Patent Publication Number: US-6986587-B2

Title: Variable-shape reflection mirror and method of manufacturing the same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2002-301995, filed Oct. 16, 2002, the entire contents of which are incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a variable-shape reflection mirror, in particular, a small-sized variable-shape reflection mirror capable of high-precision shape control, and to a method of manufacturing the variable-shape reflection mirror using semiconductor fabrication technology. 
   2. Description of the Related Art 
   In the field of micro-optical systems applied to microoptics, such as optical pickups, a very small variable-focus mirror capable of varying the curvature of its reflective surface has been proposed for the purpose of simplifying a mechanism relating to focusing, etc., which conventionally uses an electromagnetic actuator. The application of such a variable-focus mirror contributes greatly to further miniaturization of small-sized imaging optical systems. 
   As regards this type of variable-focus mirror, high-precision products can be manufactured at low cost by applying so-called micro-electromechanical system (MEMS) technology. An example of this technology is proposed in Jpn. Pat. Appln. KOKAI Publication No. 2-101402, for instance. The technique of this document is described below. 
   As is shown in  FIG. 1A  and  FIG. 1B , a fixed-side electrode layer  12  formed of an electrically conductive film is provided on an upper surface of an insulating substrate  11  formed of, e.g. glass. A silicon dioxide (SiO 2 ) film  14  is formed as an insulating film on one major surface of a silicon substrate  13 . A recess  15  is formed on a central portion of the other major surface of the silicon substrate  13 . The recess  15  enables a central portion of the SiO 2  film  14  to be displaced in its thickness direction. In addition, a movable-side electrode layer  16  is laminated on the SiO 2  film  14 . Central portions of the SiO 2  film  14  and the electrode layer  16  constitute a mirror portion  17 . With a voltage applied between the electrode layers  12  and  16 , the mirror portion  17  is deformed in a convex shape toward the fixed-side electrode layer  12 . 
   The silicon substrate  13  is coupled to the insulating substrate  11  via a spacer  18 , with the SiO 2  film  14  being situated downward (in  FIGS. 1A and 1B ). Further, an SiO 2  film  19  is formed on the other major surface of the silicon substrate  13 . 
   A method of manufacturing the above-described mirror device will now be explained with reference to  FIGS. 2A to 2E . To start with, as shown in  FIG. 2A , SiO 2  films  14  and  19  each having a thickness of 400 nm to 500 nm are formed on both mirror-polished surfaces of a silicon substrate  13 , which has a plane direction &lt;100&gt;. A metal film with a thickness of about 100 nm is formed as an electrode layer  16  on the lower-side film  14 . Then, as shown in  FIG. 2B , a photoresist  20  with a predetermined pattern is coated, and a circular window  21  is formed by photolithography. Using the photoresist  20  as a mask, an opening is formed in the SiO 2  film  14  with a hydrofluoric-acid-based solution, with the lower-side surface of the substrate being protected. Subsequently, as shown in  FIG. 2C , the silicon substrate  13  is immersed in an aqueous solution of ethylenediamine Pyrocatechol and the silicon substrate  13  is etched from the window  21  shown in  FIG. 2B . The etching stops when the SiO 2  film  14  on the lower side of the substrate  13  is exposed. As a result, a film mirror portion  17  formed of the SiO 2  film  14  and electrode layer  16  remains. 
   On the other hand, as shown in  FIG. 2D , a metal film with a thickness of 100 nm, which serves as a fixed electrode, is formed as an electrode layer  12  on the upper surface of the insulating substrate  11  having a thickness of 300 μm. As is shown in  FIG. 2E , the silicon substrate  13  is bonded to the insulating substrate  11  with a polyethylene spacer portion  18  with a thickness of about 100 μm interposed, whereby the mirror device shown in  FIGS. 1A and 1B  is manufactured. 
   In the above-described variable-shape mirror, a uniform potential difference is provided between the SiO 2  film  14  and the fixed-side electrode layer  12 . The deformation shape in this case is generally as shown in  FIG. 3 , compared to a spherical surface having an equal maximum deformation amount. In particular, the amount of deformation in a peripheral portion is deficient and a large spherical aberration occurs. Consequently, high focusing performance cannot be attained. Moreover, when a small-sized mirror is applied to an imaging optical system, oblique light incidence occurs in usual cases. In such cases, in order to obtain good focusing performance, a rotation-asymmetric aspherical surface is required. 
