Abstract:
This invention is for a flexible telescope mirror. A mirrored film is stretched across a frame, and deformed into a rough parabola using a partial vacuum. The film is then deformed into a more perfect parabola using electric fields. In some embodiments, a feedback system based on a laser projector and a camera is used to fine tune the resulting parabola for optical performance. The invention allows the creation of large telescope mirrors for a substantially lower price than conventional ground glass mirrors, and allows the creation of substantially lighter mirrors, suitable for space-based applications.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority benefit, under 35 U.S.C. §119(e), of U.S. Provisional Patent Application 61/672,289, filed Jul. 17, 2012 by Rachel Andreasen and titled “Flexible telescope mirror,” which is incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to the field of telescopes, and more specifically to high-quality adaptive and adjustable telescopes which may be built relatively inexpensively, for use by amateur astronomers. 
     BACKGROUND OF THE INVENTION 
     While traditional ground-glass telescope mirrors offer very-high-quality imaging, they are very expensive and difficult to make. This invention promises to reduce the price of a one-meter primary mirror, currently costing on the order of $100,000, to under $1,000. It can also reduce or eliminate optical aberrations due to creep, flex, or thermal expansion and contraction. 
     U.S. Pat. No. 6,679,611, which issued on 20 Jan. 2004 to Robert J. Howard and is titled “Adaptive, Aluminized Mylar Mirror,” is incorporated herein by reference. Howard describes an infrared beam directed to the surface of a Mylar mirror, and the mirror reflects that beam. The reflected beam is detected, and data gleaned from the reflected beam is used to determine whether the optics of the mirror must be adjusted. The optics of the mirror are adjusted by varying voltage applied to electrostatic actuators on the frame of the mirror, or varying the pressure in chambers formed by the mirror frame and mirror surface. 
     U.S. Pat. No. 6,754,006 entitled “Hybrid metallic-dielectric grating” issued Jun. 22, 2004 to Barton et al. and is incorporated herein by reference. This patent describes a diffraction grating having a metallic base layer and layers of dielectric materials of varying refractive index, where a bottom interface of the layers is adherent to the metallic base layer. The dielectric layers are periodically spaced on top of the metallic base layer, leaving the metallic base layer exposed in regions. This grating allows for the polarization-insensitive reflective properties of the base metallic layer to operate in conjunction with the polarization sensitive diffraction properties of the multilayer grating structure to provide near 100% diffraction efficiency over a reasonable wavelength bandwidth, independent of the polarization of the incident beam. 
     U.S. Pat. No. 5,907,436 entitled “Multilayer dielectric diffraction gratings” issued May 25, 1999 to Perry et al., and is incorporated herein by reference. This patent describes the design and fabrication of dielectric grating structures with high diffraction efficiency. The gratings have a multilayer structure of alternating index dielectric materials, with a grating structure on top of the multilayer, and obtain a diffraction grating of adjustable efficiency, and variable optical bandwidth. 
     Other background to the present invention is described in a book chapter titled “Experiments with Pneumatically-Formed Metalized Polyester Mirrors,” by Bruce D. Holenstein, Richard J. Mitchell, Dylan R. Holenstein, Kevin A. Iott and Robert H. Koch, that appears in Genet, Johnson, &amp; Wallen, Eds. (2010), “The Alt-Az Initiative: Telescope, Mirror, &amp; Instrument Developments.” 
     The concept of a flexible mirror is not new. A 1988 technical-report publication by Waddell, titled “Development of a stretchable concave imaging membrane mirror of variable focus,” describes a membrane mirror which is shaped by differences in air pressure. European Patent Application Publication EP 0252034 A2 of Ugo, published 7 Jan. 1988 and titled “Electronic corrector of curvature defects on image, for telescopes provided with large diameter light weight catoptric parts, to be used in orbit as well,” is incorporated by reference. Ugo describes projecting a laser onto a telescope-mirror surface to obtain actual curvature characteristics of a telescope mirror, comparing the actual telescope-mirror surface characteristics against an ideal model, and calculating discrepancies between the two, and subsequently using the data for correcting telescope images. 
     What is needed, and what the present invention provides, is a refined control system for a flexible mirror to achieve greater optical acuity. 
     SUMMARY OF THE INVENTION 
     The present invention provides a flexible telescope mirror. In some embodiments, a thin flexible metalized plastic film is stretched over a frame, then deformed into a parabola through the application of air pressure and electric fields. This allows for the creation of a primary telescope mirror significantly cheaper than traditional ground-glass mirrors. With projected costs well under $1,000 for a one-meter-diameter telescope, even elementary schools could afford to perform astronomical observations at near-professional levels. 
     In some embodiments, a peristaltic pump is used to create the fluid pressure differential which deforms the thin flexible metalized plastic film. This allows for precise and continuous control of the pressure. 
     In some embodiments, for the electrostatic tuning of the mirror, electrodes are first constructed as a set of conventional printed circuit boards. These circuit boards are then connected together to form a three-dimensional (3-D) geometric dome, roughly conforming to the parabolic mirror. This design does not require precision placement of electrodes, and reduces the amount of charge required for precise tuning of the mirror. 
     In some embodiments, to calibrate the mirror, a laser projects a grid onto the mirror, which is captured by the same camera used to view the magnified images of the subject. This eliminates the need for a separate, complex camera system to test for aberrations. 
