Refractive microlenses with more than 50 µm sag are fabricated using grayscale lithography. Mechanical assembly features are made simultaneously alongside the microlenses to facilitate high precision assembly of miniature optical systems. The microlens elements are formed using lithographic patterning of photosensitive hybrid sol-gel glass requiring no etch transfer to the substrate material. Grayscale lithography enables the straightforward patterning of aspheric lenses and arbitrary surfaces within the material depth. Lessons learned in the design of a grayscale photomask are described. Characterization of the fabricated lens elements is reported including lens shape, surface quality, and image quality of a complete assembled imaging system.
©2004 Optical Society of America
Grayscale photomasks are becoming more commonly applied in lithographic fabrication of optical structures using negative tone photosensitive materials. One class of these photosensitive materials is hybrid glasses based on sol-gel synthesis technique. The optical structures can be directly patterned on the exposed material without the need for etch transfer to the underlying substrate material. Eliminating the need for an additional etching step in the fabrication will reduce equipment demands and costs, speed up the fabrication, and shorten the process cycle. Furthermore, hybrid glasses based on sol-gel synthesis can be tuned to exhibit a range of material properties suitable for lithographically produced optics.
We have previously reported on the fabrication of large-sag refractive microlenses [1–3] and on the design of a miniature imaging system composed of refractive microlenses fabricated simultaneously with mechanical alignment and assembly features . Other groups are also investigating the fabrication of refractive microoptics using grayscale photomasks and sol-gel synthesis technique based materials [5–6]. In this paper we present our most recent accomplishments in fabricating these refractive surfaces and mechanical alignment features with a custom designed grayscale photomask.
The hybrid glass material can be spin-coated to thicknesses of over 100 µm which defines the maximum sag in the structures to be fabricated. The material is exposed through a Canyon Materials (CMI) HEBS glass gray-scale photomask . The custom designed mask has an optical density (OD) range from 0.12 to 1.403 and is distributed over 129 discrete levels. The limits in optical power of the lenses are determined by two factors: material thickness (lens sag) and lens diameter. For example, we have fabricated lenses with 56 µm sag and 1.3 mm diameter.
In this paper, the parameters of these fabricated lenses including curvature, sag, shape, and roughness are presented. A discussion of some of the aspects of gray-scale photomask design is also included and the optical performance of the lenses is reported. This is followed by a discussion of some of the current limitations and future directions.
2.1 Materials and process
The photosensitive material used in creating the lenses is a custom engineered hybrid glass material. The material is created by a sol-gel synthesis technique reported previously [1–3]. The material behaves like negative tone resist and has the properties required for generating relief profiles of more than 100 µm. After development and baking, the material is mechanically and optically similar to glass, so no etch step is needed to transfer the pattern into the underlying glass substrate.
In previous studies a preliminary empirical model or calibration curve for the surface depth dependence on grayscale mask optical density was presented . Recent improvements in material and process parameters have increased the dynamic range and linearized the material response over the OD range of interest. The hybrid glass is spin coated to a desired thickness and then exposed through a photomask using proximity exposure. The material is polymerized by the UV exposure and when immersed in developer the unexposed regions are removed more quickly than the exposed regions. A gradually varying exposure dose is translated into material height, so generating the desired lens shapes is simply a matter of exposing the material with a specifically designed gray scale irradiance pattern.
Figure 1 shows the material surface height after exposure and development as a function of optical density of the photomask. The values shown in Fig. 1 were obtained by using a grayscale calibration photomask (HEBS5N) available from Canyon Materials, Incorporated (CMI). The grayscale calibration photomask contained binary features (100 µm×100 µm rectangles) with a range from 0.12 to 1.5 optical density. These data were then utilized to design the actual photomask used in the lens-element fabrication. As can be seen from Fig. 1, the material response is linear over the range of optical densities present in the calibration mask. A linear fit of the data in Fig. 1 results in a 0.9985 R2 value (R=correlation coefficeint).
