Fractal tiling for multiple mirror optical devices

Claim 2

An optical device, comprising: a plurality of groups of mirrors, each of said groups having seven substantially identically shaped mirrors wherein one of the mirrors in each of said groups is bounded symmetrically by the other six mirrors, each mirror having an approximately fractal peripheral boundary such that each group of seven mirrors has a boundary shape of more than six sides which is approximately geometrically similar to that of each of the mirrors forming the group; and means for supporting said mirrors on a multifaceted objective surface, said surface having a peripheral boundary and an optical axis, each of said mirrors covering a portion of said surface so as to be oriented approximately orthogonal to said optical axis and being movable independently of, and unconstrained by the locations of the other mirrors, said supporting means including means for individually moving each of said mirrors in the direction of said optical axis.

Claim 3

A device as in claim 1, forming a multiple mirror reflective surface of a multiple mirror telescope.

Claim 4

A device as in claim 1, wherein said mirrors have planar reflecting surfaces.

Claim 5

A device as in claim 1, wherein said mirrors have reflecting surfaces with the same uniform radius of curvature.

Claim 6

An optical device, comprising: a plurality of groups of mirrors, each of said groups having seven substantially identically shaped mirrors, wherein one of the mirrors in each group is bounded symmetrically by the other six mirrors, said mirrors having centers disposed at the points of a regular hexagonal lattice; means for supporting said mirrors on and substantially covering a multifaceted objective surface, said surface having a peripheral boundary and an optical axis, each of said mirrors being oriented approximately orthogonal to said optical axis and being movable independently of, and unconstrained by the locations of the other mirrors, said supporting means including means for moving each of said mirrors individually, in the direction of said optical axis; defining a hexagonal region R 1 in an X,Y plane having equal sides of length S and oriented with two of its sides parallel to the Y axis, (√3)S being equal to the spacing between the centers at adjacent pointed of said lattice, and defining regions R N+1 in the X,Y plane for an integer N≧1, such that R.sub.N+1 =(aR.sub.N)U(U.sub.M=0,1,2,3,4,5 (aR.sub.N +(X(M,N),Y(M,N)))), where a=1/√7, and the translation vector defined by X(M,N)=√3 cos(πM/3+(N-2)Φ) and Y(M,N)=-√3 sin(πM/3+(N-2)Φ), where the angle Φ in radians is equal to arctangent √3/2, then R N+1 defines the shape and size of each of said mirrors.

Claim 7

An optical device, comprising: a plurality of groups of mirrors, each of said groups having seven substantially identically shaped mirrors, wherein one of the mirrors in each group is bounded symmetrically by the other six mirrors, said mirrors having centers disposed at the points of a regular hexagonal lattice; means for supporting said mirrors on and substantially covering a multifaceted objective surface, said surface having a peripheral boundary and an optical axis, each of said mirrors being oriented approximately orthogonal to said optical axis and being movable independently of, and unconstrained by the locations of the other mirrors, said supporting means including means for moving each of said mirrors individually, in the direction of said optical axis; defining a hexagonal region R 1 in an X,Y plane having equal sides of length S and oriented with two of its sides parallel to the Y axis, (√3)S being equal to the spacing between the centers at adjacent pointed of said lattice, and defining regions R N+1 in the X,Y plane for an integer N≧1, such that R.sub.N+1 =(aR.sub.N)U(U.sub.M=0,1,2,3,4,5 (aR.sub.N +(X(M,N),Y(M,N)))), where a=1/√7, and the translation vector defined by X(M,N)=√3 cos(πM/3+(N-2)Φ) and Y(M,N)=-√3 sin(πM/3+(N-2)Φ), where the angle Φ in radians is equal to arctangent √3/2, then R N+1 defines the shape and size of each of said mirrors.

Claim 8

A device as in claim 5, forming a multiple mirror reflective surface of a multiple mirror telescope.

Claim 9

A mirror for use in a multiple mirror reflecting telescope having a large number of substantially identically shaped mirrors, said mirror having an approximately fractal peripheral boundary of more than six sides such that a group of seven such mirrors, one of which is bounded symmetrically by the other six, has a boundary shape which is approximately geometrically similar to that of each of the mirrors forming the group.

Claim 10

A mirror for use in a multiple mirror reflecting telescope having a large number of substantially identically shaped mirrors, said mirror having an approximately fractal peripheral boundary of more than six sides such that a group of seven such mirrors, one of which is bounded symmetrically by the other six, has a boundary shape which is approximately geometrically similar to that of each of the mirrors forming the group.

Claim 11

A mirror as in claim 7, having a planar reflecting surface.

Claim 12

A mirror as in claim 7, having a reflecting surface with a uniform radius of curvature.

Claim 13

A mirror for use in a multiple mirror reflecting telescope having a plurality of groups of mirrors, each of the groups having seven substantially identically shaped mirrors, wherein one of the mirrors in each group is bounded symmetrically by the other six mirrors, the mirrors having centers disposed at the points of a regular hexagonal lattice, said mirror having a shape which is defined such that by defining a hexagonal region R 1 in an X,Y plane having equal sides of length S and oriented with two of its sides parallel to the Y axis, (√3)S being equal to the spacing between the centers at adjacent points of the lattice, and by defining regions R N+1 in the X,Y plane for any integer N≧1, such that R.sub.N+1 =(aR.sub.N)U(U.sub.M=0,1,2,3,4,5 (aR.sub.N +(X(M,N),Y(M,N)))), where a=1/√7, and the translation vector defined by X(M,N)=√3 cos(πM/3+(N-2)Φ) and Y(M,N)=-√3 sin(πM/3+(N-2)Φ), where the angle Φ in radians is equal to arctangent √3/2, then R N+1 defines the planar shape and size of each of said mirrors.

Claim 14

A mirror for use in a multiple mirror reflecting telescope having a plurality of groups of mirrors, each of the groups having seven substantially identically shaped mirrors, wherein one of the mirrors in each group is bounded symmetrically by the other six mirrors, the mirrors having centers disposed at the points of a regular hexagonal lattice, said mirror having a shape which is defined such that by defining a hexagonal region R 1 in an X,Y plane having equal sides of length S and oriented with two of its sides parallel to the Y axis, (√3)S being equal to the spacing between the centers at adjacent points of the lattice, and by defining regions R N+1 in the X,Y plane for any integer N≧1, such that R.sub.N+1 =(aR.sub.N)U(U.sub.M=0,1,2,3,4,5 (aR.sub.N +(X(M,N),Y(M,N)))), where a=1/√7, and the translation vector defined by X(M,N)=√3 cos(πM/3+(N-2)Φ) and Y(M,N)=-√3 sin(πM/3+(N-2)Φ), where the angle Φ in radians is equal to arctangent √3/2, then R N+1 defines the planar shape and size of each of said mirrors.