Abstract

A systematic approach for paraxial design of anamorphic lenses with double telecentricity is provided. Six types of anamorphic lens systems with double telecentricity are discussed. For available lens types, formulas defining the interval distances between lens components, the object position, the stop position, and the anamorphic ratio are derived. Illustrating figures and examples are also provided. If the telecentric zoom attachment is place behind the stop, the magnification of the whole lens system can be changed continuously, and a fixed distance between the object and the image can be guaranteed during zooming. The paraxial lens design method for the rear telecentric zoom attachment is also provided.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (2)

2014 (2)

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with three components,” Appl. Opt. 53(22), 4957–4967 (2014).
[Crossref]

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with four components,” Opt. Eng. 53(11), 115103 (2014).
[Crossref]

2012 (2)

2010 (1)

2009 (2)

2008 (1)

T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” Proc. SPIE 7141, 71411Y (2008).
[Crossref]

Bannert, C.

A. Dodoc, C. Bannert, V. Blahnik, and H. Sehr, “Anamorphic Objective,” US 8858099 B2 (2014).

Blahnik, V.

A. Dodoc, C. Bannert, V. Blahnik, and H. Sehr, “Anamorphic Objective,” US 8858099 B2 (2014).

Bowron, J. W.

J. W. Bowron and R. P. Jonas, “Optical System Including An Anamorphic Lens,” US 7289272 B2 (2007).

Chen, X.

Dodoc, A.

A. Dodoc, C. Bannert, V. Blahnik, and H. Sehr, “Anamorphic Objective,” US 8858099 B2 (2014).

Garrido, C. A.

A. V. Navarro, A. V. Navarro, and C. A. Garrido, “Anamorphic Lens,” US 9063321 B2 (2015).

Jonas, R. P.

J. W. Bowron and R. P. Jonas, “Optical System Including An Anamorphic Lens,” US 7289272 B2 (2007).

Kryszczynski, T.

T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” Proc. SPIE 7141, 71411Y (2008).
[Crossref]

Li, F.

Liu, H.

Ma, M.

Miks, A.

Navarro, A. V.

A. V. Navarro, A. V. Navarro, and C. A. Garrido, “Anamorphic Lens,” US 9063321 B2 (2015).

A. V. Navarro, A. V. Navarro, and C. A. Garrido, “Anamorphic Lens,” US 9063321 B2 (2015).

Neil, I. A.

I. A. Neil, “Anamorphic Imaging System,” US 7085066 B2 (2006).

I. A. Neil, “Anamorphic Objective Lens,” US 9341827 B2 (2016).

Novak, J.

Plotkin, M.

D. K. Towner and M. Plotkin, “Anamorphic Prisms,” US 7751124 B2 (2010).

Sasian, J.

Sehr, H.

A. Dodoc, C. Bannert, V. Blahnik, and H. Sehr, “Anamorphic Objective,” US 8858099 B2 (2014).

Slyusarev, G.G.

G.G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (CRC Press, 1984).

Sun, X.

Towner, D. K.

D. K. Towner and M. Plotkin, “Anamorphic Prisms,” US 7751124 B2 (2010).

Wu, Z.

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with four components,” Opt. Eng. 53(11), 115103 (2014).
[Crossref]

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with three components,” Appl. Opt. 53(22), 4957–4967 (2014).
[Crossref]

Xi, J.

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with four components,” Opt. Eng. 53(11), 115103 (2014).
[Crossref]

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with three components,” Appl. Opt. 53(22), 4957–4967 (2014).
[Crossref]

Yuan, S.

Zhang, J.

Appl. Opt. (7)

Opt. Eng. (1)

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Paraxial analysis of double-sided telecentric zoom lenses with four components,” Opt. Eng. 53(11), 115103 (2014).
[Crossref]

OSA Continuum (1)

Proc. SPIE (1)

T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” Proc. SPIE 7141, 71411Y (2008).
[Crossref]

Other (8)

G.G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (CRC Press, 1984).

Б.Н. Бегунов, Трансформирование оптических изображений, Искусство, 1965.

