3D-printing polymer optics using Printopticalc Technology can compliment, for prototyping and small series of production, the existing injection-molding mass manufacturing technology in terms of manufacturing cost. The print-ing error can be minimized by optimizprint-ing the printprint-ing parameters usprint-ing the calibration measurement data of the print-head nozzles [88]. This process helps to turn off nozzles with defects from depositing polymer droplets. The substrate is usually silanized before the polymer deposition process in order to ease the separation of the printed sample from the glass substrate [89].
The printing technology is limited to Lux-OpticlearTM material for now, which prohibits direct 3D-printing of achromatic lens systems. However, silicon molding and vacuum casting techniques [90] can be implemented with printoptical technology in order to increase the prototyping options of the lens material. As a result, polymer materials with Abbe numbers smaller or larger than that of Lux-OpticlearTM can be employed. In the future, a mixture of SiO2 nanoparticles and polymer material could be used to 3D print glass optics by modifying this technology and adding post-processing steps [91]. A mixture of TiO2 and Lux-OpticlearTM has been investigated in our research group for 3D-printing a high-refractive index apochromatic lens [92].
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4 SURFACE METROLOGY
The performance of the printed lens depends on the surface quality of the op-tics. Thus, accurate optical surface metrology is needed in order to check the form quality of the printed lenses. If the metrology of the fabricated optics is not performed well, the side effects can be immense as in the case of the famous Hubble Space Telescope [93]. Surface characterization of 3D-printed optics has been performed with techniques including an optical profilome-ter [94], inprofilome-terferometry [95] and a 3D Measuring Macroscope [96]. The next sections discuss briefly some of the measurement methods that are applied for characterizing the 3D-printed optics.
4.1 OPTICAL PROFILOMETER
An optical profilometer (see Fig. 4.1) is used to measure both the surface roughness of the printed lenses, using Phase-Shifting Interferometry (PSI) [97], and their surface profile deviation, using Vertical-Scanning Interferom-etry (VSI) [98].
Surface roughness measurement using PSI involves scanning the lens in vertical direction and measuring the phase-shift. However, PSI works only when the surface slope of the lens sample is below λ/4 between two ad-jacent sample data points; otherwise ambiguities due to multiples of half-wavelengths occur. VSI compliments this limitation of PSI and is used to measure the surface topography of the sample lens, see Fig. 4.1(b). The
! !
Figure 4.1: Optical profilometer: (a) Veeco Wyko-9300 and (b) internal schematic of white light interferometer (Courtesy of Veeco [99]).
ference image formed at the camera by combining the reference and scanned beam is used to characterize the surface being measured. The objective mag-nification determines the measurement area, i.e., higher-resolution images need higher-magnification objectives but are limited within a small area [94].
4.2 DEKTAK 150 SURFACE PROFILER
Dektak 150 surface profiler (see Fig. 4.2) is based on a stylus needle with a diamond tip that touches the surface of the sample with constant force (1−15 mg) to measure the surface profile using the information obtained while maintaining the constant force. It resolves 15 nm features (in the ver-tical direction) with a repeatability of 0.6 nm for up to 1 mm thick samples.
The profiler can measure a maximum sample length of 55 mm with vertical resolution of 0.1 nm [100].
Figure 4.2: Stylus profilometer (Courtesy of Veeco [100]).
4.3 MITUTOYO FORMTRACE CONTOUR MEASURING SYS-TEM
The Formtrace contour measuring system works by moving the needle with XY stage movement and contact with sample to be measured. The needle tip has a radius of 5.4μm [101]. Thus, this technique can introduce scratches on the sample and is suitable for measuring surface features greater than 5.4μm. It can measure a sample with maximum length of 100 mm, width of 200 mm and thickness of 60 mm with accuracy of 0.8 μm, 2μm and 2 μm, respectively.
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Sample
Z stage movement XY stage movement Niddle
Figure 4.3: Mitutoyo contour measuring system (Courtsy of Diamond Turning LAB, Karelia UAS ).
