Off-axis mirror fabrication from spherical surfaces under mechanical stress

Transcription

1 Off-axis mirror fabrication from spherical surfaces under mechanical stress R. Izazaga-Pérez*, D. Aguirre-Aguirre, M. E. Percino-Zacarías, and F. S. Granados-Agustín Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE, Departamento de Óptica, Apdo. Postal 51 y 216, C.P , Puebla, Pue., México. ABSTRACT The preliminary results in the fabrication of off-axis optical surfaces are presented. The propose using the conventional polishing method and with the surface under mechanical stress at its edges. It starts fabricating a spherical surface using ZERODUR optical glass with the conventional polishing method, the surface is deformed by applying tension and/or compression at the surface edges using a specially designed mechanical mount. To know the necessary deformation, the interferogram of the deformed surface is analyzed in real time with a ZYGO Mark II Fizeau type interferometer, the mechanical stress is applied until obtain the inverse interferogram associated to the off-axis surface that we need to fabricate. Polishing process is carried out again until obtain a spherical surface, then mechanical stress in the edges are removed and compares the actual interferogram with the theoretical associated to the off-axis surface. To analyze the resulting interferograms of the surface we used the phase shifting analysis method by using a piezoelectric phase-shifter and Durango interferometry software from Diffraction International TM. Keywords: Off-axis mirror, off-axis conic section, polishing, mechanical stress, interferogram analysis, phase shifting interferometry. 1. INTRODUCTION Conical surfaces plays an important role in optics, especially in the design of instruments, such as light concentration systems and spectrometers 1. A conical mirror with a circular aperture has a rotational symmetry axis around the optical axis, which is an imaginary line passing through the vertex and contains the paraxial curvature center. If we move transversely at some distance from the center of the aperture and take a circular section of the mirror we have an off-axis mirror section. Using off-axis conic mirrors optimizes the design of optical instruments, making possible to use or analyze the deflected light beam without disturbing the incident one, and also when needed extremely compact systems. We present the preliminary results in the fabrication of an off-axis mirror from a spherical surface under mechanical stress, a similar procedure is found in mirror fabrication jobs developed by Nelson et al It starts fabricating a spherical surface using ZERODUR optical glass with the conventional polishing method, the surface is deformed by applying tension and/or compression at the surface edges using a specially designed mechanical mount made of aluminum and iron. To know the necessary deformation, the interferogram of the deformed surface is analyzed in real time with a ZYGO Corp. Mark II Fizeau type interferometer 4, the mechanical stress is applied until obtain the interferogram associated to the offaxis surface that we need to fabricate. Conventional polishing process is carried out again until obtain a new spherical surface, then, mechanical stress in the edges of the surface is removed, so, we can compare the actual interferogram with the theoretical associated to the off-axis surface. To analyze the resulting interferograms of the surface we will use the phase shifting analysis method by using a piezoelectric phase-shifter and Durango interferometry software from Diffraction International TM. This paper presents only results of the first stage of the process. 2. OFF-AXIS MIRROR FABRICATION We propose using the conventional polishing method to fabricate an off-axis mirror section made of ZERODUR optical glass 5-6. Starting with the conventional polishing method, and applying mechanical stress at its edges, this off-axis section will have its aberrations on the mechanical axis, Fig. 1 is a scheme describing the entire fabrication process, in the following subsections we present the results obtained so far. *izazagax@gmail.com, phone:

2 Figure 1. Scheme representing the mirror fabrication process. 2.1 Initial spherical surface The fabrication method starts fabricating an initial spherical surface using ZERODUR optical glass with the conventional polishing method, the surfaces has a hexagonal shape at its edges, in order to fix the edges with the mechanical mount by using a type of nail made of aluminum, so, at the edges we will apply the mechanical stress. The spherical was a concave meniscus and had the following parameters: 60 cm of curvature radius, 10 cm in diameter and a 0.6 cm of thickness. Figure 2 shows the spherical surface polished (left) with the mechanical mount nails fixed at its edges, and its interferogram obtained with a Zygo Corp. Mark II interferometer (right), the surface quality was P-V=λ/2.94 and RMS=λ/22.4 (wavefront error), with λ= µm. Figure 2. Spherical surface made of ZERODUR optical glass (left). Interferogram of the initial spherical surface (right). 2.2 Mechanical stress Now, the initial spherical surface is deformed by applying stress at the surface edges using a specially designed mechanical mount. The mechanical mount apply stress at six points at the edges of the surface, it was made of aluminum and iron. The spherical surface is placed and fixed on six points with an epoxy resin by using a set of iron rods and aluminum bases, and

3 with an arrangement of nuts and bolts in a form of David s star we can apply tension and/or compression in different zones of the surface. The surface is deformed until obtain an inverse interference pattern with its aberrations associated to an offaxis conic section. Figure 3 (top left) is the CAM design 7 of the mechanical mount showing a detail of the arrangement and the surface placed over the mount. Figure 3 (top right) shows a bottom view of the mechanical mount, circles with dots and circles with lines are David s star arrangement with two separate triangles, this configuration give us the freedom to apply forces in four directions on every point of the mount, by using the combination of nuts and bolts to compress y/o tense the surface on the top of the mechanical mount, and so, we can deform the surface at the points fixed in the nails. A deformed interferogram was obtained with a Zygo Corp. Mark II interferometer (Fig. 3 bottom), circles represent the point in the surface where the stress was applied, arrows represent the direction of the forces applied, and the circles that don t have an arrow are fixed and serves as a reference points. This interferogram is the initial pattern that we will use to continue with the proposed fabrication process, and has the aberrations associated to an off-axis section. The dominant aberrations for an off-axis section are astigmatism and coma. Figure 3. CAM design of the mechanical mount (top left). Representation of the stress applied by the mechanical mount (top right). Final interferogram with the stress applied (bottom).

