Common-pull, multiple-push, vacuum-activated telescope mirror cell Elfego Ruiz,1,* Erika Sohn,1 Luis Salas,1 Esteban Luna,1 and José A. Araiza-Durán1,2 1
2
Universidad Nacional Autónoma de México, Instituto de Astronomía, Observatorio Astronómico Nacional Km 103 Carr. Tijuana—Ensenada, Ensenada, B.C. 22860, Mexico
Instituto Nacional de Astrofísica, Optica y Electrónica, Luis Enrique Erro # 1, Santa Maria Tonantzintla, Puebla 72840, Mexico *Corresponding author: [email protected] Received 28 August 2014; revised 15 October 2014; accepted 20 October 2014; posted 22 October 2014 (Doc. ID 221897); published 18 November 2014
A new concept for push–pull active optics is presented, where the push-force is provided by means of individual airbag type actuators and a common force in the form of a vacuum is applied to the entire back of the mirror. The vacuum provides the pull-component of the system, in addition to gravity. Vacuum is controlled as a function of the zenithal angle, providing correction for the axial component of the mirror’s weight. In this way, the push actuators are only responsible for correcting mirror deformations, as well as for supporting the axial mirror weight at the zenith, allowing for a uniform, full dynamic-range behavior of the system along the telescope’s pointing range. This can result in the ability to perform corrections of up to a few microns for low-order aberrations. This mirror support concept was simulated using a finite element model and was tested experimentally at the 2.12 m San Pedro Mártir telescope. Advantages such as stress-free attachments, lighter weight, large actuator area, lower system complexity, and lower required mirror-cell stiffness could make this a method to consider for future large telescopes. © 2014 Optical Society of America OCIS codes: (220.1000) Aberration compensation; (220.1080) Active or adaptive optics; (350.1260) Astronomical optics; (350.1270) Astronomy and astrophysics; (110.1080) Active or adaptive optics; (110.6770) Telescopes. http://dx.doi.org/10.1364/AO.53.007979
1. Introduction
Active optics, in the sense of being capable of actively altering the mirror figure in order to improve image quality, has been in use ever since it was first applied to the New Technology Telescope (NTT) in 1989 [1] and has revolutionized the design of the subsequent generations of telescopes. Active optics allows for corrections of telescope errors that comprise polishing defects of the mirrors in the form of low-order aberrations, misalignments, as well as deformations induced by gravity and temperature. These corrections remove all errors, except for atmospheric variations, and allow for seeing-limited observations. For a review of active optics applied to 1559-128X/14/337979-06$15.00/0 © 2014 Optical Society of America
telescopes refer to [2]. An important consequence of the implementation of active optics is the relaxation in stiffness requirements that enabled considerable weight reductions of primary mirrors and telescope mechanical structures in general, making the construction of a generation of large telescopes feasible. Although active optics is now a standard in modern telescopes, there are only a few types of support systems which are unique to each telescope. Among these types, we can count the motorized counterweights and spring-loaded levers, originally used in the NTT, to more sophisticated and generally large actuators, that include pneumatic, hydraulic, electromechanic, electromagnetic and hybrid embodiments, and that range from push-only, push–pull, axial-plus-lateral and axial-only support systems. Examples of telescopes using motorized, springloaded levers are the NTT, TNG [3] and VST [4]. 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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Telescopes basing their active systems on pneumatic force actuators are, for example, the lightweighted honeycomb-construction mirrors such as the Magellan telescopes [5], LBT [6], the MMT [7], and future telescope designs [8]. Among segmented mirror telescopes, a warping harness is used to correct the mirror figure of individual segments. Although in the Keck telescopes the figure control for each segment is passive [9], in the case of the GTC [10], this has been converted to active. However, it has to be noted that the total mirror figure in segmented telescopes is achieved by means of relative position control between segments. The VLT telescope bases its support system on a combination of passive hydraulic and spring-loaded electromechanical actuators [11]. The Subaru active support system consists of a load-cell controlled spring for axial support and a counterweighted fulcrum lever for lateral support [12]. An example of a hybrid suspension system that incorporates passive hydraulic cylinders and active pneumatic actuators that are embedded in a positive-pressure, sealed mirror cell that supports most of the mirror weight, is the Gemini telescope [13]. Some of these actuators are in free contact with the mirror, while others are glued or inserted into the mirror in order to be able to exert pull-forces. The area of contact of most of these actuators is usually very small and can generate actuator print-through. A simpler type of support system consists of controlled-pressure airbags as the force actuators. These are used in, for example, [4,14], and [15]. These systems are much simpler, smaller, more lightweight, and have a much lower profile than the above mentioned. They, however, have the disadvantage of being relatively low-stiffness systems and are not able to provide pull forces or lateral mirror support, although some of these disadvantages are shared with some of the systems just described. For push-only mirror supports, a means of providing an increased pull force needs to be implemented for the case where the axial mirror weight at the largest zenithal angle in the telescope’s operating range is insufficient to allow for “negative” primary mirror shape corrections. This paper presents a concept that adds pullcapability to a push-only airbag-based actuator support by means of a common vacuum. 2. Vacuum-Airbag System Concept
