Lens arrays are fundamental optics that have a variety of functional features including light collection from a wide angle, light homogenization, and anti-reflection^[1,2]. Owing to the outstanding functionality, lens arrays are widely used as key components in many apparatuses and instruments such as photolithography equipment, photovoltaic systems, light-field cameras, and three-dimensional (3D) displays^[3–5]. In the field of optical lens manufacturing, besides traditional manufacturing techniques such as milling techniques, various advanced fabrication techniques for producing lens arrays have been demonstrated and present extraordinary features.

Highly packed lens arrays can be rapidly produced by the thermal reflow technique, in which an array of polymer cylinders is melted into a spherical cap^[6,7]. Laser interference lithography, which can achieve patterning in nanoscale resolution, is also a powerful technique for lens array fabrication^[8]. Moreover, the laser direct writing (LDW) technique can precisely engrave polymer and protein gel with the structure of lens array^[9–12]. LDW followed by the etching process can produce lens arrays with diverse profiles^[13,14]. To break through the bottleneck of the processing speed of LDW, parallel LDW, which is based on the nonlinear exposure, is a promising powerful technique for micro/nano-fabrication^[15]. In addition, the photolithography technique can directly produce lens arrays by transferring gray-scale patterns that correspond to the morphology of the lens array to the photoresist^[16,17]. By using the microfluid-manipulation technique, uniform lenses can be formed by harnessing the surface tension of the microfluid^[18–20]. However, these advanced techniques requiring high-cost equipment and sophisticated professional operators are not cost effective. Besides, once the lens arrays are fabricated, individual lenses cannot be changed, and the optical property of the lens array is fixed.

Recently, droplet lenses have attracted lots of research interests because of their simplicity in manufacturing, low cost, and special features in functions^[21–23]. Droplet lenses can be easily produced by dripping a small portion of high-refractive-index liquid on a pedestal or inside other relatively low-refractive-index-curable liquid^[24,25]. Tension force makes the surface of the liquid curved. The profiles of the lenses, which correspond to the optical properties, e.g.,  focal length and numerical aperture, can be controlled by adjusting the amount of the liquid during the fabrication. There is a wide selection range for lens material. Droplet lenses can be made of a diversity of materials, including photo-curable photosensitive resin, thermal-curable polymer, and silicone oil. The entire fabrication procedure is straightforward and does not require any complex, expensive equipment. Thus, droplet lenses are very suitable for some do-it-yourself applications such as microscopic imaging for resource-limited areas and teaching aids for science education. Nevertheless, fabricating droplet lens arrays is not common because they have to use a mold of a grid to isolate the droplets to avoid fusion, which, to some extent, sacrifices the packing density.

In most lens arrays, individual lenses have a uniform focal length. The intrinsic nature of the lens array limits the depth of field for 3D imaging and 3D display. Only a few lens arrays with lenses of different focal lengths have been proposed by using the thermal reflow technique and the hot embossing technique^[26–28]. Lenses with different focal lengths could be realized by melting an array of photoresist cylinders with different pre-defined diameters^[26]. The thermally reflowed hemispherical caps had different curvatures that could be precisely modeled by the initial diameter of the cylinders. The variation of the lenses resulted from the diameter of the cylinders, but the aperture of these lenses was also affected by the difference of the cylinders. Furthermore, the lenses with different curvatures could be developed by melting the multi-stacked cylinders of various heights, which were prepared by multilayer photolithography^[27]. The complex fabrication process limits the diversity of the lenses, and the lens array consisting of lenses with only three different focal lengths was demonstrated. Even so, the lens arrays present good optical imaging performance with a large depth of field. Besides the thermal reflow technique, multifocal microlenses with different apertures and the same sag height can also be produced by the silicon-based contactless polymer hot embossing technique^[28].

