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Abstract
Fresnel lenses are fabricated directly upon the end face of gradient index (GRIN) lenses by F2-laser machining at 157 nm wavelength. The employed laser processing technique combines a mask projection configuration at 25-x demagnification with a rotation of the structured lens. The ablation characteristics of the GRIN materials require very high pulse fluences with typical values above 7 J/cm2. Topography measurements on the Fresnel lenses reveal a good contour accuracy with residual deviations from the design profile well below 100 nm. Such hybrid optical elements, combining GRIN lenses with diffractive lenses in one element, can serve as the basis for high-performance micro-optical imaging systems with diameters up to 2 mm. Examples of possible applications include imaging sensors like proximity sensors or color-corrected microscope objectives with high numerical aperture for endoscopy applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In various areas of optical technologies, there is an increasing demand for fiber-coupled micro-optical imaging systems with special properties, often including high-resolution capabilities and correspondingly high numerical aperture. Since the performance of gradient index (GRIN) lenses depends on a continuous change of the refractive index within the lens material, GRIN lenses offer plane optical end faces. With their cylindrical shape and small size, GRIN lenses are ideally suited for the construction of micro-optical systems. They are usually made from highly doped glasses in a silver or lithium ion exchange process [1].
The manufacturing technology already allows the creation of application-specific refractive index profiles. However, the simultaneous fulfillment of competing design requirements can hardly be achieved by a proper design of the gradient index profile alone. An example is the simultaneous minimization of spherical and chromatic aberration, as it is required for color-corrected high numerical aperture (NA) lenses, for example. Due to restrictions in available space and complex mounting requirements, micro-optical systems are often limited to a small number of optical components. One possibility to improve system performance in both conventional and micro-optical systems is the integration of diffractive optical elements (DOE). The DOEs for these so-called hybrid optical systems are usually produced by means of lithographic processes, which are often economical only with large piece numbers. In addition, the process usually requires large planar substrates, ruling out the structuring of surfaces of existing micro-optical elements [2].
In this work, we use an F2-laser processing system to fabricate diffractive micro lenses directly upon the end face of GRIN elements. A similar technique has already been used to structure Fresnel lenses on planar glass and fused silica substrates [3,4]. While the brittle and highly doped GRIN material shows adverse material modifications when processed at most conventional laser wavelengths and even at ultra-short pulse processing, the 157 nm wavelength of the F2-laser allows precise structuring. The approach allows an increase of the design degrees of freedom without increasing the number of optical elements. A vital benefit of the hybrid optical elements is the monolithic bonding of the DOE to the GRIN-elements, leading to a significantly simplified adjustment and packaging, and improved durability.
2. Laser processing
Micromachining by direct laser ablation generally relies on sufficient absorption. For optical materials that are transparent in the visible range of the spectrum, UV or IR wavelength are required. While IR lasers like the CO2-laser can be employed for tasks like cutting or bonding, structuring with µm or sub-µm resolution can only be achieved with lasers in the UV spectral range. A precise structuring of materials like quartz or fused silica, where the transmission range extends to below 200 nm, often requires an F2-laser emitting at 157 nm wavelength [5–8].
The transmission range of the GRIN lens material hardly extends to below 350 - 400 nm. However, processing the GRIN glasses with standard UV-laser wavelengths like 193 nm (ArF-laser) or 248 nm (KrF-laser) leads to distinct haze and staining, both on the surface and in the volume of the material. The haze cannot be removed by subsequent cleaning or etching processes, thus ruling out the application of standard excimer-lasers as well as frequency-tripled or quadrupled YAG-lasers. On the other hand, clean and precise material ablation can be observed when using an F2-laser at 157 nm wavelength. This holds for both, Ag and Li doped GRIN glasses. The fabrication of sub-micron pitch gratings on GRIN-lenses with this laser has already been demonstrated [9].
The laser processing system used in the present work to machine the GRIN lenses is illustrated in Fig. 1. The employed laser (Lambda Physik LPF 220i) delivers up to 25 mJ single-pulse energy with ~15 ns pulse duration at 1 to 200 Hz repetition rate. The optical system consists of a 157 nm beam-shaping and -delivery system (MicroLas Lasersystem) using a fly’s eye homogenizer based on two pairs of crossed cylindrical lens arrays for beam homogenization. The processing station also comprises high precision target positioning stages and beam and sample-alignment diagnostics. A nitrogen purging system covering the complete beam path provides transparency at 157 nm. In addition, the space directly above the sample might be flushed with He instead of N2 in order to reduce the redeposition of debris. Ablative processing of the target material is performed in a mask projection configuration at 25x demagnification using a Schwarzschild objective of 0.4 NA with a target field size of 200 x 200 μm2. Due to the short wavelength in combination with the high NA of the Schwarzschild objective the depth of field is very limited. The necessary precise control of the focal plane position is accomplished by the integration of an optical coherence tomography (OCT) module into the sample-alignment optics of the processing system [10].
