First-order analysis of zoom system based on variable focal power lens

Hongtao Cheng; Hang Liu; Hengyu Li

doi:10.1364/OE.23.012258

Abstract

We present our analysis of a zoom system based on the variable focal power lens, and we demonstrate how our analysis can be used in zoom system design. The transverse magnification is considered as an independent first-order optics control parameter in the zoom system. The zoom system equations are established through the use of matrix optics. Formulas related to the zoom principles and performance of such optical systems are derived, and numerical and theoretical values are compared using examples.

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References

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P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]
Y. Lin, M. Chen, and H. Lin, “An electrically tunable optical zoom system using two composite liquid crystal lenses with a large zoom ratio,” Opt. Express 19(5), 4714–4721 (2011).
[Crossref] [PubMed]
N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
[Crossref] [PubMed]
A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18(7), 6797–6810 (2010).
[Crossref] [PubMed]
Q. Hao, X. Cheng, and K. Du, “Four-group stabilized zoom lens design of two focal-length-variable elements,” Opt. Express 21(6), 7758–7767 (2013).
[Crossref] [PubMed]
A. Miks and J. Novak, “Paraxial analysis of three-component zoom lens with fixed distance between object and image points and fixed position of image-space focal point,” Opt. Express 22(13), 15571–15576 (2014).
[Crossref] [PubMed]
A. Miks and J. Novak, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable- focus lenses,” Opt. Laser Eng. 53(2), 86–89 (2014).
[Crossref]
A. Miks and J. Novak, “Three-component double conjugate zoom lens system from tunable focus lenses,” Appl. Opt. 52(4), 862–865 (2013).
[Crossref] [PubMed]
C. Tao, “Design of zoom system by the varifocal differential equation,” Appl. Opt. 31(13), 2265–2273 (1992).
[Crossref]
A. D. Clark, Zoom Lenses (Adam Hilger, 1973).
R. Ditteon, Modern Geometrical Optics (Wiley, 1998).

2014 (2)

A. Miks and J. Novak, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable- focus lenses,” Opt. Laser Eng. 53(2), 86–89 (2014).
[Crossref]

A. Miks and J. Novak, “Paraxial analysis of three-component zoom lens with fixed distance between object and image points and fixed position of image-space focal point,” Opt. Express 22(13), 15571–15576 (2014).
[Crossref] [PubMed]

Clark, A. D.

A. D. Clark, Zoom Lenses (Adam Hilger, 1973).

Ditteon, R.

R. Ditteon, Modern Geometrical Optics (Wiley, 1998).

Dodge, M. R.

P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]

Du, K.

Q. Hao, X. Cheng, and K. Du, “Four-group stabilized zoom lens design of two focal-length-variable elements,” Opt. Express 21(6), 7758–7767 (2013).
[Crossref] [PubMed]

Hao, Q.

Q. Hao, X. Cheng, and K. Du, “Four-group stabilized zoom lens design of two focal-length-variable elements,” Opt. Express 21(6), 7758–7767 (2013).
[Crossref] [PubMed]

Lin, H.

Y. Lin, M. Chen, and H. Lin, “An electrically tunable optical zoom system using two composite liquid crystal lenses with a large zoom ratio,” Opt. Express 19(5), 4714–4721 (2011).
[Crossref] [PubMed]

Lin, Y.

Y. Lin, M. Chen, and H. Lin, “An electrically tunable optical zoom system using two composite liquid crystal lenses with a large zoom ratio,” Opt. Express 19(5), 4714–4721 (2011).
[Crossref] [PubMed]

Miks, A.

A. Miks and J. Novak, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable- focus lenses,” Opt. Laser Eng. 53(2), 86–89 (2014).
[Crossref]

A. Miks and J. Novak, “Paraxial analysis of three-component zoom lens with fixed distance between object and image points and fixed position of image-space focal point,” Opt. Express 22(13), 15571–15576 (2014).
[Crossref] [PubMed]

A. Miks and J. Novak, “Three-component double conjugate zoom lens system from tunable focus lenses,” Appl. Opt. 52(4), 862–865 (2013).
[Crossref] [PubMed]

A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18(7), 6797–6810 (2010).
[Crossref] [PubMed]

Novak, J.

