Abstract

A new method to improve the design of the panoramic annular lens (PAL) optical system with long focus is introduced. Cemented lenses are used in a PAL block to improve the design freedom. A multilayer diffractive optical element (MDOE) is used in relay optics to simplify the structure of the system and to increase diffractive efficiency of the design spectral range. The diffractive efficiency of MDOE in a wide spectral range is investigated theoretically. A seven piece PAL system with a total effective focal length of 10.8  mm is realized, and the diffractive efficiency of the whole design wavelength is above 99.3%. A PAL system with all spherical surfaces is described as a comparison.

© 2007 Optical Society of America

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References

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  1. P. Greguss, "Panoramic imaging block for three-dimensional space," U.S. patent 4,566,763 (1 November 1986).
  2. D. R. Matthys, J. A. Gilbert, and P. Greguss, "Endoscopic measurement using radial metrology with digital correlation," Opt. Eng. 30, 1455-1460 (1991).
    [CrossRef]
  3. I. Powell, "Panoramic lens," Appl. Opt. 33, 7356-7361 (1994).
    [CrossRef] [PubMed]
  4. D. R. Matthys, J. A. Gilbert, and S. B. Fair, "Characterization of optical systems for radial metrology," in Proceedings of the SEM IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 104-107.
  5. S. B. Fair, D. R. Matthys, and J. A. Gilbert, "Out-of-plane displacement analysis using panoramic ESPI," in Proceedings of the 1999 SEM Spring Conference on Theoretical, Experimental and Computational Mechanics (Society for Experimental Mechanics, 1999), pp. 257-260.
  6. G. N. Ehan Weech, J. A. Gilbert, and D. R. Matthys, "A stereoscopic system for radial metrology," in Proceedings of the 2001 SEM Annual Conference and Exposition (Society for Experimental Mechanics, 2001), pp. 199-202.
  7. J. A. Gilbert and D. R. Matthys, "Digital image correlation of stereoscopic images for radial metrology," in Proceedings of SEM X International Congress (Society for Experimental Mechanics, 2004), pp. 223-231.
  8. J. A. Gilbert, D. R. Matthys, and C. M. Lindner, "Endoscopic inspection and measurement," in Applications of Digital Image Processing XV, Proc. SPIE 1771, 106-112 (1992).
  9. T. Nakai, "Diffractive optical element," U.S. patent 6,587,272 (1 July 2003).
  10. T. Ma, "Design theory of multi-layer diffractive optical element and its application," Ph.D. dissertation (Zhejiang University, 2006) (in Chinese).
  11. D. Faklis and G. M. Morris, "Spectral properties of multiorder diffractive lenses," Appl. Opt. 34, 2462-2468 (1995).
    [CrossRef] [PubMed]
  12. D. W. Sweeney and G. E. Sommargren, "Harmonic diffractive lenses," Appl. Opt. 34, 2469-2475 (1995).
    [CrossRef] [PubMed]
  13. ZEMAX, Optical Design Program, "User's Guide Version 8.0," Focus Software, Incorporated, Bellevue, Wash., March, (1999).

2003 (1)

T. Nakai, "Diffractive optical element," U.S. patent 6,587,272 (1 July 2003).

1999 (1)

ZEMAX, Optical Design Program, "User's Guide Version 8.0," Focus Software, Incorporated, Bellevue, Wash., March, (1999).

1995 (2)

1994 (1)

1992 (1)

J. A. Gilbert, D. R. Matthys, and C. M. Lindner, "Endoscopic inspection and measurement," in Applications of Digital Image Processing XV, Proc. SPIE 1771, 106-112 (1992).