The mask projection scheme for the fabrication of the Fresnel lenses is illustrated in Fig. 2(a). While the mask is kept stationary, the GRIN lens is rotated about the cylinder axis during laser operation to achieve the specified concentric structures. The mask is equipped with appropriately designed apertures for each zone of the Fresnel lens. The distance of a single aperture to the rotation axis is determined by the radius of the respective Fresnel zone, and the aperture width in dependence of the radius is determined by the specified lens profile. The processing scheme requires a careful collinear alignment of the rotation axis with both the lens center and the mask center. The mask is a free-standing structure fabricated in stainless steel. It is cut from a 30 µm thick high-alloy steel sheet by a ps-UV-laser operating at a wavelength of 355 nm using a focus scanning technique with focus spot size of ~8 µm and a lateral precision in the order of 1 µm.
Fig. 2 (a) Schematic illustration of the mask projection scheme and the resulting GRIN-Fresnel hybrid optical element. (b) 3D-surface profile of the inner zones of a 23-zone Fresnel lens fabricated on the end face of a GRIN element as recorded by confocal microscopy.
The mask is designed according to the following schedule: r is the radial coordinate of the Fresnel lens (center at r = 0 (rotation axis)); R is the radial coordinate of the mask, so that R = 0 is imaged on r = 0 and every mask point with coordinate R is imaged onto a sample point with coordinate r. If the desired depth profile of the Fresnel lens is given by h(r), the opening angle θ(R) of the mask is given by θ(R) = h(r) ω d−1 F−1 × 360°, with the rotational speed ω (cycles per second), the ablation depth per pulse d (µm) at the given fluence, and the repetition frequency F (Hz) of the laser. As an example, if at a radius r an ablation depth of h = 1.5 µm is desired, this can be obtained with a fluence delivering an ablation depth per pulse of d = 0.15 µm, a rotational speed of ω = (60 s)−1, a repetition frequency of 20 Hz, and an angular opening of the mask of θ(R) = 3°.
To analyze the processing characteristic, the GRIN material is initially irradiated with a square ablation spot of size 50 x 50 µm2 while varying laser fluence and pulse number. The resulting ablation profile is analyzed with conventional wide field and confocal microscopy. An example in the case of Li ion doped glass is shown in Fig. 3 for 20 pulses at fluences of 2 and 5 J/cm2. While a clean ablation spot is obtained at 5 J/cm2, a rough and grainy surface structure can be observed in the spot irradiated at 2 J/cm2. The appearance of this roughness also depends on the number of applied pulses. For example, the ablation profile basically remains smooth for the first 3 to 5 pulses when irradiated at 2 J/cm2. A similar behavior can be observed for Ag doped GRIN material.
Fig. 3 Surface quality of ablation spots of size 50 x 50 µm2 in Li doped GRIN glass after irradiation with 20 laser pulses. At a fluence of 2 J/cm2 (a,b) the ablation profile exhibits a depth of 1.5 µm. At 5 J/cm2 (c,d) the profile shows a depth of 2.8 µm. (a,c): wide field microscopy images recorded with DIC contrast; (b,d): surface topography in false color representation as recorded by confocal microscopy.
Figure 4 shows microcopy recordings of two Fresnel lenses fabricated at fluences of 5.2 J/cm2 and 7.5 J/cm2. The images recorded with differential interference contrast (DIC, left) show rather smooth surfaces for both fluences. In dark field contrast (right) micro cracks become visible in the deeper parts of the contour at a fluence of 5.2 J/cm2. Provided the profile depth is kept constant, the number of micro cracks increases with decreasing fluence. Vice versa, the crack density decreases with increasing laser fluence with only a marginal number of micro cracks remaining at a fluence of 7.5 J/cm2. This behavior, which can also be observed for Li ion doped glass, distinctly restricts the range of suitable laser energy density for GRIN material processing.
Fig. 4 Surface quality of Fresnel lenses fabricated in Ag doped GRIN glass at different fluences ((a,b): 5.2 J/cm2, (c,d): 7.5 J/cm2) as recorded by wide field microscopy with DIC contrast (a,c) and dark field contrast (b,d). In dark field contrast, micro cracks become visible as white lines due to increased scattering.
