Microlens Array Fabrication by Using a Microshaper

micromachines

Article Microlens Array Fabrication by Using a Microshaper

Meng-Ju Lin * and Cheng Hao Wen

Department of Mechanical and Computer-Aided Engineering, Feng Chia University, Taichung City 407, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-4-2451-7250#3554

Abstract: A simple, easy, inexpensive, and quick nonsilicon-based micromachining method was developed to manufacture a microlens array. The spherical surface of the microlens was machined using a microshaper mounted on a three-axis vertical computer numerical control (CNC) machine with cutter-path-planning. The results show the machined profiles of microlens agree well with designed profiles. The focus ability of the machined microlens array was verified. The designed and measured focal lengths have average 1.5% error. The results revealed that the focal lengths of micro lens agreed with the designed values. A moderate roughness of microlens surface is obtained by simply polishing. The roughness of the lens surface is 43 nm in feed direction (x-direction) and 56 nm in path interval direction (y-direction). It shows the simple, scalable, and reproducible method to manufacture microlenses by microshaper with cutter-path-planning is feasible.

Keywords: micro surface shaping; cutter-path planning; micro-optoelectromechanical system (MOEMS); microshaper; isoplane; nonsilicon-based micromachining

1. Introduction Citation: Lin, M.-J.; Wen, C.H. Micro-optoelectromechanical systems (MOEMSs) [1,2] are a critical category of mi- Microlens Array Fabrication by Using croelectromechanical systems. Microlenseses are essential components used in MOEMS a Microshaper. Micromachines 2021, devices and are used in applications such as tracking [3], collimation, coupling of lights [4,5], 12, 244. https://doi.org/10.3390/ imaging with complementary metal-oxide semiconductor and charge-coupled devices [6], mi12030244 imaging of confocal microscopes [7], and pop-up displays [8] because of their light focusing and collimation ability. Moreover, recent developments show microlenses have Academic Editor: Atanas Ivanov more specific and novel applications. The micro lenses can be used in Mirau interferome- ters [9], imaging scanners [10], integrated photonic platform [11], vertical cavity surface Received: 1 February 2021 emitting lasers beam shaping [12], etc. Apparently, microlenses play more important role Accepted: 25 February 2021 in MOEMSs. Published: 28 February 2021 Traditionally, techniques for manufacturing microlenses often involved silicon-based micromachining. Microlenses can be fabricated by injecting droplets from microjets and Publisher’s Note: MDPI stays neutral solidifying the droplets to form lens surfaces [13]. Photomask lithography with LIGA-like with regard to jurisdictional claims in manufacturing is also used to fabricate microlenses [14]. Furthermore, reactive-ion etching published maps and institutional affil- with modified parameters [15] and the reflow method are used to fabricate microlenses. iations. The photoresist is heated to its liquid phase and allowed to flow into a curved surface under capillary force [16]. By using a cross-linked network of photoactive polymers, microlens fabrication was performed with an optically induced dielectrophoresis system [17]. In these methods, reflow methods have well developed. The microlenses of OCT Copyright: © 2021 by the authors. system made by photoresist reflow and ICP plasma etching processes have good quality of Licensee MDPI, Basel, Switzerland. small sizes and roughness [18]. Reflow of glass on silicon cavity can form convex lens and This article is an open access article assembled with the other planar lens by anodic bonding. It would generate lens doublets distributed under the terms and with good quality [19]. conditions of the Creative Commons Attribution (CC BY) license (https:// Reflow and selective etching can fabricate microlenses used in THz antenna integrated creativecommons.org/licenses/by/ heterodyne array [20]. Silicon collimating microlenses made by reflow and RIE have 4.0/). high numerical aperture for mid-infrared quantum cascade lasers [21]. Combining the

