3.1.

Temperature-Controlled In Situ PDMS Lens Formation

To prepare a preheated surface, a coverslip was cleaned and placed atop a hotplate. $50\mu \mathrm{L}$ of PDMS was dropped on the coverslip from a 20 mm height with the print head, as demonstrated in Figs. 1(a) and 1(b). PDMS cures at room temperature, but exhibits accelerated curing with increasing temperatures. The procedure was repeated with temperature increments of 20°C, from 60 up to 200°C.

At lower temperatures, PDMS droplets require a longer time to cure (roughly 350 s at 60°C), allowing the viscous liquid to spread across the surface as gravity pulls the liquid toward the surface. The viscosity of the uncured PDMS increases as the curing process starts, and an equilibrium is attained when the viscous forces balance out the gravitational force. This forms a very thin, flat lens with negligible curvature and little optical power. In contrast, heat-accelerated curing solidifies the liquid droplet in situ, in effect stopping the spreading process. This limits the droplet to spread into a smaller diameter and at the same time, retains significant surface curvature effective for refractive ray bending.

Figure 2 shows the morphological evolution of $50\mu \mathrm{L}$ droplets during in situ curing at 80 and 200°C. At 80°C, it can be seen that the initial droplet spread is wider and continues to flow out into a thin shape before curing completes at $\sim 80\mathrm{s}$ after dispensing. At 200°C, the PDMS droplet virtually cures on contact, causing significant curvature. No burning or charring was observed at these temperatures. Side views of droplets cured at 60 to 200°C are shown in Fig. 3 for comparison. It is seen that as the surface temperature increases, the time required for droplet curing decreases, the flow of the droplet is limited, and the subsequent droplet exhibits a decreased diameter, increased height, and increased surface contact angle, thus forming a smaller radius of curvature which leads to a higher optical power.

Fig. 2

Morphological evolution of PDMS droplet cured at (a) 80°C and (b) 200 °C. While the 80°C droplet flows into a thin pancake shape with time, the 200°C droplet attains its final shape at 2 s. Scale bar is 5 mm.

Fig. 3

Side view of PDMS droplets ($50\mu \mathrm{L}$) deposited onto a surface at various temperatures. Scale bar is 5 mm.

3.2.

Volume-Controlled In Situ PDMS Lens Formation

To investigate the relationship between focal length and droplet volume, the hotplate was set to a constant temperature of 200°C and different volumes of PDMS were deposited on the surface while all other conditions remained identical. Volumes of 10 to $200\mu \mathrm{L}$ were used, respectively, with the resulting side views and geometrical measurements shown in Fig. 4. As the droplet volume increases, the lens diameter increases intuitively; however, the contact angle only varies within $\pm 4.4\%$. The center portion of the lens is found to exhibit decreasing curvature and eventually flattens for increasing volume. This limitation makes it difficult to create high-magnification lenses $>1\mathrm{cm}$ in diameter using this method.

Fig. 4

Side view of PDMS droplets (various volumes) deposited onto a surface at 200°C temperature. Scale bar is 5 mm.

The properties of the lens are determined by its geometric parameters. Since the curing temperature of PDMS determines the speed of polymerization, and thus the contact angle and diameter of the lens droplet, the focal length of the lens can be accurately tuned in a single step. Similar to other liquid lenses, the droplet experiences uniform surface forces from all sides during curing, which greatly eliminates surface roughness.

3.3.

Printing Repeatability

To demonstrate the repeatability of the inkjet printing technique in fabricating lenses, 20 lenses were made for each volume of 10, 25, 50, 75, and $100\mu \mathrm{L}$, at each temperature between 100 and 200°C. Due to limited hotplate area, only five lenses were made for the volumes $>100\mu \mathrm{L}$ due to their larger size. Figure 5 shows the trend of the lens diameter with respect to the lens volume and curing temperature. It is observed that for volumes $<100\mu \mathrm{L}$, the diameter deviated $<5\%$ in all cases, but was generally controlled within 2.7% in most cases.

Fig. 5

Lens diameter as a function of various lens volumes and curing temperatures. The line indicates the mean, while the upper and lower limits of the error bar indicate the diameter deviation.

3.4.

Optical Characterization of Lenses Cured at 200°C

From the preceding sections, it is shown that at a certain fixed hotplate temperature, decreasing the droplet volume creates a smaller droplet with a smaller radius of curvature, or a shorter focal length. As the PDMS lenses cured at 200°C have the smallest diameter, we next characterized the focal lengths of the sequence of different volume lenses cured at 200°C.

