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Variable-focus lens with 1-kHz bandwidth

Hiromasa Oku, Koichi Hashimoto, and Masatoshi Ishikawa

Open Access Open Access

Abstract

This paper proposes a variable-focus lens with 1-kHz bandwidth. The lens transforms its shape rapidly using the liquid pressure generated by a piezo stack actuator. This mechanism also includes a built-in motion amplifier with high bandwidth to compensate for the short working range of the piezo stack actuator. Prototypes have been developed to validate the proposed design. A 1-kHz bandwidth of the lenses was confirmed by measuring the frequency responses. Refractive power ranging from -1/167 to 1/129 mm-1 and a maximum resolution of 12.3 cycles/mm were attained.

©2004 Optical Society of America

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Figures (10)
Fig. 1.
Fig. 1. (a) Schematic diagram of the proposed lens structure, and (b) its focusing mechanism.

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Fig. 2.
Fig. 2. Disk model.

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Fig. 3.
Fig. 3. Materials [4][9][10]: Glasses were arbitrarily selected from a thin sheet glass catalogue (Corning Inc.). Metals are plotted because they can be used as a material for the cylinder.

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Fig. 4.
Fig. 4. Prototype #1 :(a) photograph, and (b) schematic figure of the structure and fabrication process

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Fig. 5.
Fig. 5. Prototype #2:(a) photograph, and (b) schematic diagram of the structure and fabrication process.

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Fig. 6.
Fig. 6. Bode plot of frequency response for prototype #1 (a) and prototype #2 (b). The input was the displacement of the piezo stack actuator, and the output was the displacement of the center of the lens surface. The gain is the ratio of the maximum amplitude of the lens to the maximum amplitude of the piezo stack actuator. In this plot, the gain was normalized by dividing the entire set using a certain value. The phase plot shows the shift between the output and the input.

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Fig. 7.
Fig. 7. Trajectories of the lens surface and the piezo stack actuator displacement during the measurement of frequency response of 1 kHz for prototype #1 (a) and prototype #2 (b).

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Fig. 8.
Fig. 8. Refractive power versus piezo stack actuator displacement

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Fig. 9.
Fig. 9. Measured surface profiles, fitted curves, and error profiles. Surface profiles (a) of prototype #2 were measured at various focal lengths. Each surface profile was fitted with a fourth-order polynomial. Fitted curves are shown in column (b). Column (c) shows the error between the measured surface profile and the fitted curve.

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Fig. 10.
Fig. 10. Image of the positive standard test chart using the proposed lens prototype when the focal length was 174 mm.

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Tables (4)

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Table 1. Relations between parameters

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Table 2. Mechanical specifications

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Table 3. Deflected lens surfaces were fitted with theoretical fourth-order polynomials. The displacement of the piezo stack actuator (δ), coefficients of the fitted curves (r 4, r 2), goodness of the fit (Q), estimated focal length (f), and estimated Seidel spherical aberration (SA) are shown.

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Table 4. Resolution was measured using a USAF 1951 standard test target at various focal lengths f. Vertical and horizontal resolutions are shown.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ω m , n = k m , n 2 d 1 12 ( 1 − ν 2 ) E ρ ( m , n = 0,1,2 , ⋯ ) .
I m ( k m , n a ) J m − 1 ( k m , n a ) − J m ( k m , n a ) I m − 1 ( k m , n a ) = 0 .
R ( r ) = a 4 P 64 D { ( r a ) 4 − 2 ( r a ) 2 + 1 } ,
D = E d 3 12 ( 1 − ν 2 ) .
c = a 2 16 D P .
S = c P = a 2 16 D = 3 4 a 2 ( 1 − ν 2 ) E d 3 .
1 f = 4 ( n r − 1 ) a C 2 a L 4 Δ C + K ,
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