A. Miks and J. Novak, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable- focus lenses,” Opt. Laser Eng. 53(2), 86–89 (2014).
[Crossref]

A. Miks and J. Novak, “Paraxial analysis of three-component zoom lens with fixed distance between object and image points and fixed position of image-space focal point,” Opt. Express 22(13), 15571–15576 (2014).
[Crossref] [PubMed]

A. Miks and J. Novak, “Three-component double conjugate zoom lens system from tunable focus lenses,” Appl. Opt. 52(4), 862–865 (2013).
[Crossref] [PubMed]

A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18(7), 6797–6810 (2010).
[Crossref] [PubMed]

Peyghambarian, N.

N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
[Crossref] [PubMed]

P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]

Peyman, G.

N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
[Crossref] [PubMed]

P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]

Savidis, N.

N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
[Crossref] [PubMed]

Schwiegerling, J.

N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
[Crossref] [PubMed]

P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]

Tao, C.

C. Tao, “Design of zoom system by the varifocal differential equation,” Appl. Opt. 31(13), 2265–2273 (1992).
[Crossref]

Valley, P.

P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]

Appl. Opt. (3)

N. Savidis, G. Peyman, N. Peyghambarian, and J. Schwiegerling, “Nonmechanical zoom system through pressure-controlled tunable fluidic lenses,” Appl. Opt. 52(12), 2858–2865 (2013).
[Crossref] [PubMed]

A. Miks and J. Novak, “Three-component double conjugate zoom lens system from tunable focus lenses,” Appl. Opt. 52(4), 862–865 (2013).
[Crossref] [PubMed]

C. Tao, “Design of zoom system by the varifocal differential equation,” Appl. Opt. 31(13), 2265–2273 (1992).
[Crossref]

Opt. Express (4)

A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18(7), 6797–6810 (2010).
[Crossref] [PubMed]

Q. Hao, X. Cheng, and K. Du, “Four-group stabilized zoom lens design of two focal-length-variable elements,” Opt. Express 21(6), 7758–7767 (2013).
[Crossref] [PubMed]

A. Miks and J. Novak, “Paraxial analysis of three-component zoom lens with fixed distance between object and image points and fixed position of image-space focal point,” Opt. Express 22(13), 15571–15576 (2014).
[Crossref] [PubMed]

Y. Lin, M. Chen, and H. Lin, “An electrically tunable optical zoom system using two composite liquid crystal lenses with a large zoom ratio,” Opt. Express 19(5), 4714–4721 (2011).
[Crossref] [PubMed]

Opt. Laser Eng. (1)

A. Miks and J. Novak, “Paraxial imaging properties of double conjugate zoom lens system composed of three tunable- focus lenses,” Opt. Laser Eng. 53(2), 86–89 (2014).
[Crossref]

Opt. Lett. (1)

P. Valley, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett. 35(15), 2582–2584 (2010).
[Crossref] [PubMed]

Other (2)

A. D. Clark, Zoom Lenses (Adam Hilger, 1973).

R. Ditteon, Modern Geometrical Optics (Wiley, 1998).

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Fig. 1 Two-element variable focal power lens zoom system.

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Fig. 2 Control curve relating focal power with magnification.

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Fig. 3 Plot of aperture stop size R_Px as function of magnification.

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Tables (3)

Table 1 System parameters.

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Table 2 Select values of magnification and corresponding focal powers of lenses a and b.

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Table 3 Comparison of calculated values (obtained using proposed approach) with theoretical values (obtained using ray-tracing) for select values of magnification.

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Equations (31)

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S = [\begin{matrix} 1 - d_{2} ϕ_{a} & d_{2} \\ d_{2} ϕ_{a} ϕ_{b} - ϕ_{a} - ϕ_{b} & 1 - d_{2} ϕ_{b} \end{matrix}] .

ϕ = \frac{1}{f^{'}} = ϕ_{a} + ϕ_{b} - d_{2} ϕ_{a} ϕ_{b} .

m = \frac{1}{(d_{2} ϕ_{a} ϕ_{b} - ϕ_{a} - ϕ_{b}) \times d_{1} + 1 - d_{2} ϕ_{b}},

d_{3} = \frac{1}{d_{2} ϕ_{a} ϕ_{b} - ϕ_{a} - ϕ_{b}} [m - (1 - d_{2} ϕ_{a})],

d_{1} + d_{2} + d_{3} = d .

ϕ_{a} = \frac{d + (d_{1} + d_{2}) (m - 1)}{m d_{1} d_{2}},

ϕ_{b} = \frac{d + d_{1} (m - 1)}{d_{2} (d - d_{1} - d_{2})} .

