1. Introduction

Microlens array (MLA) is a useful optical element with wide applications in liquid crystal display, wavefront sensor, image recorder, optical signal processing, and interconnection, etc [1–4]. Fabrication of MLAs in a low cost, highly efficient and highly reliable way is of great interest to many engineering applications. A number of methods have been reported so far. Apart from conventional injection molding, fluidic lens, slow tool servo method and roller imprinting are some among others [5–11]. All of them are more applicable for larger sized lenses (i.e., in millimeter and above scale for the diameter). It is difficult to make micro sized lenses (i.e., with a diameter less than 100 μm) due to reasons, such as high flow resistance during filling in micro channel/mold, difficulties in master mold fabrication and ultraprecision position controlling. Some special techniques have been developed for fabricating small sized lens array, such as ink-jet printing [12, 13], soft lithography [14, 15], electrohydrodynamic instability method [16], and some novel liquid\solvent approaches [17], etc. However, all these methods require to fabricate a pre-patterned mold/mask by semiconductor processing techniques (e.g. lithography and etching), which is expensive and complicate. In addition, most of the reported methods are based on polydimethylsiloxane (PDMS). It is well known that poly(methyl methacrylate) (PMMA) is a widely used optical polymer with excellent optical properties. However, few PMMA MLAs are reported today [18, 19].

In this paper, we demonstrate a simple two-step approach to fabricate PMMA micro protrusions, which is much simpler than many previous ones (e.g. indentation-polishing-heating method and buckling/wrinkling method) [20, 21]. This novel method can be utilized in MLAs fabrication.

2. Fabrication of individual micro protrusions

Figure 1 shows the fabrication procedure of micro protrusions. A cast PMMA sheet with a thickness of 1 mm and a glass transition temperature of 110°C (from Ying Kwang Acrylic, Singapore) was cut into small pieces for our experiments. A micro hardness tester (CSM instruments) was used to make two different shaped indents atop PMMA at room temperature (refer to Figs. 1(a1) and 1(a3)). One indenter is a spherical conical diamond indenter with a radius of 20 μm and a conical angle of 90°. The other is a square pyramid indenter, with an angle of 130° between two edges. All indentation tests were conducted at room temperature (about 22°C) with a maximum load of 150 mN and a loading/unloading speed of 5 mN/s (with 10s holding time between loading and unloading). The resulted indents were characterized by an optical imaging profiler (Sensofar ^® PLu), which is a combination of confocal and interferometry techniques, as shown in Figs. 1(a2) and 1(a4).

 

Fig. 1 Formation of micro protrusions.

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Upon indented to a maximum load of P, the corresponding maximum depth and diameter/width of the indent are denoted as h_i and w_i, respectively (Figs. 1(a1) and 1(a3)). After indentation, the residual maximum depth and diameter/width of indent are denoted as h_r and w_r, respectively (Figs. 1(b1) and 1(b3)). Subsequently, the PMMA samples were immersed in room temperature ethanol (concentration 95%) for 24 hours. Figures 1(b1) and 1(b3) show ethanol induced protrusions atop PMMA samples with a height of h_f and diameter (width) of w_f. A spherical indent results in a spherical protrusion (Fig. 1(b2)); while a pyramid indent produces a pyramid protrusion (Fig. 1(b4)). The formation of protrusions is a result of residual stress (in the indents) enhanced swelling during absorption of ethanol by PMMA [22, 23].

3. Fabrication of microlens array and thermal stability

The simple two-step method (in section 2) can be utilized in MLAs fabrication. Refer to Fig. 2 . First, two indent arrays with different patterns/density were fabricated atop two pieces of PMMA (Fig. 2(a)); and then these samples were immersed into room temperature ethanol, which resulted in lens arrays with different patterns after 9 hours (Fig. 2(b)). Cross-sectional view of indents/protrusions is presented in Fig. 2(c1) for comparison. These lenses are well-ordered, densely packed and have an individual size of about 40 μm (w_f) and a height (h_f) of about 1 μm (refer to Fig. 1 for definitions of w_f and h_f). Figure 2(c2) further reveals the evolution process from indent to protrusion after being immersed into ethanol for different periods of time. As indentation was conducted at room temperature, at which PMMA is hard, the resulted spherical indent is actually pile-up [24]. Upon immersing into ethanol, pile-up grows gradually before spherical protrusion is finally formed (after about 4-hour immersion) and then grows (a useful phenomenon, which can be used to control the density of lenses array and size of lenses, and consequently, to manipulate curvature, conic constant and focus length of lens). As we can see, after 9 hours, w_f is about 40 μm, which is about doubled from w_r; while h_f is about 1 μm, which is about 0.5 times larger than h_r.

