Use of Mangin and aspheric mirrors to increase the FOV in Schmidt- Cassegrain Telescopes

Use of Mangin and aspheric mirrors to increase the FOV in Schmidt- Cassegrain Telescopes A. Cifuentes a, J. Arasa* b,m. C. de la Fuente c, a SnellOptics, Prat de la Riba, 35 local 3, Interior Terrassa 08222 Spain *b CD6, Technical University of Catalonia, Rambla Sant Nebridi 10, Terrassa 08222 Spain c Indra Sistemas, Aranjuez, Madrid, Spain ABSTRACT The Schmidt-Cassegrain configuration has advantages from the point of view of the packaging constraint but doesn t provide enough optical quality through the full field of view when a larger F-number (3.6) and a FOV of 1º are necessary to reach the minimum illumination threshold in the sensor. Moreover, to improve the global performance the telescope s window must be spherical instead of flat. All these factors produce a poor image optical quality that must be increased. We had overcome those problems introducing two changes in the traditional Schimdt-Cassegrain configuration. First, we had changed the spherical primary mirror to a Mangin mirror. This introduces a second surface and an extra thickness that can be used to optimize the system without adding new elements. Secondly, as the Mangin mirror is the entrance pupil of the system with a 200 mm diameter, the use of aspherical surfaces on it is too expensive. Instead we have aspherized the telescope s secondary mirror to obtain the required image quality. This aspheric coefficient of the secondary mirror, introduced in an element with a diameter not larger than 50 mm, replaces the third order coefficient of the second surface of the telescope window. Keywords: Mangin mirrors, Image telescopes. 1. INTRODUCTION Our objective is to obtain an optical device in the shortest track possible while achieving good quality over all the FOV. To obtain a system with the shortest total track possible it is mandatory to fold it using reflective elements, so we began the design with the well-known Schmidt-Cassegrain telescope solution 1,2. In the following table you can find the most relevant design parameters. Table 1. Design Parameters. Magnitude Value 1 Volume Design target: 500 x 300 x 300mm 2 Temperature -30º to +60º C 3 Vibration operating range Must support vibration type I & type II as detail in MIL-STD-167-1. 4 Environment conditions Full compatibility of MIL-STD-108E. for water splashes 2. PRELIMINARY STUDY In tables 2 and 3 the global specifications for the optical system and the associated image sensor are listed. * arasa@oo.upc.edu; phone +34 93 739 83 55 Optical Design and Engineering III, edited by Laurent Mazuray, Rolf Wartmann, Andrew Wood, Jean-Luc Tissot, Jeffrey M. Raynor, Proc. of SPIE Vol. 7100, 71000M 2008 SPIE CCC code: 0277-786X/08/$18 doi: 10.1117/12.797265 2008 SPIE Digital Library -- Subscriber Archive Copy Proc. of SPIE Vol. 7100 71000M-1

Table 2. Detector parameters (relevant for the optical design) # Magnitude Valor 1 Detector Optical Area 9.6 mm x 12.8 mm 2 pixels n 494 x 659 3 Optical Window: material & thickness Borosilicate / 5.5 mm 4 Window s Flange distance 13.8 mm 5 Mechanical interface C-mount. Table 3. Relevant optical specifications. # Parameters Valor 1 Aperture 200 mm 2 FOV (NFoV, MFoV, WFoV) 0.3º x 0.4º - 0.525º x 0.7º - 0.75º x 1º 3 EFL 1833 mm - 1048 mm - 733 ± 1 % 4 Distortion < 1% 5 Focusing range From 300m to infinity 6 Central obscuration < 25% During the first analysis performance we found that, in order to obtain good agreement between focal length and available volume, the best configuration must involve the use of a catadioptric system. Also, considering that the final use requires only three discrete fields of view it was decided that a interchanging zooming group would be more efficient than a continues zoom configuration. We started from the configuration shown in figure 1. In this system, the catadioptric group is very simple and easy to manufacture but the mechanical track is too large and the obscuration ratio (0.35) is unacceptable. Finally the group used to obtain the WFoV is to complex in comparison of the NFoV and MFoV. Our objective is to obtain an optical device in the shortest track possible while achieving a good quality over all the FOV. ZEMAX was used for the initial studies 4. To obtain a system with the shortest total track possible it was found that folding the system using reflective elements was necessary, so we have start the design with the well-known Schmidt-Cassegrain telescope solution. Window I Primary Secondary H Focousing group Fig. 1. Layout of the first configuration used. The system doesn t accomplish the first level specifications, but it is close in many of the optical parameters. Proc. of SPIE Vol. 7100 71000M-2

