Abstract

Relay systems in rigid endoscopes can compensate for aberrations in the objective and the eyepiece. Five classes of rigid relay systems are examined: conventional; glass Hopkins; plastic lens, glass-rod Hopkins; modified Hopkins; and gradient index. First-order theory, including achromatization, is developed for these systems. Design results are presented, and aberration, vignetting, and system length tradeoffs are analyzed.

© 1996 Optical Society of America

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References

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  1. D. C. Leiner, “Miniature optics in the operating room,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. P. Rees, eds., Proc. SPIE935, 52–62 (1988).
  2. H. H. Hopkins, U.K. Patent954,629 (8April1964).
  3. H. H. Hopkins, “Optical principles of the endoscope,” in Endoscopy, G. Berci, ed. (Appleton-Century-Crofts, New York, 1976), pp. 3–26.
  4. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), pp. 67–74.
  5. P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).
  6. D. T. Moore, “Design of optical systems with negative gradient-index dispersion,” presented at the Micro-Optics/Gradient-Index Conference, Kawasaki, Japan, 21, Oct. 1993.
  7. C. Saxer, The Institute of Optics, University of Rochester, Rochester, New York 14627 (personal communication, 1994).
  8. Gradient Lens Corporation, Rochester, New York.
  9. codev v. 8.0, Optical Research Associates, Pasadena, California.
  10. Optical Glass, Schott Glass Technologies, Inc., Duryea, Pennsylvania.
  11. D. C. Leiner, “Disposable rigid endoscope,” U.S. Patent4,964,710 (23October1990).
  12. D. C. Leiner, W. G. Peck, “Optical system for an endoscore,” U.S. Patent5,412,504 (2May1995).
  13. A. Fletcher, T. Murphy, A. Young, “Solution of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216–225 (1953).

1953 (1)

A. Fletcher, T. Murphy, A. Young, “Solution of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216–225 (1953).

Fletcher, A.

A. Fletcher, T. Murphy, A. Young, “Solution of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216–225 (1953).

Hopkins, H. H.

H. H. Hopkins, U.K. Patent954,629 (8April1964).

H. H. Hopkins, “Optical principles of the endoscope,” in Endoscopy, G. Berci, ed. (Appleton-Century-Crofts, New York, 1976), pp. 3–26.

Leiner, D. C.

D. C. Leiner, W. G. Peck, “Optical system for an endoscore,” U.S. Patent5,412,504 (2May1995).

D. C. Leiner, “Miniature optics in the operating room,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. P. Rees, eds., Proc. SPIE935, 52–62 (1988).

D. C. Leiner, “Disposable rigid endoscope,” U.S. Patent4,964,710 (23October1990).

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), pp. 67–74.

McLaughlin, P. O.

P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).

Miceli, J. J.

P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).

Moore, D. T.

P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).

D. T. Moore, “Design of optical systems with negative gradient-index dispersion,” presented at the Micro-Optics/Gradient-Index Conference, Kawasaki, Japan, 21, Oct. 1993.

Murphy, T.

A. Fletcher, T. Murphy, A. Young, “Solution of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216–225 (1953).

Peck, W. G.

D. C. Leiner, W. G. Peck, “Optical system for an endoscore,” U.S. Patent5,412,504 (2May1995).

Ryan, D. P.

P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).

Saxer, C.

C. Saxer, The Institute of Optics, University of Rochester, Rochester, New York 14627 (personal communication, 1994).

Stagaman, J. M.

P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).

Young, A.

A. Fletcher, T. Murphy, A. Young, “Solution of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216–225 (1953).

Proc. R. Soc. London, Ser. A (1)

A. Fletcher, T. Murphy, A. Young, “Solution of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216–225 (1953).

Other (12)

D. C. Leiner, “Miniature optics in the operating room,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. P. Rees, eds., Proc. SPIE935, 52–62 (1988).

H. H. Hopkins, U.K. Patent954,629 (8April1964).

H. H. Hopkins, “Optical principles of the endoscope,” in Endoscopy, G. Berci, ed. (Appleton-Century-Crofts, New York, 1976), pp. 3–26.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), pp. 67–74.

P. O. McLaughlin, J. J. Miceli, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a gradient-index binocular objective,” in 1980 International Lens Design Conference, R. E. Fischer, ed., Proc. SPIE237, 369–379 (1980).

D. T. Moore, “Design of optical systems with negative gradient-index dispersion,” presented at the Micro-Optics/Gradient-Index Conference, Kawasaki, Japan, 21, Oct. 1993.

C. Saxer, The Institute of Optics, University of Rochester, Rochester, New York 14627 (personal communication, 1994).

Gradient Lens Corporation, Rochester, New York.

codev v. 8.0, Optical Research Associates, Pasadena, California.

Optical Glass, Schott Glass Technologies, Inc., Duryea, Pennsylvania.

D. C. Leiner, “Disposable rigid endoscope,” U.S. Patent4,964,710 (23October1990).

D. C. Leiner, W. G. Peck, “Optical system for an endoscore,” U.S. Patent5,412,504 (2May1995).

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Figures (15)

Fig. 1
Fig. 1

One stage of a conventional relay system. The chief ray enters and exits with zero slope.

Fig. 2
Fig. 2

First-order layout: second half of a relay stage.

Fig. 3
Fig. 3

One stage of a Hopkins relay system.