     This invention differs from the prior art in four main ways:
         First, some embodiments of this invention use a precision peristaltic pump, or other pump, to create the pressure differential across the plastic film, instead of solenoid valves.   Second, some embodiments of this invention use a fixed laser-projection pattern for calibration instead of a scanning laser.   Third, some embodiments of this invention use a conventional digital camera for both calibration and telescope viewing, instead of a specialized dedicated calibration camera.   Fourth, some embodiments of this invention use a 3-D geometric circuit board for the electrode array.       

     In some embodiments, the present invention provides an apparatus which includes: a frame; a mirrored, electrically conductive film having a first face which is highly reflective and a second face facing the frame, wherein the mirrored, electrically conductive film is stretched across the frame in a manner which creates an enclosed chamber against the second face of the mirrored, electrically conductive film; a pump operably coupled to the enclosed chamber facing the second face of the mirrored, electrically conductive film; an electrode array located in the enclosed chamber facing the second face of the mirrored film; a camera facing the first face of the mirrored, electrically conductive film; and a computer-control system operably coupled to receive signals from the camera, and configured to send control signals to the pump and to the electrode array, in order to reshape the mirrored, electrically conductive film into an optically suitable shape. 
     In some embodiments, the present invention provides: providing a frame; providing a mirrored, electrically conductive film having a first face which is highly reflective and a second face facing the frame; stretching the mirrored, electrically conductive film across the frame in a manner which creates an enclosed chamber against the second face of the mirrored, electrically conductive film; pumping a fluid from the enclosed chamber facing the second face of the mirrored, electrically conductive film; applying an electrostatic force to one or more sub-areas of the second face of the mirrored film; acquiring an image of the first face of the mirrored, electrically conductive film; and calculating correction factors based on the acquired image; and sending control signals to control the pumping and to control the applying of electrostatic force to the one or more sub-areas of the second face of the mirrored film, in order to reshape the mirrored, electrically conductive film into an optically suitable shape. 
     In some embodiments, the present invention provides: a frame; a mirrored, electrically conductive film having a first face which is highly reflective and a second face facing the frame; means for stretching the mirrored, electrically conductive film across the frame in a manner which creates an enclosed chamber against the second face of the mirrored, electrically conductive film; means for pumping a fluid from the enclosed chamber facing the second face of the mirrored, electrically conductive film; means for applying an electrostatic force to one or more sub-areas of the second face of the mirrored film; means for acquiring an image of the first face of the mirrored, electrically conductive film; and means for calculating correction factors based on the acquired image; and means for sending control signals to control the pumping and to control the applying of electrostatic force to the one or more sub-areas of the second face of the mirrored film, in order to reshape the mirrored, electrically conductive film into an optically suitable shape. 
     Benefits 
     The benefits of this invention are primarily economic. It is designed to be cheap and easy to manufacture, assemble, and maintain. Complex glass-grinding machinery is not required, allowing the mirror to be produced with common machining equipment. The mirrored film does have a shorter estimated lifespan than glass, but it can be replaced within minutes, and at a relatively low cost. 
     The comparatively low mass and low cost of the mirror facilitate easy astronomical observations in the field, or locations without a modern infrastructure. The active tuning system does require electrical power to run, but this can be provided by a simple battery. 
     Unlike glass mirrors, a flexible film is not limited to a single focal length. The fluid pressure and electric fields can be adjusted to shift the focus from infinity, allowing the telescope to be used for terrestrial surveying. In some embodiments, the invention is scaled up for use in space-based telescopes, where the low mass provides the greatest advantage. 
     The low cost of this telescope mirror opens the door to new astronomers. Large-diameter telescopes, which currently are well out of the price range for all but large institutions, would become widely available to the amateur community. The amateur community is integral—perhaps even vital—to astronomical discovery. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A, 1B, 1C, and 1D  show different aspects of an embodiment of the telescope system  100  of the present invention. 
         FIG. 2  is an isolated view of an embodiment of the telescope mirror  220 . 
         FIGS. 3A, 3B, and 3C  show different embodiments of the electrode array. 
         FIG. 4  shows an embodiment using a secondary mirror, and an embodiment using an alternative laser calibration system. 
         FIG. 5  is a schematic of an embodiment using pressure reservoirs and valves. 
         FIG. 6  is a view of an embodiment of the electrostatic feedback system. 
         FIG. 7  is a flowchart of an embodiment of the algorithm used to finely regulate the shape of the telescope mirror. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     Although the following detailed description contains many specifics for the purpose of illustration, a person of ordinary skill in the art will appreciate that many variations and alterations to the following details are within the scope of the invention. Very narrow and specific examples are used to illustrate particular embodiments; however, the invention described in the claims is not intended to be limited to only these examples, but rather includes the full scope of the attached claims. Accordingly, the following preferred embodiments of the invention are set forth without any loss of generality to, and without imposing limitations upon the claimed invention. Further, in the following detailed description of the preferred embodiments, reference is made to the accompanying drawings that form a part hereof, and in which are shown by way of illustration specific embodiments in which the invention may be practiced. It is understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. The embodiments shown in the Figures and described here may include features that are not included in all specific embodiments. A particular embodiment may include only a subset of all of the features described, or a particular embodiment may include all of the features described. 
