Fabrication of Large-Scale Microlens Arrays Based on Screen Printing

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Fabrication of large-scale micro-lens arrays based on screen printing for integral imaging 3D display Xiongtu Zhou, Yuyan Peng, Rong Peng, Xiangyao Zeng, Yongai Zhang, and Tailiang Guo ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b08278 • Publication Date (Web): 19 Aug 2016 Downloaded from http://pubs.acs.org on August 27, 2016

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ACS Applied Materials & Interfaces

Fabrication of Large-scale Micro-lens Arrays Based on Screen Printing for Integral Imaging 3D Display

Xiongtu Zhou, Yuyan Peng, Rong Peng, Xiangyao Zeng, Yong-ai Zhang, * and Tailiang Guo *

College of Physics and Information Engineering, Fuzhou University, 350002 Fuzhou, Fujian, PR China

*Corresponding authors: Tel: +86 591 87893299, Fax: +86 591 87892643 E-mail: [email protected] (Y.Z.), [email protected] (T.G.)

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ABSTRACT: The low-cost large-scale fabrication of micro-lens arrays (MLAs) with precise alignment, great uniformity of focusing and good converging performance are of great important for integral imaging 3D display. In this work, a simple and effective method for large-scale polymer micro-lens arrays using screen printing has been successfully presented. The results show that the MLAs possess high quality surface morphology and excellent optical performances. Furthermore, the micro-lens’ shape and size, i.e., the diameter, the height and the distance between two adjacent micro-lenses, of the MLAs can be easily controlled by modifying the reflowing time and the size of open apertures of the screen. MLAs with the neighboring micro-lenses almost tangent can be achieved under suitable size of open apertures of the screen and reflowing time, which can remarkably reduce the color moiré patterns caused by the stray light between the blank areas of the MLAs in the integral imaging 3D display system, exhibiting much better reconstruction performance. KEYWORDS: micro-lens array; screen printing; surface wettability; integral imaging 3D display; optical performance; image reconstruction

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1.

INTRODUCTION Integral imaging (II), also known as integral photography, is an autostereoscopic 3D display

technology that was first proposed by Lippmann in 1908.1 It uses double micro-lens arrays (MLAs) to record and reconstruct the 3D characteristics of the target information, and is regarded as one of the most promising and convenient ways to realize the 3D display system due to its many advantages, such as glasses free, full parallax, quasi-continuous view points, virtual and real 3D display.2-4 Fruitful researches have been conducted using new pick-up and reconstruction methods and models for the improvements of display performances.5-13 For example, Navarro et al. proposed a method to extend the depth of field of II systems in the reconstruction stage based on the combination of deconvolution tools and depth filtering of each elemental image using disparity map information.4 Luo et al. put forward a crosstalk free integral imaging 3D display with wide viewing angle by using periodic black mask.14 Ji et al. proposed a tilted elemental image array generation method for computer generated integral imaging display with reduced moiré patterns.13 However, few substantial progress has been made on the prototype and industrialization of integral imaging, mainly due to the unavailability of mature fabrication technologies for high quality and cost-effective MLAs, which is a core optical device in integral imaging 3D display system. Integral imaging is based on the reversibility principle of light rays, to reconstruct a 3D scene, elemental images are displayed on a display device and the rays pass through a MLA to reproduce the 3D scene in space. The optical performance of MLA affects remarkably the image quality. Thus, the fabrication of MLAs with good repeatability of geometry parameters, great uniformity of focusing and good converging performance is of great important for integral image

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3D display. Besides the application in II 3D display, micro-lenses and MLAs, as micro-optical components with excellent light collecting efficiencies, have attracted more and more attentions as they are acquiring a key role in several other application fields, such as micro-optical sensors, optical communication, organic light emitting diodes (OLEDs), and so on.15 Thus, the fabrication of MLAs has been extensively studied. Several fabrication techniques of MLAs have been proposed such as photo-resist reflow method,16,

