Chinese Optics Letters, Volume. 23, Issue 8, 081102(2025)
Compact mechanical Alvarez lenses with a wide varifocal range using a cam-driver
Figures & Tables(16)
Fig. 1. Schematic of the varifocal principle of the Alvarez lenses. (a) The Alvarez lenses act as a convex lens. (b) The Alvarez lenses act as a parallel plate. (c) The Alvarez lenses act as a concave lens.
Fig. 2. 3D layout of the proposed optimized varifocal Alvarez lenses.
Fig. 3. Spot diagrams of the proposed varifocal Alvarez lenses at focal lengths of (a) 15, (b) 45, and (c) 75 mm, respectively.
Fig. 4. (a)–(c) MTF and (d)–(f) image simulation results of the proposed varifocal lenses at focal lengths of 15, 45, and 75 mm, respectively.
Fig. 5. (a) Explosion diagram of cam-driven structure. (b) When the driving ring rotates to the left, the front frame for phase plates moves to the right, and the back frame moves to the left. (c) When the driving ring rotates to the right, the front frame moves to the left, and the rear frame moves to the right.
Fig. 6. (a) A pair of phase plates of the Alvarez lenses. (b) Surface roughness test results of freeform surfaces of the phase plate. (c) The fabricated varifocal Alvarez lenses.
Fig. 8. Measurement principle of the focal length of the proposed varifocal Alvarez lenses by the shearing interferometer.
Fig. 9. Experimental measurement diagram of the focal length of the varifocal Alvarez lenses.
Fig. 10. (a) Varifocal imaging experiment with a fixed object distance. The resolution test chart is placed at 500 mm in front of the proposed varifocal Alvarez lenses. The images captured by the proposed varifocal Alvarez lenses with back focal lengths of (b) 6, (c) 14, and (d) 19 mm.
Fig. 11. (a) Varifocal imaging experiment with fixed image distance. When the back focal length is 6 mm, the proposed varifocal Alvarez lenses focus on objects at different object distances. (b)–(d) Images captured by the varifocal Alvarez lens when the object is positioned at distances of 130, 217, and 331 mm from the varifocal Alvarez lenses.
Fig. 12. (a) Measurement experimental schematic of proposed varifocal Alvarez lenses. (b)–(d) Zernike coefficients when the focal lengths of the proposed varifocal Alvarez lenses are 75, 36.80, and 15 mm, respectively.
Table 1. Design Specifications for Proposed Varifocal Alvarez Lenses
View tableView in ArticleTable 1. Design Specifications for Proposed Varifocal Alvarez Lenses
f′ = 15 mm f′ = 45 mm f′ = 75 mm Entrance pupil diameter (mm) 3 3 3 Field of view (°) 24.20 8.62 4.90 Displacement (mm) 1.19 −0.45 −0.79 Image circle (mm) 6.56 6.87 6.51 F/# number 5 15 25 Distortion (%) 0.99 0.84 0.32 Sensor 1/2.7′′ Working wavelength 486–656 nm
Table 2. Prescription Data of the Proposed Optimized Varifocal Alvarez Lenses
View tableView in ArticleTable 2. Prescription Data of the Proposed Optimized Varifocal Alvarez Lenses
