## A study of optical design and optimization of zoom optics with liquid lenses through modified genetic algorithm |

Optics Express, Vol. 19, Issue 17, pp. 16291-16302 (2011)

http://dx.doi.org/10.1364/OE.19.016291

Acrobat PDF (1632 KB)

### Abstract

A new concept for the optimization and optical design of miniature digital zoom optics with liquid lens elements is proposed in this research. The liquid lens elements are limited to the discrete configuration in order to obtain the optimal performance for digital zoom. We propose a newly developed digital zoom layout and optimization with a modified genetic algorism (GA) method, in order to meet the demands of a certain specification. The results show that we achieve a successful optical design and the optimization of the digital zoom optics with liquid optics, whose performance is greatly improved up to 48.68%, from the standpoint of on-axis spot size.

© 2011 OSA

## 1. Introduction

1. H. W. Ren, H. Q. Xianyu, S. Xu, and S.-T. Wu, “Adaptive dielectric liquid
lens,” Opt. Express **16**(19),
14954–14960 (2008). [CrossRef] [PubMed]

6. Y. C. Fang and C. M. Tsai, “Miniature lens design and optimization with
liquid lens element via genetic algorithm,” J.
Opt. A, Pure Appl. Opt. **10**(7), 075304
(2008). [CrossRef]

1. H. W. Ren, H. Q. Xianyu, S. Xu, and S.-T. Wu, “Adaptive dielectric liquid
lens,” Opt. Express **16**(19),
14954–14960 (2008). [CrossRef] [PubMed]

4. Varioptic Web, http://www.varioptic.com/en/index.php.

6. Y. C. Fang and C. M. Tsai, “Miniature lens design and optimization with
liquid lens element via genetic algorithm,” J.
Opt. A, Pure Appl. Opt. **10**(7), 075304
(2008). [CrossRef]

6. Y. C. Fang and C. M. Tsai, “Miniature lens design and optimization with
liquid lens element via genetic algorithm,” J.
Opt. A, Pure Appl. Opt. **10**(7), 075304
(2008). [CrossRef]

8. Y. C. Fang, T. K. Liu, C. M. Tsai, J.-H. Chou, H.-C. Lin, and W. T. Lin, “Extended optimization of chromatic
aberrations via a hybrid Taguchi–genetic algorithm for zoom optics with a
diffractive optical element,” J. Opt. A, Pure
Appl. Opt. **11**(4), 045706
(2009). [CrossRef]

9. J. N. Nash, “Direct torque control, induction motor
vector control without an encoder,” IEEE Trans.
Ind. Appl. **33**(2), 333–341
(1997). [CrossRef]

10. I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency
control strategy of an induction motor,” IEEE
Trans. Ind. Appl. **IA-22**(5),
820–827 (1986). [CrossRef]

13. R. Raman, “Image processing data flow in digital
cameras,” Proc. SPIE **3302**, 83–89
(1998). [CrossRef]

## 2. Layout and methodology of optical zoom design

4. Varioptic Web, http://www.varioptic.com/en/index.php.

## 3. Modified genetic algorithm (GA) optimization applied to zoom lens with liquid optics for extended optimization

**10**(7), 075304
(2008). [CrossRef]

8. Y. C. Fang, T. K. Liu, C. M. Tsai, J.-H. Chou, H.-C. Lin, and W. T. Lin, “Extended optimization of chromatic
aberrations via a hybrid Taguchi–genetic algorithm for zoom optics with a
diffractive optical element,” J. Opt. A, Pure
Appl. Opt. **11**(4), 045706
(2009). [CrossRef]

15. C. C. Chen, C. M. Tsai, and Y. C. Fang, “Optical design of LCOS optical engine and
optimization with genetic algorithm,” J. Disp.
Technol. **5**(8), 293–305
(2009). [CrossRef]

*p*, the population size of offspring

_{p}*p*, crossover rate

_{o}*p*, and mutation probability

_{c}*p*.

_{m}*p*individuals will be randomly created in the initial setting.

_{p}*Fit*(

*n*) in the proposal is defined as follows:where

*w*

_{1}~

*w*

_{9}are weights to tune the fitness value for various situations.

*k*of each zoom

*z*.

*z*.

*z*.

