Open Access
Add to BibSonomyAbstract
We report a novel process technology of hemispherical shaped microlenses, using isotropic wet etching of silicon in an acid solution to produce the microlenses molds. Governed by process parameters such as temperature and etchant concentration, the isotropic wet etching is controlled to minimize various defects that appear during the molding creation. From the molds, microlenses are fabricated in polymer by conventional replication techniques such as hot embossing and UV-molding. The characterization of molds and measurements of replicated microlenses demonstrate high smoothness of the surfaces, excellent repeatability of mold fabrication and good optical properties. Using the proposed method, a wide range of lens geometries and lens arrays can be achieved.
©2009 Optical Society of America
1. Introduction
The development of refractive microlenses has emerged as a crucial optical technology. For the last 15 years, several research groups and industrial research institutes have focused their attention on the development of fabrication techniques for refractive microlenses. Lens arrays made of glass have been studied for a relatively long time compared to those made in other materials and various fabrication techniques have been proposed for this purpose: CO2 laser melting of glass [1,2], diamond turning [3], embossing techniques [4], melting techniques [5,6], and other less conventional methods [7-9]. Most of these fabrication methods yield microlenses arrays that satisfy many of the optical quality requirements. However, some fabrication methods are more suitable either for rapid prototyping, for mass-scale fabrication or for monolithic integration than others [10]. Among them, we focus our interest on silicon micromachining technology, and in particular silicon etching which is well suited to the fabrication of high precision micro-optical components. It permits relative easy alignment procedures and offers a potential for monolithic integration at low cost [10-12].
In this framework, we present a novel microlens wafer-scale fabrication technique, based on isotropic wet etching of silicon to produce the mold and using techniques of micromolding for the replication of optics. These last processes can change depending on the choice of the microlens material, but the key step of the proposed technology is the isotropic wet etching of silicon in acid solution used to produce the wafer-scale molds. This technique allows the production of high quality surface molds at rather low-cost. During the fabrication of the silicon mold, the important parameters to take into account are the design of the mask and the choice of parameters of the etchant solution, such as its concentration. The isotropic wet etching of silicon is characterized, theoretically, by an etch ratio that is independent of the orientation of the crystallographic planes [13-15], and consequently, allows the fabrication of spherical molds, where the shape depends on the initial shape of the mask and the etching parameters. The next step, in order to demonstrate the ability of the molds to generate micro-optical elements, is the microlens replication. Various well-known techniques can be used for this purpose [16,18]. In this study, two of them, i.e. hot-embossing and UV-molding, have been tested using the same molds for each replication process.
The paper is organized as follows: In Section 2, the fabrication of the molds is detailed. In particular, we discuss the procedure of protecting the substrate with a hard mask, the development of the initial footprints of the spherical microlenses through the mask and the wet etching procedure to obtain the final molds. In Section 3, the fabrication of polymer microlenses is presented. Section 4 focuses on the characterization of silicon molds, polymer microlenses as well as metal shims produced from silicon masters and used as replication tools for polymeric microlenses. Finally, conclusions and perspectives are given in Section 5.
2. Fabrication of silicon molds
The isotropic etching of silicon is one of standard techniques in micro-electro-mechanical systems (MEMS) micromachining, able to produce a spherical cavity with excellent sphericity, minimal surface roughness and good uniformity. Usage of monocrystalline silicon which has very few imperfections, offers the advantage of an integrated circuit-compatible (IC-compatible) batch process, which could lower the manufacturing costs. For these reasons, chemical isotropic etching methods have been widely explored to fabricate micromachined devices such as microfluidic channels or reaction chambers without sharp corners, with varying diameters, smooth surfaces and uniform bends [19].
The properties of isotropic wet etching of silicon using solutions containing a mixture of hydrofluoric acid (HF) and nitric acid (HNO3) have been studied extensively. According to Robbins and Schwartz [13-15], HNO3 creates an oxide layer at the silicon surface that can subsequently be etched away with HF. They found that the etch rate depends only on the HF concentration when concentration of HNO3 is high. Thus, the etch rate is influenced mainly by the flow of reagent to the surface by diffusion. Other more recent studies [20-24] demonstrate that mass-transfer effects are significant in the etching procedure. The chemical reaction involves elementary reactions [20,21], coming up to a complex mechanism with different proposed equations for the dissolution of silicon dioxide under various conditions.
