A piezoelectric actuator for use in a deformable mirror, comprising: a level connector, comprising a first connection surface and a second connection surface which are parallel and opposite to each other, a first piezoelectric single crystal and a second piezoelectric single crystal, both of rectangular shapes, and a third piezoelectric single crystal and a fourth piezoelectric single crystal, all of rectangular shapes, wherein one end of the first piezoelectric single crystal and one end of the second piezoelectric single crystal are bonded onto the first connection surface of the level connector and one end of the third piezoelectric single crystal and one end of the fourth piezoelectric single crystal are bonded onto the second connection surface of the level connector, thereby forming a two-layered structure, such that both the first and second piezoelectric single crystals are spaced apart and parallel to one another both in their length, or axial, direction and in their width direction, that both the first and the second piezoelectric single crystals are adapted to extend or contract in their length direction causing the plane connecting to both free ends of the first and second single crystals to displace axially and to tilt about an axis parallel to the width direction of both crystals under effect of externally applied electric fields, that both the third and fourth piezoelectric single crystals (121, 122) are spaced apart and parallel in both their length, or axial, direction and in their width direction, their axial direction being the same but their width direction being at an angle to the axial and width directions, respectively, of the first and second piezoelectric crystals (111, 112), and that both the third and fourth piezoelectric single crystals (121, 122) are adapted to extend or contract in their length direction causing the plane connecting to the free ends of both the third and fourth single crystals to displace axially and to tilt about a different axis which is parallel to the width direction of the third and fourth piezoelectric single crystals under effect of externally applied electric fields; and a base and a pedestal, wherein the free ends of the first and second piezoelectric single crystals (111, 112) are both bonded onto the upper surface of the base, and the free ends of the third and fourth piezoelectric single crystals (121, 122) are both bonded onto the lower surface of the pedestal; wherein the top face of the pedestal is able to display three-degree-of-freedom displacement actuation, and wherein a first layer of the two-layered structure is composed of the first piezoelectric single crystal and the second piezoelectric single crystal and a second layer of the two-layered structure is composed of the third piezoelectric single crystal and the fourth piezoelectric single crystal. a level connector, comprising a first connection surface and a second connection surface which are parallel and opposite to each other, a first piezoelectric single crystal and a second piezoelectric single crystal, both of rectangular shapes, and a third piezoelectric single crystal and a fourth piezoelectric single crystal, all of rectangular shapes, wherein one end of the first piezoelectric single crystal and one end of the second piezoelectric single crystal are bonded onto the first connection surface of the level connector and one end of the third piezoelectric single crystal and one end of the fourth piezoelectric single crystal are bonded onto the second connection surface of the level connector, thereby forming a two-layered structure, such that both the first and second piezoelectric single crystals are spaced apart and parallel to one another both in their length, or axial, direction and in their width direction, that both the first and the second piezoelectric single crystals are adapted to extend or contract in their length direction causing the plane connecting to both free ends of the first and second single crystals to displace axially and to tilt about an axis parallel to the width direction of both crystals under effect of externally applied electric fields, that both the third and fourth piezoelectric single crystals (121, 122) are spaced apart and parallel in both their length, or axial, direction and in their width direction, their axial direction being the same but their width direction being at an angle to the axial and width directions, respectively, of the first and second piezoelectric crystals (111, 112), and that both the third and fourth piezoelectric single crystals (121, 122) are adapted to extend or contract in their length direction causing the plane connecting to the free ends of both the third and fourth single crystals to displace axially and to tilt about a different axis which is parallel to the width direction of the third and fourth piezoelectric single crystals under effect of externally applied electric fields; and a base and a pedestal, wherein the free ends of the first and second piezoelectric single crystals (111, 112) are both bonded onto the upper surface of the base, and the free ends of the third and fourth piezoelectric single crystals (121, 122) are both bonded onto the lower surface of the pedestal; wherein the top face of the pedestal is able to display three-degree-of-freedom displacement actuation, and wherein a first layer of the two-layered structure is composed of the first piezoelectric single crystal and the second piezoelectric single crystal and a second layer of the two-layered structure is composed of the third piezoelectric single crystal and the fourth piezoelectric single crystal.