High-Identical Numerical Aperture, Multifocal Microlens Array through Single-Step Multi-Sized Hole Patterning Photolithography

Imaging applications based on microlens arrays (MLAs) have a great potential for the depth sensor, wide field-of-view camera and the reconstructed hologram. However, the narrow depth-of-field remains the challenge for accurate, reliable depth estimation. Multifocal microlens array (Mf-MLAs) is perceived as a major breakthrough, but existing fabrication methods are still hindered by the expensive, low-throughput, and dissimilar numerical aperture (NA) of individual lenses due to the multiple steps in the photolithography process. This paper reports the fabrication method of high NA, Mf-MLAs for the extended depth-of-field using single-step photolithography assisted by chemical wet etching. The various lens parameters of Mf-MLAs are manipulated by the multi-sized hole photomask and the wet etch time. Theoretical and experimental results show that the Mf-MLAs have three types of lens with different focal lengths, while maintaining the uniform and high NA irrespective of the lens type. Additionally, we demonstrate the multi-focal plane image acquisition via Mf-MLAs integrated into a microscope.


Introduction
Over the last few decades, microlens arrays (MLAs) have become an indispensable optical component, owing to their wide field-of-view (FOV) and simple configurations, and are applied in a wide range of fields, such as bio-inspired compound eye systems [1][2][3][4], computational holograms [5,6], and surveillance cameras [7,8]. In particular, the multiple parallax images from the MLAs have attracted the attention of many research groups working on the application of 3D imaging, and particularly 3D medical imaging systems [9,10], and light field imaging [11][12][13]. However, to actively apply the MLAs in 3D imaging systems, the depth-of-field (DoF) of the conventional MLAs should be sufficiently enlarged for achieving an accurate depth estimation. The DoF can be widened by lowering the lens' sag-height [14], which has a low numerical aperture (NA), but it is noted that an accurate depth estimation and a high optical resolution are mutually incompatible from the wide DoF and low NA. As an alternative approach, MLAs with multiple foci can resolve this limitation, achieving not only the accurate depth estimation, but also the high optical resolution [15,16].
In the fabrication of wafer-level MLAs, the MEMS-based precision machining method and the resistance to thermal reflow are commonly employed as main fabrication techniques [17,18]. In addition, the combined and tweaked fabrication methods allow for the design of MLAs with various functions, such as aspheric MLAs [19], high NA [20], or and antireflection [21,22]. For multifocal MLAs, several approaches were newly demonstrated, such as a guided resistance to thermal reflow and multi-stacked microposts [23,24], which cannot be broadly used because of the multiple photolithography step, sophisticated align process, high cost, non-uniform NA among lenses, and low yield rate. Moreover, for utilizing the multifocal MLAs in 3D depth estimation systems (e.g., light field camera), uniform NA among lenses with different foci is required to reduce the computational cost [11]. Hence, the above-mentioned limitations demand a novel fabrication technique for high and identical NA and cost-effective, multifocal MLAs.
In this study, we propose a novel wafer-level fabrication method for multifocal MLAs (Mf-MLAs) with steady and high NA through one-step photolithography. The fabricated Mf-MLAs have a high NA, of~0.43, which attains not only a high optical resolution, but also an accurate depth estimation through the extended DoF. Mf-MLAs' mold can be readily fabricated at the wafer level by the isotropic chemical wet etching of multi-sized holes created by single-step photolithography. Individual lens' design parameters such as radius of curvature and lens diameter are satisfied by varying the etch time during the chemical wet etching process.

Design and Fabrication of Mf-MLA
Conventional MLAs with a single focal length inevitably have a narrow DoF, which leads to the restriction of the accurate depth estimation from the parallax images of individual lenses. On the contrary, Mf-MLA is composed of several types of lenses with different focal lengths, so that it is possible to collect the parallax images from two or more object planes in different distances. Thus, the Mf-MLA provides an extended DoF, as shown in Figure 1a, enabling us to get accurate depth information on the target object. For the lens' material, we were particularly concerned with two features: flexibility and compatibility. To this end, poly-dimethylsiloxane (PDMS, Sylgard 184, Dow Corning Corporation, Midland, MI, USA) was selected as a representative material for our Mf-MLA. Figure 1b shows the comparison between bare PDMS and PDMS Mf-MLAs, and they have a good compatibility with other optoelectronic elements, such as an image sensor array and glass or plastic optics, easily attachable by van der waals force [25]. The "GIST" logo is clearly imaged under the bare PDMS (Figure 1b; left). In contrast, the fabricated Mf-MLAs shows a blurred image owing to the microscale structure at the surface, but maintains the color information beneath the Mf-MLAs (Figure 1b; right). The shaping of the lens' surface is conducted mainly by the wet etching process. The Mf-MLA mold is isotropically etched forming the nearly hemispherical-shaped lens surface regardless of its size, which allows for high-NA Mf-MLAs, providing not only an accurate depth estimation but also a high optical resolution. Focal lengths in Mf-MLA are modulated by the different hole-size patterns in the photolithography step. Note that the different false-color (red, yellow, blue) indicates the three types of lenses in Mf-MLA formed by a different hole-size patterning and the same etch time (Figure 1c). Figure 1d shows images of letter "E" as an object through the engineered Mf-MLA, photographed by the microscope system. According to each focal length of the lenses, the object is clearly focused from each object plane.
The Mf-MLA fabrication process can be conducted by two primary steps: multi-sized hole patterning photolithography and chemical wet etching. First, the Mf-MLAs' mold is patterned with multi-sized holes by single-step photolithography of positive photoresist (PR, AZ 5214, AZ Electronic Materials, Co., Ltd, Luxembourg), and then the wet etching process is carried out, consecutively ( Figure 2a). The entire fabrication procedure of Mf-MLA is as follows: (i) 700 nm thick Poly-Si is deposited on a quartz substrate in order to prevent the penetration of hydrofluoric acid (HF) in the next wet etching process. Hole-patterning was performed by using a multi-sized hole mask on one side of the Poly-Si through photolithography. Note that we set 2 µm as the minimum hole size, due to the resolution (refer as the minimum critical dimension) of the mask aligner (M100, Prowin, Incheon, Korea) using our demonstration. In Figure 2b, the scanning electron microscope (SEM, Hitachi S-4700, Hitachi, Tokyo, Japan) images show the geometrical information of the fabricated master quartz mold for Mf-MLA (Figure 2a; (ii)). The cross sectional view (Figure 2b; right) from the dashed deep-red line in the top view (Figure 2b; left) clearly shows that each lens is formed with different lens diameters. Likewise, the pitch and geometric shape (i.e., 200 µm and hemispheric form, respectively) of adjacent lenses satisfies the designed value. For the quantitative analysis, the fabricated Mf-MLA was scrutinized by using a confocal laser scanning microscope (CLSM). Figure 2c represents the surface morphology variation according to the change in the via-hole diameter at the same wet etch time. Moreover, the results show a fine surface roughness (arithmetical mean deviation, R a ) below 0.045 µm ( Table 1). The wet etch time is 85 min and each diameter of the hole is 2, 6 and 10 µm, respectively. As the via-hole diameter increased, microlens was formed with enlarged radius and sag height. In addition, the diameter and radius of curvature (RoC) of individual microlenses were also measured along with the via-hole diameter variation (Figure 2d,e), indicating that lens parameters such as RoC and diameter are easily manipulated through via-hole diameter and the wet etch time.

