Abstract:
This invention concerns improvements relating to a deformable-mirror holder for holding a mirror in a desired position, to within accepted tolerances, even whilst the mirror is deforming or in a deformed state. More particularly but not exclusively, this invention relates to a holder for a bimorph mirror. A deformable mirror holder ( 31 ) is provided comprising a body with a receiving portion for receiving a deformable mirror ( 30 ), and wherein the receiving portion is defined by a passive flexible support structure ( 41 ) such that, in use, to the support structure provides a supporting surface to the mirror. This invention extends to a deformable mirror and a deformable mirror holder as described above.

Description:
FIELD OF THE INVENTION 
   This invention concerns improvements relating to a deformable mirror holder for holding a mirror in a desired position, to within accepted tolerances, even whilst the mirror is deforming or in a deformed state. More particularly but not exclusively, this invention relates to a holder for a bimorph mirror. 
   BACKGROUND OF THE INVENTION 
   Deformable mirrors are often used in the field of adaptive optics. For example, phase distortions in a signal may be sensed by a wavefront sensor and these distortions may be corrected for by an adaptive mirror. Such adaptive mirrors may be employed in numerous fields, including:
         imaging, for example adaptive mirrors are used in astronomy to improve the resolution of earth-based telescopes that are otherwise affected by atmospheric distortions;   laser sensing, where the amount of laser light that can be delivered onto a target is significantly increased by using an adaptive mirror to correct for atmospheric distortions—this enables either better information to be obtained or objects to be identified at a greater range; and   laser generation, where an adaptive mirror can be used intracavity within a high power laser to counter the thermal blooming that can be otherwise induced by the high concentration of laser light inside the cavity.       

   Bimorph deformable mirrors have been proposed as low cost adaptive mirrors. The two main operational parameters of a bimorph mirror are its bandwidth and its stroke. Bandwidth determines how quickly the mirror can be deformed and hence, for example, how quickly the mirror can respond to the variations in atmospheric turbulence. Stroke corresponds to the maximum displacement of the mirror when deformed and this determines, for example, the level of turbulence that can be corrected. Ideally, both bandwidth and stroke would be maximised. However, conventional designs mean that there is a reciprocal relationship between these two parameters, and one parameter can only be improved at the expense of the other. Therefore, to date, designers have always looked for ways to improve either the resonant frequency or the stroke independently from each other. 
   Conventionally, deformable mirrors are supported rigidly around their edge, for example an annular ring overlapping the periphery of the mirror is used to hold the mirror firmly in position. Such an arrangement benefits from being simple yet rugged. However, it has an inherent disadvantage in that it creates a dead space around the mirror&#39;s edge. This corresponds both to the area of the mirror held firmly under the annular ring and also to the adjacent area. This is because the useable area of the deformable mirror (the active area) must bend to adopt a desired profile, for example either a concave or a convex shape. The annular area between the active area and the annular ring must bend in the opposite sense and so forms an area of inflexion that has undesirable optical properties. Hence the active area occupies only a central portion of the whole mirror. This is illustrated in  FIGS. 1 to 3 , albeit with the deformation of the mirror exaggerated for the sake of clarity. 
   One way of alleviating this problem is to clamp the mirror at only three positions, such that the mirror edge can twist. However, this arrangement is to the detriment of ruggedness and the twisting introduces unwanted distortions leading to an optically inferior performance. 
   It is also known that for smaller mirrors, bonded piezoelectric elements (e.g. bimorph deformable mirrors) are preferred due to their relatively low cost. Such mirrors provide an adequate balance between bandwidth and stroke. However, the balance between bandwidth and stroke is especially important when looking to make larger mirrors e.g. mirrors with active apertures greater than 10 to 15 cms. In order to keep the resonant frequency and thus the bandwidth of the mirror constant, the thickness of the substrate must also increase. For the larger mirrors this will adversely affect the minimum curvature available from the mirror. For this reason, larger mirrors have historically been zonal mirrors. The fact that the substrate is supported by a large number of actuators means that the resonant frequency, and therefore bandwidth, is no longer directly linked to the mirror diameter. However, the overriding issue with this type of deformable mirror is the cost. Although there are a number of different actuator technologies available, none of them are cheap. This makes large mirrors expensive because as many as 300 actuators may be required. For a bonded piezoelectric element mirror, although a large piezoelectric element will be more expensive than a smaller one, the cost differential will not be as great. A second issue is that it is not always possible to place discrete actuators as close to each other as required because of their fairly large size. 
   Against this background, the Applicant has filed a UK patent application (No. 0309976.9, 30 Apr. 2003 filing date) directed to a deformable mirror comprising a reflective surface provided on a substrate and a layer of deformable material attached to the substrate that is operable to deform the mirror and wherein the substrate is supported by an actuator that is operable to deform the mirror. The actuator can be used to provide the basic deformation required of the mirror (e.g. focus), while the deformable material can be used to provide fine tuning of the mirror shape. 
