7.2 Fresnel and Conventional Lenses
7.2.2 Imaging Optics: Spherical Lens
Figure 7.7: Experimental setup for testing the Fresnel lens array: (a) 3D-printed Fresnel lens array placed in a lighting box and (b) the Fresnel lens array with LEDs. (c) Layout of the goniometer and (d) the measured target distribution.
Figure 7.8: Target distribution for the Fresnel lens arrays. (a) simulation, (b) printed (full intensity) and (c) printed (80% intensity).
7.2.2 Imaging Optics: Spherical Lens
The 3D printed spherical lens was characterized by constructing a micro-scope setup illustrated in Fig. 7.9 and resolving a USAF 1951-IX MTF (Ed-mund Optics) resolution test target. Then, the imaging resolution of the 3D-printed lens in contrast to the Thorlab LA1509 N-BK7 lens was measured using the Modulation Transfer Function (MTF) in reflection mode. The
chro-Camera Detector
Light collimating tube Aperture 3D printed objective lens
USAF 1951-1X Resolution tarrget Light Source
Spectral filter
Figure 7.9: Experimental setup of a microscope in reflection mode to char-acterize the 3D-printed lens image resolution.
matic aberration of the spherical (singlet) lenses was eliminated using a spec-tral filter centered at 550 nm and having a 100 nm passband.
Figure 7.10 demonstrates the imaging resolution of the printed and com-mercial N-BK7 singlet lenses. Considering the image resolving power of the human-eye, we used 10% MTF as a threshold. Thus, considering Fig. 7.10(c), the two elements of Group 7 corresponding to 143.7 lines/mm of the USAF resolution target are resolved by the 3D-printed lens. However, element 3 of group 7, which corresponds to 161.3 lines/mm, is resolved clearly by the commercial lens. The lower resolution of the 3D-printed lens could be due to the surface profile deviations and/or the non-uniformity of the material inside the printed lens as compared to the commercial glass lens.
In comparison, Trioptics ImageMaster HR imaging quality testing de-vice [105], see Sec. 4.5, was applied to check the optical performance of the 3D-printed lens. The experimentally measured MTF values shown in Fig. 7.11 demonstrate that the MTF curve for the 3D printed and reference lenses are close to each other but below the diffraction limit. Zernike polyno-mial is used in Zemax Optic Studio 16 to aproximate the surface irregularity shown in Fig. 6.6 on the spherical lens design [127]. The imaging resolutions are recorded to be 125 lp mm−1 and 135 lp mm−1 at the 10% MTF thresh-54
Figure 7.10: Experimental imaging resolution comparison between the 3D printed and commercial singlet lenses. Record of the USAF 1951-1X MTF resolution target image for (a) the 3D-printed lens and (b) a commer-cial NBK-7 singlet lens with an aperture diameter of 12 mm using a green bandpass filter centered at 550 nm. Group 6-7 resolution target for the (c) 3D-printed and (d) commercial lenses. Magnified images of Group 7 in (e) and (g), and cross-sectional intensity profiles in (f). The red line marks the results with the printed lens and light blue with the reference lens.
old, respectively, which are comparable to the results found using the USAF 1951 resolution target. The common limitations of polymer optics, such as scratch, could be the reason for the difference in the MTF curves. The
mea-sured focal length of the printed lens is within±3% tolerance value from the target, relative to ±1% for the commercial lens. This result demonstrates an advancement in optical performance to the first batch of 3D printed lenses by Luxexcel [128].