In the case of a push-only active system, gravitational pull is the only means to counteract the actuators. The effectiveness of a desired deformation correction is limited by the zenithal angle Z. That is, the pressure that a given actuator i must bear is given by: Pib Pw cosZ Pid ;
(1)
where Pib is the actuator pressure, Pw is the pressure due to the mirror weight assuming, for simplicity, that it is common to all actuators, and Pid is the 7980
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pressure needed to produce the desired deformation at a particular position. This pressure can be either negative or positive, but the resultant needs to remain positive for all zenithal angles. This clearly limits the overall performance of the system. We propose to generate a common pull-force, Pv A, induced by a homogeneous partial vacuum that goes as 1 − cosZ, applied between the mirror cell and the back of the primary mirror (M1, with area A), in order for the airbags to feel a constant “mirror weight” that is independent of Z: Pib Pw cosZ Pid − Pv 1 − cosZ Pw Pid ; (2) when Pv −Pw . Figure 1 shows this concept in a graphical way. A set of actuators are shown, that are capable of providing the required range of force correction at the zenith. However, as the telescope points away from the zenith, gravity is not enough to provide the required pull force for a given actuator [Pib < 0, in Eq. (1)], resulting in an incomplete correction. Note the shaded area in the figure that goes below the zero-level floor (Pb 0). This is corrected in the form of a common pull force by increasing the vacuum in the mirror cell as 1 − cosZ. This increments the effective weight of the mirror on each actuator by the same factor and in turn raises the average mirror weight, so that the force balance the system had at the zenith is recovered. Prior to the experiment, this idea was thoroughly simulated and a finite element model (FEA) of the 2.12 m SPM telescope mirror, together with its associated suspension was developed. This model aided in proving the concept and allowed us to make sure that the reflecting surface could be optimally corrected with these additional forces applied to the back of the mirror (Fig. 2). We ran a FEA analysis using ALGOR software, simulating an 18-actuator active system using 30 cm diameter airbags, actuating over a 2 m, 26 cm thick Cervit hyperbolic F/2.25 mirror. This model maintained the active system’s original actuator spatial distribution, which is not entirely even. Variations among airbags of up to 10% are thus present in both, separation and weight carried (Fig. 2). In this case, Eq. (2) is not entirely valid, since Pw must be replaced by Piw. Here the force balance equation must include the sum of the pressures of all actuators. In this case, Pv has to be equal to minus the total mirror weight divided by its total area, in order for the cosZ terms to cancel out. The final effect is still the equivalent of the telescope always pointing at the zenith. In this numerical experiment, to test an extreme case, the mirror weight was doubled at the zenith. This represents the worst-case scenario. It can be appreciated from the figure that the back of the mirror is deformed by approximately 120 nm peak-to-valley (P–V), which is attenuated down to an actuator printthrough of 27 nm P–V at the reflecting surface
Fig. 1. Common-pull concept. This figure shows actuator pressures for two different zenithal angles. The upper graph is for the telescope pointing at the zenith. Note that pressure corrections are in range. The lower graph shows actuator pressures at a higher zenithal angle. For some actuators, mirror weight is insufficient to effect the correction.
Fig. 2. Numerical experiment that shows the deformation of the back of the 26 cm thick Cervit mirror due to positive push forces and an induced common pull force that effectively duplicates the mirror weight. This was simulated in order to test mirror integrity.
(Fig. 3). The stresses induced in this test are 200 times smaller than the material’s breaking strength. These deformations and stresses are mirrorthickness and actuator-diameter dependent and have to be taken into account in each particular design. 3. Experimental Demonstration A.
Implementation of the Concept in the 2.1 m OAN SPM
To test this concept, we modified the existing active support system of the 2.1 m telescope at the Observatorio Astronómico Nacional, San Pedro Mártir. This telescope consists of a 2.1 m diameter, 26 cm thick, 2 ton Cervit M1, which at its time (1970s) was considered thin. It has a suite of three interchangeable secondary mirrors (F/7.5, F/13.5 and F/30). The original M1 passive suspension was reconverted to active in 1995 [14]. The lateral passive suspension system
Fig. 3. Effect of the actuators supporting the equivalent of a doubled mirror weight. Deformations are 27 nm P–V.