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dose-modulated lithography and reflow process, high quality aspheric microlens array are successfully fabricated [22]. Combining reflow, ultraviolet nanoimprint lithography, and replica mold processes, micro-lens array with antireflection structure can be fabricated [23]. The silicon solid immersion lenses for mid-infrared imaging can be made by nanoimprint used PDMS stamp and reflow [24]. PDMS nanoimprint and reflow can also fabricate well-defined shape microlenses [25]. Silicon-based micromachining has the advantages of batch fabrication for mass production, small dimensions, and integration with electronic devices. However, as designing devices and producing prototype, it needs cyclically modified. And in each modification, only several devices are made. These several devices of prototype often do not need massive production. And in each round of silicon-based micromachining, it may spend several days due to preparing photo mask for lithography and some processes needing vacuum environment. Therefore, if a simple, easy, and quick fabricate method could be used to fabricate microlenses. It would help the design and prototype modification. In conventional mechanical machining, complex three-dimensional curved surfaces can be effectively manufactured due to well develop of CNC machine. Milling is often used for machining three-dimensional curved surfaces. Efficient machining can be achieved through ball-end milling on multiaxis CNC machines [26–31]. Complex or free form surfaces can be precisely machined through profile milling of work pieces on a CNC machine with path-planning [32–38]. To improve the machining of complex surfaces through CNC milling, parameter tuning and path-planning were investigated [39]. Furthermore, the effect of milling machining on roughness was explored [40]. Although milling with path-planning has the advantages of complex-surface fabrication, the constraints of the knife radius limit path-planning applications for micro components. Therefore, the development of specific methods is necessary for fabricating surface profiles with small dimensions. Moreover, mechanical machining is hard compatible to integrated circuit (IC). Therefore, mechanical machining micro components need specific techniques to be compatible with IC. In this study, a simple and easy method was proposed for fabricating microlens arrays. By this developed nonsilicon-based micromachining method, producing the prototype of micro lens does not need to prepare masks used in lithography. The method also has no vacuum processes like depositions to produce devices. It could be fast, easily, and inexpensively fabricated. Moreover, due to path planning, specific curves and surfaces of MEMS devices can be made. It would help the optical devices design. Instead of a milling knife, a microshaper with a small nose radius (as shown in Figures1 and2) was mounted on a CNC machine. It has the advantages for easily manufacturing micro lenses with specific profiles. Combined with path-planning, the curved surfaces of a microlens were successfully fabricated using the microsphere. The machined profiles agreed with the designs. The microlens could effectively focus light, and the measured focal length was in agreement with the theoretical focal length calculated from the design. By simply polishing, the results also show the roughness can reduce to about fifty nano meters. It is feasible to manufacture micro lenses easily and simply by method developed in this work. And it also shows that this manufacture method has potential to be used in manufacturing aspheric microlens array or micro convex-concave lenses. It can further more be used in microscraping of MEMS devices. And this method could be used to manufacture stamps of nanoimprint. Therefore, it can further more be used in micromachining over silicon wafer. Micromachines 2021, 12, x 3 of 15 Micromachines Micromachines 2021, 12, x 2021, 12, 244 33 of 15

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Figure 1. Tungsten steel microshaper. The microshaper in mounted on CNC machine to machine Figure 1. FigureTungsten 1. Tungsten steel microshaper. steel microshaper. The microshape The microshaper in mountedr in mountedon CNC machineon CNC tomachine machine to machine the microlens. the microlens.Figurethe microlens. 1. Tungsten steel microshaper. The microshaper in mounted on CNC machine to machine the microlens.

Figure 2. Nose radius of of the the microshaper microshaper measured measured on on a amicroscope. microscope. The The knife knife radius radius has has radius radius of 50Figure μm. 2. Nose radius of the microshaper measured on a microscope. The knife radius has radius of Figure 2. ofNose 50 µ m.radius of the microshaper measured on a microscope. The knife radius has radius of 50 μm. 50 μm. 2. Materials and Methods 2. Materials2. Materials InInand thisthis Methods work, work, and spherical sphericalMethods microlenses microlenses were were machined machined due due to spherical to spherical surfaces surfaces often often used inused convex in convex lenses. lenses. As displayed As displayed in Figure in Figure3, the function 3, the function of spherical of spherical surface surface is expressed is ex- In this work,In this spherical work, spherical microlenses microlenses were machined were machined due to spherical due to spherical surfaces surfacesoften often aspressed follows: as follows: used in convexused in lenses.convex As lenses. displayed As displayed in Figure in 3, Figureq the function 3, the functionof spherical of spherical surface issurface ex- is ex- Z = −R + R2 − q2 (1) pressed aspressed follows: as follows: Z=−𝑅+𝑅 −𝑞 (1) p 2 2 where q = x +y is the distance measured from the symmetric axis of the con- where q= 𝑥 +𝑦 is the distanceZ=−𝑅+ measured from𝑅 −𝑞 the symmetric axis of the con- (1) Z Z=−𝑅+𝑅 −𝑞 (1) volutevolute surface,surface, Z isis thethe proﬁleprofile heightheight measuredmeasured fromfrom thethe qq axis,axis, andand RR isis thethe radiusradius ofof curvature of the apex of the aspheric surface. wherecurvature q=where 𝑥of the+𝑦q= apex 𝑥 is of+𝑦the the distance aspheric is the distance measuredsurface. measured from the from symmetric the symmetric axis of the axis con- of the con- volute surface,volute surface,Z is the Zprofile is the height profile measured height measured from the from q axis, the and q axis, R is and the Rradius is the of radius of curvaturecurvature of the apex of the of theapex aspheric of the aspheric surface. surface.

