Microlenses fabrication has attracted a lot of attention for the last two decades. Today, many different fabrication methods exist, depending on the required cost and optical quality. However, when it comes to integration of high quality microlenses in complex microsystems, the methods are much fewer, although it becomes among the most needed features of microoptics.
In this framework, well-known methods to get rid of optical aberrations usually rely on aspherical profiles or diffractive corrections but are not easy to apply to micro-optics. Indeed, micro-fabrication technologies allowing the generation of aspherical components by controlling accurately their profiles can be difficult to master. They are moreover limited to specific fabrication methods, e.g., excimer laser ablation of polycarbonate,1 transfer of the aspheric resist profile generated by a gray-level mask into glass by Reactive Ion Etching (RIE),2 or its variation, i.e., transfer of spherical melted resist lenses into glass by RIE with varying etch mixture.3 An alternative approach concerns the micro-fabricated diffractive lenses that can provide arbitrary wavefront deformation, and in particular aberration correction generated by an appended refractive spherical micro-lens.4 Nevertheless, some of these methods employs also polymers which cannot be associated when such lenses are to be used in integrated devices requiring high temperature process for their further assembly and eventual separation.
Hence, among the different approaches in macro-optics, the most common and widely employed, e.g., in microscope or camera objective lenses, remains the lens splitting that consists in dividing the focusing power between two or more optical components. Combining lenses is very well-known in order to deal with chromatic aberrations. For this purpose, materials with different dispersion features are associated to reduce the lens wavelength dependence. In micro-optics technologies, choice of materials is limited, mostly because of the need for fabrication process compatibility. Thus, it often results in combining glass and polymer.5 For instance, glass microspheres trapped in a polymer layer, have been used to generate high numerical aperture (NA) lens doublets.6 Long focal-length microlens arrays have been also fabricated by combining resist-reflowed lenses embedded in polydimethysiloxane (PDMS).7
In here, we investigate such lens-splitting method applied to micro-fabricated lenses but for monochromatic aberration correction by generating a glass lens doublet. The used materials, i.e., glass and silicon are robust and the method of glass reflow in silicon cavities provides inherent alignment as well as thin supports for the lenses. Glass microlenses offer advantages regarding aging and suitability for harsh environments in terms of mechanical and thermal shocks. Microlens arrays are directly fabricated in the substrate so that refractive index matching issues and mechanical stress at the interface between different materials are avoided. Concerning glass lenses, first realizations based on photosensitive glass were reported in the 80s.8 Laser glass melting allowed the fabrication of good quality microlenses having high numerical apertures (NA) in standard glass9 and also in semiconductor-doped glass.10’11 These techniques evolved by using different lasers wavelengths and types of glass,12 and more recently with femtosecond lasers,13 the combination of laser and thermal glass reflow14 or combined with wet etching. 15
Among the different types of glass, borosilicate one is an interesting candidate for microlenses generation thanks to its good thermal stability and its compatibility with silicon processing regarding thermal expansion properties. Indeed, silicon-based micro-opto-electro-mechanical systems (MOEMS) require assembly methods which usually involve high temperatures and mechanical stress. Monolithic integration of microcomponents can be based on the assembly of borosilicate glass and silicon by anodic bonding, usually performed at temperatures over 300 °C. It is actually the case of the lenses under consideration which are intended to be a part of a miniaturized Mirau interferometer, whose in-line architecture is attractive for generation of dense matrices thanks to MOEMS technologies.
The dense array configuration allows building integrated parallel inspection systems, e.g. devoted to biomedical applications16 where it becomes possible to image relatively large zone thanks to stitching of the acquisition from adjacent channels. However, fabrication of dense matrix is another challenge for glass lens fabrication.
As mentioned earlier, we consider in here the Glass Flow Process (GFP) which was first reported by Merz et al.17 for sub-millimeter diameters microlenses fabrication. In this process, a glass substrate located on top of cylindrical silicon cavities is heated so that it melts. the deformation towards the bottom of the Si-cavity thanks to the pressure difference during the reflow forms the convex shape. Hence, grinding and polishing of both stack sides allow, on the first hand, to form the planar lens backside and, on the other hand, to open the silicon cavity. Silicon frames are then kept and thinned down to form well-controlled and auto-aligned spacers between the lenses for the doublet generation. The assembly is then performed by anodic bonding ensuring a high level of alignment both laterally and axially since no additional material is required. Thanks to polishing, the generated lens doublets are then as thin as several hundreds of microns. In the following, the generated lens doublets are fabricated, characterized and their optical performances are shown to be better than equivalent single lenses.
