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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 19 — Sep. 12, 2011
  • pp: 18665–18670
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Microlenses with defined contour shapes

V. J. Cadarso, J. Perera-Núñez, L. Jacot-Descombes, K. Pfeiffer, U. Ostrzinski, A. Voigt, A. Llobera, G. Grützer, and J. Brugger  »View Author Affiliations


Optics Express, Vol. 19, Issue 19, pp. 18665-18670 (2011)
http://dx.doi.org/10.1364/OE.19.018665


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Abstract

Ink-jet printing of optical ink over SU-8 pillars is here proposed as a technology for obtaining microlenses with shape control. To demonstrate the flexibility of this method, microlenses with five different contour shapes (ranging from circular and elliptical to toric or more advanced geometries) have been fabricated. Furthermore, the optical properties of the different fabricated lenses have been experimentally investigated. Focal distance, numerical aperture (NA) and full-width at half maximum (FWHM) of the microlenses have been determined. Arrays of microlenses showed an identical behavior with a standard deviation in the total intensity of only 7%. Additionally, the focal plane of the fabricated symmetric microlenses and the Sturm interval of the non-symmetric ones have been obtained. The experimental results demonstrate the validity and flexibility of the proposed technology.

© 2011 OSA

1. Introduction

The progress of miniature optical systems has generated increased interest during the last years in the development of microlenses. Several fabrication methods (e.g. grayscale lithography [1

1. J. D. Rogers, A. H. O. Kärkkäinen, T. Tkaczyk, J. T. Rantala, and M. R. Descour, “Realization of refractive microoptics through grayscale lithographic patterning of photosensitive hybrid glass,” Opt. Express 12(7), 1294–1303 (2004). [CrossRef] [PubMed]

] or ink-jet printing (IJP) [2

2. B. J. de Gans, P. C. Duineveld, and U. S. Schubert, “Inkjet printing of polymers: State of the art and future developments,” Adv. Mater. (Deerfield Beach Fla.) 16(3), 203–213 (2004). [CrossRef]

]), have been proposed to obtain such micro-optical structures, all of them showing some advantages and disadvantages. Among these methods IJP is well known to be a cost-effective and flexible technique that has been successfully applied for the development of microlenses [3

3. W. R. Cox, T. Chen, C. Guan, D. J. Hayes, R. E. Hoenigman, B. T. Teipen, and D. L. MacFarlane, “Micro-jet printing of refractive microlenses,” in Proceedings of OSA Diffractive Optics and Micro-optics Topical Meeting, Kailua-Kona, Hawaii, June 1998.

, 4

4. J. Y. Kim, N. B. Brauer, V. Fakhfouri, D. L. Boiko, E. Charbon, G. Grutzner, and J. Brugger, “Hybrid polymer microlens arrays with high numerical apertures fabricated using simple ink-jet printing technique,” Opt. Mater. Express 1(2), 259–269 (2011). [CrossRef]

]. Rapid prototyping capability, high precision dispensing, non-contact multi-material deposition, low material waste and 3D patterning are the key advantages of this technology [2

2. B. J. de Gans, P. C. Duineveld, and U. S. Schubert, “Inkjet printing of polymers: State of the art and future developments,” Adv. Mater. (Deerfield Beach Fla.) 16(3), 203–213 (2004). [CrossRef]

]. This method and others have been used to obtain microlenses that have been applied in the development of several systems and devices, as can be MOEMS [5

5. A. Llobera, V. J. Cadarso, K. Zinoviev, C. Dominguez, S. Buttgenbach, J. Vila, J. A. Plaza, and S. Biittgenbach, “Poly(Dimethylsiloxane) waveguide cantilevers for optomechanical sensing,” IEEE Photonic Tech. Lett. 21(2), 79–81 (2009). [CrossRef]

] or lab-on-a-chip [6

6. R. P. J. Barretto, B. Messerschmidt, and M. J. Schnitzer, “In vivo fluorescence imaging with high-resolution microlenses,” Nat. Methods 6(7), 511–512 (2009). [CrossRef] [PubMed]