has not been modified and consists of a Hg-belt around the periphery of the mirror. The lateral component of the mirror weight is supported by a buoyancy force that is applied at the mirror’s center of mass by means of this Mercury belt. This axial active suspension system consists of 18 flat airbags, distributed along two rings in the mirror cell that act as force actuators. The original active system velocity is low due to the regulator–restrictor combination used to inflate the airbags, which limits the telesscope’s “jog” speed. Three hard points, equipped with load cells, define the position of the mirror. The 81 g airbags are 30 cm in diameter and inflate to approximately 3 mL thickness. They are fabricated from Nylon Cordura reinforced polyurethane laminate material, which is durable, very thin, nonelastic, and has a texturized surface. The mirror weight is 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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supported by the active system such that the pressure on each actuator or hardpoint is evenly distributed. The average pressure in each airbag is approximately 1.8 pounds-per-square-inch (psi) (0.127 kg∕cm2 ), supporting 106 kg of the total mirror weight. The hard points (10 cm in diameter) carry only 2% of the mirror weight due to their relatively smaller area. Given the M1 stiffness, this system is only capable of correcting astigmatism and other low-order aberrations, which represent the main optical figure errors. Corrections are secondary-mirror dependent. However, being a push-only system, the possible corrections are limited by the zenithal angle, which is different for each secondary mirror. For two of the secondary mirrors, the original correction range is adequate, whereas for the mid-infrared F/30, the astigmatism amounts to 2.5 μm, which limits corrections to only 60 deg Z. When the telescope is pointing at the zenith, the actuators push against the mirror’s weight. As the telescope is inclined toward other positions, the axial component of the weight decreases, as does the effectiveness of a push-only system. We recently air-tightened the existing mirror cell so that, together with M1, a confined 40 l volume that encloses the airbags, could be defined. A vacuum is then generated in this volume which pulls the back of the mirror against the mirror cell, sandwiching the airbags. This vacuum acts as a common pull force against the push forces of the individual airbags (Fig. 4). Vacuum is achieved by means of a three cubic feet per minute, two-stage pump which in turn is connected to a vacuum reservoir that acts as a pneumatic buffer to handle peak demands. It is then fed to the pull-end of a set of electro-valves that regulate
the pressure in this volume. This allows for a precise pressure control in the range of −1 to 0 psi (atmospheric pressure), which can generate up to 2 tons of additional mirror weight. These electro-valves were chosen to compensate for leaks and to adequately handle the enclosed volume. The electrovalves are set up in a push–pull configuration, biased to 11 psi pressure supplies, and are controlled by a microcontroller working in a pulse-width modulation (PWM) mode. The minimum pulse duration is set to 4 ms, corresponding to a 2 mL volume. This allows for pressure corrections better than 1∕1000. The maximum flow rate is determined by the restrictor formed when either valve is left fully open. This corresponds to approximately 14 l/s, which is faster than the telescope’s pointing speed. The control cycle time was adjusted to 100 ms, which is fast enough to handle the telescope’s 1 deg/s pointing movements. As a bonus, the airbags are no longer responsible for the Z-angle correction, which is now managed by the common pull-force in a faster way, increasing overall system performance. Additionally, the mirror cell volume acts as an efficient pulse dampener. In general, the overall system efficiency is high in terms of air consumption, since air is required only when the telescope is moving. When the telescope is pointing at the zenith, the vacuum pressure is kept to a minimum, such that the pressure in the airbags carries the mirror’s weight and exerts the correcting deformations. As the telescope points away from the zenith, the vacuum control system senses a decrease in mirror weight through the load cells and increases vacuum pressure to maintain a constant weight on the load cells. This is done by means of a proportional-integral-derivative (PID) control system that acts inside a defined error interval. If the
Fig. 4. Block diagram of the modified active cell. The right-hand side of the diagram represents the original active system. The left-hand side shows the addition of a common pull force by a controlled vacuum, as described in the text. 7982
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Fig. 5. Radial intensity profiles of stars observed close to the zenith with the original nonvacuum active system (left) and the new, common-vacuum pull implementation (right). Intensity is given in counts.
error exceeds a threshold value, full open-valve correction is applied. The original active control system is tricked to believe that the telescope keeps pointing at the zenith and maintains the mirror deformation pressures accordingly. The mirror rests on the airbags, and their texture allows for free air circulation between them and the mirror back, allowing for the vacuum to act over the entire M1 area. This combination between controlled vacuum and positivepressure airbag correction constitutes an effective push–pull active system. B.
Experimental Results
Experiments were designed to prove that seeinglimited image quality can be maintained with the new system and to show that large mirror deformations can be achieved and kept constant at large zenithal angles. We tested this system over two observing nights that were available during a maintenance week. Only the F/7.5 configuration was available at this time. The first night the overall system performance was checked, and a comparison between the original active system and the new push–pull implementation was made by observing point sources at different zenithal angles. Figure 5 shows typical radial profiles for two stars with the original system (left) and the new implementation (right). In both cases, the full width at half-maximum (FWHM) is around 1.0 0.1 arc-seconds, which corresponds to the night’s seeing value; although images down to 0.8 arcsec were observed that night. This proves that the new implementation does not negatively affect the image quality. As explained above, there are certain telescope configurations where large deformations are required to correct the image quality, which is not possible for high Z values, given that the original system is push-only. To test the ability of the new system to solve this issue, we performed an experiment in which an exaggerated value of astigmatism (3.5 μm, much larger than the intrinsic mirror errors) was induced onto the primary mirror, while observing at different Z-angles. This test is advantageous in that deformations are
