1. Introduction

Microlenses or microlens arrays (MLAs) [1–3], which act as typical micro-optical elements, have promoted the burgeoning advancement of technologies such as those in visual sensors [4], nanofabrication [5], light out-coupling [6], integral imaging [7,8] etc. The small geometric footprint and unique performances of these optical elements would push the development of various photonic devices toward miniaturization, multi-function and large-scale integration to meet the growing requirements of modern industry [9]. As a result, the realization of novel MLAs with interesting properties and its mass manufacturing with high quality has always been a topic of interest and a difficult issue in both academia and industry [10–12]. A variety of strategies have been adopted for fabricating MLA structures which can be generally classified into following categories: 1) surface-tension-driven techniques [13–16] such as melt-reflow and ink-jet printing; 2) direct write techniques [17–19] such as ion-beam writing, femtosecond laser writing and diamond point machining; 3) lithographic approaches [20,21] such as grayscale photolithography and anisotropic etching. However, the surface-tension-driven techniques are limited to the fabrication of MLAs comprised of optical elements with fixed focal lengths, identical diameters and undefined heights. While the direct write techniques offer a reliable route to control the parameters of each element in the MLAs, the point-to-point nature suffers from very low fabrication efficiency and is applicable to a limited effective MLA area. In addition, the aforementioned approaches require multiple steps in expensive clean room facilities, including baking, developing and etching. It would be a significant advancement if an array of micron-scale imaging elements could be prepared in a facile, inexpensive, and scalable fashion while still preserving the capability to control the shape and array formation of each element.

The fill-factor (FF), which refers to the ratio of the effective microlens area to the total array area, is a paramount factor in defining the performance of fabricated MLAs. The closely packed microlens array is beneficial in avoiding stray light effects to improve the signal-to-noise of optical sensor or imagers integrated with MLAs and is key in enhancing photon collection efficiency in light-extraction applications [6]. As a result, various methods have been developed for the fabrication of high-FF MLA. Hexagonal MLAs approaching 100% FF have been demonstrated by self-assembly methods [22–24] based on surface wrinkling, dewetting, and localized water condensation, but these approaches typically lack control in the design, positioning of the microlenses with further shortcomings in fabrication uniformity and repeatability. Another critical issue is to construct dynamic microlens arrays of which the focal length or focusing capabilities of individual elements can be addressed on demand, enabling new applications of MLAs in switchable 2D/3D displaying [25], foveated vision [26], and beam steering [27]. The development of liquid [28] or liquid crystal (LC) MLAs [29] represents a feasible approach to reach this goal. The shape or diameter of the liquid microlens could be adjusted by varying the parameters of the confinement and the molecular director of liquid crystals could be modulated by applying external stimuli such as the electric-field and the temperature, emerging as soft photonics with unrivaled characteristics of self-assembling and tunablity. Techniques such as inkjet printing and microfluidics [30,31] have been developed for forming arrays of liquid droplets acting as MLAs, and the positioning and fabrication efficiency is still a critical issue. As for the liquid crystal MLAs, they could be realized by either confining the material in a parabola profile or directing a refractive index profile via controlling the distribution of LC molecule directors. Thus, approaches such as the patterned driving electrodes [29,32], surface relief structures [33,34] and holography [35] are adopted to yield LC MLAs, and they often have to resort to conventional lithography techniques, requiring the steps such as development, deposition and etching. While microlens array technology is constantly being improved with respect to fabrication methods, materials and optical functionalities, these arrays typically have relatively low FF, limited effective area, and lack of controllability in each element, in addition, the fabrication techniques have to deal with problems including meticulous processing steps and writing stability when involving with a large number of elements.

In this work, we present a novel method for the realization of high-FF microlens arrays with high efficiency and flexibility, aiming to address the limitations of traditional photolithographic and direct-write approaches. The polarization pattern was generated on the LCOS spatial light modulator by modulating the phase delay of the optical wavefront in digitalized manners. The polarization pattern was designed to obtain a parabola phase profile based on the geometrical phase rules and was demagnified to be recorded into the LC polymer medium through the photo-alignment mechanism, thus snapshot forming the LC microlens without steps of development and etching. The polarization pattern defining the microlens was refreshed in real-time and a programmable 2D mechanical stage allowed precise control of the position of each element, providing the 100% FF MLAs array with high throughput and controllability. The fabricated LC polymer MLA with high FF and circular polarization dependence showed nearly diffraction-limited focusing performance and was further integrated with a CCD sensor as a compact fingerprint imaging system, invoking the innovative potential of planar LC polymer MLA in under-display fingerprint biometrics. The main advantages of the approach, compared to traditional MLA fabrication methods, are a reduction in processing complexity, an improvement in the FF factor and the array area, and the versatility in controlling the number of array elements and array architectures, presenting new opportunities for applications in compact imaging, 3D displaying, beam shaping, and other photonics technologies.