 

Fig. 2 MLAs and surface profile.

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Since this method is based on swelling of PMMA upon immersing into ethanol, desorption of ethanol may be an issue which brings the reliability issue of these MLAs into question. To address this point, different sized spherical lenses were fabricated on different PMMA samples following the above two-step method and then put inside an oven of 25°C or 60°C.

Figure 3 (a1) shows surface profile of an indent array, in which three different sized indents were made by a 20 μm spherical indenter under three different maximum loads (namely, 150 mN, 100 mN and 80 mN, respectively). Figure 3(a2) reveals the surface profile (MLA) after immersion in ethanol for 24 hours. Figures 3(a3) and 3(a4) present two typical MLA surface profiles after being kept inside an oven for thermal stability test. It was found that MLAs were stabilized after 168 hours inside a 25°C oven, while it took 24 hours if the oven temperature was set to be 60°C. Figure 3(b) compares the profiles of lenses after 24, 168 and 360 hours inside 60°C oven. It is concluded that all three sized lens arrays are stable after 24 hours at 60°C. Figure 3(c) plots the evolution of the center points of three different sized indents/protrusions (depth/height) against time of the whole process (i.e., after indentation, immersion in ethanol and placed in 60°C oven). It can be seen that there are three major stages during the whole process. The first is the gradual formation of micro lens during immersion in ethanol (from indent to protrusion in 24 hours). Relaxation due to desorption of ethanol is followed (decrease in protrusion height in 60°C oven for 24 hours). After this, MLA becomes stable (no visible change in height in 60°C air for 360 hours).

 

Fig. 3 Thermal stability of MLAs.

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The stabilized MLA (Fig. 2(b1)), after being put in 60°C oven for 24 hours) have a diameter of 39.95 ± 0.55 μm, center-to-center distance of 40 μm and a sag height of 0.8 ± 0.02 μm.

4. Characterization

Projection experiment was conducted on stabilized MLAs. Refer to Fig. 4(a) for the experimental setup. The optical scope is a microscope (Axiotech 100 HD, Zeiss). A PMMA MLA was placed atop a stage and illuminated with white light from bottom through a mask with a letter E (size 12 × 18 mm) in the middle. The projected image at the top was recorded by a CCD system. Figures 4(b) and 4(c) show the focus spot and projected images through two MLAs (as shown in Figs. 2(b1) and 2(b2)). The focus length of these MLAs measured to be 500 μm by this optical microscope system. It can be seen that letter Es are clearly projected.

 

Fig. 4 Projection experiment and results.

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For an ideal spherical curve, the radius (R), focal length (f) and numerical aperture (NA) of the lens can be calculated from [25]

For the MLAs shown in Fig. 4, the calculated radius is 249.8 μm, the focal length is 508.3 μm (close to the measured value of 500 μm) and the numerical aperture is 0.04. For the three types of MLAs (1, 2 and 3) shown in Fig. 3, the calculated radii are 120, 130 and 210 μm, respectively; the focal lengths are 240, 260 and 440 μm, respectively; and the numerical apertures are 0.055, 0.043 and 0.021, respectively. The numerical aperture is related to fabrication parameters. The theoretical maximum numerical aperture is 0.35 using the same spherical conical indenter by this method.

5. Conclusions

In summary, we developed a two-step method to fabricate MLAs by means of immersing pre-indented PMMA samples in ethanol. This method is simple, low cost and efficient for massive fabrication over a large area. Furthermore, as demonstrated, the size and shape of lenses are tunable by varying the indentation parameters and ethanol absorption time. After following the thermal stability process, the resulted MLAs become highly stable.