   To meet this requirement and to deform the variable-shape mirror in a desired shape or an ideal shape, there is an idea of the fixed-side electrode layer being divided into a plurality of regions and different potential differences provided between the divided regions, on the one hand, and the electrode of the deformable surface, on the other hand. Examples of the division mode of the electrode include a concentric shape, a lattice shape and a honeycomb shape. For instance, J. Opt. Soc. Am., Vol. 67, No. 3, March 1977, “The membrane mirror as an adaptive optical element”, proposes a method of dividing the fixed-side electrode in a honeycomb shape. 
   In addition, the paper of the Japan Society for Precision Engineering, Vol. 61, No. 5, 1995, entitled “Aberration reduction of Si diaphragm dynamic focusing mirror”, discloses a method for making the shape of deformation conform to a specific shape such as a spherical surface shape or a parabolic surface shape. In this method, a deformable surface having a different thickness from location to location is formed. 
   BRIEF SUMMARY OF THE INVENTION 
   According to a first aspect of the present invention, there is provided a variable-shape mirror comprising a flexible film having a plurality of electrodes and a reflective surface whose shape varies when electrostatic forces are applied to the plurality of electrodes, 
   the plurality of electrodes being divided in a circumferential direction and in a radial direction of the flexible film, and 
   the flexible film having a greater number of circumferential-directional divisions in a peripheral portion thereof than in a central portion thereof. 
   According to a second aspect of the present invention, there is provided a variable-shape mirror comprising a flexible film having a plurality of electrodes and a reflective surface whose shape varies when an electrostatic force is applied to the plurality of electrodes, 
   the flexible film having, in a peripheral region, a portion having a rigidity lower than a rigidity of remaining region of the flexible film. 
   According to a third aspect of the present invention, there is provided a variable-shape mirror comprising a flexible film having a plurality of electrodes and a reflective surface whose shape varies when an electrostatic force is applied to the plurality of electrodes, 
   the flexible film including a portion with a low rigidity in a circumferential direction thereof, and a ratio of the portion with the low rigidity varies in the circumferential direction of the flexible film. 
   According to a fourth aspect of the present invention, there is provided a variable-shape mirror comprising a flexible film having a plurality of electrodes and a reflective surface whose shape varies when an electrostatic force is applied to the plurality of electrodes, 
   the flexible film including openings in a circumferential direction thereof, and a ratio of the openings varies in the circumferential direction of the flexible film. 
   According to a fifth aspect of the present invention, there is provided a variable-shape mirror comprising: 
   a plurality of fixed lower electrodes; and 
   a flexible film having a reflective surface and a plurality of upper electrodes, 
   the lower electrode has, in a region thereof, a plurality of openings arranged at different intervals, and 
   the flexible film has, in a peripheral portion thereof, a portion having a rigidity lower than a rigidity of other regions of the flexible film. 
   According to a sixth aspect of the present invention, there is provided a method of manufacturing a variable-shape mirror, comprising: 
   forming first and second protection films on first and second major surfaces of a semiconductor substrate; 
   forming a flexible film on the first protection film; 
   forming a plurality of openings in the flexible film; 
   forming an electrode film on the flexible film; 
   forming an opening in the second major surface and the second protection film, and forming a frame by a residual portion of the semiconductor substrate. 
   Advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention, and together with the general description given above and the detailed description of the embodiments given below, serve to explain the principles of the invention. 
