Abstract:
The present invention provides a small and fast zoom system using micromirror array lens (MMAL). Thanks to the fast response and compactness of the MMAL as well as absence of the macroscopic mechanical movements of lenses, the zoom system of the present invention fastens the speed of the zooming and reduces the space and weight for the zoom system. Also the present invention provides magnifying the area not on the optical axis and can compensate the aberration of the zoom system.

Description:
REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation-in-part of, and claims priority to U.S. patent application Ser. No. 10/806,299 filed Mar. 22, 2004, now U.S. Pat. No. 7,057,826 U.S. patent application Ser. No. 10/855,715 filed May 27, 2004, now U.S. Pat. No. 7,031,046 U.S. patent application Ser. No. 10/872,241 filed Jun. 18, 2004, U.S. patent application Ser. No. 10/893,039 filed Jul. 16, 2004, U.S. patent application Ser. No. 10/983,353 filed Nov. 8, 2004, U.S. patent application Ser. No. 10/896,146 filed Jul. 21, 2004, now U.S. Pat. No. 7,215,882 U.S. patent application Ser. No. 11/072,597 filed Mar. 4, 2005, U.S. patent application Ser. No. 11/076,616 filed Mar. 10, 2005, U.S. patent application Ser. No. 11/191,886 filed Jul. 28, 2005, now U.S. Pat. No. 7,095,548 U.S. patent application Ser. No. 11/218,814 filed Sep. 2, 2005, and U.S. patent application Ser. No. 11/369,797 filed Mar. 6, 2006, all of which are hereby incorporated by reference. 

   FIELD OF INVENTION 
   The present invention relates to an optical zoom device and operational methods for the device. 
   BACKGROUND OF THE INVENTION 
   Conventional zoom devices require coupled mechanical motions to adjust the axial separations between individual or group elements in order to change the optical magnification as disclosed in U.S. Pat. No. 3,970,367 to Tsuji, U.S. Pat. No. 3,975,089 to Betensky, U.S. Pat. No. 4,097,124 to Watanabe, and U.S. Pat. No. 4,189,213 to Iizuka. 
     FIG. 1  illustrates a conventional mechanical zoom system. At the very basic level, a zoom system includes at least one moving lens for zooming. One lens or group of lenses to change the image size is called the variator  11  and another lens or group or lenses to maintain focus throughout the zoom range is called the compensator  12 . The variator  11  is moved to change the image size of an object. However, the image is defocused because the imaging position is also changed while the variator changes the image size of the object. Therefore, the variator  12  must move in unison with the compensator lens  12  to zoom and keep the image  13  in-focus. These movements are usually mechanically controlled by a zoom ring on the lens barrel. 
   The mechanical motions decrease the speed of zooming, increase space and weight as well as the power consumption and possibly induce of unwanted jitter. In addition, the mechanical zoom system is restricted to magnifying the area on-axis. 
   U.S. Pat. No. 4,407,567 to Michelet discloses a zoom device comprising piezoelectric multilayer structures. This system requires a high voltage, a large structure, a high manufacturing and maintenance cost, which make it difficult to implement in the small portable devices such as camera phone, PDA, portable computer, etc. 
   U.S. Pat. No. 4,190,330 to Berreman discloses a variable focus system comprising a nematic liquid crystal material. Its focal length is changed by modulating the refractive index. It has a slow response time typically on the order of hundreds of milliseconds. Even though the fastest response liquid crystal lens has the response time of tens of milliseconds, it has small focal length variation and low focusing efficiency. 
   Therefore, there has been a need for a small and fast zoom device that can change magnification. 
   SUMMARY OF THE INVENTION 
   The present invention contrives to solve the disadvantages of conventional zoom systems described in the above section. 
   An objective of the invention is to provide a small and fast zoom system without macroscopic mechanical movements of lens or lenses. 
   Another object of the invention is to provide a zoom system that consumes minimal power. 
   Still another object of the invention is to provide a zoom system that can compensate for the aberration of the system. 
