Abstract

A new zoom mechanism was proposed for the realization of a freeform varifocal panoramic annular lens (PAL) with a specified annular center of the field of view (FOV). The zooming effect was achieved through a rotation of the varifoal PAL around an optical axis, which is different from a conventional zooming method by moving lenses back and forth. This method solves the problem of FOV deviation from the target scope during the zooming process, since the optical axis was not taken as the zooming center of the FOV. The conical surface corresponding to a certain acceptance angle was specified as the annular center of the FOV, and it was adopted as the reference surface of zooming for the FOV. As an example, the design principle and optimization process of a freeform varifocal PAL was discussed in detail. The annular center of the FOV was specified at the acceptance angle of 90°. The absolute FOV in the direction of acceptance angles is relative to the specified annular center, with cosine deviation from ± 20° at 0° rotational angle to ± 10° at ± 180° rotational angle on both sides around optical axis. An X–Y polynomial (XYP) was used for the representation of freeform surfaces for its simple form and convergence efficiency. The correction for irregular astigmatism and distortion and the position offset of an entrance pupil caused by an irregular aperture spherical aberration are also discussed. The results from the analysis of the modulus of the optical transfer function (MTF) and f-theta distortion show that the zooming method by a rotation of the varifocal freeform PAL is feasible.

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References

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  1. P. Greguss, “Panoramic imaging block for three-dimensional space,” U.S. Patent 4566763 (January 28, 1986).
  2. D. R. Matthys, J. A. Gilbert, and P. Greguss, “Endoscopic measurement using radial metrology with digital correlation,” Opt. Eng. 30(10), 1455–1460 (1991).
    [Crossref]
  3. M. A. Stedham and P. P. Banerjee, “The panoramic annular lens attitude determination system (PALADS),” Proc. SPIE 2466, 108–117 (1995).
    [Crossref]
  4. A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. 9(7), 1669–1671 (1970).
    [Crossref] [PubMed]
  5. S. Niu, J. Bai, X. Y. Hou, and G. G. Yang, “Design of a panoramic annular lens with a long focal length,” Appl. Opt. 46(32), 7850–7857 (2007).
    [Crossref] [PubMed]
  6. ZEMAX Optical Design Program, User’s Guide Version 8.0, Focus Software, Inc. (1999).

2007 (1)

1995 (1)

M. A. Stedham and P. P. Banerjee, “The panoramic annular lens attitude determination system (PALADS),” Proc. SPIE 2466, 108–117 (1995).
[Crossref]

1991 (1)

D. R. Matthys, J. A. Gilbert, and P. Greguss, “Endoscopic measurement using radial metrology with digital correlation,” Opt. Eng. 30(10), 1455–1460 (1991).
[Crossref]

1970 (1)

Bai, J.

Banerjee, P. P.

M. A. Stedham and P. P. Banerjee, “The panoramic annular lens attitude determination system (PALADS),” Proc. SPIE 2466, 108–117 (1995).
[Crossref]

Gilbert, J. A.

D. R. Matthys, J. A. Gilbert, and P. Greguss, “Endoscopic measurement using radial metrology with digital correlation,” Opt. Eng. 30(10), 1455–1460 (1991).
[Crossref]

Greguss, P.

D. R. Matthys, J. A. Gilbert, and P. Greguss, “Endoscopic measurement using radial metrology with digital correlation,” Opt. Eng. 30(10), 1455–1460 (1991).
[Crossref]

Hou, X. Y.

Lohmann, A. W.

Matthys, D. R.

D. R. Matthys, J. A. Gilbert, and P. Greguss, “Endoscopic measurement using radial metrology with digital correlation,” Opt. Eng. 30(10), 1455–1460 (1991).
[Crossref]

Niu, S.

Stedham, M. A.

M. A. Stedham and P. P. Banerjee, “The panoramic annular lens attitude determination system (PALADS),” Proc. SPIE 2466, 108–117 (1995).
[Crossref]

Yang, G. G.

