sub-mirror alignment method for annular spliced ​​telescopes based on a laser tracker, which measures the degree of freedom of the sub-mirrors indirectly. Summary of the invention

[0005] The present invention aims at the technical problems raised by the background technology and designs a sub-mirror alignment method based on a laser tracker for annular spliced ​​telescopes. The method can measure the degree of freedom within the sub-mirror surface and adjust it to the allowable error range; at the same time, it can also measure the degree of freedom outside the sub-mirror surface and adjust it to the capture range of the subsequent confocal and common phase measurement system.

[0006] The technical solution adopted by the present invention is

[0007] The present invention provides a method for aligning annular spliced ​​sub-mirrors based on a laser tracker. First, fixed points are designed on a reference sub-mirror and a sub-mirror to be measured, and their coordinates in a global coordinate system are measured by a laser tracker. Next, the conversion parameters of the local coordinate system of the sub-mirror relative to the global coordinate system are determined by least squares fitting. Then, the relationship between the local coordinate systems of the two sub-mirrors is calculated, and the out-of-plane and in-plane degrees of freedom of the sub-mirror to be measured relative to the reference sub-mirror are extracted. Finally, the sub-mirror is adjusted by an actuator based on the calculated angle and position relationship to achieve high-quality optical imaging.

[0008] The present invention also provides a method for aligning annular spliced ​​sub-mirrors based on a laser tracker, which specifically comprises the following steps:

[0009] Step 1: Design fixed points on the reference sub-mirror and the sub-mirror to be tested respectively, and set their coordinates in their respective local coordinate systems as P B and P C ; Use the laser tracker to measure the fixed points on the two sub-mirrors, and then obtain their coordinates P in the global coordinate system respectively A-B and P A-C , and then substitute the data into the coordinate transformation formula:

[0010]

[0011] In the formula, [R i , D i ]for:

[0012]

[0013] In the formula, α i , β i , γ i They are the rotation angles of the sub-mirror local coordinate system relative to the X, Y, and Z axes in the global coordinate system, Δx i , Δy i , Δz i is the coordinate of the origin of the sub-mirror's local coordinate system in the global coordinate system. The six transformation parameters of the two sub-mirrors can be obtained by least squares fitting, thereby determining the local coordinate systems of the two sub-mirrors.

[0014] Step 2: Calculate the relationship between the two sub-mirrors based on their local coordinate systems:

[0015]

[0016] According to equations (3) and (4), the transformation parameters α, β, γ, Δx, Δy, Δz of the sub-mirror to be tested relative to the reference sub-mirror can be calculated from the transformation matrix of equation (5);

[0017] Step 3: Extract the degrees of freedom of the sub-mirror to be tested relative to the reference sub-mirror from the conversion parameters, where the out-of-plane degrees of freedom are:

[0018] Tip=α, Tilt=β, Piston=Δz......(6)

[0019] The in-plane degrees of freedom are:

[0020]

[0021] Where α is the angle between the reference sub-mirror and the sub-mirror to be measured when they are in the theoretical position, and the counterclockwise direction is defined as the positive direction, and γ 0 , Δx 0 , Δy 0 It represents the relationship between the theoretical spatial position of the sub-mirror to be measured and the reference sub-mirror, and the degree of freedom in the plane. These parameters are related to the size of the sub-mirror, the position of the sub-mirror to be measured, and the local coordinate system of the sub-mirror, and are calculated by the following formula:

[0022]

[0023] Where R is the distance between the local coordinate system of the sub-mirror and the center of the main mirror ring.

[0024] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0025] (1) This method can be applied to the alignment of sub-mirrors of annular spliced ​​telescopes, which is crucial for achieving common phase adjustment of annular spliced ​​telescopes.

[0026] (2) This method can not only measure the out-of-plane degrees of freedom of the sub-mirror, but also measure the in-plane degrees of freedom of the sub-mirror, which is of great significance for the in-plane degree of freedom adjustment of the primary mirror using an aspheric surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0028] Figure 1 It is a schematic diagram of the global coordinate system and the sub-mirror local coordinate system provided by this application;

[0029] Figure 2 It is a parameter diagram provided by the present application when the sub-mirror to be tested and the reference sub-mirror are in theoretical spatial positions;

[0030] Figure 3 It is a schematic diagram of the CGST primary mirror model and fixed point positions provided in the embodiments of the present application. DETAILED DESCRIPTION

[0031] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0032] The embodiment of the present application uses the local coordinate system of the sub-mirror to represent the posture of the sub-mirror, such as Figure 1 As shown, the degree of freedom of the sub-mirror to be measured relative to the reference sub-mirror is reflected by the relationship between the local coordinate systems of the two sub-mirrors.

