Abstract

This work presents the fabrication of a one-lens camera using a biologically inspired artificial compound eye with multiple focal lengths. Traditional camera designs that consist of many separated lenses are difficult to assemble due to tight tolerance. The one-lens camera design is demonstrated experimentally in this work to avoid tolerance buildups. This structure is based on the principles of both the human eye as well as an insect’s compound eye. The artificial compound eye is a curved hexagonal microlens array, like an ommatidial array, wherein each artificial ommatidium collects light with a small angular acceptance. The ommatidia, in a typical hexagonal arrangement of 37 lenses, are arranged across a hemispherical photopolymer dome. The curved hexagonal array helps us to achieve a compact and wide field-of-view camera module. The fabrication process for the curved array is divided into two parts: creation of a planar hexagonal multi-lens array, and a replication process. To create the planar array, we use inkjet printing technology with the hydrophilic confinement effect to establish microlens shapes with different profiles. Next, the replication process converts the planar array into a curved shape. The spherical configuration of the hexagonal array is accomplished by applying the template architecture to a reconfigurable surface shape, that is, a photopolymer duplication using a deformed elastomer membrane with the hexagonal array pattern. In our experimental demonstration, microlenses in four rings with different focal lengths are fabricated on a single hemispherical lens with radius of curvature of 2.4 mm. The thickness of our proposed system is 3.04 mm, the f-number is 1.68, and the diagonal field of view is 92.6 deg. Above all, our presented camera module system uses a single one-piece lens.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Cameras are widely used in recording or capturing images [1], which may be stored locally, transmitted to another device, or both. Portable devices also give users convenient access to business and personal data on the go [2]. Because cameras can provide an abundance of information, integrating cameras and portable devices has become a well-established consumer trend [3]. Most consumers want a camera of high quality that executes the basics brilliantly. Hence, camera quality becomes an important factor in purchasing camera-equipped portable devices, such as smartphones, cell phones, personal digital assistants (PDAs), tablets, laptops, and other image-capturing devices [4].

To improve quality, reducing optical aberrations is critical. The use of multiple lenses can minimize aberrations and provide sharp images free of visible imperfections. Therefore, most cameras contain lenses which are composed of several lens elements [5]. Furthermore, improving photographic quality requires lens elements of different compositions and shapes.

To get sharp images from traditional lens assemblies in actual production, optical arrangements consisting of several built-in ball lenses or aspherical lenses fixed in metal housings must meet tight tolerances. When mounting multiple lenses into a metal barrel, factories must determine tolerances that minimize production cost while maximizing the reliability of optical performance [6]. However, this is difficult to accomplish in traditional lens design, given the trade-off between production cost and performance.

Increasing the number of lens elements is the most common method to optimize image quality. However, the greater the number of lens elements used in the camera, the greater its thickness. Achieving compactness in cameras of portable devices has been hindered mainly by the large number of lenses. A thick camera module is quite unsuitable for a portable device. Moreover, more lens elements not only increase cost, but also make aligning the axisymmetric optical elements more difficult. To improve commercial products, it is worth attempting to minimize the number of lens elements and increase image quality at the same time.

Since the number of lens elements increases camera thickness, and tolerance allocation affects production cost and reliability of performance, we investigate a novel lens design to reduce camera thickness and provide high image quality while maintaining cost effectiveness. Our previous research has demonstrated that the number of lens components in a camera module can be reduced by implementing a curved hexagonal microlens array (MLA) [7,8]. This inspiration arises from the human eye [9] as well as the compound eye of an insect [10]. In the human eye, the lens focuses the object light onto a curved retina [11,12]. However, commercial camera products favor the use of low-cost, highly efficient planar image sensors [13], rather than curved sensors [14]. In focusing the light onto a planar surface, a conventional singlet lens unavoidably introduces significant optical aberration [15]. Therefore, we introduce a curved hexagonal MLA that mimics an insect’s compound eye to correct aberrations. In short, we use a complex multichannel system to simplify the lens components. Furthermore, this work combines a one-piece lens with a curved MLA into a single lens element, so the biologically inspired artificial compound eyes are developed with a small form factor in a curved configuration. It is difficult to accurately locate multiple lenses correctly, but if there is only one lens element in the camera, we avoid tolerance buildups owing to combining many lenses.

In the previous study, we explored and validated these concepts using simulations [7,8]. To implement the hexagonal MLA in a real imaging system, we need a technique to fabricate microlenses with different radii of curvature. In this paper, we present what is, to the best of our knowledge, the first experimental verification of a hexagonal MLA camera imaging system. To that end, our laboratory has developed a series of micromachining processes to fabricate a planar hexagonal MLA with different radii of curvature for different microlenses, using inkjet printing [16]. We thereby establish an optical imaging system based on a curved hexagonal MLA with different focal lengths for different microlenses. The microlenses in this system are arranged across a hemispherical lens such that they provide a wide field of view (FOV).

2. DESIGN AND FABRICATION

The paradigm of photographic lens design is to create a camera lens system that projects images onto a flat image plane. Traditional cameras capture light onto a photographic plate or photographic film using an optical lens or assembly of lenses. A single lens usually produces poor image quality. However, as discussed above, an assembly of lenses not only incurs more material cost and greater camera length, but the axisymmetric optical elements are more difficult to align than a single lens.

To achieve a flat field of focus at the image plane using a single lens system, a hemispherical lens is used to mimic the human eye, in conjunction with a curved hexagonal MLA that mimics an insect’s compound eye. In this section, we present specific design principles and the fabrication process for a camera module system using a curved hexagonal MLA attached to a hemispherical lens.

A. Principle of a Wide-Angle Camera System with a Curved Hexagonal MLA

There are several advantages of using a hemispherical lens for a camera system, such as wide FOV collection, reduction of astigmatism aberration, and avoidance of coma aberration (see Supplement 1 for more detail). Although there is only slight astigmatism aberration and no coma aberration in a hemispherical lens system, when light rays emitted from an object are incident onto a hemispherical lens, the curved nature of the optical element projects the image in a curved manner, rather than flat, as shown in Fig. 1(a). This common optical problem is known as field curvature aberration, and the curved surface can be referred to as a curved Petzval surface. However, most digital camera sensors are flat, due to the lithographic fabrication process. The image from a hemispherical lens appears sharp only in a central region of a sensor, instead of being uniformly sharp across the entire sensor. The entire image cannot be captured in perfect focus.

 

Fig. 1. Designing a single-lens system for correction of significant field curvature. (a) Sharpest focus of a hemispherical lens is in a portion of the image space. (b) Curved hexagonal MLA consists of four hexagonal microlens rings on a spherical substrate; hexagonal microlenses of the same radius of curvature are arranged in a ring of the same color. (c) Curved hexagonal MLA is attached to hemispherical lens. (d) Curved hexagonal MLA is used to project a sharp image onto a flat surface.