Fig. 4
Fig. 4

Throughput advantage of a Hopkins system compared with that of a conventional system.

Fig. 5
Fig. 5

One stage of a GRIN relay system.

Fig. 6
Fig. 6

Relating the pitch, diameter, and f# of a GRIN rod.

Fig. 7
Fig. 7

Chromatic effects of a glass slab in (a) a converging beam, (b) a diverging beam.

Fig. 8
Fig. 8

Achromatization of a Hopkins relay.

Fig. 9
Fig. 9

Conventional relay: (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots. CUY, curvature; THI, thickness; GLA, glass; OBJ, objective; STO, stop; IMG, image.

Fig. 10
Fig. 10

Glass Hopkins relay: (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots.

Fig. 11
Fig. 11

Plastic Hopkins relay with singlet lenses: (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots.

Fig. 12
Fig. 12

Plastic Hopkins relay with doublet lenses: (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots.

Fig. 13
Fig. 13

Modified Hopkins relay: (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots.

Fig. 14
Fig. 14

GRIN relay: (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots.

Fig. 15
Fig. 15

Conventional relay (shortened): (a) lens drawing, (b) surface data, (c) field plot, (d) ray aberration plots.

Tables (5)

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Table 1 Achromatization of Hopkins System with Singlet Lenses: Required Relay Lens V# for SF2 Field Lens and Various Relay Rod Glasses

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Table 2 Achromatization of Hopkins System with Singlet Lenses: Required Relay Lens V# for SF56 Rod and Various Field Lens Glasses

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Table 3 GRIN and Plastic Material Specifications

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Table 4 Summary of Design Performances for Single Stage of Various Endoscope Relays

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Table 5 System Cost Factors for Various Three-Stage Endoscope Relay Systems

Equations (41)

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Φ = 1 2 y s f # .
t h = [ 1 Φ 2 ( L t i ) t i 1 Φ t i n h ] n h Φ ,
ϕ r = ( 1 Φ t i ) n h t h ,
ϕ f = [ 1 Φ ( L t i t h ) ] n h t h .
t s = L t h t i ,
L o = d 2 F d A proj d Ω ,
F L o = π 2 H 2 n obj 2 ,
f # = t h 2 y s n h .
H h H c = f # c f # h = n h .
f # h = n h t i ( t h + t i L ) y s { t h ± [ t h 2 + 4 n h 2 t i ( t h + t i L ) ] 1 / 2 } .
t i max = [ L ( L 2 16 f # 2 y s 2 ) 1 / 2 ] / 2 .
N ( r ) = N 00 + N 10 r 2 + N 20 r 4 + .
y ( z ) = θ 0 α sin ( α z ) + y 0 cos ( α z ) ,
α = ( 2 N 10 N 00 ) 1 / 2 ,
t i = 1 N 00 α tan ( α d ) .
d = 1 α [ tan 1 ( 1 t i N 00 α ) + n π ]
f # = 1 N 00 D lens α sin ( α d ) .
N 10 = 1 2 N 00 ( t i 2 f # 2 D lens 2 ) .
n h Λ [ 1 t i ( ϕ f Λ + ϕ r Λ ) ] t h ϕ r Λ ( 1 t i ϕ f Λ ) = 0 ,
ϕ r Λ = n h Λ ( 1 t i ϕ f Λ ) n h Λ t i + t h ( 1 t i ϕ f Λ ) = ( 1 n r Λ ) c r ,
n Λ = n d + χ Λ n d 1 V ,
χ Λ = λ Λ λ d λ F λ C .
n Λ 1 = ( V + χ Λ ) n d 1 V .
ϕ r F ϕ r C = V r + χ F V r + χ C ,
V r = χ C ϕ r F χ F ϕ r C ϕ r C ϕ r F .
ϕ f Λ = ( 1 + χ Λ V f ) ϕ f d .
n F = n d P 1 V ( n d 1 ) , n C = n d P V ( n d 1 ) .
ϕ f F = ( 1 P f 1 V f ) ϕ f d , ϕ f C = ( 1 P f V f ) ϕ f d .
ϕ r 1 + ϕ r 2 = ϕ r ,
ϕ r 1 V r 1 + ϕ r 2 V r 2 = ϕ r V r ,
ϕ r 2 = V r 2 V r ( V r V r 1 ) ( V r 2 V r 1 ) ϕ r ,
ϕ r 1 = ϕ r ϕ r 2 .
C r 1 = 0 , C r 2 = ϕ r 1 ( 1 n r 1 ) , C r 3 = ϕ r 2 ( 1 n r 2 ) + C r 2 ,
p = 2 π ( N 00 2 N 10 ) 1 / 2 .
V G = N 10 , d N 10 , F N 10 , C ,
V G A = N 00 , d N 00 , F N 00 , C .
z = c r 2 1 + ( 1 c 2 r 2 ) 1 / 2 + A r 4 ,
P G = N 10 , d N 10 , C N 10 , F N 10 , C
N 20 , F = ( 1 P G 1 V G ) N 20 , d , N 20 , C = ( 1 P G V G ) N 20 , d .
N ( r ) = N 00 sech ( 2 π r p ) = N 00 [ 1 1 2 ( 2 π p ) 2 r 2 + 5 24 ( 2 π p ) 4 r 4 ] ,
N 20 , d = 5 6 N 10 , d 2 N 00 , d .

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