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Abstract
A variety of techniques have been proposed for fabricating high-density, high-numerical-aperture microlens arrays. However, a microlens array with a uniform focal length has a narrow depth of field, limiting the ability of depth perception. In this paper, we report on a fabrication method of multi-focus microlens arrays. The method for the preparation of the mold of the microlens array is based on 3D printing and microfluidic manipulation techniques. In the preparation of the mold, curved surfaces of the photo-curable resin with different curvatures are formed in the 3D printed microholes whose walls are inclined with different angles. The replicated microlens array consists of hundreds of lenslets with a uniform diameter of 500 µm and different focal lengths ranging from 635 µm to 970 µm. The multi-focus microlens array is capable of extending the depth of field for capturing clear images of objects at different distances ranging from 14.3 mm to 45.5 mm. The multi-focus microlens array has the potential to be used in a diversity of large-depth-of-field imaging and large-range depth perception applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microlens arrays consist of arrays of micrometer or sub-millimeter lenslets which are regularly packed on a one-dimensional line or a two-dimensional plane. Microlens arrays are key components that are widely used in various optics and photonics applications, including stereoscopic display, light homogenization, beam shaping, and 3D imaging [1–7]. In comparison with single-lenses, microlens arrays allow to collect every bit of rich information, i.e., intensity of incoming rays as well as angular information. In an integral imaging system, lenslets arranged on the microlens array capture a group of sub-images at different spatial positions from different viewing angles. The group of sub-images can be reconstructed together to provide a pseudoscopic vision [8]. Additionally, in a light-field imaging system, a microlens array placed in between an objective lens and an image sensor is able to collect spatial and directional information under a single photographic exposure without focusing on the 3D object [9]. In the most microlens arrays, the focal length of all the lenslets is identical. It results in that the depth of field is narrow and the ability of depth perception is limited. These microlens arrays cannot directly retrieve clear images of an object at different distances.
A diversity of techniques have been explored and applied to fabricate microlens arrays. Thermal reflow technique is an efficient way to produce microlens arrays by preparing an array of photoresist polymer cylinders regularly distributed on a substrate and melting the cylinders into a hemispherical shape [10,11]. Microlens arrays of high filling factor can be formed by reflowing closely packed cylinders [12]. Alternatively, laser direct writing (LDW) is capable of fabricating complex microstructures by removing unwanted parts from a resin or protein building block [13–16]. Two-photon polymerization (TPP) 3D printing can also achieve the fabrication with hundred-nanometer-scale or sub-micrometer-scale resolution, in which two-photon absorption occurring at a focused spot inside the photoresist can trigger a local polymerization and then un-polymerized photoresist can be washed away [17–20]. By using LDW or TPP 3D printing techniques, microlens arrays consisting of lenslets of any desired profile and curvature can be easily realized [21,22]. Nevertheless, LDW and TPP 3D printing techniques are based on point-by-point structural modification and require a long fabrication time for producing large-sized components; thus, the productivity for producing large-scale components is limited. Furthermore, gray-scale lithography can efficiently produce large-footprint three-dimensional microstructures. A microlens array can be easily formed by projecting a two-dimensional gray-scale pattern onto photoresist in a single exposure [23,24]. Recently, microfluidic manipulation technique becomes a new candidate to realize optical lenses [25–30]. In the fabrication of the microlens arrays using the microfluidic manipulation technique, the curvature of the lenslets can be well controlled by harnessing surface tension or applying pressure to reshape the profile of microfluid in the mold.