]. It is common that microlenses used in such applications focus light into punctual spots. Nevertheless, there are some applications in which a more complex lens characteristics is required, as for example in the development of lab-on-a-chip using lenses that focus the light into lines [7

7. S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003). [CrossRef] [PubMed]

, 8

8. E. Schonbrun, P. E. Steinvurzel, and K. B. Crozier, “A microfluidic fluorescence measurement system using an astigmatic diffractive microlens array,” Opt. Express 19(2), 1385–1394 (2011). [CrossRef] [PubMed]

], to enhance optical fiber coupling efficiency using hemi-elliptic lenses [9

9. J.-Y. Hu, C.-P. Lin, S.-Y. Hung, H. Yang, and C.-K. Chao, “Semi-ellipsoid microlens simulation and fabrication for enhancing optical fiber coupling efficiency,” Sens. Act. A Phys. 147, 93–98 (2008). [CrossRef]

] or in micro-optical systems where correction of astigmatism is required [10

10. S.-Y. Lee, W.-C. Chen, H.-W. Tung, and W. Fang, “Microlens with tunable astigmatism,” IEEE Photonic Tech L. 15(18), 1383–1385 (2007). [CrossRef]

]. Microlenses with such behavior have previously been fabricated following different methods, such as astigmatic diffractive microlenses by means of e-beam [8

8. E. Schonbrun, P. E. Steinvurzel, and K. B. Crozier, “A microfluidic fluorescence measurement system using an astigmatic diffractive microlens array,” Opt. Express 19(2), 1385–1394 (2011). [CrossRef] [PubMed]

], using capillary forces [11

11. A. Llobera, R. Wilke, D. W. Johnson, and S. Büttgenbach, “Polymer microlenses with modified micromolding in capillaries technology,” IEEE Photon. Tech. Lett. 17(12), 2628–2630 (2005). [CrossRef]

], mechanically deforming fabricated soft microlenses [12

12. V. J. Cadarso, A. Llobera, G. Villanueva, C. Dominguez, and J. A. Plaza, “3-D modulable PDMS-based microlens system,” Opt. Express 16(7), 4918–4929 (2008). [CrossRef] [PubMed]

] or performing IJP of adjacent drops to obtain microlenses with different contour shapes [3

3. W. R. Cox, T. Chen, C. Guan, D. J. Hayes, R. E. Hoenigman, B. T. Teipen, and D. L. MacFarlane, “Micro-jet printing of refractive microlenses,” in Proceedings of OSA Diffractive Optics and Micro-optics Topical Meeting, Kailua-Kona, Hawaii, June 1998.

]. However, some of these methods rely on complex and expensive fabrication techniques, or have limitations in terms of the sizes and shapes that can be obtained.

It has been previously demonstrated that it is possible to take into benefit the capability of IPJ to perform aligned local deposition to confine polymers into platforms. This allows controlling the final shape of the deposited structures [13

13. L. Jacot-Descombes, M. R. Gullo, V. J. Cadarso, and J. Brugger, “Fabrication of polymeric micro structures by controlled drop on demand inkjet printing,” in Proceedings of 22nd Micromechanics and Micro systems Europe Workshop, Toensberg, Norway, June 2011.

]. In this work we apply this simple, reliable and cost efficient method for the fabrication of microlenses with controlled contour shapes. Transparent platforms with different defined contour shapes have been designed and fabricated to confine an epoxy-based optical ink and to obtain microlenses with the desired shapes. Additionally, such microlenses have been optically characterized.

2. Concept and design

To provide an idea of the flexibility of the herein proposed technology, the second type of non-symmetric microlenses has been designed as a combination of two concentric identical ellipses tilted 90°, as it can be seen in Fig. 1d. The behavior of such a microlens will be a combination of the behavior of both elliptic shape lenses. Hence, instead of the standard Sturm interval, this microlens will focus the light into a zone that is a combination of the Sturm interval of the perpendicular elliptic lenses.