[0033] The local coordinate system of the sub-mirror is measured and calculated by a laser tracker: the laser tracker works in the global coordinate system. According to the characteristics of the annular fan-shaped sub-mirror, the reflector can be installed on the inner and outer circles of the sub-mirror, thus becoming the link for determining the relationship between the local coordinate system of the sub-mirror and the global coordinate system.

[0034] The least squares fitting method is used in this process. Since the relationship between any two coordinate systems can be determined by 6 transformation parameters, at least two reflector installation positions, i.e., fixed points, need to be designed on the sub-mirror.

[0035] The specific steps of sub-mirror alignment based on the above theory are as follows:

[0036] Step 1: Design fixed points on the reference sub-mirror and the sub-mirror to be tested respectively, and set their coordinates in their respective local coordinate systems as P B and P C .

[0037] The laser tracker is used to measure the fixed points on the two sub-mirrors, and then their coordinates P in the global coordinate system are obtained respectively. A-B and P A-C , and then substitute the data into the coordinate transformation formula:

[0038]

[0039] In the formula, [R i , D i ]for:

[0040]

[0041] In the formula, α i , β i , γ i They are the rotation angles of the sub-mirror local coordinate system relative to the X, Y, and Z axes in the global coordinate system, Δx i , Δy i , Δz i is the coordinate of the origin of the sub-mirror local coordinate system in the global coordinate system;

[0042] The six transformation parameters of the two sub-mirrors can be obtained through least squares fitting, thereby determining the local coordinate systems of the two sub-mirrors.

[0043] Step 2: Calculate the relationship between the two sub-mirrors based on their local coordinate systems:

[0044]

[0045] According to equations (3) and (4), the transformation parameters α, β, γ, Δx, Δy, Δz of the sub-mirror to be measured relative to the reference sub-mirror can be calculated from the transformation matrix of equation (5).

[0046] Step 3: Extract the degrees of freedom of the sub-mirror to be tested relative to the reference sub-mirror from the conversion parameters, where the out-of-plane degrees of freedom are:

[0047] Tip=α, Tilt=β, Piston=Δz……(6)

[0048] The in-plane degrees of freedom are:

[0049]

[0050] Where θ is the angle between the reference sub-mirror and the sub-mirror to be measured when they are in the theoretical position (counterclockwise direction is defined as the positive direction), such as Figure 2 As shown, γ 0 , Δx 0 , Δy 0 It represents the relationship between the theoretical spatial position of the sub-mirror to be measured and the reference sub-mirror (in-plane degrees of freedom). These parameters are related to the size of the sub-mirror, the position of the sub-mirror to be measured, and the local coordinate system of the sub-mirror, and are calculated by the following formula:

[0051]

[0052] Where R is the distance between the local coordinate system of the sub-mirror and the center of the main mirror ring.

[0053] The following introduces a case of simulating the alignment of annular spliced ​​sub-mirrors on the "China Giant Solar Telescope".

[0054] like Figure 3 As shown in the figure, the CGST primary mirror is composed of 24 ring-shaped sub-mirrors, with an outer diameter of 8m, a ring width of 1m, and a thickness of 0.075m. The local coordinate system of the sub-mirror is defined as follows: the centroid of the back of the sub-mirror is taken as the origin, the direction perpendicular to the back of the sub-mirror and pointing to the optical surface is defined as the Z axis, the tangential direction along the circumscribed circle of the sub-mirror is defined as the X axis, and the radial direction is defined as the Y axis. The coordinates of the three fixed points ABC in the local coordinate system are: A (-488, 480, 10) mm, B (488, 480, 10) mm, C (0, -510, 10) mm.

[0055] (1) Mirror 1 is used as the reference sub-mirror and mirror 24 is used as the sub-mirror to be tested. The initial degrees of freedom of mirror 24 relative to mirror 1 are set as follows: Tip = 12', Tilt = 9', Clocking = 12', Dx = -1 mm, Dy = 0.5 mm, Piston = 0.1 mm.