0 20 40 60 80 100 120 140 160 180 200
Spatial Frequency [lp/mm]
0 0.1 0.2 0.4 0.6 0.8 1
Modulus of OTF
Measured result for Thorlab LA1509 N-BK7 lens Simulation result for ideal Thorlab LA1509 N-BK7 lens Diffraction limit for Thorlab LA1509 N-BK7 lens Measured result for LUX-Opticlear 3D-printed lens Simulation result for ideal LUX-Opticlear 3D-printed lens Diffraction limit for LUX-Opticlear 3D-printed lens Simulation result for LUX-Opticlear 3D printed lens considering surface profile deviation
Figure 7.11:MTF measurement results with ImageMaster (HR)
The 3D-printed lens can be used on various low-cost application areas like dermascope [42], field imaging [129], and even as a microscope objective lens for resolving subpixels of LCDs, as demonstrated in Fig. 7.12. Other appli-cation areas of 3D printed lens could be found in low-cost Digital single-lens reflex (DSLR) mini cameras as shown in Fig. 7.13. The qualitative imaging results of the singlet lens show that the printed lens works relatively well, bearing in mind it is a simple plano-spherical lens.
The 3D-printed plano-convex lenses can be combined with diffractive structures using other patterning or fabrication techniques in order to im-prove the performance of the lens or to introduce new functionalities [130].
Thus, the technique presented here can be used as a starting step for 3D printing centimeter scale lenses for various applications such as full-functional eyepiece, which has been attempted in our group [131].
56
Figure 7.12: Resolution of LCD display pixels using the 3D-printed lens:
(a) LCD display and (b) resolved sub-pixels using the printed lens.
Figure 7.13: DSLR camera using 3D-printed lens : (a) the printed lens on the DSLR camera using mount and (b) arbitrary image taken through it.
7.3 DISCUSSION
The surface quality of the printed freeform lenses, especially the surface fig-ure deformation, is the main reason for the deviations of the experimental results from the theoretical simulations. The material inhomogeneity of the printed lens that arises due to the printing process introduces a scattering effect, which leads to degradation on the optical performance like the uni-formity of the target distribution. To minimize this issue, we optimize the printing process. However, the size of the LED light source, fabrication error, and misalignment while characterizing the printed lens are the major con-tributor for the required target irradiance shape deformation. However, the surface measurement techniques for cm-scale freeform lenses are limited in accuracy and capability; for example, a steep surface cannot be measured using a Mitutoyo Formtrace contour measuring system. Thus, the measure-ment has been done only at the center of the printed lens using this device
for a relatively smooth surface withinμm scale accuracy. This becomes a bot-tleneck for doing an extensive analysis of the fabrication error; future work can be done in this area. On the other hand by using wavefront surface-error correction techniques, the surface profile deviation of the printed spherical lens for imaging case has been decreased dramatically, permitting the manu-facturing of imaging-quality optics. At present, the technique only works for spherical wavefronts, but it can be upgraded in order to be used for freeform lenses by employing reference wavefronts generated with the aid of diffrac-tive/refractive hybrid elements.
In general, increasing the optical quality will lead to better optical per-formance. This can be achieved using new high-index printing materials, live surface error correction techniques, and by optimizing the printing pro-cess for individual cases. The shape of the printed lenses can be formed accurately by using thin layers (< 4.1 μm), since the lens is formed using staircase-based approximation of the spherical geometry. Such thin layers can be attained by using a smaller droplet size, < 17 μm in diameter. The small size of the droplets can also become useful in the error-correction it-eration stage. While placing each droplet at the exact location can become challenging, it could be manageable by learning the droplet location within the printing stage. This, however, might also increase the printing time.
58
8 SUMMARY AND OUTLOOK
In this thesis, designing optical elements such as free-form lenses using a source-to-target ray-mapping algorithm, as well as prototyping or small se-ries production of the designed elements using a 3D-printing technology called Printopticalc Technology has been proposed and demonstrated. As an example, freeform lenses are designed for shaping a LED source dis-tribution into a uniform rectangular target disdis-tribution and complex target images. The performance of the proposed algorithm is comparable to other designing methods found in semi-commercial software, with an advantage of being customizable for various tasks. In addition, the numerical analy-sis of manufacturing defects on the performance of the designed freeform lenses have been investigated, and the results illustrate the sensitivity of the complex target illumination on submicrometer surface figure deformity of freeform lenses. Even if the freeform lens designing methods are sufficient for the proposed 3D-printing manufacturing technology, further work can be done on the designing method like by expanding the custom algorithm into designing two freeform surfaces simultaneously for illumination application using an extended source.