Although a lot of research work about the fabrication of microlens arrays has been demonstrated, only few multi-focus microlens arrays which consist of lenslets of different focal lengths were presented. The multi-focus microlens arrays could be fabricated by hot embossing technique [31]. A pattern consisting of an array of round holes in different diameter was transferred to a silicon wafer. The structure of the lenslets could be formed by embossing a sheet of cycloolefin copolymer polymer on the silicon wafer. Moreover, multi-focus microlens arrays could also be fabricated by using single-step photolithography assisted with chemical wet etching [32]. The parameters of the lenslets could be controlled by using a photomask with a pattern of different sized holes during photolithography and controlling wet etch time. Nevertheless, in the fabrication of the multi-focus microlens arrays mentioned above, the control of the focal length and the aperture of the lenslets is interrelated. These fabrication methods cannot produce multi-focus microlens arrays with uniform-diameter lenslets. In addition, the thermal reflow technique has been exploited to fabricate multi-focus microlens arrays. Compared with uniform cylinders prepared in the conventional thermal reflow technique, an array of cylinders of non-uniform dimensions, i.e., diameters or heights, was pre-defined. The photoresist cylinders of different diameters could be prepared by using a photomask with a pattern consisting of different-diameter round holes in the photolithography [33]. To ensure that lenslets have an identical diameter, a guiding wall structure with holes of a uniform diameter was used to isolate cylinders to avoid excessive spreading of the photoresist during the thermal reflow. Besides, the multi-stacked cylinders of different heights could be realized using different photomasks with precisely aligned patterns in the repeated photolithography [34]. During the thermal reflow, the cylinders of different dimensions were melted into spherical caps of different curvatures, corresponding to different focal lengths of the lenslets. The multi-focus microlens arrays with uniform-diameter lenslets could be produced by these thermal-reflow fabrication methods.
In this paper, a rapid, cost-effective method, which is based on 3D printing and microfluidic manipulation techniques, is presented for fabrication of multi-focus microlens arrays. The microstructure of the lenslet mold can be formed by harnessing surface tension to curve the surface of the photo-curable resin in the microholes with inclined sidewalls. On the replicated microlens array, the lenslets have different focal lengths and a uniform diameter. The multi-focus microlens array has the ability to capture clear images of an object at different distances.
2. Formation mechanism of the multi-focus microlens array
Figure 1(a) illustrates the formation mechanism of the multi-focus microlens array. A group of microholes are prepared for the molds of the lenslets. Figure 1(b) shows the model of the mold for an individual lenslet. The opening size of the microholes, D, is identical. The wall of the microhole is vertical, i.e., α=0°, or inclined with an angle, 0°<α≤θC, where θC is a critical inclined angle of the wall that can ensure the formation of a curved surface in the microhole and its value can be determined as explained below. The bottom of the microhole shrinks and the depth of the microholes becomes short with the increase of the inclined angle. Every microhole is filled with the amount of fluid. The fluid used to fill the microholes can be any thermal-curable or photo-curable materials. Once the fluid in the microholes becomes stable, the fluid can be solidified and the molds for the lenslets are finished. The lenslets can be replicated from the molds. The curvatures of the lenslets are opposite to those in the molds. Consequently, a group of lenslets with an identical size but different curvatures can be produced from the different microholes.
Fig. 1. (a) Schematic diagram of the formation of the multi-focus microlens array. (b) Model of the mold for an individual lenslet. (c) Formation mechanism of the curved surface of the fluid in the microhole.
When a microhole is partially filled with some fluid, the tension forces for the fluid-air interface, γfa, the fluid-wall interface, γfw, and the wall-air interface, γwa, need to be balanced, as shown in Fig. 1(c). The relation of the three tension forces can be described by the Young equation, i.e. γwa–γfw–γfacos(θ) = 0, where θ is a tangent angle, i.e., contact angle, between the interface of the fluid and the wall at the three-phase contact point. The contact angle, θ, between the fluid and the wall is same as the equilibrium contact angle of a sessile droplet on a flat surface, θe. It is worth noting that each microhole can be regarded as an individual capillary tube, when the diameter of the microhole is less than the capillary length, i.e., $D < 2\sqrt {{\gamma _{fa}}/\rho g} $, where ρ is the density of the fluid and g is gravity of earth. Under this condition, the gravitational force of the fluid can be neglected and the surface tension dominates the deformation of the surface of the fluid. The surface would shrink into the minimum surface area. As a result, the surface of the fluid in the microhole would be deformed into a smooth spherical shape to minimize its energy state according to Laplace’s law.