A schematic of the process steps used to create the semispherical molds is shown in Fig. 1. The fabrication of a semispherical surface requires the design of an appropriate lithographic mask, the transfer of the pattern to a hard mask deposited on the silicon wafer, then, isotropic etching to form a spherical surface and finally, the removal the of mask layers. The first key step of our procedure is the mask design. The acid solution to be used is so aggressive that masking becomes a challenge. To gain quantitative understanding of the etching process and analyze the effects of mask undercut, we studied etching of silicon in a mixture of HF/HNO3 via circular mask openings and the different effect under the mask than at the center of the aperture. Circular openings with different sizes were designed with commercially available CAD software. As can be seen in Fig. 1 (3rd step), the footprints of the etched shapes are not identical to the mask because of significant underetching of the mask. This phenomenon has been used to produce the shape of the mold. It can be noted that etching effects through circular mask openings have been theoretically studied and modeled previously by different authors [24-28]. The isotropic etching of silicon in HF-based solutions exhibits some level of anisotropy [24,25]. According to Svetovoy et al. [25], the maximal anisotropy is about 9% for <100> wafers but only 1.5% for <111> wafers. Thus, the use of <111> wafers decreases significantly those effects, as the shape of the footprint to become square, and it also improves the resulting surface quality of the mold. However, <100> oriented wafers are already demonstrated as optically acceptable when creating spherical structures [24,25], and were used for the first demonstration of our technology.
The first step was the preparation of the hard mask that will be used for the wet etching of silicon. The wafers were covered with 0.5μm-thick layer of thermal oxide (SiO2) and 100 nm of low-stress silicon nitride (Si3N4) deposited by low pressure chemical vacuum deposition (LPCVD), as shown in Fig. 1(1st step). To pattern the Si3N4, an additional layer of 100-nm thick alloy of nickel/chromium (NiCr) was evaporated on top of it and patterned photolithographically using a positive photoresist S1813. Once the pattern was opened on the NiCr layer, it was then transferred to the Si3N4 mask by reactive ion etching (RIE) and the NiCr was removed. The remaining SiO2 in the opened windows was removed with buffered HF solution (BHF) (Fig. 1-2nd step). The Si3N4 mask was used to protect the areas of the silicon wafer which should not be attacked by the etchant solution. In addition, it must be noted that the Si3N4 mask has to be characterized by very low stress in order to avoid breaking of the mask in the zone of underetching. Indeed, these broken Si3N4 pieces can produce an additional masking effect while deposited.
In the next step, the wafers were immersed in the isotropic etch solution to form the molds (Fig. 1-3rd step). The etch solution consists of HF (with 49% concentration) and HNO3 (with 60% concentration), operating in proportion 1:9 and at room temperature (22°C). The proportion of etchant solution was selected following the data given by Robbins et al. [13-15], as it is slow enough to control as much as possible the etch speed, the selectivity and low rms roughness of etched surfaces.
For this etchant solution, the etching rate varies from 1 μm/min for mask apertures of 10 μm in diameter, and up to 2 μm/min for a mask aperture of 230 μm diameter. Etching over a period of 45 min resulted in molds with diameters ranging from 40 μm (the minimal size of the mask aperture was 10 μm), up to 343 μm (mask of 230 μm), and mold depths of 45 μm and 89 μm respectively.
By measuring the mold depth for different etching time, we noticed, depending on the size of the mask, that there is a minimum etching time to reach spherical shaped cavities. This time increases as the diameter of the apertures is increased. It can be noted that isotropic etching causes a faster lateral enlargement of the mold (due to lateral underetching) than vertical enlargement. As the etch time increases, the depth of the mold enlarges, as shown in Fig. 2 for two different diameters of hard mask and different etching times. For instance, after 1 min of etch, the effective diameter of a mold fabricated with 120-μm mask, is 126.7 μm while the depth of cavity is 5.7 μm (Fig. 2(a)). In the case of a 100 μm mask, 20 min of etching provides a cavity depth of 46 μm while effective diameter becomes 155.7 μm (Fig. 2(b)).
Fig. 2. Evolution of the mold shape for two different situations of isotropic etching: (a) mold diameter of 120 μm and etch time of 1 min; (b) mold diameter of 100 μm and etch time of 20 min.