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To correct field curvature aberration, we employ a curved hexagonal MLA. Hexagonal lenses can be placed sufficiently close to each other on a curved substrate to obtain a relatively high fill factor. In Fig. 1(b), the curved hexagonal MLA consists of four rings of hexagonal microlenses on a spherical substrate, where several microlenses comprise each ring (except at the center).

The hexagonal microlens rings approximate circular rings; in other words, the microlenses in a particular ring are at similar (though not identical) distances to the optical axis. To simplify the experiment, we regard the distance between each microlens in the ring and the optical axis as identical, that is, the focal lengths of the microlenses in a given ring are considered the same.

The proposed system combines a hemispherical lens and a curved hexagonal MLA, as shown in Fig. 1(c). The curved MLA is treated like an aspheric surface to correct optical aberrations. When light rays pass through the hemispherical lens with the hexagonal MLA, the FOV is split into multiple sections adjacent to each other, as shown in Fig. 1(d). After adjusting for the focal length of each microlens, the center of each small Petzval surface region formed by the microlens is focused onto a flat plane. Therefore, the overall image plane is flattened by this MLA pressed onto the hemispherical lens. Because the microlenses are attached to the hemispherical lens, the center of the curved substrate of microlenses can be regarded as the center of the hemispherical lens. When the beams of light pass through the centers of the microlenses, the light rays are still symmetric about the chief rays, so they are focused without coma aberration. Additionally, the hexagonal microlenses have shorter focal lengths than that of the hemispherical lens, so the diffraction-limited spot sizes of the segmented channels are reduced after the hexagonal microlenses are placed onto the hemispherical lens.

The advantages of the hemispherical lens and the hexagonal MLA are combined in this study. Large incident angle beams of light can be collected by the planar side of the hemispherical lens. Furthermore, when we use the hemispherical lens, there is no coma aberration and the astigmatism aberration is reduced. Then the hexagonal MLA is introduced to solve field curvature aberration. In this way, a hemispherical lens with a hexagonal MLA has the ability to collect a wide FOV.

B. Fabrication Process

In this section, the fabrication process for a curved hexagonal MLA with different focal lengths is described. The process starts with a planar array, and ends with a curved array that is transparent.

1. Microlens Fabrication Using Inkjet Printing with the Confinement Effect

The working principle for fabricating the microlenses is the confinement effect, as shown in Fig. 2(a). In our experiment, a bare silicon wafer, which is hydrophobic in nature [17], is prepared. Native oxide is the thin layer of SiO2 that forms on the surface of a silicon wafer when the wafer is exposed to air under ambient conditions. The surface of the silicon wafer is not stable and quickly oxidizes to native oxide, which is hydrophilic [18]. We coat SU-8 photoresist onto the silicon substrate and use lithography to create hexagonal cavities. Because the silicon substrate with native oxide on its surface is hydrophilic and the SU-8 layer is hydrophobic, when an inkjet printhead dispenses droplets onto the substrate, the droplets self-assemble inside the hydrophilic holes. This keeps the accumulating droplets from going outside the boundary and increases the success rate of fabrication.

 

Fig. 2. (a) and (b) Schematic of microlens fabrication using inkjet printing with the confinement effect. (c) to (h) Outline of the fabrication process for a planar hexagonal MLA. Here, the methods of (a) and (b) are used in (g) and (h). (a) Filling of hexagonal hydrophilic hole for microlens fabrication. (b) Inkjet printer system used in this research. (c) Oxidized silicon wafer whose surface is hydrophilic. (d) Spin-coating of the wafer with a negative photoresist. (e) Masked UV exposure of the negative photoresist. (f) Unexposed areas are removed during the developing stage. (g) Fluid is added with the same number of droplets into each hole in each of four hexagonal rings. (h) Planar hexagonal MLA with convex microlens shapes has been created.

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Inkjet printing is the method used to fabricate microlenses in this paper. This technique entails low cost and low material usage. But most importantly, we use inkjet printing to control the precise number of drops used in fabricating microlenses to different specifications. Different numbers of drops cause different profiles in the microlenses, so lenses of different focal lengths can be fabricated on the same substrate.

Figure 2(b) depicts an inkjet printer system that is composed of a vacuum pump, a piezoelectric printhead, two charge-coupled devices (CCDs), and a dual-axis motion platform. The vacuum pump generates negative pressure to keep ink inside an ink container that is connected to the printhead with a properly dimensioned tube. The inkjet printing process is based on piezoelectricity. The key component is the printhead (MicroFab Technology). It is made of piezoelectric material and the diameter of the nozzle hole is 80 μm. When we apply an electrical signal to the piezoelectric material, it deforms and squeezes out droplets.

The CCD camera system includes a vertically placed CCD and a horizontally placed CCD, which have different functions. The vertical CCD is used to monitor droplet quality. The droplets may be positioned outside the target boundary, so the vertical CCD is used to check for this problem. The horizontal CCD is used to verify that the droplets are squeezed out properly.

The dual-axis motion platform that is designed to control the motion of the sample has good displacement accuracy in x and y coordinates. When we are filling a hole, the dual-axis motion platform moves the sample under the nozzle. After each hole is filled, the sample is moved back under the vertical CCD to verify the precision of the operation.

2. Fabrication of Planar MLA with Convex Microlens Shapes

In this section, the use of miniaturized, arrayed optical components fabricated using semiconductor planar processes [19] and inkjet printing [16] is proposed to simultaneously create each ommatidium with its own special shape as well as the large-scale collection of ommatidia. First, for the inkjet printing process, we need to manufacture a hydrophilic surface array. We clean the silicon substrate using piranha solution (H2SO4+H2O2) and then dehydration-bake it for 10 min, as shown in Fig. 2(c). Piranha solution is used to remove organic residues from the substrate and render the silicon substrate more hydrophilic by hydroxylating the surface [20]. After the cleaning process, we start the lithography process.

We select photoresist SU-8 3035, which is a commonly used epoxy-based negative photoresist, to establish the hydrophilic confinement array. Because of the high viscosity of the photoresist, we have to dilute it with SU-8 2000 thinner. The weight ratio yields a 2:1 mixture of the photoresist and the diluent. The diluted photoresist is spin-coated onto the silicon substrate in a two-step program with spin rates of 1000 rpm for 10 s and 4000 rpm for 30 s. Then the substrate is put onto a hot plate, set at 90 °C for 5 min, for the soft bake, as shown in Fig. 2(d).

After the soft-bake process, the photoresist is exposed by a mask alignment system (EVG 620 Top Side Mask Aligner), as shown in Fig. 2(e). The exposure time is 30 s, and the separation distance between mask and photoresist for alignment is 30 μm. The mask pattern consists of 37 identical regular hexagons, and they are in hexagonal ring arrangements. The length of the longest diagonals that connect diametrically opposite vertices of each hexagon is 400 μm, and the gap between each regular hexagon is 100 μm. After exposure, a post-exposure bake is executed, which is applied above the softening point of the resist without destroying the structures to be developed due to the still-closed resist film, at 65°C for 1 min on the hot plate.