       FIG. 1A  and  FIG. 1B  show the structure of a prior-art variable-shape mirror; 
       FIGS. 2A to 2E  illustrate a method of manufacturing the prior-art variable-shape mirror; 
       FIG. 3  is a view for explaining a deformation amount of the variable-shape mirror when a uniform potential difference is provided; 
       FIG. 4  schematically shows the structure of an optical system to which a variable-shape mirror according to a first embodiment of the present invention is applied; 
       FIG. 5  is a three-dimensional view of the deformation shape of the reflective surface in the first embodiment; 
       FIG. 6  is a contour diagram representing a displacement of the reflective surface; 
       FIG. 7  is a distribution map of an error between a deformation shape and an ideal shape in a case where a uniform electrostatic force is applied to the deformation surface of the variable-shape mirror; 
       FIG. 8  shows the structure of the variable-shape mirror according to the first embodiment of the invention; 
       FIG. 9  shows the shape of the fixed electrode, and electrostatic forces applied to a central region (expressed by “1”) and to other regions; 
       FIG. 10  shows the shape of an upper substrate of a variable-shape mirror according to a second embodiment of the present invention; 
       FIG. 11  illustrates a modification of the second embodiment; 
       FIG. 12  shows the shape of an upper substrate of a variable-shape mirror according to a third embodiment of the present invention; 
       FIG. 13  is a three-dimensional view of the deformation shape of the reflective surface in the third embodiment; 
       FIG. 14  is a distribution map showing an average displacement gradient toward the central region in the third embodiment; 
       FIG. 15  shows the shape of an upper substrate of a variable-shape mirror according to a fourth embodiment of the present invention; 
       FIG. 16  is a distribution map showing an average displacement gradient toward the central region in the fourth embodiment; 
       FIG. 17A  to  FIG. 17D  illustrate a method of manufacturing the variable-shape mirror; 
       FIG. 18A  to  FIG. 18D  illustrate another method of manufacturing the variable-shape mirror; and 
       FIG. 19  shows the structure of a lower electrode of a variable-shape mirror according to a fifth embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Embodiments of the present invention will now be described with reference to the accompanying drawings. 
   [First Embodiment] 
   A first embodiment of the present invention is described.  FIG. 4  schematically shows the structure of an optical system to which a variable-shape mirror according to the first embodiment of the invention is applied. 
   An incidence-side front lens group  101  and a rear lens group  103 , which is located on the side of a solid-state imaging device  102 , are arranged such that their optical axes intersect at right angles. At the intersection, a variable-shape mirror  104  is disposed. By an electrostatic force, a deformable film  105  with the reflective surface of the variable-shape mirror  104  deforms continuously from a flat shape (indicated by a broken line in  FIG. 4 ) to a concave shape (indicated by a solid line in  FIG. 4 ). Thereby, the focal point of the optical system is varied. In short, by virtue of the deformation of the variable-shape mirror  104 , focus adjustment can be made without adjusting the lens groups. 
   When the reflective surface has a flat shape, focusing is made at infinity. When the reflective surface has a concave shape, focusing is made at a near-point. However, since a light beam falls obliquely on the concave-surface mirror, a large spherical aberration occurs when the deformed surface is simple spherical surface or a parabolic surface. In such a case, high-precision imaging cannot be performed, and so it is necessary to deform the reflective surface into a rotation-asymmetric free-form surface. 
     FIGS. 5 and 6  show an example of the shape of the reflective surface designed so as to suppress a near-point spherical aberration in relation to the actual lens construction.  FIG. 5  is a three-dimensional view of the deformation shape of the reflective surface. The size of the deformation region of the reflective surface is set such that a rectangle of 6 mm×2 mm is interposed between a pair of semicircles each having a radius of 3 mm.  FIG. 6  is a contour diagram representing a displacement of the reflective surface.  FIG. 6  also shows an image area corresponding to effective pixels of the solid-state imaging device  102  in a case where the variable-shape mirror with this reflective surface is applied to the optical system shown in  FIG. 4 . 
     FIG. 7  shows a distribution of an error between the deformation shape obtained when a uniform electrostatic force is applied to the deformation surface of the variable-shape mirror and the ideal shape based on the optical design shown in  FIG. 5  or  FIG. 6 . In fact, only the error within the image area indicated in  FIG. 7  is the problem. The error is particularly large in an outer peripheral region of the deformation surface. Further, as is understood, in the outer peripheral region of the deformation surface, the error in the circumferential direction is non-uniform, and the degree of the error varies greatly. As a matter of course, the error distribution varies due to the design of optical system. However, the error distribution has a generally similar tendency when an ordinary rotation-symmetric lens and this variable-shape mirror are combined. 
   In order to perform high-precision imaging, it is imperative to make the deformation shape of the reflective surface close to the ideal shape. To meet this requirement, it is necessary to divide one of the mutually opposed electrodes and to impart a distribution to the electrostatic force applied to the deformation surface of the variable-shape mirror. 