The resulting etched cavities can be perfectly rounded if appropriate agitation accompanies the etch process. Indeed, we observed at first that the etching ratio at the central zone of the circular apertures was lower than under the mask. This effect is due to the emitted oxides of nitrogen (released during the reaction of silicon with the etchant solution) that act like local masks, and the non uniform concentration of reagent over the surface [28]. Robbins et al. [13], studied the effect of catalyst presence during the reaction and showed that a constant etch reaction can be achieved by ensuring that the catalyst is well distributed over the area to be etched. One solution is to add extrinsic nitrogen bubbling [28], another one that we chose is to stir the solution. Stirring the solution promotes a constant exchange of the liquid in the whole volume to release the bubbles from the silicon surface and, in addition, uniforms the mass-transfer effect. Two different stirring techniques were investigated. The first technique tested involved applying a constant circular stirring during the etch procedure. However, the difference of the mass-transfer resistance, caused by the difference of shear and centrifugal force between the center of the wafer and the sides (as reported in [28]), led to a loss of symmetry in the cavities and a non-uniform surface quality over the whole area of the wafer. This problem was partially suppressed by applying a combination of circular stirring and random manual agitation of the solution while etching, taking into account that fast stirring affects the mass-transfer and increases the etch speed.
After etching, the wafer was rinsed in deionized water prior to removal of the hard mask immersing the wafer in a concentrated HF solution (Fig. 1-4th step). The wafer was rinsed again in deionized water to eliminate any residual acid and submitted to a cleaning process with Piranha solution (H2SO4+H2O2). Finally, the rinsing with deionized water was performed to prepare the molds for the fabrication of different microlenses.
Based on this process, a 3” silicon master was fabricated, to form a set-up of matrixes containing 25 different sizes of molds, from 10 μm to 230 μm with 10 μm increment, as shown in Fig. 3.
Figure 4 shows a scanning electron microscope (SEM) image of a spherical mold with a diameter of 116.7 μm. The mold, fabricated whilst agitating the etchant solution, is almost perfectly isotropic.
The presented mold fabrication technique is then appropriate for molding and for replication of high quality microlenses with high numerical aperture (> 0.3) and short focal lengths (shorter than 1.5 mm) as it will be shown in the next section.
3. Fabrication of microlenses
There are various methods available for replicating microlens arrays. The most cost-effective fabrication technology is replication in polymer materials with techniques such as hot embossing [29] and UV molding [30]. For these methods, one of the biggest challenges in our case was to replicate, with good reproducibility, an array of microlens arrays with high surface-coverage ratio. The selection of lens materials is critical in the molding processes. In particular, a slight change of refractive index can induce a significant variation of the optical parameters of a lens.
Fig. 6. SEM images of replicated microlenses, a) array of hot embossed microlenses with diameter of 262 μm and sag of 80 μm which mold aperture was 150 μm and b) array of UV-molded microlenses with diameter of 196 μm and sag of 77 μm which mold aperture was 80 μm.
Microlens array fabrication by hot embossing required the use of intermediate nickel (Ni) shims (Fig. 5) [31], made by electroplating nickel foil onto the silicon mould to produce the final micro-optical component. The major reason to use this additional replication tool is to protect the original master-mold from any process degradation. Indeed, hot-embossing is a process made under significant pressure that could lead to the destruction of the Si mold. In addition, Ni is compatible with the replication material, permitting lens reproduction without shrinkage. For instance, Fig. 6(a) shows an array of spherical microlenses, fabricated by hot embossing from the Ni shim with typical dimensions of 262 μm in diameter, sag of up to 80 μm and focal length of 0.45 mm. The replication material is polymethyl methacrylate (PMMA) characterized by a refractive index around 1.49. The process has been carried out at 130 °C, with pressure of 4 MPa applied during 5 minutes. Microlenses have also been fabricated by UV-molding process assisted by heat and solvent (Fig. 6(b)). In this case, the chosen material for the replication was SK-9 optical cement from Summers optical, which has a refractive index of 1.49. More details about the technique used can be found in Ref. 30.