*z*. The distribution area

*P*(

*n*) of the wheel is calculated as follows:where the max is a fitness value of the worst individual and the

*sum*is the sum of the fitness values in each generation.

**x**= (

*x*

_{1},

*x*

_{2}, ...,

*x*) and

_{n}**y**= (

*y*

_{1},

*y*

_{2}, ...,

*y*) from the population are selected randomly according the roulette wheel method, then the crossover operation can be determined on the basis of the crossover rate

_{n}*p*in the next step. In this case, a multi-point crossover method is used for crossover strategy. The α is a random number from 0 to 1. If α ≧ 0.5, then the chromosomes

_{c}*x*and

_{i}*y*interchange, but otherwise they do not. Figure 5 shows the multi-point crossover operation.

_{i}*p*, then execute:where

_{m}*β*is a random number from 0 to 1, and

*u*and

_{i}*l*are the upper and lower boundaries of

_{i}*x*.

_{i}*Fit*(

*n*) (Eq. (1) above the paragraph), and Table 7 gives the parameter setting, Fig. 6 gives the gene mapping in the GA program. The multi-point crossover method is used for each gene in the crossover operation. The multi-point mutation method (Eg.3) is used for each curvature and thickness gene and the glass gene is chosen randomly from the glass database in the mutation operation.

_{1}, C

_{2},… C

_{x}denote the curvature gene, and T

_{1}, T

_{2},… T

_{y}the thickness gene, while G

_{1}, G

_{2},… G

_{z}represent the glass gene. x, y, and z are the numbers of curvature, thickness, and glass gene respectively. The GA program of the optical design in this research can be divided into four steps summed up as multi-object optical design optimization, as shown in Fig. 7 . The steps are as follows:

- (a): demand of optical specifications: the system will be extendedly optimized to meet the demand of the optical specifications.
- (b): Elimination of chromatic aberrations: the system will be extendedly optimized to eliminate the chromatic aberrations by CODE V with a GA program; the curvature, thickness, and glass material of each lens will be finally determined in this step.
- (c): MTF improvement: the system will be optimized to minimize the other aberrations by a modified GA program; by this, the displacement of each compensated lens will be determined.
- (d): Further improvement of lens performance: the aspheric surface of the liquid optics, if it can be precisely measured by an advanced interferometer, will significantly improve the final performance of this zoom optics.

## 4. Simulation and analysis

## 5. Conclusions and outlook

## Acknowledgments

## References and links

1. | H. W. Ren, H. Q. Xianyu, S. Xu, and S.-T. Wu, “Adaptive dielectric liquid
lens,” Opt. Express |

2. | C. C. Cheng and J. A. Yeh, “Dielectrically actuated liquid
lens,” Opt. Express |

3. | H. W. Ren and S. T. Wu, “Variable-focus liquid
lens,” Opt. Express |

4. | Varioptic Web, http://www.varioptic.com/en/index.php. |

5. | R. L. Peng, J. B. Chen, C. Zhu, and S. Zhuang, “Design of a zoom lens without motorized
optical elements,” Opt. Express |

6. | Y. C. Fang and C. M. Tsai, “Miniature lens design and optimization with
liquid lens element via genetic algorithm,” J.
Opt. A, Pure Appl. Opt. |

7. | Y. C. Fang, C. M. Tsai, J. Macdonald, and Y.-C. Pai, “Eliminating chromatic aberration in
Gauss-type lens design using a novel genetic algorithm,”
Appl. Opt. |

8. | Y. C. Fang, T. K. Liu, C. M. Tsai, J.-H. Chou, H.-C. Lin, and W. T. Lin, “Extended optimization of chromatic
aberrations via a hybrid Taguchi–genetic algorithm for zoom optics with a
diffractive optical element,” J. Opt. A, Pure
Appl. Opt. |

9. | J. N. Nash, “Direct torque control, induction motor
vector control without an encoder,” IEEE Trans.
Ind. Appl. |

10. | I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency
control strategy of an induction motor,” IEEE
Trans. Ind. Appl. |

11. | K. Illgner, H. G. Gruber, and P. Gelabert, P., et al. “Programmable DSP platform for digital still cameras,” IEEE International Conference on Acoustics, Speech, and Signal Processing, (1999). |

