Optical system for image rotation and magnification

Optical system design for orthosymplectic transformations in phase space

“…2,8 The scaling operation, described by the second matrix, is also well studied. 4,18 The last orthosymplectic matrix ͑M t = M −1 ͒ is a general expression for a variety of attractive transforms. 14,15,18 Thus the submatrices…”

“…4,7,14,18 Some of them do not relate to pure rotation since they introduce an additional phase modulation of the rotated image. We will call them imperfect rotators.…”

“…We will call them imperfect rotators. Others are reflectors with rotation, 4 which also belong to the class of orthosymplectic systems, and are described by the submatrices…”

“…are known. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Nevertheless, to the best of our knowledge no systematic analysis of the design of these systems has been done.…”

“…We restrict ourselves to the design of systems associated with orthosymplectic matrices, 14,15,18 which describe such attractive transformations as image rotation, twisting, fractional FT, etc. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Our main objective is to find a minimal lens-free-space flexible system configuration to perform a given transform. For the case of one or two parametric transforms, as used with, for example, separable fractional FT, twisting, or image rotation, we are interested in systems that are easily adjustable for new parameter values.…”