A. V. Navarro, A. V. Navarro, and C. A. Garrido, “Anamorphic Lens,” US 9063321 B2 (2015).

J. W. Bowron and R. P. Jonas, “Optical System Including An Anamorphic Lens,” US 7289272 B2 (2007).

I. A. Neil, “Anamorphic Imaging System,” US 7085066 B2 (2006).

A. Dodoc, C. Bannert, V. Blahnik, and H. Sehr, “Anamorphic Objective,” US 8858099 B2 (2014).

D. K. Towner and M. Plotkin, “Anamorphic Prisms,” US 7751124 B2 (2010).

I. A. Neil, “Anamorphic Objective Lens,” US 9341827 B2 (2016).

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Figures (7)

Fig. 1.
Fig. 1. Configuration of a double telecentric anamorphic lens system in form of Y-X-Stop-X-Y type
Fig. 2.
Fig. 2. Configuration of a double telecentric anamorphic lens system in form of Y-X-Stop-Y-X type
Fig. 3.
Fig. 3. Configuration of a double telecentric anamorphic lens system in form of Y-Y-X-Stop-XY type
Fig. 4.
Fig. 4. Configuration of a double telecentric anamorphic lens system in form of Y-X-Y-Stop-XY type
Fig. 5.
Fig. 5. Configuration of a double telecentric anamorphic lens system in form of Y-X-XY-Stop-XY type
Fig. 6.
Fig. 6. Configuration of a double telecentric anamorphic lens system in form of Y-Y-XY-Stop-XY type
Fig. 7.
Fig. 7. Configuration of a three-component telecentric zoom attachment

Equations (112)