Then we develop the sample in SU-8 developer for about 100 s, so the exposed photoresist area remains and the unexposed photoresist areas are dissolved by the developer, forming holes. After developing, a hard-bake process is performed to increase the thermal, chemical, and physical stability of the developed photoresist structure for subsequent processes. The hard-bake temperature is 95°C and the duration is 10 min. Finally, the SU-8 hydrophobic photoresist surrounds the hydrophilic confinement array, in a layer with thickness of about 4.25 μm, as shown in Fig. 2(f).

Before the inkjet printing process is started, we need to prepare a solution for the inkjet droplets—a mixture of photoresist and a diluent in a weight ratio of 1:7—and store the solution in the ink container as the material for the microlenses. Next, inkjet printing of the hexagonal MLA commences. The sample is mounted to a dual-axis motion platform that is designed and engineered specifically to move the holes under the printhead. After we adjust the position of the printhead to the center of each hydrophilic-containment hole, the diluted SU-8 can be dispensed into and fill the hole, as shown in Fig. 2(g). Every hole in a given hexagonal ring is assigned with the same number of droplets; however, the holes in different hexagonal rings have different numbers of droplets. The gap between each hydrophilic confinement hole is used to prevent diluted SU-8 droplets from combining together after SU-8 is dropped into the adjacent holes. After the camera system is constructed, the gap will also help to suppress ghost images when we create a photo. After the inkjet printing process is finished [see Fig. 2(h)], the MLA needs to be exposed under an ultraviolet (UV) lamp to cure the SU-8 droplets.

3. Fabrication of MLA Membrane with Concave Microlens Shapes

To fabricate a curved hexagonal MLA, the planar MLA with convex microlens shapes needs to be transferred to a flexible membrane with concave microlens shapes. The elastomer polydimethylsiloxane (PDMS) is a material commonly used in replication processes due to good plasticity. In our process, we adopt PDMS (Dow Corning Sylgard 184) as the material to make an accurate copy of the convex MLA.

The PDMS is spin-coated onto the planar MLA with convex microlens shapes, as shown in Fig. 3(a). The spin-coating is performed in a two-step program. The first step is set to 500 rpm for 10 s, and the second step is set to 1000 rpm for 30 s. The PDMS membrane is stripped off [see Fig. 3(b)] after curing at 95°C for 15 min, and is now a planar hexagonal MLA with concave microlens shapes, as shown in Fig. 3(c). Figure 3(d) is a cutaway view to make the internal features visible, but without sacrificing the removed context entirely (the membrane is shown in pale red for clarity).

 

Fig. 3. Schematic view of the fabrication process (a) to (d) of a hexagonal MLA membrane with concave microlens shapes, and (f) to (i) replication process and shape inspection of a curved hexagonal MLA. (a) PDMS membrane layer is spin-coated onto the planar MLA with convex microlens shapes. (b) PDMS membrane is stripped off. (c) Released membrane is a planar MLA with concave microlens shapes. (d) Cutaway of (c). (e) 3D-printed chamber (on a U.S. $100 bill for scale). (f) Operational process of making a curved surface to fill with UV-curing adhesive. 3D-printed chamber is connected to a vacuum pump. After the concave PDMS MLA is placed onto the 3D-printed chamber and deformed by negative pressure (step 1), liquid UV-curing adhesive is dropped into the curved membrane (step 2). Glass substrate is needed to cover the adhesive (step 3). (g) Section view of the upper half of the 3D-printed chamber, with the adhesive being exposed to UV light. (h) Plano–convex adhesive lens on glass substrate with curved hexagonal MLA peeled off. (i) Hemispherical lens sectioned by a dicing saw.

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4. Fabrication of Curved Hexagonal MLA

Figure 3(f) illustrates the steps used to make a curved surface, which is then filled with UV-curing adhesive. First, 3D printing is utilized to fabricate a chamber that comprises a hemispherical space, with diameter of 4 mm, and a tube, as shown in Fig. 3(e). After placing the PDMS membrane onto the 3D-printed chamber, the center microlens of the PDMS membrane needs to be aligned to the vertex of the hemispherical surface of the chamber, as shown in step 1 of Fig. 3(f).

There are several microtubes inside the 3D-printed chamber, as shown in Fig. 3(g), and the microtubes connect the hemispherical space to a tube that in turn attaches to a vacuum pump. The vacuum pump is activated to create suction (lower pressure) on the convex side. Thus, the PDMS membrane is sucked toward the hemispherical surface. After the PDMS membrane has been deformed into a hemispherical contour, a UV-curing adhesive is poured into the curved membrane [see step 2 of Fig. 3(f)] and covered with a glass substrate [see step 3 of Fig. 3(f)] [21]. Here, Norland Optical Adhesive 65 (NOA65), with refractive index as a cured polymer of 1.524, is used.

The PDMS membrane needs to be prevented from contacting the hemispherical surface of the chamber when the chamber is pressurized, as shown in Fig. 3(g). Otherwise, the PDMS membrane will be deformed by the microholes (the ends of the microtubes) in the chamber [22]. Therefore, the suction pressure of the pump needs to be controlled carefully.

When we drip the UV-curing adhesive into the bowl formed by the PDMS membrane, and install the glass substrate over the assembly, the membrane achieves a spherical surface. Proper suction pressure locates the center of curvature of the surface of the membrane at the top surface of the glass substrate, so a hemispherical MLA is created, as indicated by the dotted curve in Fig. 3(g).

The adhesive is cured by UV light, and then the curved hexagonal MLA is peeled off [see Fig. 3(h)]. When the fabrication process is complete, to verify the surface of the curved MLA, a dicing saw (DS-150 II) is used. The saw employs a high-speed spindle fitted with an extremely thin diamond blade to cut the curved hexagonal MLA, as shown in Fig. 3(i).

3. MEASUREMENTS AND RESULTS

A. Planar MLA with Multiple Focal Lengths

1. Shape Measurement of Microlenses

From design principles to experimental fabrication, a planar hexagonal MLA with multiple radii of curvature has been successfully fabricated.

A hexagonal microlens is described by the intersection of a spherical cap and a regular hexagonal prism, as shown in Fig. 4. From Fig. 4(a), when a probe is used to scan along the scanning path of the longest diagonal of a regular hexagonal microlens, the probe will exactly pass through the vertex of the microlens. Because the longest diagonal connects diametrically opposite vertices, the sagittal height h and the base radius of the spherical cap r can be obtained.

 

Fig. 4. Hexagonal microlens described by radius of curvature (R and R), base radius (r and r), center of curvature of the spherical surface of the microlens (c and c), and height at vertex h for (a) the longest diagonals and (b) the separation of parallel sides of the microlens.