4. Testing and analysis
In the previous section, it was demonstrated that the silicon molds can be used to fabricate hemispherical microlenses. However, it is also important to check, along with the microlenses properties, that the interesting properties of the molds, such as shape and surface quality, are maintained through the replication process. For this purpose, the size of the molds and the nickel shims, as well as the size of the replicas, were characterized using a non-contact profilometer Wyko NT2000 for diameter and depth (sag in case of the microlenses). In addition, the optical properties of the replicas such as the focal length, numerical aperture (NA), peak-to-valley and rms (root mean square) wavefront aberration were characterized with a Mach-Zehnder interferometer setup developed by Erlangen-Nürnberg University [32,33]. Moreover, the focal length of the replicas was also controlled with a commercially available spherometer from Trioptics, even though the latter one is more suitable to measure microlenses whose diameter is over 500 μm.
Concerning the molds and UV-molded replicas, measurements were done for five microlenses (one for the hot embossed replicas) per each matrix (made of 5×5 microlenses and 3×3 for the matrix with the biggest apertures) and for all the matrixes from a complete row across the wafer (rows are clearly visible in Fig. 3). Measurements made for the entire row allowed for comparative analysis of the characteristics with respect to the position over the wafer.
As mentioned in Section 2, the etching time was a limiting parameter. The minimum time of etching to obtain a valid (spherical) shape increases with the size of the aperture on the mask. It can be seen from Fig. 7(a) that the depth of the mold follows a logarithmic tendency which tends to flatten as a function of aperture size and consequently the diameter of the mold increases. As a consequence, there is a loss of spherical behavior as the aperture size grows. Regarding the diameter of the mold (Fig. 7(b)), a linear dependence with the aperture size can be assumed. We have noticed that depth is a more critical parameter to control than diameter when trying to get a valid spherical shape. It can also be noted that within each matrix, deviations of molds depth as well as diameter were in all cases lower than 0.7% from the average value (Table 1).
The roughness of the surface of the molds was measured with a non-contact optical profilometer from Fogale. The obtained average values oscillated in all cases between 4 nm and 6 nm, which demonstrate the good optical quality of the surfaces.
Fig. 7. Characterization of the molds (average values after measuring 5 items per matrix), a) depth of the <100> substrate etched during 45 min as a function of aperture size, b) diameter after 45 min etching as a function of aperture size.
The Ni-shims were characterized with the same non-contact profilometer to compare the deviation from the mold size (Fig. 8). In this case, within each matrix, the deviations of molds depth reach, in some cases, 1% whereas the diameters did not differ more than 0.7% from the average value of, the silicon molds.
The same profilometry measurements were done with the molded lenses, i.e. replicas fabricated by hot-embossing and UV-molding, and were also compared to those obtained from the Si mold and the Ni-shim (Fig. 8). Comparing the sizes, the biggest differences were found for the PMMA replica generated by hot-embossing. This can be explained by the additional step which consists of the generation of a Ni-shim used as a master for the hot-embossing replication. On the other hand, the morphological characteristics of the UV-molded microlenses are very close to the mold characteristics (Table 1). This technique, which has been optimized to fulfill high fidelity [30] is moreover used directly on the silicon-mold since risks of breaking the master are a lot lower.
Table 1. Uniformity of the silicon molds compared to the UV-molded replica
The optical characteristics of microlenses such as focal length and numerical aperture are usually in the literature deduced theoretically from the shapes. It can be noted that in this paper we report, in addition to the theoretical calculations, the experimental characteristics, i.e. root mean square (RMS) and peak-to-valley (P-V) of the wavefront deformation, focal length and numerical aperture (Fig. 9). As mentioned in Section 2, as long as the diameter grows, the shape of the mould loses sphericity. This can explain why the experimentally measured focal lengths tend to be higher than the theoretical ones as the size of the microlenses increases. The optical characteristics are actually similar for both replicas for the central zones of the graph corresponding to the central zone of the wafer.
The measurements gave ranges of focal lengths from tens of microns to hundreds of microns with an upper value of around 1.2 mm in case of the SK-9 replica and 800 μm for the PMMA replica. The measured NA ranged between 0.2 to 0.37 for the SK-9 replica and 0.3 to 0.45 for the PMMA replica.
Fig. 8. Characterization of the Ni shim and Si molds depth and sag of the SK-9 and PMMA replicas (average values after measuring 5 items per matrix)
Fig. 9. Optical characterization of the replicas (average values after measuring 5 items per matrix), a) peak-to-valley wavefront deformation, b) RMS wavefront deformation, c) focal length comparison between theoretical values (Th) and measured with a Trioptics spherometer (Sph) and a Mach-Zehnder interferometer (MZ) and d) NA comparison between theoretical values (Th) and measured with a Mach-Zehnder interferometer (MZ). All these parameters are plotted as a function of the mask aperture diameter.
