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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 2 — Jan. 28, 2013
  • pp: 1751–1761
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Zoom lens design using liquid lens for laparoscope

Seungwan Lee, Minseog Choi, Eunsung Lee, Kyu-Dong Jung, Jong-hyeon Chang, and Woonbae Kim  »View Author Affiliations


Optics Express, Vol. 21, Issue 2, pp. 1751-1761 (2013)
http://dx.doi.org/10.1364/OE.21.001751


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Abstract

Traditional laparoscopic optical systems consisting of about 30 lenses have low optical magnification. To magnify tissue during surgical operations, one must change from one laparoscope to another or use a magnifying adapter between the laparoscope and the sensor. Our work focuses on how to change the sag of a liquid lens while zooming from 1 × zoom, to 2 × , and 4 × in an optical design for a laparoscope. The design includes several lenses and two liquid lenses with variable focal lengths. A pair of laparoscopes for 3-D stereoscopy is placed within a tube 11 mm in diameter. The predicted depth resolution of tissue is 0.5 mm without interpolation at 4 × zoom.

© 2013 OSA

1. Introduction

Traditional laparoscopes used in minimally invasive surgery consist of many lenses and have limited visual properties, such as a fixed field of view, low magnification of 1 × –1.5 × , and high F-number at high zoom. High-definition (HD) image quality and 3-D imaging have recently become necessary in laparoscopes. A conventional surgical laparoscope consisting of more than 30 lenses is 30–40 cm long and 5–11 mm in diameter. The magnification is limited in optical systems using a zoom adaptor between the lens and the sensor. A zoom of 4 × was reported in a laparoscope using liquid lenses, called bio-inspired fluidic lenses [1

1. F. S. Tsai, D. Johnson, C. S. Francis, S. H. Cho, W. Qiao, A. Arianpour, Y. Mintz, S. Horgan, M. Talamini, and Y.-H. Lo, “Fluidic lens laparoscopic zoom camera for minimally invasive surgery,” J. Biomed. Opt. 15(3), 030504 (2010). [CrossRef] [PubMed]

]. In this paper, a laparoscope offering high zoom and 3-D stereoscopy by using a fluidic lens is proposed. The aim of this work is to determine how to change the sag of liquid lenses from 1 × zoom to 2 × and 4 × with no moving parts. It has been shown experimentally that stereoscopes, which provide 3-D vision, improve the precision and speed of endoscopic surgery [2

2. N. Taffinder, S. G. T. Smith, J. Huber, R. C. G. Russell, and A. Darzi, “The effect of a second-generation 3D endoscope on the laparoscopic precision of novices and experienced surgeons,” Surg. Endosc. 13(11), 1087–1092 (1999). [CrossRef] [PubMed]

, 3

3. W. B. Verwey, S. Stroomer, R. Lammens, S. N. Schulz, and W. H. Ehrenstein, “Comparing endoscopic systems on two simulated tasks,” Ergonomics 48(3), 270–287 (2005). [CrossRef] [PubMed]

]. The transverse resolution depends mostly on the size of the lens, wavelength of the light, and CCD [4

4. C. Pitris, M. E. Brezinski, B. E. Bouma, G. J. Tearney, J. F. Southern, and J. G. Fujimoto, “High resolution imaging of the upper respiratory tract with optical coherence tomography: a feasibility study,” Am. J. Respir. Crit. Care Med. 157(5 Pt 1), 1640–1644 (1998). [PubMed]

]. The depth of resolution in stereoscopy, δz (also referred to as the axial resolution) is expressed as follows [5

5. J. P. O. Evens, M. Robinson, S. X. Godber, and R. S. Petty, “The development of 3-D (stereoscopic) imaging systems for security applications,” in International Carnahan Conference on Security Technology (Sanderstead, England, 1995), 505–511.

]:
δz=Z2δP1Bf
(1)
where Z is the distance from the tissue at the point of interest in object space to the CMOS sensor, δP1 is the minimum detectable disparity in the image sensor plane (resolution in the xy plane), P1 = P(L) - P(R), B is the camera lens separation, and f is the focal length of the camera lenses. According to Eq. (1), the depth of resolution of 3-D stereoscope will be small at long focal lengths. The depth of resolution of 3-D stereoscope in zoom 4 × is 4 times smaller than zoom 1 × .