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Point c is the center of curvature of the scanning profile. The radius of curvature R is a function of r and h of the spherical cap. It can be expressed as

R=r2+h22h.
The focal length f of a hexagonal microlens can be expressed by Eq. (2), which is based on the lens-maker’s formula. After substituting the value of R from Eq. (1) into Eq. (2), the focal length f can be calculated:
f=Rn1,
where n is the refractive index of the lens material, and n is 1.524 in this research.

A probe-type surface analyzer is used to obtain surface profiles of the longest diagonals for the microlenses (see the scanning path in Fig. 4.) in the four rings. Measurements of surface profiles are shown in Fig. 5. To correct for field curvature aberration, the hexagonal microlenses that are nearer to the center necessarily have shorter focal lengths. Because the inner hexagonal microlenses correspond to higher optical power 1/f, the radii of curvature of the inner hexagonal microlenses are smaller than the outer ones. The lengths of the longest diagonals of the hexagonal microlenses are all the same. Therefore, a smaller radius of curvature leads to a greater sagittal height. Per the scanning system for surface profile measurement, the sagittal heights of the hexagonal microlens in each hexagonal ring are 51.39, 46.28, 41.02, and 35.44 μm, respectively. The length of the longest diagonal of each hexagonal microlens is 380 μm, and thus r is 190 μm. According to the measurement results analysis, the inkjet printing shows a high degree of uniformity [16].

 

Fig. 5. Scanning profiles along the longest distance between corners in the hexagonal microlenses of the first (center) ring, second ring, third ring, and fourth ring of the MLA.

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The size of each microlens is slightly smaller than the patterns in the mask. This is due to the fabrication process; for example, the projected image is affected by diffraction when the photoresist is exposed to the UV light. Also, some liquid in the photoresist evaporates during the exposure.

We can use Eqs. (1) and (2) for calculating the values of R and f for the hexagonal microlenses. Alongside this, the base radius of the spherical cap r of the surface profile across flat-to-flat path is r·(32), as shown in Fig. 4(b). The radius of curvature R and the focal length f can be calculated in the same way. f and f cover a range from longest to shortest focal lengths. fm is a measured value of focal length under a microscope. For the focal length of each hexagonal microlens ring, we can use the percent error to represent the difference between the measured value and the theoretical value. The formula for calculating the percent error is as follows:

%Error=|ftfmft|×100,
where ft is the theoretical value and it is the average of f and f. Table 1 summarizes the structural parameters of the hexagonal microlenses of the four hexagonal microlens rings. The percent error is less than 5%.

Tables Icon

Table 1. Structural Parameters of the Hexagonal Micro-Lenses in the Four Rings

2. Image Verification of Microlenses

To confirm that every microlens in a given hexagonal microlens ring has the same radius of curvature, we observe the focal plane of each hexagonal microlens ring under a light microscope. Therefore, the planar hexagonal MLA needs to be rendered transparent (see Supplement 1 for more detail).

The microlenses in different hexagonal rings have different focal lengths. When the focusing plane of the microlenses of one hexagonal ring locates on the image sensor of the microscope, the other rings produce blurry images. More discussion about the multiple focal planes is provided in Supplement 1. Figure 6 shows the images of the first and second hexagonal microlens rings in focus. Supplement 1 includes figures of the first to the fourth hexagonal microlens rings in focus. It is confirmed that each hexagonal microlens ring has its own unique focal length.

 

Fig. 6. Images projected by the microlenses of the (a) first and (b) second hexagonal microlens rings.

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B. Shape Measurement of Curved MLA

A curved hexagonal MLA with microlenses of different focal lengths has been fabricated successfully. From top-view images of a scanning electron microscope (SEM) [see Figs. 7(a) and 7(b)], it is observed that the hexagonal MLA was copied onto the spherical surface perfectly. All of the hexagonal microlenses combine into an array whose contour line is a large regular hexagon with high quality.

 

Fig. 7. SEM images of hemispherical hexagonal MLA. (a) Top view, and (b) enlargement of the right corner. (c) Oblique view after cutting with a dicing saw and (d) enlargement. (e) Side view and (f) enlargement.

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To verify that the surface of the curved MLA is spherical, to confirm that the center of curvature of this surface is right at the boundary of the glass substrate, and to measure the radius of the surface, the curved hexagonal MLA is cut by a dicing saw, as shown in Figs. 7(c) to 7(f). After checking that the overall quality of the sliced MLA is perfect through oblique-view SEM images [see Figs. 7(c) and 7(d)], the surface of the curved hexagonal MLA can be scrutinized through side-view SEM images [see Figs. 7(e) and 7(f)].

Oblique-view SEM images of the sliced hemispherical hexagonal MLA are shown in Figs. 7(c) and 7(d). When the sample is fed into the cutting blade, the high-precision dicing saw perfectly passes through the centers of the microlenses. From the cross sections, we observe that a whole row of the microlenses is cut through their exact centers, as can be seen in Fig. 7(c). An enlarged view [see Fig. 7(d)] shows the halves of parallel opposite sides are perfectly separated. Consequently, we inspect the side view of the sliced hexagonal MLA to determine the radii of curvature of the microlenses.

Figures 7(e) and 7(f) show side-view SEM images of the curved hexagonal MLA. Referring to the scale bar of the microscopic photograph, the radius of curvature of the curved surface is 2.4 mm. To confirm that the entire surface shape is close to a spherical surface, we use the S-4800 control program to indicate that the lengths from the center to different points of the curved surface are all approximately 2.4 mm (see Supplement 1 for more detail). The contour of the curved hexagonal MLA in the deformed PDMS membrane is pulled into a spherical shape by the vacuum pump. The center microlens of the hexagonal MLA is exactly located at the vertex of the plano–convex lens.

Compared with the size of a mobile camera module that would contain the curved hexagonal MLA, the distance between the mobile camera module and the light that comes from a captured object is much greater. Consequently, we can assume that a single light source is at an infinite distance from the mobile camera module, so the track length from the first lens surface to the image plane is about 3.04 mm, which is derived from the radius of curvature of the curved array (2.4 mm) plus the focal length of the center microlens (638.6 μm).

In Figs. 7(a)7(d), a few defects can be seen. This is because, before the inkjet printing process [see Fig. 2(g)], we first pour the diluted SU-8 onto the entire microholes. The diluted SU-8 on the substrate is then poured off, leaving a little diluted SU-8 uniformly filled into the microholes as a result of the hydrophilic confinement effect, which can help us to save the time required for dispensing the droplets into the holes. However, the diluted SU-8 does not completely slip off the surface of the hydrophobic photoresist, so the stains become a defect. Since the stains are not deliberately designed and fabricated, they do not focus light on the same focal plane as the microlenses, nor do they produce overlapping ghost images caused by optical crosstalk; much less, most of them are located outside of the MLA.