   Additionally, against this background, the Applicant has filed a UK patent application (No. 0309979.3, 30 Apr. 2003 filing date) directed to a deformable mirror holder that simply supports the mirror uniformly around the edge. 
   OBJECTS AND SUMMARY OF THE INVENTION 
   The present invention aims to overcome or at least substantially reduce some of the above mentioned drawbacks associated with known mirror/mirror holder designs. 
   It is an object of the present invention to provide a low cost deformable mirror holder arrangement in which the substrate no longer needs to be supported from the edge and the resonant frequency and bandwidth characteristics are effectively increased over and above what it would be for a purely edge-supported arrangement. This means that it is possible to concentrate on optimising the design of the deformable material to give the maximum curvature with less constraint from the resonance effects. 
   It is another object of the present invention to provide a low cost mirror holder arrangement, for a bimorph mirror for example, in which the edge of the mirror is unconstrained and is free to move. This means that the entire mirror substrate can be used as the active mirror. 
   In broad terms, the present invention resides in the concept of providing a deformable holder for a mirror, where rather than being supported round the rim, the mirror in its upright condition is supported from underneath by a passive compliant/flexible support structure. It is to be understood that the term “passive” support herein is used to distinguish over the kind of actuator support which by application of a potential can be actively caused to expand or contract (for example, the kind of actuator formed of magnetostrictive or electrostrictive material). 
   Thus, according to the present invention there is provided a deformable mirror holder comprising a body with a receiving portion for receiving a deformable mirror, and wherein the receiving portion is defined by a passive flexible support structure such that, in use, the support structure provides a supporting surface to the mirror. 
   Preferably, the support structure comprises a plurality of discrete flexible support elements spatially arranged to support an inner face of the mirror substrate (that is, the mirror substrate in upright condition is supported from below), with each of the support elements having an end shaped to provide support to the mirror substrate and a flexible portion that connects the element&#39;s end to the holder&#39;s body. In a currently preferred embodiment, the supporting ends of the elements lie outside of the plane of the holder&#39;s body such that the mirror is held clear of the holder&#39;s body. This could be achieved by having bracket supports anchored or attached to the sidewall of the mount. 
   Optionally, at least one of the support elements is generally L-shaped such that one leg of the L-shape provides the flexible portion and the other leg of the L-shape provides the supporting surface of the element&#39;s end. This formation conveniently allows the supporting ends of the elements to bend with the mirror. It is also to be appreciated that strict compliance with the L-shape is not necessary. For example, the support element could be J-shaped rather than being L-shaped. 
   Preferably, the support elements are arrayed in equi-spaced relationship in a circle, with each of the elements being positioned so as to be in contact with each mirror electrode when in use. This kind of arrangement is particularly desirable where a large number of support elements are required to be mounted onto the base of the arrangement for use. This also means that the elements could be all positioned to lie on an inside diameter within the full outer mirror diameter of the arrangement. Alternatively, if desired, the elements could be mounted to lie on two or more separate inside diameters within the full outer mirror diameter of the arrangement. 
   Further, whilst the elements could be distributed in equi-spaced relationship within the full outer mirror diameter of the arrangement, it is equally possible instead for the elements to be randomly spaced apart within the full outer diameter of the arrangement, if desired. 
   In accordance with an exemplary embodiment of the invention which will be described hereafter in detail, the end-shaped supporting portion of each element is formed of complaint epoxy/rubber material and the remainder portion of each element is formed of metal material. Advantageously, this adds rigidity to the arrangement supporting the mirror in use and at the same time a flexible neck region is created that allows the supporting end to bend with the mirror as it deforms. 
   Optionally, the support elements are formed wholly of compliant epoxy/rubber material. 
   Conveniently, the support elements are in the form of compliant pillars mounted onto the base of the arrangement. In a currently preferred embodiment, the support elements are cylindrically-shaped compliant pillars. It is to be understood however that the support elements could have other kinds of shape and size, if desired; for example, the elements could just as easily be square pillars. It is also noted that the elements could be flanged to facilitate support of the mirror. 
   Optionally, the support elements are integrally formed as part of the holder body. This confers a degree of rigidity to the holder body arrangement. Alternatively, if desired, the support elements could be separately mounted onto the base of the arrangement. 
   Advantageously, the support elements could be made hollow inside, so that compliant material can be injected down them. It is thus possible to control the degree of flexibility of the elements by controlled injection of the compliant material. 
   Optionally, the support elements could be formed of compliant metal foam with an open cell structure. 
   In accordance with another exemplary embodiment of the invention which will be described hereafter in detail, the support structure comprises a generally solid unitary structure with compliant characteristics, which unitary structure is arranged to extend across the entire mirror substrate surface for support thereof from below. 
