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 Optical Society of America

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References

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  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]
  5. 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]
  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]
  9. 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]
  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]
  11. A. Werber and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 44(16), 3238–3245 (2005).
    [Crossref] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics, (McGraw Hill, 2005), pp. 12–15, 127–167.
  13. R. R. Shannon, The Art and Science of Optical Design, (Cambridge University Press, 1997), pp. 265–330.
  14. G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems,” (SPIE Publications, 2001), pps, 1–9, 71–73, 85–88, 94–96.
  15. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics,(John Wiley & Sons, 2007), pp. 427–432.
  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, 1, 44–45 (2008).

2008 (1)

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]

2007 (1)

2005 (3)

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

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]

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]

2004 (3)

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]

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]

2003 (2)

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]

2001 (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]

Aaron, J.

Agarwal, M.

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]

Aljasem, K.

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]

Bachman, M

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]

Bachman, M.

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]

Backman, S. M.

Berdichevsky, Y.

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]

Chen, J.

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

Chen, Z. P.

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]

Choi, J.

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]

Coane, P.

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]

Dändliker, R.

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]

deRooij, N. F.

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]

Descour, M. R.

Divetia, A.

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]

Fang, J.

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

Gunasekaran, R. A.

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]

Herzig, H. P.

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]

Hsieh, T. H.

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]

Hsu, E.

Kolehmainen, T.

Lee, J.

Li, G. P

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]

Li, G.-P.

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]

Lien, V.

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]

Lingenfelder, C.

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]

Lo, Y. H.

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]

Makynen, A. J.

Ojala, K.

Rawer, R. R.

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]

Ren, H. W.

Richards-Kortum, R.

Rogers, J. D.

Roulet, J. C.

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]

Seifert, A.

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]

Sokolov, K.

Spraul, C. W.

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]

Stork, W.

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]

Varahramyan, K.

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]

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

Verpoorte, E.

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]

Völkel, R.

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]

Wang, W.

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

Werber, A.

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]

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

Wu, S. T.

Zappe, H.

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]

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

Zhang, D. Y.

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]

Zhang, J.

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]

Appl. Opt. (1)

Appl. Phys. Lett. (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]

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. Cataract Refract. Surg. (1)

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]

J. Micromech. Microeng. (2)

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]

J. Opt. A, Pure Appl. Opt. (1)

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]

Opt. Eng. (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]

Opt. Express (3)

Other (5)

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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Figures (12)

Fig. 1
Fig. 1 Schematic diagram and photo of a pneumatically tunable micro-lens. The lens consists of a transparent glass substrate, a 0.35 mm thick silicon chip as the lens cavity and a PDMS membrane as the optical surface of the lens. Shown on the right is the lens distended above the silicon surface.

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Fig. 2
Fig. 2 Images of a test object with the tunable lens at different pressures.

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Fig. 3
Fig. 3 Diagram of the MTF measurement setup. A 2D circular object at an infinite conjugate is achieved by a multimode fiber and a collimator lens. A manually controlled microscope platform is used to fix the micro-lens under test. Objective lenses of different magnification are used for the variation of the image size of the focal point of the lens under test. A high quality CCD records the image of the focal point.

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Fig. 4
Fig. 4 Idealized MTF calculations for different focal lengths without diffraction and aberration. (a) Normalized ideal image frequency spectrum of a glass lens (f = 6 mm) and a tunable lens at 1 kPa (f = 11 mm). (b) MTF values at 100 lines/mm for different diameters D’.

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Fig. 5
Fig. 5 Integral intensity of different spatial sampling. The intensity increases linearly above the threshold as expected. Hence it is possible to calculate the background noise above the threshold area.

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Fig. 6
Fig. 6 Flow chart of MTF calculation.

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Fig. 7
Fig. 7 Results of the microscope based measurement setup and a commercial setup (Trioptics). (a) Linos lens G322250000 (A) (b) Linos lens G322201000 (B).

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Fig. 8
Fig. 8 (a) Complete lens profiles measured at different pressure values (b) BFL at different pressure from microscope measurements and ZEMAX simulation.

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Fig. 9
Fig. 9 (a) PSF images at different pressure (b) LSF at different pressure.

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Fig. 10
Fig. 10 (a) Two-dimensional MTF of a tunable lens at 1 kPa. (b) Two-dimensional MTF of a tunable lens at 1 kPa in polar coordinates.

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Fig. 11
Fig. 11 (a) Focal point of a tunable lens with assembling error. (b) Two-dimensional asymmetric MTF of a tunable lens at 2 kPa in polar coordinates.

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Fig. 12
Fig. 12 (a) Comparison of MTF results for the horizontal direction of the tunable lens at 1 kPa. (b) MTF results of a variable 2 mm tunable lens at different pressure values.

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Equations (6)

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

I i ( x i , y i ) = ∫ ∫ − ∞ + ∞ I g ( x 0 , y 0 ) h I ( x i − x 0 , y i − y 0 ) d x i d y i = I g ( x i , y i ) ∗ h I ( x i , y i )
F i ( f x , f y ) = F g ( f x , f y ) × H I ( f x , f y )
L S F ( x ) = [ δ ( x ) 1 ( y ) ] ∗ P S F ( x , y )
D ' = D × f t / f c
F g ( f x , f y ) = 2 ( J 1 ( π D ' ( f x , f y ) ) / π D ' ( f x , f y ) )
M T F ( f x , f y ) = | H I ( f x , f y ) | = F i ( f x , f y ) / F g ( f x , f y )

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