The setup to characterize the focal length is shown in Fig. 6(a). The output from a fiber-coupled diode laser (Newport Model 505 laser diode driver connected to fiber pigtailed laser diode LD-635-31A) was passed through a convex lens (L1) (Thorlabs LA1131-ML) with a focal length of 50 mm, a neutral density filter (ND) (Thorlabs ND10A), an iris (I) (Thorlabs ID25/M), and a glass slide (G) on which the PDMS lens (L2) was attached. A CCD camera (Amscope MT 300, Amscope) with a pixel size of $1.2\mu \mathrm{m}$ was affixed on a micrometer stage with a travel range of $\sim 5\mathrm{mm}$ from the PDMS lens. The error with the stage measurement was $\sim 0.05\mathrm{mm}$. For PDMS lenses with a focal length $>10\mathrm{mm}$, the micrometer stage was removed. the CCD camera was positioned manually with a ruler and the associated error was $\sim 1\mathrm{mm}$.

Fig. 6

Determining the focal length of the PDMS lenses. (a) Schematic of optical path; optical path of diverging diode laser enters a convex lens with 40 mm focal length (L1), a neutral density filter (ND), a glass slide (G) for support, and the PDMS lens (L2); the focused beam is captured by the CCD camera. (b) CCD camera image showing beam intensity profile when tested with the $10\mu \mathrm{L}$, 200°C lens, at distance of 6.0, 6.3, and 6.6 mm, respectively. (c) The trend of focal length with different lens volumes from 10 to $200\mu \mathrm{L}$.

Figure 6(b) shows the laser beam spot captured on the CCD camera with the $10\mu \mathrm{L}$ lens. The image has been transformed into gray scale before intensity analysis with MATLAB® (Mathworks). The beam intensity profiles along the vertical and horizontal directions are also shown. The images were captured at 5.4, 5.6, and 5.8 mm distances. The focal length is found to be 5.6 mm, where the full-width half-maximum of the point spread function is captured as the minimum with the CCD camera. Figure 6(c) shows the comparison of the focal length of lenses created with various droplet volumes at 200°C. The focal lengths for volumes of 10, 25, 50, 75, 100, 125, 150, 175, and $200\mu \mathrm{L}$ were $5.6\pm 0.05$, $6.3\pm 0.05$, $6.7\pm 0.05$, $8.6\pm 0.05$, $10\pm 1$, $15\pm 1$, $30\pm 1$, $62\pm 1$, and $84\pm 1\mathrm{mm}$, respectively.

The optical power of a convex lens is the degree to which it converges light and can be expressed by the equation $P=1/f$, where $P$ is the power of the lens and $f$ is the focal length. The numerical aperture of a lens is commonly expressed as $\mathrm{NA}=n\sin \theta$, where $n$ is the index of refraction of the medium in which the lens is working ($n_{\text{air}}=1$) and $\theta$ is the half-angle of the maximum cone of light that can enter or exit the lens. For the PDMS lens with a focal length of 5.6 mm ($10\mu \mathrm{L}$ cured at 200°C), the optical power was found to be $\sim 180{\mathrm{m}}^{-1}$. The lens has a usable radius of 1.02 mm, and the half-angle is found to be 10.32 deg, leading to an NA of $\sim 0.27$. Future work is needed to fully characterize the lens surface curvature for a more accurate NA estimate.

3.5.

Minimum Resolvable Feature Size

Add-on accessories to turn a smartphone into a microscopic imaging device are widely available; however, most of these attachments are bulky or require device-specific attachment components.¹⁶ To demonstrate a practical application, the PDMS lens ($10\mu \mathrm{L}$ cured at 200°C) was attached to a Nokia Lumia 520 budget smartphone camera (Microsoft, Richmond, Virginia) as shown in Fig. 1(c). The camera has a 5-megapixel sensor and the minimum focus distance of the smartphone camera is 10 cm as specified by the manufacturer. The adhesive property of PDMS on glass and plastic surfaces allowed the PDMS lens to be attached nonpermanently onto the camera window without additional support and was able to be used in our experiments for at least 30 min at a time without falling off. The effective focusing distance of the smartphone with the PDMS lens was $\sim 5\mathrm{mm}$.

In order to determine the minimum resolvable feature size of the smartphone-PDMS lens system, a binary spoke target with a minimum feature size of $1\mu \mathrm{m}$ was imaged. The spoke target was manufactured commercially using electron beam lithography with chrome on glass, as shown in Fig. 7. The central portion of the target was imaged with an Olympus IX-70 (Olympus Corp) microscope with $400\times$ magnification, as shown in Fig. 7(a). The image obtained by the smartphone-PDMS lens system with a separate backlight source is shown in Fig. 7(b). The width of the 64 spokes decrease linearly from $300\mu \mathrm{m}$ from the outer rim to $1\mu \mathrm{m}$ at the inner rim. Intensity profiles of the images were obtained using MATLAB^®.