   Conveniently, the unitary structure is formed of epoxy/rubber material. Alternatively, if desired, the unitary structure could be formed of metal (or other type) foam. 
   Conveniently, the unitary structure includes a number of hole sections for permitting access through the structure to a number of mirror electrodes when in use. 
   Optionally, the unitary structure includes a number of metallic interconnections permitting connection to a number of mirror electrodes when in use, the metallic interconnections being further arranged to respond to the deformation of the unitary structure in use. 
   Having regard to the foregoing, it is thus to be appreciated that the number and positioning of the flexible support(s) can be allowed to vary depending upon the desired application and upon how flexible the support structure/supports are. 
   Optionally, in accordance with another embodiment of the invention which will be described hereafter in detail, a bar-shaped flexure mount design incorporating a cooling system is provided with coolant being fed into and out of radially extending conduits through the flexures. Because the conduits are interconnectably joined to form a continuous through-passage in the mirror and the mirror mount, it is possible for coolant to be controllably admitted and circulated therethrough. An advantage of this embodiment thus is that effective cooling through the flexures can be realised when the mirror is supported from its underneath. Another advantage of this embodiment is that it obviates the need for O-ring seals. 
   According to another preferred embodiment of the present invention, the compliance of the support structure may vary across the structure in order to tailor the response of a supported mirror to applied electrode biases. In particular, where discrete support elements are provided, the compliance of the support elements or of the compliant material used to form at least a portion of each support element may be varied according to the position of the support element within the support structure. Where a continuous compliant layer is provided, the compliance of the layer may vary according to distance from the edge of the layer, for example by varying the thickness of the layer or by constructing the layer from a series of discrete annuli each composed of material having a different compliance. 
   The present invention also extends to a deformable mirror and a deformable mirror holder as described above. Optionally, the above described mirror and mirror holder include a tip-tilt stage. 
   The above and further features of the invention are set forth with particularity in the appended claims and will be described hereinafter with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a plan view of a deformable mirror and a mount according to the prior art; 
       FIG. 2  is a cross-section through II-II of  FIG. 1  showing the mirror in a relaxed state; 
       FIG. 3  corresponds to  FIG. 2  but with the mirror in a state of exaggerated deformation, thereby illustrating the problem of dead space and the relatively small active area; 
       FIG. 4  is a perspective view of a deformable mirror on a mount according to a first embodiment of the present invention; 
       FIG. 5  is a further perspective view of the mirror mount of  FIG. 4  showing the upstanding flexure supports (with the mirror removed); 
       FIG. 6  is a cross-sectional view of the  FIG. 4  arrangement; 
       FIG. 7  shows four typical kinds of electrode pattern to which flexures of the type shown in  FIGS. 5 and 6  can be attached; 
       FIG. 8  shows a cross-sectional view of another embodiment of the present invention; 
       FIG. 9  shows a perspective view of another arrangement embodying the invention in which a mould is used; 
       FIG. 10  corresponds to  FIG. 9  but with the mould removed; 
       FIG. 11  shows another mirror arrangement (without the base for clarity) according to another embodiment of the present invention; 
       FIG. 12  shows a perspective view of a further arrangement (without the base for clarity) according to another embodiment of the present invention; 
       FIG. 13  corresponds to  FIG. 12 , but is a cross-sectional view; 
       FIG. 14  shows a cross-sectional view of another arrangement with cooling through flexures according to another embodiment of the present invention; 
       FIG. 15  shows a bimorph arrangement in cross-sectional view, for use with a tip-tilt stage; 
       FIG. 16  shows another bimorph arrangement in cross-sectional view, for use with a tip-tilt stage; 
       FIG. 17  shows yet another bimorph arrangement in cross-sectional view, for use with a tip-tilt stage; 
       FIG. 18  shows a mirror support arrangement (without mirror mount base and tip-tilt stage), using a compliant ring at the mirror periphery only; 
       FIG. 19  shows the mirror support structure of  FIG. 17 , without the mirror mount base and tip-tilt stage for clarity; 
       FIG. 20  shows a cross-sectional view of another arrangement, with a different way of making connection to the mirror electrodes, according to another embodiment of the present invention; and 
       FIG. 21  shows a cross-sectional view of another arrangement in which the edge of the support base is extended in a flange portion to provide edge support to a continuous compliant layer. 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   In the following description, the same reference numerals as used in different Figures are used to designate same/like parts. 
   Further, in all embodiments described herein, the deformable mirror is a deformable bimorph  30  comprising a mirror substrate  32  whose outer face provides a reflecting surface  34  by virtue of a series of thin dielectric coatings provided on the outer face (not shown). At least one active piezoelectric element  33  is bonded to the non-active, inner face of the mirror substrate  32  using epoxy resin. A common electrode strip  38  is located between the non-active inner face of the mirror substrate  32  and the piezoelectric element  33 . An array of electrodes  37  is used to activate the piezoelectric element(s)  33 . Applying a bias voltage between the electrodes  37  and the common electrode  38  causes the piezoelectric element(s)  33  to deform locally so that, in turn, the mirror substrate  32  deforms to create a mirror with a desired shape, convex for example. 