   The structure of the variable-shape mirror  104  according to the first embodiment will now be described with reference to  FIG. 8 . The variable-shape mirror  104  according to the first embodiment is configured such that an upper substrate  106  and a lower substrate  107  are coupled to each other, with spacers  108  formed on the lower substrate  107  being interposed therebetween. In  FIG. 8 , for the purpose of description, the upper substrate  106  and lower substrate  107  are separated. The upper substrate  106  has a deformation film  105  supported on a frame member  109 . A fixed electrode  110 , which is divided into a plurality of regions, is formed on that region of the lower electrode  107  which is opposed to the deformation film  105 . Although not shown in  FIG. 8 , the aforementioned reflective surface is formed on the deformation film  105 . The deformation film  105  has electrical conductivity. The regions of the deformation film  105  and fixed electrode  110  are electrically connected to an external controller, and potentials can independently be applied to these regions. In order to prevent flare, it is desirable to paint the light-incidence side of the frame member  109  black, or to attach a black plate with an opening to the image area of the deformation film  105 . 
     FIG. 9  shows the shape of the fixed electrode  110 , which is so divided as to conform to the shape shown in  FIG. 5  or  FIG. 6 , and electrostatic forces applied to a central region (expressed by “1”) and to other regions of the fixed electrode  110 . If the electrostatic forces are applied in this manner, the error in shape can be limited to 100 nm or less over almost the entire region of the image area. 
   As is understood from  FIG. 9 , the number of division lines in the circumferential direction of the fixed electrode  110  is greater in the peripheral portion than in the central portion of the deformation region. This indicates that an error in the circumferential direction is greater in the outer peripheral portion than in the central portion of the deformation region, and electrostatic forces, whose intensity levels are defined in finer degrees, need to be applied to the peripheral portion. Division lines in the radial direction substantially correspond to the contour lines shown in  FIG. 6 . 
   As is understood from  FIG. 6  showing that a plurality of contour lines cross the outer periphery of the image area or the outer periphery of the deformation region, the height of the outer periphery of the deformation region is non-uniform in optical design. However, in the case of the variable-shape mirror, it is necessary, from the structural aspect thereof, to equalize the height of the outer periphery of the deformation region. To meet the requirement, the gradient in the radial direction is, in general, greater in the circumferential direction in the region between the outer periphery of the deformation region and the outer periphery of the image area. 
   In this way, the region of the electrode, which is located on the outer periphery of the deformation region, where the amount of error in the circumferential direction becomes relatively large, is divided into finer portions than the region of the electrode. Thereby, an error from the ideal shape can be reduced with a fewer number of divisions, compared to the method of simply dividing the electrode in a rectangular shape or a honeycomb shape. 
   [Second Embodiment] 
   A second embodiment of the present invention will now be described. In the first embodiment, as shown in  FIG. 9 , a considerably great electrostatic force needs to be applied to the outer peripheral region, compared to the central region. In other words, it is necessary to apply a particularly high voltage to the outer peripheral region, resulting in an increase in drive voltage. A cause of this is that the deformation film is completely fixed at the outer peripheral portion of the deformation region and a strong force is required to bend the deformation film to a large degree. 
   This problem can be solved by increasing the distance between the image area and the outer periphery of the deformation region. However, this would undesirably lead to an increase in size of the variable-shape mirror itself. The second embodiment aims at realizing a small-sized, high-shape-precision variable-shape mirror without the need to increase the drive voltage. 
     FIG. 10  shows the shape of an upper substrate of the variable-shape mirror according to the second embodiment. A circular deformation film  202  with a diameter of 7.5 mm, which is supported on a frame member  201 , has a two-layer structure. The two-layer structure comprises an aluminum film  203  with a thickness of 50 nm, which serves as a reflective film and an electrode film, and a polyimide film  204  with a thickness of 1 μm. Openings  205  are formed at regular intervals in an outer peripheral portion of the deformation film  202 . 
   The upper substrate is formed by semiconductor fabrication technology, and the openings  205  can easily be made by using ordinary photolithography technology. By forming the openings  205  in the outer peripheral portion in a discrete fashion, the flexural rigidity of the deformation film in this region is remarkably lowered. As a result, even without applying a strong electrostatic force to the outer peripheral portion of the deformation film  202 , the outer peripheral portion can be deformed in a predetermined shape. 
   For the purpose of easier understanding,  FIG. 10  shows relatively large openings. If the size of each opening is large, however, a warp may possibly occur in the reflective surface due to non-uniformity of rigidity. In fact, therefore, it is desirable to form minimum possible openings at short intervals. 