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hot embossing process,18 gray-scale

photolithography,19 photo-polymerization,20 direct laser writing21, 22 and micro-jet fabrication,23 etc. For example, MLAs with high quality have been fabricated by soft lithography using grooved PDMS24-26 or by laser technology. 27 Among the above methods, photo-resist reflow method, hot embossing process, gray-scale photolithography, light-induced cross-linking of polymerization can fabricate MLAs with mass production, but the scale is still limited and the accuracy is too low. Though direct laser writing and other micromachining methods can fabricate MLAs with high precision, it is time-consuming and requires expensive facilities. On the other hand, the above mentioned methods are particularly suitable for the fabrication of MLAs with the size (diameter) of micro-lens in the range of several micrometers to several tens of micrometers, it is difficult for them to fabricate MLAs with the size (diameter) of micro-lens in the order of around 1000 micrometers, which is normally used in the large-scale II 3D display system to adapt to the pixel of display devices. In general, these MLAs used in the II 3D display should also be smooth in morphology, with good repeatability of geometry parameters, great uniformity of focusing and good converging performance, and are fabricated by mold development, which is high cost and less effective. In our previous work, we have presented a fabrication method of MLAs used for II 3D display by combining photolithography of holes arrays and ink-jet printing of lens material, 4


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which exhibited good reconstruction performance in integral imaging 3D display, the size of micro-lens can also be controlled by the photolithographic holes and the number of ink-jet printed droplet.28 However, this technique is still time consuming and the scale of MLAs is limited by the ink-jet printing set-up. The low-cost large-area fabrication of MLAs with simple control of lens profiles still faces many technical difficulties, and is becoming an important research area in II 3D display technology. Therefore, it is necessary to develop a more convenient and efficient fabrication method of large-scale MLAs which is simple, less time-consuming and low costing. Screen printing is a printing technique whereby a mesh is used to transfer ink onto a substrate using a blade or squeegee, except in areas made impermeable to the ink by a blocking stencil, it was first appeared in a recognizable form in China more than one thousand years ago, and has now been widely used in the display industry, such as light guide plate, touch panel. In this paper, we adapt the screen printing technique to fabricate large-scale MLAs on different substrates. The parameters of screen printing were optimized and high quality MLAs were obtained, which showed good reconstruction performances in II 3D display. 2.

EXPERIMENTAL METHODS 2.1. Fabrication and characterization of micro-lens arrays. MLAs were fabricated by

screen printing, followed by reflowing and UV curing, as illustrated in Fig. 1. Firstly, precision composite screen with mesh number of 325, silk diameter of 28 µm, and square opening of 50 µm was prepared using finely woven fabric made from stainless steel fabric and polyester fabric around, which were stretched over a frame of aluminum, the detailed fabrication processes of screen are depicted in figure S1. Then, micro-cylinder arrays (MCAs) were prepared by printing UV resin from the open mesh apertures on glass, indium tin oxide (ITO) glass and polyethylene 5



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terephthalate (PET) substrates, respectively, which will form micro-cylindrical hemisphere arrays rapidly, as shown in the Fig. 1(a) and (b). A screen printing system (ATMACE1014, Taiwan, China) was employed, and the UV curable resin (6230G, Taiwan, China) with viscosity of 40000cps was used. The printed micro-cylindrical hemisphere arrays were laid flat to reflow until the MLAs were formed (Fig. 1(c)), followed by solidifying under UV light (365nm) with power density of 1700 mW/cm2 for different time to form neat MLAs (Fig. 1(d)). The contact angles were determined using instrument (SL200KS, Kono, USA), and in all case, at least three individual measurements on three different positions were taken, resulting in a mean value. Laser 3D microscope (OLS4100, OLYMPUS) was applied for the morphology characterization of MLAs. A measurement system was set up for the characterization of the focusing performance of MLAs (as shown in figure S2). In the optical set-up, laser beam of 650 nm was expanded and then incident on the MLA vertically, the transmission light was then magnified and was collected by a CCD camera equipped with beam analyzer (BC106N-VIS/M, THORLABS), the pixel size of the CCD camera is 6.45×6.45 µm. Finally, the fabricated MLAs were applied to the reconstruction process of II by setting upon elemental image arrays generated by MATLAB. 2.2. Construction of integral imaging 3D display system.