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e s = 1 ϕ 2 x
E s = 1 ϕ 3 x
e 1 + e s = 1 ϕ 1 y
e 3 + E s = 1 ϕ 4 y
ϕ 2 x > ϕ 1 y > 0
ϕ 3 x > ϕ 4 y > 0
K 3 x = K 4 y + e 3
K 3 x = A x ( e 0 + e 1 ) B x C x ( e 0 + e 1 ) D x
K 4 y = A y e 0 B y C y e 0 D y
A x = [ ϕ 2 x , e 2 e 3 ]
B x = [ e 2 e 3 ]
C x = [ ϕ 2 x , e 2 e 3 , ϕ 3 x ]
D x = [ e 2 e 3 , ϕ 3 x ]
A y = [ ϕ 1 y , e 1 e 2 e 3 e 4 ]
B y = [ e 1 e 2 e 3 e 4 ]
C y = [ ϕ 1 y , e 1 e 2 e 3 e 4 , ϕ 4 y ]
D y = [ e 1 e 2 e 3 e 4 , ϕ 4 y ]
[ ] = 1
[ a 1 ] = a 1
[ a 1 , a 2 ] = 1 + a 1 a 2
[ a 1 , a 2 , a 3 , , a N ] = [ a 1 , a 2 , a 3 , , a N 2 ] + [ a 1 , a 2 , a 3 , , a N 1 ] a N
e 4 = K 4 y
e 0 e 4 = ϕ 4 y N m ϕ 1 y D n m
N m = ϕ 2 x 2 ϕ 4 y 2 2 ϕ 2 x ϕ 1 y ϕ 4 y 2 + ϕ 3 x 2 ϕ 1 y 2 + 2 ϕ 3 x 2 ϕ 1 y ϕ 4 y 2 ϕ 3 x ϕ 1 y ϕ 4 y 2
D n m = ϕ 2 x 2 ϕ 4 y 2 2 ϕ 2 x ϕ 1 y 2 ϕ 4 y + ϕ 3 x 2 ϕ 1 y 2 + 2 ϕ 2 x 2 ϕ 1 y ϕ 4 y 2 ϕ 3 x ϕ 1 y 2 ϕ 4 y
N m > ϕ 2 x 2 ϕ 4 y 2 2 ϕ 2 x ϕ 1 y ϕ 4 y 2 + ϕ 4 y 2 ϕ 1 y 2 + 2 ϕ 3 x 2 ϕ 1 y ϕ 4 y 2 ϕ 3 x ϕ 1 y ϕ 4 y 2 > ϕ 4 y 2 ( ϕ 2 x ϕ 1 y ) 2 + 2 ϕ 3 x ϕ 1 y ϕ 4 y ( ϕ 3 x ϕ 4 y ) > 0
D n m = ϕ 2 x 2 ϕ 4 y 2 2 ϕ 3 x ϕ 1 y 2 ϕ 4 y + ϕ 3 x 2 ϕ 1 y 2 + 2 ϕ 2 x 2 ϕ 1 y ϕ 4 y 2 ϕ 2 x ϕ 1 y 2 ϕ 4 y > ϕ 2 x 2 ϕ 4 y 2 2 ϕ 3 x ϕ 2 x ϕ 1 y ϕ 4 y + ϕ 3 x 2 ϕ 1 y 2 + 2 ϕ 2 x 2 ϕ 1 y ϕ 4 y 2 ϕ 2 x ϕ 1 y 2 ϕ 4 y > ( ϕ 2 x ϕ 4 y ϕ 3 x ϕ 1 y ) 2 + 2 ϕ 2 x ϕ 1 y ϕ 4 y ( ϕ 2 x ϕ 1 y ) > 0
e 1 + e s = 1 ϕ 1 y
e 2 e s = 1 ϕ 3 y
e s = 1 ϕ 2 x
e 2 + e 3 e s = 1 ϕ 4 x
e 1 = 1 ϕ 1 y 1 ϕ 2 x
e s = 1 ϕ 2 x
e 2 = 1 ϕ 2 x + 1 ϕ 3 y
e 3 = 1 ϕ 4 x 1 ϕ 3 y
K 3 y = e 3 + K 4 x
K 3 y = A y e 0 B y C y e 0 D y
K 4 x = A x ( e 0 + e 1 ) B x C x ( e 0 + e 1 ) D x
A x = [ ϕ 2 x , e 2 e 3 ]
B x = [ e 2 e 3 ]
C x = [ ϕ 2 x , e 2 e 3 , ϕ 4 x ]
D x = [ e 2 e 3 , ϕ 4 x ]
A y = [ ϕ 1 y , e 1 e 2 ]
B y = [ e 1 e 2 ]
C y = [ ϕ 1 y , e 1 e 2 , ϕ 3 y ]
D y = [ e 1 e 2 , ϕ 3 y ]
e 0 = ϕ 2 x 2 ϕ 3 y 2 2 ϕ 1 y ϕ 2 x ϕ 3 y 2 + ϕ 1 y 2 ϕ 4 x 2 + 2 ϕ 1 y ϕ 3 y ϕ 4 x 2 2 ϕ 1 y ϕ 3 y 2 ϕ 4 x ϕ 1 y 3 ϕ 4 x 2 ϕ 1 y ϕ 2 x 2 ϕ 3 y 2
H x = ϕ 2 x ϕ 4 x
H y = ϕ 1 y ϕ 3 y
α = H y H x = ϕ 1 y ϕ 4 x ϕ 2 x ϕ 3 y
e 2 + e s = A y C y
A y = [ ϕ 1 y , e 1 ]
B y = [ e 1 ]