3. Fabrication

Fabrication of the controlled contour shape lenses starts with the preparation of platforms with the desired shapes on a transparent substrate. In this work, glass wafers with a thickness of 700 µm are used. The platforms are defined in SU-8 photostructurable epoxy material using conventional photolithography. Initially, the glass wafers are treated in O2 plasma for 7 min. Immediately after this pre-treatment procedure, a layer of 50 µm of SU-8 is spin coated over the wafers. Then a soft-bake is done at 130 °C for 30 min. and the wafers are exposed to UV light with a dose of 400 mJ/cm2. After the exposure, a post-exposure bake (PEB) is done at 100 °C for 30 min., followed by a relaxation time of 24h. Finally, the development of the structures is done in Propylene Glycol Methyl Ether Acetate (PGMEA) followed by a hard bake at 120 °C for 2h in N2 environment. At this point, the fabrication of the platforms is finished, as it is schematized in Fig. 2a
Fig. 2 (a) SU-8 platforms with different shapes are fabricated by standard photolithography process. (b) Aligned IJP of the epoxy based ink is done in the different platforms. (c) The locally deposited polymer is cross-linked.
.

In order to fabricated of the lenses, and considering the size of platforms, an IJP nozzle with a diameter of 70 µm was used. The ink-jetted material is an epoxy-based optical ink (Ink-Epo_1, Microresist GmbH, Germany) [15

15. A. Voigt, U. Ostrzinski, K. Pfeiffer, J.Y. Kim, V. Fakhfouri, J. Brugger, and G. Gruetzner, “New inks for the direct drop-on-demand fabrication of polymer lenses,” Microelectron. Eng. 88(8) 2174-2179 (2010). [CrossRef]

] which refractive index (@850 nm) after cross-linking is 1.55 ± 0.01. Alignment between nozzle and platform consisted of finding out the X-Y offset between an ink-jetted drop and an alignment mark on the substrate, visualized by means of a top view camera. Following an offset correction in the X-Y scan and theta rotation, the optical ink was then locally deposited onto each platform, as shown in Fig. 2b with a lateral precision of 5 µm. The total volume of ink was controlled by the number of drops deposited onto each platform. This printing procedure is done entirely automatic using computer aided design. In addition it has been previously demonstrated that by this method it is possible to control the contact angle of the deposited microlenses [13

13. L. Jacot-Descombes, M. R. Gullo, V. J. Cadarso, and J. Brugger, “Fabrication of polymeric micro structures by controlled drop on demand inkjet printing,” in Proceedings of 22nd Micromechanics and Micro systems Europe Workshop, Toensberg, Norway, June 2011.

]. When the platforms were fully covered with the polymer and before any overflowing, the samples were flood exposed to UV-light and a PEB was done at 140 °C for 20 min. At this point the lenses were finished as represented in Fig. 2c, and ready for subsequent characterization. Scanning electron microscope (SEM) images of the fabricated structures are presented in Fig. 3
Fig. 3 SEM images of (a) a toric lens, and (b) two identical lenses fabricated on platforms with elliptic shape. (c) Profile of 5 different circular lenses.
.

Figure 3a shows a SEM image of a toric microlens fabricated over a platform with annular shape. Figure 3b shows the picture of two lenses obtained doing the IJP process over platforms with elliptic shape. Finally, Fig. 3c shows the profile of 5 different microlenses fabricated over circular platforms obtained using a surface profiler (Tencor Alpha-Step 500). This demonstrates that the size and curvature of the different the developed microlenses are equivalent, without any roughness or defect on their surfaces. These results validate the capability of the proposed technology to develop microlens structures with relatively arbitrary contour shapes.