Prototyping of centimeter-scale optics using the 3D-printing fabrication technique to reduce the manufacturing cost, time, and material waste has also been proposed and demonstrated. Printopticalc Technology has been applied to print the optics by optimizing the printing process specific to each case. In order to place the Lux-OpticlearTMpolymer droplets from the print-head at the exact intended location, thorough experimental measurements have been performed that lead to a dramatic reduction of the surface fig-ure deformity on the printed lens. Printing errors caused by nozzle defects or other external sources have been minimized by optimizing the printing parameters and by compensating the error on the design.
3D-printing of centimeter-scale lenses for non-imaging applications has been demonstrated; here the surface quality requirements are lower than in the case of imaging lenses. The challenge with macroscopic imaging-quality optics has been addressed, considering a spherical lens as a test case, by applying a null-test Mach–Zehnder interferometric setup as a fast surface-error correction technique. The optical performance of the printed lens for illumination case studies show a promising results that are comparable to the desired target illumination.
However, 3D printing freeform lenses with sub-micrometer surface fea-tures demand droplets with smaller size and a high UV-curing polymer-ization process, which increases the yellowness index of the lens. On the
contrary, the optical performance of the printed imaging lens is measured to be close to a commercial reference lens. It is also possible to print achromatic lenses using a combination of different polymer materials in the customized printing technology.
The Printopticalc Technology is used with silicon molding and vacuum casting techniques to switch from Lux-Opticlear TM into another lens mate-rial. The presented Mach–Zehnder testing setup can also be expanded using diffractive elements in the reference arm so that aspheric or freeform lenses could be measured. It has also been demonstrated that diffraction gratings can be 3D printed at least for the millimeter wavelength spectral region.
However, it was observed that the Printopticalc Technology is more suitable for fabricating sinusoidal than binary gratings.
One of the highlights of this thesis is the first demonstration of a centimeter-scale imaging-quality 3D-printed lens. This development paves the way to-wards an expansion of the 3D printing process into more general imaging systems that can be achromatic and involve aspherical elements. The ulti-mate goal in non-imaging applications can be printing freeform lenses or reflectors with sub-micrometer surface feature structures that have been the-oretically demonstrated for complex target images. Moreover, 3D-printed re-flectors with complex freeform surface will introduce additional challenges on the printing process. For instance, while smoothing the surface roughness of the parabolic freeform reflector the droplets tend to fall and accumulate at the center of the surface that leads to destroying the complex geometry of the surface. Thus, new way of printing process is required at this area.
In addition to 3D printed imaging and beam-forming optics, printing photonics elements such as slab waveguides, diffraction gratings, beam split-ters, and diffusers is also possible by optimizing the printing parameters us-ing printhead calibration measurements. The iterative error correction tech-niques, already investigated in this thesis preliminarily, can be developed towards live monitoring while printing rather than after the component is printed. Graded Index (GRIN) lenses can also be designed and 3D printed fast, using a combination of of two carefully selected materials without any post processing. As a result, this technology provide an extra degree of free-dom for the optics designer.
60
BIBLIOGRAPHY
[1] B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “3D printed plano-freeform optics for non-coherent dis-continuous beam shaping,”Opt. Rev.25, 456–462 (2018).
[2] B. G. Assefa, T. Saastamoinen, J. Biskop, V. Nissinen, M. Kuittinen, J. Turunen, and J. Saarinen, “Realizing freeform lenses using an optics 3D-printer for industrial based tailored irradiance distribution,”OSA Continuum2, 690–702 (2019).
[3] B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,”Proc. SPIE10554, 105541J (2018).
[4] B. G. Assefa, H. Pertanen, M. Pekkarinen, J. Biskop, J. Turunen, and J. Saarinen, “Imaging-quality 3D printed centimeter-scale lens,” Opt.
Express27, 12630–12637 (2019).