2. Tunable focal length by varying the curvature of a liquid lens for zooming

A simplified conceptual model of the zoom system consists of two tunable liquid lenses which works together to adjust the total zoom as shown Fig. 1
Fig. 1 Optical lens configuration using two liquids.
. Variable focal length in a lens can be achieved by changing its shape. Both liquid lenses are enclosed in a thin, transparent elastomer membrane. The curvature of the liquid-filled lenses at either end of the membrane is changed under pneumatic control. The effective focal length f of the two variable liquid lenses can be expressed as
1f=(n11)(n21)(1R1(n21)1R2(n11)+(d1n1+d2n2)1R1R2)
(2)
where n1 and n2 are the refractive index of liquids 1 and 2, respectively, and d1 and d2 are their lengths; R1 and R2 are the curvatures of lenses 1 and 2, respectively. If we use liquids having n1 = n2, then Eq. (2) can be expressed as follows.

1f=(n11)(1R11R2+(d1+d2)(n11)R1R2n1)
(3)

3. Lens design conditions

The effective focal length of a lens system depends on the refractive index and Abbe number of the lenses. The refractive index and Abbe number of liquid lenses can be modified by making a salt solution, as shown in Fig. 3
Fig. 3 (a) Refractive index vs. salt concentration; (b) Abbe number vs. salt concentration.
, that can have a refractive index ranging from n = 1.32 to n = 1.46. The refractive index of oil ranges widely from n = 1.3 to n = 2.3. But it is not easy to keep oil from permeating through polydimethylsiloxane (PDMS). It is known that PDMS can block water, which has a surface energy density of 72.8 mJ/m2, and the surface energy of a liquid increases as the salt concentration increases [6

6. W. Yao, H. Bjurstroem, and F. Setterwall, “Surface tension of lithium bromide solutions with heat-transfer additives,” J. Chem. Eng. Data 36(1), 96–98 (1991). [CrossRef]

]. In this paper, the optical lenses are designed to use a liquid based on deionized water instead of oil. The liquid lens is enclosed by a transparent PDMS membrane (Sylgard 186, Dow Corning). PDMS has several excellent characteristics and is widely used for micro fabrication of various lab-on-a-chip devices because it is inexpensive, biocompatible, self-sealable, and highly elastic; further, it has excellent optical transparency and allows for easy device fabrication [7

7. J. C. McDonald, D. C. Duffy, J. R. Anderson, D. T. Chiu, H. Wu, O. J. A. Schueller, and G. M. Whitesides, “Fabrication of microfluidic systems in poly(dimethylsiloxane),” Electrophoresis 21(1), 27–40 (2000). [CrossRef] [PubMed]

, 8

8. J. M. K. Ng, I. Gitlin, A. D. Stroock, and G. M. Whitesides, “Components for integrated poly(dimethylsiloxane) microfluidic systems,” Electrophoresis 23(20), 3461–3473 (2002). [CrossRef] [PubMed]

]. The refractive index and Abbe number of LiCl solution increases 0.002 and 0.1377 times the salt concentration, respectively, as shown in Fig. 3. The design boundary conditions and goals for the 3-D laparoscope are given in Table 1

Table 1. Design conditions and goals for optical lens

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. The maximum lens radius must be less 2.5 mm in order to insert two lens systems.

4. Lens design results

To reduce the chromatic aberration of the optical module, a DOE lens is applied to the iris cover surface using PDMS. The DOE is described in Code V by a continuous profile. The profile can be a function of x and y, φ(x, y), or rotationally symmetric, φ(r). The form of the phase profile is determined by the command HCT (Polynomial Grating Type). In a rotationally symmetric model, φ(r) is described by Eq. (7), where C1 = −0.000183, and C2 = −0.000445. The height and focal length of the DOE can be calculated by Eqs. (8) and (9), respectively, where λ0 is the design wavelength of light; n1(λ0) and n2(λ0) are the refractive index of the DOE lens and the surrounding refractive material, respectively. Figure 7
Fig. 7 Phase profile of DOE.
shows the phase function of the DOE. The number of DOE rings obtained using Eqs. (7) and (8) is 2.

