Manufacture of a large off-axis SiC parabolic mirror

Xiaokun Wang

doi:10.3788/COL201513.S22401

Abstract

The advantages of manufacturing a space aspheric mirror of SiC material are analyzed, and the key methods and technology of fabricating and measuring SiC aspheric surfaces are introduced and researched. The off-axis SiC aspheric mirror is ground and polished by computer controlled optical surfacing (CCOS) technology with a FSGJ-2 numerical control machine, the contour and optical parameters are measured and controlled by a coordinate measuring machine (CMM) and laser tracker. Finally, an example for fabricating and testing an off-axis parabolic mirror with an aperture of 820 mm is given. A null lens is specifically designed and customized in order to test the large aspheric mirror by interferometry and null compensation. The resulting PV and RMS of the surface error are

0.335 λ

and

0.018 λ

(

λ

is 632.8 nm), respectively, which meets the requirements of the optical design.

Using aspheric surfaces in an optical system not only can reduce the complexity of the system, but also can greatly improve the performance of the system. Therefore, an aspheric surface becomes a very important component of the military and civilian optical system; it is used in various photoelectric fields such as remote space sensing, astronomical observation, exploration and photoelectric tracking equipment, lithography lenses, and high-performance cameras^[1–4].

The mirror is a key component of the space camera system. In order to guarantee the stability and reliability of the space mirror during application, the material of the mirror should have a low density, high specific stiffness, a small thermal expansion coefficient, good heat conduction performance, and a strong ability to resist radiation characteristics, etc.^[5–7]. In addition, the material that the mirror is made of may have good mechanical and optical processing performance, and it can obtain the required shape and roughness.

At present, the common material of the optical mirror includes ULE (ultra low expansion glass produced by Corning), Zerodur (a glass ceramic produced by Schott), Be (beryllium), and SiC (silicon carbide), etc. In order to reduce the launch weight and keep the form of the surface, the mirror must be very light in weight and have good thermal stability^[8–10]. A comparison of comprehensive performance with SiC and other traditional optical materials is given in Fig. 1. It can be seen that SiC has a higher stiffness and thermal stability than other traditional materials and it is the ideal choice of optical materials.

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Figure 1.Primary characters of the SiC and traditional mirror materials.

In this Letter, the key technology for the fabrication and measurement of a large SiC mirror has been researched, combined with engineering practice, and an excellent SiC off-axis asphere has been manufactured.

In order to realize the fabrication of a SiC mirror, we have designed and developed the FSGJ-2 numerical control machine^[11,12] shown in Fig. 2. In order to meet different processing requirements, the machine has 6 dofs (degrees of freedom): X, Y, Z for translational degree of freedom, and U, V, W for rotational degree of freedom. It is established on the basis of CCOS technology and it can grind and polish the aspheric surfaces consecutively; the maximum fabricating capacity of the FSGJ-2 is 1000 mm.

Figure 2.Computer controlled FSGJ-2 machine for manufacturing large aspheric surfaces.

The flow chart of the fabrication and testing of the SiC aspheric mirror is given in Fig. 3. First, we generate the aspheric surface using a milling machine. Second, the surface is ground and polished with a FSJG-2. During milling and grinding, the surface error is tested by a CMM. Third, when the PV (peak to valley) value of the surface error is less than 3 μm the aspheric surface is polished by a FSGJ-2, and when the RMS (root mean square) of the surface error is less than $1 / 20 λ$ it is finished by IBF (iron beam finishing). During polishing and finishing, it is measured by null testing, and a laser tracker is used to calibrate and gauge the optical path of the interferometry. Last, when the RMS is less than $1 / 50 λ$ , the asphere can meet the requirements of the optical design.

Figure 3.Flow chart for manufacturing a large aspheric mirror.

Combined with engineering examples, a large SiC off-axis aspheric mirror with an aperture of 820 mm has been fabricated and tested by the proposed method. The vertex radius of curvature is 4573.97 mm, the conic constant is $- 1$ , the off-axis quantity is 573.32 mm, and the rate of lightweight reaches 70%.