The integral image 3D display

system is illustrated in figure S3. In order to reduce the image quality degradation because of diffraction and limitations of optical devices, the pick-up stage was realized by computer graphics techniques instead of using the MLA. Briefly, 3DsMax was used to create a 3D object model, which was then imported in Matlab source codes. Light field camera, including a principal lens and a MLA, was simulated using computer graphics techniques by tracing the desired rays emanating from the 3D object from different perspectives. By using computer graphics 6


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techniques in the pick-up stage, the parameters, such as the focus length of lenses, can be set directly to be the values of the fabricated MLA which was to use in the reconstruction stage, thus to increase the quality of reproduced image. The elemental image arrays captured using computer graphics techniques were displayed on a monitor (HP LE2001w) with resolution of 1600×900 and pixel pitch of 277 µm. The number of elemental images was 320×180, and each elemental image was resized to 5×5 pixels and 1385×1385 µm (277µm×5 pixels). The fabricated MLAs were put in front of the monitor with distance of around 10 mm, depending on the parameters of MLAs. 3. RESULTS AND DISCUSSION 3.1. Shape and morphology of MLAs on different substrates. The size of an elemental image was set as 1385×1385 µm, corresponding to 5 pixels of monitor. Accordingly, the pitch of circular open mesh apertures (the center distance between two neighboring open apertures) in the screen was also 1385 µm. However, the diameters of the open apertures should be smaller than the pitch of the apertures, since the printed UV resin will spread to some extent as the screen rebounds away from the substrate. In our work, the diameters of the open apertures were selected to be 1290 µm, 1310 µm, 1330 µm and 1350 µm, respectively, with an array of 350×200. The surface wetting conditions of substrates are very important for the parameter adjustment of MLAs, more wettable substrates will cause easier spread of UV resin on the substrates. Therefore, besides the glass, we also studied the screen printing of the MLAs on the ITO glass and PET substrates, considering that the MLAs on ITO glass substrate might be promoted to forming adaptive-focus lens arrays by combining with liquid crystal, and the MLAs on PET substrate might yield to form curved or flexible MLAs to adapt to the curved or flexible monitors. 7



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Fig.2 (a-c) show the typical contact angles of UV resin on the three substrates, it can be found that the mean values of water contact angles are around 52º, 65º and 73º on the glass, ITO glass and PET substrates, respectively, showing different wetting properties. The screen with diameter of open aperture of 1290 µm and pitch of 1385 µm from center-to-center was used to study the shape of printed MLAs on the three substrates. As illustrated in Fig. 2 (d-f), geometrical differences were obviously observed for micro-lenses printed on the substrates with different surface wetting conditions. The contour of micro-lens fabricated on glass, ITO glass and PET are shown in Fig.2 (g-i), where the fitting to an ideal spherical surface is also provided. As expected, the spreading behaviors of micro-droplet were different when the substrates were differing, and the diameter and height of the micro-lens were strongly dependent on the surface wetting conditions of the substrates, with decreased wetting conditions, the diameter of the micro-lenses decreased and the height increased. That is to say, the spreading extent of micro-cylinder was inversely proportional to the value of the substrate’s contact angle. It is also found that the largest sag happened on the sides of the lens, while not in the central part, the maximum profile deviation for lenses fabricated on glass, ITO glass and PET substrates are 0.92 µm, 1.76 µm and 4.76 µm, respectively. According to the hydrodynamics,29 the farther UV resin from the substrate in the micro-cylindrical hemisphere has larger flowing speed, and the center of gravity gradually lowers when it flows out due to the gravity. Furthermore, the farther away from the central fluid micro-cylindrical hemisphere, the center of gravity lowers more, forming the flat convex micro-lens. If the substrate is more wettable, the interaction force between the UV resin and the substrate is smaller, leading to greater spreading. The sphericity of a lens is determined by the force balance between surface tension and gravity. For the lenses printed on the glass, the spreading force caused by the gravity is closed to that caused by surface tension, leading to a very 8


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small profile deviation. With decreasing the wettabliity, the surface tension increases, the spreading speed of UV resin on the substrate becomes slower, since the flowing speed of UV resin at the edge is larger than that at the central micro-cylindrical hemisphere, leading to larger profile deviation on the sides of lenses. The above results indicate that the surface tension plays an important role in final profile formation of lens using screen printing. The spaces between two neighboring micro-lenses are expected to be as small as possible, because the larger spaces would cause more serious moiré patterns in the reconstruction process of II. Generally, the spaces between two neighboring micro-lenses can be adjusted by both the blank areas coated with an impermeable substance between micro-lenses in the screen and the spreading time of MLAs. However, the screen with too small blank areas is difficult to fabricated, moreover, too small blank areas will cause linkage of micro-lens more easily. We took ITO glass substrate as example to investigate the effects of blank areas (or diameter of the open apertures) and spreading time on the shape of the MLAs, by considering that the glass substrate is a very hydrophilic surface and the PET substrate is too hydrophobic, which would lead to too fast or too slow spreading of UV resin. The UV resin would be pulled out of the mesh apertures and remain on the ITO glass substrate as the screen springed back after the blade has passed, and the printed UV MCAs were fully solidified under UV light with power density of 1700 mW/cm2 after standing for time of t for the reflowing. The high power density of UV light could make the UV resin solidify rapidly to seize the best lens profile and desired distance between neighboring lenses. We then studied the evolution of the height (denoted as h) and radius (denoted as r) of MLAs with reflowing time (from 30 s to 600 s) using laser 3D microscope, which scans layer by layer in the Z-axis direction and detect reflecting light intensity, subsequently to reconstruct the 3D geometric morphology of 9