φ(r)=2πλon=110Cnr2n
(7)
height=λon2(λo)n1(λo)=0.572μm1.49231=1.17μm
(8)
f=0.5Qudratic_Phase_Coefficient=0.5C1=2735.6
(9)

5. Lens design characterizations

The modulation transfer function (MTF) is an important parameter for evaluating the optical performance. Figures 8(a)
Fig. 8 Design result; MTF (a),(b) Wide angle mode 1 × , (left 0–0.5F, right 0.6F–1.0F). (c),(d) Middle angle zoom 2 × ; (c), (d) Tele angle, zoom 4 ×.
8(f) illustrate the MTF value and the optical distortion is shown in Fig. 9
Fig. 9 Design result; Optical distortion.
in wide-angle, medium-angle, and tele-angle mode. The optical performances are summarized in Table 2

Table 2. Summary of design result

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. Figure 10
Fig. 10 Image simulation result using USAF1951 chart; (a) zoom 1 × , (b) zoom 2 × ,(c) zoom 4 ×.
is the result of 2D image simulation using USAF 1951 chart by CODE V utility.

Table 3. Optical lens parameters

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Table 4. Lens parameters of liquid lens and iris

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Table 5. Lens parameters of aspheric polymer lens

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6. Conclusion

Using two tunable liquid lenses, several lenses, a DOE, and one iris, we designed a variable zoom system that can achieve 1 × , 2 × , and 4 × zoom for a laparoscope with no moving parts. The trace of the sag of the liquid lens from 1 × zoom to 4 × zoom was optimized in the liquid lens module. The total length of the module is 23.26 mm. Its diameter is less than 4.1 mm, so two modules can be placed in a laparoscope 11 mm in diameter. The effective focal lengths of the wide-angle zoom, medium-angle zoom, and zoom-in modes are 3.24 mm, 6.4 mm, and 12.94 mm, respectively. The MTFs in the zoom-out and zoom-in modes are 35% and 30% at a frequency of 140 lp/mm. The fluidic zoom at lower F-number (4.9–6.04) is brighter than that of a conventional solid laparoscope. The optical distortions in the zoom-out and zoom-in modes are 16% and 3%, respectively The z-direction depth resolutions of this 3-D laparoscope are expected to be <0.5 mm and <2 mm in zoom-in and zoom-out modes, respectively, without interpolation.

References and links

1.

F. S. Tsai, D. Johnson, C. S. Francis, S. H. Cho, W. Qiao, A. Arianpour, Y. Mintz, S. Horgan, M. Talamini, and Y.-H. Lo, “Fluidic lens laparoscopic zoom camera for minimally invasive surgery,” J. Biomed. Opt. 15(3), 030504 (2010). [CrossRef] [PubMed]

2.

N. Taffinder, S. G. T. Smith, J. Huber, R. C. G. Russell, and A. Darzi, “The effect of a second-generation 3D endoscope on the laparoscopic precision of novices and experienced surgeons,” Surg. Endosc. 13(11), 1087–1092 (1999). [CrossRef] [PubMed]

3.

W. B. Verwey, S. Stroomer, R. Lammens, S. N. Schulz, and W. H. Ehrenstein, “Comparing endoscopic systems on two simulated tasks,” Ergonomics 48(3), 270–287 (2005). [CrossRef] [PubMed]

4.

C. Pitris, M. E. Brezinski, B. E. Bouma, G. J. Tearney, J. F. Southern, and J. G. Fujimoto, “High resolution imaging of the upper respiratory tract with optical coherence tomography: a feasibility study,” Am. J. Respir. Crit. Care Med. 157(5 Pt 1), 1640–1644 (1998). [PubMed]

5.

J. P. O. Evens, M. Robinson, S. X. Godber, and R. S. Petty, “The development of 3-D (stereoscopic) imaging systems for security applications,” in International Carnahan Conference on Security Technology (Sanderstead, England, 1995), 505–511.

6.

W. Yao, H. Bjurstroem, and F. Setterwall, “Surface tension of lithium bromide solutions with heat-transfer additives,” J. Chem. Eng. Data 36(1), 96–98 (1991). [CrossRef]

7.