     The leading digit(s) of reference numbers appearing in the Figures generally corresponds to the Figure number in which that component is first introduced, such that the same reference number is used throughout to refer to an identical component which appears in multiple Figures. Signals and connections may be referred to by the same reference number or label, and the actual meaning will be clear from its use in the context of the description. 
       FIGS. 1A, 1B, 1C, and 1D  show different aspects of an embodiment of telescope system  100  of the present invention. As shown in  FIG. 1A , camera  101  is supported by one or more supports  102 . In some embodiments, one support  102  supports camera  101 . In other embodiments, two supports  102  support camera  101 . In yet other embodiments, three, or four, or more supports  102  support camera  101 . In some embodiments, camera  101  and mirrored film  105  may be placed on entirely different, independent structures. As used herein, the terms mirrored film and reflective film are synonymous. In some embodiments, mirrored film  105  includes at least one electrically-conductive layer, which, in combination with electrode array  321 ,  322 , and/or  323  (see  FIG. 3  below) provides an electrostatic film-distortion function. 
     In some embodiments, mirrored film  105  comprises a thin sheet of biaxially-oriented polyethylene terephthalate (also known as Mylar®) which has been coated with a thin layer of metal. In some embodiments, the metal is gold. In some embodiments, the metal is aluminum. In some embodiments, the metal is silver. In some embodiments, the metal is some other suitably optically reflective and electrically conductive metal. Such films are commercially available, and are manufactured through a variety of well-known methods. In some embodiments, mirrored film  105  comprises a thin sheet of biaxially-oriented polyethylene terephthalate which has been coated with a thin layer of other suitably optically reflective and electrically conductive material. In other embodiments, a dielectric mirror having a plurality of pairs of layers of dielectric material, each having a thickness that increases reflectivity of the structure as a whole, such as described in U.S. Pat. No. 5,907,436 entitled “Multilayer dielectric diffraction gratings” issued May 25, 1999 to Perry et al., which is incorporated herein by reference, is used. In some embodiments, a combination of metal and a plurality of dielectric layers is used, such as described in U.S. Pat. No. 6,754,006 entitled “Hybrid metallic-dielectric grating” issued Jun. 22, 2004 to Barton et al., which is incorporated herein by reference. 
     In other embodiments, the mirrored film  105  comprises a thin sheet of polypropylene which has been coated with a thin layer of metal, or other conductive material as described above, and elsewhere in this application. In some embodiments, the mirrored film  105  comprises a thin sheet of polyester. In some embodiments, the mirrored film  105  comprises a thin sheet of polyethylene. In some embodiments, the mirrored film  105  comprises a thin sheet of polyimide. In some embodiments, the mirrored film  105  comprises a thin sheet of polytetrafluoroethylene. In some embodiments, the mirrored film  105  comprises a thin sheet of solid metal without a substrate. In some embodiments, the mirrored film  105  comprises some other suitable material. 
     The mirrored film  105  is stretched taut across a frame  109 , forming a seal. This forms an enclosed chamber  107 . In some embodiments, the opening of frame  109 , to which the mirrored film  105  is attached, or across which the mirrored film  105  is stretched, is in the shape of a circle. In other embodiments, the opening of frame  109  may be in another shape. In some embodiments, the mirror film  105  has a thickness less than 0.05 mm. In some embodiments, the mirror film  105  has a thickness of between 0.05 mm and 0.12 mm. In some embodiments, the mirror film  105  has a thickness of between 0.12 mm and 0.30 mm. In some embodiments, the mirror film  105  has a thickness of between 0.30 mm and 1.00 mm. In some embodiments, the mirror film  105  has a thickness of between 1.00 mm and 5.00 mm. In other embodiments, the mirror film  105  has a thickness greater than 5.00 mm, which is suitable to deforming to the optically suitable shape. In some embodiments, the mirror film  105  is such as available from McMaster-Carr based in Elmhurst, Ill. 
     In some embodiments, the opening of frame  109  is a rectangle. In some embodiments, the opening of frame  109  is a hexagon. In some embodiments, the opening of frame  109  is an octagon. In some embodiments, the opening of frame  109  is an oval. In other embodiments, the opening of frame  109  is some other suitable shape. 
     In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.1 and 0.2 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.2 and 0.3 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.3 and 0.4 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.4 and 0.5 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.5 and 0.6 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.6 and 0.7 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.7 and 0.8 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.8 and 0.9 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 0.9 and 1.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 1.0 and 1.25 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 1.25 and 1.5 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 1.5 and 1.75 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 1.75 and 2.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 2.0 and 3.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 3.0 and 4.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 4.0 and 5.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 5.0 and 6.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 6.0 and 10.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 10.0 and 15.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is between 15.0 and 20.0 m. In some embodiments in which frame  109  is in the shape of a circle, the diameter of the circle is greater than 20.0 m. 
     In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 10 and 100 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 100 and 200 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 200 and 400 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 400 and 1,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 1,000 and 5,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 5,000 and 10,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 10,000 and 20,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 20,000 and 50,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 50,000 and 100,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 100,000 and 500,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 500,000 and 1,000,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 1,000,000 and 5,000,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is between 5,000,000 and 10,000,000 cm 2 . In some embodiments in which the opening of frame  109  is non-circular, the area of the opening covered by the mirrored film  105  is greater than 10,000,000 cm 2 . 
