1. Introduction

Spherical micro-lenses represent the most important elements of optical microsystems. Even though they are based on the same refractive principles as their macro equivalents, the development of micro-optical lenses opens new opportunities for many applications, as for example minimally invasive diagnostics. At the same time, these new opportunities introduce new challenges that call for novel solutions. To achieve comparable performance to systems in the macro-domain, micro-optical devices need to have numerical apertures NA in the same order. This requires lenses with high optical power and hence, small radii, which are difficult to fabricate by standard technology.

Lenses for optical systems with dimensions of several millimeters are usually made of glass using well-established manufacturing methods. However, for lenses with smaller diameters, fabrication by classical methods becomes increasingly complex, costly and slow or even unfeasible. This limits rapid prototyping of micro-optical systems and thus impedes the development of new devices and concepts.

To overcome this problem, different techniques for the fabrication of micro-lenses have been presented, such as photoresist reflow [1, 2], hot embossing [3], pattern transfer [4], dip coating [5], dispensing of UV curable materials [6, 7] and jet printing [8–10]. The last technique received a lot of attention over the last years, as it has shown a huge versatility regarding the dispensed material. Jet printers successfully demonstrated printing of a wide range of polymer-based materials [11], DNA [12] and solutions featuring nanoparticles [13].

Drop-on-demand (DOD) jet printing offers advantages such as simplicity, low costs, maturity and flexibility. Furthermore, it allows precise deposition of specific volumes, enabling a potent rapid prototyping technique. Moreover, it is a promising fabrication tool due to its cost-effectiveness and has proven its suitability for the fabrication of micro-lenses [10, 14, 15].

Nevertheless, open issues as inaccurate deposition with respect to position and volume and predefined contact angles between substrate and dispensed liquid present challenges which impair effectiveness and versatility of DOD. To overcome these issues, pinning edges on the substrate provide an approach towards self-positioning of the landing droplets, and they support varying contact angles on the substrate. The pinning edges can be implemented either by locally changing the wettability of the surface [9,16,17] or by structuring the topology of the substrate [8, 18–20].

In this paper, we use both of the aforementioned approaches to create pinning edges, as depicted in Fig. 1. To form convex micro-lenses, we pattern the substrate with hydrophobic edges, where the jet-printed liquid pins to a wettability step. To create concave interfaces, we define 300 μm deep hydrophilic wells. While filling the wells, the liquid establishes a concave spherical interface. When the filling process exceeds a certain volume, the liquid pins to the upper edge, which allows the tuning of the curvature of the interface by further increasing the liquid volume.

The research presented in this paper is motivated by the need for a simple and cost-effective fabrication method for micro-lenses with arbitrary focal length. This work demonstrates the feasibility of combining DOD jet printing with MEMS fabricated pinning architectures to fabricate convex as well as concave micro-lenses. In contrast to prior work in this field [8,9,17,20], we are extensively investigating the optical properties of the fabricated lenses.

 

Figure 1 Manipuation of contact angles by surface treatment. a) Due to local changes in wettability, the contact angle θ can vary between the contact angles θ₁ and θ₂ of the hydrophilic and hydrophobic surfaces, respectively. b) As a result of topological changes, the contact angle can be tuned between the contact angle θ₁ and θ₁ + α, where α is the angle between the initial and the final surface orientation.

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2. Concept

Solid/liquid interaction

The shape of a liquid drop on a flat substrate is governed by the interplay of surface and bulk forces. The relation between the two effects is given by the Bond number

Therefore, for Bo ≪ 1, a sessile drop on an untreated substrate will always show a spherical shape and a specific contact angle, independent of its volume. However, it is possible to tune the contact angle and therefore the curvature of the droplet by locally changing either the substrate’s wettability or its topology. Both principles confine the liquid and cause it to pin at an edge, where the contact angle is allowed to vary in a range defined by the aforementioned treatments of the substrate.

If the wettability of the substrate changes from high to low, the liquid will be confined within the area of high wettability, as depicted in Fig. 1 (a). An approaching contact line will pin to the wettability step, that is the border between high and low wettability. By further increasing the liquid’s volume, the contact angle θ can be adjusted between θ₁ < θ < θ₂, where θ₁ and θ₂ describe the contact angles in the hydrophilic and hydrophobic areas, respectively.