C y = [ ϕ 1 y , e 1 , ϕ 2 y ]
D y = [ e 1 , ϕ 2 y ]
e s = 1 ϕ 3 x
K 2 y = K 3 x + e 2
K 2 y = A y e 0 B y C y e 0 D y
K 3 x = 1 ϕ 3 x 1 e 0 + e 1 + e 2
H x = K 3 x e 0 + e 1 + e 2
H y = 1 D y C y e 0
e 0 = ϕ 2 y ϕ 3 x α 3 ( ϕ 2 y 2 + ϕ 3 x 2 ) α 2 + ( 2 ϕ 1 y ϕ 3 x + ϕ 2 y ϕ 3 x 2 ϕ 1 y ϕ 2 y ) α ϕ 1 y 2 ϕ 1 y ϕ 2 y ϕ 3 x α ( α 2 1 )
e 1 = ϕ 1 y + ϕ 2 y ϕ 3 x α ϕ 1 y ϕ 2 y
e 2 + e s = 1 ϕ 2 x
e s = A y C y
A y = [ ϕ 1 y , e 1 e 2 ]
B y = [ e 1 e 2 ]
C y = [ ϕ 1 y , e 1 e 2 , ϕ 3 y ]
D y = [ e 1 e 2 , ϕ 3 y ]
K 2 x = K 3 y + e 2
K 2 x = 1 1 ϕ 2 x 1 e 0 + e 1
K 3 y = A y e 0 B y C y e 0 D y
H x = K 2 x e 0 + e 1
H y = 1 D y C y e 0
e 0 = ϕ 2x ϕ 3y α 3 ( ϕ 2 x 2 + ϕ 3 y 2 ) α 2 ( 2 ϕ 1y ϕ 3y ϕ 2x ϕ 3y 2 ϕ 1y ϕ 2x ) α ϕ 1 y 2 ϕ 1y ϕ 2x ϕ 3y α ( α 2 1 )
e 1 = ϕ 2 x 2 α 2 + ( ϕ 1 y ϕ 3 y ϕ 2 x ϕ 3 y 2 ϕ 1 y ϕ 2 x ) α + ϕ 1 y 2 ϕ 1 y ϕ 2 x ϕ 3 y α
e 2 = ϕ 1 y ( ϕ 2 x ϕ 3 y ) α ϕ 2 x ϕ 3 y α
e s = ϕ 2 x α ϕ 1 y ϕ 2 x ϕ 3 y α
e 1 = 1 ϕ 1 y 1 ϕ 2 x
K 1 y = K 2 x + e 1
K 1 y = 1 1 ϕ 1 y 1 e 0
K 2 x = 1 1 ϕ 2 x 1 e 0 + e 1
e 0 = ϕ 1 y ϕ 2 x ϕ 1 y ( ϕ 1 y + ϕ 2 x )
H y = ϕ 1 y + ϕ 2 x 2 ϕ 2 x
H x = ϕ 1 y + ϕ 2 x 2 ϕ 1 y
m = ϕ 1 y ϕ 2 x
[ A y B y C y D y ] [ 1 0 ] = [ α 0 ]
A y = [ ϕ 1 y , e 1 ]
B y = [ e 1 ]
C y = [ ϕ 1 y , e 1 , ϕ 2 y ]
D y = [ e 1 , ϕ 2 y ]
C y = 0
α = A y
e 1 = 1 ϕ 1 y + 1 ϕ 2 y
α = ϕ 1 y ϕ 2 y
K 2 y = e 0 e 1
e 0 = ϕ 1 y + ϕ 2 y ϕ 1 y ( ϕ 1 y ϕ 2 y )
E s = D C
A = [ ϕ 1 , e 1 , ϕ 2 , e 2 ]
B = [ e 1 , ϕ 2 , e 2 ]
C = [ ϕ 1 , e 1 , ϕ 2 , e 2 , ϕ 3 ]
D = [ e 1 , ϕ 2 , e 2 , ϕ 3 ]
e 0 = e s + E s
m = 1 D e 0 C
e 2 = e s e 1 m ϕ 1 2 + 1 e s ϕ 3 m ( e 1 ϕ 1 2 + e 1 ϕ 1 ϕ 3 ϕ 3 )
e 3 = A e 0 B C e 0 D
L = e 0 + e 1 + e 2 + e 3
e 12 e 1 2 + e 11 e 1 + e 10 = 0
e 12 = 4 e s ϕ 1 2 m ( ϕ 1 + ϕ 3 ) ( e s ϕ 1 2 m + e s ϕ 1 ϕ 3 m + ϕ 3 ) 2
e 11 = 4 e s ϕ 1 2 m ( ϕ 1 + ϕ 3 ) ( e s ϕ 1 2 m + e s ϕ 1 ϕ 3 m + ϕ 3 ) ( e s ϕ 3 m 2 2 e s ϕ 3 m L ϕ 3 + e s ϕ 3 + 2 )
e 10 = 4 ϕ 1 ( e s ϕ 1 2 m + e s ϕ 1 ϕ 3 m + ϕ 3 ) ( e s 2 ϕ 3 2 m 3 + 2 e s 2 ϕ 3 2 m 2 e s 2 ϕ 3 2 m + L e s ϕ 3 2 m + 1 )
e s ( e s ϕ 1 2 m + e s ϕ 1 ϕ 3 m + ϕ 3 ) 2 ( ϕ 1 + ϕ 3 ) 0

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