First, the aspheric mirror was milled and ground by the DMG milling machine and the FSGJ-2, successively, and the surface error was tested by the CMM, which is shown in Fig. 4. When the PV of the surface error was less than 3 μm we polished the mirror, as shown in Fig. 5.

Figure 4.Testing large mirror by a CMM.

Figure 5.Polishing large mirror with a FSGJ-2.

In order to test the mirror by interferometry an Offner lens corrector was designed and customized. The null corrector can introduce enough aberration into the test beam so that it eliminates the aberration produced by testing the aspheric surface at its center of curvature^[13–15]. The design and manufacture accuracy of the null lens is better than $λ / 100$ RMS. The setup of the interferometry is shown in Fig. 6. The laser tracker was used to guide and survey the optical path and the initial surface map measured by the interferometer is given in Fig. 7. The surface map of the final grinding, which was tested by a CMM, is given in Fig. 8. The distributions of the two maps are consistent and the difference of the PV and RMS error between them is $0.184 λ$ and $- 0.002 λ$ , respectively, so the test results are precise and believable.

Figure 6.Testing of aspheric mirror by null compensation.

Figure 7.Initial surface map tested by interferometry.

Figure 8.Final test result by a CMM.

The test results must be used to guide the fabrication, but the test results are in the testing coordinates, which are in units of pixels, while the fabricating coordinates are in units of millimeters. Also, the surface map is distorted; the shape of the mirror is round, but the shape of the surface map is elliptical. We needed to calibrate and unify these two kinds of coordinates^[16]. Several marked points were used to accomplish the calibration, which is shown in Fig. 9.

Figure 9.Configuration for coordinate calibration.

The coordinates of targets in the test results can be described as $(x_{i}, y_{i})$ , $i = 1,2, 3 \dots$ , while the relative coordinates of the fabrication can be written as $(X_{i}, Y_{i})$ , $i = 1,2, 3 \dots$ . By a homogeneous coordinate transformation, the relationship between them is given by $[\begin{matrix} X_{i} \\ Y_{i} \\ 1 \end{matrix}] = T \cdot [\begin{matrix} x_{i} \\ y_{i} \\ 1 \end{matrix}],$ (1) $T = [\begin{matrix} s_{i} \cdot \cos θ & - s_{i} \cdot \sin θ & t_{x} \\ s_{i} \cdot \sin θ & s_{i} \cdot \cos θ & t_{y} \\ 0 & 0 & 1 \end{matrix}],$ (2)where $(t_{x}, t_{y})$ is the relative translation between the two coordinates, $θ$ is the relative rotation degree between them; $s_{i}$ is the magnification to each pixel in the testing resultsand, because of the distortion, is a variable of the different pixels: $s_{i} = R_{i} / r_{i},$ (3) $r_{i} = \sqrt{{(x_{i} - x_{0})}^{2} + {(y_{i} - y_{0})}^{2}},$ (4) $R_{i} = \sqrt{{(X_{i} - X_{0})}^{2} + {(Y_{i} - Y_{0})}^{2}},$ (5)where $(x_{0}, y_{0})$ is the test coordinate of the vertex of the test asphere, and $(X_{0}, Y_{0})$ is the fabrication coordinate of the vertex of the test asphere.

The relationship between $R$ and $r$ is nonlinear and can be described as $R_{i} = a_{0} + a_{1} r_{i} + a_{2} r_{i}^{2} + a_{3} r_{i}^{3} + \dots$ (6)

In general, taking the first four terms can meet the precision requirement, the best coefficients will be obtained by the least squares fitting, and the distortion can be corrected as follows: $\sum_{i}^{n} {[R_{i} - (a_{0} + a_{1} r_{i} + a_{2} r_{i}^{2} + a_{3} r_{i}^{3})]}^{2} = \min,$ (7) $[\begin{matrix} a_{0} \\ a_{1} \\ a_{2} \\ a_{3} \end{matrix}] = {[\begin{matrix} n & \sum r_{i} & \sum r_{i}^{2} & \sum r_{i}^{3} \\ \sum r_{i} & \sum r_{i}^{2} & \sum r_{i}^{3} & \sum r_{i}^{4} \\ \sum r_{i}^{2} & \sum r_{i}^{3} & \sum r_{i}^{4} & \sum r_{i}^{5} \\ \sum r_{i}^{3} & \sum r_{i}^{4} & \sum r_{i}^{5} & \sum r_{i}^{6} \end{matrix}]}^{- 1} [\begin{matrix} \sum R_{i} \\ \sum r_{i} R_{i} \\ \sum r_{i}^{2} R_{i} \\ \sum r_{i}^{3} R_{i} \end{matrix}] .$ (8)