   In the second embodiment, each opening  205  is a complete through-hole. This is because it is important to discretely form regions with low flexural rigidity. Alternatively, openings  205  may be formed only in one of the aluminum film  203  or polyimide film  204 . 
   In the second embodiment, a single row of openings is formed in the circumferential direction. Alternatively, two rows of openings  205  may be formed, as shown in  FIG. 11 . If a plurality of rows of openings are formed, the flexural rigidity in the region with the openings can remarkably be decreased. 
   [Third Embodiment] 
   A third embodiment of the present invention will now be described.  FIG. 12  shows the shape of an upper substrate of a variable-shape mirror according to the third embodiment. A deformation film  302 , which is supported on a frame member  301 , has a two-layer structure. The two-layer structure comprises an aluminum film  303  with a thickness of 50 nm, which serves as a reflective film and an electrode film, and a polyimide film  304  with a thickness of 1 μm. Circular openings  305  are formed at irregular intervals in an outer peripheral portion of the deformation film  302 . In general, the variable-shape mirror applied to the configuration shown in  FIG. 4  is required to have a rotation-asymmetric deformation shape, and thus the displacement gradient of an outer peripheral portion of the deformation film toward a central portion of the deformation film varies from location to location. 
     FIG. 13  is a three-dimensional view of the deformation shape based on optical design in the third embodiment. The deformation region of the variable-shape mirror is circular with a diameter of 7.5 mm, as shown in  FIG. 12 .  FIG. 14  shows an average displacement gradient toward the central portion of the deformation region, which is plotted in the anticlockwise direction about the center of the deformation region, beginning from a location C indicated in  FIG. 12 . As is understood from  FIG. 14 , the displacement gradient is small in portions C and E in  FIG. 12 , and the displacement gradient is large in portions D and F. When an electrostatic force is applied to the deformation film  302 , it is desirable, therefore, to increase the flexural rigidity of the portions C and E and to decrease the flexural rigidity of the portions D and F. The flexural rigidity of the outer peripheral portion varies depending on the interval of openings  305 . Hence, the flexural rigidity can be decreased by decreasing the intervals. On the other hand, the flexural rigidity can be increased by increasing the intervals or by not forming the opening  305 . 
   In short, if the intervals of openings  305  are adjusted according to the displacement gradient of each location on the outer peripheral portion, the deformation shape of the deformation film  302  can be made close to that shown in  FIG. 13  without the need to greatly change the electrostatic force applied to the deformation film  302  from location to location on the deformation film  302 . 
   In the third embodiment, the size or shape of all openings  305  is made equal and the intervals of openings  305  are varied from location to location. Needless to say, the same advantages can be obtained by changing the size or shape of each opening  305  while setting equal intervals. Moreover, as in the case shown in  FIG. 11 , a difference in flexural rigidity among respective locations can be increased by forming two rows of openings  305 . 
   [Fourth Embodiment] 
   A fourth embodiment of the present invention will now be described.  FIG. 15  shows the shape of an upper substrate of a variable-shape mirror according to the fourth embodiment. A deformation film  402 , which is supported on a frame member  401 , has a two-layer structure. The two-layer structure comprises an aluminum film  403  with a thickness of 50 nm, which serves as a reflective film and an electrode film, and a polyimide film  404  with a thickness of 1 μm. Circular openings  405  are formed at irregular intervals in an outer peripheral portion of the deformation film  402 . In addition, circular openings  406  are formed at irregular intervals along a circumferentially extending portion of the deformation film  402 , which is located at a radial distance of 2 mm from the center of the deformation film  402 . A deformation shape of the deformation film  402 , which is to be obtained, is the same as that shown in  FIG. 13 , and the deformation region is also the same as shown in  FIG. 13 . Assume that the openings  405  are arranged with the same shape and intervals as the openings  305  shown in  FIG. 12 . 
     FIG. 16  shows an average displacement gradient toward the central portion of the deformation region, which is plotted in the anticlockwise direction along the circumferentially extending portion at a radial distance of 2 mm from the center of the deformation film  402 , beginning from a location G indicated in  FIG. 15 . As is understood from  FIG. 16 , the displacement gradient is large in portions G and I in  FIG. 15 , and the displacement gradient is small in portions H and J. When an electrostatic force is applied to the deformation film  402 , it is desirable, therefore, to decrease the flexural rigidity of the portions G and I and to increase the flexural rigidity of the portions H and J. The flexural rigidity of the circumferentially extending portion passing through locations GHIJ varies depending on the interval of openings  406 . Hence, the flexural rigidity can be decreased by decreasing the intervals. On the other hand, the flexural rigidity can be increased by increasing the intervals or by not forming the opening  406 . 