C. Photographic Results

1. Captured Images

In this study, the experimental setup of the camera module system is built up of one lens component using the curved hexagonal MLA. The diagonal, horizontal, and vertical FOV values for this camera are 92.6°, 84.4°, and 61.4°, respectively. Supplement 1 presents a method for measuring the FOV of the camera. The effective focal length (EFL) of the camera lens, which is the distance from the vertex of the curved hexagonal MLA to the focal point on the optical axis, is the focal length of the center microlens (638.6 μm). The f-number of the camera lens is 1.68, which is the ratio of EFL to the base diameter of the hexagonal microlens (380 μm).

A captured image is shown in Fig. 8(a). Each microlens within its segmented channel forms an image, so a camera image is composed of multiple sub-images. In addition, because the MLA consists of four hexagonal microlens rings, the captured image also consists of four hexagonal sub-image rings. However, each sub-image provides only a small portion of the total scene. For the image centered on the optical axis, four sub-images from the hexagonal MLA need to be matched to the four vertices of the rectangular image sensor (see Supplement 1).

 

Fig. 8. (a) Image captured by the proposed optical system. (b) Image trimming.

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Because there are gaps between hydrophilic confinement holes (see Fig. 2), there is also a gap between each microlens after the curved hexagonal MLA is fabricated. The gap not only prevents diluted SU-8 droplets from combining together after the SU-8 is dropped into the holes, but also prevents overlapping contact areas between the neighboring sub-images. Consequently, the gap helps prevent optical crosstalk, so there are no overlapping ghost images on the image plane [23].

Tracing the path of a light beam emitted from a point source toward the image sensor, the rays of the light beam are separated by neighboring microlenses and produce several convergent beams of light. This phenomenon causes duplicate regions in neighboring sub-images, and these duplicate regions become an advantage for the subsequent image stitching. The captured photo is trimmed, and every small segmented image stitched together [8].

2. Final Image Stitching and Processing

To extract some useful information from the original image and provide enhancement, image processing is used after a photo is captured [24]. Each sub-image is trimmed and the blurred portion is removed, as shown in Fig. 8(b), and every partial image is stitched into a combined image [25] after photo trimming [7,8]. The duplicate regions of neighboring sub-images are conducive to stitching the sub-images together.

To make the connected partial images closer to the source image, the partial images are corrected by digital image processing, using computer algorithms such as gain compensation and multi-band blending [26]. The final processed image is shown in Fig. 9. More captured photos and stitched images are provided in Supplement 1.

 

Fig. 9. Completely stitched photograph processed from sub-images.

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4. CONCLUSION AND OUTLOOK

A biomimetic effort to implement an artificial compound eye is presented along with an outline of a biologically inspired imaging system in this work. This study is devoted to improving photographic lens design. Traditional camera lenses typically comprise an assembly of many lenses that work together to provide a sharp, high-quality image. This approach not only leads to thicker cameras but also higher material costs. Moreover, more lens elements lead to greater potential for misalignment, such as tilting or decentering, whereas lens elements must be optimally aligned for best performance. On the other hand, a camera with a one-piece lens usually has relatively poorer image quality. To solve these problems, we demonstrated a systematic process of theoretical design and experimental fabrication of a wide-angle camera module using a one-piece lens based on a curved hexagonal MLA.

For its advantages of no coma aberration and reduced astigmatism aberration, a hemispherical lens was chosen for use in this study. However, a hemispherical lens inherently gives rise to field curvature aberration. To solve this problem, we combined the hemispherical lens with a curved hexagonal MLA.

The most crucial component of the proposed wide-angle camera system is the curved hexagonal MLA with hexagonal microlenses at different focal lengths, because it provides a correction for field curvature aberration. These omnidirectionally arranged artificial ommatidia collect incident light with a narrow range of angular acceptance and independently contribute to a wide FOV. The work presented here is the continuation of our earlier simulational studies [7,8], but we put forward a strategy to facilitate implementation and sustainability processes; that is, combining together a single lens and the MLA. The MLA is adhered to the curved surface of a plano–convex lens attached to a glass substrate, which enhances the wide-view feature of the system while further reducing the track length of the entire lens assembly.

Most mobile phone cameras need several lens elements to provide sharp images, but our design uses only one lens element to attain a wide FOV of 92.6°. The EFL and the f-number of this lens element are 638.6 μm and 1.68, respectively. Since an only one-piece lens is used, the outcome will be not only a reduction in material costs but also a reduction of camera thickness to 3.04 mm. Moreover, because tolerance considerations impact manufacturing cost and optical performance, this work pursues a single-lens system to drastically decrease the impacts of tolerance corrections. We have sought to write a new chapter in the history of camera innovation.

We operated only one inkjet printhead in this study. If a factory wants to implement rapid manufacturing to produce our product, an array of nozzles in an inkjet printhead [27] should be developed as future work. This inkjet printing fabrication method for a biologically inspired optical system has potential for a broad range of applications, such as image capture, data storage and readout, target detection and tracking, medical diagnostics, surveying and mapping, surveillance imaging, collision-free navigation of terrestrial, light-field cameras, and aerospace vehicles.

Funding

Ministry of Science and Technology, Taiwan (MOST) (106-3114-E-002-011, 105-2221-E-002-158 -MY3); National Taiwan University.

 

See Supplement 1 for supporting content.

REFERENCES

1. D. J. Brady, W. B. Pang, H. Li, Z. Ma, Y. Tao, and X. Cao, “Parallel cameras,” Optica 5, 127–137 (2018). [CrossRef]  

2. G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997). [CrossRef]  

3. K. Ozcan and S. Velipasalar, “Wearable camera- and accelerometer-based fall detection on portable devices,” IEEE Embedded Syst. Lett. 8, 6–9 (2016). [CrossRef]  

4. C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018). [CrossRef]  

5. B. Ma, K. Sharma, K. P. Thompson, and J. P. Rolland, “Mobile device camera design with Q-type polynomials to achieve higher production yield,” Opt. Express 21, 17454–17463 (2013). [CrossRef]  

6. S. Jung, D. H. Choi, B. L. Choi, and J. H. Kim, “Tolerance optimization of a mobile phone camera lens system,” Appl. Opt. 50, 4688–4700 (2011). [CrossRef]  

7. W. L. Liang, H. K. Shen, and G. D. J. Su, “Wide-angle camera with multichannel architecture using microlenses on a curved surface,” Appl. Opt. 53, 3696–3705 (2014). [CrossRef]  

8. W. L. Liang and G. D. J. Su, “Wide-angle and ultrathin camera module using a curved hexagonal microlens array and all spherical surfaces,” Appl. Opt. 53, H121–H128 (2014). [CrossRef]  

9. M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011). [CrossRef]  

10. S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016). [CrossRef]  

11. J. Skeivalas and E. Parseliunas, “On identification of human eye retinas by the covariance analysis of their digital images,” Opt. Eng. 52, 073106 (2013). [CrossRef]  