easily measured, regardless of seeing variations, and because astigmatism is the lowest-energy, mirror-bending Zernike term. Astigmatism was subsequently measured through the ellipticity of slightly out-of-focus images, as described in [16]. The result can be appreciated in Fig. 6. The blue crosses represent individual measurements with the original push-only system, while the red dots show similar measurements using the new vacuum-induced pull. It is noted that, as the Z-angle increases, the measured astigmatism decreases, implying that the original system cannot maintain the desired shape of the primary mirror, whereas, in the case of the new implementation, the red dots indicate a constant shape within the measurement errors. Least square fits for both of these cases have been included to guide the eye. Having demonstrated the effectiveness of this concept, it is expected that an increase in dynamic range of the actuators is also achievable, since a vacuum much larger than the mirror weight may allow
Fig. 6. Measured astigmatism as a function of zenithal angle. Blue crosses show the behavior of the original nonvacuum active system, while the red dots indicate the new common vacuum-pull implementation. 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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for a larger negative excursion of the actuators. With this increase in dynamic range, the area of the airbags could be reduced, in order to increase their number for higher-order corrections. As mentioned in Introduction, the low stiffness of an airbag-based system may also be of concern. In the case of the 2.12 m telescope, the actuator’s width-to-area ratio is approximately 3 × 10−4 cm−1, resulting in a stiffness that is about two orders of magnitude lower than that of a typical hydraulic actuator. Nevertheless, for this particular telescope, this is not a problem, since its first eigenfrequency is high enough (>100 Hz) to resist the wind-induced vibrations. However, for a case where stiffness is problematic, the use of smaller or compartmentalized actuators that are filled with a noncompressible liquid, instead of air, could increase the stiffness for higher resistance to wind buffeting. These ideas will be further investigated in the future. 4. Conclusions
The concept of an active mirror cell with multiplepush airbag actuators and a common pull-force, implemented by means of a vacuum between M1 and its mirror-cell, has been proposed and demonstrated through the above-described experiment. The modifications necessary to test this idea were quite easy to implement, increased the overall system response of our existing active system, and several advantages have been identified: • The actuators are not attached or glued to the back of the mirror, so no lateral deformations and stresses are present. • Air-bag area is relatively large. This reduces the number of actuators necessary in order to minimize print-through and mirror sag. • There is a considerable weight reduction, since actuators are essentially weightless. • The mirror cell need not be stiff, since the position defining supports carry only a fraction of the mirror weight. • In the particular case of the 2.12 m telescope, this modification could increase system response velocity by a factor of approximately 3. These results were satisfactory and could represent a boost in performance for our 2.12 m telescope. We have proposed that these modifications be made permanent. This experiment demonstrated that individual push–pull actuators are not necessary; a common pull can be sufficient. This could reduce overall system complexity and cost for a future generation of large, membrane-based telescopes, where the number of actuators could be in the thousands. We are preparing experiments to demonstrate this concept, which will be published shortly. This work was made possible due to the invaluable help offered by Eduardo López, Fernando Quiroz,
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Joel Herrera, Gerardo Guisa, Carolina Durán and Augusto Sarabia, and the personnel of the Observatorio Astronómico Nacional to set up this experiment. We also thank Leonel Gutiérrez and Michael Richer for granting us two extra observing nights. We thank the reviewers for valuable feedback. The project was funded by a grant awarded by Instituto de Astronoma, UNAM and partly by grant IT-100512 PAPIIT-UNAM. The data used for this paper were based upon observations acquired at the Observatorio Astronómico Nacional in the Sierra San Pedro Mártir (OAN-SPM), Baja California, México. References 1. R. Wilson, “The history and development of the ESO active optics system,” Messenger 113, 2–9 (2003). 2. L. Noethe, “Active optics in modern, large optical telescopes,” Prog. Opt. 43, 1–36 (2002). 3. F. Bortoletto, D. Fantinel, R. Ragazzoni, C. Bonoli, and M. D. Alessandro, “Active optics handling inside Galileo telescope,” Proc. SPIE 2199, 212–222 (1994). 4. P. Schipani, S. D’Orsi, L. Ferragina, D. Fierro, L. Marty, C. Molfese, and F. Perrotta, “Active optics primary mirror support system for the 2.6 m VST telescope,” Appl. Opt. 49, 1234–1241 (2010). 5. P. L. Schechter, G. Burley, C. Hull, M. Johns, B. Martin, S. Schaller, S. A. Shectman, and S. C. West, “Active optics on the Baade 6.5 m (Magellan I) telescope,” Proc. SPIE 4837, 619–627 (2003). 6. H. M. Martin, B. Cuerden, L. R. Dettmann, and J. M. Hill, “Active optics and force optimization for the first 8.4 m LBT mirror,” Proc. SPIE 5489, 826–837 (2004). 7. H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. DeRigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998). 8. R. A. Bernstein, P. J. McCarthy, K. Raybould, B. C. Bigelow, A. H. Bouchez, J. M. Filgueira, G. Jacoby, M. Johns, D. Sawyer, S. Shectman, and M. Sheehan, “Overview and status of the Giant Magellan Telescope project,” Proc. SPIE 9145, 91451C (2014). 9. R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Liacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, and C. Witebsky, “The W. M. Keck telescope segmented primary mirror active control system,” Proc. SPIE 1236, 996–1008 (1990). 10. B. Lefort and J. Castro, “The GTC primary mirror control system,” Proc. SPIE 7019, 70190I (2008). 11. S. Stanghellini, P. Legrand, A. Baty, and T. Hovsepian, “Design and construction of the VLT primary mirror cell: support of the large, thin primary mirror,” Proc. SPIE 2871, 314–325 (1997). 12. M. Iye and K. Kodaira, “Primary mirror support system for the SUBARU telescope,” Proc. SPIE 2199, 762–772 (1994). 13. L. Stepp, E. Huang, and M. Cho, “Gemini primary mirror support system,” Proc. SPIE 2199, 223–238 (1994). 14. L. Salas, L. Gutirrez, M. H. Pedrayes, J. Valdez, C. Carrasco, M. Carrillo, B. Orozco, B. García, E. Luna, E. Ruiz, S. Cuevas, A. Iriarte, A. Cordero, O. Harris, F. Quiroz, E. Sohn, and L. A. Martinez, “Active primary mirror support for the 2.1-m telescope at the San Pedro Martir Observatory,” Appl. Opt. 36, 3708–3716 (1997). 15. M. K. Cho, R. S. Price, and Il. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006). 16. E. Luna, L. Salas, L. Gutirrez, and J. M. Nuñez, “Geometric method to measure astigmatism aberration at astronomical telescopes,” Appl. Opt. 46, 3439–3443 (2007).