   In short, if the intervals of openings  406  are adjusted according to the displacement gradient of each location on the outer peripheral portion, the deformation shape of the deformation film  402  can be made close to that shown in  FIG. 13  without the need to greatly change the electrostatic force applied to the deformation film  402  from location to location on the deformation film  402 . 
   In the fourth embodiment, the size or shape of all openings  406  is made equal and the intervals of openings  406  are varied from location to location. Needless to say, the same advantages can be obtained by changing the size or shape of each opening  406  while setting equal intervals. 
   Moreover, like the case shown in  FIG. 11 , a difference in flexural rigidity among respective locations can be increased by forming two rows of openings  406 . In the fourth embodiment, for the purpose of simple description, the openings  406  are arranged only along the circumferentially extending portion GHIJ on the deformation film  402 . Needless to say, openings  406  may be arranged over the entire area of the deformation film  402  with a density corresponding to the displacement gradient. 
   In addition, even if the openings  406  are formed on the circumferentially extending portion GHIJ or over the entire area of the deformation film  402  at a uniform density, the rigidity of the deformation film  402  can advantageously be decreased and this contributes to a decrease in drive voltage. Unlike the second and third embodiments, in the fourth embodiment wherein the openings  406  are formed in the image area, the focusing performance of the optical system is inevitably degraded to some degree. Thus, the number of openings  406  is determined based on a tolerable decrease in focusing performance. From two standpoints, i.e. diffraction and optical loss at end portions, it is desirable that the size of each opening  406  be as small as possible. In particular, it is desirable that the size of each opening  406  be set to have a diameter not greater than a wavelength of light. 
   In the fourth embodiment, openings  405  and  406  are provided along two circumferentially extending portions, one being located near the outer periphery and the other being located at a radial distance of 2 mm from the center. Alternatively, openings may be arranged on more than two circumferentially extending portions at a density corresponding to the displacement gradient along these circumferentially extending portions, or openings may be arranged over the entire area of the deformation film at a density corresponding to the displacement gradient of the deformation shape to be obtained. In the fourth embodiment, the deformation film  402  is circular. However, the embodiment is applicable even when the deformation film  402  has another shape such as an oval shape. 
   The second to fourth embodiments have been described, presupposing the configuration of the electrostatic drive type variable-shape mirror according to the first embodiment. However, these embodiments are applicable to an electromagnetic variable-shape mirror wherein a coil is formed on the deformation film and a magnet for producing a magnetic field crossing the coil at right angles is disposed. As is described in Jpn. Pat. Appln. KOKAI Publication No. 8-334708, for instance, in the case of a small-sized electromagnetic variable-shape mirror, it is difficult, from structural aspects, to apply different forces to respective locations on the deformation film. Thus, the method of providing a rigidity distribution to the deformation film, as shown in the second to fourth embodiments, is particularly effective in consideration of the shape control performance. 
   A method of fabricating the upper substrate of the variable-shape mirror according to the fourth embodiment will now be described referring to  FIG. 17A  through  FIG. 17D . To begin with, as shown in  FIG. 17A , silicon nitride films  452  are formed on both surfaces of a silicon substrate  451 . An opening portion  453  is formed in the back-side silicon nitride film  452  by an ordinary photolithography technique. Then, as shown in  FIG. 17B , a polyimide film  404  with a thickness of 1 μm is formed by on the upper-side silicon nitride film  452  by spin coat method. Openings  405  and  406  are formed at predetermined locations on the polyimide film  404  by photolithography. Subsequently, as shown in  FIG. 17C , with the upper side being protected, the silicon substrate is etched from the back side through the opening portion  453  in the silicon nitride film  452  using an alkaline aqueous solution, until the upper-side silicon nitride film  452  is exposed. In this case, the residual portion of the silicon substrate  451  becomes the frame member  401  of the upper substrate. Next, as shown in  FIG. 17D , the exposed upper-side silicon nitride film  452  is etched from the back side by reactive ion etching. Thereafter, an aluminum film  403  with a thickness of 50 nm is formed on the upper surface of the polyimide film  404  by means of sputtering or evaporation. At this time, the openings  405  and  406  become through-holes by setting the size of each opening  405 ,  406  to be sufficiently greater than the thickness of the aluminum film  403 . The aluminum film  403  serves as a reflective surface and an electrode for applying electrostatic force. 