Figure 2 shows the optical density profile in the designed grayscale lens mask. The optical density increases from the lens center towards the edge of the lens in 129 steps. This profile is designed to produce the aspheric lenses described in the next section. The actual lens was written using the region from 0.12 to 1.40 OD in 128 gray levels. The entire region of lenses and alignment features was surrounded by a darker area with 1.5 OD. This allows the region surrounding the lenses to be developed completely away down to the substrate. The grayscale photo-masks were written by CMI.
2.2 System design and layout
The optical system under development is a miniature imaging microscope constructed from refractive microlenses. The detailed design of this system has been presented in a previous publication . Figure 3 shows a schematic of the optical part of the 4M device and the optical layout. Each lens is also patterned with mechanical alignment features designed to provide passive alignment of the lenses with respect to a system substrate thus eliminating the need for post-assembly adjustments. This alignment is achieved by inserting the lens elements into slots containing complementary grooves and a micro-machined spring. The scheme requires mechanical alignment features to be positioned very precisely with respect to the lenses. The alignment between the lens and the mechanical alignment features is automatically achieved, because they are patterned on the same photomask and fabricated in the same lithography step. One photomask may contain a number of these individual lens elements. The lens elements can be readily diced out from the substrate requiring low dicing accuracy for the individual lens-element edges. The mechanical alignment features provide constraint of all degrees of freedom that the lenses might have with respect to the system substrate. The fold mirror (see Fig. 3) is also constrained and positioned by lithographically defined mechanical features on the top of the lens element and in the system substrate. The result is a miniature imaging microscope objective completely defined by lithography photomasks.
3. Photomask design
Design of a photomask for grayscale lithography is a detailed and subtle task that requires some description. There are many possible ways to encode the desired optical density profiles into a mask. The choice can affect the exposure patterns in dramatic ways.
The first choice to make is whether to encode lens shape as an optical density contour map or by appropriately varying the OD over some set of uniform spatial zones. If one were to assume that the profile is to be written in uniform increments of OD, different regions of the same OD should be grouped on the same layer in the mask design like a contour map. The problem with this method is that a different contour map is required for every lens that has even slightly different surface shape, which is very inefficient and increases the cost of writing the mask by requiring more fracture time. A better way to encode the mask is to use uniform regions and assign each region a specific OD (see Fig. 4). This is discussed in more detail on the CMI website .
The axial symmetry of the lenses tempts one to write these spatially uniform regions as concentric annuli of uniform width creating a bull’s-eye pattern for all the lenses as seen in Fig. 4 (the lens on the right). This method is also a poor choice because it produces slight variations in OD depending on the local angle of the annulus edges with respect to the electron-beam address grid. This phenomenon may be caused by fracturing during mask fabrication. The resulting artifact is a radial spoke pattern superimposed on the lenses after fabrication (see Fig. 5, top). The better method suggested by Chuck Wu and Laurie Wu of CMI is to break the features up into a grid of square pixels of a uniform size (i.e., 4×4 µm) and then assign OD based on the position of each pixel (see Fig. 5, bottom).
Figure 5(a) shows a schematic of the mask written with four annular zones. The actual mask is written with 128 zones over a 1.3 mm diameter. The result of using these continuous annular zones is a radial spoke pattern of slightly higher OD’s. This can be seen in the image of the mask [Fig. 5(b)] taken with a 10x microscope objective microscope and CCD camera as dark spokes radiating from the center of the lens. This spoke pattern transfers to the lens profile and can be seen in the Scanning Electron Microscope (SEM) image [Fig. 5(c)]. The bottom row of Fig. 5 shows the result of “pixelating” the mask so that the OD zones are written in a grid of uniform pixels. The radial spoke pattern is eliminated as can be seen in Fig. 5(e) and Fig. 5(f). Careful inspection of the mask images and SEM images reveal that in addition to the radial spoke pattern, there is a circular ring pattern (variation in OD) present in both of the lenses. This artifact is due to e-beam dose calibration when writing the gray-scale mask and should be eliminated in future masks.