The optical elements based on the Pancharatnam–Berry (PB) phase are emerging as the fourth generation optics, featuring light-weight, ultra-thin thickness and multi-function [36]. The spatially variant optical axes of birefringent materials were distributed according to the phase profile of the specific optical element, where the position-dependent phase delay is half the azimuth angle of the micro-plate orientation, whose thickness is designed to offer the half-wavelength phase delay to maximize the optical efficiency. Liquid crystals are particularly attractive in terms of the PB optics, because of their nearly 100% efficiency, continuous molecular ordering, broadband operation, and stimuli responsiveness [9]. LC photoalignment technique, where the irradiation of polarization light onto the photo-sensitive layer would generate anisotropic physical or chemical properties to induce the directional anchoring of LC molecules in contact, is the main enabler for the LC planar optics [37]. In this work, we have proposed the fabrication of LC polymer MLA via the snapshot polarization patterning technique. The digitalized polarization pattern directing the LC molecular spatial ordering with regard to the phase profile of each microlens was delivered via the LCOS and distributed in the plane controlled by a high resolution stage, resulting in 100% FF MLA with the capability in controlling the parameters of each element. In addition, the recording of each element was completed in one laser pulse, indicating the potential to provide unlimited array size with high efficiency. Subsequent coating the photo-alignment layer with LC polymer and the UV curing would complete the MLA, which released itself from additional steps such as developing or etching.

2. Experimental details

The snapshot polarization patterning system was consisted of the digitalized polarization pattern generation component, the imaging component, the auto-focusing component and the precision stage (Fig. 1). The digital polarization pattern generation component could output linear polarization light field with arbitrarily distributed polarization direction at the resolution of the LCOS pixel size. This core component was consisted of a 445 nm blue laser diode (8W, Changchun New Industries Optoelectro. Tech. Co., Ltd.) as the light source, a linear polarizer to define the incident light polarization, a LCOS device (1024*1920, 6.4 µm, Xi’an Cas Microstar Optoelectro. Techno. Co., Ltd.) to provide pixel addressed phase delay and a quarter-wavelength plate (QWP) for circular polarization superposition. The laser light was collimated and expanded to illuminate the whole LCOS. The incident polarization was at 45° with respect to the orientation axis of the LCOS and was decomposed into o-ray and e-ray of equal amplitude but a δ phase difference determined by the voltage applied on the LCOS pixel. The crystallographic axis of the QWP was situated at 45° with respect to LOCS orientation direction, where the aforementioned o-ray and e-ray became circular polarizations with opposite handedness and they got superposed to generate a linear polarization with a direction change of δ/2. The polarization states of light passing through the LCOS and QWP are selectively marked in Fig. 1. The LCOS device consisted of a LC micro wave-plate array where the phase delay from each pixel could be independently addressed with a range of 2 pi, thus outputting a light-field with arbitrarily distributed linear polarization. The polarization-modulated lightfield was projected onto the sample plane using a switchable objective lens with variable magnification. When the magnification was 20X, the theoretical linear polarization pattern resolution is 0.32 µm and the diameter of the element has an up limit around 300 µm. The photo-alignment molecules would respond to the light-field pattern by rotating the molecular axis perpendicular to the incident polarization, exerting a high-resolution spatial control of the LC director. As a result, the specific LC director configuration directed by the programmed polarized light-field could yield the parabola phase profile of the microlens, completing the single array element in one exposure. After that, the precision stage (accuracy ±50 nm) would move to the next position and trigger the LCOS to deliver the next exposure, where an auto-focusing component was used to ensure the sample plane was in the depth of focus of the objective lens. The auto-focusing component is particularly important in fabricating large-area MLA, to correct the height difference when the stage is moved over a long sample distance. Thus, the system is potentially applicable for the fabrication of planar LC MLAs with features of large-area, high-throughput and controllability.