     In some embodiments, a peristaltic pump  108  is used to reduce the fluid pressure (such as air pressure) in the enclosed chamber  107 , causing the mirrored film  105  to deform into a rough parabola. In other embodiments, the mirror film  105  is deformed into a rough hyperbola. In other embodiments, the mirror film  105  is deformed into a rough spheroid. In other embodiments, the mirror film  105  is deformed into another optically suitable shape. In other embodiments, other sorts of pumps are used. In some embodiments, fluids other than air used to provide the pressure differential across the mirrored film  105 . In some embodiments, such as certain spaced-based applications, no air or other fluid is used to provide the initial rough-parabolic deformation. 
     In some embodiments, the enclosed chamber  107  is filled with a fluid which is a gas (such as air or one or more other suitable gasses), while in other embodiments, the enclosed chamber  107  is filled with a fluid which is a liquid (such as a dielectric fluid such as deionized non-conductive water, ethylene glycol, an electrically insulating, stable fluorocarbon-based fluid such as Fluorinert® available from 3M Corporation, or the like). 
     In some embodiments, electrode array  106  is used to further deform the mirrored, electrically conductive film  105  into a substantially optically perfect parabola. The mirrored film  105  is connected to one polarity of an electrostatic generator  111 . A selected value (e.g., charge, or voltage) of the same polarity, or of the opposite polarity, of the electrostatic generator  111  is connected to selected ones of the individual electrodes of the electrode array  106 , based on the calculated error of the mirror shape, as described below. (In other words, a particular one of the electrodes is driven by a signal corresponding to that electrode, based on the mirror-shape-measurement calculation derived from the laser pattern projector  113  for that electrode.) Electrical circuits of a computer-control system  112 , suitably programmed, control the voltages of the electrodes (such as elements  321 ,  322 , or  323  in  FIG. 3A, 3B , or  3 C, and elements  623  in  FIG. 6 ) in the electrode array  106 . The electric potential between the individual points on the electrode array  106  and the mirrored film  105  create an electrostatic attractive force. This force further deforms the mirrored film  105 . If the voltages of the electrodes are suitably controlled, the mirrored film  105  will be deformed, in some embodiments into an optically suitable parabola. In other embodiments, the mirrored film  105  will be deformed into an optically suitable hyperbola. In other embodiments, the mirrored film  105  will be deformed into an optically suitable spheroid. In other embodiments, the mirrored film  105  will be deformed into another optically suitable shape. In some embodiments, computer-control system  112  controls some other, or all other, of the elements of telescope system  100 . In some embodiments, the computer-control system  112  is connected to the other elements of the telescope with electrical wires. In some embodiments, the computer-control system  112  is connected to the other elements of the telescope with fibre-optic cables. In some embodiments, the computer-control system  112  is connected to the other elements of the telescope wirelessly. In some embodiments, the computer-control system  112  is connected to the other elements of the telescope with a combination of the means previously described. 
     In some embodiments, some of the electrodes may be driven by the same polarity as that of the mirrored film  105 , in order to generate a variable amount of repulsive electrostatic force, while others of the electrodes may be driven by opposite polarity as that of the mirrored film  105 , in order to generate an attractive electrostatic force. The amount of electrostatic force can be varied by applying different magnitudes of voltage. 
     In other embodiments (not shown), electrostatic generator  111  generates an electric potential which is routed to computer control system  112 , which then sends individually controlled voltages to the individual electrodes (such as electrodes  323  shown in  FIG. 3C ) of the electrode array  106 . In some embodiments (not shown), the electrostatic generator  111  is not contained within the enclosed chamber  107 . 
     In other embodiments, the electrode array  106  comprises conductors in the form of concentric rings placed on a flat nonconductive substrate. Each ring is individually controlled by a suitable algorithm executed by the computer-control system  112  (control system  112  executes all algorithms described in this specification) to control the voltage of the rings, causing the mirrored, electrically conductive film  105  to deform into an optically suitable shape, as described elsewhere in this application. 
     In other embodiments, the electrode array  106  comprises a set of printed-circuit boards which have been arranged into a three-dimensional polygon. Each circuit board has numerous individual electrodes on its surface, each connected to the electrostatic generator  111  which is controlled by the computer-control system  112 . 
     Referring to  FIG. 1A , in some embodiments a pressure sensor  114  is used to measure the pressure differential between the enclosed chamber  107  and the surrounding environment. The measurement is used by the computer control system  112 , executing instructions (such as a suitable algorithm), to better control the pump or valves. 
     In some embodiments, such as shown in  FIG. 1C , laser projector  113  projects a known pattern onto the mirrored, electrically conductive film  105 . This laser light reflects to the camera  101 , which sends a signal to the computer control system  112 . A suitable algorithm executed in the computer control system  112  uses the image from the camera  101  in order to vary, via electrostatic generator  111 , the voltages of individual electrodes of the electrode array  106 , in a manner which corrects defects in the shape of the mirrored film  105 , to obtain, in some embodiments, a more perfect parabola. In other embodiments, the suitable algorithm causes mirrored film  105  to be shaped into a more perfect hyperbola. In other embodiments, the suitable algorithm causes mirrored film  105  to be shaped into a more perfect spheroid. In other embodiments, the suitable algorithm causes mirrored film  105  to be shaped into a different more perfect optically suitable shape. 