From this initial design improvement was accomplished by introducing optical power to the window (first element). This solution adds two extra curvature surfaces that can be use to correct aberrations. The second surface of the window plays the role of support for the secondary mirror. Also an alternative solution was considered, the use of a Mangin type primary mirror. The Mangin mirror introduces an additional refractive surface before the reflective surface, providing this new element with an extra surface that contributes to the minimization of the aberration s system 3. Figure 2 shows both configurations. (a) Fig. 2. Configuration with powered window (first element) and the first surface primary mirror changed to a Mangin mirror. In the figure 2(a), we observe that the second face of the first element is convex. In this case, the obscuration ratio is so high that it does not meet the first order specifications. In the figure 2(b) the second face of the first element is concave, and introduces a high convergence in the incident beam, so it would be complex and expensive to obtain an optical group that corrects the resulting divergence after the intermediate image that would form. Both configurations use a Mangin type primary mirror. As consequence of the complexity of the proposed solutions another possible configuration was devised. This configuration adds a secondary mirror of a Mangin type. Figure 3 shows the scheme of this configuration. The advantages of this configuration are that the secondary mirror acts like a convex mirror, like the one in figure 2(a), but is actually concave. In figure 4 a drawing of the configuration is shown. This new configuration allows for the reduction of the obscuration ratio to 0,25, which is the design specification. ray (b) diam: 253.12 mm Primary 7/, /, p Reflection Aspherical sup diam: 52.274 Fig. 3. Configuration with both Primary and Secondary mirrors of the Mangin type. Proc. of SPIE Vol. 7100 71000M-3

(a) Fig. 4. Comparison between ray tracing when using a Mangin mirror as the secondary (a) or a traditional mirror (b). An important factor that must be considered when we decide a configuration is the manufacturing tolerances. To study this point we introduced small variations in the curvature of the secondary mirror for both proposed solutions (secondary convex regular mirror or concave Mangin mirror) and analyzed the changes in the image quality. The considered criterion of quality was the RMS of the spot diameter for the central field of view (0º). Taking this as a starting point two systems with equal initial quality, the Mangin mirror behaves better by errors in curvature, by two orders of magnitude, as figure 5 shows. (b)... E :...:. E i- - r : S S -....1-.. 1.:... C...., S S. S. U S.., S :....S S (a) (b) Fig. 5. Tolerance s comparison between the use of a secondary Mangin mirror (a) and a traditional one (b). To show the importance of the selection an equivalent increment of the curvature radius (1%) was introduced in both cases and the transversal aberration calculus was performed. The Mangin solution (a) is, clearly, the best because the RMS is two orders of magnitude lower. So we have adopted the solution to change the traditional secondary mirror for a Mangin mirror but forcing that the second surface of the window and the mirrored Mangin surface were flats. This solution guaranteed the fixation between the window and the secondary mirror. In summary: Considering that requires three focal fixed ones, it was decided on an interchanger of focal, instead of a continuous zoom lens Proc. of SPIE Vol. 7100 71000M-4