 

Fig. 1. Schematic illustration of the snapshot polarization patterning system. The four components of digital polarization pattern generation, imaging, auto-focusing and precision stage were integrated together to enable large-scale and high efficiency MLA fabrication.

Download Full Size | PDF

As for the fabrication of the LC polymer MLA, the glass substrate was cleaned and spin-coated with the photo-alignment solution (SD1, 0.5 wt.% in DMF, 3000 rpm), resulting in a photo-alignment layer with a thickness around 10 nm. The coated substrate was then placed on a heating stage (100 °C) for 5 min to allow the full evaporation of the solvent. In common refractive optics, the phase profile of the element was expressed using the dynamic phase which was attributed to the optical path in different media and was realized by machining the geometrical profile of the lens. The design rules can be also applicable to planar LC optics in this work, where the phase profiled was realized by the LC molecular director distribution. For simplicity, we have designed and fabricated the common spherical Fresnel microlens in this work, which shows a parabolic phase profile along the radial direction. The Fresnel phase profile was designed based on parameters of the operation wavelength, the focal length F and the microlens diameter D, in addition, the F/D was restricted by the photo-alignment resolution of the technique. We also found that four polarization steps were sufficient to obtain high efficiency and low aberration LC optics, and this was attributed to the molecular smoothing effect at the ordering interface, giving rise to continuous phase modulation in each period. The glass substrate coated with the photo-alignment layer was then mounted on the precision stage and was exposed automatically using the snap-shot polarization patterning system. Commonly, the photo-alignment layer SD1 requires an exposure density higher than 1 J/cm² to reach the stable molecular re-orientation under the polarized light. With the help of the high power blue laser and the focusing effect of the objective lens, the system could complete recording the single microlens pattern in microseconds and the fabrication efficiency (number of microlens elements per second) was around 30 frames per second. After polarization patterning the photo-alignment layer, the LC polymer solution (OCM-A1, Zhangjiagang Raito Materials Co., Ltd.) was spin-coated onto the substrate at a speed of 2000rpm and was cured using the UV light for 30 s in air, resulting in a patterned transparent LC polymer film. The film thickness was optimized (2.25 µm) to fulfill the half wavelength condition at the operation wavelength of 633 nm to approach the 100% focusing efficiency. Thus, the manufacturing of the LC polymer MLA only involves procedures of coating the photoalignment layer, snapshot polarization patterning by the system and coating the LC polymer layer or injecting the LC material (Fig. 2(a)–2(d)), without resorting to complex steps such as developing or etching. The simplifying in the fabrication process not only reduces the cost for industrial up-scaling, but also improves uniformity and stability when involving volume manufacturing. In addition, the real-time updating of the polarization pattern using the LCOS device enables facile control of each microlens performance, achieving customized MLAs for unexplored applications.

 

Fig. 2. Fabrication of the LCP MLA using the snapshot polarization patterning. (a) Coating the photo-alignment layer, (b) Digital polarization pattering using the system to direct the molecular director configuration in the alignment layer, (c) Coating the LCP solution, (d) UV curing the LCP to stabilize the molecular orientation. (e) POM image of the MLA, (f) Spot array on the CCD camera formed by irradiating the MLA with a collimated beam.