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objects. In this work, it was found that the lens profile was almost formed after reflowing time of 30 s, hence we selected the beginning time to be 30 s with an interval of 30s. In all samples, the resulting values of h and r were taken as the mean value for at least 50 individual measurements of randomly selected micro-lenses. The evolution of h and r of MLAs with t for samples with diameter of open apertures of 1290 µm, 1310 µm, 1330 µm and 1350 µm are shown in Fig.3, respectively. It can be seen that, with the increase of t, r gradually increased and h decreased. For the samples with smaller open apertures, r and h tended stable and the distance between adjacent micro-lenses changed little when t reached a certain value. MLAs prepared using screen with smaller open apertures did not exist linkage problems between adjacent micro-lenses when r and h became stable, so it was possible to stand for a long time so that the micro-cylindrical hemispheres could reflow enough to obtain sufficiently good shape, as shown in Fig.3 (a) and Fig.3 (b), respectively. While MLAs prepared using screen with larger open apertures existed linkage problems between adjacent micro-lenses when r and h haven’t become stable, that is, the adjacent micro-lenses would spread and fuse together, as shown in Fig.3 (c) and Fig.3 (d), respectively. The MLAs fabricated with different parameters of screen and with the same standing time would have different contour, in general, no matter how large the size of the open apertures, the morphology of micro-cylindrical hemispheres was not ideal when t was too small, micro-cylindrical hemispheres need enough time for deformation to form ideal lens surface. On the other hand, the standing time of micro-cylindrical hemispheres made from large open apertures cannot too long, otherwise h will has a sharp decline because of the fuse of adjacent micro-lenses, as shown in Fig.3 (c) and Fig.3 (d), the morphology of fused micro-lenses were irregular. 3.2. Characterization and calculation of optical parameters. From the above results, the 10


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MLAs with desired r and h, as well as the distance between two adjacent micro-lenses can be easily tuned and controlled by adjusting the size of open apertures and the reflowing time. Fig. 4(a-c) show the three-dimensional surface topography of MLAs fabricated using screens with diameters of open apertures of 1290 µm, 1310 µm and 1330 µm, respectively. Their average diameters and height were listed in table 1. It can be found that, when the diameter of open apertures increased, the spread became severer, the diameter of micro-lens increased and the height decreased. For the MLAs fabricated using screen with diameters of open apertures of 1330 µm, the micro-lenses were almost tangent and the blank areas became the smallest, which was expected to have the least stray light irrelevant to the imaging during the integral imaging. To measure the effective focal lengths and characterize the focusing performance of micro-lens fabricated, a set-up consisting of a laser source, an automated stage with position readout, a viewing system with beam analyzer and equipped with CCD camera was built. The light beam passed through beam expander can be considered as parallel light beam. The position of laser beam, beam expander, magnifier and CCD were fixed, the MLAs were then moved away from the magnifier along its optical axis, and the light intensity distribution at different distance between MLAs and CCD has been recorded. When the MLAs were related far away from the CCD, the light was divergent, when the surface of CCD overlapped with the focal plane of MLAs, the sharpest focus spots can be obtained, as shown in Fig.4. Fig.4 (g-i) show the corresponding 3D light intensity distribution of Fig.4 (d-f), whose outline is found to meet Gaussian distribution, as can be seen more clearly from the magnification in Fig.4 (j-l). The effective diameters of the focal points were 83.3 µm, 159.8 µm and 266.4 µm for the micro-lenses fabricated using screens with diameter of the open apertures of 1290 µm, 1310 µm and 1330 µm, accounting for 6.46%, 12.1% and 20.0% with respect to that of micro-lens, indicating good converging performance. 11