The grayscale photomask used in fabrication of the lens elements for the miniature imaging system presented in this paper was composed of 4 µm square regions of 129 discrete levels ranging from 0.12 to 1.5 in optical density. The mask was designed using the “pixelating” approach described above [Figs. 5(d)-5(f)].
4. Fabrication results
The fabricated lens elements were characterized by several methods as no one tool is capable of providing data on all vital aspects of the fabricated lens. An optical profilometer (Veeco NT2000 and NT3000) was used to measure the lens sag and assess the surface roughness. A Fizeau interferometer (Wyko 6000) was used to measure radius of curvature directly. The transmitted wavefront of the lenses was also measured using a Mach-Zehnder interferometer and a Shack-Hartmann wavefront sensor. The material’s bulk optical characteristics are represented in our previous publications and are not discussed here [1–3].
4.1 Material thickness and lens sag
The sag of the lenses or mechanical alignment features is primarily dependent on the initial material thickness. In fact, the same OD range can be used to achieve different sags by modifying the initial film thickness, exposure, and development process appropriately. The result is an effective stretching of the height profile over the thickness of the material. It has been possible to fabricate lenses and other structures with more than 100 µm of sag using the same grayscale mask designed for 56 µm sag lenses. This stretching of the shapes provides a degree of freedom when fine tuning the process to achieve the desired lens shape. Once a process is fine-tuned, the results are consistent: A particular run using the same set of parameters to fabricate 12 lenses yielded an average sag of 44.94 µm with a sag standard deviation of 1.36 µm.
4.2 Radius of curvature and focal length
The focal length, and hence radius of curvature of the microlenses is the most basic parameter affecting the paraxial properties of an optical system. It is therefore important to demonstrate control over this parameter during fabrication. As described earlier, the material has a linear response over the range of optical densities from 0.12 to 1.4, so the mask was designed to have OD values that correspond directly to the desired lens shape (see Fig. 2).
Measuring the radius of curvature of the small diameter aspheric lenses proves to be challenging and several methods were employed to determine this value. In particular, the optical profilometer cannot provide reliable results due to the large sag, high slopes, and aspheric nature of the lenses. The first method used the Wyko 6000 Fizeau interferometer to measure the translation from a concentric null fringe to the cat’s-eye position . The tool works well for measuring large optics, but proved to be a challenge while measuring these microlenses. The primary limitation is that the thin substrate produces double reflections that result in many superimposed interference fringes. Locating the null fringe position becomes a difficult task and results in an estimated measurement error of +/-0.05 mm for the radius of curvature. Nonetheless, the radii of several lenses were measured to have a radius of curvature of 3.85 mm. This value will be shown to agree quite well with a less direct method discussed next.
The transmitted wavefront was measured with a Mach-Zehnder interferometer developed by Williby and Greivenkamp [9–10]. The power of the lenses is high enough that the wavefront slope cannot be measured directly, so a partial index matching fluid was used to reduce the power of the element. Accurate knowledge of the index difference allows one to calculate the wavefront that would be produced if the lens was used in air. The radius of curvature of the wavefront was measured using this method and the result was in close agreement with the Fizeau test. The radius of curvature for three lens elements is presented in Table 1. Immersion was used only for the Mach-Zehnder measurement of curvature and not for the roughness measurements described in the following section.
4.3 Surface roughness
Surface roughness is present over a range of different length scales . At the high spatial frequency end of the spatial-frequency spectrum corresponding to scattered light (and hence reduced image contrast), a roughness of less than 20 nm RMS is desired since this corresponds to an acceptable signal to noise ratio for the 4M-device application. To measure the high spatial-frequency roughness, the optical profilometer was used with a 50x objective and a 2x field of view lens. This setup corresponds to a lateral sampling of 0.09 µm on lens surface. The profile map is recorded and a 25×25 µm square sub-region is selected for the calculation of roughness. Choosing this small region ensures that the lower spatial frequency errors are not considered. The roughness increases from the center of a convex lens (4.4 nm RMS) to the edge (13.5 nm RMS), probably due to magnification of variations as the surface is developed away during lens fabrication. Since the center of the convex lens is not developed very deep, the roughness remains small. Near the edge of the lens the full initial thickness of material is developed away and variations in the material cause a greater magnitude of roughness near the edge.