5. Conclusions
We proposed, developed and characterized a technique dedicated to the fabrication of semispherical silicon-molds based on isotropic wet etching. It is shown that these molds can be used to fabricate microlenses with polymer materials by conventional replication techniques which can then further be integrated with silicon. The molds are characterized by high smoothness of the surface, high uniformity and repeatability. It is experimentally demonstrated that parameters such as etching time and aperture size of the mask permit the generation of a large spectrum of molds with diameters varying between 40 μm to 343 μm. These molds are then used to fabricate microlenses whose numerical aperture varies from 0.2 to 0.45 and focal lengths from tens of microns to 1.2 mm. Two different techniques of polymer replication have been demonstrated to illustrate the utility of this technology within the area of low-cost production of high quality microlenses.
Acknowledgments
The authors want to acknowledge Dr. Sylwester Bargiel for his help with SEM pictures and Dr. Michael Withford for his help redacting the manuscript. This research project has been developed under the framework of the Network of Excellence on Micro-Optics (NEMO).
References and links
1. M. Wakaki, Y. Komachi, and G. Kanai, “Microlenses and microlens arrays formed on a glass plate by use of a CO2 laser,” Appl. Opt. 37, 627–631 (1998). [CrossRef]
2. S. Calixto, M. Rosete-Aguilar, FJ. Sanchez-Marin, and L. Castañeda-Escobar, “Rod and spherical silica microlenses fabricated by CO2 laser melting,” Appl. Opt. 44, 4547–4556 (2005). [CrossRef] [PubMed]
3. A. Y. Yi and L. Li, “Design and fabrication of a microlens array by use of a slow tool servo,” Opt. Lett. 30, 1707–1709 (2005). [CrossRef] [PubMed]
4. L. Jiang, T. Huang, C. Chiu, C. Chang, and S. Yang, “Fabrication of plastic microlens arrays using hybrid extrusion rolling embossing with a metallic cylinder mold fabricated using dry film resist,” Opt. Express 15, 12088–12094 (2007). [CrossRef] [PubMed]
5. Z. Popovic, R. Sprague, and G. A. Neville Conell, “Technique for monolithic fabrication of microlens arrays,” Appl. Opt. 23, 1281–1284 (1988). [CrossRef]
6. M. He, X.-C. Yuan, N. Q. Ngo, J. Bu, and V. Kudryashov, “Simple reflow technique for fabrication of a microlens array in solgel glass,” Opt. Lett. 28, 731–733 (2003). [CrossRef] [PubMed]
7. M. Kubo and M. Hanabusa, “Fabrication of microlenses by laser chemical vapor deposition,” Appl. Opt. 29, 2755–2759 (1990). [CrossRef] [PubMed]
8. H. Hisakuni and K. Tanaka, “Optical fabrication of microlenses in chalcogenide glasses,” Opt. Lett. 20, 958–960 (1995). [CrossRef] [PubMed]
9. B. P. Keyworth, D. J. Corazza, J. N. McMullin, and L. Mabbott, “Single-step fabrication of refractive microlens arrays,” Appl. Opt. 36, 2198–2202 (1997). [CrossRef] [PubMed]