   Still another object of the invention is to provide a zoom system that can have a variable optical axis. 
   To achieve the above objectives, the zoom system comprises one or more MMALs, wherein the MMAL comprises a plurality of micromirrors, wherein the focal length of the MMAL is changed by controlling the translation and/or rotation of each micromirror of the MMAL, wherein each micromirror of the MMAL is actuated by the electrostatic force. 
   The MMAL comprises a plurality of micromirrors to reflect light. The following U.S. patents and applications describe the MMAL: U.S. Pat. No. 6,934,072 to Kim, U.S. Pat. No. 6,934,073 to Kim, U.S. Pat. No. 6,970,284 to Kim, U.S. Pat. No. 6,999,226 to Kim, U.S. Pat. No. 7,031,046 to Kim, U.S. patent application Ser. No. 10/857,714 filed May 28, 2004, U.S. patent application Ser. No. 10/893,039 filed Jul. 16, 2004, and U.S. patent application Ser. No. 10/983,353 filed Nov. 8, 2004, all of which are hereby incorporated by reference. 
   The MMAL comprising micromirrors provides a very fast response time, a large focal length variation, a high optical focusing efficiency, a simple focusing structure, low power consumption, and a low production cost thanks to the mass production advantage. Also, the MMAL is an adaptive optical component which compensates aberration of the system and changes the optical axis without macroscopic mechanical movements of lenses. 
   A zoom system changing the magnification of an imaging system without macroscopic mechanical movements of lenses comprises a first MMAL and a second MMAL. The focal length of each MMAL is changed to form an image in-focus at a given magnification. The translation and/or rotation of each micromirror in the MMALs are controlled to change the focal lengths of the MMALs. Each micromirror of the MMALs is actuated by electrostatic force and/or electromagnetic force. 
   The zoom system includes a beam splitter positioned between the first MMAL and the second MMAL, as illustrated in  FIG. 3   a . Alternatively, the first MMAL and the second MMAL are positioned so that the path of the light reflected by the first MMAL and the second MMAL is not blocked as illustrated in  FIG. 3   b . The MMAL can be tilted in the zoom system so that the normal direction of the MMAL is different from the optical axis of the zoom system. When the MMAL is tilted about an axis, which is perpendicular to the optical axis, the surface profile of the MMAL is symmetric about an axis which is perpendicular to the normal direction of the MMAL and tilting axis. 
   The zoom system may further include a focus lens group to focus an image, an erector lens group to produce the bottom-side-up mirror image, and a relay lens group to focus the image onto the image sensor while the first MMAL forms a variator lens group, and the second MMAL forms a compensator lens group. 
   Furthermore, a conventional moving lens or a variable focal length lens can be used as a variator or a compensator while a MMAL is being used as the other. 
   Since the MMAL is an adaptive optical element, the zoom system can compensate for the aberration of the system by controlling each micromirror of the MMAL. The aberration of the system include, but not limited to, phase errors of light introduced by the medium between an object and its image and the defects of the zoom system that may cause the image to deviate from the rules of paraxial imagery. Further, an object which does not lie on the optical axis can be imaged by the MMAL without macroscopic mechanical movements of the zoom system. 
   The MMAL is further controlled to compensate for chromatic aberration by satisfying the same phase condition for each wavelength of Red, Green, and Blue (RGB) or Yellow, Cyan, and Magenta (YCM), respectively, to get a color image. The zoom system may further include a plurality of bandpass filters for color imaging. Also, the zoom system may further include a photoelectric sensor. The photoelectric sensor includes Red, Green, and Blue (RGB) or Yellow, Cyan, and Magenta (YCM) sensors. A color image is obtained by treatment of electrical signals from the corresponding colored sensors. The treatment of electrical signals from corresponding colored sensors is synchronized and/or matched with the control of the MMAL to satisfy the same phase condition for each wavelength respectively. Instead of satisfying three different wavelength phase matching condition, the MMAL can be controlled to satisfy phase matching condition at an optimal wavelength to minimize chromatic aberration. Even though the image quality of color is not perfect, this optimal wavelength phase matching can also be used for getting a color image. 