LENS DOUBLET PERFORMANCES
We consider that the lenses are to be used in a miniature imaging system so that they are associated to a tube lens whose focal length is f’= 25 mm in order to form a miniaturized microscope optical system, working at the wavelength λ = 633nm. The considered field of view (FOV) is 400 μm x 400 μm.
Such parameters associated to a matrix arrangement allow imaging a large area thanks to enface acquisition based on stitching. A lateral resolution in the object space of approximately 6 μm is sought after. One important requirement is to image all FOV points without changing the resolution. Hence, off-axis points are also considered in the analysis.
The system analysis has been performed with ZEMAX (EE version 2013). First, a single plano-convex lens of spherical profile with the following features: NA = 0.1, ϕ = 1.9mm, f’ = 7.47mm, radius of curvature ROC = 3.51 mm, conic = 0, sag =131 μm is considered. The corresponding spot diagram is shown in Fig. 1 (a), where two field points in the object plane (center and border of the FOV) are taken into account.
Because of the system magnification M = 3.35, the Airy radius of 13.15 μm in the image space corresponds to 3.92 μm in the object space. It can be seen that whereas on-axis rays are located within the Airy spot diameter (geometrie radius = 12.2μm), it is not the case for off-axis rays (geometric radius = 60.77 μm). The modulation transfer function (MTF) displayed in Fig. 1 (b) shows in addition rather low contrasts. For instance, the MTF contrast for an object structure of 5 μm is 0.16 and 0.13 for the on-axis and off-axis field points, respectively.
Secondly, a lens doublet made of two identical plano-convex lenses with twice less refractive power than the previous lens is considered. The doublet is based on two identical lenses mostly because of fabrication reasons but no significant improvement is experienced when using two different lenses. The equivalent objective lens has the following parameters f’ = 7.44mm, NA = 0.1, ROC = 6.922 mm, conic = 0, sag = 65.5 μm. The corresponding spot diagram with the same two field coordinates is shown in Fig. 2 (a). The lens doublet increases clearly the optical performance since the geometric spot radius for the off-axis field point is reduced from 60 μm to 10 μτη and since the MTF shows a nearly diffraction-limited curve for the whole FOV. The contrast for an object structure of 5 μm was increased from 0.13 to 0.22 (Fig. 2 (b)). The peak to valley wavefront error is less than λ/10 (on-axis) and λ/5 (off-axis) for the doublet whereas it is only around λ/2 (on-axis) and 1 λ for the equivalent single lens. Consequently, and as expected, assembling two lenses with less refractive power instead of a single lens reduces significantly the generated aberrations so that such system can be diffraction limited even for off-axis field points, meaning a homogeneous imaging performance for the whole FOV.
The plano-convex glass lenses are fabricated by glass melting inside silicon cavities. Technological steps for their fabrication are summarized on the Fig. 3. First, the silicon cavities are generated by spin-coating a 2.5 μm thick layer of MEGAPOSIT™ SPR™ 220 3.0 photoresist over a 500 μm thick silicon wafer, and by patterning it by photolithography in order to create an etching mask. This step allows to define the footprint of the lens arrangement (Fig. 3(a)). Deep reactive ion etching (DRIE) performed with a Pegasus Rapier ICP DRIE system from SPTS generates a series of 300 μm deep cylindrical cavities (Fig. 3(b)). Once the remaining resist is removed and the Si-wafer thoroughly cleaned, it is joined by anodic bonding to a 4” borosilicate glass wafer under vacuum, in order to induce a pressure difference between the sealed cavities and the environment (Fig. 3(c)). The generated wafer stack is then introduced in a furnace (oxidation tube, AET Technologies) where temperature is raised at a speed of 20 °C/minute until a value between the annealing and the softening point of the used borosilicate glass. By doing so, the glass substrate deforms toward the bottom of the Si cavities and the inner surface can be used as the convex side of the lens (Fig. 3(d)). It can be noted that this surface is formed without contact with silicon, leading to its high quality. The surface saggita (sag) is then controlled by the time spent inside the furnace at a temperature between 625 and 675 °C. Figure 4(a) displays the sag evolution as a function of time for different reflow temperatures. In this range of temperatures, the sag evolution over time is linear with slopes depending only on the viscosity. This indicates that the forces (generated by both pressure difference and resistance through viscosity) remain constant over time. Note that time origin is when the set temperature is reached. Hence, once the sag value is reached, melting must be slowed down by a relatively abrupt temperature drop. However, to avoid stresses at the Si-glass interface, this drop is stopped at a temperature around 600 ° C for which the viscosity of glass is sufficiently high again, and the cooling speed is then reduced to allow structural relaxation and avoid wafer stack bowing. Therefore, the substrates are kept at 560 °C during several hours.