In this Letter, we demonstrate a movable-type lens array, in which individual droplet lenses of specific focal length could be flexibly reorganized based on a certain combination. The scheme is inspired by the movable-type printing technology that was first, to the best of our knowledge, invented in China around 1040 and is an efficient way to use a combination of movable-type pieces to reproduce documents. In the proposed lens array, groups of movable lenses, which have different focal lengths, were assembled to form a lens array, and the lens array can achieve a large focus range for imaging.

Figure 1(a) illustrates the fabrication procedure of the proposed scheme. The individual lenses are firstly prepared by dripping liquid-state polydimethylsiloxane (PDMS) with a mixture ratio 10:1 (weight ratio between elastomer and curing agent) (refractive index: 1.403) onto a square glass substrate, which is used as pedestals to hold the PDMS. The gravitational force makes the PDMS spread over the pedestals, while the surface tension prevents the PDMS from sliding off the pedestals and curves the surface of the PDMS remaining on the pedestals, forming lenses. The curvature of the PDMS surface is proportional to the amount of the droplets. Then, the lenses are solidified at 80°C for 2 h.

Meanwhile, a mount is designed and produced by 3D printing. A hollow square whose size matches that of the group of the lenses is designed in the center of the mount. The perimeter of the hollow square is embedded with a square silicone ring. After that, a group of prepared lenses, just like the movable-type pieces in the movable-type printing system, are selected and flexibly organized according to a certain combination based on their optical properties. Finally, the lenses are installed into the mount. The whole assembly is tightly bound together by the silicone ring in the mount to form a lens array.

The spare fabricated lenses and the assembled lens array are shown in Fig. 1(b). The size of each lens is 3 mm $\times 3\mathrm{mm}(\mathrm{length}\times \mathrm{width})$. The $4\times 4$ lenses of different focal length are arranged in a good order. Since the lenses are made into a square shape, the lenses can be closely packed without any gap, achieving a 100% filling factor. The combination of the lenses can be flexibly changed based on the requirement for the resolution and depth of field.

The focusing capability of the lenses is investigated. Figure 2(a) illustrates the experimental setup for focal length measurement. A white-light source is used to generate a collimated light beam. A $2\times 2$ lens array equipped with four lenses of the identical focal length is used in the measurement. Behind the lens array, a charge-coupled device (CCD) is used to record the output image. The image distance is measured by scanning the light spot along the optical axis. Once the light spot observed by the CCD turns to the minimum and brightest, the image distance is determined. Figure 2(b) shows the captured image of the four focus points. The relation between the image distance and the mass of the droplet is depicted in Fig. 2(c). The error bars stand for the deviation of the results obtained from the four lenses. With the increase of droplet mass, the image distance becomes short, because a large amount of PDMS on the pedestal results in a significant curvature of the lens.

The droplet lenses are fabricated on a square substrate. They can be easily assembled in the lens array with extremely high packing density. The droplet lenses in the square shape are astigmatic lenses. The meridians have different curvatures and periodically vary. The model of the droplet lenses is depicted in Fig. 3. The lens is on a square pedestal with the length of $D$. The convex surface represents the top surface of the lens. The profile of the surface can be described by the curvature of the meridians. The curvature of the meridians changes with the angles of the meridians, i.e., the intersection angle of each meridian and $x$ axis, $\theta$. The meridians along the $x$ axis and $y$ axis are the flattest, while those along the diagonals of the square are the steepest. As a result, the lens has variable focusing power along the different meridians, and the astigmatism aberration cannot be avoided.

Then, the difference in curvature of the meridians is investigated. In the theoretical calculation, the height of the lens, $h$, is measured. The radius of curvature of the meridian can be expressed as$$r=\frac{d^2+4{(h\cos \theta )}^2}{8h{\cos }^2\theta },$$(1)where $\theta$ is the intersection angle between the projection of the meridian and the $x$ axis.

In the experimental measurement, the side views of the lenses, corresponding to different angles of the meridians, $\theta$, within the range of 0° to 45°, are recorded by using a contact angle meter, as shown in Fig. 4(a).