Download Full Size | PDF

We further fabricated planar spherical Fresnel MLA and demonstrated its application in optical fingerprint identification to illustrate the capability of proposed approach. It is well-known that the phase of a spherical Fresnel microlens should fulfil the equation $\emptyset = \frac{{2\pi }}{\lambda }\left( {\sqrt {{f^2} + {r^2}} - f} \right)$, where f is the focal length the microlens and r is the distance from the radial distance from the lens center. As a result, we could obtain the LC director distribution θ according to the PB phase relation of $\theta = \frac{\emptyset }{2}$, which could be converted to the linear polarization pattern generated via modulating the digitalized phase front on the LCOS. The determination of the parameters of each microlens should involve the factors of application purpose, the patterning solution of the method, the phase steps of the LC optics and the diameter of the LCOS. In this study, we have designed a uniform square-shaped LC polymer MLA with identical focal length of 3.5 mm and diameter of 500 um and a 5× objective lens was utilized in the patterning system. It was further deduced that each imaging element contains 14 periods and the narrowest linewidth at the microlens edge reaches 1.2 um. It should be stressed that we have a great flexibility in providing LC microlens with desired performance due to the facile control of the recording parameters of the system. In this work, we aimed at the fingerprint identification application using the MLA and an effective area of 1 cm² is sufficient for this purpose which corresponds to a 20×20 array of the PB LC polymer microlens. Due to the snapshot recording characteristic of the proposed method, the polarization patterning would only cost several minutes and subsequent simple coating and curing steps of the LC polymer solution completed the MLA. The obtained LC polymer MLA was observed under the polarization optical microscope (POM), where the interlaced bright and dark regions indicated the director difference of LC molecules (Fig. 2(e)). In this work, we have designed a square-shaped microlens element and was densely distributed to maximize the FF factor for efficient light utilization and improvement of the signal to noise factor of the compact imaging system. The MLA contained highly uniform LC polymer microlens and a FF factor of 100% was achieved. When the MLA was irradiated with a collimated laser beam, an array of focusing spots was detected using a CCD camera (Fig. 2(f)). (See Fig. 7 Appendix A for the evolution of MLA focusing at different cut planes). The uniformly distributed focusing laser spots indicate the precise positioning of each element by the system.

3. Results and discussions

The molecular configuration and the imaging performance of the fabricated LC polymer MLA was analyzed in more detail here. The magnified POM images of each LC polymer microlens depicted alternate dark and bright rings (Fig. 3(a)–3(b)). For a 2 pi phase coverage of each ring, we have assigned four LC regions with molecular orientations of 0°, 45°, 90° and 135°. As the LC regions with perpendicular molecular orientations have same brightness under the POM, the ring appearance inversed when the sample was rotated by 45°. Unlike the binary optics using relief microstructures where the optical efficiency was strictly limited by the number of phase steps, the efficiency of the LC PB optics would be significantly higher than 90% with a step number of four. This was attributed to the self-assembling nature of the LC molecules, as they are in contact with each other and the molecules should experience a continuous director change at the interface which brings a smooth phase profile and improved optical performance. The morphology quality of the LC polymer microlens was further investigated by enlarging the edge texture (Fig. 3(c)-3(d)). The LC polymer ring at the edge stayed intact and smooth, indicating a linewidth of 1.8 um which approaches the resolution limit of the POM. The patterning resolution could be improved to around 0.3 um by using a 20× objective lens, preserving the capability of offering microlens with higher numerical aperture. The focusing performance of each microlens was characterized using the optical setup in Fig. 3(e). The laser beam (633 nm) was converted into circular polarization after passing through s polarizer and s QWP and was collimated using L1 and L2 with a focal length of 3 mm and 50 cm, respectively. The collimated laser beam was then focused by the LC polymer microlens and the focused laser spot was imaged onto a CCD camera by an objective lens (2 mm) and a tube lens (25 cm). The angular symmetric profile and the Gaussian distribution of the intensity of the focused spot implies excellent imaging quality of the fabricated MLA (Fig. 3(f)-3(g)). We further extract the intensity data of the focused spot along perpendicular directions (labeled as X and Y axis) and fitted it with a Gaussian curve (Fig.3(h)-3(i)). The diameter of the focused spot along the X and Y axis was 9.86 um and 9.98 um. The theoretical diameter L of a focused spot by a perfect lens was governed by the Airy equation of $L = 1.22\lambda /NA$ which was calculated to be 8.86 um for the microlens here. As a result, the MLA fabricated using the proposed patterning system was nearly diffraction-limited and was expected to offer high-quality imaging performance for practical applications.

 

Fig. 3. Characterization of the LCP MLA. (a)-(b) POM images of the single LCP microlens with the sample orientation of 0° and 45°. (c)-(d) POM images of the LCP microlens at a high observing magnification. (e) Schematic optical setup used to measure the focusing performance of the MLA. (f) Focused spot captured by the CCD. (g) 3D intensity profile of the focused spot. (h)-(i) Intensity distribution of the focused spot at different directions.