12. | S. Venkataraman, K. Peters, and R. Hecht, “Next generation digital camera integration
and software development issues,” Proc.
SPIE |

13. | R. Raman, “Image processing data flow in digital
cameras,” Proc. SPIE |

14. | G. Mitsuo and C. Runwei, “Genetic algorithms and engineering design,” (New York: John Wiley & Sons, 1997) |

15. | C. C. Chen, C. M. Tsai, and Y. C. Fang, “Optical design of LCOS optical engine and
optimization with genetic algorithm,” J. Disp.
Technol. |

**OCIS Codes**

(080.0080) Geometric optics : Geometric optics

(080.1010) Geometric optics : Aberrations (global)

(080.3620) Geometric optics : Lens system design

(080.1753) Geometric optics : Computation methods

**ToC Category:**

Geometric Optics

**History**

Original Manuscript: June 3, 2011

Revised Manuscript: July 28, 2011

Manuscript Accepted: August 2, 2011

Published: August 10, 2011

**Virtual Issues**

Vol. 6, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Yi-Chin Fang, Cheng-Mu Tsai, and Cheng-Lun Chung, "A study of optical design and optimization of zoom optics with liquid lenses through modified genetic algorithm," Opt. Express **19**, 16291-16302 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-16291

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### References

- H. W. Ren, H. Q. Xianyu, S. Xu, and S.-T. Wu, “Adaptive dielectric liquid lens,” Opt. Express 16(19), 14954–14960 (2008). [CrossRef] [PubMed]
- C. C. Cheng and J. A. Yeh, “Dielectrically actuated liquid lens,” Opt. Express 15(12), 7140–7145 (2007). [CrossRef] [PubMed]
- H. W. Ren and S. T. Wu, “Variable-focus liquid lens,” Opt. Express 15(10), 5931–5936 (2007). [CrossRef] [PubMed]
- Varioptic Web, http://www.varioptic.com/en/index.php .
- R. L. Peng, J. B. Chen, C. Zhu, and S. Zhuang, “Design of a zoom lens without motorized optical elements,” Opt. Express 15(11), 6664–6669 (2007). [CrossRef] [PubMed]
- Y. C. Fang and C. M. Tsai, “Miniature lens design and optimization with liquid lens element via genetic algorithm,” J. Opt. A, Pure Appl. Opt. 10(7), 075304 (2008). [CrossRef]
- Y. C. Fang, C. M. Tsai, J. Macdonald, and Y.-C. Pai, “Eliminating chromatic aberration in Gauss-type lens design using a novel genetic algorithm,” Appl. Opt. 46(13), 2401–2410 (2007). [CrossRef] [PubMed]
- Y. C. Fang, T. K. Liu, C. M. Tsai, J.-H. Chou, H.-C. Lin, and W. T. Lin, “Extended optimization of chromatic aberrations via a hybrid Taguchi–genetic algorithm for zoom optics with a diffractive optical element,” J. Opt. A, Pure Appl. Opt. 11(4), 045706 (2009). [CrossRef]
- J. N. Nash, “Direct torque control, induction motor vector control without an encoder,” IEEE Trans. Ind. Appl. 33(2), 333–341 (1997). [CrossRef]
- I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency control strategy of an induction motor,” IEEE Trans. Ind. Appl. IA-22(5), 820–827 (1986). [CrossRef]
- K. Illgner, H. G. Gruber, and P. Gelabert, P., et al. “Programmable DSP platform for digital still cameras,” IEEE International Conference on Acoustics, Speech, and Signal Processing, (1999).
- S. Venkataraman, K. Peters, and R. Hecht, “Next generation digital camera integration and software development issues,” Proc. SPIE 3302, 76–82 (1998). [CrossRef]
- R. Raman, “Image processing data flow in digital cameras,” Proc. SPIE 3302, 83–89 (1998). [CrossRef]
- G. Mitsuo and C. Runwei, “Genetic algorithms and engineering design,” (New York: John Wiley & Sons, 1997)
- C. C. Chen, C. M. Tsai, and Y. C. Fang, “Optical design of LCOS optical engine and optimization with genetic algorithm,” J. Disp. Technol. 5(8), 293–305 (2009). [CrossRef]

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