Figure 3. Figure 3. Spherical curve dimensions.

Figure 3. FigureSpherical 3. Sphericalcurve dimensions. curve dimensions.

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In optical properties of microlenses, the focal length is important and considered in this Inwork. optical The properties focal length of microlenses, of convex the lens focal was length designed is important using and the considered following in equation this[41]: work. The focal length of convex lens was designed using the following equation [41]: 1 𝑛 1 1 1 n = −11 1 − (2) = 𝑓 − 1𝑛 − 𝑅 𝑅 (2) f n0 R1 R2

where n and n0 are the indexes of refraction of the lens and air, respectively, and R1 where n and n0 are the indexes of refraction of the lens and air, respectively, and and R2 are the radii of curvature of the first and second surfaces, respectively. For a R1 and R2 are the radii of curvature of the ﬁrst and second surfaces, respectively. For a planoconvex lens, lens, the the radius radius of curvatureof curvatureR2 of R the2 of second the second surface surface is inﬁnite. is infinite. Therefore, Therefore, Equation (2) (2) can can be be expressed expressed as follows:as follows:

1 1n 𝑛 1 1 = =− 1 −1 (3) (3) f 𝑓n0 𝑛R1 𝑅

ForFor air air and and PMMA, PMMA, the the indexes indexes of refraction of refraction are 1 are and 1 1.49, and respectively. 1.49, respectively. ForFor measuring measuring focal focal length length effectively, effectively, a simple a simple method method is used is two used conjugates. two conjugates. As As displayed in in Figure Figure4, the4, the focal focal length lengthf can f can be determined be determined through through two conjugates two conjugates of the of the lens. WhenWhen lens lens is atis theat twothe conjugates,two conjugates, the well-known the well-known two conjugate two methodconjugate states method that states thethat object the object would would have clear have images clear and images the distance and the between distance object between and image object is ﬁxed. and In image is Figurefixed. 4In, when Figure the 4, lens when is at the either lens of is the at two eith conjugates,er of the two which conjugates, are separated which by a are distance separated by d, the distance between the object and the image l would be a ﬁxed value. Therefore, the a distance d, the distance between the object and the image l would be a fixed value. focal length can be calculated using the following equation: Therefore, the focal length can be calculated using the following equation: 2 2 l − d f = 𝑙 −𝑑 (4) 𝑓4=l (4) 4𝑙

Figure 4. Focal length measurement using two conjugates method. Figure 4. Focal length measurement using two conjugates method. Traditionally, CNC machine with cutter path planning was used to machine complex surfaceTraditionally, shape because CNC of itsmachine excellent with surface cutter cutting path ability.planning Therefore, was used it isto used machine to com- manufactureplex surface sphericalshape because microlens of it ins thisexcellent study. surface However, cutting because abilit they. microlens Therefore, is onit is a used to micrometermanufacture scale, spherical a special microlens knife is required. in this As stud displayedy. However, in Figure because1, a stiff the tungsten microlens steel is on a microshapermicrometer withscale, a smalla special cutting knife nose is radiusrequired. was As mounted displayed on a CNCin Figure machine 1, a for stiff use tungsten as the machining knife. Furthermore, this knife could also be coated with diamond layer steel microshaper with a small cutting nose radius was mounted on a CNC machine for use as the machining knife. Furthermore, this knife could also be coated with diamond layer on the tip. Therefore, some brittle and hard materials could be scraped [42]. For example, wedge-type light guide plate of efficiency of a LED backlight module. The knife

