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Rapid fabrication of a micro-ball lens array by extrusion for optical fiber applications

Open Access Open Access

Abstract

Batch-fabrication of a micro-ball lens array (MBA) could not only reduce micro assembly costs but also replace conventional ball lenses or costly GRINs (Gradient Refractive Index) without compromising performance. Compared with conventional half-spherical micro-lenses, the MBA is a spherical micro-lens that can focus light in all directions, thus providing the flexibility required for optical applications. Current MBAs are made of SU-8 photoresist by an extrusion process rather than the traditional thermal reflow process. The aim of this study was to develop a new process for MBA batch-fabrication, performed at ambient temperature, by spin-coating SU-8 onto a silicon-wafer surface, which serves as an extrusion plate, and extruding it through a nozzle to form an MBA. The nozzle consists of a nozzle orifice and nozzle cavity, the former being defined and made from SU-8 photoresist using ultra-violet (UV) lithography, which results in good mechanical properties. In this paper, the fabrication of 4×4 MBAs with diameters ranging from 60 to 550 um is described. Optical measurements indicated a diameter variance within 3% and a maximum coupling efficiency of approximately 62% when the single mode fiber (SMF) was placed at a distance of 10um from the MBA. The results of this study proved that MBA fabrication by the extrusion process can enhance the coupling efficiency.

©2009 Optical Society of America

1. Introduction

Internet and optical communications have attracted more and more attention in recent years. Many studies have focused on the integration of optics technologies for the miniaturization and development of high-performance apparatus, and these aims are clearly represented in the field of micro-optical devices, because micro-optical elements often require unique and precise fabrication processes. For this reason, the optical switch is an important component in a variety of applications in the field of optical communications, particularly in optical fiber networks, where the optical system requires a large quantity of optical components [1]. In optical fiber coupling systems, spherical micro-lens integrated systems such as the wavelength division multiplexing (WDM) transmission system provide independent plural signals of different wavelengths. These systems have some advantages, such as low-cost transmission lines and flexible system designs. The 1.2/1.3µm band for the single mode fiber (SMF) WDM with commercially-available ball lens collimators used in the optical coupling system was developed in order to achieve high performance, high stability and versatility; however, the traditional ball lens is larger in size, which results in the size of the WDM also increasing [2]. Therefore, many researchers have dedicated themselves to the development of a miniature ball lens, with the aim of integrating the micro-ball lens into the components of micro optical systems by developing integrated optical components to reduce loss of optical transmission.

Micro-scale refractive lenses offer several important advantages over diffractive optics lenses, for example, wavelength sensitivity, large numerical apertures, and high light efficiency [3]. Several fabrication technologies have already been applied for the manufacture of refractive micro-lenses, such as melting a cylindrical photoresist to produce a refractive micro-lens [4]. Gale et al. [5] used a laser-writing system to fabricate continuous-relief micro-optical elements in a photoresist. Moreover, an excimer laser has been used to ablate photoresist cylinders to form the desired spherical shape. Several studies of micro-ball lens applications have been performed [6]; however, the fabrication methods used in these studies were based on the thermal reflow method. Most researchers have used a thermal reflow technique to fabricate a micro-lens array [7], a process in which the surface of the material melts when the heating temperature rises above the material glass temperature, and the surface tension effect on the melted material surface results in a spherical profile. Mass production of these optical components is possible [8]; however, most of the above-mentioned approaches for fabricating micro-lens arrays or spherical micro-lenses involve complicated processes. Therefore, in the current study, a concept of Micro-Electro-Mechanical Systems (MEMS) technology was used to fabricate micro-molds, which, combined with extrusion technology, formed a manufacturing process for MBAs. In this process, only SU-8 coating, extrusion, and UV exposure are required for the production of MBAs in large quantities, which simplifies the complex and high-temperature conventional MBA manufacturing process, and also makes the reuse of micro molds possible, rendering rapid, low-cost production of MBAs achievable.