4. Characterization

Characterization of the fabricated microlenses was done using an optical fiber with a core diameter of 50 µm connected to a diode laser (Thorlabs GmbH, Germany) with a working wavelength of 635 nm. The lenses are placed on a holder at a fixed position and the light passing through is focused on a CCD camera (Pixelfly, Spain) by means of a microscope objective (x10). The lenses with symmetric contour shapes were considered first (Fig. 4
Fig. 4 (a) CCD image capturing the focal plane of an array of 3x3 microlenses fabricated over platforms with circular contour shapes and (b) the 3D spatial reconstruction of the intensity distribution. (c) CCD image capturing the focal plane of a microlens fabricated over a platform with annular contour shape.
).

Figure 4a shows a CCD image of the focal plane of a circular lens array with a diameter of 100 µm. Figure 4b shows a 3D spatial reconstruction of the experimental intensity distribution. As it can be observed, the focal points of all these microlenses are focused in the same plane and have a similar intensity, with a standard deviation of only 7%. The NA of these microlenses has been measured at 0.19 ± 0.01, the FWHM at 5.2 ± 0.7 µm and the focal distance at 260 ± 20 µm. Conversely, Fig. 4c presents the focal plane of a lens with a toric shape with D1 of 125 µm and D2 of 275 µm, as it was schematically represented in Fig. 1b. As it can be observed in this case, instead of a focal point, the light is focused into a ring, as it was expected. The NA of this toroid lens is 0.16 ± 0.01, the FWHM is 4.3 ± 1.5 µm and the focal distance is 480 ± 20 µm.

Lenses with asymmetric shapes were also characterized. As it was introduced in section 2, such microlenses present different curvatures in their orthogonal axes resulting in the formation of the Sturm interval. This phenomenon can be observed in Fig. 5
Fig. 5 CCD images of the interval of Sturm of a microlens fabricated over elliptic platforms including: (a) the VLF, (b) the CLC and (c) the HLF.
for a lens fabricated over a platform with an elliptic shape with D1 of 110 µm and D2 of 300 µm, as it was represented in Fig. 1c. Concretely, the VLF can be observed at Fig. 5a as a vertical line with a FWHM in the horizontal axis (FWHM-h) of 3.7 ± 1.0 µm and at a focal distance of 500 ± 24 µm. The CLC is shown in Fig. 5b at a distance of 1070 ± 42 µm as a blurred circle equally focused in both axes. Finally, Fig. 5c shows the HLF with a FWHM in the vertical axis (FWHM-v) of 5.4 ± 1.5 µm and a focal distance of 1640 ± 80 µm. Hence, the total distance of the Sturm interval for this microlens was 1140 ± 83 µm. The NA of this lens was 0.11 ± 0.01 in the vertical axis (NA-v) and 0.09 ± 0.01 in the horizontal axis (NA-h). Conversely, Fig. 6
Fig. 6 CCD images of the interval of Sturm of a microlens fabricated over tilted elliptic platforms including: (a) the HLF, (b) the CLC and (c) the VLF.
shows the Strum interval of an array of three elliptic lenses with a D1 of 430 µm and a D2 of 100 µm. In this case the Sturm interval starts with the HLF due to the lens orientation, as it is observed in Fig. 6a. Its focal distance is 230 ± 25 µm and its FWHM-v is 1.9 ± 0.3 µm. The CLC is shown in Fig. 6b with a focal distance of 800 ± 15 µm. Finally, the VLF can be seen in Fig. 6c, it has a focal length of 1360 ± 20 µm and a FWHM-h of 11.2 ± 0.6 µm. In this case the total distance of the interval of Sturm is of 1130 ± 32 µm. As it can be observed both the CLC and the VLF of the three microlenses are overlapping due to the short distance between them. Furthermore, the different elements of the Sturm interval are located in the same focal planes for the three microlenses of the array, demonstrating that their size and curvature are equivalent.