4.4 KEYENCE VR 3000 C 62288
The VR-3000 3D-surface profile measurement system, shown in Fig. 4.4, works by measuring the forms of the samples using a telecentric lens and
Telecenteric lens
XY stage for sample
Anti-vibration material
Figure 4.4: Contactless high-precision 3D measurement system (Courtesy of Keyence [96]).
a triangulation scanning system. This method can measure a sample with length of 184 mm, width of 88 mm and height of 90 mm. The height and width measurement accuracy using this technique is within ±3 μm and
±5μm, respectively. It can also resolve feature sizes up to 0.1μm.
4.5 TRIOPTICS IMAGEMASTERR HR
Trioptics ImageMasterHR device shown in Fig. 4.5 can be used to measure the modulation transfer function (MTF) of optics image resolution by illu-minating a slit as an object. Then the slit is imaged into the image plane of the sample. The slit image that is captured in the camera is not perfect due to diffraction and aberrations. The slit image corresponds to the line spread function (LSF) [102, 103]. The Fourier analysis of the LSF leads to MTF [104].
The measuring device has effective focal length accuracy of ± 0.2 % for focal length of 10 mm. The MTF accuracy across the on-off axis is 2%. The maximum spatial frequency that can be measured is around 1000 lp/mm.
Figure 4.5: Trioptics ImageMaster@HR device for image resolution mea-surement (Courtesy of Trioptics [105]).
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4.6 NULL-TEST MACH-ZEHNDER INTERFEROMETRY
Large-area surface profile deviations can be measured with an optical pro-filometer by combining different sample measurements using stitching tech-niques. However, we built a simple interferometric setup, shown in Fig. 4.6, to measure the wavefront errors of the printed lens against a reference lens.
A collimated laser beam of wavelength λ = 633 nm is split into two parts using a beam splitter. The beams pass separately through the 3D printed lens and the reference plano-convex lens (Thorlabs LA1509, diameter of 1 inch, focal length of 100 mm) before being recombined again using a beam combiner. Finally the interference pattern of the two refracted wavefronts formed by the lenses is detected using a camera after passage through an imaging objective.
The measurement of the interference fringes with a convenient spatial frequency is achieved by shifting the reference lens off-axis after ensuring the mean curvatures of the two output waves are equal by first arranging the lens positions along the optical axis. Since the lenses are placed with the planar surface facing the collimated beam, the reference wavefront has spherical aberration. However, if the 3D printed lens is identical with the ref-erence lens, it produces the same wave front as the refref-erence lens (the same amount spherical aberration) and straight fringes are seen. The wavefront retrieval technique introduced by Takeda et al. [95] is applied to the mea-sured interference pattern. Three images are captured in order to remove the effect of un-even illumination. The first image is captured with only the reference arm open (intensity profile I1), the second with only the object arm open (profile I2), and the third with both arms open (profile I). Then, the
Figure 4.6: Null-test Mach-Zehnder interferometer.
normalized fringe pattern is calculated using the formula Inorm = I−I1−I2
2√ I1I2
. (4.1)
Figure 4.7(a) shows an example of such a pattern.
In order to remove the dc peak from the Fourier transform of Inorm, Eq. (4.1) is limited to an interval [−1,+1]. Then the Fourier transform re-sult is cropped, as shown by the white rectangle in Fig. 4.7(b), to keep only one of the two Fourier peaks. The wrapped phase difference between the reference and object wave fronts, seen in Fig. 4.7(c), is then calculated by shifting the maximum intensity value to the center of the Fourier coordi-nates and applying the inverse Fourier transform. The unwrapped phase shown in Fig. 4.7(d) is finally constructed by adding integer multiples of 2π into the wrapped phase. The surface profile height can be calculated from the unwrapped phase using the method presented in Ref. [106].
Figure 4.7: Detection of the phase profile difference from a measured in-terferogram: (a) intensity-normalized interferogramInorm, (b) fourier trans-form ofInormand the cropping area, (c) wrapped phase and (d) un-wrapped phase.