Download Full Size | PDF

As a biometrics technique, the optical fingerprint identification approach is receiving increasing attention due to the imperviousness to electromagnetic interference and its commercial potential in full screen smart phones [38]. Common optical fingerprint sensors, such as using a right-angle prism or multiple cameras, have bulky sizes and are not suitable for integration with consumer electronics. In order to illustrate the diffraction-limited quality of the fabricated LC polymer MLA and explore the application potential as a compact compound eye imaging system for under-screen biometrics, we further utilized the fabricated PB MLA for fingerprint capturing (Fig. 4(a)). The barrier layer [39], to eliminate crosstalk in traditional compound eye imaging device, was not the imperative component in our demonstration, which was attributed to the 100% FF advantage of the planar MLA. The basic microlens unit in a specific direction captures part of the scene and yields a unit image containing part of effective information, which creates an intact fingerprint image with a superposition of all unit images. The imaging fundamentals of the device was depicted in more detail in Fig. 4(b). When the human finger was in contact with the collecting glass and illuminated by environmental light or backlighting light, scattering at the finger texture forms the object for imaging. Part of the object in the imaging field of view was captured by each LC polymer microlens according to the formula $\frac{1}{{{L_1}}} + \frac{1}{{{L_2}}} = \frac{1}{f}$, where L₁ is the distance from the object plane to the MLA plane and L₂ is the distance from the MLA plane to the sensing plane. The magnification ratio M of each imaging unit was $\frac{{{L_2}}}{{{L_1}}}$. When M is smaller than 1, the unit image captured by each microlens element contained repeated object information at the edge and an intact fingerprint texture could be re-constructed by trimming the redundant information (Fig. 4(c)). When M is larger than 1, the effective unit fingerprint image overlapped with effective unit images captured by adjacent microlenses (Fig. 4(d)) and the texture information at the edges of each unit image cannot be extracted, leading to an incomplete fingerprint image which is inappropriate for biometrics purposes.

 

Fig. 4. The working principles of the compact imaging system based on the LCP MLA. (a) Schematic optical setup of the compound-eye imaging system. (b) Schematic light rays to provide the details of the imaging process. (c)-(d) The unit image formed on the sensor when the magnification ratio was below and beyond 1.

Download Full Size | PDF

As a result, the magnification ratio of the compact imaging system using the LC polymer MLA was regulated to be smaller than 1 for intact fingerprint reconstruction, which was also beneficial to lowering the crosstalk from adjacent imaging channels. The original images captured by the CCD sensor at magnification ratios of 0.3, 0.4, 0.7 and 0.9 were presented in Fig. 5(a)–5(d), in which an array of unit images captured by the MLA could be observed. The total thickness of the imaging system was about quadruple the focal length. For example, when the magnification is 0.9, the object distance was 7.3 mm and the image distance was 6.6 mm. We have also labeled the effective imaging region (without redundant information) in each unit image and its area ratio to the total area of the unit image increases with the increased magnification ratio. We stitched together these effective imaging regions from all unit images and presented the reconstructed fingerprint images in Fig. 5(e)–5 (h). Although the reconstructed fingerprint images at different magnification ratios have different image sizes, they preserved the same features when compared with the original fingerprint texture (Fig. 5(i)). In order to quantify the characteristic fingerprint features captured using the novel imaging system, we have further proposed a similarity calculation procedure (Fig. 5(j)) which have steps of binary matrices creation, feature points extraction, feature details convolution and weighted similarity calculation. We first extracted characteristic points of the restored image and the original image, and then converted the two images into gray-scale matrices of the same size. Finally, the gray-scale matrix was binarized according to the light intensity threshold, and then the two matrices were compared pixel by pixel to get the maximum weighted sum. The calculation results based on the model indicated that the similarity value of the reconstructed fingerprint image increased from 75.86% to 89.61% when the magnification ratio increased from 0.3 to 0.9. As illustrated in Fig. 4(c), higher magnification ratio implies a more efficient utilization of the CCD sensor pixels, which means more sensing pixels are utilized for effective information extraction, yielding fingerprint texture images with higher resolution. We also provided the biometrics results when different fingerprint textures were detected by the compact imaging system. The similarity value is beyond 80% when the finger in contact with the object glass is paired with the fingerprint in the data base and is below 20% when they are unpaired (Fig. 8 in Appendix B), indicating the reliability and accuracy of the compound-eye fingerprint imaging system.

 

Fig. 5. Fingerprint identification using the proposed compact compound-eye imaging system. The unit image array captured by the sensor when the magnification ratio was (a) 0.3, (b) 0.4, (c) 0.7 and (d) 0.9. The reconstructed fingerprint image when the magnification ratio was (e) 0.3, (f) 0.4, (g) 0.7 and (h) 0.9. (i) The original fingerprint image. (j) Schematic similarity function value calculation process.

