## Highly flexible MTF measurement system for tunable micro lenses

Optics Express, Vol. 18, Issue 12, pp. 12458-12469 (2010)

http://dx.doi.org/10.1364/OE.18.012458

Acrobat PDF (978 KB)

### Abstract

We present an efficient, low-cost modulation transfer function (MTF) measurement approach, optimized for characterization of tunable micro-lenses; the MTF may easily be measured at a variety of different focal lengths. The approach uses a conventional optical microscope with an optimized approach for lens illumination and the measurement results have been correlated with a commercial MTF measurement system. Measurements on fixed-focus and tunable micro-lenses were performed; for the latter, resolution for lenses with back focal length of 11 mm was 55 lines/mm, decreasing to 40 lines/mm for a back focal length of 4 mm. In general, it was seen that performance was better for lenses with longer focal lengths.

© 2010 OSA

## 1. Introduction

1. J. C. Roulet, R. Völkel, H. P. Herzig, E. Verpoorte, N. F. deRooij, and R. Dändliker, “Microlens systems for fluorescence detection in chemical microsystems,” Opt. Eng. **40**(5), 814–821 (2001). [CrossRef]

2. A. Divetia, T. H. Hsieh, J. Zhang, Z. P. Chen, M. Bachman, G.-P. Li, M Bachman, and G. P Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. **86**(10), 103902 (2005). [CrossRef]

3. K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optical tunable probe for endoscopic optical coherence tomography,” J. Opt. A, Pure Appl. Opt. **10**(4), 044012 (2008). [CrossRef]

4. J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable-focusing microlens with microfluidic chip,” J. Micromech. Microeng. **14**(5), 675–680 (2004). [CrossRef]

6. H. W. Ren and S. T. Wu, “Variable-focal liquid lens,” Opt. Express **15**(10), 5931–5936 (2007). [CrossRef] [PubMed]

7. D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tenability,” Appl. Phys. Lett. **82**(19), 3171–3172 (2003). [CrossRef]

8. J. Lee, J. D. Rogers, M. R. Descour, E. Hsu, J. Aaron, K. Sokolov, and R. Richards-Kortum, “Imaging quality assessment of multi-modal miniature microscope,” Opt. Express **11**(12), 1436–1451 (2003). [CrossRef] [PubMed]

10. R. R. Rawer, W. Stork, C. W. Spraul, and C. Lingenfelder, “Imaging quality of intraocular lenses,” J. Cataract Refract. Surg. **31**(8), 1618–1631 (2005). [CrossRef] [PubMed]

## 2. Tunable micro-lens

11. A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. **44**(16), 3238–3245 (2005). [CrossRef] [PubMed]

## 3. Measurement setup

## 4. Theoretical basics

### 4.1 System response

*I*is given by the convolution of the ideal image and the system impulse response as where

_{i}(x_{i}, y_{i})*I*is the real intensity distribution in the image plane,

_{i}(x_{i}, y_{i})*h*is the system impulse response (PSF or LSF), and represents the convolution operation [14].

_{I}(x_{i}, y_{i})*I*is the intensity distribution of the ideal image predicted by geometrical optics (considering the magnification of the optical system). If there are no diffraction and aberration effects in the optical system, the system impulse response

_{g}(x_{i}, y_{i})*h*is a delta function, and this perfect optical system is capable of generating a point image of a point object.

_{I}(x_{i}, y_{i})*F*corresponds to the frequency spectrum of the real image,

_{i}(f_{x}, f_{y})*F*is the frequency spectrum of the ideal image, and

_{g}(f_{x}, f_{y})*H*is the OTF; the latter can thus easily be calculated by a point-by-point division of

_{I}(f_{x}, f_{y})*F*and

_{i}(f_{x}, f_{y})*F*. The MTF, our ultimate goal, is then simply found as the absolute value of

_{g}(f_{x}, f_{y})*H*The intensity distribution is recorded by the integrated CCD camera, readout by the microscope software and analyzed by Matlab routines.

_{I}(f_{x}, f_{y}).### 4.2 Relationship between PSF and LSF

*x*and constant in

*y*.

### 4.3 Spatial frequency calibration

#### 4.3.1 Calibration of the image-receiver MTF (real image frequency correction)

#### 4.3.2 Calibration of the finite illumination source (ideal image frequency correction)

*H*is directly the image spectrum

_{I}(f_{x}, f_{y})*F*However, in reality one has a source of finite size in order to obtain sufficient flux, hence a non-delta-function ideal image limits the bandwidth of the input source spectrum.