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5 3D-PRINTED FREEFORM OPTICS
Printoptical technology, which was briefly introduced in Chapter 3, has been applied to 3D-print the freeform lenses designed in Chapter 2. The following sections demonstrate the printed lenses and their surface profile deviations from the desired surface shapes, which are presented and analyzed in Paper I and Paper II.
5.1 3D-PRINTED FREEFORM LENS: CASE STUDY 1
The Plano freeform lens shown in Fig. 5.1 (a and b) is 3D printed within 4 hours using a printing layer thickness of 4.1μm. No surface post processing (like polishing or coating) were used, which is usually necessary in other 3D-printing technologies [32]. The surface profile deviation of the printed lens from the design, shown in Fig. 5.1, was measured using the Formtrace surface contour measuring system (see Sec. 4.3). The result shows that the surface fidelity is±100μm. However, the surface measurement is done only at the center of the printed lens since the edges are almost vertical that are difficult to analyse with the needle-based contact measuring system.
The 3D-printed freeform lens for an industrial illumination application is shown in Fig. 5.2, together with its surface fidelity. Figure 5.2 shows the printed lens and its surface profile deviation measured using the Keyence VR-3000 wide area 3D measurement system. The measurement
Figure 5.1: Freeform lens for uniform rectangular distribution: (a) lens design, (b) 3D-printed lens and (c) surface profile deviation between the design and the 3D-printed lens.
Figure 5.2: Freeform lens for paper web illumination : (a) lens design, (b) top view of the 3D-printed freeform lens and (c) surface profile deviation between the design and printed lens.
strates a surface profile variation of ±40 μm at the center and ±100μm at the edge of the lens. The higher deviation at the edge of the lens is due to the challenge of accurately placing droplets at the exact location above 200 μm thickness. The RMS surface roughness of the printed lens is measured to be 10±2 nm (σ, N=25) using the Wyko optical profilometer.
Freeform lenses can be printed also in matrix format for rapid prototyp-ing, as shown in Fig. 5.3. Arrays of this type are often applied to improve the uniformity of illumination in, e.g., camera systems of the paper web case study by using LED arrays [2].
Figure 5.3: 3D printed freeform lens matrices 34
Figure 5.4: Freeform lens for LED light splitter case study: (a) design in mesh form, (b) top view of the 3D-printed freeform lens and (c) surface conformity between the design and printed lens.
The printed lenses can be used to make highly transparent lenses using silicone molding and isophorone diamine (5-Amino-1,3,3-trimethylcyclohexane-methylamine) based epoxy casting [2, 90, 107]. However, the surface feature precision of the lens could decreases due to uncontrolled environment. But for a smooth freeform lens, this replication technique could work.
Freeform lenses with trajectory surfaces have also been investigated for various beam shaping applications. Figure 5.4 shows the printed freeform lens that distributes a LED beam into rectangular five-spot target distribu-tion. An ATOS triple scan system [108] is applied to measure the shape con-formity between the design and lens. The surface shape deviation is within
±50 μm over a large area as shown Fig. 5.4(c), but at some sampling areas the surface profile deviation is measured to be around 100μm. The average surface roughness is measured to be Ra = 6.6 ±0.5 nm (σ, N = 25) and the RMS surface roughness is Rq = 12.3±0.8 nm (σ, N = 25) using the WYKO-NT9300 optical profilometer.
Similarly, the printed lens for MTF-like target distribution is shown in Fig. 5.5. The surface profile deviation between the design and fabricated lens varies between ±40 μm over the wider surface area. The deviations may be due to the droplet position error on the substrate that arise from atmospheric pressure, temperature, air moisture, and the like. The average surface roughness values are measured to be Ra= 8.6±0.8 nm (σ, N =25) and the RMS Rq=11.1±1 nm (σ, N=25) in the middle of the printed lens.