Download Full Size | PDF

The PB phase has an opposite sign dependence on the LC orientation for circular polarizations with opposite helicities, as a result, the right-handed and left-handed polarized incident light would experience opposite signed focal lengths at each LC polymer microlens, corresponding to light convergence and divergence effects. The polarization dependence of the MLA imaging system was investigated by irradiating the finger in contact with the object glass with linear, right-handed circular and left-handed circular polarized light. The original image captured by the CCD sensor and the reconstructed fingerprint image by recombining the effective information of each unit image were shown in Fig. 6. Accordingly, the similarity value reaches a highest values of 86.14% under left-handed circular polarization and exhibits a lowest value of 26.14% under the right-handed circular polarization, attributed to the reduced signal to noise ratio as light was apt to diverge after passing the MLA under right-handed circular illumination. The polarization dependence of the compact fingerprint imaging system based on the LC polymer MLA is well-suited for integration as under-screen biometrics, as the back light from the LC displays and the self-generating light from the organic light emitting diode displays is well polarized in nowadays display industry. Thus, the novel compact fingerprint imaging system based on the LC polymer MLA has potential commercial interest in full-screen smart phones.

 

Fig. 6. Polarization dependent performance of the compact imaging system. The unit image array captured by the sensor when illumination light was (a) linearly, (b) left-handed circularly and (c) right-handed circularly polarized. The reconstructed fingerprint image when illumination light was (d) linearly, (e) left-handed circularly and (f) right-handed circularly polarized.

Download Full Size | PDF

4. Conclusion

In conclusion, we have proposed the snapshot polarization patterning method for fabricating LC planar MLAs with high efficiency and flexibility. The arbitrary linear polarization pattern was generated via a digitalized LCOS at a frequency of 50 Hz and the on-demand polarization pattern distribution was monitored and controlled in real-time with an error of 0.1 um. The spherical Fresnel lens phase profile was expressed via the PB phase, which was converted into the LC orientation pattern in accordance with the polarization pattern. The digital polarization pattering system could complete exposing the area of 1 cm² in several minutes with upscaling capabilities in volume manufacturing. In addition, the fabrication process only consists of polarization patterning, coating the LC polymer and UV curing, which does not involve developing or etching steps. The LC orientation configuration and the focusing capabilities were characterized, which indicated smooth orientation profile with almost diffraction-limited focused spots. We further demonstrated a novel compact imaging system for biometrics using the LC polymer MLA with a high FF approaching 100%, which showed reliability and correctness in identifying fingerprint textures. Due to the short focal length and the polarization dependence of the LC polymer MLA, the imaging system has a very compact size and holds great promise for integration in full-screen smart phones, opening a new route for MLA commercial applications.

Appendix A

 

Fig. 7. The evolution of MLA focusing at different cut planes. A collimated laser beam at 633 nm was used for illumination. The laser beam was converted into left-handed circular polarization using a linear polarizer and a quarter-wave plate. The focusing performance of the MLA was recorded by placing the CCD camera at different distances to the MLA plane. The focal plane of the MLA was determined by the size of the focused laser spots and was further shown in the inset.

Download Full Size | PDF

Appendix B

 

Fig. 8. Biometrics identification performance using the compact imaging system at a magnification ratio of 0.85. (a), (b) and (c) are original fingerprint images in the data base and (d), (e) and (f) are reconstructed fingerprint images by the proposed imaging system. (g) Similarity values when different images were compared. The similarity values were calculated via the procedure in Fig. 5(j). When the contact fingerprint was paired with the image in the data base, the similarity value was beyond 80%. When they are unpaired, the valued was below 20%, verifying the reliability of the biometrics recognition system.