J. C. McDonald, D. C. Duffy, J. R. Anderson, D. T. Chiu, H. Wu, O. J. A. Schueller, and G. M. Whitesides, “Fabrication of microfluidic systems in poly(dimethylsiloxane),” Electrophoresis 21(1), 27–40 (2000). [CrossRef] [PubMed]

8.

J. M. K. Ng, I. Gitlin, A. D. Stroock, and G. M. Whitesides, “Components for integrated poly(dimethylsiloxane) microfluidic systems,” Electrophoresis 23(20), 3461–3473 (2002). [CrossRef] [PubMed]

9.

J.-H. Chang, K.-D. Jung, E. Lee, M. Choi, and S. Lee, “Microelectrofluidic iris for variable aperture,” Proc. SPIE 8252, 82520O, 82520O-6 (2012). [CrossRef]

10.

P. Muller, N. Spengler, H. Zappe, and W. Monch, “An optofluidic concept for a tunable micro-iris,” J. Microelectromech. Syst. 19(6), 1477–1484 (2010). [CrossRef]

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(220.3620) Optical design and fabrication : Lens system design

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: October 19, 2012
Revised Manuscript: December 9, 2012
Manuscript Accepted: December 12, 2012
Published: January 16, 2013

Virtual Issues
Vol. 8, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Seungwan Lee, Minseog Choi, Eunsung Lee, Kyu-Dong Jung, Jong-hyeon Chang, and Woonbae Kim, "Zoom lens design using liquid lens for laparoscope," Opt. Express 21, 1751-1761 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1751


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References

  1. F. S. Tsai, D. Johnson, C. S. Francis, S. H. Cho, W. Qiao, A. Arianpour, Y. Mintz, S. Horgan, M. Talamini, and Y.-H. Lo, “Fluidic lens laparoscopic zoom camera for minimally invasive surgery,” J. Biomed. Opt.15(3), 030504 (2010). [CrossRef] [PubMed]
  2. N. Taffinder, S. G. T. Smith, J. Huber, R. C. G. Russell, and A. Darzi, “The effect of a second-generation 3D endoscope on the laparoscopic precision of novices and experienced surgeons,” Surg. Endosc.13(11), 1087–1092 (1999). [CrossRef] [PubMed]
  3. W. B. Verwey, S. Stroomer, R. Lammens, S. N. Schulz, and W. H. Ehrenstein, “Comparing endoscopic systems on two simulated tasks,” Ergonomics48(3), 270–287 (2005). [CrossRef] [PubMed]
  4. C. Pitris, M. E. Brezinski, B. E. Bouma, G. J. Tearney, J. F. Southern, and J. G. Fujimoto, “High resolution imaging of the upper respiratory tract with optical coherence tomography: a feasibility study,” Am. J. Respir. Crit. Care Med.157(5 Pt 1), 1640–1644 (1998). [PubMed]
  5. J. P. O. Evens, M. Robinson, S. X. Godber, and R. S. Petty, “The development of 3-D (stereoscopic) imaging systems for security applications,” in International Carnahan Conference on Security Technology (Sanderstead, England, 1995), 505–511.
  6. W. Yao, H. Bjurstroem, and F. Setterwall, “Surface tension of lithium bromide solutions with heat-transfer additives,” J. Chem. Eng. Data36(1), 96–98 (1991). [CrossRef]
  7. J. C. McDonald, D. C. Duffy, J. R. Anderson, D. T. Chiu, H. Wu, O. J. A. Schueller, and G. M. Whitesides, “Fabrication of microfluidic systems in poly(dimethylsiloxane),” Electrophoresis21(1), 27–40 (2000). [CrossRef] [PubMed]
  8. J. M. K. Ng, I. Gitlin, A. D. Stroock, and G. M. Whitesides, “Components for integrated poly(dimethylsiloxane) microfluidic systems,” Electrophoresis23(20), 3461–3473 (2002). [CrossRef] [PubMed]
  9. J.-H. Chang, K.-D. Jung, E. Lee, M. Choi, and S. Lee, “Microelectrofluidic iris for variable aperture,” Proc. SPIE8252, 82520O, 82520O-6 (2012). [CrossRef]
  10. P. Muller, N. Spengler, H. Zappe, and W. Monch, “An optofluidic concept for a tunable micro-iris,” J. Microelectromech. Syst.19(6), 1477–1484 (2010). [CrossRef]

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