Appl. Opt. (2)

Opt. Eng. (1)

D. R. Matthys, J. A. Gilbert, and P. Greguss, “Endoscopic measurement using radial metrology with digital correlation,” Opt. Eng. 30(10), 1455–1460 (1991).
[Crossref]

Proc. SPIE (1)

M. A. Stedham and P. P. Banerjee, “The panoramic annular lens attitude determination system (PALADS),” Proc. SPIE 2466, 108–117 (1995).
[Crossref]

Other (2)

ZEMAX Optical Design Program, User’s Guide Version 8.0, Focus Software, Inc. (1999).

P. Greguss, “Panoramic imaging block for three-dimensional space,” U.S. Patent 4566763 (January 28, 1986).

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Figures (9)

Fig. 1
Fig. 1

Path of rays traveling inside a PAL.

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Fig. 2
Fig. 2

Schematics of the changing FOV of conventional zoom mechanism and the new zoom mechanism with freeform lenses. (a) The conventional zoom mechanism. (b) The new zoom mechanism with freeform lenses.

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Fig. 3
Fig. 3

Zooming effect through the rotation of freeform lenses.

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Fig. 4
Fig. 4

Simplified ray-tracing model of a freeform imaging system.

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Fig. 5
Fig. 5

Optical layout of the original configuration.

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Fig. 6
Fig. 6

Transition process of FOV of the varifocal PAL. (a) Annular FOV. (b) The transformation of annular FOV from polar to rectilinear coordinate.

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Fig. 7
Fig. 7

Layout of the freeform varifocal PAL. (a) 2-D layout. (b) 3-D layout.

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Fig. 8
Fig. 8

MTF of the FOV at different rotational angle.

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Fig. 9
Fig. 9

F-theta distortion of the freeform varifocal PAL.

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Tables (2)

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Table 1 Specifications of the Freeform Varifocal PAL

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Table 2 Coordinates of Image Points in the Tangential Planes

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Equations (22)

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r j + 1 = r j + d s j ⋅ s j ,
s j + 1 = n s j + e j ⋅ [ 1 − n 2 + ( n e j ⋅ s j ) 2 − n e j ⋅ s j ] ,
Φ 1 , 2 = Φ 1 + Φ 2 - D 1 Φ 1 Φ 2 ,
D 1 = d 1 n 1 ,
Φ 1 , 3 = Φ 1 , 2 + Φ 3 - D 2 Φ 1 , 2 Φ 3 ,
D 2 = d 2 n 2 + d 1 Φ 1 n 1 ( Φ 1 + Φ 2 - D 1 Φ 1 Φ 2 ) .
Φ 1 , k = Φ 1 , k - 1 + Φ k - D k - 1 Φ 1 , k - 1 Φ k ,
D k - 1 = d k - 1 n k - 1 + d k - 2 Φ k - 2 n k - 2 ( Φ k - 2 + Φ k - 1 - D k - 2 Φ k - 2 Φ k - 1 ) .
Φ 1 , k = f ( Φ 1 , Φ 2 ... Φ k ) .
Φ j = ( n j − n j - 1 ) c j .
Φ 1 , k = F ( c 1 , c 2 ... c k ) .
c j , ∥ = c h 1 j cos 2 θ + c h 2 j sin 2 θ ,
c j , ⊥ = c h 1 j sin 2 θ + c h 2 j cos 2 θ .
Φ 1 , k , ∥ = F ( c 1 , ∥ , c 2 , ∥ ... c k , ∥ ) ,
Φ 1 , k , ⊥ = F ( c 1 , ⊥ , c 2 , ⊥ ... c k , ⊥ ) .
A s t i g ≜ | Φ 1 , k , ∥ − Φ 1 , k , ⊥ | .
e j = e j , T + e j , R .
s j = ( s j ⋅ e j , T ) e j , T + ( s j ⋅ e j , R ) e j , R ,
s j + 1 = ( s j + 1 ⋅ e j , T ) e j , T + ( s j + 1 ⋅ e j , R ) e j , R .
( s 1 ⋅ e 1 , R ) e 1 , R = 0.
( s k + 1 ⋅ e k , R ) e k , R = 0.
z ( x , y ) = c r 2 1 + 1 − ( 1 + k ) c 2 r 2 + ∑ i = 1 N A i x 2 m y n ,

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