Besides, in order to form a curved surface with predicted curvature, the critical inclined angle could be set as θC = 90° – θe. In the different microholes, the contact angles between the fluid and the wall are all identical, but the walls are inclined with different angles. The intersection angles, φ, between the vertical datum line and the tangent line of the fluid surface at the three-phase contact point vary with the inclined angles, i.e., φ=α+θ. Therefore, the curvatures of the fluid surfaces in the different microholes are not identical and related to the inclined angles of the wall. Furthermore, based on structural features and the equilibrium contact angle, the focal length of the replicated lenslet can be pre-defined as follows.
where n is the refractive index of the material for the lenslet and R is the radius of the curvature of the lenslet that can be expressed as3. Fabrication of the multi-focus microlens array
The fabrication procedure of the multi-focus microlens array is depicted in Fig. 2. A micrometer-scale microhole array with different inclined walls is firstly designed using a computer-aided design (CAD) software. Figure 3(a) shows the design of the microhole array. The dots in different color represent the microholes with the inclined walls with different inclined angles. The microholes are hexagonally distributed. The microhole at the center has a vertical wall. The walls of the microholes on the six vertices have the maximum inclined angle of 38°. The diameter of each microhole is 500 µm and the separation between the two adjacent microholes is 100 µm. There are 169 microholes in total. The distribution and the arrangement of the microholes with specific inclined angles can be flexibly organized.
Fig. 3. (a) Design of the mulit-focus microlens array. (b) The 3D printed microhole array. (c) Photo of the fabricated multi-focus microlens array. (d) Microscopic image of the lenslets on the multi-focus microlens array.
The microhole array can be fabricated by using projection micro-stereolithography 3D printing technique (nanoArch P140, BMF Precision Technology Co., China) which has the printing resolution of 10 µm. The structural features, i.e., the size of the microhole and the separation, can be further optimized if a higher-resolution 3D printer is used in the fabrication of the microhole array. Figure 3(b) shows the printed microhole array. The walls of the microholes are inclined with different angles according to the design.
In the mold preparation, a little photo-curable resin (type: 3011, Aroh Alona, China) is poured on the surface of the microhole array. The density and the viscosity of the resin are 1.02 g/cm3 and 130 mPa·s. The microhole array covered with the resin is placed in the vacuum machine to make the resin fully fill in the microholes and remove micro-bubbles from the microholes. Then, the microhole array containing resin in the microholes is spin coated at spin rate of 3600 rpm. After spin coating, the microhole array sits quietly for 5 minutes to ensure the resin in the microholes to achieve a static state. The microhole array is exposed in the 395 nm UV light for 8 minutes to cure the resin. The intensity of the UV light is 20 mW/cm2. After UV curing, the mold for the microlens array is ready. The solidified resin has hardness of 70 Shore D and melting point of 290 °C.
Liquid polydimethylsiloxane (PDMS) with a mixture of silicone elastomer and curing agent at a weight ratio of 10:1 (Sylgard 184, Dow Corning, USA) is then prepared and poured onto the mold to replicate the structure of the resin. After removal of the bubbles, the PDMS is heated at 80 °C for 4 hours. After thermal curing, the solidified PDMS is peeled off from the mold. The structure of the resin is transferred to the PDMS. The PDMS microlens array consisting of convex lenslets with different curvatures is formed. The photo and the microscopic image of the fabricated microlens array is shown in Fig. 3(c) and 3(d). The lenslets have spherical shapes. The diameters of all the lenslets are identical but the heights are slightly different.
4. Characterization of the multi-focus microlens array
The lenslet mold formed by the microfluidic manipulation technique is investigated. Five microholes arranged in a line are 3D printed. One of the microholes has a vertical wall, while the others have inclined walls. The 3D printing can precisely produce the microholes with the desired shapes and dimensions. The shape of the microhole turns from a cylinder (α=0°) to a conical frustum (0°<α<18°) and then to a cone (α≥18°). Figure 4(a) shows the cross-section of the microholes. The hole diameters are all 500 µm. The depth of the microholes becomes shallow with the inclination of the walls.
Fig. 4. (a) 3D printed microholes with different inclined walls. (b) Microholes partially filled with the resin. (c) Side view of a resin droplet on the diacrylate polymer substrate.