In case of topological changes of the substrate, the confinement is based on the fact that the contact angle will change due to the surface inclination, as shown in Fig. 1 (b). Again, if the transition is sharp, the contact line will be pinned to this edge, which allows the tuning of the contact angle θ between θ₁ < θ < θ₁ +α, where θ₁ describes the contact angle on the substrate and α the angle between the initial and the final surface orientation [19].

Both concepts, presented here, allow the adjustment of the contact angle and therefore, the tuning of the final spherical shape of the droplet. Changing the volume of the droplet, directly influences its contact angle and radius of curvature r, which ultimately defines the optical power P

UV-curable polymers

Materials that polymerize in the presence of UV light are widely known and have been thoroughly investigated. The timing as well as the speed of polymerization (curing) can be adjusted by setting the level of UV irradiation, which is a big advantage in the fabrication process. After curing, the polymer has changed its aggregate state and becomes solid. Due to the volume shrinkage ζ_Vol during polymerization, the solid polymer usually has a higher density ρ than the uncured liquid. We will see here that dispensing UV-curable polymers on substrates equipped with specifically tailored pinning architecture facilitates the fabrication of micro-lenses with arbitrary focal lengths.

3. Fabrication

The realization of spherical micro-lenses consists of two basic process steps:

Substrate fabrication

The substrates are completely fabricated by MEMS micromachining. Transparent Pyrex wafers with a thickness of 300 – 500 μm serve as starting material for both pinning architectures. Lithography followed by chromium deposition and a lift-off process create chromium structures that serve as marks for chip dicing as well as orientation markers for chip handling.

The implementation of both aforementioned pinning principles is done in the following steps and outlined in Fig. 2. To create a pinning edge by a step in wettability, we spin coat a 1 μm thick hydrophobic fluoropolymer layer (Cytop, 7 wt.%) onto the Pyrex substrate. Subsequent photolithography and reactive ion etching of the Cytop film forms circular areas of higher wettability, where the original Pyrex substrate is circumscribed by Cytop rings that show much lower wettability and therefore, pin the approaching liquid. To facilitate pinning on a topological feature, we deposit an SU-8 negative tone resist onto the substrate. SU-8 allows to achieve high resolution and high aspect ratios. 300 μm deep wettable wells are lithographically structured into the resist layer and serve as container structures for the dispensed liquid.

 

Figure 2 MEMS fabrication process for both pinning principles. Pinning can be achieved by either changing the wettability (Cytop) or the topology (SU8) of the substrate. b) Photographs of substrates with SU8 wells.

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Jet printing of UV-curable polymer

We use a BioFluidix PipeJet P9 DOD nanodispenser to print the polymer onto the substrate, which holds the pinning architecture. The PipeJet P9 is an automated dispenser based on piezo jet printing. A piezo-driven piston pushes an elastic pipe that is filled with liquid. At the orifice, a drop forms and breaks off. It features non-contact dispensing with disposable fluid hoses. The advantages of this particular device are its adjustable dosage volume, ranging from a few nanoliters to several microliters, and the easy exchange of the liquid.

The dispensed liquid needs to fulfill a wide range of requirements. Most importantly, it has to show good optical properties, suitable wetting behavior on all materials involved, as well as good dispensing characteristics. We chose the custom-made UV-curable polymer S72E [21] as our dispensing liquid, as it offers good performance in all three aforementioned domains.

With an absorption coefficient α_d of 0.28 cm⁻¹, which was evaluated at 589 nm, S72E offers good optical transmission at a refractive index n_d of 1.532 and an Abbe number ν of 46.6. Figure 3(a) shows the optical characterization for the complete visible spectrum. The interplay of the PipeJet P9 and the liquid polymer S72E provides stable dispensing, which allows the precise adjustment of the dispensed volume and hence the radius of curvature of the liquid interface and therefore, the focal length. Figure 3(b) depicts a long-term measurement of dispensed droplets. 250 single droplets were shot and weighted using a high precision balance (Sartorius SC2). Over a period of two hours, the droplet volume was found to be 5.011 nL ± 0.085 nL. In addition, S72E exhibits excellent wetting properties on all materials, Pyrex, Cytop, and SU8. With contact angles of θ_Pyrex = 4° ±2°, θ_Cytop = 46° ±1° and θ_SU8 = 32° ± 2° the interplay of polymer and solid allows to tune the focal length in a wide range.