12. J. Polans, B. Jaeken, R. P. McNabb, P. Artal, and J. A. Izatt, “Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations,” Optica 2, 124–134 (2015). [CrossRef]  

13. J. J. Ma, S. Masoodian, D. A. Starkey, and E. R. Fossum, “Photon-number-resolving megapixel image sensor at room temperature without avalanche gain,” Optica 4, 1474–1481 (2017). [CrossRef]  

14. M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017). [CrossRef]  

15. Y. P. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEJ Trans. Electr. Electron. Eng. 5, 474–485 (2010). [CrossRef]  

16. W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013). [CrossRef]  

17. X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016). [CrossRef]  

18. I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017). [CrossRef]  

19. J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991). [CrossRef]  

20. K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007). [CrossRef]  

21. K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006). [CrossRef]  

22. Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014). [CrossRef]  

23. J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent 7,897,903 B2 (March 1, 2011).

24. P. D. Cott and C. S. Levin, “Image processing algorithms to facilitate and enhance sentinel node detection using a hand-held gamma ray camera in surgical breast cancer staging,” Phys. Medica 21, 99–101 (2006). [CrossRef]  

25. D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012). [CrossRef]  

26. M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74, 59–73 (2007). [CrossRef]  

27. S. Fathi and P. Dickens, “Jet array driven flow on the nozzle plate of an inkjet printhead in deposition of molten nylon materials,” J. Mater. Process. Technol. 213, 383–391 (2013). [CrossRef]  

References

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  1. D. J. Brady, W. B. Pang, H. Li, Z. Ma, Y. Tao, and X. Cao, “Parallel cameras,” Optica 5, 127–137 (2018).
    [Crossref]
  2. G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997).
    [Crossref]
  3. K. Ozcan and S. Velipasalar, “Wearable camera- and accelerometer-based fall detection on portable devices,” IEEE Embedded Syst. Lett. 8, 6–9 (2016).
    [Crossref]
  4. C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
    [Crossref]
  5. B. Ma, K. Sharma, K. P. Thompson, and J. P. Rolland, “Mobile device camera design with Q-type polynomials to achieve higher production yield,” Opt. Express 21, 17454–17463 (2013).
    [Crossref]
  6. S. Jung, D. H. Choi, B. L. Choi, and J. H. Kim, “Tolerance optimization of a mobile phone camera lens system,” Appl. Opt. 50, 4688–4700 (2011).
    [Crossref]
  7. W. L. Liang, H. K. Shen, and G. D. J. Su, “Wide-angle camera with multichannel architecture using microlenses on a curved surface,” Appl. Opt. 53, 3696–3705 (2014).
    [Crossref]
  8. W. L. Liang and G. D. J. Su, “Wide-angle and ultrathin camera module using a curved hexagonal microlens array and all spherical surfaces,” Appl. Opt. 53, H121–H128 (2014).
    [Crossref]
  9. M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
    [Crossref]
  10. S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
    [Crossref]
  11. J. Skeivalas and E. Parseliunas, “On identification of human eye retinas by the covariance analysis of their digital images,” Opt. Eng. 52, 073106 (2013).
    [Crossref]
  12. J. Polans, B. Jaeken, R. P. McNabb, P. Artal, and J. A. Izatt, “Wide-field optical model of the human eye with asymmetrically tilted and decentered lens that reproduces measured ocular aberrations,” Optica 2, 124–134 (2015).
    [Crossref]
  13. J. J. Ma, S. Masoodian, D. A. Starkey, and E. R. Fossum, “Photon-number-resolving megapixel image sensor at room temperature without avalanche gain,” Optica 4, 1474–1481 (2017).
    [Crossref]
  14. M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
    [Crossref]
  15. Y. P. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEJ Trans. Electr. Electron. Eng. 5, 474–485 (2010).
    [Crossref]
  16. W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013).
    [Crossref]
  17. X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
    [Crossref]
  18. I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
    [Crossref]
  19. J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991).
    [Crossref]
  20. K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
    [Crossref]
  21. K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
    [Crossref]
  22. Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
    [Crossref]
  23. J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent7,897,903 B2 (March1, 2011).
  24. P. D. Cott and C. S. Levin, “Image processing algorithms to facilitate and enhance sentinel node detection using a hand-held gamma ray camera in surgical breast cancer staging,” Phys. Medica 21, 99–101 (2006).
    [Crossref]
  25. D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
    [Crossref]
  26. M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74, 59–73 (2007).
    [Crossref]
  27. S. Fathi and P. Dickens, “Jet array driven flow on the nozzle plate of an inkjet printhead in deposition of molten nylon materials,” J. Mater. Process. Technol. 213, 383–391 (2013).
    [Crossref]

2018 (2)

D. J. Brady, W. B. Pang, H. Li, Z. Ma, Y. Tao, and X. Cao, “Parallel cameras,” Optica 5, 127–137 (2018).
[Crossref]

C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
[Crossref]

2017 (3)

J. J. Ma, S. Masoodian, D. A. Starkey, and E. R. Fossum, “Photon-number-resolving megapixel image sensor at room temperature without avalanche gain,” Optica 4, 1474–1481 (2017).
[Crossref]

M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
[Crossref]

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

2016 (3)

X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
[Crossref]

K. Ozcan and S. Velipasalar, “Wearable camera- and accelerometer-based fall detection on portable devices,” IEEE Embedded Syst. Lett. 8, 6–9 (2016).
[Crossref]

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (4)

S. Fathi and P. Dickens, “Jet array driven flow on the nozzle plate of an inkjet printhead in deposition of molten nylon materials,” J. Mater. Process. Technol. 213, 383–391 (2013).
[Crossref]

J. Skeivalas and E. Parseliunas, “On identification of human eye retinas by the covariance analysis of their digital images,” Opt. Eng. 52, 073106 (2013).
[Crossref]

B. Ma, K. Sharma, K. P. Thompson, and J. P. Rolland, “Mobile device camera design with Q-type polynomials to achieve higher production yield,” Opt. Express 21, 17454–17463 (2013).
[Crossref]

W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013).
[Crossref]

2012 (1)

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

2011 (2)

S. Jung, D. H. Choi, B. L. Choi, and J. H. Kim, “Tolerance optimization of a mobile phone camera lens system,” Appl. Opt. 50, 4688–4700 (2011).
[Crossref]

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

2010 (1)

Y. P. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEJ Trans. Electr. Electron. Eng. 5, 474–485 (2010).
[Crossref]

2007 (2)

M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74, 59–73 (2007).
[Crossref]

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

2006 (2)

K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref]

P. D. Cott and C. S. Levin, “Image processing algorithms to facilitate and enhance sentinel node detection using a hand-held gamma ray camera in surgical breast cancer staging,” Phys. Medica 21, 99–101 (2006).
[Crossref]

1997 (1)

G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997).
[Crossref]

1991 (1)

J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991).
[Crossref]

Abbas, W.