[5] B. G. Assefa, H. Partanen, M. Pekkarinen, J. Biskop, J. Turunen, and J. Saarinen, “Imaging-quality 3D printed inch scale lenses with 10 Å surface quality for swift small or medium volume production,” Proc.
SPIE10915, 1091504 (2019).
[6] J. Saarinen, B. G. Assefa, M. Pekkarinen, and J. Biskop, “3D printing for versatile optics,”Proc. SPIE10675, 1067502 (2018).
[7] B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” The Eleventh Japan-Finland Joint Symposium on Optics in EngineeringOIE2015, 72 (2015).
[8] A. Halder, M. Koivurova, B. G. Assefa, M. Pekkarinen, and J. Turunen,
“Temporal and spectral coherence modulation of pulse trains by rotat-ing diffusers,”OSA papers (Manuscript)(2019).
[9] C. Teyssier and C. Tribastone, “Plastic optics : challenging the high-volum myth,”Lasers & OptronicsDec., 50–53 (1990).
[10] J. Lytle, Polymeric Optics(McGraw-Hill, New York, 1995).
[11] P. Tolley, “Polymer optics gain respect,”Photon. spectra37, 76–79 (2003).
[12] P. Vilmi, S. Varjo, R. Sliz, J. Hannuksela, and T. Fabritius, “Disposable optics for microscopy diagnostics,”Sci. Rep.5, 16957 (2015).
[13] O. Cakmakci, K. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “De-sign of a free-form single-element head-worn display,”Proc. SPIE7618, 761803 (2010).
[14] F. Fang, N. Zhang, and X. Zhang, “Precision injection molding of freeform optics,”Adv.Opt.Techn.5, 303–324 (2016).
[15] R. Rashed, “A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses,”I.S.I.S.81, 464–491 (1990).
[16] E. Abbe, “Lens system,”U.S. Patent697/959(1902).
[17] M. Born and E. Wolf, Principle of Optics(Pergamon Press, 1998).
[18] C. Kanolt, “Multifocal opthalmic lenses,”U.S. Patent2(878):721(1959).
[19] L. W. Alvarez, “Two-element variable-power spherical lens,” U.S.
Patent No.3,305,294(1967).
[20] W. T. Plummer, “Unusual optics of the Polaroid SX-70 land camera,”
Appl. Opt.21, 196–202 (1982).
[21] W. T. Plummer, “Photographic optical systems with nonrotational as-pheric surfaces,”Appl. Opt.38, 3572–3592 (1999).
[22] J. Owen, J. A. Shultz, T. J. Suleski, and M. A. Davies, “Error correction methodology for ultra-precision three-axis milling of freeform optics,”
CIRP Annals-Manufacturing Technology66(2017).
[23] D. Gurganus, J. D. Owen, B. S. Dutterer, S. Novak, A. Symmons, and M. A. Davies, “Precision glass molding of freeform optics,”Proc. SPIE 10742(2018).
[24] E. Fess, J. Ross, and G. Matthews, “Grinding and polishing of confor-mal windows and domes,”Proc. SPIE10179(2017).
[25] T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives„”Nature Pho-ton.10, 554–560 (2016).
[26] S. Thiele, K. Arzenbacher, T. Gissibl, H. Giessen, and A. M. Herkom-mer, “3D-printed eagle eye: Compound microlens system for foveated imaging,”Sci. Adv.3, e1602655 (2017).
[27] Z. Hong and R. Liang, “IR-laser assisted additive freeform optics man-ufacturing,”Sci. Rep.7, 7145 (2017).
62
[28] C. Hull, “Apparatus for production of three-dimensional objects by stereolithography,”U.S. Patent No.4(1986).
[29] E. Sachs, M. Cima, and J. Cornie, “Three dimensional printing:rapid tooling and prototypes directly from a CAD model,”J. Eng. Ind. 114, 481–488 (1992).
[30] E. Sachs, M. Cima, and J. Cornie, “Life-cycle economic analysis of dis-tributed manufacturing with open-source 3-D printers,” Mechatronics 23, 713–726 (2013).