   A deformable bimorph mirror  10  and its mount  12  according to the prior art are first shown in  FIGS. 1 to 3 . As can be seen, the mirror  10  is disc-shaped and is supported by the mount body  12 . The mirror  10  is held firmly in position by an annular ring  14  that urges the mirror  10  against the mount body  12  via four screws  16 .  FIG. 3  shows the mirror  10  in a deformed state such that, in this example, it adopts a convex profile for light approaching from above. Ideally, the desired convex profile should extend across all the mirror  10 , such that all the mirror  10  is available for reflecting light in the desired manner. However, the peripheral edge  18  of the mirror  10  is held firmly between the annular ring  14  and the mount body  12  and so cannot bend. Moreover there is a region  20  of the mirror  10  that adopts an area of inflexion to bridge the peripheral edge  18  of the mirror  10  and the convex portion  22  at the centre of the mirror  10 . It is of course this convex-shaped part  22  of the mirror  10  that forms the active (i.e. useable) part  22  of the mirror  10 . This active part  22  of the mirror  10  is shown in  FIG. 3 . 
   A deformable bimorph mirror  30  and a mount  31  according to a first embodiment of the present invention are shown in  FIG. 4 . The mount  31  is a unitary structure made from stainless steel material. The mount  31  comprises a round body that defines a receiving portion (as partially shown) sized and shaped to receive and support the disc-shaped deformable bimorph mirror  30  on top. As is shown in the Figure, the mirror  30  in its assembled (upright) condition on top of the mount  31  is held clear of the mount  31 . 
     FIG. 5  shows the mirror mount  31  of  FIG. 4 , without the mirror  30  for sake of clarity. The mount has a stepped profile  42  defining a generally circular aperture in the centre. Four flexure supports  41  are formed in equispaced relationship around the top most stepped section  42  of the mount body, each support being arranged to extend inwardly towards the centre of the aperture before turning upwards through 90° to extend in an upward direction for supporting the mirror (not shown). The four flexure supports  41  are formed as part of the mount body. The supports are of identical size and shape. The flexure supports and the mount body are formed of the same metal material. Thus, as shown in  FIG. 5 , each of the flexure supports  41  has a flexible upstanding end portion shaped to provide support to the mirror substrate (not shown) when in use, and a bridging flexible portion connecting the end portion to the mount holder&#39;s body. Because the supporting ends of the flexure supports are configured to lie outside of the plane of the holders body, the mirror in use is held clear of the holder&#39;s body on top. 
     FIG. 6  is an exploded cross-sectional view of the assembled mirror/mirror mount arrangement of  FIG. 4 . As can be seen, the non-active inner face of the substrate  32  is supported from below by each of the four passive flexure supports  41 . With this kind of support there is significant benefit insofar as there is no longer any need to support the mirror  30  round its edge. With the edge of the mirror free to move, there will be fewer constraints on the mirror deformation around its edge. 
   As can also be seen in  FIG. 6 , each flexure support  41  has an L-shaped cross-section with one leg of the L-shape at one end attached to the base  45  of the mount and the other leg of the L-shape at its other end, bonded via glue  36 , to the piezoelectric element  33 . It is noted here that the mirror supporting end portion of each support is in the shape of a narrow neck  46  with flexible characteristics. It is this flexible neck portion  46  which can be flexed to permit the support to bend as the mirror substrate deforms. The length and thickness of the neck of each support are chosen to achieve the desired flexing properties. 
   Thus, in operation of the  FIG. 6  arrangement, by applying a potential between the array of electrodes  37  and the common electrode strip  38  causes the piezoelectric element  33  to locally expand/contract, and this in turn induces a local curvature in the piezoelectric element/mirror substrate sandwich. In this way, the mirror  30  is controllably deformed. It is to be understood here that whilst only one piezoelectric element layer  33  is shown in the Figure, there are situations where it is advantageous to use two or more piezoelectric element layers (refer to the content of recently filed UK patent application No. 0309976.9, as filed by the Applicant on 30 Apr. 2003). 
   In this embodiment, the internal sides  47  of the mount body are stepped so as to provide shoulder formations for attachment to the leg portions of the supports  41 . In this way, as can be seen, the supports  41  are formed as part of the mirror mount base (see also shaded region in the Figure). 