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Artal, P.

Arvanitis, P.

G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997).
[Crossref]

Bissen-Miyajima, H.

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Brady, D. J.

D. J. Brady, W. B. Pang, H. Li, Z. Ma, Y. Tao, and X. Cao, “Parallel cameras,” Optica 5, 127–137 (2018).
[Crossref]

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Braeuer, A.

J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent7,897,903 B2 (March1, 2011).

Brown, M.

M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74, 59–73 (2007).
[Crossref]

Brueckner, A.

J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent7,897,903 B2 (March1, 2011).

Cao, X.

Carthew, R. W.

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

Cassidy, J. J.

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

Chang, Y. H.

C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
[Crossref]

Chen, W. C.

W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013).
[Crossref]

Chen, Y. T.

C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
[Crossref]

Chi, M.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Choi, B. L.

Choi, D. H.

Cott, P. D.

P. D. Cott and C. S. Levin, “Image processing algorithms to facilitate and enhance sentinel node detection using a hand-held gamma ray camera in surgical breast cancer staging,” Phys. Medica 21, 99–101 (2006).
[Crossref]

Dannberg, P.

J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent7,897,903 B2 (March1, 2011).

Deng, Y.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Dickens, P.

S. Fathi and P. Dickens, “Jet array driven flow on the nozzle plate of an inkjet printhead in deposition of molten nylon materials,” J. Mater. Process. Technol. 213, 383–391 (2013).
[Crossref]

Duparre, J.

J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent7,897,903 B2 (March1, 2011).

Fan, J.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Fathi, S.

S. Fathi and P. Dickens, “Jet array driven flow on the nozzle plate of an inkjet printhead in deposition of molten nylon materials,” J. Mater. Process. Technol. 213, 383–391 (2013).
[Crossref]

Feller, S. D.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Fossum, E. R.

Gehm, M. E.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Golish, D. R.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Hao, P.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Haque, F.

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

Haynes, G.

G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997).
[Crossref]

Hilgenfeldt, S.

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

Hirakata, A.

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Hovis, J. S.

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

Hsieh, C. L.

C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
[Crossref]

Imtiaz, M.

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Inoue, M.

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Izatt, J. A.

Jaeken, B.

Jeong, K. H.

K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref]

Jung, S.

Kim, H. M.

M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
[Crossref]

Kim, J.

K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref]

Kim, J. H.

Kim, M. S.

M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
[Crossref]

Kim, S.

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

Kittle, D. S.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Lee, G. J.

M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
[Crossref]

Lee, L. P.

K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref]

Levin, C. S.

P. D. Cott and C. S. Levin, “Image processing algorithms to facilitate and enhance sentinel node detection using a hand-held gamma ray camera in surgical breast cancer staging,” Phys. Medica 21, 99–101 (2006).
[Crossref]

Li, H.

Li, X. L.

X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
[Crossref]

Liang, W. L.

Liu, C. S.

C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
[Crossref]

Liu, Y.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Lowe, D. G.

M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74, 59–73 (2007).
[Crossref]

Ma, B.

Ma, J. J.

Ma, X. W.

X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
[Crossref]

Ma, Z.

Marks, D. L.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Masoodian, S.

McNabb, R. P.

Mihashi, T.

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Noda, T.

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Ohguchi, O.

J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991).
[Crossref]

Ohnuma, K.

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Overdyk, F.

G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997).
[Crossref]

Ozcan, K.

K. Ozcan and S. Velipasalar, “Wearable camera- and accelerometer-based fall detection on portable devices,” IEEE Embedded Syst. Lett. 8, 6–9 (2016).
[Crossref]

Pandey, A. P.

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

Pang, W. B.

Parseliunas, E.

J. Skeivalas and E. Parseliunas, “On identification of human eye retinas by the covariance analysis of their digital images,” Opt. Eng. 52, 073106 (2013).
[Crossref]

Polans, J.

Proctor, E. A.

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

Ribbe, A. E.

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

Rolland, J. P.

Sawada, R.

J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991).
[Crossref]

Seu, K. J.

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

Sharma, K.

Shen, H. K.

Shimada, J.

J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991).
[Crossref]

Skeivalas, J.

J. Skeivalas and E. Parseliunas, “On identification of human eye retinas by the covariance analysis of their digital images,” Opt. Eng. 52, 073106 (2013).
[Crossref]

Song, Y. M.

M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
[Crossref]

Stack, R. A.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Starkey, D. A.

Su, G. D. J.

Sun, P.

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Tao, Y.

Thompson, K. P.

Ueda, T.

Y. P. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEJ Trans. Electr. Electron. Eng. 5, 474–485 (2010).
[Crossref]

Velipasalar, S.

K. Ozcan and S. Velipasalar, “Wearable camera- and accelerometer-based fall detection on portable devices,” IEEE Embedded Syst. Lett. 8, 6–9 (2016).
[Crossref]

Vera, E. M.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Wu, T. J.

W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013).
[Crossref]

Wu, W. J.

W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013).
[Crossref]

Wu, Y.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Yang, B. Y.

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

Zada, I.

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Zhang, D.

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Zhang, H. C.

X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
[Crossref]

Zhang, L.

X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
[Crossref]

Zhang, P.

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

Zhang, W.

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Zhang, Y. P.

Y. P. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEJ Trans. Electr. Electron. Eng. 5, 474–485 (2010).
[Crossref]

Am. J. Ophthalmol. (1)

M. Inoue, T. Noda, T. Mihashi, K. Ohnuma, H. Bissen-Miyajima, and A. Hirakata, “Quality of image of grating target placed in model of human eye with corneal aberrations as observed through multifocal intraocular lenses,” Am. J. Ophthalmol. 151, 644–652 (2011).
[Crossref]

Anesthesiology (1)

G. Haynes, F. Overdyk, and P. Arvanitis, “Perioperative data management with a portable memory device,” Anesthesiology 87, 1015A (1997).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

I. Zada, W. Zhang, P. Sun, M. Imtiaz, W. Abbas, and D. Zhang, “Multifunctional, angle dependent antireflection, and hydrophilic properties of SiO2 inspired by nano-scale structures of cicada wings,” Appl. Phys. Lett. 111, 153701 (2017).
[Crossref]

Biophys. J. (2)

K. J. Seu, A. P. Pandey, F. Haque, E. A. Proctor, A. E. Ribbe, and J. S. Hovis, “Effect of surface treatment on diffusion and domain formation in supported lipid bilayers,” Biophys. J. 92, 2445–2450 (2007).
[Crossref]

S. Kim, J. J. Cassidy, B. Y. Yang, R. W. Carthew, and S. Hilgenfeldt, “Hexagonal patterning of the insect compound eye: facet area variation, defects, and disorder,” Biophys. J. 111, 2735–2746 (2016).
[Crossref]