2
Universidad Nacional Autónoma de México, Instituto de Astronomía, Observatorio Astronómico Nacional Km 103 Carr. Tijuana—Ensenada, Ensenada, B.C. 22860, Mexico
Instituto Nacional de Astrofísica, Optica y Electrónica, Luis Enrique Erro # 1, Santa Maria Tonantzintla, Puebla 72840, Mexico *Corresponding author: [email protected] Received 28 August 2014; revised 15 October 2014; accepted 20 October 2014; posted 22 October 2014 (Doc. ID 221897); published 18 November 2014
A new concept for push–pull active optics is presented, where the push-force is provided by means of individual airbag type actuators and a common force in the form of a vacuum is applied to the entire back of the mirror. The vacuum provides the pull-component of the system, in addition to gravity. Vacuum is controlled as a function of the zenithal angle, providing correction for the axial component of the mirror’s weight. In this way, the push actuators are only responsible for correcting mirror deformations, as well as for supporting the axial mirror weight at the zenith, allowing for a uniform, full dynamic-range behavior of the system along the telescope’s pointing range. This can result in the ability to perform corrections of up to a few microns for low-order aberrations. This mirror support concept was simulated using a finite element model and was tested experimentally at the 2.12 m San Pedro Mártir telescope. Advantages such as stress-free attachments, lighter weight, large actuator area, lower system complexity, and lower required mirror-cell stiffness could make this a method to consider for future large telescopes. © 2014 Optical Society of America OCIS codes: (220.1000) Aberration compensation; (220.1080) Active or adaptive optics; (350.1260) Astronomical optics; (350.1270) Astronomy and astrophysics; (110.1080) Active or adaptive optics; (110.6770) Telescopes. http://dx.doi.org/10.1364/AO.53.007979
1. Introduction
Active optics, in the sense of being capable of actively altering the mirror figure in order to improve image quality, has been in use ever since it was first applied to the New Technology Telescope (NTT) in 1989 [1] and has revolutionized the design of the subsequent generations of telescopes. Active optics allows for corrections of telescope errors that comprise polishing defects of the mirrors in the form of low-order aberrations, misalignments, as well as deformations induced by gravity and temperature. These corrections remove all errors, except for atmospheric variations, and allow for seeing-limited observations. For a review of active optics applied to 1559-128X/14/337979-06$15.00/0 © 2014 Optical Society of America
telescopes refer to [2]. An important consequence of the implementation of active optics is the relaxation in stiffness requirements that enabled considerable weight reductions of primary mirrors and telescope mechanical structures in general, making the construction of a generation of large telescopes feasible. Although active optics is now a standard in modern telescopes, there are only a few types of support systems which are unique to each telescope. Among these types, we can count the motorized counterweights and spring-loaded levers, originally used in the NTT, to more sophisticated and generally large actuators, that include pneumatic, hydraulic, electromechanic, electromagnetic and hybrid embodiments, and that range from push-only, push–pull, axial-plus-lateral and axial-only support systems. Examples of telescopes using motorized, springloaded levers are the NTT, TNG [3] and VST [4]. 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
7979
Telescopes basing their active systems on pneumatic force actuators are, for example, the lightweighted honeycomb-construction mirrors such as the Magellan telescopes [5], LBT [6], the MMT [7], and future telescope designs [8]. Among segmented mirror telescopes, a warping harness is used to correct the mirror figure of individual segments. Although in the Keck telescopes the figure control for each segment is passive [9], in the case of the GTC [10], this has been converted to active. However, it has to be noted that the total mirror figure in segmented telescopes is achieved by means of relative position control between segments. The VLT telescope bases its support system on a combination of passive hydraulic and spring-loaded electromechanical actuators [11]. The Subaru active support system consists of a load-cell controlled spring for axial support and a counterweighted fulcrum lever for lateral support [12]. An example of a hybrid suspension system that incorporates passive hydraulic cylinders and active pneumatic actuators that are embedded in a positive-pressure, sealed mirror cell that supports most of the mirror weight, is the Gemini telescope [13]. Some of these actuators are in free contact with the mirror, while others are glued or inserted into the mirror in order to be able to exert pull-forces. The area of contact of most of these actuators is usually very small and can generate actuator print-through. A simpler type of support system consists of controlled-pressure airbags as the force actuators. These are used in, for example, [4,14], and [15]. These systems are much simpler, smaller, more lightweight, and have a much lower profile than the above mentioned. They, however, have the disadvantage of being relatively low-stiffness systems and are not able to provide pull forces or lateral mirror support, although some of these disadvantages are shared with some of the systems just described. For push-only mirror supports, a means of providing an increased pull force needs to be implemented for the case where the axial mirror weight at the largest zenithal angle in the telescope’s operating range is insufficient to allow for “negative” primary mirror shape corrections. This paper presents a concept that adds pullcapability to a push-only airbag-based actuator support by means of a common vacuum. 2. Vacuum-Airbag System Concept
In the case of a push-only active system, gravitational pull is the only means to counteract the actuators. The effectiveness of a desired deformation correction is limited by the zenithal angle Z. That is, the pressure that a given actuator i must bear is given by: Pib Pw cosZ Pid ;
(1)
where Pib is the actuator pressure, Pw is the pressure due to the mirror weight assuming, for simplicity, that it is common to all actuators, and Pid is the 7980