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The diameters of focused spot correspond to the full width at half maximum after taking into account the magnification of the imaging system (3.28), were 15.2 µm, 36.6 µm and 66.4 µm for the micro-lenses fabricated using screens with diameter of the open apertures of 1290 µm, 1310 µm and 1330 µm, Compared to the calculated theoretical values of 11.1 µm, 12.8 µm and 14.1 µm based on d / 2 = 1.22 fλ D , the deviation is found to increase with the increase of the base diameter of lenses, which might be attributed to the profile deviation of lenses. The relations between the curvature (Rc) , the effective focal length (f), the numerical aperture (NA), the f-number (f#) and the radius (r), the height (h) of plano-convex micro-lens can be described as formula (1-4), respectively:30 Rc = h 2 + r 2 2h

(

f = Rc (n −1) = r 2 + h 2

（1）

) (2h(n −1))

（2）

NA = r f

（3）

f # = f 2r

（4）

Table 1 summarizes the experimentally measured geometrical properties and the theoretically calculated optical parameters of micro-lenses. Where the index of refraction of the solidified UV resin is n=1.5. It was confirmed that the optical properties of MLAs can also be tuned by modifying the open apertures of screen.

3.3. Integral imaging properties of micro-lens arrays. Fabrication of polymer MLAs by screen printing solves the key technical problems of large area MLAs’ preparation with high production efficiency and low cost. Fig.5 (a) and (b) illustrate the photos of 21 inch MLAs on ITO glass and PET substrates, respectively. The MLAs on PET substrate can be bent to different angle because of PET’s flexibility, and it can be applied to curved screens or even flexible displays to achieve the improvement of viewing angle,31 which will be further studied in our 12


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future work. In this work, we focus on the integral imaging properties of MLAs on ITO glass substrate. To confirm the uniformity in terms of the diameter and height, 50 randomly selected micro-lenses from the MLAs on ITO glass substrate with reflowing time of 300 s have been measured and shown in the Fig.5 (c) and (d). The radius (c) and height (d) of the micro-lenses are 686.3±0.4 µm and 38.7±1.1 µm, respectively, It was confirmed that micro-lenses fabricated by screen printing exhibited smooth morphology with great uniformity and repeatability, which was expected to have good image reconstruction performance in integral imaging 3D display system. It is implied that the focus ability enhanced with smaller diameter and larger height of micro-lens. However, in the application of integral imaging, the blank areas should be as small as possible to decrease the stray light. In comparison experiments, we used the MLAs with different optical properties (as shown in Fig. 4) to reconstruct integral imaging 3D display system and to study their imaging performances. The elemental image arrays were captured digitally and then displayed on monitor (HP LE2001w). The MLAs were then putted in front of the elemental images,32 followed by adjusting the distance between the monitor and the micro-lens arrays until obtaining the best reconstruction images. Fig.6 (a-c) show the reconstruction images obtained using MLAs fabricated with the open apertures of 1290 µm, 1310 µm and 1330 µm, respectively. The distances between the neighboring lenses for the three MLAs are 164.1µm, 145.8µm and 33.9µm, respectively. It can be found obviously that the images reconstructed using MLAs fabricated by screen printing show reasonable 3D images. We can also make the following conclusions by observing and comparing Fig. 6(a), (b) and (c). The reconstructed 3D image using the MLAs with smaller diameter and larger height shows clear image, however, it has severe color moiré patterns, which can be attributed to the periodical stray light from the blank areas due to the larger distance between the neighboring lenses. When the diameter increased and the height 13



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decreased, the edge of 3D image show a little blurry, while the color moiré patterns reduced remarkably. The reconstructed 3D image using the MLAs with almost tangent adjacent micro-lens show little color moiré patterns. Thus, the image in Fig. 6(c) exhibited better quality than that in Fig. 6(a). In the future work, MLAs with high numerical aperture and high packing density might be achieved by further improving the wetting conditions of substrates and the reflowing time, to obtain higher quality of reconstructed 3D image. It is worth pointing out that, the size of patterns fabricated using screen printing can be able to miniaturize to the order of 50 µm. However, in order to obtain MLAs with lenses of high sphericity and high focal number, we used UV resin with viscosity of as high as 40000cps to decrease their spreading after screen printing, and the minimum diameter of lenses we obtained using the method presented in this work was around 200 µm. The screen printing method we demonstrated in this work is particularly suitable for the fabrication of micro-lens arrays over large areas. With regard to the size of individual micro-lens, it is suitable for the fabrication of micro-lens with diameter in the range of 200 µm to several millimeters, which is important for the display applications. As to thermal reflow method, it seems problematic to fabricate micro-lens in this range, because dips will easily turn up in the center of the molten resist patterns when its diameter increases. For the fabrication of micro-lens or micro-lens array with smaller size of individual micro-lens, conventional methods, such as thermal reflow method, have been well developed.17, 33

4.