For the measurement of optical characteristics, a commercially-available ball lens fulfils the low-cost specification, but it is bulky and its coupling efficiency is limited due to large spherical aberration. If the size of the micro-ball lens can be reduced, spherical aberration of the elements can also be reduced. In addition, by integrating a micro-optics positioning unit in the micro-optical elements, the optical energy can be coupled into the optical fiber through the micro-ball lens, which can successfully enhance the optical fiber coupling efficiency. Therefore, more efficient light coupling from fiber to fiber collimation, placing a laser diode into the SMF, or focusing and coupling light from a light-emitting diode (LED) into the SMF can be achieved using the MBA. This paper presents a new method for the fabrication of an integrated MBA based on the extrusion process. In the following section, the new MBA fabrication process is discussed, and a coupling solution for obtaining a high coupling efficiency with a large distance between the optical elements is described.

2. Principle and fabrication

This study applies the extrusion method and the principle of surface tension to form MBAs in which the cohesion force is balanced between the molecules of SU-8. However, when the SU-8 surface comes into contact with gas molecules, the cohesion force of the SU-8 molecules changes, producing a pulling force, which leads the surface to develop towards the smallest area possible. The effect of tension along the tangential direction of the SU-8 surface can be determined by Eq. (1),

σ=dFdS

where σ is the surface tension; dS represents a line segment of perpendicular tension; and F is the pulling force perpendicular to S running along the SU-8 surface.

From Eq. (1), we can see that the unit of surface tension σ is N/m. This study makes use of the effects of surface tension, similar to a flexible membrane layer contracting to the minimum area. The surfaces of lenses formed by surface tension are smooth and thus excellent for use in optical components. The schematic evolution of the geometry of an MBA after the extrusion process is shown in Fig. 1. Figure 1(a) shows schematically the transient profiles of the MBA, and the change of the SU-8 photoresist pattern into an MBA is shown in Fig. 1(b).

 figure: Fig. 1.

Fig. 1. Schematic evolution of the volumetric variation of a micro-lens after extrusion: (a) initial stage; (b) steady state.

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The MBA fabrication process developed in this study differs from the traditional thermal reflow process. A thick SU-8 photoresist was chosen to form the MBA because of its high light transparence and excellent mechanical strength. The disadvantage of using SU-8 is its difficulty in being stripped after cross-linking. The current study explored the feasibility of using SU-8 in an extrusion process to form an MBA. The nozzle consisted of a nozzle orifice in the obverse side and a nozzle cavity in the rear side. The SU-8-based nozzle orifice, which had a diameter between 40µm and 80µm, was defined on the obverse side of the wafer by lithography, and the nozzle cavity on the rear of the wafer was fabricated using the anisotropic bulk wet etching method on a (100) wafer. In this process, an etching mask of silicon nitride of a width of 1240 µm was opened in the rear of the wafer. The experimental results for the nozzle are shown in Fig. 2.

Figure 3 presents a schematic flow chart of the MBA fabrication process. First, a double-polished (100)-oriented silicon wafer of a thickness of 1500A was deposited using silicon nitride by PECVD (Plasma-Enhanced Chemical Vapor Deposition). Then, the obverse side of the wafer was spin-coated with negative-tone photoresist SU-8 at 1000rmp for 30 sec, with a resulting thickness of about 30µm, as shown in Fig. 3(a). Next, the SU-8 was soft-baked at 65°C for 2 min, then 95°C for 10min, and exposed for 350mJ/cm2, and then subjected to PEB (post-exposure baking) at 90°C for 10min. The SU-8 was subsequently developed in MicroChem’s SU-8 developer for 1 min. The schematic development of the nozzle orifice is shown in Fig. 3(b). The rear side of the wafer was then spin-coated with Hoechst photo-resist AZ4620 at 1000rmp for 30 sec to a thickness of about 20µm. Next, the AZ4620 was soft-baked at 90°C for 7 min, exposed for 300mJ/cm2, and developed in Hoechst AZ400K developer (1:4 in DI water) for 1 min to define the etching mask, followed by conventional RIE (reactive ion etching) to remove the silicon nitride, as shown in Fig. 3(c). A Teflon mold was used to protect the nozzle orifice in the obverse side from KOH etching at 90°C for 270min, as shown in Fig. 3(d), and finally, SU-8 was spun on an extrusion plate and extruded through the nozzle orifice (see Fig. 3(e)), and an exposure process without a mask (flooding exposure) was used to cure the MBA instead of the traditional thermal reflow process, as shown in Fig. 3(f). SU-8 was coated onto the extrusion plate, a process in which the thickness can be well-controlled.