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pressure needed to produce the desired deformation at a particular position. This pressure can be either negative or positive, but the resultant needs to remain positive for all zenithal angles. This clearly limits the overall performance of the system. We propose to generate a common pull-force, Pv A, induced by a homogeneous partial vacuum that goes as 1 − cosZ, applied between the mirror cell and the back of the primary mirror (M1, with area A), in order for the airbags to feel a constant “mirror weight” that is independent of Z: Pib Pw cosZ Pid − Pv 1 − cosZ Pw Pid ; (2) when Pv −Pw . Figure 1 shows this concept in a graphical way. A set of actuators are shown, that are capable of providing the required range of force correction at the zenith. However, as the telescope points away from the zenith, gravity is not enough to provide the required pull force for a given actuator [Pib < 0, in Eq. (1)], resulting in an incomplete correction. Note the shaded area in the figure that goes below the zero-level floor (Pb 0). This is corrected in the form of a common pull force by increasing the vacuum in the mirror cell as 1 − cosZ. This increments the effective weight of the mirror on each actuator by the same factor and in turn raises the average mirror weight, so that the force balance the system had at the zenith is recovered. Prior to the experiment, this idea was thoroughly simulated and a finite element model (FEA) of the 2.12 m SPM telescope mirror, together with its associated suspension was developed. This model aided in proving the concept and allowed us to make sure that the reflecting surface could be optimally corrected with these additional forces applied to the back of the mirror (Fig. 2). We ran a FEA analysis using ALGOR software, simulating an 18-actuator active system using 30 cm diameter airbags, actuating over a 2 m, 26 cm thick Cervit hyperbolic F/2.25 mirror. This model maintained the active system’s original actuator spatial distribution, which is not entirely even. Variations among airbags of up to 10% are thus present in both, separation and weight carried (Fig. 2). In this case, Eq. (2) is not entirely valid, since Pw must be replaced by Piw. Here the force balance equation must include the sum of the pressures of all actuators. In this case, Pv has to be equal to minus the total mirror weight divided by its total area, in order for the cosZ terms to cancel out. The final effect is still the equivalent of the telescope always pointing at the zenith. In this numerical experiment, to test an extreme case, the mirror weight was doubled at the zenith. This represents the worst-case scenario. It can be appreciated from the figure that the back of the mirror is deformed by approximately 120 nm peak-to-valley (P–V), which is attenuated down to an actuator printthrough of 27 nm P–V at the reflecting surface
Fig. 1. Common-pull concept. This figure shows actuator pressures for two different zenithal angles. The upper graph is for the telescope pointing at the zenith. Note that pressure corrections are in range. The lower graph shows actuator pressures at a higher zenithal angle. For some actuators, mirror weight is insufficient to effect the correction.
Fig. 2. Numerical experiment that shows the deformation of the back of the 26 cm thick Cervit mirror due to positive push forces and an induced common pull force that effectively duplicates the mirror weight. This was simulated in order to test mirror integrity.
(Fig. 3). The stresses induced in this test are 200 times smaller than the material’s breaking strength. These deformations and stresses are mirrorthickness and actuator-diameter dependent and have to be taken into account in each particular design. 3. Experimental Demonstration A.
Implementation of the Concept in the 2.1 m OAN SPM
To test this concept, we modified the existing active support system of the 2.1 m telescope at the Observatorio Astronómico Nacional, San Pedro Mártir. This telescope consists of a 2.1 m diameter, 26 cm thick, 2 ton Cervit M1, which at its time (1970s) was considered thin. It has a suite of three interchangeable secondary mirrors (F/7.5, F/13.5 and F/30). The original M1 passive suspension was reconverted to active in 1995 [14]. The lateral passive suspension system
Fig. 3. Effect of the actuators supporting the equivalent of a doubled mirror weight. Deformations are 27 nm P–V.
has not been modified and consists of a Hg-belt around the periphery of the mirror. The lateral component of the mirror weight is supported by a buoyancy force that is applied at the mirror’s center of mass by means of this Mercury belt. This axial active suspension system consists of 18 flat airbags, distributed along two rings in the mirror cell that act as force actuators. The original active system velocity is low due to the regulator–restrictor combination used to inflate the airbags, which limits the telesscope’s “jog” speed. Three hard points, equipped with load cells, define the position of the mirror. The 81 g airbags are 30 cm in diameter and inflate to approximately 3 mL thickness. They are fabricated from Nylon Cordura reinforced polyurethane laminate material, which is durable, very thin, nonelastic, and has a texturized surface. The mirror weight is 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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supported by the active system such that the pressure on each actuator or hardpoint is evenly distributed. The average pressure in each airbag is approximately 1.8 pounds-per-square-inch (psi) (0.127 kg∕cm2 ), supporting 106 kg of the total mirror weight. The hard points (10 cm in diameter) carry only 2% of the mirror weight due to their relatively smaller area. Given the M1 stiffness, this system is only capable of correcting astigmatism and other low-order aberrations, which represent the main optical figure errors. Corrections are secondary-mirror dependent. However, being a push-only system, the possible corrections are limited by the zenithal angle, which is different for each secondary mirror. For two of the secondary mirrors, the original correction range is adequate, whereas for the mid-infrared F/30, the astigmatism amounts to 2.5 μm, which limits corrections to only 60 deg Z. When the telescope is pointing at the zenith, the actuators push against the mirror’s weight. As the telescope is inclined toward other positions, the axial component of the weight decreases, as does the effectiveness of a push-only system. We recently air-tightened the existing mirror cell so that, together with M1, a confined 40 l volume that encloses the airbags, could be defined. A vacuum is then generated in this volume which pulls the back of the mirror against the mirror cell, sandwiching the airbags. This vacuum acts as a common pull force against the push forces of the individual airbags (Fig. 4). Vacuum is achieved by means of a three cubic feet per minute, two-stage pump which in turn is connected to a vacuum reservoir that acts as a pneumatic buffer to handle peak demands. It is then fed to the pull-end of a set of electro-valves that regulate