1991 (1)

D. R. Matthys, J. A. Gilbert, and P. Greguss, "Endoscopic measurement using radial metrology with digital correlation," Opt. Eng. 30, 1455-1460 (1991).
[CrossRef]

1986 (1)

P. Greguss, "Panoramic imaging block for three-dimensional space," U.S. patent 4,566,763 (1 November 1986).

Appl. Opt. (3)

Opt. Eng. (1)

D. R. Matthys, J. A. Gilbert, and P. Greguss, "Endoscopic measurement using radial metrology with digital correlation," Opt. Eng. 30, 1455-1460 (1991).
[CrossRef]

Other (9)

P. Greguss, "Panoramic imaging block for three-dimensional space," U.S. patent 4,566,763 (1 November 1986).

ZEMAX, Optical Design Program, "User's Guide Version 8.0," Focus Software, Incorporated, Bellevue, Wash., March, (1999).

D. R. Matthys, J. A. Gilbert, and S. B. Fair, "Characterization of optical systems for radial metrology," in Proceedings of the SEM IX International Congress on Experimental Mechanics (Society for Experimental Mechanics, 2000), pp. 104-107.

S. B. Fair, D. R. Matthys, and J. A. Gilbert, "Out-of-plane displacement analysis using panoramic ESPI," in Proceedings of the 1999 SEM Spring Conference on Theoretical, Experimental and Computational Mechanics (Society for Experimental Mechanics, 1999), pp. 257-260.

G. N. Ehan Weech, J. A. Gilbert, and D. R. Matthys, "A stereoscopic system for radial metrology," in Proceedings of the 2001 SEM Annual Conference and Exposition (Society for Experimental Mechanics, 2001), pp. 199-202.

J. A. Gilbert and D. R. Matthys, "Digital image correlation of stereoscopic images for radial metrology," in Proceedings of SEM X International Congress (Society for Experimental Mechanics, 2004), pp. 223-231.

J. A. Gilbert, D. R. Matthys, and C. M. Lindner, "Endoscopic inspection and measurement," in Applications of Digital Image Processing XV, Proc. SPIE 1771, 106-112 (1992).

T. Nakai, "Diffractive optical element," U.S. patent 6,587,272 (1 July 2003).

T. Ma, "Design theory of multi-layer diffractive optical element and its application," Ph.D. dissertation (Zhejiang University, 2006) (in Chinese).

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Figures (14)

Fig. 1
Fig. 1

(Color online) Imaging principle of PAL. Light is emitted from point P on the wall. P is the virtual image behind PAL, P is the real image on the image plane, and γ denotes position angle. L represents relay optics, which is usually composed of a series of lenses.

Fig. 2
Fig. 2

(Color online) Principle of FCP. (a) Space of object, where z represents the optical axis, α and β denote position angles of imaging area and blind area, respectively. (b) Image plane. The imaging area is a ring, and k is a constant. The circle in the center does not engage in imaging.

Fig. 3
Fig. 3

(Color online) Doublet PAL. 1, 2, and 5 are refractive surfaces, and 3 and 4 are reflecting surfaces. n 1 and n 2 are the refractive indices of two lenses. θ 1 and θ 2 are the incident and refractive angles of the first pass of light on surface 2.

Fig. 4
Fig. 4

(Color online) Optical paths of rays in PAL, which is mirrored twice. Tangents of reflecting points are the symmetric axes, and the optical path is unfolded at the reflecting points.

Fig. 5
Fig. 5

Geometric structure of a double-layer DOE. H 1 and H 2 are the heights of the microstructure of the DOE.

Fig. 6
Fig. 6

Structure of a doublet PAL. The materials of the two lenses are LAK9 and SF3.

Fig. 7
Fig. 7

(Color online) Diffractive efficiency of MDOE, whose substrates are FK5 and SF6, in the spectral range of 0.4 0.8 μ m . H 1 = 15.7803 μ m , H 2 = 8.7976 μ m . m = 1 , 0 , −1, 2.

Fig. 8
Fig. 8

(Color online) Amplification of Fig. 7 in the spectral range of 0.48 0.66 μ m , in the first order ( m = 1 ) .