3. Results and discussions

In this study, SU-8 layers of differing thicknesses were coated on extrusion plates and nozzle orifices of different diameters were used to fabricate MBAs. There is a relationship between the thickness of SU-8 on the extrusion plate and the rotational speed of the spin-coater: specifically, the thickness of SU-8 is dependent upon the rotational speed of the spin-coater, and the higher the spin-coater speed, the thinner the layer of SU-8. Figure 4 shows the relationship between the diameter D of the MBA and SU-8 nozzle orifice size under different SU-8 thicknesses on the extrusion plate, from which it can be seen that the diameter D is proportional to the nozzle orifice size. At different thickness of SU-8 (see Fig. 4), nozzle orifices of 40, 50, 60, 70, and 80µm in diameter were used to fabricate MBAs of different diameters, and the results showed that the largest diameter of MBA obtained was 550µm at a nozzle orifice size of 80µm. Using this process, MBAs with diameters of 60–550µm can be fabricated, as shown in Fig. 4. These graphs provide a useful reference for the fabrication of MBAs of various sizes.

 figure: Fig. 2.

Fig. 2. Illustration of nozzle

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 figure: Fig. 3.

Fig. 3. Process flow chart for the fabrication of eyeball-like spherical micro-lens arrays. (a) Deposit silicon nitride and photoresist SU-8. (b) Define nozzle orifice by photolithography (obverse side). (c) Define nozzle cavity (rear side). (d) Bulk etch the rear side with Teflon for protection. (e) Perform extrusion process. (f) Expose without mask (flooding exposure).

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 figure: Fig. 4.

Fig. 4. The relationship between the diameter D of the MBA and the SU-8 nozzle orifice size under different rotational speeds of the spin-coater.

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Extrusion and UV exposure processes were used to define and cure the MBA, resulting in a clear spherical profile, as illustrated by the SEM images in Fig. 5. In Fig. 5(a), the SU-8 is shown being extruded through the nozzle orifice to form a spherical shape before it becomes a complete MBA. A mushroom-shaped lens was obtained due to the low UV exposure dosage, as shown in Fig. 5(b). Figure 5(c) shows the successful fabrication of an MBA of 80µm in diameter. Figure 5(d) shows the cross-sectional and top views of the spherical micro-lens. The spherical micro-lens profile and radius R were measured using a commercial image processing software, and the results showed that the diameter variance of the MBA was within 3%. These MBA parameters were used in subsequent optics measurement and analysis.

 figure: Fig. 5.

Fig. 5. SEM images of MBAs. (a) SU-8 is extruded through the nozzle orifice before forming MBAs. (b) MBAs of a mushroom shape were formed due to the low UV exposure dosage. (c) A 3×3 MBA array. (d) Cross-sectional and top views of the spherical micro-lens

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Figure 6 shows the experimental setup for light field measurement. In this study, theoretical calculation of a thick lens is used to find the focal length f. As the spherical micro-lens is proportional to focal length by n’=1.67, then

f=n2(n1)R=1.2463R

where n’ is the refractive index of SU-8, f is the focal length, and R is the radius of the spherical micro-lens. The front focal length (FF) and the back focal length (BF) are more useful measurements than the principal planes: FF is measured from the front focal point to the vertex of the first surface of the lens; BF is measured from the vertex of the last surface of the lens to the back focal point; and EF is measured from the center of the spherical micro-lens to the focus point. BF is calculated as shown in Eq. (3).

BF=fR

The optics measurement method was used in this study to verify the above-described analysis results. A laser light source of a wavelength of 635nm, which is in the visible light range, was used in this study for easy observation, and a TEC (thermal expanded cord) SMF with a wide opening was used to measure the coupling efficiency. An MBA was placed between the laser and fiber, and the laser beam coupled directly into the fiber through the MBA. Figure 7 shows the variation of coupling efficiency with distance between the spherical micro-lens and the fiber. The maximum coupling efficiency was approximately 62% when the fiber was placed 10µm from the spherical micro-lens surface. When n’=1.67 and R=80um were substituted into Eqs. (2) and (3), the theoretical BF was calculated as 9.85µm. This calculated result may assist in quickly finding the position at which the highest coupling efficiency is achieved.

 figure: Fig. 6.