We decided to use a catadioptric system, to reduce the total mechanical track. The catadioptric system will include Mangin mirror type. In those conditions we explored the possibilities of realizing the design parting form a starting design configuration with regular quality and a total mechanical track of 400 mm. 3. FINAL DESIGN In this section we discuss the final design parameters starting with the nominal design. Then we analyze the effect of focusing and athermalization and the strategy to achieve these variations from the nominal design. 3.1 Nominal design The nominal results obtained are showed in table 4. All the demanded requirements are fulfilled. For the final design stage both ZEMAX and CODE V 5 software packages were used. The required design specifications were met for each zoom position. The value of the modulation at 24 c/mm is the average of the sagittal and tangential values of MTF. Table 3. Relevant optical parameters Field of view Parameter NFoV MFoV WFoV EFL (mm) 1833 1048 733 Window diameter(mm) 255 255 255 F-number 7.3 4.2 3.0 MTF at 24 c/mm (at full field) 0.69 0.77 0.79 Distortion (%) 0.45 0.53 0.85 No. de elements* 9 9 + 3 9 + 4 Total Track (mm) 400 400 400 *The total is the addition of the common used elements (9) and the specific element for each field of view Though the Nyquist frequency of the associated detector was determined to be 30 c/mm, the measured resolution was actually 24 c/mm, therefore, the design goal was specified using the measured resolution of the detector. The diffraction limited MTF at 24 c/mm was determined to be MTF(24c/mm) = 78%. From this value, the design goal was set to obtain 60% modulation at 24c/mm on axis. Figures 6, 7 and 8 show for each demanded field of view a layout of the system and its corresponding MTF graph up to 24 c/mm. (a) (b) Fig. 6. NFoV. a) Optical elements layout, b) Polychromatic MTF obtained from the optical system drawn in (a). The MTF s value is over 0.6 at 24 c/mm for all the fields of view.. Proc. of SPIE Vol. 7100 71000M-5

a) b) Fig. 7.MFoV. a) Optical elements layout, b) Polychromatic MTF obtained from the optical system drawn in (a). The MTF s value is over 0.7 at 24 c/mm for all the fields of view. a) b) Fig. 8. WFoV. a) Optical elements layout, b) Polychromatic MTF obtained from the optical system drawn in (a). The MTF s value is over 0.8 at 24 c/mm for all fields of view. Analyzing the system layout (figures 6(a), 7(a) and 8(a)) the system is comprised of four groups that we have defined as: 1. The catadioptric group: Window Primary mirror and secondary mirror. 2. Main relay group: Comprises the two doublets. 3. The interchangeable zoom group. 4. Field corrector group: Last element before the detector. The first group actually forms an intermediate image before the second group. During the design process this intermediate image was corrected for third order aberrations. The second group is the main relay group and, as will be shown in section 3.2, also functions as a focusing group. Finally the interchangeable zoom group follows, but for the NFoV, as can be seen in figure 6(a), this group consists of zero elements. Since this field of view was determined to be the most critical for the application, during design it was considered the reference zoom position and in/out elements were avoided to assure the best alignment of the optical axis. For the remaining fields of view a group of elements was introduced in the optical path to achieve the correct focal length. As stated in the previous section, the focal lengths range from 1833 mm to 733 mm, which is 2.5x zoom, restricted within a total mechanical track of 400 mm. Proc. of SPIE Vol. 7100 71000M-6

3.2 Focus and athermalization Taking as starting point the nominal design, we have performed the quality s study when: a) the distance to the scene changes, b) thermal variations are considered. The minimum scene distance was set by specification to be 300 mm from the window of the optical system under consideration. The temperature range for optical functionality was specified between -30ºC and +60ºC. One of the important factors was deciding which element or elements should be moved for focusing and for athermalization. The power contribution of the element chosen for focusing should be considerable in order to achieve the correct focal length for the finite conjugate system as the scene moves closer. But at the same time image quality must be maintained. At the same time mechanical constraints must be observed. For example, focusing or athermalization using the interchangeable zoom groups was not a possibility due to the complexity of the design. Also, considering moving the large window and primary mirror was also considered impractical. The choices for displacing elements axially were reduced to two doublets following the secondary mirror along the optical path or the last element before the Analyzing the current system, the first doublet should be discarded, as it is close to an intermediate image and therefore has low power contribution. The second doublet seems like the better choice. Upon simulation, the image quality was not adequate as the scene moved closer. Finally, the best solution was to move both doublets, in a coupled manner. In this fashion the two double system was repositioned with respect to the intermediate image, obtaining better image correction throughout the focusing range. This same coupled movement of the doublets was also used for athermalization. The compensation was realized such that for a specific temperature and scene distance, the position of the focusing elements did not change as the zoom configuration was cycled. This was an important advantage in reducing the complexity of the focusing and athermalization control. Movement of the coupled doublets for focusing & compensation 5 mm doublet 1 doublet 2 Fig. 9. WFoV. Layout of the system that shows the movement of the coupled doublets for focusing, thermal compensation and manufacturing error compensation. The doublets total travel is +/- 5 mm. In all the cases the compensation element is the movement of the two only doublets presents in the system. The maximum displacement was determined in +/- 5 mm. In figure 9 you can find, circled in red, the elements that are to be displaced axially in order to realize the focusing and athermalization. The movement always is coupled, so both elements move in the same direction and the same distance. Proc. of SPIE Vol. 7100 71000M-7