     As shown in  FIG. 1B , the telescope mirror  120  is aimed at a subject of observation  110  to be viewed. Light strikes the mirrored film  105 , and is reflected back to the camera  101 . In some embodiments. In some embodiments, an eyepiece is used instead of a camera  101 . 
     In some embodiments, the pump  108  is used to create a pressure differential between enclosed chamber  107  and the surrounding environment. In some embodiments, the pump  108  is controlled by a stepper motor, servo-motor, or other mechanism. In other embodiments, a different positive displacement pump may be used to create the pressure differential. In some embodiments, the pump  108  is operably coupled to the enclosed chamber  107  through a flexible hose. 
       FIG. 1D  is an isometric view of the telescope  100 . Shown are elements: camera  101 , supports  102 , mirrored film  105 , electrode array  106 , and enclosed chamber  107 . Other elements of the telescope  100  are not shown. 
       FIG. 2  is an isolated view of an embodiment of the telescope mirror  220 . Shown are elements mirrored film  205 , enclosed chamber  207 , pump  208 , pressure sensor  214 , and electrode array  206 . Other elements of the telescope mirror  220  are not shown. 
       FIGS. 3A, 3B, and 3C  show different embodiments of the electrode array, which is used to control the shape of the telescope&#39;s mirrored film (such as described elsewhere in this application as element  105  in  FIG. 1 ).  FIG. 3A  shows an embodiment  300  in which concentric conductive rings are utilized as the electrode array. In some embodiments, these concentric conductive rings  321  comprise metal etched on a printed-circuit board. In some embodiments, these concentric conductive rings  321  comprise conductive rings attached to a suitable nonconductive substrate. In some embodiments, the suitable nonconductive substrate is flat. In some embodiments, the suitable nonconductive substrate is not flat. In some such embodiments, the suitable nonconductive substrate roughly conforms to the desired final shape of the deformed mirrored film  105 . In some embodiments, there are between 1 and 10 concentric conductive rings  321 . In some embodiments, there are between 10 and 20 concentric conductive rings  321 . In some embodiments, there are between 20 and 40 concentric conductive rings  321 . In some embodiments, there are between 40 and 80 concentric conductive rings  321 . In some embodiments, there are between 80 and 150 concentric conductive ring  321 . In some embodiments, there are between 150 and 300 concentric conductive rings  321 . In some embodiments, there are between 300 and 500 concentric conductive rings  321 . In some embodiments, there are between 500 and 1,000 concentric conductive rings  321 . In some embodiments, there are more than 1,000 concentric conductive rings  321 . The individual concentric conductive rings  321  are controlled by a suitable algorithm, executed in a computer control system (such as shown elsewhere in this application as element  112  in  FIG. 1 ), controlling the voltage of each ring. The electrostatic attraction causes the mirrored film (such as shown elsewhere in this application as element  105  in  FIG. 1 ) to deform into an optically suitable shape, as described elsewhere in this application. 
       FIG. 3B  shows an embodiment  310  in which a precision gradient of resistive medium is utilized as electrode array  306 ′. The electrode array  306 ′ comprises a single conductor in the form of a precision gradient of resistive medium  322  placed on a suitable substrate. In some embodiments, the substrate is electrically conductive. In some embodiments, the substrate is not electrically conductive. In some embodiments, the suitable nonconductive substrate is flat. In some embodiments, the suitable nonconductive substrate is not flat. In some such embodiments, the suitable nonconductive substrate roughly conforms to the desired final shape of the deformed mirrored film  105 . The gradient  322  is controlled by a suitable algorithm, executed in a computer control system (such as shown elsewhere in this application as element  112  in  FIG. 1 ), controlling the voltage of a single input electrode. The measured voltage of individual points on the surface of the precision gradient will vary according to the distance from the centre, and according to the voltage of the single input electrode. The electrostatic attraction causes the mirrored film (such as shown elsewhere in this application as element  105  in  FIG. 1 ) to deform into an optically suitable shape, as described elsewhere in this application. In some embodiments, the resistive medium comprises graphite. In other embodiments, the resistive medium comprises a metal film. In yet other embodiments, the resistive medium comprises a conductive polymer. In some embodiments, the precision gradient of resistive medium  322  is created by a laser which etches the surface of a layer of resistive medium according to predefined pattern. 
       FIG. 3C  shows an embodiment  320  in which discrete electrode points  323  are utilized as electrode array  306 ″. In some embodiments, these discrete electrode points  323  comprise metal etched on a printed circuit board. In some embodiments, these discrete electrode points  323  comprise a conductor attached to a suitable nonconductive substrate. In some embodiments, the suitable nonconductive substrate is flat. In some embodiments, the suitable nonconductive substrate is not flat. In some such embodiments, the suitable nonconductive substrate roughly conforms to the desired final shape of the deformed mirrored film  105 . In some embodiments, there are between 1 and 10 discrete electrode points  323 . In some embodiments, there are between 10 and 20 discrete electrode points  323 . In some embodiments, there are between 20 and 40 discrete electrode points  323 . In some embodiments, there are between 40 and 80 discrete electrode points  323 . In some embodiments, there are between 80 and 150 discrete electrode points  323 . In some embodiments, there are between 150 and 300 discrete electrode points  323 . In some embodiments, there are between 300 and 500 discrete electrode points  323 . In some embodiments, there are between 500 and 1,000 discrete electrode points  323 . In some embodiments, there are more than 1,000 discrete electrode points  323 . The discrete electrode points  323  are controlled by a suitable algorithm, executed in a computer control system (such as shown elsewhere in this application as element  112  in  FIG. 1 ), controlling the voltage of the discrete electrode points  323 . The electrostatic attraction causes the mirrored film (such as shown elsewhere in this application as element  105  in  FIG. 1 ) to deform into an optically suitable shape, as described elsewhere in this application. 