Finally, a microlens structure consisting in the crossing of two identical ellipses was also characterized. Figure 7
Fig. 7 CCD images of the interval of Sturm of a microlens consisting on two ellipses crossed in the center including: (a) the first combination of the HLF and the VLF, (b) the CLC, and (c) the second combination of the VLF and the HLF.
shows the Sturm interval of this microlens system. In this case, instead of the standard HLF, CLC and VLF, a combination of these elements was observed. First a square focal shape is shown, as presented in Fig. 7a. Such distribution of the light power corresponds to the combination of the HLF of the horizontal lens and the VLF of the vertical lens. Its focal distance is 1000 ± 40 µm. Figure 7b shows a focal point that corresponds to the CLC of the Sturm interval, but in this case the blurring of this point is reduced since the lens system is almost symmetric and similar to a standard spherical microlens in the center. The focal distance of the CLC is 1065 ± 25 µm, while its FWHM-h is 11.1 ± 1.6 µm and its FWHM-v is 10.0 ± 0.9 µm. The low and similar values of both horizontal and vertical FWHM of the CLC demonstrate that in this region this microlens system behaves almost as a standard lens with circular shape. Finally, a rhombus focal shape is observed, as can be seen in Fig. 7c. This power distribution of the light corresponds to the combination of the VLF of the horizontal lens and the HLF of the vertical lens. This final element can be found at a focal distance of 1130 ± 25 µm. The NA of this optical system is similar in both axes, being the NA-h of 0.17 ± 0.01 and the NA-v of 0.15 ± 0.01, resulting in a short interval of Sturm of only 130 ± 50 µm. The results obtained from the characterization of both symmetrical and non-symmetrical microlenses validate the proposed technology for the reliable development of microlenses with an arbitrary contour shape.

5. Conclusions

Lenses with five different contour shapes have been designed, fabricated and characterized. We demonstrated that it is possible to achieve microlenses with different optical focusing characteristics using a simple and reliable method, consisting in the aligned local deposition of optical ink over transparent SU-8 platforms. Both symmetric and non-symmetric microlenses have been designed, fabricated and characterized as proof of concept. The first symmetric structure studied is an array of standard circular-shape microlenses. The second one is a microlens with toric shape showing a ring on its focal plane. Conversely, the non-symmetric microlenses have shown, as expected, the Sturm interval. Two elliptic lenses with different geometries have been studied; in both cases it was possible to clearly observe the horitzontal line focus, the circle of least confusion and the vertical line focus. Furthermore, a microlens system consisting in two identical ellipses crossed by the central point was also investigated. For this optical system, instead of the standard Sturm interval, a combination of the HLF, the CLC and the VLC of the two ellipses has been confirmed. These results validate both the proposed technology to develop microlenses with a large degree of freedom for the desired contour shape and the capability and flexibility of the fabrication procedure. Such micro-optical components are of great interest for the future development of systems where microlenses with particular optical characteristics are required, as can be optical scanning systems, imaging applications or lab-on-a-chip platforms.

Acknowledgements

This work has been funded by the IAPP Marie Curie action ACAPOLY nº PIAP-GA-2008-218075 and the European Research Council (FP7/2007-2013) / ERC n° 209243, both from the EC's 7th FP. The authors are pleased to acknowledge the EPFL CMi for their valuable discussions and help. J. Perera-Núñez acknowledges the Junta de Extremadura for her grant, the Spanish Ministry for Science and Technology (MAT2009-14695-C04-01) and FEDER.

References and links

1.

J. D. Rogers, A. H. O. Kärkkäinen, T. Tkaczyk, J. T. Rantala, and M. R. Descour, “Realization of refractive microoptics through grayscale lithographic patterning of photosensitive hybrid glass,” Opt. Express 12(7), 1294–1303 (2004). [CrossRef] [PubMed]

2.

B. J. de Gans, P. C. Duineveld, and U. S. Schubert, “Inkjet printing of polymers: State of the art and future developments,” Adv. Mater. (Deerfield Beach Fla.) 16(3), 203–213 (2004). [CrossRef]

3.