 

Figure 3 a) Measured dispersion and absorption of S72E in the visible spectrum. b) Long-term measurement of dispensing behavior yields a droplet volume of 5.011 nL ± 0.085 nL. c) & d) Theoretical curves for both pinning concepts at different lens diameters. The contact angle θ of S72E on the solids defines the tuning range of the focal length.

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Figure 3(c) and Fig. 3(d) show the tuning range for both presented pinning architectures calculated by theory. In case of pinning on a wettability step, which is depicted in Fig. 3(c), the tuning range amounts to approximately 18 mm for a lens diameter of 1.5 mm, and 6 mm for lenses with a diameter of 0.5 mm. In case of pinning on topological features, which is shown in Fig. 3(d), we can achieve both convex as well as concave interfaces, with the capability to form an uncurved interface yielding an infinite focal length. The tuning range spans from −1.6 mm to +2.8 mm for a lens diameter of 1.5 mm, and from −0.5 mm to +1 mm for a diameter of 0.5 mm.

In this work, we fabricated lenses with a diameter of 1.5 mm, as they provide larger tuning ranges and higher possible NAs due to the bigger aperture. To create convex lenses, we solely used substrates that facilitate pinning on a step in wettability. The substrates holding topological features were exclusively used for the fabrication of concave lenses.

The fabrication process of the two lens types is schematically shown in Fig. 4(a) – Fig. 4(c). After fabrication of the pinning architecture, we mount the diced lens chip on an automated dispenser setup, which comprises a computer controlled 2D-stage. A back side microscope allows to precisely position the chip with respect to the nanodispenser. A computer routine automatically dispenses a predefined volume of liquid polymer onto the chip, before moving to the next position and continuing the dispensing process. The routine allows the fabrication of single lenses as well as lens arrays yielding liquid domes with defined diameters and radii of curvature. Finally, the liquid polymer is cured in a nitrogen atmosphere at an irradiance of 6 J/cm² resulting in an average shrinkage ζ_Vol of the polymer of about 20 %.

 

Figure 4 Schematic of the lens fabrication process: a) Fabrication of functionalized substrates. b) Automated jet printing of liquid polymer onto the pinning architecture. c) UV curing of the polymer yielding convex and concave solid body lenses. d) Photograph of a convex (left) and a concave (right) lens chip after the dispensing process.

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4. Characterization

The quality of the jet-printed polymer lenses is characterized in two different ways:

Lens surface

The surface profile as well as the surface roughness of the lenses are obtained by WLI. To obtain the lens profile within the optical clear aperture, a stitching algorithm is applied that combines multiple frames. A spherical fit through the measurement data yields the radius of curvature, as shown in Fig. 5(a). The central frame around the vertex is taken as a characteristic measurement to determine the surface roughness for each lens.

 

Figure 5 a) Surface characterization: Acquisition of the surface profile by white light interferometry yields the lens diameter D and the lens height h. A spherical fit of the measured data delivers the radius of curvature r. b) & c) show one measurement for convex and concave lenses each, and the residual figure error (grey) between measurement (red) and spherical fit (black). d) Measured radii of 15 convex (green) and 18 concave (blue) microlenses plotted against their expected radii.

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As an example for a convex and concave lens profile, respectively, Fig. 5(b) and Fig. 5(c) show measurements of both polymeric lens types as well as their corresponding residual figure error, which describes the difference between the measurement and the fit. In case of convex lenses, we see that measurement and fit match quite well within the whole diameter. The residual figure error ranges from 10 to 50 nm rms (root mean square). Their concave counterparts show much higher deviation, especially towards the edges. This can be explained by the curing process of the polymer. During curing the liquid stays pinned at the upper edge of the SU8 well. However, as the liquid becomes a solid, the material shrinks by about 20 %, which pulls the interface sideways towards the edges. This deformation results in steep slopes at the outer rim and larger radii than expected in the central part, and reduces the usable lens diameter. With a reduced aperture of 1 mm for the concave lenses, we find rms values of the residual figure error in the range of 150 to 270 nm.