_{i}(f_{x}, f_{y}).*D'*. The resultant frequency spectrum of the ideal image is then given by [12]where

*J*represents a Bessel function which is plotted in Fig. 4 . The figure illustrates the normalized ideal image frequency spectrum calculated for different circular apertures using this ideal flattop image. In Fig. 4(a), the solid line shows the ideal image frequency spectrum of a commercial glass lens (3 mm aperture,

_{1}*f*= 6 mm) with an ideal image of 3.75 µm diameter, and the dashed line shows the ideal image frequency spectrum of a tunable micro-lens (2 mm aperture,

*f*= 11 mm, at 1 kPa) with a 7 µm ideal image according to Eq. (4). This shows that a shorter focal length produces a smaller ideal image (3.75 μm) and thus a wider frequency band. Figure 4(b) illustrates the MTF value for different diameters

*D’*at a resolution of 100 lines/mm. When the diameter of the ideal image increases to 12.3 µm, this value drops down to zero.

### 4.4 Correction of non-idealities

#### 4.4.1 Finite pinhole size

*D'*and its frequency spectrum can be obtained from Equations Eq. (4) and Eq. (5), respectively. To remove the influence of the finite pinhole size, the overall optical system MTF may be calculated by a point-by-point division of the initially measured image frequency spectrum and the calculated ideal image frequency spectrum, namely

#### 4.4.2 Influence of spatial sampling area and noise

#### 4.4.3 Influence of the objective lens and summary of the calculation process

*F*to

_{i}*F*compensates for the effect of both the finite size of the light source as well as the influence of the focal lengths of the collector and the lens under test. Since the system is linear, the MTF of the lens under test can be inversely calculated by a point-by-point division of the overall optical system MTF and the MTF of the objective lens [14]. For the used high performance microscope objective lenses, the diffraction limited MTF of the microscope objectives are used as a suitable approximation, because the lens errors are assumed to be relatively small.

_{g}_{i}or integrated to yield the LSF, from which F

_{i}can be calculated using a (faster) 1D Fourier transform. The resultant value of

*F*is then corrected by a division by

_{i}*F*, yielding

_{g}*H*

_{I}_{;}taking the absolute value, finally yields the MTF.

## 5. Experimental results

### 5.1 Reference measurements

*F*was then determined by taking the Fourier transform and the correction due to the finite pinhole size was applied.

_{i}### 5.2 Measurements of the tunable micro-lens

*f*represents the effective focal length (efl), the distance between the focal point and the principle plane of the lens. Since the tunable lens (as seen in Fig. 1) is a thick plano-convex lens, the efl cannot be measured directly, only the back focal length (bfl) is directly available. The difference between efl and bfl depends on the focal value, thus on the applied pressure or curvature. bfl is smaller than efl, and for an operating pressure of 10 kPa, for example, the difference is roughly 0.7 mm. At lower pressures, the difference becomes smaller. Generally, the influence of this small difference is not significant and thus bfl is used in the correction.

_{t}*f*= 11 mm. In Fig. 10(b), the 2D MTF result becomes more clear at different angles in polar coordinates. One can easily see deviations from the axial symmetry, indicating lens errors which are not rotationally symmetric, as shown in Fig. 11 . From the shape of the PSF or MTF curves, it is possible to examine limitations in the performance of the micro-lens due to fabrication and design errors.

## 6. Conclusion

## Acknowledgment

## References and link

1. | J. C. Roulet, R. Völkel, H. P. Herzig, E. Verpoorte, N. F. deRooij, and R. Dändliker, “Microlens systems for fluorescence detection in chemical microsystems,” Opt. Eng. |

2. | A. Divetia, T. H. Hsieh, J. Zhang, Z. P. Chen, M. Bachman, G.-P. Li, M Bachman, and G. P Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. |

3. | K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optical tunable probe for endoscopic optical coherence tomography,” J. Opt. A, Pure Appl. Opt. |

4. | J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable-focusing microlens with microfluidic chip,” J. Micromech. Microeng. |

5. | M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. |

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

7. | D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tenability,” Appl. Phys. Lett. |