   As described above, a great number of fine through-holes can easily be formed with high precision by photolithography. 
   Another method of fabricating the upper substrate of the variable-shape mirror is described referring to  FIGS. 18A to 18D . To begin with, as shown in  FIG. 18A , silicon nitride films  452  are formed on both surfaces of a silicon substrate  451 . An opening portion  453  is formed in the back-side silicon nitride film  452  by an ordinary photolithography technique. Then, as shown in  FIG. 18A , a polyimide film  404  with a thickness of 1 μm and an aluminum film  403  with a thickness of 50 nm are formed on the upper-side silicon nitride film  452  by spin coat method. Subsequently, as shown in  FIG. 18B , openings  454  and  455  are formed in the aluminum film  403  by ordinary photolithography. The positions of these openings correspond to those of the openings  405  and  406  in  FIG. 17B . Thereafter, as shown in  FIG. 18C , with the upper side being protected, the silicon substrate is etched from the back side through the opening portion  453  in the silicon nitride film  452  using an alkaline aqueous solution until the upper-side silicon nitride film  452  is exposed. Next, as shown in  FIG. 18D , the exposed upper-side silicon nitride film  452  is etched from the back side by reactive ion etching. 
   In the upper substrate formed by this fabrication method, the openings  454  and  455  are not through-holes. However, since the rigidity of the deformation film in this region with the openings is decreased, the similar advantage to the case of the through-holes can be expected although there is a difference to some degree. 
   [Fifth Embodiment] 
   A fifth embodiment of the present invention will now be described.  FIG. 19  shows the structure of the electrode on the lower substrate in the fifth embodiment. A lower electrode  503  is formed on a silicon substrate  501  via an insulating film  502 . A great number of openings  504  are formed in a central region of the lower electrode  503 . In addition, spacers  505  are formed on the outside of the lower electrode  503 . The spacers  505  correspond to the spacers  108  in  FIG. 8 . Assume that the upper substrate to be bonded to the lower electrode has openings at irregular intervals in an outer peripheral portion of the deformation region thereof, as shown in  FIG. 15 . In operation of the variable-shape mirror of this embodiment, the deformation film and the silicon substrate  501  are grounded and a voltage is applied to the lower electrode  503 . 
   In the case of the upper substrate described in connection with the third embodiment, the flexural rigidity is varied in accordance with the displacement gradient in the circumferential direction of the outer peripheral portion. Thereby, the deformation shape is made close to the optical design shape. In general, however, if a uniform potential difference is applied to the deformation region thereby to produce an electrostatic force, an error occurs between the actual shape and the ideal shape. Thus, as in the first embodiment, the lower electrode needs to be divided into some regions, although the number of divided regions may be less than in the case where no opening is formed in the deformation film. 
   In the fifth embodiment, however, openings are formed in a portion of the lower electrode. Thereby, a distribution is provided to the electrostatic force acting on the deformation film, and thus the deformation shape is controlled. If the technique of the fifth embodiment is compared to that of the fourth embodiment, a drive voltage becomes higher since there is no advantage of decreasing the rigidity of the deformation film itself excluding the outer peripheral portion. However, there is no degradation in the focusing performance due to diffraction at openings in the deformation film. Therefore, in the variable-shape mirror of the fifth embodiment, the deformation film can be deformed in a predetermined shape with a single drive voltage or a very small number of drive voltages. Hence, the control circuit can be simplified, contributing to a decrease in cost and size. 
   For the purpose of simple description, in the fifth embodiment, relatively large openings are arranged at uniform density in the central region. However, the density of openings is decreased in a region where a large electrostatic force needs to be applied to deform the deformation film into a predetermined shape. On the other hand, in a region where a small electrostatic force needs to be applied, it is desirable that the density of openings be increased and the size of each opening be reduced as much as possible. 
   In the fifth embodiment, in order to provide a predetermined distribution to the electrostatic force acting on the deformation film, the openings are arranged at different densities on regions of the lower electrode. It should suffice, however, if the ratio of the region of the lower electrode, which is opposed to the deformation film and is supplied with a potential different from a potential applied to the deformation film, varies from location to location. 
   Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.