IEEE Embedded Syst. Lett. (1)

K. Ozcan and S. Velipasalar, “Wearable camera- and accelerometer-based fall detection on portable devices,” IEEE Embedded Syst. Lett. 8, 6–9 (2016).
[Crossref]

IEEJ Trans. Electr. Electron. Eng. (1)

Y. P. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEJ Trans. Electr. Electron. Eng. 5, 474–485 (2010).
[Crossref]

Int. J. Comput. Vis. (1)

M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” Int. J. Comput. Vis. 74, 59–73 (2007).
[Crossref]

J. Lightwave Technol. (1)

J. Shimada, O. Ohguchi, and R. Sawada, “Microlens fabricated by the planar process,” J. Lightwave Technol. 9, 571–576 (1991).
[Crossref]

J. Mater. Process. Technol. (1)

S. Fathi and P. Dickens, “Jet array driven flow on the nozzle plate of an inkjet printhead in deposition of molten nylon materials,” J. Mater. Process. Technol. 213, 383–391 (2013).
[Crossref]

J. Micromech. Microeng. (2)

Y. Liu, P. Zhang, Y. Deng, P. Hao, J. Fan, M. Chi, and Y. Wu, “Polymeric microlens array fabricated with PDMS mold-based hot embossing,” J. Micromech. Microeng. 24, 095028 (2014).
[Crossref]

W. C. Chen, T. J. Wu, W. J. Wu, and G. D. J. Su, “Fabrication of inkjet-printed SU-8 photoresist microlenses using hydrophilic confinement,” J. Micromech. Microeng. 23, 065008 (2013).
[Crossref]

Microsyst. Technol. (1)

C. L. Hsieh, Y. H. Chang, Y. T. Chen, and C. S. Liu, “Design of VCM actuator with L-shape coil for smartphone cameras,” Microsyst. Technol. 24, 1033–1040 (2018).
[Crossref]

Nature (1)

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref]

Opt. Eng. (1)

J. Skeivalas and E. Parseliunas, “On identification of human eye retinas by the covariance analysis of their digital images,” Opt. Eng. 52, 073106 (2013).
[Crossref]

Opt. Express (1)

Optica (3)

Phys. Medica (1)

P. D. Cott and C. S. Levin, “Image processing algorithms to facilitate and enhance sentinel node detection using a hand-held gamma ray camera in surgical breast cancer staging,” Phys. Medica 21, 99–101 (2006).
[Crossref]

Science (1)

K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref]

Sensors (1)

M. S. Kim, G. J. Lee, H. M. Kim, and Y. M. Song, “Parametric optimization of lateral NIPIN phototransistors for flexible image sensors,” Sensors 17, 1774 (2017).
[Crossref]

Surf. Coat. Technol. (1)

X. L. Li, L. Zhang, X. W. Ma, and H. C. Zhang, “Dynamic characteristics of droplet impacting on prepared hydrophobic/superhydrophobic silicon surfaces,” Surf. Coat. Technol. 307, 243–253 (2016).
[Crossref]

Other (1)

J. Duparre, P. Dannberg, A. Brueckner, and A. Braeuer, “Image detection system of optical channels arranged next to one another,” U.S. patent7,897,903 B2 (March1, 2011).

Supplementary Material (1)

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Figures (9)

Fig. 1.
Fig. 1. Designing a single-lens system for correction of significant field curvature. (a) Sharpest focus of a hemispherical lens is in a portion of the image space. (b) Curved hexagonal MLA consists of four hexagonal microlens rings on a spherical substrate; hexagonal microlenses of the same radius of curvature are arranged in a ring of the same color. (c) Curved hexagonal MLA is attached to hemispherical lens. (d) Curved hexagonal MLA is used to project a sharp image onto a flat surface.
Fig. 2.
Fig. 2. (a) and (b) Schematic of microlens fabrication using inkjet printing with the confinement effect. (c) to (h) Outline of the fabrication process for a planar hexagonal MLA. Here, the methods of (a) and (b) are used in (g) and (h). (a) Filling of hexagonal hydrophilic hole for microlens fabrication. (b) Inkjet printer system used in this research. (c) Oxidized silicon wafer whose surface is hydrophilic. (d) Spin-coating of the wafer with a negative photoresist. (e) Masked UV exposure of the negative photoresist. (f) Unexposed areas are removed during the developing stage. (g) Fluid is added with the same number of droplets into each hole in each of four hexagonal rings. (h) Planar hexagonal MLA with convex microlens shapes has been created.
Fig. 3.
Fig. 3. Schematic view of the fabrication process (a) to (d) of a hexagonal MLA membrane with concave microlens shapes, and (f) to (i) replication process and shape inspection of a curved hexagonal MLA. (a) PDMS membrane layer is spin-coated onto the planar MLA with convex microlens shapes. (b) PDMS membrane is stripped off. (c) Released membrane is a planar MLA with concave microlens shapes. (d) Cutaway of (c). (e) 3D-printed chamber (on a U.S. $100 bill for scale). (f) Operational process of making a curved surface to fill with UV-curing adhesive. 3D-printed chamber is connected to a vacuum pump. After the concave PDMS MLA is placed onto the 3D-printed chamber and deformed by negative pressure (step 1), liquid UV-curing adhesive is dropped into the curved membrane (step 2). Glass substrate is needed to cover the adhesive (step 3). (g) Section view of the upper half of the 3D-printed chamber, with the adhesive being exposed to UV light. (h) Plano–convex adhesive lens on glass substrate with curved hexagonal MLA peeled off. (i) Hemispherical lens sectioned by a dicing saw.
Fig. 4.
Fig. 4. Hexagonal microlens described by radius of curvature (R and R), base radius (r and r), center of curvature of the spherical surface of the microlens (c and c), and height at vertex h for (a) the longest diagonals and (b) the separation of parallel sides of the microlens.
Fig. 5.
Fig. 5. Scanning profiles along the longest distance between corners in the hexagonal microlenses of the first (center) ring, second ring, third ring, and fourth ring of the MLA.
Fig. 6.
Fig. 6. Images projected by the microlenses of the (a) first and (b) second hexagonal microlens rings.
Fig. 7.
Fig. 7. SEM images of hemispherical hexagonal MLA. (a) Top view, and (b) enlargement of the right corner. (c) Oblique view after cutting with a dicing saw and (d) enlargement. (e) Side view and (f) enlargement.
Fig. 8.
Fig. 8. (a) Image captured by the proposed optical system. (b) Image trimming.
Fig. 9.
Fig. 9. Completely stitched photograph processed from sub-images.

Tables (1)

Tables Icon

Table 1. Structural Parameters of the Hexagonal Micro-Lenses in the Four Rings

Equations (3)

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

R=r2+h22h.
f=Rn1,
%Error=|ftfmft|×100,

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