For both lens types, we find excellent surface roughness between 1 and 10 nm rms. Table 1 summarizes the surface properties of both convex and concave lenses determined by WLI.

Table 1. Measured surface properties of 15 convex and 18 concave lenses. In contrast to the convex lens type, the interface of the concave lenses deforms drastically during the curing process, which reduces the usable lens diameter to 1 mm in the center of the clear aperture. The residual figure error is given in terms of rms as well as PV (peak-to-valley).

View Table

Lenses with radii ranging from −8.7 mm to +5.1 mm were produced. Fig. 5(d) plots the measured radii of convex and concave lenses against their expected value, calculated by considering the pinning geometry, the dispensed volume and the shrinkage of the polymer. While the measured radii of the convex lenses match quite well to the expectation, the radii of the concave lenses show a steeper slope than predicted by theory. As mentioned before, this can be conclusively explained by the curing process, which shrinks the polymer. The shrinkage causes steep slopes at the outer rim of the lens, which stretches the lens in the center and results in lenses with larger radii than expected.

However, linear fits through the convex and concave data points reveal a linear relation between expectation and measurement, implying a stable process. The respective confidence bands (±σ) are depicted by the shaded areas. The main contribution to the process uncertainties is the curing of the polymer, as the inherent polymer shrinkage is extremely sensitive to the amount of oxygen remaining in the curing atmosphere. During processing, the oxygen concentration slightly changed from one production cycle to the next. The related uncertainty in predicting the target focal length is up to 9 % for convex and 13 % for concave lenses. However, within a single production cycle, all lenses are exposed to the same curing atmosphere. Among such lenses, the standard deviation of the focal length amounts to only 1 %.

Imaging quality

A back-illuminated USAF1951 resolution test chart was used to assess the imaging quality of the polymer lenses. As concave lenses only form virtual images, auxiliary optics (AO) were used to relay the images to a scientific CCD camera. Figure 6(a) and Fig. 6(b) show a schematic of the measurement setup. To prevent the AO from affecting the imaging results, the aperture stop is placed at the plane of the lens under test (LUT). This way the diffraction limit is defined by the LUT. The AO consists of an infinity corrected objective (Plan Apochromat; NA = 0.28) and a tube lens, which ensures an optical performance close to the diffraction limit. Under these conditions, the influence of the auxiliary optics on the imaging quality can be neglected [22].

 

Figure 6 a) & b) Schematic of the measurement setup. The intermediate image is relayed to a scientific CCD by an infinity corrected microscope. c) & d) Images of a USAF1951 resolution test chart acquired by two convex lenses at a magnification M = 1 and a field of view FOW of 1.15 × 0.86 mm². e) & f) Images acquired by two concave lenses at M = 0.33. The insets show the the full field of view FOV of 3.46 × 2.59 mm². The zoom-in correspond to the FOV of the convex lenses.

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Figure 6(c) – Fig. 6(f) depict images captured from the USAF1951 resolution test chart. The images allow the qualitative analysis of the imaging performance. All images were taken with an aperture stop size of 1 mm and an object distance equalling two times the focal length yielding magnifications of 1 and 0.33 for convex and concave lenses, respectively. The convex lenses image an area of 1.15 × 0.86 mm². Due to their smaller magnification, the concave lenses deliver an image area of 3.46 × 2.59 mm². However, vignetting effects clip the images at the margins, as shown in the insets of Fig. 6(e) and Fig. 6(f).

To quantify the imaging performance, we evaluated the contrast of the acquired images. The relative image contrast is given by the absolute value of the optical transfer function, a function commonly referred to as the modulation transfer function (MTF). The MTF can be calculated by Fourier transform from the impulse response of the optical system. Depending on the input object, the system response is described by the point spread function (PSF), the line spread function (LSF) or the edge spread function (ESF), with PSF, LSF, and ESF being the system responses to a point-object, a line-object, and an edge-object, respectively.

