Abstract

New matrix formulas for structural optical design have been obtained from analysis of derivative of the system matrix in respect to construction parameters and movements of components. Functional parameters of the optical system become elements of the matrix, presenting working conditions of the optical system. Developed methodology of structural design multi-group zoom systems with unlimited number of components and with mechanical-electronic compensation is presented. Any optical system, such as the objective lens, reproduction system, or telescopic system, can be analyzed with this methodology. Kinematics of components pertaining to a full tract of the zoom system is determined for a discrete number of positions. Three examples of the structural design of complex zoom systems with five-components and high zooming ratio are provided.

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References

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  1. K. Yamaji, “Design of zoom lenses”, in Progress in Optics, Vol. 6, (North-Holland 1967), pp.105–170.
  2. K. Tanaka, Paraxial Theory of Mechanically Compensated Zoom Lenses by Means of Gaussian Brackets, Research Report of Canon Inc. (6), (Canon Inc. 1991).
  3. A. D. Clark, Zoom Lenses: Monographs in Applied Optics (7) (Adam Hilger 1973).
  4. I. I. Pahomov, Zoom Systems (Mashinostroene, Moskva 1976) – in Russian.
  5. T. H. Jamieson, “Thin-lens theory of zoom systems,” Opt. Acta (Lond.)17(8), 565–584 (1970).
    [CrossRef]
  6. Selected Paper on Zoom Lenses, A. Mann, Editor, Vol. MS 85, (SPIE Optical Engineering Press 1993).
  7. S. P. I. E. Proceedings, 2539, Zoom Lenses, A. Mann, Editor, (1995).
  8. S. P. I. E. Proceedings, 3129, Zoom Llenses II, E. I. Betensky, A. Mann, and I. A. Neil, Editors, (1997).
  9. A. Mann, Infrared Optics and Zoom Lenses, Vol., TT83, (SPIE Press 2009).
  10. A. Mikš, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt.47(32), 6088–6098 (2008).
    [CrossRef] [PubMed]
  11. A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover Publication 1994), Chap.II.
  12. G. Kloos, Matrix Methods for Optical Layout, Vol. TT77, (SPIE Press 2007).
  13. T. Kryszczyński, M. Leśniewski, and J. Mikucki, “New approach to the method of the initial optical design based on the matrix optics,” 16th Polish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE 7141, 71411X1–7 (2008).
    [CrossRef]
  14. T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” 16th Polish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE 7141, 71411Y (2008).
    [CrossRef]
  15. T. Kryszczyński and J. Mikucki, “Interactive matrix method for analysis and construction of optical systems with elaborated components,” 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE7746, 77461M (2010).
    [CrossRef]
  16. K. Tanaka, “Recent development of zoom lenses,” Proc. SPIE 3129, in Zoom lenses II, ed. E. I. Betensky, A. Mann, I. A. Neil, 13–22 (Sep. 1997).
  17. M.S. Stephansky, N.A. Gradoboeva, and I.E. Isaeva, “Five-component wide field zoom systems,” Sov. J. Opt. Technol. (8), 22–25 (1977) – in Russian.
  18. EF lens work III the eyes of EOS, “Sixteen technologies used in high-performance EF lenses,” (Canon Inc. Lens Products Group 2006), pp. 175–177.
  19. T. B. Andersen, “Optical aberration functions: derivatives with respect to axial distances for symmetrical systems,” Appl. Opt.21(10), 1817–1823 (1982).
    [CrossRef] [PubMed]

2010 (1)

T. Kryszczyński and J. Mikucki, “Interactive matrix method for analysis and construction of optical systems with elaborated components,” 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE7746, 77461M (2010).
[CrossRef]

2008 (1)

1982 (1)

1977 (1)

M.S. Stephansky, N.A. Gradoboeva, and I.E. Isaeva, “Five-component wide field zoom systems,” Sov. J. Opt. Technol. (8), 22–25 (1977) – in Russian.

1970 (1)

T. H. Jamieson, “Thin-lens theory of zoom systems,” Opt. Acta (Lond.)17(8), 565–584 (1970).
[CrossRef]

Andersen, T. B.

Gradoboeva, N.A.

M.S. Stephansky, N.A. Gradoboeva, and I.E. Isaeva, “Five-component wide field zoom systems,” Sov. J. Opt. Technol. (8), 22–25 (1977) – in Russian.

Isaeva, I.E.

M.S. Stephansky, N.A. Gradoboeva, and I.E. Isaeva, “Five-component wide field zoom systems,” Sov. J. Opt. Technol. (8), 22–25 (1977) – in Russian.