Then, after calibration and correction the relationship between the two coordinates can be written as $[\begin{matrix} X_{i}^{'} \\ Y_{i}^{'} \end{matrix}] = [\begin{matrix} x_{i} \cdot s_{i} \cdot \cos θ - y_{i} \cdot s_{i} \cdot \sin θ + t_{x} \\ x_{i} \cdot s_{i} \cdot \sin θ + y_{i} \cdot s_{i} \cdot \cos θ + t_{y} \end{matrix}],$ (9)where $(X_{i}^{'}, Y_{i}^{'})$ is the coordinate of pixel $(x_{i}, y_{i})$ after calibration between testing and fabricating. By minimizing the sum, $\sum_{i = 1}^{M} ({(X_{i}^{'} - X_{i})}^{2} + {(Y_{i}^{'} - Y_{i})}^{2}) = \min,$ (10)where $M$ is the number of targets, matrix $T$ can be calculated, and the relationship between the fabricating and testing coordinates can be obtained.

By testing and polishing the mirror many cycles, when the RMS of the surface map was better than $1 / 20 λ$ , the aspheric mirror was finished by IBF, and the final test results of the surface are shown in Fig. 10. The PV value is $0.335 λ$ and the RMS value is $0.018 λ$ .

Figure 10.Final test results of the aspheric mirror. Test results of (a) surface map and (b) interferogram.

The key technology and method of fabricating and testing a large aspheric surface especially for a SiC mirror is studied and analyzed, and a reasonable flow chart and processing steps are proposed. The aspheric mirror is ground and polished by a FSGJ-2 with CCOS technology, and a customized null compensator is designed and aligned for the interferometry. As an engineering example, a large SiC parabolic mirror with an aperture of 820 mm is ground, polished, and finished by a FSGJ-2 and an IBF machine sequentially, and the surface map is measured by a CMM and interferometer. Finally, the resulting surface error is better than $1 / 50 λ$ RMS, and it meets the design requirements.

References

[1] D. D. Walker, A. T. H. Beaucamp, R. G. Bingham. Proc. SPIE, 4842, 73(2003).

[2] D. Malacara. Optical Shop Testing(1992).

[3] R. B. Huxford. Proc. SPIE, 5249, 230(2004).

[4] J. Chang, Y. T. Wang, T. C. Zhang, M. M. Talha. Proc. SPIE, 6342, 63421Q(2006).

[5] J. Robichaud, J. Schwartz, D. Landry, W. Glenn, B. Rider, M. Chung. Proc. SPIE, 5868, 1(2005).

[6] S. Williams, P. Deny. Proc. SPIE, 5868, 1(2005).

[7] M. Bougoin, P. Deny, T. Zhang, M. M. Talha. Proc. SPIE, 5494, 9(2004).

[8] G. Zhang. The study on fabrication technique of large-scale silicon carbide mirror blank(2008).

[9] P. Su. Absolute measurements of large mirrors(2008).

[10] L. Xu. Study of surface polishing technique and the properties of coated RB-SiC mirrors(2009).

[11] F. Zhang. Opt. Prec. Eng., 18, 2557(2010).

[12] X. Zhang, Z. Zhang, Z. Li. Proc. SPIE, 6721, 672109(2007).

[13] P. Guo, J. Yu. Proc. SPIE, 6150, 259(2006).

[14] D. L. Xue, L. G. Zheng, X. J. Zhang. Proc. SPIE, 5638, 752(2005).

[15] J. M. Sasian, S. A. Lerner, J. H. Burge. Proc. SPIE, 3739, 444(1999).

[16] L. Yan, X. Wang, L. Zheng. Opt. Express, 21, 22628(2013).