Fig. 6. Design of the light fields measurement platform.

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 figure: Fig. 7.

Fig. 7. Relationship of coupling efficiency to the distance between the spherical micro-lens surface and the fiber.

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4. Conclusion

In this study, a method for MBA fabrication at low temperatures using an extrusion process was devised. The nozzle consisted of the nozzle orifice and the nozzle cavity: the SU-8-based nozzle orifice, which ranged in diameter from 40µm to 80µm, was created by lithography, and the nozzle cavity was fabricated using an anisotropic bulk wet etching process. A 4×4 MBA array with diameters ranging from 60 to 550 µm was designed and fabricated, and the optical measurements indicated that the diameter variance was within 3%. Future study will involve measuring the optical properties of MBAs fabricated by this process and applying them in micro-opto-electromechanical systems (MOEMS).

Acknowledgement

The authors would like to thank National Science Council (NSC) for their financial supports to the project (granted number: NSC 97-2622-E-006-014-CC3, NSC 97-2628-E-124-MY2).

References and links

1. D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol. 1(8), 759–766 (1990). [CrossRef]  

2. C. S. Lee and C. H. Han, “A novel refractive silicon microlens array using bulk micromachining technology,” Sens. Actuators A Phys. 88(1), 87–90 (2001). [CrossRef]  

3. S. Sinzinger and J. Jahns, Microoptics, (WILEY-VCH Verlag GmbH, Weinheim, 1999) pp. 85–103.

4. M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37(2), 253–265 (1990). [CrossRef]  

5. M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33(11), 3556–3566 (1994). [CrossRef]  

6. H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng. 14(2), 277–282 (2004). [CrossRef]  

7. T. Hirai and S. Hayashi, “Lens Functions of Polymer Microparticle Arrays,” Colloids Surf. A 153(1–3), 503–513 (1999). [CrossRef]  

8. N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt. 24(16), 2520 (1985). [CrossRef]  

References

  • View by:

  1. D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
    [Crossref]
  2. C. S. Lee and C. H. Han, “A novel refractive silicon microlens array using bulk micromachining technology,” Sens. Actuators A Phys.  88(1), 87–90 (2001).
    [Crossref]
  3. S. Sinzinger and J. Jahns, Microoptics, (WILEY-VCH Verlag GmbH, Weinheim, 1999) pp. 85–103.
  4. M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt.  37(2), 253–265 (1990).
    [Crossref]
  5. M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
    [Crossref]
  6. H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
    [Crossref]
  7. T. Hirai and S. Hayashi, “Lens Functions of Polymer Microparticle Arrays,” Colloids Surf. A  153(1–3), 503–513 (1999).
    [Crossref]
  8. N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
    [Crossref]

2004 (1)

H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
[Crossref]

2001 (1)

C. S. Lee and C. H. Han, “A novel refractive silicon microlens array using bulk micromachining technology,” Sens. Actuators A Phys.  88(1), 87–90 (2001).
[Crossref]

1999 (1)

T. Hirai and S. Hayashi, “Lens Functions of Polymer Microparticle Arrays,” Colloids Surf. A  153(1–3), 503–513 (1999).
[Crossref]

1994 (1)

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
[Crossref]

1990 (2)

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
[Crossref]

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt.  37(2), 253–265 (1990).
[Crossref]

1985 (1)

N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
[Crossref]

Bellman, R. H.

N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
[Crossref]

Borrelli, N. F.

N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
[Crossref]

Chao, C. K.

H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
[Crossref]

Daly, D.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
[Crossref]

Davies, N.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
[Crossref]

Gale, M. T.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
[Crossref]

Han, C. H.

C. S. Lee and C. H. Han, “A novel refractive silicon microlens array using bulk micromachining technology,” Sens. Actuators A Phys.  88(1), 87–90 (2001).
[Crossref]

Hayashi, S.

T. Hirai and S. Hayashi, “Lens Functions of Polymer Microparticle Arrays,” Colloids Surf. A  153(1–3), 503–513 (1999).
[Crossref]

Hirai, T.