10. H. P. Herzig, Micro-Optics. Elements, systems and applications (Taylor & Francis, 1997).
11. D.W. de Lima Monteiro, O. Akhzar-Mehr, P. M. Sarro, and G. Vdovin “Single-mask microfabrication of aspherical optics using KOH anisotropic etching of Si,” Opt. Express 11, 2244–2252 (2003). [CrossRef] [PubMed]
12. K. P. Larsen, J. T. Ravnkilde, and O. Hansen, “Investigations of the isotropic etch of an ICP source for silicon microlens mold fabrication,” J. Micromech. Microeng. 15, 873–882 (2005). [CrossRef]
13. H. Robbins and B. Schwartz, “Chemical etching of Silicon I,” J. Electrochem. Soc. 106, 505–508 (1959). [CrossRef]
14. H. Robbins and B. Schwartz, “Chemical etching of Silicon II,” J. Electrochem. Soc. 107, 108–111 (1960). [CrossRef]
15. H. Robbins and B. Schwartz, “Chemical etching of Silicon III,” J. Electrochem. Soc. 108, 365–372 (1961). [CrossRef]
16. B.-K. Lee, D. S. Kim, and T. H. Kwom, “Replication of microlens arrays by injection molding,” Microsyst. Technolog. 10, 531–535 (2004). [CrossRef]
17. P. Huang, T. Huang, Y. Sun, and S. Yang, "Fabrication of large area resin microlens arrays using gas-assisted ultraviolet embossing," Opt. Express 16, 3041–3048 (2008). [CrossRef] [PubMed]
18. R. K. Dutta, J. A. van Kan, A. A. Bettiol, and F. Watt, “Polymer microlens replication by Nanoimprint Lithography using proton beam fabricated Ni stamp,” Nucl. Instrum. Methods Phys. Res. B 260, 464–467 (2007). [CrossRef]
19. J. Dziuban, A. Gorecka-Drzazga, L. Nieradko, and K. Malecki, “Silicon-glass micromachined chromatographic microcolumn,” J. Capillary Electrophor. 6, 37–41 (1999).
20. J. P. John and J. McDonald, “Spray etching of silicon in the HNO3/HF/H2O system,” J. Electrochem. Soc. 140, 2622–2625 (1993). [CrossRef]
21. D. L. Klein and D. J. D’Stefan, “Controlled etching of silicon in the HF-HNO3 system,” J. Electrochem. Soc. , 109, 37–42 (2000). [CrossRef]
22. H. K. Kuiken, J. J. Kelly, and P. H. L. Notten, “Etching profiles at resist edges I. Mathematical models for Diffusion-Controlled cases,” J. Electrochem. Soc. 133, 1217–1226 (1986). [CrossRef]
23. P. H. L. Notten, J. J. Kelly, and H. K. Kuiken, “Etching profiles at resist edges II. Experimental confirmation of models using GaAs,” J. Electrochem. Soc. 133, 1226–1232 (1986). [CrossRef]
24. V. B. Svetovoy, J. W. Berenschot, and M. C. Elwenspoek, “Precise test of the diffusion-controlled wet isotropic etching of silicon via circular mask openings,” J. Electrochem. Soc. 153, C641–C647 (2006). [CrossRef]
25. V. B. Svetovoy, J. W. Berenschot, and M. C. Elwenspoek, “Experimental investigation of anisotropy in isotropic silicon etching,” J. Micromech. Microeng. 17, 2344–2351 (2007). [CrossRef]
26. H. K. Kuiken, “A mathematical model for wet-chemical diffusion-controlled mask etching through a circular hole,” J. Eng. Math. 45, 75–90 (2003). [CrossRef]
27. C. B. Shin and D. J. Economou, “Forced and natural convection effects on the shape evolution of cavities during wet chemical etching,” J. Electrochem. Soc. 138, 527–538 (1991). [CrossRef]
28. M. S. Kulkarni and H. F. Erk, “Acid based etching of silicon wafers: mass-transfer and kinetic effects,” J. Electrochem. Soc. 147, 176–188 (2000). [CrossRef]
29. X. J. Shen, L. Pan, and L. Lin, “Microplastic embossing process: experimental and theoretical characterizations,” Sens. Actuators A 97-98, 428–433 (2002). [CrossRef]
30. J. Pietarinen, V. Kalima, T. T. Pakkanen, and M. Kuittinen, “Improvement of UV-moulding accuracy by heat and solvent assisted process,” Microelectron. Eng. 85, 263–270 (2008). [CrossRef]
31. J. Pietarinen, S. Siitonen, N. Tossavainen, J. Laukkanen, and M. Kuittinen, “Fabrication of Ni-shims using UV-moulding as an intermediate step,” Microelectron. Eng. 83, 492–498 (2006). [CrossRef]
32. J. Schwider, N. Lindlein, R. Schreiner, J. Lamprecht, G. Leuchs, J. Pfund, and M. Beyerlein, “Optikprüfung von refraktiven Mikrolinsen,” Tech. Messen. 69, 467–482 (2002). [CrossRef]
33. H. Ottevaere and H. Thienpont, “Refractive Optical Microlenses: an Introduction to Nomenclature and Characterization Techniques,” Encyclo. Mod. Opt. 4, 21–43 (Elsevier, Oxford, 2004).