The 3D-printed microholes are partially filled with the resin which is dyed with red solvent dye for observation, as shown in Fig. 4(b). The resin inside the microholes has concave surface. The contact angles between the resin and the walls are measured by using an optical contact angle meter (SL200B, KINO Scientific Instrument Inc., USA). Although the walls are inclined with different angles, the contact angles are almost identical, which is equivalent to the equilibrium contact angle of a 10 µL resin droplet on a flat diacrylate polymer surface as illustrated in Fig. 4(c). As a result, the concave surfaces of the resin inside the microholes present different curvatures.
The lenslets can be easily replicated from the molds. The profile of each lenslet is examined by using the optical contact angle meter. Figure 5(a) shows the side view of the lenslets. The lenslets have the shapes of spherical caps. The diameters of the lenslets are 500 µm. The heights of the lenslets demolded from the microholes with very inclined walls are short. The radii of curvature (ROC) (blue square markers) and the focal length (red dot markers) of the representative lenslets are measured, as plotted in Fig. 5(b). The red solid line represents the pre-defined focal length which is calculated based on the structure in the design. The curvatures of the lenslets become low with the increase of the inclination of the hole walls. Accordingly, the focal length has a monotonic increment. The range of the focal length is 635 µm to 970 µm for the lenslets demolded from the microholes with the inclined angles of 0° to 38°. The corresponding F-number is 1.27 to 1.94 and the numerical aperture is higher than 0.26.
Fig. 5. (a) Lenslets demolded from the microholes with different inclined walls as shown in Fig. 4(b). (b) Measured radius of curvature and focal length of the lenslets. Blue square: the ROC of the lenslets. Red dot: the focal length. Red solid line: pre-defined focal length of the lenslets.
5. Demonstration of multi-focus imaging
Figure 6 illustrates the experiment setup and the operation principle of the imaging system in which the multi-focus microlens array is used. A white light-emitting diode (LED) is used as a light source to illuminate a mask. There is a black letter ‘A’ on the transparent mask. The multi-focus microlens array, as presented in Section 3, is placed behind the mask. The position of the mask relative to the microlens array is adjustable. The multi-focus microlens array is capable of capturing the images of the object at different depths of field and projecting the images onto the backside. A camera is to record the images after the microlens array via an objective lens.
Fig. 6. (a) Experimental setup of the imaging system equipped with the multi-focus microlens array. (b) Operation principle of the multi-focus imaging.
Figures 7 and 8 show the recorded images with the movement of the mask relative to the position of the microlens array. If the mask is close to the microlens array with the object distance of 14.3 mm, clear images can be observed from the central lenslets. When the mask is moved away from the microlens array, the images from the peripheral lenslets gradually become clear. The letter ‘A’ is apparently distinguishable through the lenslets on the edges of the microlens array for the object distance of 45.5 mm. Each lenslet of a particular focal length is able to retrieve a clear image of the object at a specific distance with a limited depth of field, while the microlens array consisting of a series of multi-focus lenslets has the ability to directly capture a group of clear images of the objects within a significant range of the distances.
Fig. 7. The captured image when the mask is placed 14.3 mm away from the multi-focus microlens array.
6. Conclusion
In summary, we demonstrated a rapid, cost-effective fabrication method for producing multi-focus microlens arrays. The mold of the microlens array can be simply prepared by 3D printing and microfluidic manipulation techniques. The surface of the photo-curable resin in the microholes can be deformed into a concave shape due to surface tension. The curvature of the surface is inversely proportional to the inclined angle of the wall of the microhole. Thus, the convex lenslets of different focal length, whose profiles are the replicates of the resin surface, can be precisely produced by using the microholes with the different inclination of the walls. Moreover, the diameter of the lenslets is related to the diameter of the microholes. It indicates that the proposed fabrication method can independently control the focal length and the diameter of the lenslets. Thanks to the flexibility of the fabrication method, the arrangement of the lenslets with specific focal length and desired aperture in the microlens array is discretionary. In the demonstration, the lenslets with focal length ranging from 635 µm to 970 µm are realized. The multi-focus microlens array can capture clear images of an object placed at different distances ranging from 14.3 mm to 45.5 mm. We expect that the fabrication method would be widely applied to produce diverse multi-focus microlens arrays for various imaging and depth perception applications.
Funding
Science and Technology Commission of Shanghai Municipality (18142200800); National Natural Science Foundation of China (61775140); Shanghai Rising-Star Program (20QA1407000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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