   Advantageously in this embodiment, the flexure supports  41  and the mirror mount base  45  are formed of metal material. Further, the flexure supports  41  are configured to provide a small (typically up to ˜20 microns) amount of movement to be induced by the piezoelectric element (although they will also stiffen up the piezoelectric element). Thus, it is to be appreciated that any number of such flexure support, can be placed on an inside diameter for effective support of the mirror—for example, where the full mirror diameter is 60 mm, such flexure supports could be equispaced on an inside diameter of 40 mm. 
     FIG. 7  shows, by way of example only, four typical different electrode patterns  37  that can be used for activation of the piezoelectric element in the arrangement according to the first embodiment of the invention. 
     FIG. 8  shows a second embodiment of the present invention in cross-sectional view, which is very similar to the first embodiment as shown in  FIG. 6 . It differs in that the mirror supporting end portion of each passive flexure support comprises a layer of compliant epoxy/rubber material  48 . 
   As shown in  FIG. 8 , the remainder portion of each support comprises metal material (see shaded area surrounding  48  in  FIG. 8 ). 
   This arrangement bears definite advantage in that most of the desired compliance can come from the layer of epoxy/rubber material  48 , whilst at the same time a degree of stiffness/rigidity in the supports is controllably achieved by virtue of the presence of metal flexure support material. 
   To facilitate assembly of the arrangement of  FIG. 8 , it is envisaged that the epoxy/rubber material is injected onto each flexure support from the back through a hole drilled vertically through the flexure (not shown)—in this case, it is to be understood that the mirror is required to be assembled upside down. 
     FIG. 10  shows a third embodiment of the present invention, without the mirror mount base for clarity. In common with the first and second embodiments, this embodiment has a mirror substrate  32 , which is supported on its non-active, inner face by a plurality of flexure supports. With this kind of support there is significant benefit insofar as there is no longer any need to support the mirror  30  round its edge. With the edge of the mirror free to move, there will be fewer constraints on the mirror deformation around its edge. Further as shown in  FIG. 10 , each of the supports is bonded to the inner face of the mirror substrate  32  via the piezoelectric element  33 /electrode array  37 . This embodiment however differs in that there are eight flexure supports in the form of eight cylindrical-shaped pillars  70  arranged concentrically halfway along eight equispaced radii of the mirror. The eight support pillars  70  are formed of compliant epoxy/rubber material. 
     FIG. 9  shows how the arrangement of  FIG. 10  can be obtained in practice. As shown in  FIG. 9 , the eight support pillars  70  are formed by injecting epoxy/rubber material into a mould  39  that is placed against the piezoelectric element  33 . The mould  39  has a release agent so that when the epoxy/rubber material is set inside receiving sections  70 ′, the mould  39  can be removed thereby leaving behind the desired formation of the compliant pillars on the mirror substrate. Thus, in this case, all the compliance takes place in the pillars which are in turn bonded onto the mount base. 
     FIG. 11  shows a fourth embodiment of the present invention, without the mirror mount base for clarity (i.e. as viewed from the mirror&#39;s reverse side). In common with the third embodiment of  FIG. 10 , this embodiment has a mirror substrate  32  which is supported on its non-active, inner face by a plurality of flexure supports. With this kind of support there is significant benefit insofar as there is no longer any need to support the mirror  30  round its edge. With the edge of the mirror free to move, there will be fewer constraints on the mirror deformation around its edge. Further, as shown in  FIG. 11 , each of the supports is bonded to the inner face of the mirror substrate  32  via the piezo electric element  33 /electrode array  37 . This embodiment however differs in that there are a total of seventeen flexure supports in the form of seventeen cylindrical-shaped pillars  70  arranged as follows: there is a single central pillar  70  surrounded by two concentric rings of eight pillars  70 . The rings are placed about one third and two thirds of the way along the radius of the mirror and the pillars  70  within each of the rings are arranged to sit on a common radius. In this embodiment, the pillars  70  are arranged such that they are attached to every mirror electrode  37  when in use. As described previously in the  FIG. 10  embodiment, the support pillars  70  are formed of compliant epoxy/rubber material. 
   It is to be understood that the procedure using a mould as described in relation to  FIGS. 9 and 10  can be suitably modified and adopted to produce the arrangement of  FIG. 11 . 
   For some applications it may be advantageous to use conductive compliant pillars to form the flexure supports  70  in the embodiment of  FIG. 11  in which each electrode is supported by a different compliant pillar. Such pillars can be made from metallic foams. The pillars can then be used to make connections to the electrode array  37 , greatly simplifying the overall mirror structure since there is no need for additional components to make electrical connections to the lower electrodes. Conductive adhesive can be used to attach the pillars to the electrodes. 
   Where the electrode pattern is closed packed hexagonal, as shown in  FIG. 7   d , and each electrode is supported by a compliant pillar, deformations in a supported mirror are likely to be more localised and as such can be described as ‘zonal’. For all preferred embodiments of the present invention involving multi-pillar support, and especially where each electrode is independently supported, the supported mirror structure is scalable to larger diameters and element array sizes without the need to significantly increase the thickness (and therefore reduce the maximum curvature) of the mirror structure. 