Download Full Size | PDF

Funding

National Natural Science Foundation of China (62175170); Priority Academic Program Development of Jiangsu Higher Education Institutions.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data that support the findings of this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. W. B. Veldkamp, “Overview of micro-optics: past, present, and future,” Proc. SPIE 1544, 287–298 (1991). [CrossRef]  

2. S. Juodkazis, “3D printed micro-optics,” Nat. Photonics 10(8), 499–501 (2016). [CrossRef]  

3. W. Yuan, L.-H. Li, W.-B. Lee, and C.-Y. Chan, “Fabrication of microlens array and its application: a review,” Chin. J. Mech. Eng 31(1), 16 (2018). [CrossRef]  

4. Z. Yang, Z. Wang, Y. Wang, X. Feng, M. Zhao, Z. Wan, L. Zhu, J. Liul, Y. Huang, J. Xia, and M. Wegener, “Generalized Hartmann-Shack array of dielectric metalens sub-arrays for polarimetric beam profiling,” Nat Commun 9(1), 4607 (2018). [CrossRef]  

5. P. S. Salter and M. J. Booth, “Addressable microlens array for parallel laser microfabrication,” Opt. Lett. 36(12), 2302–2304 (2011). [CrossRef]  

6. S. Möller and S. R. Forrest, “Improved light out-coupling in organic light emitting diodes employing ordered microlens arrays,” J. Appl. Phys. 91(5), 3324–3327 (2002). [CrossRef]  

7. W. Liu, D. Ma, Z. Li, H. Cheng, D.-Y. Choi, J. Tian, and S. Chen, “Aberration-corrected three-dimensional positioning with a single-shot metalens array,” Optica 7(12), 1706–1713 (2020). [CrossRef]  

8. R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, Y.-T. Huang, J.-H. Wang, C. H. Chu, P. C. Wu, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14(3), 227–231 (2019). [CrossRef]  

9. N. V. Tabiryan, D. E. Roberts, Z. Liao, J.-Y. Hwang, M. Moran, O. Ouskova, A. Pshenichnyi, J. Sigley, A. Tabirian, R. Vergara, L. D. Sio, B. R. Kimball, D. M. Steeves, J. Slagle, M. E. McConney, and T. J. Bunning, “Advances in transparent planar optics: enabling large aperture, ultrathin lenses,” Adv. Opt. Mater. 9(5), 2001692 (2021). [CrossRef]  

10. J. Aizenberga and G. Hendler, “Designing efficient microlens arrays: lessons from Nature,” J. Mater. Chem. 14(14), 2066–2072 (2004). [CrossRef]  

11. M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37(2), 253–265 (1990). [CrossRef]  

12. P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997). [CrossRef]  

13. H. Zhang, T. Qi, X. Zhu, L. Zhou, Z. Li, Y.-F. Zhang, W. Yang, J. Yang, Z. Peng, G. Zhang, F. Wang, P. Guo, and H. Lan, “3D Printing of a PDMS cylindrical microlens array with 100% fill- factor,” ACS Appl. Mater. Interfaces 13(30), 36295–36306 (2021). [CrossRef]  

14. D. Kang, C. Pang, S. M. Kim, H. S. Cho, H. S. Um, Y. W. Choi, and K. Y. Suh, “Shape-controllable microlens arrays via direct transfer of photocurable polymer droplets,” Adv. Mater. 24(13), 1709–1715 (2012). [CrossRef]  

15. S. Surdo, R. Carzino, A. Diaspro, and M. Duocastella, “Single-shot laser additive manufacturing of high fill- factor microlens arrays,” Adv. Optical Mater. 6(5), 1701190 (2018). [CrossRef]  

16. D. L. MacFarlane, V. Narayan, J. A. Tatum, W. R. Cox, T. Chen, and D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photonics Technol. Lett. 6(9), 1112–1114 (1994). [CrossRef]  

17. D. Wu, S.-Z. Wu, L.-G. Niu, Q.-D. Chen, R. Wang, J.-F. Song, H.-H. Fang, and H.-B. Sun, “High numerical aperture microlens arrays of close packing,” Appl. Phys. Lett. 97(3), 031109 (2010). [CrossRef]  

18. S. Thiele, K. Arzenbacher, T. Gissibl, H. Giessen, and A. M. Herkommer, “3D-printed eagle eye: Compound microlens system for foveated imaging,” Sci. Adv. 3(2), e1602655 (2017). [CrossRef]  

19. X.-Q. Liu, L. Yu, S.-N. Yang, Q.-D. Chen, L. Wang, S. Juodkazis, and H.-B. Sun, “Optical nanofabrication of concave microlens arrays,” Laser Photonics Rev. 13(5), 1800272 (2019). [CrossRef]  

