Fractal tiling for multiple mirror optical devices

• US 4,904,073 A
• Filed: 08/10/1988
• Issued: 02/27/1990
• Est. Priority Date: 08/10/1988
• Status: Expired due to Term

• Current Assignee: Aware Incorporated One Cambridge Center Cambridge MA 02142
• Original Assignee: Aware Incorporated (Crowley Holdings Preferred LLC)
• Inventors: Resnikoff, Howard L., Lawton, Wayne M.
• Primary Examiner(s): NOT, DEFINED
• Assistant Examiner(s): Lerner, Martin
• Application Number:
  US07/230,529
• Time in Patent Office: 566 Days
• Field of Search: 350/611, 350/613, 350/616, 350/627
• US Class Current: 359/851
• CPC Class Codes: G02B 23/02 involving prisms or mirrors G02B23/14 takes precedence
• CPC Class Codes: G02B 26/06 for controlling the phase of light G02B26/08 takes precedence , measuring optical phase difference G01J9/00
• CPC Class Codes: G02B 27/58 Optics for apodization or superresolution; Optical synthetic aperture systems
• CPC Class Codes: G02B 5/09 Multifaceted or polygonal mirrors , e.g. polygonal scanning mirrors; Fresnel mirrors

Abstract

A multiple mirror reflective surface for use in a multiple mirror telescope in which the objective surface of telescope is tiled with substantially identical planar mirrors having irregular boundaries and a mirror for use therein. The mirrors are groupable into groups of seven, one of which is bounded symmetrically by the other six, each mirror having an approximately fractal peripheral boundary such that each group of seven mirrors has a boundary shape which is approximately geometrically similar to that of the mirrors forming the group. The mirrors of such an array have their centers on a hexagonal lattice of points in the objective surface. In a particular embodiment, the mirrors have shapes which approximate that of a fractal shaped mirror by being defined by a combination of hexagonal shapes. With mirrors of this shape, the multiple mirror telescope experiences less optical aberrations which would otherwise be caused by linear edges of the mirrors, without reducing light gathering power.

Claims

1. 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.

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

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

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

5. 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 R₁ 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

space="preserve" listing-type="equation">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

space="preserve" listing-type="equation">X(M,N)=√

3 cos(π

M/3+(N-2)Φ

)

and

space="preserve" listing-type="equation">Y(M,N)=-√

3 sin(π

M/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.

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

7. 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.

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

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

10. 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 R₁ 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

space="preserve" listing-type="equation">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

space="preserve" listing-type="equation">X(M,N)=√

3 cos(π

M/3+(N-2)Φ

) and

space="preserve" listing-type="equation">Y(M,N)=-√

3 sin(π

M/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.