   The pillars should preferably have a Young&#39;s modulus of ˜0.5-5 GPa. The Young&#39;s modulus of a conducting foam can be altered by altering the density of the foam structure. The size of the pillars can be varied to take account of variations in Young&#39;s modulus; a higher stiffness can be accounted for by a larger pillar, and a lower Young&#39;s modulus can be accommodated by a smaller pillar. The pillars can be made for any compliant conducting material of suitable stiffness; examples include metallic, silicon or silicon carbine foams, or graphite foams such as PocoFoam™. 
   The interconnect at the opposite end of the pillars (not shown), on which the pillars are mounted, can be a board with connections for each electrode. For particularly large mirrors, with large numbers of electrodes, it may be necessary to use a multilayer board, with the upper layer connecting to the pillars, whilst lower layers are used to make connection tracks that may be found in any convenient configuration to connect to an external driver. The thermal expansivity of the interconnect board should be matched to that of the mirror to avoid distortion of the mirror due to temperature variation. Suitable materials for fabrication of the substrate for the board thus include aluminium, that has a thermal expansion coefficient of ˜1-3 ppm/° C. 
   The greater simplicity of the mirror when the pillars are used to form the connections to the electrodes enhances of the scalability of the design. Very large deformable mirrors can be made by combining individual mirrors so that they cover large areas. Such large deformable mirrors are used in astronomical telescopes. It is expected that the simplicity of the mirror when the pillars are used to form connections will make this design particularly suitable for such large, segmented mirrors. 
   It is to be also understood that it is possible to assemble the base (not shown) onto the mirror substrate  32  in the  FIG. 11  embodiment at the same time as forming the compliant pillars if a mould is used that can be dissolved or heated to remove it without disturbing either the base or the mirror substrate  32 . 
     FIG. 12  shows a fifth embodiment of the present invention, without the mirror mount base for clarity (i.e. as viewed from the mirror&#39;s reverse side). In this embodiment, almost the entire inner face of the mirror substrate  32  is supported by a generally solid compliant material  60 . This arrangement broadly corresponds to an inversion of the  FIG. 11  arrangement in that whilst there are seventeen hole formations  61  in the compliant material  60  to permit connection to each of the mirror electrodes, most of the backside of the mirror is effectively supported by the compliant material  60 . 
   In this embodiment, the compliant material of the passive support structure is rubber, epoxy or some form of metal (or other type foam). If desired, the compliant material could be readily configured as a narrow ridge structure (i.e. similar to the type of ridges that are used to stiffen up light structures) that follows the gaps between the mirror electrodes. 
     FIG. 13  shows an exploded cross-sectional view of the  FIG. 12  arrangement. As can be clearly seen, the compliant material  60  is arranged to cover the whole area of the piezoelectric element  33  except for where a hole formation  61  is required to enable a connection to be made to a mirror electrode  37 . 
     FIG. 14  shows a sixth embodiment of the present invention in cross-sectional view, and which is based on the first embodiment as shown in  FIG. 6 . It differs in structure in that it provides a structural modification achieving cooling through the flexures when the mirror is supported from its underneath. The cooling system of  FIG. 14  is described hereinafter. 
   As shown in  FIG. 14 , a modified bar flexure structure  81  is used to support the mirror  30  from its underneath. A plurality of radially extending through-passages  86  are provided in the mount  31  which go through the centre of the bar flexure structure  81  and meet with the radially extending conduits  80  in the mirror  30  from its underneath. As shown, the ends of the radially extending conduits  80  in the mirror  30  are plugged  88 . The outer ends of the through-passages  86  in the mount  31  are sealed with a plug  85 . In this embodiment, as shown, vertical passages  87  are formed in the mount  31  in such a way as to meet with the through-passages  86  near their outer ends. In this embodiment, it is to be also understood that holes are required to be formed through the piezoelectric element  33  (as shown). 
   Thus, in operation of the arrangement of  FIG. 14 , water coolant is fed into and out of the radially-extending conduits through the flexures from underneath the mirror. As shown in  FIG. 14 , the route for the water coolant is up through the vertical passages  87 , then along and up the through-passages  86  in the mount and then through the radially-extending conduits  80  in the mirror  30 . 
   In this way, effective cooling through the flexures of the arrangement of  FIG. 14  can be achieved when the mirror is supported from its underneath. Another advantage of such an arrangement is that it obviates the need for O-ring seals. 
   Whilst water has been described as the coolant above, other types of coolant can also be used, if desired, such as any gas, a liquefied gas such as liquefied nitrogen, an anti-freeze solution or mercury. 