   The zoom system may further include optical filters for image enhancement. 
   The present invention is summarized again to facilitate understanding the structure of the claims. 
   The present invention provides a zoom system that includes one or more micromirror array lenses (MMALs). The MMAL includes a plurality of micromirrors. The focal length of the MMAL is changed by controlling the translation and/or rotation of each micromirror of the MMAL. 
   In one aspect of the invention, the zoom system includes a first MMAL having a plurality of micromirrors; and a second MMAL having a plurality of micromirrors, and optically coupled to the first MMAL. The first MMAL is closer to the object side of the zoom system, and the second MMAL is closer to the image side of the zoom system. 
   The first MMAL is a variator to control magnification of the zoom system by controlling the micromirrors and the second MMAL is a compensator to maintain focus throughout the zoom range by controlling the micromirrors. 
   Alternatively, the first MMAL is a compensator to maintain focus throughout the zoom range by controlling the micromirrors and the second MMAL is a variator to control magnification of the zoom system by controlling the micromirrors. 
   Alternatively, the first MMAL and the second MMAL both control magnification and maintain focus of the zoom system by controlling the micromirrors. 
   The first MMAL and the second MMAL are positioned so that the path of the light reflected by the first MMAL and the second MMAL is not blocked. 
   Alternatively, the zoom system includes a beam splitter positioned between the first MMAL and the second MMAL. 
   The zoom system may further include an auxiliary lens or group of lenses. The auxiliary lens or group of lenses include a focus lens, an erector lens and/or a relay lens. 
   In another aspect of the invention, the zoom system includes a fixed-focus lens or a group of fixed-focus lenses having mechanical motion; and a MMAL including a plurality of micromirrors. 
   The fixed-focus lens or group of fixed-focus lenses having mechanical motion is a variator to control magnification of the zoom system and the MMAL is a compensator to maintain focus throughout the zoom range by controlling the micromirrors. 
   Alternatively, the MMAL is a variator to control magnification of the zoom system by controlling the micromirrors and the fixed-focus lens or a group of fixed-focus lenses having mechanical motion is a compensator to maintain focus throughout the zoom range. 
   Alternatively, the fixed-focus lens or group of fixed-focus lenses having mechanical motion and the MMAL both control magnification and maintain focus of the zoom system by controlling the position of the conventional lens or a group of lenses and/or controlling micromirrors. 
   The zoom system may further include an auxiliary lens or group of lenses. The auxiliary lens or group of lenses include a focus lens, an erector lens and/or a relay lens. 
   In still another aspect of the invention, the zoom system includes a non-MMAL variable focus lens, wherein the focal length of the non-MMAL lens is changed; and a MMAL including a plurality of micromirrors. The MMAL is optically coupled to the non-MMAL variable focus lens. A non-MMAL optical element includes all optical elements that are constructed without MMAL technology. 
   The he non-MMAL variable focus lens is a variator to control magnification of the zoom system and the MMAL is a compensator to maintain focus throughout the zoom range by controlling the micromirrors. 
   Alternatively, the non-MMAL variable focus lens is a compensator to maintain focus throughout the zoom range and the MMAL is a variator to control magnification of the zoom system by controlling the micromirrors. 
   Alternatively, the non-MMAL variable focus lens and the MMAL both control magnification and maintain focus of the zoom system by controlling the focal length of the variable focus lens and controlling micromirrors. 
   The zoom system may further include an auxiliary lens or group of lenses. The auxiliary lens or group of lenses include a focus lens, an erector lens and/or a relay lens. 
   In still another aspect of the invention, the zoom system includes one MMAL including a plurality of micromirrors. The MMAL controls the magnification of the zoom system by controlling the micromirrors. The zoom system has a large depth of focus, whereby a pan focus zoom system is provided. 
   The zoom system may further include an auxiliary lens or group of lenses. The auxiliary lens or group of lenses comprise a focus lens, an erector lens and/or a relay lens. 