It can be noted that the dense matrix arrangement leads to non-symmetrical neighboring conditions for each lens, in particular concerning the glass share (which can be understood as the available amount of glass to fill the cavities) and the thermal environment. It is then required to implement compensation strategies such as the Si-rings instead of filled-Si between cavities. This method along with the improvements obtained, are described in details in.18 After lapping and chemical-mechanical-planarization (CMP) based polishing of the back glass surface in order to make it optically flat (Fig. 3(e)), the silicon wafer is only selectively eliminated (by the same equipments) so that it can be used as a frame for further assembly procedure (Fig. 3(f) and Fig. 5(a)). In particular, because of its auto-aligned nature and accurately controlled thickness, it is used as a spacer for the doublet generation. Thus, building a lens doublet by multi-wafer anodic bonding is quite straightforward, provided that a careful alignment is performed during the bonding process (Fig. 3(g)). The employed anodic bonding equipment (Applied Microengineering Ltd) allows performing alignments with four degrees of freedom so that lateral misalignments do not exceed 10 μm. In our case, misalignment due to parallax is expected to reach approximately 30 μm but this value, corresponding to lateral mismatch between lens axes, is optically negligible. Cross-section of a 4 x 4 matrix of doublets obtained after saw dicing of one stack can be seen in Fig. 5(b). Thicknesses of glass and silicon (on the side) are 297 μm and 140 μm thick, respectively. Since each lens sag is 65.5 μm, the two glass surfaces at the lens apex are, once bonded, about 78 μm apart. The lens doublets fabricated at wafer-level (4”) are shown in Fig. 5(c), displaying a stack of 4 wafers (a bonded Si-Glass-Si-Glass set). Because of the specific fabrication method, the complete stack is as thin as 874μm although thin wafers are never handled.
First, topography of the generated lenses having different sags have been measured with an optical profilometer (MSA-500 from Polytec). From such topography measurements, the usable diameters of the lenses depending on different criteria were derived (Fig. 4(b)). For instance, the lenses can be considered diffraction limited (according to the Marechal criterion: root mean square RMS wavefront error < λ/14) if 50% of their real diameter are used leading to NA=0.05 and about 70% for NA=0.02. When the criteria is relaxed to RMS wavefront error < λ/4, the usable aperture diameter increases to about 80% for an equivalent of NA=0.05. This is this diameter that we use in the following to characterize the doublets. Note that (Fig. 4(b)) reports data for sag lower than 50 μm due to the limited NA of the MSA-500 optical profilometer.
The lens doublet performance is qualified in the following by comparing two single lenses having sags of 115 μm and 145 μm to a doublet lens equivalent to a 131 μm sag lens (i.e. single lens focal lengths, 8.47mm and 6.78mm, surround the one - 7.47mm - of the doublet). An aperture of 1.5 mm diameter is located in front of the lens under test to illuminate or collect about 80% of its full diameter. First, several intensity planes of the focal volume generated by the lenses are recorded at λ=633nm. These point spread function (PSF) measurements19 gives an on-axis lateral resolution estimated from the full-width-half-maximum (FWHM) of the in-focus PSF, equal to 4.8 μm for the doublet, whereas it is equal to 6.1 μm and 4.6 μm for the two single lenses. These values are 60-70% larger than the expected aberration-free, i.e. diffraction-limited, spots (δ = 0.51 λ / NA) for the single lenses but only 50% larger for the doublet. These differences are attributed to the large illuminated diameter.
The lens doublet is consequently slightly less aberrated, as it can be seen also when a basic phase retrieval algorithm is applied to the recorded intensity planes20 allowing to derive wavefront distribution and optical aberrations. Indeed, wavefront aberration is then 0.7 λ whereas it is found to be 1.4 λ for an equivalent single lens. For a similar focal length, the total wavefront aberration is thus twice lower than for a single lens.
Hence, the measured wavefront is decomposed with Zernike polynomials and the weights of the different aberrations terms are reported on Fig. 6. In particular, the lens doublet shows lower spherical aberration (Noll index 11), i.e. 28% lower than the average value of the single lenses coefficients.
Finally, we investigated by imaging selected spatial frequencies of a negative USAF 1951 resolution target21as well as Ronchi targets located within the focus plane of the lenses the ability to image fields of view of 400 μm x 400 μm. It appeared that the resolution deterioration across the field of view was larger (20 % variation) for the single lenses than for the doublet (8% variation). The lens doublets are thus likely to image larger fields of view for a given resolution than equivalent single lenses.
This work was funded by the collaborative project VIAMOS of the European Commission (FP7, ICT Program, grant no. 318542) and supported by the Labex Action program (ANR-11-LABX-0001-01), by the French RENATECH network and the collegium SMYLE.