   It is to be appreciated that any of the above described passively supported arrangements of the embodiments could be integrated with a tip-tilt stage, if desired.  FIGS. 15 to 17  show three different ways of accomplishing this, by way of example only. 
     FIG. 15  shows a bimorph arrangement  90 ′ in cross-sectional view which is supported by a plurality of spaced-apart compliant pillars  93  integrated onto a tip-tilt stage. As shown in  FIG. 15 , the arrangement  90 ′ comprises a base  90 , a plurality of actuators  91 , and a support disc  92 . When the lower stage is used to correct for tip-tilt only, it is envisaged that the use of three or four actuators is adequate, provided that the support disc is thick enough so that it does not deform during operation. Alternatively, if desired, a larger number of actuators (i.e. use of five or more actuators) could be used instead in conjunction with a thin, deformable support disc. In this case, corrections for large scale distortions could be achieved by means of transferring deformations via the support disc and the pillars to the deformable mirror. This means that the bimorph mirror would remain active, but that it would only be required to correct for higher order distortions. 
     FIG. 16  shows another bimorph arrangement  100 ′ in cross-sectional view which broadly corresponds to the arrangement of  FIG. 15 , the only difference being that the mirror of  FIG. 16  is supported by a continuous compliant strip  93 ′ (rather than by a plurality of discrete, spaced-apart complaint pillars as shown in  FIG. 15 ). It is to be understood that many features of this arrangement  100 ′ are the same as for the arrangement  90 ′ shown in  FIG. 15  and so have been assigned same reference numerals. 
     FIG. 17  shows another bimorph arrangement  110 ′ in cross-sectional view which broadly corresponds to the arrangement of  FIG. 15 , the only difference being that the mirror of  FIG. 17  is supported by a compliant ring  111  at its periphery, together with a single compliant pillar  112  at its centre. It is to be understood that many features of this arrangement  110 ′ are the same as for the arrangements  90 ′ and  100 ′ shown in  FIGS. 15 and 16  and so have been assigned same reference numerals. 
   It is to be noted that omission of the central compliant pillar  112  from the arrangement of  FIG. 17  means that the lower stage can then only be used to provide tip-tilt control, there being no mechanism for the transfer of distortions to the centre of the mirror. Without the mirror mount base and tip-tilt stage shown, this then corresponds to the mirror support arrangement  120  of  FIG. 18 , using a compliant ring  111  at the periphery only (i.e. as viewed from the mirror&#39;s reverse side). 
   Whereas the use of a single layer of actuators is described in relation to the arrangements of  FIGS. 15 ,  16  and  7 , additional layers of actuator can be incorporated (not shown) for use with large mirrors. The particular configuration/number of the actuators can also be varied. For example, where there is a requirement for a very rigid coupling between the base and the support disc, the actuators could be configured to form a hexapod arrangement (not shown), thereby providing a highly stable, 3-point mounting system based upon the use of six actuators. 
     FIG. 19  shows the mirror support structure of  FIG. 17 , without the mirror mount base and tip-tilt stage for clarity (i.e. as viewed from the mirror&#39;s reverse side). As clearly shown by the arrangement  130  in the Figure, the mirror is supported by a ring of compliant epoxy/rubber material  111  round the rim of the mirror, and also by a single compliant pillar  112  in the centre of the mirror. The central pillar  112  is designed to provide additional structural support, but it does not stop the deformable mirror from providing tip-tilt correction. 
   Whereas the ring and the central pillar of the above described  FIG. 19  arrangement are formed of compliant epoxy/rubber material, other compliant materials (metal foam for example) could equally be used instead, if desired. In addition, the shape, size and number of compliant supports used is not critical—for example, the compliant ring could alternatively be arranged to extend across part of the mirror substrate surface for support thereof from below (as opposed to being confined to support the rim of the mirror, as shown in  FIG. 19 ), and additional compliant pillars could also be positioned at various locations across the mirror substrate surface, if desired (not shown). 
   A further embodiment of the present invention is shown in  FIG. 20 . In common with the embodiment of  FIG. 13 , compliant material  60  is arranged to cover the whole area of the piezoelectric element  33 . However, the embodiment of  FIG. 20  shows a different method for making connection to the mirror electrodes  37 . As shown in the arrangement  140  of  FIG. 20 , each PZT electrode  37  is connected to a pad  142  on an interconnection PCB  143  via a thin metal strip  144  which is in turn embedded into the compliant material  60  (see dotted region in Figure). In this embodiment, the metal material comprises phosphor bronze which is resilient with elastic properties and each of the strips has an S-type shaped bend to allow the thin metal strip to follow the deformation of the compliant material. As also shown in the Figure, a wrap around electrode  145  is provided on the piezoelectric element  33  which facilitates connection to the common electrode  38 . Whereas the metal material in the arrangement of  FIG. 20  is phosphor bronze, other materials which are resilient with suitable elastic properties could be used instead, if desired. In addition, the shape, size and/or number of the metal strips used in  FIG. 20  is not critical—for example, the metal strips could each have two or more bends (not shown) as long as these can follow the deformation of the compliant material. 