     In some embodiments, the discrete electrode points  323  are arranged in evenly spaced rows and columns. In some embodiments, the discrete electrode points  323  are arranged on a hexagonal grid. In some embodiments, the discrete electrode points  323  are arranged in an uneven distribution, with areas of higher electrode density. In other embodiments, the discrete electrode points  323  are arranged in other suitable patterns. 
     In some embodiments, the closest point on electrode array  106  is located at a distance of less than 1 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance between 1 and 5 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance between 5 and 10 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance between 10 and 20 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance between 20 and 50 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance between 50 and 100 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance between 100 and 200 mm from the mirrored film  105 . In some embodiments, the closest point on electrode array  106  is located at a distance greater than 200 mm from the mirrored film  105 . 
     In some embodiments, the electrodes used in the electrode array  106  comprise an electrically conductive metal. In some such embodiments, the metal is copper. In other such embodiments, the metal is aluminium. In other such embodiments, the metal is gold. In other such embodiments, the metal is silver. In other such embodiments, the metal is steel. In other such embodiments, a suitable conductive metal is used. In some embodiments, the electrodes used in the electrode array  106  comprise carbon. In some embodiments, the electrodes used in the electrode array  106  comprise a conductive polymer. In other embodiments, the electrodes used in the electrode array  106  comprise some other suitable conductive material. 
     In some embodiments, the different electrode array  106  configurations as described elsewhere in this application are used concurrently, or in combination with one another. 
     As shown in  FIG. 4 , in some embodiments there are one or more secondary mirrors  412  altering the light path to the camera  401 . This prevents the camera  401  from blocking incoming light. The secondary mirror  412  may be used in conjunction with other embodiments of the invention. In some embodiments, the secondary mirror  412  is supported by one or more supports  402 . In some embodiments, one support  402  supports secondary mirror  412 . In other embodiments, two supports  402  support secondary mirror  412 . In yet other embodiments, three, or four, or more supports  402  support secondary mirror  412 . In some embodiments, secondary mirror  412  and mirrored film  405  may be placed on entirely different, independent structures. 
     In some embodiments, instead of a laser grid projector projecting a pattern onto the first surface of the mirrored film  405  and being reflected into the camera  401 , a laser  404  projects a point onto the second surface of mirrored film  405 , which is reflected to a photosensor array  402 , such as shown in  FIG. 4 . A suitable algorithm, executed in computer control system  412 , uses the data from the photosensor array  402  to control the pressure differential between the enclosed chamber  407  and the surrounding environment, in order to create a suitable shape as described elsewhere in this application. 
     In the embodiment shown in  FIG. 4 , no electrostatic control system is being used, and the shaping of mirrored film  405  is accomplished entirely with a pressure differential across the mirrored film  405 . In other embodiments, the mirrored film  405  may be further shaped using the electrostatic control system described elsewhere in this application, but not shown in  FIG. 4 . 
     In other embodiments, such as shown in  FIG. 5 , which shows a schematic of the pressure control system, the pressure differential, monitored by pressure sensor  514 , is maintained by a higher-pressure reservoir  516  and a lower-pressure reservoir  517 , each connected to the enclosed chamber  507  with valves  515  controlled by a suitable algorithm executed in the computer control system  512 . A pump  519  creates a pressure differential between the higher- and lower-pressure reservoirs. When the computer control system  512  determines the pressure in enclosed chamber  507 , as measured by pressure sensor  514 , is too low, valve  515  is opened to allow high pressure fluid to pass from the high-pressure reservoir  516  to the enclosed chamber  507 . When the computer control system  512  determines the pressure in enclosed chamber  507 , as measured by pressure sensor  514 , is too high, valve  515 ′ is opened to allow high pressure fluid to pass from the enclosed chamber  507  to the low-pressure reservoir  517 . 
       FIG. 6  is a view of an embodiment of electrostatic feedback system  600 . In some embodiments, a camera  601  is positioned to obtain an image of mirrored film  605 , which is located adjacent an electrode array  606  having a plurality of electrode points  623 . In some embodiments, camera  601  is connected to computer control system  612 , which is connected to electrostatic generator  611 . In some embodiments, electrostatic generator  611  includes a plus “+” output terminal that is connected to mirrored film  605 , and a plurality of minus “−” output terminals each of which is connected to a respective one of the plurality of electrode points  623 . 
     In some embodiments such as shown in  FIG. 7 , an algorithm as depicted in the flowchart is used to finely regulate the shape of the telescope mirror. 