W. R. Cox, T. Chen, C. Guan, D. J. Hayes, R. E. Hoenigman, B. T. Teipen, and D. L. MacFarlane, “Micro-jet printing of refractive microlenses,” in Proceedings of OSA Diffractive Optics and Micro-optics Topical Meeting, Kailua-Kona, Hawaii, June 1998.

4.

J. Y. Kim, N. B. Brauer, V. Fakhfouri, D. L. Boiko, E. Charbon, G. Grutzner, and J. Brugger, “Hybrid polymer microlens arrays with high numerical apertures fabricated using simple ink-jet printing technique,” Opt. Mater. Express 1(2), 259–269 (2011). [CrossRef]

5.

A. Llobera, V. J. Cadarso, K. Zinoviev, C. Dominguez, S. Buttgenbach, J. Vila, J. A. Plaza, and S. Biittgenbach, “Poly(Dimethylsiloxane) waveguide cantilevers for optomechanical sensing,” IEEE Photonic Tech. Lett. 21(2), 79–81 (2009). [CrossRef]

6.

R. P. J. Barretto, B. Messerschmidt, and M. J. Schnitzer, “In vivo fluorescence imaging with high-resolution microlenses,” Nat. Methods 6(7), 511–512 (2009). [CrossRef] [PubMed]

7.

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003). [CrossRef] [PubMed]

8.

E. Schonbrun, P. E. Steinvurzel, and K. B. Crozier, “A microfluidic fluorescence measurement system using an astigmatic diffractive microlens array,” Opt. Express 19(2), 1385–1394 (2011). [CrossRef] [PubMed]

9.

J.-Y. Hu, C.-P. Lin, S.-Y. Hung, H. Yang, and C.-K. Chao, “Semi-ellipsoid microlens simulation and fabrication for enhancing optical fiber coupling efficiency,” Sens. Act. A Phys. 147, 93–98 (2008). [CrossRef]

10.

S.-Y. Lee, W.-C. Chen, H.-W. Tung, and W. Fang, “Microlens with tunable astigmatism,” IEEE Photonic Tech L. 15(18), 1383–1385 (2007). [CrossRef]

11.

A. Llobera, R. Wilke, D. W. Johnson, and S. Büttgenbach, “Polymer microlenses with modified micromolding in capillaries technology,” IEEE Photon. Tech. Lett. 17(12), 2628–2630 (2005). [CrossRef]

12.

V. J. Cadarso, A. Llobera, G. Villanueva, C. Dominguez, and J. A. Plaza, “3-D modulable PDMS-based microlens system,” Opt. Express 16(7), 4918–4929 (2008). [CrossRef] [PubMed]

13.

L. Jacot-Descombes, M. R. Gullo, V. J. Cadarso, and J. Brugger, “Fabrication of polymeric micro structures by controlled drop on demand inkjet printing,” in Proceedings of 22nd Micromechanics and Micro systems Europe Workshop, Toensberg, Norway, June 2011.

14.

M. Katz, Introduction to Geometrical Optics (World Scientific Publishing Co., 2002), Chap. 8.

15.

A. Voigt, U. Ostrzinski, K. Pfeiffer, J.Y. Kim, V. Fakhfouri, J. Brugger, and G. Gruetzner, “New inks for the direct drop-on-demand fabrication of polymer lenses,” Microelectron. Eng. 88(8) 2174-2179 (2010). [CrossRef]

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(350.3950) Other areas of optics : Micro-optics

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: June 22, 2011
Revised Manuscript: August 4, 2011
Manuscript Accepted: August 8, 2011
Published: September 9, 2011

Citation
V. J. Cadarso, J. Perera-Núñez, L. Jacot-Descombes, K. Pfeiffer, U. Ostrzinski, A. Voigt, A. Llobera, G. Grützer, and J. Brugger, "Microlenses with defined contour shapes," Opt. Express 19, 18665-18670 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18665