Characterization of Mf-MLA
The multifocal features of the fabricated Mf-MLA were measured by using  Figure 2e and the approximated lens maker formula, f = RoC/(n-1), where n is the refractive index (Figure 3b). Then, the point spread function (PSF) was elicited from the beam spots of each type of the microlens. The PSFs clearly show that each lens has a similar beam-spot diameter of~2.1 µm (full width at 1/e2 maximum) regardless of the focal length increase from 128 to 192 µm. This can be explained by the identical NA of the Mf-MLA, which is enabled by the isotropic wet etching processes. The measured PSFs are also well matched to the calculated PSFs from the ray-tracing simulation based on the Monte Carlo method (Figure 3c-e).

Multifocal Arrayed Images
For the practical analysis, we constructed a light field imaging system to capture multifocal images formed by fabricated Mf-MLAs. Figure 4a depicts the schematic of the light field microscopy system using Mf-MLA, which is adopted in this study. The angular information can be extracted by the Mf-MLA along the x-axis, which has the intermediate image formed by the main optics as an object. A Lena image (1 mm × 1 mm) was used as an object for the light field imaging test at three different focal points. The imaging system operates as a relay optics between main optics and an individual micro-image, which operate as a virtual camera. The object was precisely placed to align with a 5.1-megapixel complementary metal-oxide-semiconductor image sensor array (CMOS ISA) (SONY IMX 264, SONY Corp., Tokyo, Japan, pixel size = 3.45 µm). To maximize the range of the extended DoF, we adopted the formula for the DoF of the Mf-MLAs and its maximizing condition as the left and right boundary of the three types of lenses. The equation is as follows [26]: where a − 0 and a + 0 are the left and right boundaries of the DoF, g is the distance between the Mf-MLA and the CMOS ISA, d is the diameter of the microlens, and p is the pixel size, respectively. Then, the DoF is Thus, the optimized condition for the maximum extended DoF is as follows: When the g is the variable, the optimized positions of the Mf-MLAs (f 1 = 128 µm, f 2 = 157 µm, f 3 = 192 µm at d 1 = 110 µm, d 2 = 136 µm, d 3 = 165 µm) are 100, 97, and 94 µm respectively. Figure 4c shows the obtained images at the optimized g of each type of microlens by using a xyz translation stage. The DoF ranges are −783.8 to −316.6 µm, −316.3 to −211 µm, and −210.9 to −164.7 µm for the Galilean light field mode [27]. The results show that the Mf-MLAs reached the~6 times extended whole DoF range from 105.3 µm to 619.1 µm, implying the enlarged depth estimation range in the light-field system.

Conclusions
In summary, we present a simple, but clever fabrication of multifocal microlens arrays (Mf-MLAs) with high numerical aperture and extended DoF. The systematic fabrication of Mf-MLAs was simply performed by a single photolithography step using a multi-sized hole lithography mask and the chemical wet etching step sequentially. Unlike conventional approaches to Mf-MLA, all the lens surface of newly fabricated Mf-MLAs successfully maintains the hemispherical shape by using isotropic etched properties of the quartz substrate, thus achieving a high NA of the Mf-MLA. Individual lens parameters are also elaborately handled by the wet etch time and the diameter of the hole. In addition, the fabricated Mf-MLAs clearly present the extended DoF ranges through the captured image at the multifocal plane. Therefore, the Mf-MLAs, as an essential micro-optics, are expected to pave the way for the advanced imaging systems such as 3D telemedicine endoscopes, holographic display, and the unmanned vehicles.