     In some embodiments, instead of projecting a laser grid pattern on the first surface of mirrored film  105 , the reflection of which is captured by camera  101 , light from a laser star guide, such as described in U.S. Patent Application Publication No. US 2012/0224243 of Friedenauer et al., titled “Laser system to generate a laser guide star,” which is incorporated herein by reference, is used. Friedenauer et al. describe a laser system which includes a laser light source which emits electromagnetic radiation, at least one optical amplifier which amplifies the radiation emitted from the laser light source, and a frequency multiplier which converts the amplified radiation by resonant frequency multiplying and/or summation-frequency generating. The laser system has a modulation facility which causes a modulation of the electromagnetic radiation emitted from the laser light source in such a manner that the spectrum encompasses a carrier frequency and at least one sideband, with the frequency multiplier being resonant at the carrier frequency and at the frequency of the at least one sideband. 
     General Method of Operation 
     According to one embodiment of the invention, a film of aluminized biaxially-oriented polyethylene terephthalate, commonly known as Mylar®, is stretched over a circular frame. A vacuum pump is used to reduce the pressure in a sealed chamber behind the mirrored film, which is monitored by a pressure sensor. The difference in air pressure across the film causes it to deform into a concave parabola. 
     In some such embodiments, while very close, this vacuum-formed parabola is not precise enough on its own to form a sharp image of the subject. To calibrate the mirror to a more perfect parabola, a laser is used to project a precise grid onto the mirror. A conventional digital camera detects the lines, and an algorithm measures irregularities in the grid to calculate the optical distortion. Feedback is sent to an array  106  of high-voltage electrodes, which create an electrostatic attraction between the mirror  105  and the array  106 . The differing electric field strength fine-tunes the mirror distortion, correcting it to bring an image into clear focus. Several rounds of calibration may be needed to perfect the parabola. Once complete, the laser is turned off, and the camera is used to view an image. The image is stable for several hours of observation. 
     In some embodiments, the present invention provides an apparatus which includes: a mirrored, electrically conductive film stretched across a frame in a manner which creates a seal and an enclosed chamber beneath the mirrored film; a pump with its input side open to the enclosed chamber beneath the mirrored film; an electrode array located beneath the mirrored film; a camera supported at a distance from the mirrored film; a computer-control system operably coupled to the pump, the electrode array, and the camera, to shape the mirrored film into an optically suitable shape. In some such embodiments, the apparatus is used as a telescope. 
     Some embodiments further include algorithms which, when executed by the computer-control system, use input signals to the computer-control system from the camera, and output signals from the computer-control system to the pump and to the electrode array, to shape the thin mirrored film to an optically suitable shape. 
     Some embodiments further include a laser pattern projector which projects a pattern onto the mirrored, electrically conductive film, the reflection of which is captured by the camera supported at a distance above the mirrored film, which sends signals to the computer-control system, upon which an algorithm is executed which sends signals to appropriate electrodes of the electrode array in a manner which creates an electrostatic attraction to appropriate locations on the thin mirrored film, resulting in the film&#39;s acquiring an optically suitable shape. 
     Some embodiments further include a second laser which reflects light off the mirrored, electrically conductive film and onto a separate photosensor array, which sends signals to the computer-control system, upon which an algorithm is executed which sends signals to appropriate electrodes of the electrode array in a manner which creates an electrostatic attraction to appropriate locations on the thin mirrored film, resulting in the film&#39;s acquiring an optically suitable shape. 
     In some embodiments, the electrode array (e.g., electrode array  106  shown in  FIG. 1A ) comprises flat printed-circuit boards arranged in a 3D geometric shape. In some embodiments, the electrode array comprises a plurality of concentric conductive rings. In some embodiments, the electrode array comprises a plurality of discrete electrode points. In some embodiments, the electrode array comprises a conductive material having a gradient of conductivity. 
     In some embodiments, a first voltage is applied to at least some of the electrodes, wherein the first voltage is opposite in sign to a second voltage applied to the mirrored, electrically conductive film, in order to create an attractive electrostatic force to a selective area of the film. 
     In some embodiments, a third voltage is applied to at least some of the electrodes, wherein the third voltage is equal in sign to a second voltage applied to the mirrored, electrically conductive film, in order to create an repulsive electrostatic force to a selective area of the film. 
     In some embodiments, the present invention provides an apparatus which includes: a frame; a mirrored, electrically conductive film having a first face which is highly reflective and a second face facing the frame, wherein the mirrored, electrically conductive film is stretched across the frame in a manner which creates an enclosed chamber against the second face of the mirrored, electrically conductive film; a pump operably coupled to the enclosed chamber facing the second face of the mirrored, electrically conductive film; an electrode array located in the enclosed chamber facing the second face of the mirrored film; a camera facing the first face of the mirrored, electrically conductive film; and a computer-control system operably coupled receive signals from the camera, and configured to send control signals to the pump and to the electrode array, in order to reshape the mirrored, electrically conductive film into an optically suitable shape. 
     Some embodiments further include a computer-readable medium having instructions stored thereon which, when executed by the computer-control system, perform a method comprising: performing calculations in the computer-control system based on input signals from the camera, and outputting signals from the computer-control system to the pump and to the electrode array, to shape the mirrored, electrically conductive film to an optically suitable shape. 
     Some embodiments further include a first laser system which projects a pattern of light onto the first face of the mirrored, electrically conductive film, the reflection of which is captured by the camera which faces the mirrored, electrically conductive film, wherein the camera sends signals to the computer-control system, wherein the computer-control system calculates correction factors and sends signals to appropriate electrodes of the electrode array in a manner which creates an electrostatic force to one or more appropriate selected locations on the mirrored, electrically conductive film, in order to reshape the film to an optically suitable shape. 