   Features common to all the aspects of the present invention are explained below: 
   The MMAL is tilted in the zoom system so that the normal direction of the MMAL is different from the optical axis of the zoom system. The profile of MMAL is symmetric about an axis which is perpendicular to the normal direction of the MMAL and the tilting axis. 
   The optical axis of MMAL is changed by controlling micromirrors. 
   The MMAL compensates for the aberration of the system by controlling micromirrors. The aberration is caused by phase errors of light introduced by the medium between an object and its image, or the aberration is caused by the zoom system. 
   The zoom system may further include an extra MMAL or MMALs to compensate for the aberration of the system including chromatic aberration. 
   The MMAL is further controlled to compensate for chromatic aberration by satisfying the same phase condition for each wavelength of Red, Green, and Blue (RGB) or Yellow, Cyan, and Magenta (YCM), respectively, to get a color image. 
   The MMAL is controlled to satisfy phase matching condition at an optimal wavelength to minimize chromatic aberration. The optimal wavelength phase matching is used for getting a color image. 
   The zoom system may further include an optical filter or filters for image enhancement. 
   The zoom system may further include an auxiliary lens or group of lenses. The auxiliary lens or group of lenses comprise a focus lens, an erector lens and/or a relay lens. 
   Each micromirror of the MMAL is actuated by electrostatic force. 
   The zoom system of the present invention has advantages: (1) a compact zoom system is provided; (2) the system has a very high zooming speed; (3) the system has a large variation of magnification; (4) the system has a variable optical axis; (5) the system has a high optical efficiency; (6) the cost is inexpensive because the MMAL is inexpensive and the macroscopic mechanical movements of lenses are not necessary; (7) the system compensates for the aberration of the system; (8) the system has a very simple structure because there is no macroscopic mechanical movements of lenses; (9) the system requires small power consumption when the MMAL is actuated by electrostatic force. 
   Although the present invention is briefly summarized, the full understanding of the invention can be obtained by the following drawings, detailed description, and appended claims. 

   
     DESCRIPTION OF THE FIGURES 
     These and other features, aspects and advantages of the present invention will become better understood with reference to the accompanying drawings, wherein: 
       FIG. 1  is a schematic diagram showing a conventional mechanical zoom system; 
       FIG. 2  shows a zoom system using one or more variable focal length lenses; 
       FIGS. 3   a  and  3   b  show zoom systems using one or more micromirror array lenses (MMALs); 
       FIG. 4  illustrates a zoom system using two micromirror array lenses (MMALs); 
       FIG. 5  illustrates a zoom system comprising a MMAL and a conventional lens or a group of conventional lenses having mechanical motion; 
       FIGS. 6   a  and  6   b  illustrate a zoom system comprising a MMAL and a conventional variable focus lens; 
       FIG. 7  illustrates a zoom system with a MMAL for pan focus zooming system; 
       FIGS. 8   a  and  8   b  are schematic representations for optical axis changes in the MMAL; 
       FIG. 9   a  is a schematic diagram showing how a refractive Fresnel lens replaces an ordinary single-bodied lens; 
       FIG. 9   b  is a schematic diagram showing how a reflective Fresnel lens replaces an ordinary single-bodied mirror; 
       FIG. 10  is a schematic plan view showing a MMAL that is made of many micromirrors. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 2  shows a zoom system  21  using one or more variable focal length lenses. In the embodiment shown in  FIG. 2 , the zoom system includes a first variable focal length lens  22  and a second variable focal length lens  23 . Changing the magnification of an imaging system is accomplished by utilizing the variable focal length lenses  22 ,  23 . The first variable focal length lens  22  changes the image size. But, the image is defocused because the imaging position is also changed. Therefore, the focal length of the two variable focal length lenses  22 ,  23  must be changed in unison to magnify and keep the image  24  in-focus. 