We recorded the ESF by imaging a back-illuminated chromium edge of the USAF1951 resolution test chart. Subsequent differentiation orthogonal to the imaged edge yields the LSF, from which the MTF is computed [22] by

Each measurement determines only the MTF along a single axis ξ orthogonal to the edge, oriented along x. If the optical system cannot be assumed to be axially symmetric, repeated measurements at different orientations become necessary. As the polymer shrinks by about 20 %, we can not assume that the lenses show perfect axial symmetry after the curing process. Accordingly, we record two ESFs for each LUT, one in horizontal and one in vertical direction, yielding two orthogonal MTF curves.

Figure 7 shows the measured MTFs of six LUTs evaluated on the optical axis. We analyzed three convex and three concave lenses, where the object distance was again set to two times the respective focal length, resulting in comparable MTF curves for LUTs with similar focal length. Beyond that, we simulated the lenses as perfect spheres with Zemax, where the material thicknesses, the object distances and the measured material dispersion (see Fig. 3a)) were taken into account. The simulation gives the diffraction limited MTF as well as the MTF of the perfect sphere for every measured LUT, which provides a benchmark for the measurement. For larger focal lengths, we find the MTF of the perfect sphere close to the diffraction limit. However, with decreasing focal length, spherical aberrations increase, thereby lowering the MTF curve drastically with respect to the diffraction limit.

 

Figure 7 Measured (red & purple dots) and simulated (green & black lines) MTFs of three convex (top) and three concave (bottom) lenses. All measurements were done at an object distance equalling two times the respective focal length, which yields comparable NAs and thus MTFs for lenses with similar focal lengths.

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For all six lenses, we find the two orthogonal MTFs to be in good agreement, implying that the polymer shrinks homogeneously in both spatial directions. In case of the convex lenses (see Fig. 7(a) – Fig. 7(c)), the measured MTFs coincide well with their corresponding simulated spheres, which suggests a low amount of added aberrations introduced by the curing process. Especially for larger focal lengths, we find an excellent conformity between measurement and simulation. Again, in case of the concave lenses, the measured MTFs of lenses with the short focal length match well with the simulation. However, going to larger radii the discrepancy between measurement and simulation increases strongly.

Both convex and concave lenses show better results when the lens volume is lower, which corresponds to shorter focal lengths in case of concave lenses and larger focal lengths in case of convex lenses. With increasing volume, the influence of the polymer shrinkage also increases and explains the discrepancy between measurement and simulation for lenses with larger lens volumes.

To confirm the reproducibility of the fabrication technique, seven nominally identical convex lenses with a target focal length of 6.7 mm were prepared. Figure 8(a) compares the target focal length with the measured focal lengths and corresponding standard deviation. Figure 8(b) plots the average value of the measured MTFs and the respective standard deviation. The maximum standard deviation, 0.06, is found at an MTF value of 0.59.

 

Figure 8 Evaluation of the reproducibility of the jet printed polymer lenses. a) focal length of seven nominally identical convex lenses with a target focal length of 6.7 mm. The measured focal length amounts to 6.83 mm ± 0.07 mm. b) simulated (green & black lines) and measured (red dots) MTFs of the seven nominally identical convex lenses with target focal length of 6.7 mm. All measurements were done at an object distance of two times the focal length.

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5. Conclusion

We report a drop-on-demand (DOD) ink jet process to fabricate refractive concave and convex micro-lenses. We employ MEMS surface treatments to glass substrates to facilitate contact line pinning on either a step in wettability and on topological features. These surface treatments allow the fabrication of convex and concave optical interfaces by DOD ink jet printing. Clean room fabrication of the pinning architectures guarantees very high precision and repeatability of the lens dimensions. With dispensed droplet volumes of 5.011 nL ± 0.085 nL, we are able to precisely control the dispensed volume and therefore, predict the resulting focal length of the cured polymeric lens. In this work, we fabricated and characterized lenses with diameters of 1.5 mm and focal lengths ranging from −16.4 mm to +9.6 mm. Within their clear aperture, all lenses show surface roughnesses below λ/50 (evaluated at 589 nm) and good sphericity. Especially the convex lenses show a very low residual figure error between measurement and spherical fit ranging from only λ/50 to λ/10.

We believe that the presented technology enables the development of cheap, reliable and flexible rapid prototyping methods for micro-optical components. As the substrate fabrication is based on well-known MEMS processes, bonding of multiple lens wafers becomes possible, which allows the design and fabrication of micro-optical objectives to be used in medical imaging or consumer electronics.