5.2 3D-PRINTED FREEFORM LENS: CASE STUDY 2
3D printing freeform lenses with complex surface features, as in the case of Lena target image, is challenging to achieve. However, we have printed and checked the surface profile deviation at the center of the top surface of the lens. The surface deviation varies from±50 μm at the center up to±100μm
Figure 5.5:Freeform lens for MTF like case study: (a) design in mesh form, (b) top view of the 3D-printed freeform lens and (c) surface conformity between the design and printed lens.
at the edge, as measured using the Formtrace contour measuring system.
However, the average surface roughness is measured to be around 12 nm as in the other case studies.
5.3 DISCUSSION
Realizing centimeter-scale freeform lenses within 3-5 hours, without any sur-face smoothing post-processing technique, has been demonstrated. Usually the surface roughness of the printed lenses is around 10 nm, which is accept-able optical quality. However, the surface profile deviation of the printed lens from the desired shape is tens of micrometers. This issue could be remedied (in the future) using real-time surface metrology while printing. It has been observed that when the thickness of the lens increases above 5 mm, the airflow inside the printer cabinet has a tremendous effect on the print-ing position of the droplets. Thus, in addition to surface metrology, further improving the printing conditions lead to lower surface figure deformity of the printed lens as demonstrated in next chapter. Expanding the printing process or printing area of 6×7 cm2 into industrial scale for swift small or medium volume production, as Luxexcel already does, can be accomplished by aligning more than three print-heads parallel to each other.
The printed lenses may sometimes have higher yellowness index which comes when high dosage UV-curing process is applied at the polymerization stage. Usually Blue-LED cabinets can be used to reduce this yellowness effect. The other post-processing technique used usually is to tint the lens by immersing it into a container of solution of organic dyes for a specific period of time.
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6 3D-PRINTED CONVENTIONAL OPTICS AND PHOTONICS ELEMENTS
The Luxexcel Printopticalc Technology, which was briefly introduced in Chapter 3, also has been applied to 3D-print conventional optics and pho-tonics elements. In this chapter we introduce a waveguide and a diffuser as examples of photonics elements, and a Fresnel lens as a non-imaging opti-cal component, in addition to a conventional spheriopti-cal imaging lens that is demonstrated in Paper III.
6.1 NON-IMAGING OPTICS: FRESNEL LENS
In home lighting systems, Fresnel lenses are usually preferred over spherical or aspherical lenses because of the decrease in packaging size of the optical system [109, 110]. Here, we investigate Printopticalc Technology for proto-typing the Fresnel lens designed in the following subsection.
6.1.1 Fresnel Lens Design
Illumination requirements for industrial applications as shown in Fig. 6.1 are challenging to meet even in design, especially when an array of LEDs is considered as a light source. Commercial software, like ZEMAX Opticstudio 16, has only limited non-sequential optimization capabilities, and ffOPTIK is limited to single-point-source approximation. Thus, we design the Fresnel lens using a custom algorithm. The design layout and the desired target distribution of an indoor illumination system are shown in Fig. 6.1, in which the LEDs and the Fresnel lens array are placed just one meter above the target distribution (3×3 m2). The design process consists of four steps:
first, the initial surface profile is calculated by one-dimensional mapping of the source energy into the desired target illumination considering extrusion based manufacturing technique [111]. The mapping technique presented in chapter 2 is also applied here by using only a one-dimensional single integral equation [112]. Second, the freeform surface are represented by gaussian basis functions.Third, the freeform surface is converted to fresnel surface by dividing into segments of equal width and different thickness [113]. Finally, the optimization is done by Monte Carlo technique [114].
Figure 6.1:Indoor illumination case study: (a) design layout, (b) LED array arrangement and (c) desired target distribution.
Figure 6.2(a & b) shows the designed Fresnel lens and its zoom out fea-tures considering two LEDs (size of 2.3×4.6 mm2) separated by 9.7 mm and placed 18.2 mm away from the lens. The ray-trace simulation of the fres-nel lens using 200×103 rays in MATLAB as shown in Fig. 6.2(c) is in close proximity with the required target distribution, see Fig. 6.2(d). The cross-sectional radiant intensity of the simulation in Fig. 6.2(e) clearly shows the resemblance, and also the deviation from the required target in Fig. 6.2(f).