Surface No. Surface type Radius (mm) Thickness (mm) Material Description 1 Standard 14.04 5.00 F5 — 2 Standard 7.24 1.20 Air — 3 Standard 6.48 3.29 H-K12 — 4 Standard −5.66 4.39 H-LAF7 — 5 Standard −11.66 0.55 Air — 6 Standard Infinity 0.50 Air Stop 7 Coordinates Break — 0 Air X-displacement 8 Extended Polynomial Infinity 3.00 PMMA Alvarez element 1 9 Extended Polynomial Infinity 0.70 Air Alvarez element 1 10 Coordinates Break Infinity 0 Air X-displacement 11 Coordinates Break — 0 Air X-displacement 12 Extended Polynomial Infinity 3.00 PMMA Alvarez element 2 13 Extended Polynomial Infinity 0 Air Alvarez element 2 14 — 2.56 Air X-displacement 15 Standard −5.18 1.27 H-FK95N — 16 Standard 69.40 1.79/13.77/25.80 Air — 17 Standard Infinity — — —
Table 3. High-Order Term Coefficients of the Freeform Surface of Alvarez Lenses
View tableView in ArticleTable 3. High-Order Term Coefficients of the Freeform Surface of Alvarez Lenses
Surface 8 (13) Surface 9 (12) Surface 8 (13) Surface 9 (12) X0Y1 — 3.95 × 10-3 X1Y4 1.95 × 10−4 X1Y0 — 3.04 × 10−2 X6Y0 1.26 × 10−5 X0Y2 −1.05 × 10−3 −1.14 × 10−5 X4Y2 6.38 × 10−5 X1Y1 7.69 × 10−6 4.22 × 10−4 X3Y3 3.22 × 10−5 X2Y0 −4.53 × 10−4 6.86 × 10−4 X0Y6 −9.84 × 10−5 X3Y0 7.06 × 10−4 0.01 X5Y2 −7.64 × 10−5 X2Y1 −4.22 × 10−5 −3.86 × 10−5 X3Y4 1.08 × 10−5 X1Y2 2.03 × 10−3 0.02 X2Y5 1.58 × 10−6 X0Y3 2.03 × 10−4 1.66 × 10−3 X8Y0 1.10 × 10−5 X4Y0 −6.74 × 10−5 1.97 × 10−4 X6Y2 −1.20 × 10−5 X3Y1 2.92 × 10−6 2.22 × 10−5 X5Y3 −7.92 × 10−6 X2Y2 — 1.07 × 10 X2Y6 −1.71 × 10−6 X1Y3 4.99 × 10−5 −1.16 × 10−5 X0Y8 −5.95 × 10−6 X0Y4 −4.50 × 10−6 3.84 × 10−5 X8Y1 5.63 × 10−8 X3Y2 — 3.12 × 10−4 X7Y2 6.98 × 10−6 X2Y3 — −4.35 × 10−6
Table 4. Comparison of the Proposed Alvarez Varifocal Lenses With Other References
View tableView in ArticleTable 4. Comparison of the Proposed Alvarez Varifocal Lenses With Other References
Ref. Actuator Displacement (mm) Focal length/Zoom range Largest dimension (mm) Resolution (lp/mm) F/# [ 12 ]Piezoelectric bender 0.11 3× — 120 — [ 21 ]Displacement platform 2 103.50–34.50 mm (3×) — — 2.80–4.30 [ 22 ]Micro-electro-mechanical system 0.04 4.65–3.00 mm (1.55×) — — — [ 26 ]Liquid crystal elastomer 0.18 28.4–25.1 mm (1.13×) — 2.20 — [ 29 ]Displacement platform 1.80 170–40 mm (4.25×) — — 3.80–9.50 [ 34 ]Piezo actuator 0.13 19.64–10.63 mm (1.85×) — — — [ 35 ]Voice coil motor 3 14.10–4.45 mm (3.17×) 25 176 2.42–3.40 [ 36 ]Dielectric elastomer 2 10× 65 25 — This paper Cam-driver 2 75–15 mm (5×) 30.50 40 5–25
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Cancan Yao, Qun Hao, Lin Liu, Jie Cao, Haoyue Xing, Zhaohui Li, Yang Cheng, "Compact mechanical Alvarez lenses with a wide varifocal range using a cam-driver," Chin. Opt. Lett. 23, 081102 (2025)
Paper Information
Category: Imaging Systems and Image Processing
Received: Feb. 28, 2025
Accepted: Apr. 8, 2025
Published Online: Jul. 23, 2025
The Author Email: Yang Cheng (yangcheng2007@163.com)
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