20. M. B. Stern and T. R. Jay, “Dry etching for coherent refractive microlens arrays,” Opt. Eng. 33(11), 3552 (1994). [CrossRef]  

21. M.-H. Wu, C. Park, and G. M. Whitesides, “Fabrication of arrays of microlenses with controlled profiles using gray-scale microlens projection photolithography,” Langmuir 18(24), 9312–9318 (2002). [CrossRef]  

22. R. Ahmed, A. K. Yetisen, and H. Butt, “High numerical aperture hexagonal stacked ring-based bidirectional flexible polymer microlens array,” ACS Nano 11(3), 3155–3165 (2017). [CrossRef]  

23. E. P. Chan and A. J. Crosby, “Fabricating microlens arrays by surface wrinkling,” Adv. Mater. 18(24), 3238–3242 (2006). [CrossRef]  

24. K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S.-W. Lee, S. B. Park, H. Cölfen, and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3(1), 725 (2012). [CrossRef]  

25. T.-H. Jen, Y.-C. Chang, C.-H. Ting, H.-P. D. Shieh, and Y.-P. Huang, “Locally controllable liquid crystal lens array for partially switchable 2D/3D display,” J. Disp. Technol. 11(10), 839–844 (2015). [CrossRef]  

26. K. Yin, J. Xiong, Z. He, and S.-T. Wu, “Patterning liquid-crystal alignment for ultrathin flat optics,” ACS Omega 5(49), 31485–31489 (2020). [CrossRef]  

27. A. Tuantranont, V. M. Bright, J. Zhang, W. Zhang, J. A. Neff, and Y. C. Lee, “Optical beam steering using MEMS-controllable microlens array,” Sensors and Actuators A: Physical 91(3), 363–372 (2001). [CrossRef]  

28. C. U. Murade, D. V. D. Ende, and F. Mugele, “High speed adaptive liquid microlens array,” Opt. Express 20(16), 18180–18187 (2012). [CrossRef]  

29. S.-U. Kim, J.-H. Na, C. Kim, and S.-D. Lee, “Design and fabrication of liquid crystal-based lenses,” Liq. Cryst. 44, 2121–2132 (2017). [CrossRef]  

30. H. T. Dai, Y. J. Liu, X. W. Sun, and D. Luo, “A negative–positive tunable liquid-crystal microlens array by printing,” Opt. Express 17(6), 4317–4323 (2009). [CrossRef]  

31. N. Chronis, G. L. Liu, K.-H. Jeong, and L. P. Lee, “Tunable liquid-filled microlens array integrated with microfluidic network,” Opt. Express 11(19), 2370–2378 (2003). [CrossRef]  

32. M. Kawamura, K. Nakamura, and S. Sato, “Liquid-crystal micro-lens array with two-divided and tetragonally hole-patterned electrodes,” Opt. Express 21(22), 26520–26526 (2013). [CrossRef]  

33. H. Ren, Y.-H. Fan, and S.-T. Wu, “Liquid-crystal microlens arrays using patterned polymer networks,” Opt. Lett. 29(14), 1608–1610 (2004). [CrossRef]  

34. Z. He, Y.-H. Lee, D. Chanda, and S.-T. Wu, “Adaptive liquid crystal microlens array enabled by two-photon polymerization,” Opt. Express 26(16), 21184–21193 (2018). [CrossRef]  

35. U. Ruiz, P. Pagliusi, C. Provenzano, E. Lepera, and G. Cipparrone, “Liquid crystal microlens arrays recorded by polarization holography,” Appl. Opt. 54(11), 3303–3307 (2015). [CrossRef]  

36. Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in Pancharatnam–Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017). [CrossRef]  

37. O. Yaroshchuk and Y. Reznikov, “Photoalignment of liquid crystals: basics and current trends,” J. Mater. Chem. 22(2), 286–300 (2012). [CrossRef]  

38. M. L. R and D. Khosla, “Fingerprint identification in biometric security systems,” International Journal of Computer and Electrical Engineering 2, 852–855 (2010).

39. Y. Kitamura, R. Shogenji, K. Yamada, S. Miyatake, M. Miyamoto, T. Morimoto, Y. Masaki, N. Kondou, D. Miyazaki, J. Tanida, and Y. Ichioka, “Reconstruction of a high-resolution image on a compound-eye image-capturing system,” Appl. Opt. 43(8), 1719–1727 (2004). [CrossRef]