Two lenses made of PDMS of different mass, $m=1.2\mathrm{mg}$ and $m=3.6\mathrm{mg}$, representing highly curved and less-curved cases, are analyzed. The relation between the curvature and the angle of the meridians is plotted in Fig. 4(b). The curvature gradually flattens with the increase of the angles of the meridians. In addition, the meridians in the highly curved lens have a small deviation in the radius of curvature.

Furthermore, the imaging performance of the lenses is evaluated. Figure 5(a) illustrates the imaging system. The white-light collimated beam directly illuminates the object. The USAF 1961 resolution target is used in the testing. A microlens array is placed behind the object. The CCD camera equipped with a telecentric lens is used to record the images. The distance between the object and the lens array changes, while the distance between the lens array and the CCD camera is fixed. Four identical lenses, which are made of 3.6 mg PDMS droplets, are installed in the lens array. Figure 5(b) shows the images captured by the imaging system when the object distance is $u=10.5\mathrm{cm}$. The pattern of Element 4 in Group 2 on the resolution target can be clearly distinguished. The line width is 88.34 µm. The images obtained from the four lenses are uniform. The central part of the images has very low distortion.

The lens array can be flexibly equipped with the lenses from a combination of desired focal lengths. Figure 6(a) depicts the principle of the imaging by using the lenses of a variety of focal lengths. The image distance is fixed, while the object distance varies according to the optical property of the lenses. The lenses of a variety of focal lengths are capable of collecting the images of the object at different distances. With the change of the object distance, magnification is different. The image of the object collected by the lenses of short focal lengths can get high magnification.

Figures 6(b)–6(e) demonstrate the images collected by a $4\times 4$ lens array. The lenses are made of PDMS droplets with the mass range of 1.2 mg to 4.8 mg. The object moves away from the lens array. The range of the object distance is from 4.9 cm to 16.3 cm. The pattern of Element 4 in Group 2 on the resolution target is observed. The line width of the pattern is 88.34 µm. Sixteen images for the objects at different depths of field can be collected at the same time without mechanical adjustment of the distance of the lens array. With the movement of the object, clear images can be obtained from the lenses in proper sequence. The images highlighted with red dashed boxes represent the object in focus. Although the image size gradually shrinks with the increase of the object distance, the pattern can always be clearly visualized. Therefore, the lens array can achieve imaging with a wide range of field depth.

The square lenses are easy to put together to form a high-filling-factor lens array, but it also causes astigmatism aberration in imaging. To eliminate astigmatism aberration and improve imaging quality, two schemes can be adopted, as illustrated in Fig. 7. Scheme 1: each lens is formed on a round substrate. When dripping the droplet on a round substrate, the liquid spreads over the substrate and stops spreading when it reaches the edges of the substrate. The liquid gradually bulges into a spherical cap, and a spherical lens can be formed. The droplet lenses formed on the round substrate have no astigmatism aberration and can present good imaging quality^[22,23]. The spherical lens in a round shape can be placed into a square mount for flexible assembling. Scheme 2: each lens is formed on a relatively large round substrate and then cut into a square shape. Even though the lens after cutting is in a square shape, the curvature of the meridians is angular-position independent, because the curvature only depends on the radius of the round substrate. In this way, the square lenses can be easily assembled together to form a high-filling-factor lens array.

In conclusion, we have demonstrated a cost-efficient way for fabricating a high-filling-factor lens array, in which movable lenses can be flexibly reorganized according to a preferred combination. By using the lens array equipped with lenses of different focal lengths, the depth of field for imaging can be significantly extended. In future work, the optical performance of the individual lens, especially the imaging quality, could be improved by avoiding astigmatism aberration. Moreover, the size of the lenses can be reduced to the several-hundred-micrometer scale to enhance the resolving power in some advanced microscopic imaging applications^[29]. The substrate can be prepared by laser cutting or 3D printing techniques, while the nanoliter-scale droplet can be generated by the inkjet printing technique. We believe that the proposed scheme can be applied in the field of light-field imaging and 3D display.