Jamieson, T. H.

T. H. Jamieson, “Thin-lens theory of zoom systems,” Opt. Acta (Lond.)17(8), 565–584 (1970).
[CrossRef]

Kryszczynski, T.

T. Kryszczyński and J. Mikucki, “Interactive matrix method for analysis and construction of optical systems with elaborated components,” 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE7746, 77461M (2010).
[CrossRef]

Mikš, A.

Mikucki, J.

T. Kryszczyński and J. Mikucki, “Interactive matrix method for analysis and construction of optical systems with elaborated components,” 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE7746, 77461M (2010).
[CrossRef]

Novák, J.

Novák, P.

Stephansky, M.S.

M.S. Stephansky, N.A. Gradoboeva, and I.E. Isaeva, “Five-component wide field zoom systems,” Sov. J. Opt. Technol. (8), 22–25 (1977) – in Russian.

Appl. Opt. (2)

Five-component wide field zoom systems (1)

M.S. Stephansky, N.A. Gradoboeva, and I.E. Isaeva, “Five-component wide field zoom systems,” Sov. J. Opt. Technol. (8), 22–25 (1977) – in Russian.

Opt. Acta (Lond.) (1)

T. H. Jamieson, “Thin-lens theory of zoom systems,” Opt. Acta (Lond.)17(8), 565–584 (1970).
[CrossRef]

Proc. SPIE (1)

T. Kryszczyński and J. Mikucki, “Interactive matrix method for analysis and construction of optical systems with elaborated components,” 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE7746, 77461M (2010).
[CrossRef]

Other (14)

K. Tanaka, “Recent development of zoom lenses,” Proc. SPIE 3129, in Zoom lenses II, ed. E. I. Betensky, A. Mann, I. A. Neil, 13–22 (Sep. 1997).

EF lens work III the eyes of EOS, “Sixteen technologies used in high-performance EF lenses,” (Canon Inc. Lens Products Group 2006), pp. 175–177.

K. Yamaji, “Design of zoom lenses”, in Progress in Optics, Vol. 6, (North-Holland 1967), pp.105–170.

K. Tanaka, Paraxial Theory of Mechanically Compensated Zoom Lenses by Means of Gaussian Brackets, Research Report of Canon Inc. (6), (Canon Inc. 1991).

A. D. Clark, Zoom Lenses: Monographs in Applied Optics (7) (Adam Hilger 1973).

I. I. Pahomov, Zoom Systems (Mashinostroene, Moskva 1976) – in Russian.

Selected Paper on Zoom Lenses, A. Mann, Editor, Vol. MS 85, (SPIE Optical Engineering Press 1993).

S. P. I. E. Proceedings, 2539, Zoom Lenses, A. Mann, Editor, (1995).

S. P. I. E. Proceedings, 3129, Zoom Llenses II, E. I. Betensky, A. Mann, and I. A. Neil, Editors, (1997).

A. Mann, Infrared Optics and Zoom Lenses, Vol., TT83, (SPIE Press 2009).

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover Publication 1994), Chap.II.

G. Kloos, Matrix Methods for Optical Layout, Vol. TT77, (SPIE Press 2007).

T. Kryszczyński, M. Leśniewski, and J. Mikucki, “New approach to the method of the initial optical design based on the matrix optics,” 16th Polish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE 7141, 71411X1–7 (2008).
[CrossRef]

T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” 16th Polish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Proc. SPIE 7141, 71411Y (2008).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

The track of the optical system: O-O’ (object-image distance) or F-F’ (between focuses) or P-P’ (between pupils) and coordinates of two characteristic rays on both sides of the system.

Fig. 2
Fig. 2

Diagram linking construction parameters: transfer matrices T, optical power matrices M of the optical system (matrix S) with working conditions represented by matrices of coordinates of characteristic ray J0 and Jk + 1.(matrix W)

Fig. 3
Fig. 3

The moving component with index i within a fragment of the optical system.

Fig. 4
Fig. 4

Two moving components with indices i and n determined by numerical methods to obtain stabilization conditions.

Fig. 5
Fig. 5

Two diagrams of movement z vs. cycle parameter i: a) for p = 10 and different parameters e, b) for z = 10 and different parameters e1.

Fig. 6
Fig. 6

Interactive diagram of the structural optical design of the multi-group zoom system.

Fig. 7
Fig. 7

Diagram of the multi-group zoom objective lens at the edge arrangements.

Fig. 8
Fig. 8

Components kinematics of the objective lens.