6.1.2 3D-Printed Fresnel Lens
The designed Fresnel lens is printed in four parts since the printing area of the 3D-printer is (7×7 cm2). Figure 6.3(a) shows a quarter (5.9×5.9 cm2) of the designed lens. The printed lenses are assembled as shown in Fig. 6.3 and the assembly performance is investigated in Chapter 7. The printing takes place within 40 minutes, and a high UV-polymer curing process has been applied in order to make the sharp edge and form the prism surfaces.
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Figure 6.2: Simulation results for indoor illumination case study: (a) de-signed lens profile and (b) its zoom in features. (c) Desired target irradiance and (d) simulated irradiance distributions.
Figure 6.3: 3D-printed Fresnel lens: (a) one quarter and (b) the full array of assembled 3D-printed Fresnel lenses.
6.2 IMAGING LENS
We proceed to explore the feasibility of manufacturing imaging quality 3D printed optics using Printopticalc Technology.
6.2.1 Plano-convex Spherical Lens Design
We chose to design a simple plano-convex spherical lens that can be com-pared with an off-the-shelf commercial lens with parameters shown in Table 6.1.
Table 6.1: Lens parameters
Lens Material LUX-OpticlearTM N-BK7
Radius of Curvature (mm) 51.5 51.5
f# (mm) 8.25 8.33
Diameter (mm) 25.4 25.4
Abbe number 45 64.17
Refractive indexnatλ=588 nm 1.53 1.51
As a proof-of-concept, the designed lens is optimized atλ=486 nm, a center wavelengthλ=588 nm andλ=656 nm. The simulated optical performance and image resolution of the lenses is compared in Fig. 6.4 using the Huygens point spread function (PSF) in Zemax OpticStudio 16. The image resolution is around 5 μm for both N-BK7 and LUX-Opticlear lenses using an aperture of 12 mm.
-35 -25 -15 -5 0 5 15 25 35
Lateral cross section ( m) 0
N-BK7 with 12 mm aperture LUX-Opticlear with 12 mm aperture N-BK7
LUX-Opticlear
Figure 6.4:Point spread function comparison of N-BK7 and LUX-Opticlear lenses.
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6.2.2 3D-Printed Spherical Lens
Null-test Mach Zehnder interferometry metrology technique presented in Chapter 4 is implemented to iteratively compensate the surface profile devi-ation on the design part, thus the sliced layers for printing are modified for example as shown in Fig. 6.5 [4]. The spherical lens in Fig. 6.6(a) is obtained after five iterations between the 3D-printing process and surface metrology.
As a result, the surface figure deformation between the design and the 3D-printed lens is decreased from±5μm into less than±500 nm within a 12 mm aperture diameter as shown in Fig. 6.6(b) [4].
Figure 6.5: Sliced layer pixels after error-correction layer.
Figure 6.6: Imaging lens: (a) 3D-printed lens and (b) surface profile devia-tion after 5 iteradevia-tions using a 12 mm aperture.
Using The Wyko optical profilometer, the average (RMS) surface rough-ness values of the 3D printed lens were measured to be Rq=0.93±0.33 nm (σ, N=25) and Ra=0.712±0.25 nm (σ, N=25) as shown in Fig. 6.7.
Figure 6.7: Surface roughness of 3D-printed lens: (a) a 2D map of the surface over an area of 60μm×50μm and (b) cross-sectional surface profile at the center in nanometer scale.
6.3 PHOTONICS ELEMENT: DIFFRACTION GRATING
3D printing photonics elements such as diffraction gratings is one of the promising areas of Printopticalc Technology. Here we investigate 3D-printing a binary grating in the TeraHerz (THz) region of the spectrum for realization of a guided-mode resonance filter [115,116]. The refractive index of Opticlear material is measured in the THz range using TeraPulse 4000 [117] as shown in Fig. 6.8.
Figure 6.8: Refractive index of Lux-Opticlear based thin plate at the
Figure 6.8: Refractive index of Lux-Opticlear based thin plate at the