Table 5 resume the MTF s values for the upper frequency 24 c/mm, when the system focuses at a distance of 300 meters for all the configurations and all the field of view required, the focusing distance (300 meters) is also a specifications of the system. Table 5. Focusing at 300 meters. NFOV 0.73 0.73 0.59 0.63 0.66 0.70 MFOV 0.84 0.84 0.74 0.80 0.63 0.66 WFOV 0.88 0.88 0.82 0.86 0.67 0.73 Following the same structure of table 5, tables 6, 7, 8 and 9 meet the results of the MTF s values for a frequency 24 c/mm (tangential and sagittal profiles) on axis, at 0.7 of the full field and al full field corresponding to each configuration (NFoV, MFoV, WFoV) when the temperature raises the larger values specificity. Tables 6 and 7 correspond to a temperature of -30ºC and the object located in the infinite and at 300 meters, respectively. Tables 8 and 9 correspond to a temperature of +60ºC and, with object in the infinite and to 300 meters Table 6.Athermalization Analysis: Temperature: -30ºC. Object placed at infinity. NFOV 0.62 0.62 0.56 0.55 0.50 0.45 MFOV 0.83 0.83 0.82 0.84 0.78 0.78 WFOV 0.88 0.88 0.81 0.85 0.67 0.72 Table7. Athermalization Analysis: Temperature: -30ºC. Object placed at 300 meters. NFOV 0.56 0.56 0.50 0.55 0.43 0.48 MFOV 0.84 0.84 0.77 0.82 0.69 0.70 WFOV 0.85 0.85 0.63 0.76 0.36 0.52 Table 8. Athermalization Analysis: Temperature: +60ºC. Object placed at infinity. NFOV 0.61 0.61 0.57 0.64 0.54 0.64 MFOV 0.85 0.85 0.82 0.82 0.78 0.71 WFOV 0.84 0.84 0.82 0.85 0.75 0.88 Table 9. Athermalization Analysis: Temperature: +60ºC. Object placed at 300 meters. NFOV 0.66 0.66 0.63 0.69 0.61 0.66 MFOV 0.84 0.84 0.69 0.76 0.57 0.57 WFOV 0.86 0.86 0.86 0.87 0.81 0.83 Proc. of SPIE Vol. 7100 71000M-8

4. CONCLUSION The selected configuration based in a Schimdt-Cassegrian telescope, but using Mangin mirrors for the primary and the secondary achieve the specified quality requirement and enabled the possibility of obtaining a great compression in the total mechanical track. An effective focal length of 1833 mm was obtained in a mechanical track of 400 mm and a maximum field of view of 1º and an f/# of 3.6 for the widest field of view configuration. The movements of the two doublets, coupled so that the linear displacement was equal, were enough to achieve focus of the a scene form infinity to 300 m, and this movement also served as an athermalization mechanism, so no additional movements must be used along the optical axis. REFERENCES [1] [2] [3] [4] [5] Smith, Warren [J. Modern Optical Engineering]. 4 th Ed. Mcgraw Hill Companies, Inc. New York (2008). Fischer, R. Tadic-Galeb, B. Yoder, P. Optical System Design, 2 nd Ed. McGraw-Hill Companies, Inc. New York (2008) M. J. Riedl, "The Mangin Mirror and Its Primary Aberrations," Appl. Opt. 13, 1690-1694 (1974) Zemax Optical Software. ZEMAX Development Corporation. Bellevue, WA. Code V Optical Design Sofware. Optical Research Associates. Pasadena, CA. Proc. of SPIE Vol. 7100 71000M-9