CONCLUSIONS In summary, this work successfully presents a simple and effective method for large-scale

polymer micro-lens arrays using screen printing. The lens shape and size, i.e., the diameter, the

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height and the distance between two adjacent micro-lenses, of the MLAs can be easily controlled by modifying the reflowing time and the size of open apertures of the screen. With the increase of reflowing time, the UV resin gradually spreads, therefore the diameter of micro-lens increases, the height of micro-lens decreases. MLAs with the neighboring micro-lenses almost tangent can be achieved under suitable size of open apertures of the screen and reflowing time, which can remarkably reduce the color moiré patterns caused by the stray light between the blank areas of the MLAs during the integral imaging 3D display system, exhibiting much better reconstruction performance.

Acknowledgements This work was financially supported by the Natural Science Foundation of China (No. 61306071 and No. 61474024), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20133514120011). The content of this work is the sole responsibility of the authors.

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Figure captions: Figure 1. Schematic fabrication processes of micro-lens arrays (MLAs) using screen printing. (a) Scheme of screen printing processes, (b) The micro-cylindrical hemisphere array was fabricated using screen printing, (c) MLAs were formed after reflowing of micro-cylinder array, (d) MLAs were solidified under UV light.

Figure 2. The contact angles of UV resin in the air on different substrates were illustrated in the top row: (a) glass, (b) ITO glass, (c) PET, showing different wetting conditions. The according 3D perspective images of a typical printed cured micro-lens on (d) glass, (e) ITO glass, (f) PET were shown in the middle row. The height profiles (blue solid line) taken along the equatorial plane of a typical micro-lens and fitting of a ideal surface to the lens profiles (red dash line) on (g) glass, (h) ITO glass, (i) PET were shown in the down row.

Figure 3. The relationships between the height (h) and radius (r) of MLAs with the reflowing time (t) on ITO glass substrate using screens with different diameters of open apertures: (a) 1290 µm, (b) 1310 µm, (c) 1330 µm, (d) 1350 µm. The insets show the height profiles taken along the equatorial plane of a typical cured micro-lens and the microscope images at the designated points.

Figure 4. The focusing performances of fabricated MLAs. The 3D perspective images of MLAs on ITO glass substrate with reflowing time of 300 s using screens with different diameters of open apertures: (a) 1290 µm, (b) 1310 µm, (c) 1330 µm. (d-f) the 2D light intensity distribution when the CCD was placed on the focal plane of MLAs of samples (a-c) with the sharpest focus spots, each focused spot of the three samples corresponds to 13×13 pixels, 25×25 pixels and 41×41 pixels in the CCD camera, respectively. (g-i) The corresponding 3D light intensity distribution for the three samples. (j-l) 3D light intensity distribution of a randomly selected focusedl spot from the three samples.

Figure 5. The photos of a 21 inch MLAs on (a) ITO glass substrate and (b) PET substrate. The radius (c) and height (d) information of 50 randomly selected micro-lenses from the MLAs fabricated on ITO glass substrate with reflowing time of 300 s are provided, showing the printing 19



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repeatability.

Figure 6. Reconstructed images obtained using MLAs fabricated on ITO glass substrate using screens with different diameters of open apertures: (a) 1290 µm, (b) 1310 µm and (c) 1330 µm.

Table captions: Table 1 The geometrical properties and the optical parameters of micro-lenses fabricated using screens with different open apertures. The base diameter (D) and height (h) are experimentally measured values, while curvature (Rc), the focal length (f), numerical aperture (NA), and f-number (f#) are theoretically calculated values from the general equations

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Figure 1

Figure 2

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Figure 3

Figure 4

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Figure 5

Figure 6

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Table 1 Diameters of open apertures /µm 1290

1310

1330

Avg D/µm

1324.6

1351.6

1372.6

Avg h/µm

47.6

42.1

38.7

Rc/mm

4.6

5.4

6.1

f/mm

9.3

10.9

12.2

0.072

0.062

0.056

7.0

8.1

8.9

NA f#

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Table of Contents Graphic

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Fabrication of Large-Scale Microlens Arrays Based on Screen Printing

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