Abstract

On the basis of the modified Iwasawa decomposition of a lossless first-order optical system as a cascade of a lens, a magnifier, and a so-called orthosymplectic system, we show how to synthesize an arbitrary ABCD system (with two transverse coordinates) by means of lenses and predetermined sections of free space such that the lenses are located at fixed positions.

© 2006 Optical Society of America

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References

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  1. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966).
  2. E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  4. A. W. Lohmann, J. Opt. Soc. Am. A 10, 2181 (1993).
    [CrossRef]
  5. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
  6. K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).
  7. R. Simon and K. B. Wolf, J. Opt. Soc. Am. A 17, 342 (2000).
    [CrossRef]
  8. R. Simon and N. Mukunda, J. Opt. Soc. Am. A 15, 2146 (1998).
    [CrossRef]
  9. M. Nazarathy and J. Shamir, J. Opt. Soc. Am. 72, 356 (1982).
    [CrossRef]
  10. T. Alieva and M. J. Bastiaans, Opt. Lett. 30, 3302 (2005).
    [CrossRef]

2005

2000

1998

1993

1985

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

1982

Alieva, T.

Bastiaans, M. J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Lohmann, A. W.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966).

Mukunda, N.

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 15, 2146 (1998).
[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

Nazarathy, M.

Ozaktas, H. M.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Shamir, J.

Simon, R.

Sudarshan, E. C. G.

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

Wolf, K. B.

R. Simon and K. B. Wolf, J. Opt. Soc. Am. A 17, 342 (2000).
[CrossRef]

K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).

Zalevsky, Z.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

Opt. Lett.

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966).

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Equations (20)

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A B C D
[ r o p o ] = T [ r i p i ] = [ A B C D ] [ r i p i ] .
[ 1 λ z 0 1 ] , [ 1 0 1 λ f 1 ] , [ 0 w 2 w 2 0 ]
T f ( θ ; w ) = [ cos θ w 2 sin θ w 2 sin θ cos θ ] = [ w 0 0 w 1 ] [ cos θ sin θ sin θ cos θ ] [ w 1 0 0 w ] ,
T f ( θ ; w ) = [ 1 d f λ d ( 2 d f ) ( d f ) λ d 1 d f ] ,
w 2 tan ( θ 2 ) = λ d ,
T f ( θ ; w ) = [ 1 d f λ d ( d f ) ( 2 d f ) λ d 1 d f ] ,
w 2 sin θ = λ d ,
[ W 1 0 0 W ] [ r o p o ] = [ a b c d ] [ W 1 0 0 W ] [ r i p i ] ,
[ W 0 0 W 1 ] [ x y y x ] [ W 1 0 0 W ] ,
t f ( θ x , θ y ) = [ cos θ x 0 sin θ x 0 0 cos θ y 0 sin θ y sin θ x 0 cos θ x 0 0 sin θ y 0 cos θ y ] ,
t r ( θ ) = [ cos θ sin θ 0 0 sin θ cos θ 0 0 0 0 cos θ sin θ 0 0 sin θ cos θ ] ,
u f ( θ x , θ y ) = [ exp ( i θ x ) 0 0 exp ( i θ y ) ] ,
u r ( θ ) = [ cos θ sin θ sin θ cos θ ] ;
[ a b c d ] = [ I 0 g I ] [ s 0 0 s 1 ] [ x y y x ] ,
G = [ g 11 g 12 g 12 g 22 ] = u r ( φ g ) [ g 1 0 0 g 2 ] u r ( φ g ) ,
S = [ s 11 s 12 s 12 s 22 ] = u r ( φ s ) [ s 1 0 0 s 2 ] u r ( φ s ) ;
[ 1 0 1 λ ( z o f o ) 1 ] [ 1 λ z o 0 1 ] [ 1 0 1 λ f o 1 ] [ 1 λ d o 0 1 ] = [ ( z o f o ) f o 0 0 f o ( z o f o ) ] [ s 0 0 s 1 ] .
[ 0 w 2 w 2 0 ] [ 1 0 1 λ f 1 ] [ 0 w 2 w 2 0 ] = [ 1 w 4 λ f 0 1 ] [ 1 λ z o 0 1 ] .
R ( φ g ) L ( 1 λ g 1 , 1 λ g 2 ) R ( φ g ) R ( φ s ) L ( z 1 f 1 , z 2 f 2 ) F b ( π 2 ; w ) L ( w 4 λ 2 z 1 , w 4 λ 2 z 2 ) F b ( π 2 ; w ) L ( f 1 , f 2 ) S ( d o ) R ( φ s ) R ( β ) F ( γ x , γ y ; w x , w y ) R ( α ) .

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