T. Hirai and S. Hayashi, “Lens Functions of Polymer Microparticle Arrays,” Colloids Surf. A  153(1–3), 503–513 (1999).
[Crossref]

Hutley, M. C.

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt.  37(2), 253–265 (1990).
[Crossref]

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
[Crossref]

Jahns, J.

S. Sinzinger and J. Jahns, Microoptics, (WILEY-VCH Verlag GmbH, Weinheim, 1999) pp. 85–103.

Lee, C. S.

C. S. Lee and C. H. Han, “A novel refractive silicon microlens array using bulk micromachining technology,” Sens. Actuators A Phys.  88(1), 87–90 (2001).
[Crossref]

Lin, C.-P.

H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
[Crossref]

Morgan, W. L.

N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
[Crossref]

Morse, D. L.

N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
[Crossref]

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
[Crossref]

Rossi, M.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
[Crossref]

Schutz, H.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
[Crossref]

Shen, S.-C.

H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
[Crossref]

Sinzinger, S.

S. Sinzinger and J. Jahns, Microoptics, (WILEY-VCH Verlag GmbH, Weinheim, 1999) pp. 85–103.

Stevens, R. F.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
[Crossref]

Yang, H.

H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
[Crossref]

Appl. Opt. (1)

N. F. Borrelli, D. L. Morse, R. H. Bellman, and W. L. Morgan, “Photolytic technique for producing microlenses in photosensitive glass,” Appl. Opt.  24(16), 2520 (1985).
[Crossref]

Colloids Surf. A (1)

T. Hirai and S. Hayashi, “Lens Functions of Polymer Microparticle Arrays,” Colloids Surf. A  153(1–3), 503–513 (1999).
[Crossref]

J. Micromech. Microeng. (1)

H. Yang, C. K. Chao, C.-P. Lin, and S.-C. Shen, “Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers,” J. Micromech. Microeng.  14(2), 277–282 (2004).
[Crossref]

J. Mod. Opt. (1)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt.  37(2), 253–265 (1990).
[Crossref]

Meas. Sci. Technol. (1)

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, “The Manufacture of Microlenses by Melting Photoresist,” Meas. Sci. Technol.  1(8), 759–766 (1990).
[Crossref]

Opt. Eng. (1)

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng.  33(11), 3556–3566 (1994).
[Crossref]

Sens. Actuators A Phys. (1)

C. S. Lee and C. H. Han, “A novel refractive silicon microlens array using bulk micromachining technology,” Sens. Actuators A Phys.  88(1), 87–90 (2001).
[Crossref]

Other (1)

S. Sinzinger and J. Jahns, Microoptics, (WILEY-VCH Verlag GmbH, Weinheim, 1999) pp. 85–103.

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Figures (7)

Fig. 1.
Fig. 1. Schematic evolution of the volumetric variation of a micro-lens after extrusion: (a) initial stage; (b) steady state.
Fig. 2.
Fig. 2. Illustration of nozzle
Fig. 3.
Fig. 3. Process flow chart for the fabrication of eyeball-like spherical micro-lens arrays. (a) Deposit silicon nitride and photoresist SU-8. (b) Define nozzle orifice by photolithography (obverse side). (c) Define nozzle cavity (rear side). (d) Bulk etch the rear side with Teflon for protection. (e) Perform extrusion process. (f) Expose without mask (flooding exposure).
Fig. 4.
Fig. 4. The relationship between the diameter D of the MBA and the SU-8 nozzle orifice size under different rotational speeds of the spin-coater.
Fig. 5.
Fig. 5. SEM images of MBAs. (a) SU-8 is extruded through the nozzle orifice before forming MBAs. (b) MBAs of a mushroom shape were formed due to the low UV exposure dosage. (c) A 3×3 MBA array. (d) Cross-sectional and top views of the spherical micro-lens
Fig. 6.
Fig. 6. Design of the light fields measurement platform.
Fig. 7.
Fig. 7. Relationship of coupling efficiency to the distance between the spherical micro-lens surface and the fiber.

Equations (3)

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

σ = dF dS
f = n 2 ( n 1 ) R = 1.2463 R
BF = f R

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