[0056] (2) The laser tracker is simulated to measure fixed points A, B, and C on mirrors 1 and 24 at a working distance of 8 meters. Since the measurement error of the laser tracker is 3σ r =15μm+6μm / m, so add σ to the measurement data of the laser tracker r =21μm of normally distributed random error. The least squares fitting of the laser tracker measurement data and the coordinates of the fixed points in their respective local coordinate systems was performed to obtain the transformation parameters of the two sub-mirrors relative to the global coordinate system: the transformation parameters of mirror 1 relative to the global coordinate system are -110.2061°, 35.1825°, 70.4986°, 76692.4925mm, -12785.1465mm, 19497.4777mm; the transformation parameters of mirror 24 relative to the global coordinate system are -115.5600°, 49.1468°, 62.3234°, 76427.6676mm, -13409.4919mm, 20111.3275mm.

[0057] (3) Based on the local coordinate systems of mirror 1 and mirror 24, the transformation parameters of mirror 24 relative to mirror 1 are calculated according to equations (3), (4), and (5). The results are: 0.20°, 0.15°, 15.20°, -906.96 mm, -119.04 mm, and 0.10 mm, respectively.

[0058] (4) According to equations (6), (7) and (8), the degrees of freedom of mirror 24 relative to mirror 1 can be extracted from the above conversion parameters, which are: Tip = 11.9988', Tilt = 9.0007', Clocking = 12.0046', Dx = -0.9998 mm, Dy = 0.5000 mm, Piston = 0.0990 mm. This result is very close to the set initial value.

[0059] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application. The above-described embodiments are only used to illustrate the technical solution of the present application, not to limit it; although the present application is described in detail with reference to the aforementioned embodiments, those of ordinary skill in the art should understand that: it is still possible to modify the technical solutions recorded in the aforementioned embodiments, or to replace some of the technical features therein by equivalent; and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the scope of protection of the present application.

Claims

1. A method for aligning annular spliced ​​sub-mirrors based on a laser tracker, characterized in that: First, fixed points are designed on the reference sub-mirror and the sub-mirror to be tested, and their coordinates in the global coordinate system are measured by a laser tracker. Next, the transformation parameters of the sub-mirror's local coordinate system relative to the global coordinate system are determined by least squares fitting. Then, the relationship between the local coordinate systems of the two sub-mirrors is calculated, and the out-of-plane and in-plane degrees of freedom of the sub-mirror to be tested relative to the reference sub-mirror are extracted. Finally, based on the calculated angle and position relationship, the sub-mirror is adjusted using an actuator to achieve high-quality optical imaging.

2. The method for aligning annular spliced ​​sub-mirrors based on a laser tracker according to claim 1, comprising the following steps: Step 1: Design fixed points on the reference sub-mirror and the sub-mirror to be tested respectively, and set their coordinates in their respective local coordinate systems as P B and P C ; Use the laser tracker to measure the fixed points on the two sub-mirrors, and then obtain their coordinates P in the global coordinate system respectively A-B and P A-C , and then substitute the data into the coordinate transformation formula: In the formula, [R i , D i ]for: In the formula, α i , β i , γ i They are the rotation angles of the sub-mirror local coordinate system relative to the X, Y, and Z axes in the global coordinate system, Δx i , Δy i , Δz i is the coordinate of the origin of the sub-mirror's local coordinate system in the global coordinate system. The six transformation parameters of the two sub-mirrors can be obtained by least squares fitting, thereby determining the local coordinate systems of the two sub-mirrors. Step 2: Calculate the relationship between the two sub-mirrors based on their local coordinate systems: According to equations (3) and (4), the transformation parameters α, β, γ, Δx, Δy, Δz of the sub-mirror to be tested relative to the reference sub-mirror can be calculated from the transformation matrix of equation (5); Step 3: Extract the degrees of freedom of the sub-mirror to be tested relative to the reference sub-mirror from the conversion parameters, where the out-of-plane degrees of freedom are: Tip=α, Tilt=β, Piston=Δz……(6) The in-plane degrees of freedom are: Wherein, θ is the angle between the reference sub-mirror and the sub-mirror to be measured when they are in the theoretical position, the counterclockwise direction is defined as the positive direction, γ0, Δx0, Δy0 represent the relationship between the sub-mirror to be measured and the reference sub-mirror in the theoretical space position, and the in-plane degree of freedom. These parameters are related to the size of the sub-mirror, the position of the sub-mirror to be measured, and the local coordinate system of the sub-mirror, and are specifically calculated by the following formula: Where R is the distance between the local coordinate system of the sub-mirror and the center of the main mirror ring.

Images