Fig. 9
Fig. 9

(Color online) Diffractive efficiency of a single FK5 DOE on the design wavelength of 0.587 μ m , m = 1 , 0 , 1 , 2 .

Fig. 10
Fig. 10

(Color online) Curved surface of the diffractive efficiency of the harmonic DOE.

Fig. 11
Fig. 11

(Color online) Structure of the PAL optical system with MDOE.

Fig. 12
Fig. 12

(Color online) MTF of 50°, 60°, 70°, 80°, 90°, and 100° fields below 100 lp / mm . Different colors represent longitudinal and sagittal MTF of different fields. The black curve denotes the MTF of diffractive limitation.

Fig. 13
Fig. 13

(Color online) OPD fan of different fields from 50° to 100°, (a) 50°, (b) 60°, (c) 70°, (d) 80°, (e) 90°, (f) 100°, and f - θ distortion of the system.

Fig. 14
Fig. 14

(Color online) Structure of the PAL optical system with all spherical surfaces.

Tables (3)

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Table 1 Radii of Surfaces 1–5

Tables Icon

Table 2 Design Data of Relay Optics (Regular)

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Table 3 Design Data of Relay Optics (Surface Phase Parameter of BOE Between the Sixth and the Seventh Lenses)

Equations (17)

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φ ( x , y ) = 2 π λ 0 ( n 0 1 ) H = 2 π ,
η ( λ ) = sin   c 2 { m λ 0 λ [ n ( λ ) 1 n ( λ 0 ) 1 ] } ,
η ( λ ) = sin   c 2 { m λ 0 λ [ n ( λ ) 1 n ( λ 0 ) 1 ] } sin   c 2 ( m λ 0 λ ) .
φ ( x , y ) = 2 π λ 0 ( n 0 1 ) H = M 2 π ,
η ( λ ) = sin   c 2 { m M λ 0 λ [ n ( λ ) 1 n ( λ 0 ) 1 ] } .
η ( λ ) = sin   c 2 { m M λ 0 λ [ n ( λ ) 1 n ( λ 0 ) 1 ] } sin   c 2 ( m M λ 0 λ ) .
φ ( λ ) = 2 π λ [ n 1 ( λ ) 1 ] H 1 2 π λ [ n 2 ( λ ) 1 ] H 2 = 2 π ,
η m = sin   c 2 [ m OPD ( λ ) λ ] ,
OPD ( λ ) = [ n 1 ( λ ) 1 ] H 1 + [ 1 n 2 ( λ ) ] H 2 .
[ n 1 ( λ ) 1 ] H 1 + [ 1 n 2 ( λ ) ] H 2 = λ
[ n 1 ( λ ) 1 ] H 1 + [ 1 n 2 ( λ ) ] H 2 λ
η m sin   c 2 ( 0 ) = 1 ,
[ n 1 ( λ 1 ) 1 ] H 1 + [ 1 n 2 ( λ 1 ) ] H 2 = λ 1 ,
[ n 1 ( λ 2 ) 1 ] H 1 + [ 1 n 2 ( λ 2 ) ] H 2 = λ 2 .
H 1 = λ 2 [ 1 n 2 ( λ 1 ) ] λ 1 [ 1 n 2 ( λ 2 ) ] [ n 1 ( λ 1 ) 1 ] [ n 2 ( λ 2 ) 1 ] [ n 2 ( λ 1 ) 1 ] [ n 1 ( λ 2 ) 1 ] ,
H 2 = λ 2 [ n 1 ( λ 2 ) 1 ] λ 1 [ n 1 ( λ 1 ) 1 ] [ n 1 ( λ 1 ) 1 ] [ n 2 ( λ 2 ) 1 ] [ n 2 ( λ 1 ) 1 ] [ n 1 ( λ 2 ) 1 ] .
n 2 1 = K 1 λ 2 λ 2 L 1 + K 2 λ 2 λ 2 L 2 + K 3 λ 2 λ 2 L 3 ,

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