Fig. 9
Fig. 9

Diagram of the multi-group zoom reproduction system at the edge arrangements.

Fig. 10
Fig. 10

Components kinematics of the reproduction system.

Fig. 11
Fig. 11

Diagram of the multi-group zoom telescopic system at the edge arrangements.

Fig. 12
Fig. 12

Components kinematics of the telescopic system.

Tables (4)

Tables Icon

Table 1 Coordinates of characteristic rays and elements of the working conditions matrix

Tables Icon

Table 2 Data structure of the multi-group zoom objective lens

Tables Icon

Table 3 Data structure of the multi-group zoom reproduction system

Tables Icon

Table 4 Data structure of the multi-group zoom telescopic system

Equations (34)

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( h α 1 )=( 1 t 1 0 1 )( h 1 α 1 )=T( h 1 α 1 ),
( h α )=( 1 0 φ 1 )( h α 1 )=M( h α 1 ).
( h α )=MT ( h α ) 1 =S ( h α ) 1 ,
( h α ) k+1 = S 0,k+1 ( h α ) 0 .
S 0,k+1 = T k M k T k1 M k1 T 2 M 2 T 1 M 1 T 0 ,
T i =( 1 t i 0 1 ), M i =( 1 0 φ i 1 ).
J 0 = [ h y α β ] 0 , J k+1 = [ h y α β ] k+1 ,
S 0,k+1 [ h y α β ] 0 = [ h y α β ] k+1 ,
S 0,k+1 J 0 = J k+1 .
S 0,k+1 = J k+1 J 0 1 .
W 0,k+1 = J k+1 J 0 1 .
S 0,k+1 = W 0,k+1 .
| J |=βhαy.
| J i |=const.fori=0...k+1.
| J |= β 0 h 0 α 0 y 0 = β k+1 h k+1 α k+1 y k+1 .
W 0,k+1 = 1 β 0 h 0 α 0 y 0 [ h k+1 β 0 y k+1 α 0 y k+1 h 0 h k+1 y 0 α k+1 β 0 β k+1 α 0 β k+1 h 0 α k+1 y 0 ].
W 0,k+1 =( 0 1 Φ Φ 0 ), W 0,k+1 =( m 0 Φ 1 m ), W 0,k+1 =( 1 g 0 0 g ).
ΔS= x ( T k M k T j M j M 1 T 0 )Δx.
M i φ i =( 0 0 1 0 )= M φ .
ΔS=( T k M k M i φ i M 1 T 0 )Δ φ i .
T j t j =( 0 1 0 0 )= T t .
S 0,k+1 t i = T k M k T k1 T i t i T 1 M 1 T 0 . ΔS=( T k M k T i t i M 1 T 0 )Δ t i .
ΔS= 2 xy ( T k M k M i M j M 1 T 0 )ΔxΔy.
ΔS=( T k M k M i φ i M j φ j M 1 T 0 )Δ φ i Δ φ j .
ΔS=( T k M k T i t i T j t j M 1 T 0 )Δ t i Δ t j .
ΔS= S φ i Δ φ i + S φ j Δ φ j + 2 S φ i φ j Δ φ i Δ φ j .
ΔS= S t i Δ t i + S t j Δ t j + 2 S t i t j Δ t i Δ t j .
ΔS= S φ i Δ φ i + S t j Δ t j + 2 S φ i t j Δ φ i Δ t j .
2 S 0,k+1 φ i φ j = T k M k T k1 M i φ i M j φ j T 1 M 1 T 0 . 2 S 0,k+1 t i t j = T k M k T k1 T i t i T j t j T 1 M 1 T 0 .
Δ S 0,k+1 = S 0,k+1 t i1 z i ,Δ S 0,k+1 = S 0,k+1 t i z i ,Δ S 0,k+1 = 2 S 0,k+1 t i1 t i z i 2 .
Δ S 0,k+1 =( S 0,k+1 t i1 S 0,k+1 t i ) z i 2 S 0,k+1 t i1 t i z i 2 .
Δ S 0,k+1 =( S 0,k+1 t i1 S 0,k+1 t i ) z i 2 S 0,k+1 t i1 t i z i 2 +( S 0,k+1 t n1 S 0,k+1 t n ) z n 2 S 0,k+1 t n1 t n z n 2 +( S 0,k+1 t i1 S 0,k+1 t i )( S 0,k+1 t n1 S 0,k+1 t n ) z i z n .
z(i,p,e,z,e1)=4p[ ( i N ) e ( i N ) 2e ]+z ( i N ) e1 .
A T AΔp= A T Δw,

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