The etching rate, defined as the ablation depth per laser pulse, is determined from measurements of the profile depth of ablation spots as shown in Fig. 3 with variations in pulse numbers and laser fluence. The experimental data are depicted in Fig. 5 for the case of Ag doped GRIN glass. To a good approximation, the etching rate follows a logarithmic increase with the applied laser fluence.
Fig. 5 Etching rate for laser ablation of Ag ion doped GRIN glass at wavelength 157 nm versus applied laser fluence in logarithmic scale. The straight line shows a least squares approximation when assuming a logarithmic dependence.
From Fig. 5, a threshold fluence of ~550 mJ/cm2 and an ablation rate of about 100 nm/pulse at 3 J/cm2 can be derived for the ablative processing of Ag ion doped GRIN glass at 157 nm. Similar data are obtained for Li ion doped material. Also, the observed threshold and etching rate are comparable to data obtained for instance for the ablation of soda lime glass at wavelength 193 nm [11]. However, in order to avoid surface roughening and the formation of micro cracks, laser fluences far in excess of the threshold must be applied for the precise structuring of the GRIN materials.
3. Fresnel lens characterization and optimization
The quality of the fabricated Fresnel lenses is characterized by bright and darkfield microscopy, confocal microscopy as well as atomic force microscopy (AFM). Figure 6 displays the topography of a lens in Ag-doped glass obtained by ablation at a fluence of 7.5 J/cm2 after cleaning with a KOH based cleaning agent (Borer, deconex 15pf-x). The specified profile depth and slope of the Fresnel zones are precisely met in the experiment. They are basically determined by laser fluence, pulse repetition rate and substrate feed rate. The remaining roughness is mainly due to the discrete ablation process, which directly results from the pulsed removal with a binary mask.
Fig. 6 Surface topography of a 5-zone Fresnel lens fabricated in Ag-doped GRIN glass measured by confocal microscopy. (a): 3D-representation in false color coding; (b): radial cross section (magenta) in comparison with the design specification (black).
On a small scale, the discrete ablation process results in a step like surface profile that can also be observed from AFM measurements. An example of a lens fabricated at a fluence of 7.1 J/cm2 is depicted in Fig. 7. The step height of about 150 nm corresponds to the ablation rate at the employed fluence. On the other hand, the roughness within single steps is restricted to about 10 nm. The comparison of the AFM data with the cross section obtained by confocal microscopy at the same sample shows a very good agreement.
Fig. 7 Surface topography at the outer zones of a 5-zone Fresnel lens in Ag-doped glass measured by atomic force microscopy. (a): 3D view; (b) averaged radial AFM cross section (green) in comparison with a single line cross section recorded by confocal microscopy (magenta) and the design specification (black).
The measured profiles exactly follow the specified design data except an over etching at the zone boundaries, which is also visible in Fig. 6(b). This deviation is due to a disproportionate etching at the edge of a binary mask that is frequently observed in laser ablation schemes [12,13]. In our process, the over etching at the zone boundaries can be fully corrected by a converse pre-correction of the mask shape which is incorporated into the mask design (cf. Figure 10(b)).
The single mask elements for each Fresnel zone resemble triangles with one curved side (cf. Figure 2), where the apex angle at the bottom is determined by pulse repetition rate, feed rate and the specified lens profile. However, the arrangement of the single mask elements as well as their left-right symmetry are design degrees of freedom in the mask design. The experiments show that both parameters have some influence on surface quality and crack formation and must be carefully optimized. For example, Fig. 8 displays the surface appearance obtained for two different mask layouts as shown in the insets. Regarding the rotation of the GRIN element with respect to the mask, a distinctly better surface quality and a minimization of cracks is obtained when there is a smooth processing front compared to the case with a saw-toothed front.
Fig. 8 Effect of mask arrangement on the surface quality of a 23-zone Fresnel lens fabricated in Ag doped GRIN glass as recorded by wide field microscopy. (a,b): overview, in dark field contrast; (c,d): details in DIC contrast. The insets indicate the arrangement of the mask apertures and the direction of rotation of the lens substrate during processing for (a,c) and (b,d), respectively.
During processing, small fragments and material remnants from the ablation, the debris, are deposited in the vicinity of the actual ablation spot. Since the lens substrate is continuously moved through the laser emission spot, the debris interferes with subsequent ablation and thus affects processing results and ablation depth. The amount of debris, fragment size and distribution depends on laser pulse energy and wavelength, but also on atomic weight and velocity of the ambient gas molecules [14]. When helium is used as the shielding inert gas, less debris redepostion and a more even spatial distribution is usually observed compared to purging with nitrogen.