Fig. 7

Determining minimum resolvable feature size by imaging a $1\mu \mathrm{m}$ minium line width binary spoke target: (a) obtained with $400\times$ microscope and (b) obtained with a smartphone with a $10\mu \mathrm{L}$, 200°C PDMS lens. The three line sections, respectively, indicate the region where the spoke widths are 5, 3, and $1\mu \mathrm{m}$. V, fringe visibility.

A perfect reproduction of the spoke target pattern would yield an intensity represented by a square wave with 64 cycles, each with the highest intensity at 256 bits and the lowest intensity of 0 bits. Fringe visibility ($V$) quantifies the contrast of interference of the optical system and is defined as $(I_{\text{max}}-I_{\text{min}})/(I_{\text{max}}+I_{\text{min}})$. An ideal output yields a visibility of 1, while a featureless output yields a visibility of 0. For a 256 bit mask function, where $I_{\text{max}}=256$ bit and $I_{\text{min}}=0$ bit, $\text{visibility}=1$. The respective maximum and minimum intensities and fringe visibility obtained for different spoke line widths from the microscope and smartphone-PDMS lens system are summarized in Table 1.

Table 1

Intensity and fringe visibility of spoke target image.

The visibility of the $1\mu \mathrm{m}$ pattern from the smartphone-PDMS lens system is lower than that of the microscope; however, the intensity map indicates that 62 of 64 patterns can be resolved. It is important to note that the imaging contrast highly depends on the camera hardware, and internal processing performed by the smartphone may have an important role in determining the minimum resolution of the system. A higher-end smartphone camera may yield better results than those obtained for this analysis.

A further resolution test was performed using a standard USAF 1951 resolution test target (#58-198 Edmund Optics Inc.), in order to prevent radially symmetric distortions from affecting the previous method of resolution determination. The target was separately imaged using a microscope with $400\times$ magnification, as shown in Fig. 8(a), and the smartphone-PDMS lens system with a separate backlight source, as shown in Fig. 8(b). The USAF patterns selected are, respectively, from group 8 element 6 vertical and horizontal (top), and group 8 element 5 vertical and horizontal (bottom), yielding a respective line width of 1.10 and $1.23\mu \mathrm{m}$. The dotted lines indicate the region of the pattern from where the light intensity was obtained.

Fig. 8

Determining minimum resolvable feature size by imaging a USAF 1951 resolution test target with line widths of $1.10\mu \mathrm{m}$ (top patterns) and $1.23\mu \mathrm{m}$ (bottom patterns): (a) obtained with $400\times$ microscope and (b) obtained with a smartphone with a $10\mu \mathrm{L}$, 200°C PDMS lens.

Fringe visibility was calculated for each pattern and summarized in Table 2. It is seen that the visibility of the 1.23 and $1.10\mu \mathrm{m}$ test patterns from the smartphone-PDMS lens system remains lower than that of the microscope; however, the intensity map clearly displays the three peak patterns. The minimum resolvable feature and fringe visibility is comparable to that performed using the binary spoke target.

Table 2

Intensity and fringe visibility of USAF 1951 resolution test target image.

3.6.

Smartphone Microscopy Application

Figure 9 demonstrates the potential of the smartphone-PDMS lens system to be used in biological and biomedical research. A cross-section of a human skin-hair follicle histological slide (AmScope) was employed, and the image captured by an Olympus IX-70 microscope was compared with that by the smartphone-PDMS lens system. Figures 9(a), 9(b), and 9(c) show the sample imaged under the microscope at $40\times$, $100\times$, and $200\times$, respectively, while Fig. 9(d) shows the same sample imaged with the smartphone-PDMS lens system. A magnified inset of each image is shown in Figs. 9(e) to 9(h). It can be seen that with the smartphone-PDMS lens system, individual skin cells can be observed.

Fig. 9

Comparison of human skin and hair follicle cross-section histology slide. (a), (b), (c), and (d) are, respectively, imaged with an Olympus IX-70 microscope at $40\times$ magnification, $100\times$ magnification, $200\times$ magnification, and with a Nokia Lumia 520 smartphone with PDMS lens system. (d), (e), (f), and (g) show the magnified regions, respectively.

The base magnification of the lens was found to be $120\times$ by comparing the observed size of an arbitrary structure in a clearly focused image taken with the smartphone and the aforementioned microscope. The magnification of the smartphone with PDMS lens can be further enhanced by combining software based digital magnification.