4 2.3 Synthetic interferograms for an off-axis conic section Irradiance pattern I(x,y) at all points of an interferogram can be considered as a cosine function in a two-dimensional space 8. If a light detector is placed in the observation plane, we will have a distorted irradiance pattern due the wavefront aberrations, described by 2 OPD Ixy (, ) axy (, ) bxy (, )cos cxy (, ), (1) where a(x,y) and b(x,y) are the background illumination and local contrast, respectively, the function c(x,y) corresponds to the noise introduced into the interferogram, λ is the wavelength used, while the OPD corresponds to the optical path difference between the reference wavefront and the test one, the OPD is equal to OPD W(x, y), (2) where W(x,y) can be expressed as a polynomial function (i.e., Zernike, Seidel, Kinglake, etc.), in our case W(x,y) will be the sagitta difference between an off-axis conical section (z(x,y)) and the conic that best fits this section (Z A (x,y)) With this information we can generate synthetic interferograms corresponding to an off-axis conic section, so, we compare the synthetic interferogram with the experimental one, obtained by deforming the initial spherical surface under mechanical stress. Figure 4 is a comparison between the synthetic interferogram and the experimental one, both corresponding to an off-axis conic section, the fringe pattern corresponds to a combination of astigmatism and coma aberrations. Figure 4. Comparison between the synthetic interferogram and the experimental one obtained by applying mechanical stress to the initial spherical surface. The next stage is to continue with the polishing process and the process ends until obtain a new spherical surface, as the surface is hold at its edges, we will only have a useful zone of the surface, the edge zone, fixed by the epoxy resin, will be despised due the residual mechanical stress that keeps this zone, and the central zone of the surface will be useful. When the polishing process ends, the mechanical stress at the edges is removed, and we can compare the actual interferogram with the theoretical associated to the off-axis surface. 3. CONCLUSIONS We have shown the preliminary results of the fabrication process for an off-axis mirror section, the propose using a spherical surface under mechanical stress. We have describe the CAM design for a mechanical mount used to apply stress at the edges of the surface, with this design we can tense and/or compress the surface at several points. The resulting deformations are analyzed by using a Zygo Corp. interferometer and the interference patter corresponds to an off-axis section with its aberration on the mechanical axis. This experimental pattern was reproduced by using the sagitta difference

5 between an off-axis conic section and the conic that best fits this section. This paper presents only preliminary results of the fabrication process, we will continue implementing the fabrication method in future works. AKNOWLEDGMENTS Izazaga-Pérez and Aguirre-Aguirre thank the CONACyT (México) the graduate studies scholarships granted, CVU: , and , respectively. We also thanks the staff of INAOE s Optical Shop for the support given and the use of its facilities. REFERENCES [1] R. J. Meltzer, [Applied Optics and Optical Engineering Vol. 5], Academic Press, New York, (1969). [2] J. Lubliner and J. E. Nelson, Stressed mirror polishing 1: A technique for producing nonaxisymmetric mirrors, Appl. Opt., 19(14), (1980). [3] J. Nelson, G. Gabor, L. Hunt, and J. Lubliner, Stressed mirror polishing 2: Fabrication of an off-axis section of a paraboloid, Appl. Opt., 19(14), (1980). [4] P. F. Forman, The Zygo interferometer system, Proc. SPIE 0192, 41-48, (1979). [5] R. Jedamzik, C. Kunish, and T. Westerhoff, ZERODUR for stress mirror polishing, Proc. SPIE 8126, (2011). [6] R. Jedamzik, C. Kunish, T. Westerhoff, U. Muller, and J. Daniel, ZERODUR for stress mirror polishing II: Improved modeling of the material behavior, Proc. SPIE 8450, 84504P-1 (2012). [7] P. M. Kurowsky, [Engineering Analysis with SolidWorks Simulation], SDC Publications, Kansas, (2011). [8] M. Servin, and M. Kujawinska, [Handbook of Optical Engineering], Marcel Dekker Inc., New York, (2004). [9] O. Cardona-Nunez, A. Cornejo-Rodriguez, R. Diaz-Uribe, A. Cordero-Davila, and J. Pedraza-Contreras, Conic that best fits an off-axis conic section, Appl. Opt., 25(19), (1986). [10] R. Izazaga Pérez, F. Granados-Agustin, M. Percino-Zacarias, and E. Carrasco-Licea, "Optical Testing Applied to a 6.5-Meter Mirror," in Imaging and Applied Optics Technical Papers, OSA Technical Digest (online) (Optical Society of America, 2012), paper JTu5A.6, [11] D. Aguirre-Aguirre, R. Izazaga-Perez, F. Granados-Agustin, B. Villalobos-Mendoza, M. E. Percino-Zacarias, and A. Cornejo-Rodriguez Algorithm for Ronchigram recovery with random aberrations coefficients, Opt. Eng., 52(5), (2013).