the pressure in this volume. This allows for a precise pressure control in the range of −1 to 0 psi (atmospheric pressure), which can generate up to 2 tons of additional mirror weight. These electro-valves were chosen to compensate for leaks and to adequately handle the enclosed volume. The electrovalves are set up in a push–pull configuration, biased to 11 psi pressure supplies, and are controlled by a microcontroller working in a pulse-width modulation (PWM) mode. The minimum pulse duration is set to 4 ms, corresponding to a 2 mL volume. This allows for pressure corrections better than 1∕1000. The maximum flow rate is determined by the restrictor formed when either valve is left fully open. This corresponds to approximately 14 l/s, which is faster than the telescope’s pointing speed. The control cycle time was adjusted to 100 ms, which is fast enough to handle the telescope’s 1 deg/s pointing movements. As a bonus, the airbags are no longer responsible for the Z-angle correction, which is now managed by the common pull-force in a faster way, increasing overall system performance. Additionally, the mirror cell volume acts as an efficient pulse dampener. In general, the overall system efficiency is high in terms of air consumption, since air is required only when the telescope is moving. When the telescope is pointing at the zenith, the vacuum pressure is kept to a minimum, such that the pressure in the airbags carries the mirror’s weight and exerts the correcting deformations. As the telescope points away from the zenith, the vacuum control system senses a decrease in mirror weight through the load cells and increases vacuum pressure to maintain a constant weight on the load cells. This is done by means of a proportional-integral-derivative (PID) control system that acts inside a defined error interval. If the
Fig. 4. Block diagram of the modified active cell. The right-hand side of the diagram represents the original active system. The left-hand side shows the addition of a common pull force by a controlled vacuum, as described in the text. 7982
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Fig. 5. Radial intensity profiles of stars observed close to the zenith with the original nonvacuum active system (left) and the new, common-vacuum pull implementation (right). Intensity is given in counts.
error exceeds a threshold value, full open-valve correction is applied. The original active control system is tricked to believe that the telescope keeps pointing at the zenith and maintains the mirror deformation pressures accordingly. The mirror rests on the airbags, and their texture allows for free air circulation between them and the mirror back, allowing for the vacuum to act over the entire M1 area. This combination between controlled vacuum and positivepressure airbag correction constitutes an effective push–pull active system. B.
Experimental Results
Experiments were designed to prove that seeinglimited image quality can be maintained with the new system and to show that large mirror deformations can be achieved and kept constant at large zenithal angles. We tested this system over two observing nights that were available during a maintenance week. Only the F/7.5 configuration was available at this time. The first night the overall system performance was checked, and a comparison between the original active system and the new push–pull implementation was made by observing point sources at different zenithal angles. Figure 5 shows typical radial profiles for two stars with the original system (left) and the new implementation (right). In both cases, the full width at half-maximum (FWHM) is around 1.0 0.1 arc-seconds, which corresponds to the night’s seeing value; although images down to 0.8 arcsec were observed that night. This proves that the new implementation does not negatively affect the image quality. As explained above, there are certain telescope configurations where large deformations are required to correct the image quality, which is not possible for high Z values, given that the original system is push-only. To test the ability of the new system to solve this issue, we performed an experiment in which an exaggerated value of astigmatism (3.5 μm, much larger than the intrinsic mirror errors) was induced onto the primary mirror, while observing at different Z-angles. This test is advantageous in that deformations are
easily measured, regardless of seeing variations, and because astigmatism is the lowest-energy, mirror-bending Zernike term. Astigmatism was subsequently measured through the ellipticity of slightly out-of-focus images, as described in [16]. The result can be appreciated in Fig. 6. The blue crosses represent individual measurements with the original push-only system, while the red dots show similar measurements using the new vacuum-induced pull. It is noted that, as the Z-angle increases, the measured astigmatism decreases, implying that the original system cannot maintain the desired shape of the primary mirror, whereas, in the case of the new implementation, the red dots indicate a constant shape within the measurement errors. Least square fits for both of these cases have been included to guide the eye. Having demonstrated the effectiveness of this concept, it is expected that an increase in dynamic range of the actuators is also achievable, since a vacuum much larger than the mirror weight may allow