ϕ_{a} = α + β / m,

ϕ_{b} = χ + η m,

\begin{matrix} α = \frac{d_{1} + d_{2}}{d_{1} d_{2}}, \\ β = \frac{d - d_{1} - d_{2}}{d_{1} d_{2}}, \\ χ = \frac{d - d_{1}}{d_{2} (d - d_{1} - d_{2})}, \\ η = \frac{d_{1}}{d_{2} (d - d_{1} - d_{2})} . \end{matrix}

N = T_{j - 1} R_{j - 1} \dots T_{1} R_{1} T_{0},

T_{j} = [\begin{matrix} 1 & d_{j + 1} \\ 0 & 1 \end{matrix}], R_{j} = [\begin{matrix} 1 & 0 \\ - ϕ_{j} & 1 \end{matrix}] .

[\begin{matrix} N_{11} & N_{12} \\ N_{21} & N_{22} \end{matrix}] .

| \frac{R_{1}}{N_{12}} | = | \frac{R_{a}}{d_{1}} |,

| \frac{R_{2}}{N_{12}} | = | \frac{R_{p x}}{(1 - d_{x} ϕ_{a}) d_{1} + d_{x}} |,

| \frac{R_{3}}{N_{12}} | = | \frac{R_{b}}{(1 - d_{2} ϕ_{a}) d_{1} + d_{2}} | .

{\vec{Q}}_{1} = [\begin{matrix} 1 - d_{x} ϕ_{a} & d_{x} \\ - ϕ_{a} & 1 \end{matrix}] .

l_{E} = \frac{d_{x}}{1 - d_{x} ϕ_{a}},

R_{E} = \frac{R_{P x}}{1 - d_{x} ϕ_{a}} .

{\vec{Q}}_{2} = [\begin{matrix} 1 & d_{2} - d_{x} \\ - ϕ_{b} & 1 - ϕ_{b} (d_{2} - d_{x}) \end{matrix}] .

l_{E^{'}} = - \frac{d_{2} - d_{x}}{1 - ϕ_{b} (d_{2} - d_{x})},

R_{E^{'}} = \frac{R_{P x}}{1 - ϕ_{b} (d_{2} - d_{x})} .

\frac{D}{f^{'}} = \frac{2 R_{E}}{ϕ^{- 1}} = \frac{2 R_{P x}}{1 - d_{x} ϕ_{a}} \times (ϕ_{a} + ϕ_{b} - d_{2} ϕ_{a} ϕ_{b}),

\frac{D}{f^{'}} = \frac{2 R_{P x}}{1 - d_{x} (α + β / m)} \times [α + β / m + χ + η m - d_{2} (α + β / m) (χ + η m)] .

R_{P x} = \frac{1}{2} (\frac{D}{f^{'}}) \frac{(A m + B)}{(C m^{2} + E m + F)},

\begin{matrix} A = 1 - d_{x} α, \\ B = - d_{x} β, \\ C = η (1 - d_{2} α), \\ E = α + χ - d_{2} (α χ + β η), \\ F = β (1 - d_{2} χ) . \end{matrix}

α = χ = 3 / 20, β = η = 1 / 10.

ϕ_{a} = \frac{3}{20} + \frac{1}{10 m},

ϕ_{b} = \frac{3}{20} + \frac{m}{10} .

ϕ_{a b} = - \frac{2 m^{2} + m + 2}{40 m} .

R_{P x} = - \frac{5 (m - 2)}{2 (2 m^{2} + m + 2)} .

m	ϕ_a	ϕ_b
−5	0.13	−0.35
−2.5	0.11	−0.1
−0.5/	−0.05	0.1

m	total focal power(our method)	total focal power(using ray-tracing)
−5	0.235	0.235
−2.5	0.12	0.12
−0.5	0.1	0.1

m	ϕ_a	ϕ_b
−5	0.13	−0.35
−2.5	0.11	−0.1
−0.5/	−0.05	0.1

m	total focal power(our method)	total focal power(using ray-tracing)
−5	0.235	0.235
−2.5	0.12	0.12
−0.5	0.1	0.1

Abstract

References

2014 (2)

2013 (3)

2011 (1)

2010 (2)

1992 (1)

Chen, M.

Cheng, X.

Clark, A. D.

Ditteon, R.

Dodge, M. R.

Du, K.

Hao, Q.

Lin, H.

Lin, Y.

Miks, A.

Novak, J.

Peyghambarian, N.

Peyman, G.

Savidis, N.

Schwiegerling, J.

Tao, C.

Valley, P.

Appl. Opt. (3)

Opt. Express (4)

Opt. Laser Eng. (1)

Opt. Lett. (1)

Other (2)

Cited By

Figures (3)

Tables (3)

Equations (31)

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