     FIG. 3   a  shows a zoom system  31 , in which MMALs  32  and  33  are used as variable focal length lenses  32  and  33 . Since the MMALs  32  and  33  are reflective types, it is impossible to make an in-line optical arrangement without additional optical elements. Therefore, the zoom system  31  includes a beam splitter  34  positioned in the path of light  35  between the first MMAL  32  and the second MMAL  33 . The beam splitter  34  changes the direction of the light  35  by 90 degrees, and thus simulates an in-line optical arrangement. As shown in  FIG. 3   a , the total size of the zoom system  31  is less than a conventional mechanical zoom system because necessary separation requirements between the variator and the compensator and between the compensator and an imaging sensor can be satisfied by a beam splitter  34  and the MMALs  32  and  33  in a small space. 
     FIG. 3   b  shows a zoom system  36 , in which MMALs  37  and  38  are used as variable focal length lenses  32  and  33 . Since it is impossible to make an in-line optical arrangement with MMALs  37  and  38 , the first MMAL  37  and the second MMAL  38  are positioned so that the path of the light  39  reflected by the first MMAL  37  and the second MMAL  38  is not blocked by other components. This arrangement also can reduce the total size of the zoom system  36 . 
   Since the positions of MMALs  32 ,  33 ,  37 , and  38  need not be changed, the zoom systems  31 ,  36  do not need space for lens movements, thus the zoom system  31  and  36  can be manufactured with a compact size. Also the power consumption of the zoom systems  31  and  36  is minimal since there is no need to have macro movements of the MMALs  32 ,  33 ,  37 , and  38 . 
   The zoom systems  31  and  36  may include five groups of lenses to get necessary and auxiliary performances of a zoom system instead of two variable focal length lenses. They are a focus lens group, a variator lens group, a compensator lens group, an erector lens group, and a relay lens group. Even though the zoom system using MMALs is explained with two lenses, actual zoom system using MMALs also may have some groups of lenses. 
     FIG. 4  illustrates a zoom system according to one embodiment of the present invention using two or more micromirror array lenses (MMALs). The zoom system comprises a first MMAL  41  comprising a plurality of micromirrors  42  and a second MMAL  43  comprising a plurality of micromirrors  42 , wherein the second MMAL  43  is optically coupled to the first MMAL  41 . The zoom system may further comprise a first auxiliary lens group  44  and a second auxiliary lens group  45 . In figures, lens groups are schematically illustrated by a lens for simplicity. It should be noted that in practice, each lens group may include a different kind and different number of lenses to satisfy system requirements. The first auxiliary lens group  44  is a focus lens group to bring the object into focus. 
   The first MMAL  41  is a variator to control magnification of the zoom system by controlling the rotation and/or translation of micromirrors  42 . The second MMAL  43  is a compensator to maintain focus throughout the zoom range by controlling the rotation and/or translation of micromirrors  42 . The second auxiliary lens group  45  is a relay lens group to focus the image onto an image sensor  46 . The optical axis can be changed by controlling rotation and/or translation of micromirrors  42  of the MMALs  41  and  43 , as will be explained in  FIG. 8 . Further, each micromirror  42  of the MMALs  41  and  43  can be controlled to compensate for the aberration of the system. In one alternative embodiment, the first MMAL  41  is used as a compensator to maintain focus throughout the zoom range while the second MMAL  43  is used as a variator to control magnification of the zoom system by controlling the micromirrors  42 . In another alternative embodiment, the first MMAL  41  and the second MMAL  43  both control magnification and maintain focus of the zoom system altogether by controlling the micromirrors  42 . 
   The zoom system may further comprise an additional auxiliary lens group  47  as an erector lens group in order to produce an inverted image. Also the auxiliary lens or group of lenses  47  can be used for further enhancement of the zoom system. The zoom system may further comprise extra MMAL or MMALs to compensate for the aberration of the system including chromatic aberration. The zoom system may further comprises an optical filter or filters for image enhancement. Since the zoom system of the present invention does not have macroscopic moving elements, the zoom system can be built in a simple and compact structure with advantages including low power consumption, low cost, and high zooming speed. 