The effect of the ambient gas on the processing of the GRIN materials is shown in Fig. 9 by comparing the surface appearance of two lenses fabricated under (a) nitrogen and (b) helium purging. Both lenses are processed with equal parameters concerning laser fluence, mask arrangement and substrate feed rate. In the case of helium purging, micro-cracks are distinctly reduced. Moreover, the lens profile shows a better contour accuracy and a slightly improved roughness. Note that helium purging is not applied to the full beam delivery system but restricted to a small volume in the direct vicinity of the ablation spot by a special nozzle. This allows restricting helium purging to the actual processing time and limiting the consumption to approximately 2 l/min.
Fig. 9 Effect of purging gas on the surface quality of a 5-zone Fresnel lens in Ag doped GRIN glass observed with wide field microscopy in DIC contrast. (a): nitrogen, (b): helium.
Using the corrected mask (cf. profile shown in Fig. 10(b)), the average depth error over the entire area amounts to 81 nm rms. If the deviations from the design value at spatial frequencies below 0.1 µm−1 are defined as shape deviation and above 0.1 µm−1 as roughness, one obtains a shape deviation of 66 nm rms and a roughness of Ra = 30 nm or Rq = 45 nm.
Fig. 10 Fresnel lens with 23 zones and 1.8 mm diameter on the end face of an Ag ion doped GRIN lens. (a) overview in dark field contrast; (b) radial cross section through Fresnel zones 7 - 14 measured by confocal microscopy (averaged: green; single line: magenta) in comparison with the design specification (black).
4. Summary and conclusions
Precise ablation of metal ion doped gradient index glass can be performed at a laser wavelength of 157 nm. A mask projection approach is applied to fabricate micro Fresnel lenses directly into the end face of GRIN lenses with good contour accuracy. Laser fluence and mask layout need to be optimized to obtain a good surface quality and nearly micro crack free lenses.
To form a hybrid GRIN-Fresnel optical element for a specific application, the parameters of the Fresnel lens need to be matched to the imaging task and the characteristics of the GRIN lens in the optical design. As an example, Fig. 10(a) displays a GRIN-Fresnel hybrid lens with an outer diameter of 1.8 mm intended to be used in a multi-color optical distance sensor. The Fresnel pattern with 23 zones covers the complete end face of the GRIN cylinder. For processing the full diameter, 5 rotations of the GRIN lens with 5 different mask sets were employed, requiring a precise coordinate motion of the mask stage and the lens and rotation axis. Overall processing time for this Fresnel pattern is less than 15 min. The achieved contour accuracy is illustrated in Fig. 10(b) showing a radial lens cross section in comparison to the design profile. For better visibility, the cross section is restricted to Fresnel zones 7 - 14. Deviations from the design profile are below 100 nm. Further tests show a diffraction efficiency above 75%. The performance of the combined GRIN-Fresnel hybrid lens in a confocal distance sensor is shown in Fig. 11. The coincidence of the back reflexes from a mirror at two separated wavelengths demonstrates a very good chromatic correction of this system (a). The focal spot at a working distance of 0.8 mm is shown in (b) and has a diameter of 2.0 µm (measured at 1/e2 of maximum).
Fig. 11 Performance of a GRIN-Fresnel hybrid lens (1.8 mm diameter Ag ion doped GRIN lens combined with 23 zones Fresnel lens) in a confocal distance sensor. (a) Back reflected intensity from a mirror at two different wavelengths versus axial position. (b) Cross section of the focal spot in false color representation.
The hybrid GRIN and Fresnel lenses provide additional degrees of freedom for the design of demanding micro-optical systems. This is especially useful for the design of highly corrected systems concerning axial and lateral chromatic aberrations. However, the hybrid optical elements can also be used to enable high NA imaging systems. On the other hand, since GRIN and Fresnel lens are combined in a single monolithic component, no complexity is added to the adjustment and packaging of the micro-optical systems. Possible applications may include single point imaging sensors like proximity sensors and can extend to color-corrected microscope objectives with high numerical aperture for endoscopy applications [15].
Funding
German Federal Ministry for Economic Affairs and Energy in the framework of The Central Innovation Program for SMEs (ZIM).
Acknowledgments
We thank B. Messerschmidt, Grintech GmbH, Jena, Germany, for providing the GRIN lenses, the data of Fig. 11, and for helpful discussions.
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