8. | J. Lee, J. D. Rogers, M. R. Descour, E. Hsu, J. Aaron, K. Sokolov, and R. Richards-Kortum, “Imaging quality assessment of multi-modal miniature microscope,” Opt. Express |

9. | S. M. Backman, A. J. Makynen, T. Kolehmainen, and K. Ojala, “Random target method for fast MTF inspection,” Opt. Express |

10. | R. R. Rawer, W. Stork, C. W. Spraul, and C. Lingenfelder, “Imaging quality of intraocular lenses,” J. Cataract Refract. Surg. |

11. | A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. |

12. | J. W. Goodman, |

13. | R. R. Shannon, |

14. | G. Boreman, |

15. | B. E. A. Saleh, and M. C. Teich, |

16. | K. Aljasem, A. Seifert, and H. Zappe, “Tunable multi-micro-lens system for high lateral resolution endoscopic optical coherence tomography,” in the Proceedings of IEEE Optical MEMS and Nanophotonics, |

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(110.1080) Imaging systems : Active or adaptive optics

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: April 9, 2010

Revised Manuscript: May 7, 2010

Manuscript Accepted: May 13, 2010

Published: May 26, 2010

**Virtual Issues**

Vol. 5, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Wei Zhang, Khaled Aljasem, Hans Zappe, and Andreas Seifert, "Highly flexible MTF measurement system for tunable micro lenses," Opt. Express **18**, 12458-12469 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-12-12458

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### References

- J. C. Roulet, R. Völkel, H. P. Herzig, E. Verpoorte, N. F. deRooij, and R. Dändliker, “Microlens systems for fluorescence detection in chemical microsystems,” Opt. Eng. 40(5), 814–821 (2001). [CrossRef]
- A. Divetia, T. H. Hsieh, J. Zhang, Z. P. Chen, M. Bachman, G.-P. Li, M Bachman, and G. P Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005). [CrossRef]
- K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optical tunable probe for endoscopic optical coherence tomography,” J. Opt. A, Pure Appl. Opt. 10(4), 044012 (2008). [CrossRef]
- J. Chen, W. Wang, J. Fang, and K. Varahramyan, “Variable-focusing microlens with microfluidic chip,” J. Micromech. Microeng. 14(5), 675–680 (2004). [CrossRef]
- M. Agarwal, R. A. Gunasekaran, P. Coane, and K. Varahramyan, “Polymer-based variable focal length microlens system,” J. Micromech. Microeng. 14(12), 1665–1673 (2004). [CrossRef]
- H. W. Ren and S. T. Wu, “Variable-focal liquid lens,” Opt. Express 15(10), 5931–5936 (2007). [CrossRef] [PubMed]
- D. Y. Zhang, V. Lien, Y. Berdichevsky, J. Choi, and Y. H. Lo, “Fluidic adaptive lens with high focal length tenability,” Appl. Phys. Lett. 82(19), 3171–3172 (2003). [CrossRef]
- J. Lee, J. D. Rogers, M. R. Descour, E. Hsu, J. Aaron, K. Sokolov, and R. Richards-Kortum, “Imaging quality assessment of multi-modal miniature microscope,” Opt. Express 11(12), 1436–1451 (2003). [CrossRef] [PubMed]
- S. M. Backman, A. J. Makynen, T. Kolehmainen, and K. Ojala, “Random target method for fast MTF inspection,” Opt. Express 12(12), 2610–2615 (2004). [CrossRef] [PubMed]
- R. R. Rawer, W. Stork, C. W. Spraul, and C. Lingenfelder, “Imaging quality of intraocular lenses,” J. Cataract Refract. Surg. 31(8), 1618–1631 (2005). [CrossRef] [PubMed]
- A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 44(16), 3238–3245 (2005). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics, (McGraw Hill, 2005), pp. 12–15, 127–167.
- R. R. Shannon, The Art and Science of Optical Design, (Cambridge University Press, 1997), pp. 265–330.
- G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems,” (SPIE Publications, 2001), pps, 1–9, 71–73, 85–88, 94–96.
- B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics,(John Wiley & Sons, 2007), pp. 427–432.
- K. Aljasem, A. Seifert, and H. Zappe, “Tunable multi-micro-lens system for high lateral resolution endoscopic optical coherence tomography,” in the Proceedings of IEEE Optical MEMS and Nanophotonics, 1, 44–45 (2008).

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