     FIG. 5  illustrates a zoom system according to another embodiment of the present invention by replacing one of the MMALs in  FIG. 4  with a conventional lens or a group of conventional lenses having mechanical motion. The zoom system comprises a conventional lens or a group of convention lenses  51  having mechanical motion and a MMAL  52  comprising a plurality of micromirrors  53 , wherein the MMAL  52  is optically coupled to conventional lens or a group of conventional lenses  51 . The zoom system may further comprise a first auxiliary lens group  54  and a second auxiliary lens group  55 . The first auxiliary lens group  54  is a focus lens group to bring the object into focus. The conventional lens or group of conventional lenses  51  having mechanical motion is a variator to control magnification of the zoom system and the MMAL  52  is a compensator to maintain focus throughout the zoom range by controlling the rotation and/or translation of the micromirrors  53 . The second auxiliary lens group  55  is a relay lens group to focus the image onto an image sensor  56 . The optical axis can be changed by controlling rotation and/or translation of micromirrors  53  of the MMAL  52 . Each micromirror  53  of the MMAL  52  can be controlled to compensate for the aberration of the system. The zoom system may further comprise a MMAL to compensate for the aberration of the system including chromatic aberration. In one alternative embodiment, the MMAL  52  is used as a variator to control magnification of the zoom system by controlling the micromirrors  53 , while the conventional movable lens or group of conventional lenses  51  having mechanical motion is used as a compensator to maintain focus throughout the zoom range. In another alternative embodiment, the conventional lens or group of conventional lenses  51  having mechanical motion and the MMAL  52  both control magnification and maintain focus of the zoom system by controlling the position of the conventional lens or group of lenses  51  and/or by controlling the micromirrors  53 . The zoom system of the present invention has less moving elements than those of conventional zoom systems. 
     FIG. 6   a  illustrates a zoom system according to another embodiment of the present invention by replacing one of the MMALs in  FIG. 4  with a conventional variable focus lens. The zoom system comprises a conventional variable focus lens  61 , wherein the focal length of the lens is changed and a MMAL  62  comprising a plurality of micromirrors  63 , wherein the MMAL  62  is optically coupled to the conventional variable focus lens  61 . The zoom system may further comprise a first auxiliary lens group  64  and a second auxiliary lens group  65 . The first auxiliary lens group  64  is a focus lens group to bring the object into focus. The variable focus lens  61 , which is a conventional variable focal length lens such as liquid crystal lenses, is a variator to control magnification of the zoom system. The MMAL  62  is a compensator to maintain focus throughout the zoom range by controlling the rotation and/or translation of micromirrors  63 . In one alternative embodiment, the MMAL  62  is used as a variator to control magnification of the zoom system by controlling the micromirrors  63 , while the conventional variable focus lens  61  is used as a compensator to maintain focus throughout the zoom range. In another alternative embodiment, the conventional variable focus lens  61  and the MMAL  62  both control magnification and maintain focus of the zoom system by controlling the focal length of the variable focus lens  61  and/or by controlling micromirrors  63 . The second auxiliary lens group  65  is a relay lens group to focus the image onto an image sensor  66 . The optical axis can be changed by controlling rotation and/or translation of micromirrors  63  of the MMAL  62 . Each micromirror  63  of the MMAL  62  can be controlled to compensate for the aberration of the system. As shown in  FIG. 6   b , the zoom system may further comprise extra MMAL  67  to compensate for the aberration of the system including chromatic aberration. Since the zoom system of the present invention does not have macroscopic moving elements, the zoom system can be built in a simple and compact structure with advantages including low power consumption, low cost, and high zooming speed. 