     Some embodiments further include a second laser system configured to projects light toward the second face of the mirrored, electrically conductive film; and a photosensor array configured to receive light of the second laser system reflected from the second face of the film, wherein the photosensor array sends signals to the computer-control system, wherein the computer-control system calculates correction factors based on the signals from the photosensor array, and sends signals to appropriate electrodes of the electrode array in a manner which creates an electrostatic force to one or more appropriate locations on the mirrored, electrically conductive film, in order to reshape the film to an optically suitable shape. 
     In some embodiments, the electrode array is formed from a plurality flat printed-circuit boards arranged in a three-dimensional (3D) geometric shape. In some embodiments, the electrode array is formed from a plurality of concentric conductive rings. In some embodiments, the electrode array is formed from a plurality of discrete electrode points. In some embodiments, the electrode array is formed from a material having a gradient conductivity. 
     Some embodiments further include an electrically non-conductive dielectric liquid filling the enclosed chamber, wherein the pump applies force to the dielectric liquid. 
     In some embodiments, a gas is used in the enclosed chamber against the second face of the film, wherein the pump applies force to the gas. 
     In some embodiments, the present invention provides: providing a frame; providing a mirrored, electrically conductive film having a first face which is highly reflective and a second face facing the frame; stretching the mirrored, electrically conductive film across the frame in a manner which creates an enclosed chamber against the second face of the mirrored, electrically conductive film; pumping a fluid from the enclosed chamber facing the second face of the mirrored, electrically conductive film; applying an electrostatic force to one or more sub-areas of the second face of the mirrored film; acquiring an image of the first face of the mirrored, electrically conductive film; and calculating correction factors based on the acquired image; and sending control signals to control the pumping and to control the applying of electrostatic force to the one or more sub-areas of the second face of the mirrored film, in order to reshape the mirrored, electrically conductive film into an optically suitable shape. 
     Some embodiments further include projecting a first laser light pattern onto the first face of the mirrored, electrically conductive film, and wherein the acquiring of the image of the first face captures a reflection of the first laser light pattern, wherein the calculating of the correction factors is based on the captured reflection from the first face of the mirrored, electrically conductive film. 
     Some embodiments further include projecting a second laser light pattern toward the second face of the mirrored film; and receiving light of the second laser light pattern reflected from the second face of the mirrored, electrically conductive film, wherein the calculating of correction factors correction factors is based at least in part on the received light from the second face of the film. 
     In some embodiments, the applying of the electrostatic force includes applying selected voltages to selected electrodes of an electrode array, and wherein the electrode array is formed from a plurality flat printed circuit boards arranged in a three-dimensional (3D) geometric shape. 
     In some embodiments, the applying of the electrostatic force includes applying selected voltages to selected electrodes of an electrode array, and wherein the electrode array is formed from a plurality of concentric conductive rings. 
     In some embodiments, the applying of the electrostatic force includes applying selected voltages to selected electrodes of an electrode array, and wherein the electrode array is formed from a plurality of discrete electrode points. 
     In some embodiments, the applying of the electrostatic force includes applying selected voltages to selected electrodes of an electrode array, and wherein the electrode array is formed from a material having a gradient conductivity. 
     In some embodiments, the calculating correction factors based on the acquired image includes: determining the position of reflection of n th  laser location; determining whether the position of reflection of n th  laser location is in the correct position in relation to an ideal model; if the determined position of reflection of n th  laser location is not in the correct position, adjusting the electrostatic force applied to n th  laser location, and returning to the step of determining whether the position of reflection of n th  laser location is in the correct position in relation to an ideal model; and if the determined position of reflection of n th  laser location is in the correct position, advancing to a next laser location (a next n th  laser location, where n has been incremented to the next location in the array), and returning to the step of determining whether the position of reflection of said next n th  laser location is in the correct position in relation to an ideal model. 
     In some embodiments, the present invention provides: a frame; a mirrored, electrically conductive film having a first face which is highly reflective and a second face facing the frame; means for stretching the mirrored, electrically conductive film across the frame in a manner which creates an enclosed chamber against the second face of the mirrored, electrically conductive film; means for pumping a fluid from the enclosed chamber facing the second face of the mirrored, electrically conductive film; means for applying an electrostatic force to one or more sub-areas of the second face of the mirrored film; means for acquiring an image of the first face of the mirrored, electrically conductive film; and means for calculating correction factors based on the acquired image; and means for sending control signals to control the pumping and to control the applying of electrostatic force to the one or more sub-areas of the second face of the mirrored film, in order to reshape the mirrored, electrically conductive film into an optically suitable shape. 
     Some embodiments further include means for projecting a first laser light pattern onto the first face of the mirrored, electrically conductive film, and wherein the acquiring of the image of the first face captures a reflection of the first laser light pattern, wherein the calculating of the correction factors is based on the captured reflection from the first face of the mirrored, electrically conductive film. 
     It is to be understood that the above description is intended to be illustrative, and not restrictive. Although numerous characteristics and advantages of various embodiments as described herein have been set forth in the foregoing description, together with details of the structure and function of various embodiments, many other embodiments and changes to details will be apparent to those of skill in the art upon reviewing the above description. The scope of the invention should be, therefore, determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein,” respectively. Moreover, the terms “first,” “second,” and “third,” etc., are used merely as labels, and are not intended to impose numerical requirements on their object.