[31] T. Caffrey, T. Wohlers, and I. Campbell, Wholers Report 2017 :3D Print-ing and Additive ManufacturPrint-ing State of the Industry Annual Worldwide Progress Report(Wholers Association Inc, 2017).
[32] N. Vaidya and O. Solgaard, “3D printed optics with nanometer scale surface roughness,”Microsyst. and Nanoeng.4, 713–726 (2018).
[33] B. Steyrer, B. Busetti, G. Harakaly, R. Liska, and J. Stampfl, “Hot Lithography vs. room temperature DLP 3D-printing of a dimethacry-late,”Addit. Manuf.21, 209–214 (2018).
[34] Y. Wang, J. Gawedzinski, M. Pawlowski, and T. Tkaczyk, “3D printed fiber optic faceplates by custom controlled fused deposition model-ing,”Opt. Express26, 15362–15376 (2018).
[35] K. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed Optics: 3D Printing of embedded optical elements for interactive de-vices„” in UIST’12: Proceedings of the 25th Annual ACM symposium on user interface software and technology589-598 (2012).
[36] Y.-L. Sung, J. Jeang, C.-H. Lee, and W.-C. Shih, “Fabricating op-tical lenses by inkjet printing and heat-assisted in situ curing of polydimethylsiloxane for smartphone microscopy,” J. Biomed. Opt.20, 047005 (2015).
[37] M. Blattmann, M. Ocker, H. Zappe, and A. Seifert, “Jet printing of convex and concave polymer micro-lenses,” Opt. Express 23, 24525–
24536 (2015).
[38] Z. Gan, Y. Cao, R. Evans, , and M. Gu, “Three-dimensional deep sub-diffracion optical beam lithography with 9 nm feature size,”Nat. Com-mun.4, 2061 (2013).
[39] S. Thiele, T. Gissibl, H. Giessen, and A. M. Herkommer, “Ultra-compact on-chip LED collimation optics by 3D femtosecond direct laser writing,”Opt. Lett.41, 3029–3032 (2016).
[40] S. Lightman, G. Hurvitz, R. Gvishi, and A. Arie, “Tailoring lens func-tionality by 3D laser printing,”App. Opt. 56, 9038–9043 (2017).
[41] J. Kim, N. B. Brauer, V. Fakhfouri, D. Boiko, E. Charbon, G. Grutzner, and J. Brugger, “Hybrid polymer microlens arrays with high numeri-cal apertures fabricated using simple ink-jet printing technique,” Opt.
Mater. Express1, 259–269 (2011).
[42] W. M. Lee, A. Upadhya, P. J. Reece, and T. G. Phan, “Fabricating low cost and high performance elastomer lenses using hanging droplets,”
Opt. Express5, 1626–1635 (2014).
[43] X. Chen, W. Liu, B. Dong, J. Lee, H. O. Ware, H. F. Zhang, and C. Sun,
“High-Speed 3D printing of Millimeter-size customized aspheric imag-ing lenses with sub 7 nm surface roughness,”Adv. Mater. 30, 1705683 (2018).
[44] Intel chip performs 10 trillion calculations per second, Valid on 04/3/2019, https://newsroom.intel.com/news/
intel-chip-performs-10-trillion-calculations-per-second/
#gs.3kpftw(visited on 2019-04-03).
[45] LightTools Illumination Design Software, https://www.synopsys.
com/optical-solutions/lighttools.html(visited on 2018-10-01).
[46] Zemax OpticStudio 2016 software, https://www.zemax.com/
products/opticstudio(visited on 2018-10-01).
[47] ffOptik-Free-Form Illumination Optics, , http://www.ffoptik.com (visited on 2018-07-02).
[48] M. P. Schaub, The Design of Plastic Optical Systems (SPIE Press, Belling-ham, Washington, 2009).