     FIG. 7  illustrates a zoom system with a pan focus having one MMAL  71  comprising a plurality of micromirrors  72  wherein the MMAL  71  controls the magnification of the zoom system by controlling the micromirrors  72 . The zoom system may further comprise a first auxiliary lens  73  and a second auxiliary lens  74 . The first auxiliary lens group  73  is a focus lens group to bring the object into focus. The MMAL  71  is a variator to control magnification of the zoom system by controlling the rotation and/or translation of micromirrors  72 . By using large depth of focus in the zoom system, the system removes the variable compensator part and performs zoom function with pan focus. The second auxiliary lens group  74  is a relay lens group to focus the image onto an image sensor  75 . The optical axis can be changed by controlling rotation and/or translation of micromirrors  72  of the MMAL  71 . Each micromirror  72  of the MMAL  71  can be controlled to compensate for the aberration of the system. This embodiment can be applied to a zoom system having a long depth of focus without introducing compensator group lens or lenses. Smaller aperture and longer focal length, longer depth of focus. This embodiment is advantageous to a low cost, small zoom system having a long depth of focus such as cellular phone, PDA, and potable computer since it does not require a compensator. 
     FIGS. 8   a  and  8   b  show how the optical axis of the MMAL changes. The optical axis of the MMAL  81  is changed by controlling the micromirrors  82 . A bunch of light is focused by the MMAL  81 . In  FIG. 8   a , a cube object  83  is imaged onto the image plane. The light  84 A from the object  83  is reflected by each of the micromirror  82 . The reflected light  85 A is focused onto the focal point  86 A of the image and finally makes an image of a cube  87 A in the image sensor. During the focusing process the optical axis is defined as a surface normal direction  88 A of a micromirror  82 . 
   As shown in  FIG. 8   b , the MMAL can make a different image  87 B from a different object  89  without macroscopic movements. By changing the respective angles of the micromirrors  82 , this time the MMAL accepts the light  84 B from the sphere  89 . The reflected light  85 B is focused onto a focal point  86 B and makes the image of the sphere  87 B. This time the optical axis is changed by an angle and becomes the surface normal direction  88 B of a micromirror. 
     FIG. 9   a  schematically shows how a refractive Fresnel lens  91 A replaces an ordinary single-bodied lens  92 .  FIG. 9   b  shows how a reflective Fresnel lens  91 B replaces an ordinary single-bodied mirror  93 . The reflective Fresnel lens can be formed using a MMAL. The MMAL includes a plurality of micromirrors which represents the discrete parts of the reflective Fresnel lens  94 , and each micromirror is controlled to form a reflective Fresnel lens and to change the focal length of the lens. 
   In order to obtain a bright and sharp image, the variable focal length MMAL must meet the two conditions for forming a lens. One is that all the rays should be converged into the focus, and the other is that the phase of the converged rays must be the same. Even though the rays have different optical path lengths, the same phase condition can be satisfied by adjusting the optical path length difference to be integer multiples of the wavelength of the light. Each facet converges rays to one point, and rays refracted or reflected by different facets have an optical path length difference of integer multiples of the incident light. 
   To change the focal length of the MMAL, the translational motion and/or the rotational motion of each of the micromirrors are controlled to change the direction of light and to satisfy the phase condition of the light. 
   The variable focal length MMAL is also an adaptive optical component compensating for the aberration of the zoom system by controlling the translational motion and/or the rotational motion of each micromirror. 
     FIG. 10  shows a MMAL  101  comprising a plurality of micromirrors  102  arranged to form many concentric circles. The micromirrors  102  are arranged in a flat plane as shown in  FIG. 9   b.    
   The MMAL used in the present invention has advantages: (1) the MMAL has a very fast response time because each micromirror has a tiny mass; (2) the MMAL has a large focal length variation because large numerical aperture variations can be achieved by increasing the maximum rotational angle of the micromirror; (3) the MMAL has a high optical focusing efficiency; (4) the MMAL can have a large size aperture without losing optical performance. Because the MMAL includes discrete micromirrors, the increase of the lens size does not enlarge the aberration caused by shape error of a lens; (5) the cost is inexpensive because of the advantage of mass productivity of microelectronics manufacturing technology; (6) the MMAL can compensate for the aberration of the system; (7) the MMAL makes the focusing system simple; (8) the MMAL requires small power consumption when electrostatic actuation is used to control it.