The mid-range spatial frequencies on the order of 10–20 cycles per aperture (i.e. 1.3 mm diameter in our case) exhibit a roughness of 100–200 nm RMS. This range of roughness is measured with the optical profilometer using a 10x objective with a field of view of 459×603 µm and a pixel sampling of 0.98 µm. This type of mid-spatial frequency roughness will tend to contribute to a halo around images of point-like objects .
4.4 Comparison of lens shape to design
As discussed earlier, the shape of the lens is determined by the OD profile in the grayscale mask and this shape can be stretched or compressed by tuning the processing steps. Figure 7 shows an example of this scaling. The profile of a lens with sag of 55 µm is plotted in green along with the designed lens shape in red. The profile of a lens with 43 µm sag seen in Fig. 6 is plotted below in blue along with a scaled version of the designed profile to match the sag of the actual lens plotted in pink. From this fit, it can be seen that the linear scaling matches well with the actual surface. It can also be clearly seen that there is ripple present in the lens profile. This ripple is due to the slight errors in the grayscale mask (OD variation) and can also be seen as rings in Fig. 5 and Fig. 6 (see Section 3).
4.5 Imaging results
The ultimate test of the microlenses described here is to use them to construct the miniature imaging system for which they were designed . Before assembly, the lenses were anti-reflection (AR) coated with a V-coat centered at 635 nm . The lenses and mechanical features were then scribed out into individual elements. Figure 8 shows a schematic of the lens components of the 4M device and the prototype which was assembled without the detector and electronic components.
The 4M device is designed to have a magnification of 4x, and the image was relayed to a CCD using 5x relay optics giving a total magnification of 20x. The system was used in reflection mode and the illumination source was a 635 nm laser diode. Figure 9 shows images taken with the 4M device of a 600 lp/mm grating and 10–30 µm diameter microspheres. The grating has 0.8 µm lines of chrome patterned on glass and the 4M device can resolve the structure, albeit at reduced contrast. The average on-axis Strehl Ratio was calculated to be 0.63+/-0.05 over 30 measurements using a tilted edge (edge spread function) technique . The silica microspheres represent objects of a similar size to the biological cells that the 4M system is designed to image. Although imaging quality will continue to improve through the course of our research, the contrast and resolution are already capable of imaging cell-sized structures.
A negative tone hybrid glass material and process were developed that produces a linear height profile as a function of optical density. Optical surfaces were lithographically patterned directly into the material with surface relief of over 50 microns and with surface micro-roughness less than 20 nm RMS. Lenses were fabricated with surface profiles that closely match the designed lens surface profile. A miniature imaging system was assembled using refractive microoptics fabricated directly in hybrid sol-gel glass using grayscale lithography. The individual microlenses were 1.3 mm in diameter with a sag of 44 µm corresponding to a radius of curvature of 3.85 mm or a focal length of 7.4 mm. The lenses were coated with an antireflection coating after fabrication and before system assembly. The assembled system has a 4x magnification and is capable of imaging object of dimension comparable to biological cells in reflection mode with resolution better than 0.8 µm.
These results are very promising and we expect to make significant improvements as we continue to refine photomask and process parameters. A few of the key issues that will be the focus of our attention are the reduction of mid-spatial-frequency-range surface irregularity and more consistent matching of surface shape of the fabricated lenses with the designed shape.
This work was funded by grant R21 EB002165 from the National Institute of Biomedical Imaging and Bioengineering (NIBIB).
References and links
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