[49] K. Blessing and R. van de Vrie, “Print head, upgrade kit for a con-ventional inkjet printer, printer and method for printing optical struc-tures,”U.S. Patent Application No.13/924,974(2012).
[50] H. Ries and J. Muschaweck, “Tailored freeform optical surfaces„” J.
Opt. Soc. Am. A.19, 590–595 (2002).
[51] A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Al-gorithm for irradiance tailoring using multiple freeform optical sur-faces,”Opt. Express20, 14477–14485 (2012).
[52] J. A. Shultz, Design, Tolerancing, and Experimental Characterization of Dynamic Freeform Optical Systems, PhD thesis (The University of North Carolina at Charlotte, 2017).
64
[53] A. M. Herkommer, “Advances in the design of freeform systems for imaging and illumination applications,”J. Opt.43, 261–268 (2014).
[54] What is Freeform Optics, created 02/10/2017, http://
centerfreeformoptics.org/what-is-freeform-optics/ (visited on 2019-04-12).
[55] K. Fuerschbach, Freeform, phi-Polynomial Optical Surfaces: Optical De-sign, Fabrication and Assembly, PhD thesis (University of Rochester, 2014).
[56] O. Cakmakci, B. Moore, H. Foroosh, and J. Rolland, “Optimal local shape description for rotationally nonsymmetric optical surface design and analysis,”Opt. Express16, 1583–1589 (2008).
[57] C. Brecher, S. Lange, M. Merz, F. Niehaus, C. Wenzel, M. Winter-schladen, and M. Weck, “NURBS based ultra-precision free-form ma-chining,”CIRP Ann.- Manuf. Techn.55, 547–550 (2006).
[58] T. Nakano and Y. Tamagawa, “Configuration of an off-axis three-mirror system focused on compactness and brightness,”App. Opt.44, 776–783 (2005).
[59] K. Fuerschbach, J. Rolland, and K. Thompson, “A new family of optical systems employing phi polynomial surfaces,” Opt. Express19, 21919–
21928 (2011).
[60] G. W. Forbes, “Characterizing the shape of freeform optics,” Opt. Ex-press20, 2483–2499 (2012).
[61] F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans,
“Manufacturing and measurement of freeform optics„” CIRP Ann.
Manuf. Techn.62, 823–846 (2013).
[62] J. Schruben, “Formulation of a reflector-design problem for a lighting fixture,”J. Opt. Soc. Am. 62, 1498–1501 (1972).
[63] P. Benitez, J. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,”Opt. Eng.43, 1489–1502 (2004).
[64] W. Parkyn, “Design of illumination lenses via extrinsic differential geometry,”Proc. SPIE3428, 154–162 (1998).
[65] M. Knott and C. Smith, “On the optimal mapping of distributions,”J.
Optim. Theory43, 39–49 (1984).
[66] J.-D. Benamou, Y.Brenier, and K. Guittet, “The Monge-Kantorovich mass transfer and its computational fluid mechanics formulation,”Int.
J. Numer. Meth. Fluids40, 21–30 (2002).
[67] S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comp. Vis. 60, 225–240 (2004).
[68] M. M. Sulman, J. F. Williams, and R. D. Russel, “An efficient approach for the numerical solution of Monge Ampère equation,” Appl. Numer.
Math.61, 298–307 (2011).
[69] R. Wester, G. Müller, A. Völl, M. Berens, J. Stollenwerk, and P. Loosen,
“Designing optical free-form surfaces for extended sources,” Opt. Ex-press22, A552–A560 (2014).
[70] F. Fournier, Freeform Reflector Design with Extended Sources, PhD thesis (University of Central Florida, 2010).
[71] V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric methods,”Opt. Express25, A58–A72 (2017).
[72] K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufactur-ing defects on optical performance of discontinuous freeform lenses,”
Opt. Express17, 5457–5465 (2009).
[73] I. Moreno, C.-C. Sun, and R. Ivanov, “Far-field condition for light emitting diode arrays,”Appl. Opt.48, 1190–1197 (2013).
[74] Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform
[74] Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform