Designing and 3D-printing optical components for imaging, illumination and photonics applications : a case study based on printoptical technology

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uef.fi

PUBLICATIONS OF

THE UNIVERSITY OF EASTERN FINLAND Dissertations in Forestry and Natural Sciences

ISBN 978-952-61-3191-7 ISSN 1798-5668

Dissertations in Forestry and Natural Sciences

DISSERTATIONS | BISRAT GIRMA ASSEFA | DESIGNING AND 3D-PRINTING OPTICAL COMPONENTS FOR... | No 352

BISRAT GIRMA ASSEFA

DESIGNING AND 3D-PRINTING OPTICAL COMPONENTS FOR IMAGING, ILLUMINATION AND PHOTONICS APPLICATIONS:

A Case Study Based on Printoptical^© Technology

PUBLICATIONS OF

THE UNIVERSITY OF EASTERN FINLAND

This thesis addresses a scientific in-depth study of Printoptical© Technology by designing and characterizing 3D-printable optical components using LUX-Opticlear™

polymer material. Freeform optics for illumination applications are considered as

a focal point in the study. Furthermore, a centimeter-scale 3D-printed plano-convex lens is demonstrated for imaging application.

Lastly, designing and 3D-printing a fresnel lens, binary diffractive grating and diffuser

are briefly discussed.

BISRAT GIRMA ASSEFA

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PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND DISSERTATIONS IN FORESTRY AND NATURAL SCIENCES

N:o 352

Bisrat Girma Assefa

DESIGNING AND 3D-PRINTING OPTICAL COMPONENTS FOR IMAGING, ILLUMINATION AND

PHOTONICS APPLICATIONS:

A CASE STUDY BASED ON PRINTOPTICAL

^c

TECHNOLOGY

ACADEMIC DISSERTATION

To be presented by the permission of the Faculty of Science and Forestry for public examination in the Auditorium M101 in Metria Building at the University of Eastern Finland, Joensuu, on October 18, 2019, at 12 o’clock.

University of Eastern Finland Institute of Photonics

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Grano Oy Jyväskylä, 2019

Editors: Pertti Pasanen, Jukka Tuomela, Raine Kortet, and Matti Tedre

Distribution:

University of Eastern Finland Library / Sales of publications julkaisumyynti@uef.fi

http://www.uef.fi/kirjasto

ISBN: 978-952-61-3191-7 (print) ISSNL: 1798-5668

ISSN: 1798-5668 ISBN: 978-952-61-3192-4 (pdf)

ISSNL: 1798-5668 ISSN: 1798-5676

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Author’s address: University of Eastern Finland Institute of Photonics

P.O. Box 111 80101 JOENSUU FINLAND

email: bisrat.assefa@uef.ﬁ

Supervisors: Professor Jyrki Saarinen, D.Sc.(Tech) University of Eastern Finland Institute of Photonics

email: jyrki.saarinen@uef.ﬁ

Professor Markku Kuittinen, Ph.D.

email: markku.kuittinen@uef.ﬁ Professor Jari Turunen, Ph.D.

email: jari.turunen@uef.ﬁ

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Reviewers: Professor Youri Meuret, Ph.D.

ESAT/Light & Lighting Laboratory Faculty of Engineering Technology Gebroeders De Smetstraat 1

BE-9000 GHENT BELGIUM

email: youri.meuret@kuleuven.be Professor Jouni Partanen, Ph.D.

Aalto University

Department of Mechanical Engineering P.O. Box 11000

02150 ESPOO FINLAND

email: jouni.partanen@aalto.ﬁ Opponent: Professor Alois Herkommer, Ph.D.

Universität Stuttgart

Institut für Technische Optik P.O. Box D 70569

Pfaffenwaldring 9 STUTTGART GERMANY

email: herkommer@ito.uni-stuttgart.de

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Bisrat G. Assefa

Designing and 3D-printing optical components for imaging, illumination and photonics applications: a case study based on Printoptical^c Technol- ogy

Joensuu: University of Eastern Finland, 2019 Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences N:o 352

ABSTRACT

Designing and fabricating optical components can be challenging depending on the shape and geometry of the optical surface, such as in the case of freeform optics. Freeform optics has recently been applied in various application areas, where the size and efﬁciency of the system are important parameters.

This work contains theoretical, numerical, and experimental studies on freeform optics design and 3D-printing using Printoptical^c Technology. In particular, the goal is to decrease the temporal gap that exists between optics design and fabrication stages by using 3D-printing for prototyping. As a result, an optical designer can realize his design by fabricating the designed component using a 3D-printer optimized for polymer optics manufacturing, with at most little help from the operator. This opens unprecedented potential for the designer to correct or optimize his design within a matter of days using feedback from the printed lens. The research also led to realizing a simple plano-convex lens with surface precision of imaging quality using Lux-Opticlear^TMmaterial in the Printoptical^c Technology by applying a surface error correction technique.

A theoretical and experimental investigation of photonic elements such as binary grating and diffusers have also been carried out by considering Printoptical^c Technology as the micro-fabrication technique. The investigation show that the possibility of 3D-printing sinusoidal grating for guided- mode resonance ﬁlter. In addition, the printing technology can be applied to 3D-print a functional multifaceted diffuser that generate a partial coherent pulse trains out of fully coherent pulse train.

Universal Decimal Classiﬁcation: 535.3, 535.4, 535.8, 62-4,681.5, 681.7

OCIS codes:110.2945, 110.0110, 220.0220, 239.0230, 050.1950, 080.3630, 080.4298, 120.4610

Keywords: Optical design; Optics fabrication; 3D Printed Optics; Freeform optics;

Imaging optics; Diffraction gratings; Resonance ﬁlters; Diffusers

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ACKNOWLEDGEMENTS

This thesis work happen due to the utmost encouragement and technical support from various person. I was privileged to work with Prof. Jari Turunen, Prof. Markku Kuittinen and the current Head of Department of Physics and Mathematics, Prof. Jyrki Saarinen. I would like to thank them for each unique ways of guidance and persistent support. I would like to also express my gratitude to Dr. Toni Saastamoinen, without his technical support this could not be possible. I am also thankful to Dr. Henri Partanen and Markku Pekkarinen whom I am able to work with for the past two years.

Since the thesis work involves from the designing upto characterization stage, it provides me a platform to know and work with other talented people worth mentioning from both the academic and industrial partners. These are Docent Jani Tervo, Dr. Ville Kontturi, Dr. Anni Eronen, Dr. Ville Nissinen, Dr. Pertti Silfsten, Dr. Pertti Pääkkönen, Dr. Petri Karvinen, Joris Biskop and Olli Ovaskainen.

I am grateful for the comments and suggestions from the reviewers of this thesis, Prof. Youri Meuret and Prof. Jouni Partanen. I want to mention also the former heads of the department Prof. Pasi Vahimaa, Prof. Seppo Honkanen and Prof. Timo Jääskeläinen for providing me the opportunity to work in a proliﬁc research area. My sincerest gratitude goes to Dr. Noora Heikkilä, Ms. Katri Mustonen, Ms. Hannele Karppinen, and Ms. Marita Ratilainen for the assistance at the administrative level.

Finally, I would like to thank my family, friends and all loved ones.

Helsinki Area, September 11, 2019 Bisrat Girma Assefa

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LIST OF ABBREVIATIONS

3D three dimensional

BS beam splitter

CAD computer aided design DLP digital light processing

EHD electrohydrodynamic

FDM fused deposition modelling

IR infrared

LCD liquid crystal display LED light emitting diode

MTF modulation transfer function

NCC normalized cross correlation coefﬁcient NURBS non-uniform rational B-splines

PC polycarbonate

PDMS polydimethylsiloxane PET polyethylene terephthalate PMMA poly methyl methacrylate

PS polystyrene

PSF point spread function

PSI phase-shifting interferometry

RMS root mean square

RRMSD relative root-mean square deviation

SLA stereolithography

SLS selective laser sintering

SMS simultaneous multiple surface

UV ultraviolet

VSI vertical scanning interferometry XML extensible markup language

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LIST OF SYMBOLS

r0 position of a ray vector at the source kin directional unit vector of the incident ray krf directional unit vector of the refracted ray

p scalar parameter

λ wavelength

N surface normal vector

LM Levenberg-Marquardt objective function

C transportation cost

pd period of binary grating c ridge width of binary grating h height of binary grating

Ra average of the absolute height proﬁle deviations

Rq root mean square average of the proﬁle height deviations

σ standard deviation

m order of the lambertian source emission

ψ convex scalar function

f mapping function in x-direction g mapping function in y-direction

J jacobian matrix

n refractive index

N surface normal

Imax maximum intensity

Inorm normalized intensity proﬁle

S luminous intensity

T target irradiance distribution

Oh Ohnesorge

We Weber number

Re Reynolds number

η jet velocity

ρ density of ink

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d nozzle diameter

IUV0 intensity at the surface of the liquid polymer

LT layer thickness

DM 1/e penetration depth of light inside polymer ET radiant energy for speciﬁc time

ECr critical radiant energy required for photo-polymerization process

x

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LIST OF ORIGINAL PUBLICATIONS

This dissertation consists of a review of the author’s work in the ﬁeld of designing and 3D-printing optics. It is based on an overview and the following selection of the author’s publications in these ﬁelds.

I. Bisrat G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “3D Printed plano-freeform optics for non-coherent beam shaping,” Optical Review25(3), 456–462 (2018).

II. Bisrat G. Assefa, T. Saastamoinen, M. Pekkarinen, Ville Nissinen, J.

Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Realizing freeform lenses using an optics 3D-printer for industrial based tailored irradiance distribution,” OSA Continuum2(3), 690–702 (2019).

III. Bisrat G. Assefa, M. Pekkarinen, H. Partanen, J. Biskop, J. Turunen, and J. Saarinen, “Imaging-quality 3D printed centimeter-scale lens,”

Optics Express27(9), 12630–12637 (2019).

Throughout the overview, these papers will be referred to by Roman numer- als. Other papers by the author, which are related to the thesis topic, are included in the bibliography [1–8].

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AUTHOR’S CONTRIBUTION

The publications selected in this dissertation are original research papers on designing 3D-printable optics. The research reported in this dissertation is a result of group work that has been carried out at the 3D-printed photonics and freeform optics research group of the University of Eastern Finland (UEF) and Luxexcel, the industrial partner from the Netherlands.

The author has contributed to all aspect of the research work. He has designed and theoretically analysed the optics in Papers I-III. The lenses in Papers II and Paper III were 3D-printed ﬁrst by him and later under his su- pervision. He has also characterized the performance of the optics in Papers I and III.

The author has actively participated in planning and reporting the research work in all Papers. The author wrote Paper I and Paper II under the supervisors’ guidance, and prepared the draft manuscript for Paper III.

He has also presented the results of the work in national and international conferences.

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1 INTRODUCTION

This chapter covers the background of polymer optics in general, from design to manufacturing, as well as the motivation behind this work and an outline of the contents of this dissertation.

1.1 BACKGROUND

Just three decades ago, having precision plastic optics for volume production was considered as a myth [9, 10]. However, in the 21st century, polymer optics have gained numerous application areas due to its various benefits over traditional glass optics. Some of such benefits can be found in circum- stances where reduction in packaging weight and size, resistance to impact, functional integration, and cost reduction in volume production are important. Some representative applications are found in medical disposable diagnostics, guided weapons, biomedicine and biometry, surgical laparoscopic devices, head-up displays, image scanners, and identification and tracking devices [11–13].

Diamond turning and injection moulding are the established polymer optics manufacturing techniques. Diamond turning, using single-crystal diamond or cubic boron nitride, is the favorite for prototyping of precision lenses. However, high-volume production is usually achieved only in com- bination with injection moulding. The precision molded lenses for optical applications are required to have small form deviation, high transparency, high replication ﬁdelity, short cycle time, and high production efﬁciency [14].

History shows that the introduction of refraction and spherical lenses is due to a mathematician Ibn Sahl in late tenth century [15]. Until the patent of an aspheric lens by Ernst Abbe in 1902 [16], a substantial amount of high- order aberration was unavoidable. Abbe’s innovation allows a designer to minimize the monochromatic aberrations in the system. Some principles of aspheric optical design are presented in the classic textbook of Born and Wolf [17]. However, until freeform optics was introduced, achieving an effi- cient optical mapping of the source intensity into a specified target distribution was unthinkable. Freeform optics, in general, has no axial or rotational symmetry. The first freeform optics for multi-focal optical system was designed in 1959 using anxy-polynomial progressive surface [18]. The Alvarez lens [19] can be also classified as a freeform lens since it uses two freeform cubic polynomial surfaces to form the composite lens. Later in 1970s, low- order freeform optical surfaces became a part of a commercial product: the Polaroid SX-70 camera [20, 21]. The manufacturing limitations of the tradi-

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tional methods such as ultraprecision diamond turning was a drawback that hindered the realization of the full potential of freeform lenses. However, the recent progress in diamond milling [22], coordinated axis diamond turning [23], and deterministic micro-grinding and polishing [24] have made it possible to form freeform surfaces with less than 3 nm surface roughness quality.

Lately, 3D-printing, also known as additive manufacturing, has been considered for prototyping of freeform lenses with micrometer- to millimeter dimensions [25–27]. Actually, 3D-printing has been investigated as a manufacturing process from the late 1980s especially for metals and ceramic materials [28–31]. 3D-printing of optical components can be implemented with various technologies such as stereolithography (SLA), digital light processing (DLP), selective laser sintering (SLS), fused deposition modelling (FDM), poly-jet, and ink-jet. The optical component is fabricated in SLA by polymer- izing the resin using a beam of ultraviolet (UV) laser [28, 32]. In DLP, a light display such as a liquid crystal display (LCD) is used to polymerize a liquid resin and form an entire single layer of the printed part at once [33]. SLS- based optical components are usually formed by sintering a high power laser on the liquid resin [32], while FDM-based 3D-printing works by depositing a molten thermoplastic material using a heated print heads and ﬁlament extrusion [34].

In poly-jet 3D-printing, the droplet of liquid photopolymer is deposited and UV-cured instantly [35]. Similarly, ink-jet 3D-printing works by depositing droplets of liquid material onto the substrate surface from the ink- jet print head, and to form the shape of the optics from the interaction of surface energy, fluid viscocity, inertia, gravity, and other fluid mechan- ics [36,37]. Moreover, two-photon-absorption based multiphoton lithography has pushed the 3D-printing resolution to less than 10 nm, and it allows the realization of micro-freeform optics [25, 38–40]. Honget al.[27] have demonstrated 3D-printed transparent freeform optics, with root mean square (RMS) surface roughness of 15 nm and surface profile deviation of ±²⁰ μm at the center of a printed lens, using pulsed infrared (IR) laser and thermally curable optical silicones in layer-by-layer printing methods.

3D-printing of imaging quality optics involves material and technological demands that make it challenging as compared to non-imaging optics. Nev- ertheless, imaging quality microlenses have been demonstrated using simple ink-jet printing techniques [41]. Sung et al. [36] have also demonstrated a 3D-printed microlens with resolving power of 1 μm using an ink-jet print head and in situ curing liquid polydimethylsiloxane droplets on a preheated smooth surface. Another approach to 3D-printing an imaging lens is based on curing a transparent polydimethylsiloxane (PDMS) elastomer droplet on a curved substrate [42]. Alternatively, 3D-printing of imaging lenses of 2−3 mm diameter size has been demonstrated with external lens surface roughness quality of RMS = 7 nm [43].

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The applications of 3D-printing optics can be found in biomedical imaging, such as disposable optics in microscopy diagnostics [12] and in elastomer [42] in addition to illumination and optical interconnect applications [35].

1.2 MOTIVATION AND RESEARCH SUMMARY

The latest Intel Stratix 10 chip can compute ten trillion calculations per second [44], which allows non-sequential tracing of rays through freeform surfaces for non-imaging applications. The common commercial illumination design software, LightTools, includes a freeform optics design module [45].

ZEMAX can also be used to design freeform lenses for simple target distributions using a polynomial optimization technique [46]. ffOptik is the commonly used stand-alone semi-commercial software [47]; however, the output designs require further post-processing on the boundary condition at the CAD ﬁles in order to make the lens suitable for the manufacturing process [7]. Thus, a custom-algorithm was developed in this work for freeform optics design to relax the manufacturing limitations [2].

Freeform optics fabrication based on the injection molding process is still limited to surface form deviation of around 10 μm [23]. Thus, it is chal- lenging to achieve the optical form and surface roughness requirements of the freeform design speciﬁcation using the existing technology, particularly in the visible wavelength range. The other major drawback is the start-up expense of the manufacturing process that varies from few thousands in the case of diamond-turning technology up to $25,000 in the case of molding process [48]. This manufacturing cost can be decreased substantially by using the 3D-printing process since the layer-by-layer printing uses the printable material effectively and minimized material waste.

Although different approaches have been investigated to 3D-print freeform optics for illumination applications, they are limited toμm or mm diameter size [39] or simple geometry [27]. This is because, when the size of the optics increases, the 3D-printing process becomes slow in the case of direct laser writing and accurate control of the droplets becomes challenging in the case of ink-jet 3D-printing process. Since true freeform optics is in general rotationally non-symmetric, precise control of the print droplets is necessary for resolving the details on the freeform surface. Similarly, the fabrication of 3D-printed imaging lenses has been attempted using hanging droplets techniques, which is a slow passive fabrication process [42]. An imaging quality lens has also been demonstrated using a projection micro-stereolithography 3D-printing process, which however is limited to 2−3 mm diameter [43].

Thus, due to high surface quality and ﬁdelity requirements, 3D-printing of lens with centimeter scale diameter for imaging purpose is demanding.

Luxexcel, using its Printoptical^c technology, has managed to scale the printed optics diameter onto the order of centimeters using a modiﬁed ink-

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Figure 1.1: Flow chart for realizing 3D printed optical lens.

jet and molding process [49]. This technology summons the motivation of writing this thesis. The main goal here is to gain more insight into designing and 3D-printing freeform and other classes of optics using the Printoptical^c technology for various imaging and non-imaging application areas.

The research work can be categorized into three parts, and the overall process is shown in Fig. 1.1. The ﬁrst part focuses on the design of illumination freeform optics, as inspired by Rieset al. [50] and Bäuerle [51].

In the second part Printoptical^c technology based 3D-printing process is presented in details.

The third stage includes surface characterization and error-correction in addition to analyzing the optical performance of 3D-printed lenses. Finally, the 3D-printing process is investigated for prototyping and small series production in an industrial case, and various photonics elements.

1.3 DISSERTATION OUTLINE

The thesis is organized as follows. In Chapter 2, we introduce freeform optics and present an overview of the existing design algorithms of freeform optics.

We emphasize the ray-mapping technique for designing freeform lenses and analyze the designs using numerical simulations as presented in Papers I and II. In addition, we describe a ray-mapping technique based design of a Fresnel lens for LED lighting applications.

Chapter 3 describes the current state of the art of Printoptical^c technology based 3D-printing of lenses in centimeter-diameter scale. The optical properties of the Luxexcel Opticlear^R material are also presented.

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Chapter 4 deals with the techniques that are applied to surface metrology of the printed lenses. The Null Mach-Zehnder interferometer setup that is constructed for surface error correction measurement is also presented, based on Paper III.

Chapter 5 presents the 3D-printed freeform lens and its optical surface quality based on the surface metrology presented in the previous chapter.

Chapter 6 presents the 3D printed lens for imaging application and its precision level surface quality based on the main results of Paper III. In addition, we introduce a 3D-printed diffraction grating for photonics applications with its characterized surface, as well as a quasi-deterministic diffuser for modulation of the spectral and temporal coherence of pulse trains.

Chapter 7 experimentally validates the optical performance of the 3D- printed lenses and the photonic components, and lastly, we brieﬂy recollect the main results and give directions for future work in Chapter 8.

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2 FREEFORM OPTICS

Freeform optical surfaces are rotationally non-symmetric across the axis.

This non-symmetry property allows the optic to have higher performance, as compared to a sphere or an asphere, by increasing the depth of ﬁeld, expand- ing the ﬁeld of view, reducing stray-light, and also decreasing the packaging size. Perhaps most importantly, it facilitates complex wavefront transforma- tions beyond stigmatic imaging. The recent investigations of freeform optics from design up to fabrication and characterization show its prospective for miniaturized optical systems with decreased manufacturing cost [52–55].

Freeform surfaces can be deﬁned mathematically using, e.g., radial basis functions [56] and non-uniform rational B-splines (NURBS) [57] as local descriptions, or using polynomial representations such asxy-polynomials [19], Zernike polynomials [58, 59], andQ-polynomials [60] as global descriptions.

Zernike or Q-polynomials that are orthogonal in sag and gradient, respec- tively, are usually employed for highly corrected imaging systems. Zernike polynomials are already implemented in commercial design software such as Zemax OpticStudio [46]. However, design of complex freeform surfaces requires higher-order polynomials to be included in the surface representation, which makes the optimization slow.

In the case of non-imaging optics, the aim is to optimally transfer the light from the source to the desired target distribution. For this, the required freeform optics is designed by using direct-mapping method [61]. One of the techniques to design freeform lenses is by solving the partial differential equation of energy coupling between the angle of incidence and the target surface irradiance distribution, and applying energy conservation [50, 62].

An effective and widely used freeform surface design method is the simultaneous multiple surface (SMS) method, which designs freeform surfaces simultaneously using bundle-coupling and prescribed-irradiance principles [63]. This principle means that every incident ray exits the pupil of the optical system and two input wavefronts are coupled into the two output wavefronts. This method leads to compact and efﬁcient freeform surfaces.

The SMS method works for both point and extended light sources, and is ap- plicable to the design of both imaging and non-imaging optics. Yet another design method is based on point-to-point mapping techniques, in which the source and the target areas are concatenated into grids and, by considering energy conservation, the normal vectors of the freeform surface points are obtained iteratively [64]. In the next sections we explain how to design freeform optics by adapting the ray-mapping freeform lens design algorithm to an extended and collimated light source.

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2.1 BASIC CONCEPTS

The ray-mapping design method solves the non-linear partial differential equations that arise from mapping the rays from the light source into the target irradiance distribution as shown in Fig. 2.1.

One of the basic assumptions in the mapping phase is that the system is lossless, i.e., energy is conserved. The mapping can be represented using cumulative ﬂux in two dimension as

S(θ,φ)sinθdθdφ= T(xt,yt)dxtdyt, (2.1) where S(θ,φ)is the luminous intensity radiated by a point-like source and T(xt,yt) is the target irradiance distribution. In the case of a (generalized) Lambertian point light source, the luminous intensity can be approximated as

S(θ,φ) = Imaxcosθ^m, (2.2) where Imax is the maximum intensity of the source and m is the order of the Lambertian emission. In the case of a collimated light source, luminous intensity can be represented in Cartesian rather than spherical polar coordinates: we then writeS(xs,ys).

Figure 2.1: Sketch of a freeform surface to shape irradiation from a point source at the origin of the(xs,ys)plane into the desired form at the target (xt,yt)plane. Spherical polar coordinates (θ,φ) are used to specify directions,Nandnare the surface normal and refractive index, respectively.

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Designing the freeform optics ﬁrst requires ﬁnding the mapping bijective coordinates of the target as

xt =

f(θ,φ)for a Lambertian light source,

f(xs,ys)for a collimated light source, (2.3) yt =

g(θ,φ)for a Lambertian light source,

g(xs,ys)for a collimated light source. (2.4) Since the spherical coordinate system can be approximated by a cartesian coordinate system as shown in Fig. 2.2, Eq. (2.1) can be simpliﬁed for prescribed irradiance distribution for collimated light source as

S(xs,ys)dxsdys= T[f(xs,ys)^,g(xs,ys)]^det^J^dxsdys, (2.5) where detJis the determinant of the Jacobian matrixJexpressed as

detJ = ∂xt

∂xs

∂yt

∂ys −_∂y^∂x^t

s

∂yt

∂xs

. (2.6)

The mapping coordinates using a gradient of a convex scalar functionψcan be represented as [65]

(xt,yt) =∇ψ. (2.7)

Substitution of Eq. (2.7) into Eq. (2.5) leads to S(xs,ys) =T(ψ,∇ψ)

∂²ψ

∂xs2

∂²ψ

∂ys2 −

∂²ψ

∂xs∂xs

2

, (2.8)

Figure 2.2: Rectangular LED Lambertian irradiance distribution with emission orderm=1.2 in 3D-2D coordinate systems.

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which is a Monge-Ampère type second order partial differential equation.

The solution can be calculated using optimal mass transport equation prob- lem of L² Monge-Kantorovich and minimizing the transportation cost [66]

C(M) = ξ−M(ξ)²S(ξ)dξ, (2.9) whereξ = (xs,ys),M is the map(f,g)andξ−M²is the traveled distance squared. The optimal value can be calculated from Wasserstein distance cal- culation when the mapping is unique [67]. Sulmanet al. compute a numerical solution for Eq. (2.8) by ﬁnding a steady-state solution of the logarithmic parabolic Monge-Ampère equation

∂ψ

∂t =log

T[∇ψ(ξ)]

S(ξ)

∂²ψ

∂xs2

∂²ψ

∂ys2−

∂²ψ

∂xs∂xs

2

, (2.10) with suitable boundary conditions [68]. Thus, the solution of Eq. (2.8) can be determined by taking the spatial gradient of the converged solutionψ∞.

The surface construction of the freeform lens can be calculated using least-squares optimization techniques in such a way that the source rays hit the target at the accurate position after being deﬂected by the optics surface [51]. This can be formulated using surfaces that are approximated by triangle mesh with vertices position given as

r(i) =r0(i) +p(i)kin(i), (2.11) where r0(i)is the position of ray iat the source, p(i) is a scalar parameter deﬁning the surface point of rayi, andkin(i)is the directional unit vector of the incident ray.

The integrability condition [70] has to be fulﬁlled in order to have a con- tinuous differentiable optical surface,

N·( ×N) =0, (2.12)

whereNis the surface normal, since a unique mappingM value is challenging to achieve. The surface normal can be calculated considering monotonic ray bending and the Snell’s law of refraction as

N= (krf−nkin)

1+n²+2n(krf·kin) ^(2.13) wherein n is the refractive index, k_rf denotes the refracted ray unit vector.

Thus, the point where ray that intersect the target surface (xT,y_T) can be computed givenk_rfand the position of the ray at the optical surfacer.

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Finally, the surface construction is completed by minimizing the objective function

LM(p) =

∑

i

[xT(i)−xt(i)]²+ [yT(i)−yt(i)]², (2.14)

wherexT(i)andyT(i)are the actual local coordinates at the target plane for a given vector of parametersp. The Levenberg-Marquardt algorithm has been applied to minimize Eq. (2.14). The algorithm iterates until a sufﬁciently small LMvalue is reached. The convergence of the algorithm is ensured if the initial guess of the surface shape is sufﬁciently close to the optimum.

This surface optimization allows the optical surfaces to create the required distribution using an extended sources by adapting the target distribution as explained by Wester [69] and expand it to a collimated source.

2.2 DESIGN EXAMPLES

In this section, we have presented two case studies for the freeform lenses designed using the proposed custom algorithm.

2.2.1 Case Study 1: Uniform Rectangular Illumination

As an illustration of the custom algorithm, we have designed a freeform lens for an ideal LED based uniform rectangular illumination considering Lux- Opticlear^c material with refractive index of n =1.53 at λ = 587 nm. Then, we extended the design to an industrial illumination application for inspec- tion of defects in paper web. The freeform-lens design parameters are listed in Table 2.1.

Table 2.1: Design speciﬁcations of free-form lenses for rectangular uniform illumination.

Parameters Ideal rectangular

illumination

Paper mill illumination Lambertian emitter size 1.5×1.5 mm² 3.45×3.45 mm² Distance between the source and

the lens entrance surface

5 mm 1.5 mm

Distance between the lens and the target

20 cm 200 cm

Target area/Opening angle 17×17 cm² 45^◦×35^◦ Freeform lens size 22.7×22.7×8.3

mm³

13.8×12.6×8.1 mm³

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Figure 2.3: Freeform lens designs: (a) 3D-CAD format and (b) top-view contour of the freeform lens for an ideal uniform rectangular illumination.

(c) 3D-CAD format and (d) top-view contour of the freeform lens for paper web illumination.

The designed lenses are illustrated in Fig. 2.3. Figures 2.3(a) and 2.3(c) depict the non-rotational symmetry of the designs in CAD format. The difference between the two designed geometries can be seen from the top-view contour of the designs presented in Figs. 2.3(b) and 2.3(d).

The analysis of the designs is implemented in Zemax OpticStudio 16 software using 20×10⁶ rays. The simulation result of the design for the ideal uniform rectangular illumination is presented in Fig. 2.4(a). The designed lens directs accurately the LED source into the rectangular geometry with relative irradiance uniformity of 80−90% at the center of the target distribution as illustrated in Fig. 2.4(c). Similarly, in the paper-web machine illumination case, as illustrated in Figs. 2.4(b) and 2.4(d), the irradiance pattern is highly uniform in theydirection but less satisfactory in thexdirection, in which the required beam divergence is larger.

We have compared the custom algorithm capability with ffoptik commercial software [47] that is based on Ries-Muschaweck algorithm [50]. For instance, rectangular uniform target distribution similar to the above examples, see Figs. 2.4(a) and 2.4(c), can be designed using the ffOPTIK point source algorithm as shown in Fig. 2.5.

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Figure 2.4: Simulation results: relative irradiance distribution (a) for the ideal case and (b) for the paper mill machine illumination case studies at the target plane; cross sections inxandydirection (c) in the ideal case and (d) for the paper mill machine illumination case.

As one can see, the irradiance distribution is relatively uniform for a small- sized LED source. Thus, the performance of the custom algorithm is close to the semi-commercial software for the chosen LED size. However, when the LED size increased to 10 mm², the uniformity and the target accuracy are disturbed. This effect is shown clearly in Fig. 2.6 using the custom algorithm.

Similar effect can also be observed using other algorithm including ffOPTIK software. Fournier studied the effect of extended source for freeform re- ﬂectors designed by solving the second order non-linear partial differential equation for a discrete target using an iterative approach called supporting ellipsoids method [70, 71].

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!

Figure 2.5:Simulation results for ffOptik based freeform lenses using Lam- bertian emitter size of 1.5×1.5 mm²: (a) freeform lens design, (b) the prescribed target irradiance distribution, (c) simulated relative irradiance distribution and (d) cross-sectional uniformity.

In addition to the size of the LED, the position accuracy of the LEDs also has an effect in the ﬁnal target distribution. This can be demonstrated by the freeform designs using ffOPTIK software for discontinuous target distribution as seen in Fig. 2.7. Table 2.2 shows the parameters for the designs.

The numerical simulation analysis using two million rays in ZEMAX software demonstrate the performance of the freeform lenses relative to the po- sitioning of the light source [72]. We have also simulated a Lambertian LED source with 1.25×1.4 mm² emitting area, for which the point source crite- rion of Moreno et al. [73] is satisﬁed. The simulations demonstrate that the required target distribution is achieved when the source is at the right location, see Figs. 2.8 (b,e). However, when the location of the light source is shifted by±2 mm, the simulated target distribution, as seen in Figs. 2.8 (a, c, d, and f), demonstrate distortion that deviates from the required distribution.

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Figure 2.6: LED size effect on the target illumination. The simulated irradiance pattern for LED source size (a) 4×4 mm², (b) 6×6 mm², (c) 8×8 mm², and (d) 10×10 mm².

Table 2.2:Design speciﬁcations of free-form lenses for discontinuous target illumination.

Parameters Bright squares

illumination

MTF like illumination Lambertian emitter size 1.25×1.4 mm² 1.25×1.4 mm² Distance between the source

and the lens entrance surface

12 mm 20 mm

Distance between the lens and the target

50 cm 50 cm

Target area 5×(2×2 cm²)

within 20×20 cm²

20×20 cm² Freeform lens size 24.9×24.9×9.1

mm³

31.8×31.9×9.3 mm³

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Figure 2.7: Freeform lens designs and the desired target distributions:

(a) lens design in mesh form for the LED light splitter into (b) ﬁve-section rectangular target irradiance distribution. (c) Freeform lens design in mesh form for (d) the MTF-like target irradiance distribution.

The effect of light source position is more severe for the LED light splitter case than for the MTF-like distribution. This was indeed expected since the source position relative error was higher (±16.7%) for the LED light splitter that for for MTF-like target irradiance distribution (±10%) [1].

2.2.2 Case Study 2: Complex Target Irradiance Distributions

The custom algorithm was also applied to design freeform lenses for dis- playing complex target images using a collimated light source. Two different freeform lenses are designed for complexPlato and AristotleandLenaimages as target illumination patterns. A rectangular collimated beam source of size 16

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Figure 2.8: Target irradiance distribution tolerance for distance variation between the LED source and lens entrance surface. Deviation−2 mm, 0 mm and 2 mm for the LED light splitter in (a-c) and for the MTF-like distribution in (d-f).

20×20 mm² is placed at a distance of 10 mm from the ﬂat entrance side of both lenses to design freeform lenses of size 20×20 mm², see Fig. 2.9(a) and 2.9(c). The target distributions are shown in Fig. 2.10(a) forPlato and Aristotle (50×50 mm²), and Fig. 2.10(d) for Lena(50×50 mm²). The target plane is located at a distance of 200 mm from the lens.

Figures 2.9(b) and 2.9(d) show the designed freeform lens surface feature step size in nanometer and micrometer scale forPlato and AristotleandLena target images, respectively. The feature step size of the freeform lens surface forLenatarget image is in micrometer scale. This makes it easier to fabricate than the freeform lens designed forPlato and Aristotletarget image that has feature step size below 500 nm.

The numerical simulation of the designs is implemented in ZEMAX Op- ticStudio 16 using 100×10⁶rays. The results are shown in Figs. 2.10(b) and 2.10(e). Figures 2.10(b) and 2.10(e) shows the details of the target image con- vincingly. However, some blurring is visible, which is due to the limitations of the optimal mass transport map algorithm. The other cause could come from insufﬁciently precise design conversion process in ZEMAX software from the grid sag format of the design. The absolute difference between the required and simulated target irradiance distributions is presented in Figs 2.10(c) and 2.10(f). The performance of the resulting output irradiance

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Figure 2.9: Freeform lens design for complex target irradiance distributions: (a) 3D-CAD format and (b) sub-microns features of freeform lens design forPlato and Aristotletarget image. (c) 3D-CAD format and (d) sub- microns features of freeform lens design for forLenatarget image.

can be calculated using relative root-mean square deviation (RRMSD)

RRMSD=

∑_i^p₌1∑^q_j₌1

Ireq(xt,j,yt,i)−Isim(xt,j,yt,i)²

∑_i^p₌1∑^q_j₌1Ireq(xt,j,yt,i)² ^, ^(2.15) whereinIreqis the required irradiance distribution value and Isimis the simulated irradiance distribution for p×q data points. Thus, the RRMSD is calculated to be 0.0902 and 0.157 forPlato and Aristotle andLena images, respectively.

Figure 2.11 shows the fabrication tolerance of the freeform lens designed forLenatarget image.Randomly generated surface proﬁle deviations of±100 nm, ± 250 nm and ±500 nm assigned to the printing error are considered in the numerical simulations. The results demonstrate that the optical performance of the lens is very sensitive to the fabrication error within sub-μm scale. The brightness of the target images are also reduced which could be due to the scattering effect introduced by the surface deviation. Thus, the designed lenses need to be fabricated with less than 100 nanometer precision in order to observe a good-quality image at the target plane.

A similar comparison can be made using ffOPTIK [50] (see Fig. 2.12).

However, the algorithm is limited to circular or rotationally symmetric source 18

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Figure 2.10: Numerical simulation of the freeform lens designs for complex target images: (a) and (d) show the prescribed target irradiance distributions of Plato and Aristotle and Lena images, respectively. (b) and (e) illustrate the ray-traced target image irradiance distributions, while (c) and (f) show the absolute difference between the ideal and simulated target image irradiance distributions.

Figure 2.11: Numerical simulation of the freeform lens design with randomly generated surface proﬁle deviation forLenatarget image case study:

optical performance of the design for additional surface proﬁle error of (a)±100 nm, (b)±250 nm and (c)±500 nm.

distributions. Thus we designed a new freeform lens for the Lena target image considering a circularly collimated beam source with similar design parameters as with the customized-algorithm. The RRMSD of the Lenaprescribed image has decreased by 24 %. This effect can be minimized more by using more grid points while designing the lens [74]. However, the ray- mapping errors, the surface construction error, and the diffraction effect are

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the main reasons for the performance decrement.

Figure 2.12: (a) A freeform lens designed using ffOPTIK lens in CAD format. (b) The ideal target irradiance distribution, (c) the simulated distribution, and (d) the absolute difference between (b) and (c).

2.3 CONCLUSIONS AND DISCUSSION

Freeform lenses can be used efficiently to direct light from a collimated or an extended source into uniform rectangular or complex target image irradiance distributions. The customized ray-mapping algorithm performs com- parably to the semi-commercial software, with an advantage of flexibility for modification depending on the application. The effect of the point source approximation is found to be significant when the extended-source size increases. This has been demonstrated in the BS and MTF like case studies, in which the simulated irradiance distributions show blurring at the edges due to the finite size of the LED source.

In addition, the ray-mapping algorithm that is implemented to design the freeform lenses can be expanded to include both the wavefront and irradiance control by using double freeform surfaces. However, the fabrication error, in our case the 3D-printing surface proﬁle deviation, could become a bottleneck for realizing the performance enhancement that can be gained from the design improvement.

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3 PRINTOPTICAL ^c TECHNOLOGY

3D-printing of optics with complex geometries is a promising option for prototyping and small-series production as an alternative to the established diamond turning techniques, which are expensive and time consuming. Si- mon et al. have demonstrated 3D-printed optics for various applications, such as foveated imaging and LED collimation, using a direct laser writing system [25, 26, 39]. However, the diameter of the printed lenses is in sub- millimeter range. This is due to the nanometer-scale spot area of the fem- tosecond direct laser writing system, which makes 3D-printing of millimeter- scale optics slow. Inkjet 3D-printing technology, however, can be applied to print millimeter scale optics substantially faster [36].

The inkjet 3D-printing process works by depositing ink or liquid polymer droplets on the substrate by mechanically aligning them into the exact location. The printing system can be, for example, based on piezoelectric cartridges [75] or an electrohydrodynamic (EHD) [76] jetting system. The EHD printing process use a high pulsing frequency, and the droplets formed are in the sub-femtoliter level. Thus, the minimum printed features can be in the sub-micrometer scale [76]. On the other hand, in the piezoelectric-based printing process, the droplet formation is achieved by changing the applied voltage into the system that leads to pressure pulse variation. This leads to pouring of polymer or ink from the nozzle and formation of spherical droplets, due to surface tension, while in the ﬂight stage. Unwanted satellite droplets are sometimes introduced while forming a droplet due to low surface tension of the polymer liquid. The viscosity of the polymer material is the other important physical property, since a highly viscous polymer material requires a higher pressure pulse to eject a droplet from a nozzle [77].

3D-printing of polymer optics using a modiﬁed inkjet printing technology called Printoptical^c Technology has been demonstrated by Luxexcel [49, 78]. This technology does not require the printed optics to pass through post-processing step such as polishing, which is necessary for other additive manufacturing processes like Polyjet [35], Fused Deposition Modeling (FDM) and Stereo Lithography (SLA) [79]. Printoptical^c Technology has been demonstrated for applications such as ophthalmic lenses [80] and light- guides [81]. The recent advancements in additive manufacturing of glass objects [82, 83] pushes this technology to be investigated for materials with different refractive indices [84] and for printing materials comprising sili- cone [85]. However, the advantage of polymer optics in cost, mass production with high quality and repeatability, lightness, and ability to form complex surfaces and multifunctional parts makes it competitive to glass optics.

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Since this work is done in collaboration with the Luxexcel company, the principle of operation of Printoptical^c Technology for printing functional optics is discussed in more detail below.

3.1 PRINCIPLE OF OPERATION

The working principle of Printoptical^c Technology is based on a modified ink-jet printing process, which (instead of ink) uses a UV-curable photopolymer called Lux-Opticlear^TM. This material which resembles Poly(methyl methacrylate) (PMMA), but has a higher refractive index, i.e., n = 1.53 at 587 nm [49]. Figures 3.1(a) and 3.1(b) show the body of the optic 3D-printer and the layout of the print heads, respectively. The optic 3D-printer has three print heads, each having 1000 nozzles of 23.5 μm diameter. The fea- ture size of the printed optics depends on the ejected droplet size from the nozzles and surface treatments of substrate [77]. The droplet size depends on the effect of the jet velocityη, the orifice or nozzle diameterd, the surface tension σ, and the density of the ink ρ. The droplet instability is described by the Ohnesorge (Oh) number using Weber number (We), a dimensionless number that quantifies the inertia of the liquid polymer relative to its surface tension, and Reynolds number (Re), which is also a dimensionless number that is used to predict the liquid flow patterns in different situations such as variation in speed. Thus, the Ohnesorge (Oh) number is described as [75]

Oh=

⎧⎨

⎩

√We Re or,

√η

σρd. (3.1)

When Oh is between 0.1 and 1, the droplets form without satellite droplet formation. As a result, Oh is an important ﬁgure of merit in designing the waveform for polymer jetting.

To facilitate 3D printing, the designed optics has to be first converted to a CAD format that is readable with Netfabb CAD-software. The CAD software is used to inspect the design of overhanging structures and slice the design into printable image files. The slicing layer thickness can vary between 2 and 4.8 μm. The printing process setting is created in XML data file format, a markup language with a set of rules for the printing process, that access the image file.

The printing process is shown in Fig. 3.2. First, the printheads drop polymer droplets according to the grayscale image format. Then the droplets merge with time and form a layer, and ﬁnally UV-LEDs are applied to cure and solidify the liquid layer. The build-up process of the printed layers is shown in Fig. 3.2(c). Finally, the printed layers form a lens as presented in Fig. 3.2(d). However, extra droplets have to be printed to make the surface of the lens smooth as shown in Fig. 3.2(e).

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Figure 3.1:Modiﬁed ink-jet based optics 3D-printer: (a) a custom-designed 3D-printer for optics manufacturing and (b) the general layout of the print heads.

Figure 3.2: 3D printing lens formation process: (a) Printheads depositing polymer, (b) droplets merge and form the ﬁrst layer on the substrate, (c) layer-by-layer lens build-up stage, (d) formation of lens shape and (e) smoothing the external lens surface by deposition of extra droplets.

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The layer thickness of the printed lens can be rationalized using the ex- ponential light absorption equation for the liquid polymer [43]. The light intensity at speciﬁc depth DT is expressed as

IUV(DT) = IUV0exp(−DT/DM), (3.2) where IUV0 is the intensity at the surface of the liquid polymer and DM is the 1/e penetration depth of light inside the liquid polymer. The cured layer thickness, considering the polymerization process, depends on the intensity dosage and can be expressed as

LT = DMln(ET/ECr), (3.3) where ET = IUV0t is the radiant energy for speciﬁc timet at the top surface of the liquid polymer and ECr is the critical radiant energy required for the photo-polymerization process. As a result, the layer thickness, in addition to the droplet size and merging time, depends also on the dosage and exposure time of the UV-radiant energy. UV-LEDs are used for soft-hardening pinning of the lenses, and UV-lamps are used for hard curing of the lens in order to print accurate micro structures.

3.2 MATERIAL PROPERTIES

Luxexcel Opticlear^TM is an optical quality material that is customized for Printoptical^c technology. The refractive index of a 2 mm thick plate, which is 3D-printed using Lux-Opticlear^TM material, was measured using spectral ellipsometry. The measured results shown in Fig. 3.3 demonstrate a refractive index ofn=1.53 atλ= 587 nm. The refractive index of the printed material is dependent on the UV-exposure dosage as it was the case for other printing technology [86]. The optical transmission of the printed plates using Lux- Opticlear^TM material, measured with a spectrophotometer, is shown in Fig.

3.4. The total light transmission of a 2 mm thick printed plate is around 91.1%

for the visible wavelength range from 420 nm to 780 nm, and its internal transmission (when the Fresnel reﬂections are disregarded) is around 99.5

%. The haze and yellowness indices of Lux-Opticlear^TMare measured to be 0.2% and 0.4%, respectively [87].

The Lux-Opticlear^TM material can be categorized as a thermoset resin since the material cannot return to its liquid form after the curing, which is opposite to thermoplastic resins such as PMMA.

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Figure 3.3: Refractive index measurement of a 2 mm thick 3D-printed plate.

The dispersion properties of Lux-Opticlear^TM material, using the Abbe

350 400 450 500 550 600 650 700 750 800

Wavelength [nm]

0 0,1 0.2 0.3 0,4 0,5 0.6 0.7 0.8 0.9 1

Transmittance

Lux-Opticlear (4 mm thick)

Lux-Opticlear (4 mm thick under blue light cabinet) Lux-Opticlear (2 mm thick)

PMMA (2 mm thick)

Figure 3.4: Optical transmission of Lux-Opticlear^TMmaterial compared to PMMA.

Designing and 3D-printing optical components for imaging, illumination and photonics applications : a case study based on printoptical technology

uef.fi

Dissertations in Forestry and Natural Sciences

BISRAT GIRMA ASSEFA

BISRAT GIRMA ASSEFA

Bisrat Girma Assefa

DESIGNING AND 3D-PRINTING OPTICAL COMPONENTS FOR IMAGING, ILLUMINATION AND

PHOTONICS APPLICATIONS:

A CASE STUDY BASED ON PRINTOPTICAL

TECHNOLOGY

TABLE OF CONTENTS

1 INTRODUCTION

2 FREEFORM OPTICS

∑

3 PRINTOPTICAL c TECHNOLOGY

3 PRINTOPTICAL ^c TECHNOLOGY