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References

  1. J. D. Rogers, A. H. O. Kärkkäinen, T. Tkaczyk, J. T. Rantala, and M. R. Descour, “Realization of refractive microoptics through grayscale lithographic patterning of photosensitive hybrid glass,” Opt. Express12(7), 1294–1303 (2004). [CrossRef] [PubMed]
  2. B. J. de Gans, P. C. Duineveld, and U. S. Schubert, “Inkjet printing of polymers: State of the art and future developments,” Adv. Mater. (Deerfield Beach Fla.)16(3), 203–213 (2004). [CrossRef]
  3. W. R. Cox, T. Chen, C. Guan, D. J. Hayes, R. E. Hoenigman, B. T. Teipen, and D. L. MacFarlane, “Micro-jet printing of refractive microlenses,” in Proceedings of OSA Diffractive Optics and Micro-optics Topical Meeting, Kailua-Kona, Hawaii, June 1998.
  4. J. Y. Kim, N. B. Brauer, V. Fakhfouri, D. L. Boiko, E. Charbon, G. Grutzner, and J. Brugger, “Hybrid polymer microlens arrays with high numerical apertures fabricated using simple ink-jet printing technique,” Opt. Mater. Express1(2), 259–269 (2011). [CrossRef]
  5. A. Llobera, V. J. Cadarso, K. Zinoviev, C. Dominguez, S. Buttgenbach, J. Vila, J. A. Plaza, and S. Biittgenbach, “Poly(Dimethylsiloxane) waveguide cantilevers for optomechanical sensing,” IEEE Photonic Tech. Lett.21(2), 79–81 (2009). [CrossRef]
  6. R. P. J. Barretto, B. Messerschmidt, and M. J. Schnitzer, “In vivo fluorescence imaging with high-resolution microlenses,” Nat. Methods6(7), 511–512 (2009). [CrossRef] [PubMed]
  7. S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip3(1), 40–45 (2003). [CrossRef] [PubMed]
  8. E. Schonbrun, P. E. Steinvurzel, and K. B. Crozier, “A microfluidic fluorescence measurement system using an astigmatic diffractive microlens array,” Opt. Express19(2), 1385–1394 (2011). [CrossRef] [PubMed]
  9. J.-Y. Hu, C.-P. Lin, S.-Y. Hung, H. Yang, and C.-K. Chao, “Semi-ellipsoid microlens simulation and fabrication for enhancing optical fiber coupling efficiency,” Sens. Act. A Phys.147, 93–98 (2008). [CrossRef]
  10. S.-Y. Lee, W.-C. Chen, H.-W. Tung, and W. Fang, “Microlens with tunable astigmatism,” IEEE Photonic Tech L.15(18), 1383–1385 (2007). [CrossRef]
  11. A. Llobera, R. Wilke, D. W. Johnson, and S. Büttgenbach, “Polymer microlenses with modified micromolding in capillaries technology,” IEEE Photon. Tech. Lett.17(12), 2628–2630 (2005). [CrossRef]
  12. V. J. Cadarso, A. Llobera, G. Villanueva, C. Dominguez, and J. A. Plaza, “3-D modulable PDMS-based microlens system,” Opt. Express16(7), 4918–4929 (2008). [CrossRef] [PubMed]
  13. L. Jacot-Descombes, M. R. Gullo, V. J. Cadarso, and J. Brugger, “Fabrication of polymeric micro structures by controlled drop on demand inkjet printing,” in Proceedings of 22nd Micromechanics and Micro systems Europe Workshop, Toensberg, Norway, June 2011.
  14. M. Katz, Introduction to Geometrical Optics (World Scientific Publishing Co., 2002), Chap. 8.
  15. A. Voigt, U. Ostrzinski, K. Pfeiffer, J.Y. Kim, V. Fakhfouri, J. Brugger, and G. Gruetzner, “New inks for the direct drop-on-demand fabrication of polymer lenses,” Microelectron. Eng.88(8) 2174-2179 (2010). [CrossRef]

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