   Is has been noted by the inventors in the present case that for preferred embodiments of the present invention having either multi-pillar supports (e.g. those shown in  FIGS. 6 ,  8 ,  10  and  11 ) or continuous compliant supports (e.g. those shown in  FIGS. 13 and 20 ), the amount of movement induced in a supported bimorph mirror as a result of applying a given bias to any particular electrode varies according to the distance of the electrode from the mirror edge. In an ideal situation, a bias applied to one of the electrodes should result in a smoothly varying displacement response across the whole mirror. 
   To improve the performance of supported bimorph mirrors towards the ideal, the compliance of supports in preferred multi-pillar and continuous compliant support embodiments of the present invention may be varied according to distance of the support or part of the support from the edge of the mirror. In this way the response of the supported mirror to applied electrode biases can be tailored to a predetermined response function. For example, for a continuous compliant support, the compliance may be increased towards the centre of the support so that when a uniform bias (not necessarily the maximum possible applied bias) is applied to each of the electrodes the mirror provides a purely spherical response. Other response functions can be provided by applying a different compliance profile across the support(s). 
   In preferred multi-pillar support embodiments, it may be advantageous to modify the compliance of the supports to ensure that each electrode has the same ‘zonal’ response function. It would also be possible to modify the compliance of the supports so that the mirror provides a curved response when a uniform field is applied to all the electrodes. 
   There are a number of ways in which the compliance of the supports can be modified. For a multi-pillar mirror support, any of the following preferred techniques may be used individually or in combination:
         a) varying the stiffness (or Young&#39;s modulus) of the material that the pillar is made from according to the distance of the pillar from the edge of the mirror, e.g. by using epoxies/silicon rubber with different stiffness or using foams with different densities;   b) using a material with uniform stiffness, but varying the pillar diameter;   c) using a material with uniform stiffness, but varying the height of the pillar. This could be smoothly varying, or in the form of a number of discrete steps.       

   For a continuous mirror support, any of the following preferred techniques may be used individually or in combination:
         d) varying the stiffness of the compliant material with respect to the edge of the mirror. This may be achieved by making the support material in the form of a number of discrete annuli each having a different compliance. If the compliant material is in the form of a foam, then the foam density may be varied as a function of distance to the mirror edge;   e) using a material with a uniform stiffness, but varying the thickness of the material as a function of distance to the mirror edge.       

   It has been noted that in both the multi-pillar and the continuous compliant support embodiments, in order to enable sufficient movement at the mirror centre, any support at that point needs to have a very high compliance. This can lead to undesirable low frequency torsion and sheer modes in a supported mirror. In a preferred embodiment, such undesirable modes may be damped, for a mirror supported by a continuous compliant layer, by adding extra support around the edge of the compliant layer. A preferred technique for adding extra support around the edge of a continuous compliant layer is shown in  FIG. 21 . 
   Referring to  FIG. 21 , the edge of the support base  45  is extended in a flange portion  150  so as to enclose the compliant layer  60  at least partially. A gap  152  may be provided between the upper surface of the flange portion  150  and the underside of any projecting portion of a supported mirror  30 . Alternatively, the gap  152  may be filled with a compliant epoxy/silicon rubber, for example, to provide extra support to the outer portion of a supported mirror. Moreover, the flange portion  150 , together with the compliant epoxy/silicon rubber gap filler, or any other type of compliant supporting element deployed at the outer edge of the support structure, may be used in respect of any of the preferred embodiments of the present invention described above, whether having multi-pillar or continuous compliant layer support structures, to provide extra support to the outer portion of a supported mirror and hence have the effect of damping undesirable low frequency torsion and sheer modes in the mirror. 
   Having thus described the present invention by reference to various preferred embodiments, it is to be appreciated that the embodiments are in all respects exemplary and that modifications and variations are possible without departure from the spirit and scope of the invention. For example, the number, positioning, shape and size of the flexible support(s) could be allowed to vary depending upon the desired application and upon how flexible the support structure/supports are. For example, the performance of the  FIG. 11  embodiment could possibly be improved, if desired, by provision of additional supports on the inner face of the mirror substrate and by using square or other shaped flexible supports with inclusion of a flange where the supports meet the piezoelectric element. 
   Whilst the mount of the above embodiments is made from stainless steel, many other materials such as other metals, plastics, glasses or ceramics could be used instead. 
   Whilst the described arrangements of the embodiments in  FIGS. 15 ,  16  and  17  are integrated onto a tip-tilt stage, the respective various component parts can alternatively be assembled separately without need for integration. 
   The present invention is perfectly well suited for use in supporting all types of unimorph or bimorph mirror structures.