Fig. 6. Measured astigmatism as a function of zenithal angle. Blue crosses show the behavior of the original nonvacuum active system, while the red dots indicate the new common vacuum-pull implementation. 20 November 2014 / Vol. 53, No. 33 / APPLIED OPTICS
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for a larger negative excursion of the actuators. With this increase in dynamic range, the area of the airbags could be reduced, in order to increase their number for higher-order corrections. As mentioned in Introduction, the low stiffness of an airbag-based system may also be of concern. In the case of the 2.12 m telescope, the actuator’s width-to-area ratio is approximately 3 × 10−4 cm−1, resulting in a stiffness that is about two orders of magnitude lower than that of a typical hydraulic actuator. Nevertheless, for this particular telescope, this is not a problem, since its first eigenfrequency is high enough (>100 Hz) to resist the wind-induced vibrations. However, for a case where stiffness is problematic, the use of smaller or compartmentalized actuators that are filled with a noncompressible liquid, instead of air, could increase the stiffness for higher resistance to wind buffeting. These ideas will be further investigated in the future. 4. Conclusions
The concept of an active mirror cell with multiplepush airbag actuators and a common pull-force, implemented by means of a vacuum between M1 and its mirror-cell, has been proposed and demonstrated through the above-described experiment. The modifications necessary to test this idea were quite easy to implement, increased the overall system response of our existing active system, and several advantages have been identified: • The actuators are not attached or glued to the back of the mirror, so no lateral deformations and stresses are present. • Air-bag area is relatively large. This reduces the number of actuators necessary in order to minimize print-through and mirror sag. • There is a considerable weight reduction, since actuators are essentially weightless. • The mirror cell need not be stiff, since the position defining supports carry only a fraction of the mirror weight. • In the particular case of the 2.12 m telescope, this modification could increase system response velocity by a factor of approximately 3. These results were satisfactory and could represent a boost in performance for our 2.12 m telescope. We have proposed that these modifications be made permanent. This experiment demonstrated that individual push–pull actuators are not necessary; a common pull can be sufficient. This could reduce overall system complexity and cost for a future generation of large, membrane-based telescopes, where the number of actuators could be in the thousands. We are preparing experiments to demonstrate this concept, which will be published shortly. This work was made possible due to the invaluable help offered by Eduardo López, Fernando Quiroz,
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Joel Herrera, Gerardo Guisa, Carolina Durán and Augusto Sarabia, and the personnel of the Observatorio Astronómico Nacional to set up this experiment. We also thank Leonel Gutiérrez and Michael Richer for granting us two extra observing nights. We thank the reviewers for valuable feedback. The project was funded by a grant awarded by Instituto de Astronoma, UNAM and partly by grant IT-100512 PAPIIT-UNAM. The data used for this paper were based upon observations acquired at the Observatorio Astronómico Nacional in the Sierra San Pedro Mártir (OAN-SPM), Baja California, México. References 1. R. Wilson, “The history and development of the ESO active optics system,” Messenger 113, 2–9 (2003). 2. L. Noethe, “Active optics in modern, large optical telescopes,” Prog. Opt. 43, 1–36 (2002). 3. F. Bortoletto, D. Fantinel, R. Ragazzoni, C. Bonoli, and M. D. Alessandro, “Active optics handling inside Galileo telescope,” Proc. SPIE 2199, 212–222 (1994). 4. P. Schipani, S. D’Orsi, L. Ferragina, D. Fierro, L. Marty, C. Molfese, and F. Perrotta, “Active optics primary mirror support system for the 2.6 m VST telescope,” Appl. Opt. 49, 1234–1241 (2010). 5. P. L. Schechter, G. Burley, C. Hull, M. Johns, B. Martin, S. Schaller, S. A. Shectman, and S. C. West, “Active optics on the Baade 6.5 m (Magellan I) telescope,” Proc. SPIE 4837, 619–627 (2003). 6. H. M. Martin, B. Cuerden, L. R. Dettmann, and J. M. Hill, “Active optics and force optimization for the first 8.4 m LBT mirror,” Proc. SPIE 5489, 826–837 (2004). 7. H. M. Martin, S. P. Callahan, B. Cuerden, W. B. Davison, S. T. DeRigne, L. R. Dettmann, G. Parodi, T. J. Trebisky, S. C. West, and J. T. Williams, “Active supports and force optimization for the MMT primary mirror,” Proc. SPIE 3352, 412–423 (1998). 8. R. A. Bernstein, P. J. McCarthy, K. Raybould, B. C. Bigelow, A. H. Bouchez, J. M. Filgueira, G. Jacoby, M. Johns, D. Sawyer, S. Shectman, and M. Sheehan, “Overview and status of the Giant Magellan Telescope project,” Proc. SPIE 9145, 91451C (2014). 9. R. C. Jared, A. A. Arthur, S. Andreae, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Liacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, and C. Witebsky, “The W. M. Keck telescope segmented primary mirror active control system,” Proc. SPIE 1236, 996–1008 (1990). 10. B. Lefort and J. Castro, “The GTC primary mirror control system,” Proc. SPIE 7019, 70190I (2008). 11. S. Stanghellini, P. Legrand, A. Baty, and T. Hovsepian, “Design and construction of the VLT primary mirror cell: support of the large, thin primary mirror,” Proc. SPIE 2871, 314–325 (1997). 12. M. Iye and K. Kodaira, “Primary mirror support system for the SUBARU telescope,” Proc. SPIE 2199, 762–772 (1994). 13. L. Stepp, E. Huang, and M. Cho, “Gemini primary mirror support system,” Proc. SPIE 2199, 223–238 (1994). 14. L. Salas, L. Gutirrez, M. H. Pedrayes, J. Valdez, C. Carrasco, M. Carrillo, B. Orozco, B. García, E. Luna, E. Ruiz, S. Cuevas, A. Iriarte, A. Cordero, O. Harris, F. Quiroz, E. Sohn, and L. A. Martinez, “Active primary mirror support for the 2.1-m telescope at the San Pedro Martir Observatory,” Appl. Opt. 36, 3708–3716 (1997). 15. M. K. Cho, R. S. Price, and Il. K. Moon, “Optimization of the ATST primary mirror support system,” Proc. SPIE 6273, 62731E (2006). 16. E. Luna, L. Salas, L. Gutirrez, and J. M. Nuñez, “Geometric method to measure astigmatism aberration at astronomical telescopes,” Appl. Opt. 46, 3439–3443 (2007).