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on the tip. Therefore, some brittle and hard materials could be scraped [42]. For example, wedge-type light guide plate of efficiency of a LED backlight module. The knife has length ofhas 50 length mm and of diameter50 mm and of 4diameter mm. The of knife 4 mm. nose The radius knife was nose 50 µradiusm (Figure was2 ).50 Due μm to(Figure remove 2). materialsDue to remove by the materials knife being by notthe similarknife being to traditional not similar machining to traditional milling, machining the cutter milling, path planningthe cutter of path CNC planning machine of would CNC machine be different. would And be its different. machining And properties its machining of roughness proper- isties also of different.roughness Conventionally, is also different. for ball-endConventionally, milling, for the machiningball-end milling, paths arethe orthogonalmachining topaths the machiningare orthogonal directions to the machining when the materialsdirections are when removed the materials or cut. Unlikeare removed milling, or thecut. machiningUnlike milling, direction the machining of microshaper direction cutting of microshaper materials is thecutting same materials as the machining is the same path. as Becausethe machining the nose path. tip Because of the microshaper the nose tip (Figureof the microshaper2) scrapes the (Figure material, 2) scrapes the nose the tip mate- of therial, microshaper the nose tip shouldof the microshaper be in the forward should direction be in the in forward the tool path.direction Because in the machining tool path. differsBecause considerably machining betweendiffers considerably ball-end milling between and microshaper ball-end milling scraping, and the microshaper cutter-path planningscraping, of the the cutter-path microshaper planning is different of the in micr ball-endoshaper milling. is different For the in novel ball-end microshaper, milling. theFor path-planningthe novel microshaper, was nonparametric. the path-plannin For nonparametricg was nonparametric. path-planning, For isoplane, nonparametric isolevel, isoscallop,path-planning, and isoparametricisoplane, isolevel, methods isoscallop have been, and developedisoparametric [37]. methods Because ofhave the been specific de- cuttingveloped characteristic [37]. Because of the specific microshaper cutting mounted characteristic on a of three-axes the microshaper CNC machine, mounted the on isoplanea three-axes method CNC is machine, simple and the was isoplane therefore method preferred is simple for path-planningand was therefore in this preferred study. Asfor displayedpath-planning in Figure in this5, the study. feed As direction displayed of the in knife Figure was 5, the the x-direction. feed direction As theof the knife knife moved was forwardthe x-direction. in the x-direction, As the knife the moved microshaper forward changed in the x-direction, the scraping the height microshaper (z-direction) changed to obtain the desired surface profile (Figure5). After finishing this path, the microshaper the scraping height (z-direction) to obtain the desired surface profile (Figure 5). After returned to its initial position without machining any materials and moved a path interval finishing this path, the microshaper returned to its initial position without machining any in the y-direction to the next path. Then the microshaper will scrape the materials on materials and moved a path interval in the y-direction to the next path. Then the mi- next path. croshaper will scrape the materials on next path.

(a)

(b)

FigureFigure 5.5. CuttingCutting pathpath ofof thethe microshaper:microshaper: ( a(a)) x-y x-y plane plane and and ( b(b)) x-z x-z plane. plane. The The x-direction x-direction is is the the feed directionfeed direction of the of microshaper. the microshaper. As the As shaper the shaper ﬁnishing finishing machining machining the paththe path in feed in feed direction, direction, it will it movewill move to next to pathnext path in y directionin y direction and continueand continue to machine. to machine.

The motion of the microshaper in the x-z plane is displayed in Figure 5b. The microshaper performed x- and z-axis movements simultaneous to obtain the curved sur-

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The motion of the microshaper in the x-z plane is displayed in Figure5b. The mi- face. However, when the microshaper moved an interval in the y-direction to the ma- croshaper performed x- and z-axis movements simultaneous to obtain the curved surface. chineHowever, in the when next the path, microshaper as displayed moved in an Figu intervalre 5a, in thescallops y-direction were to produced the machine between in the two paths.next path, Figure as displayed6 displays in the Figure scallops5a, scallops between were every produced adjacent between paths. two The paths. scallop Figure is6 an error induceddisplays by the the scallops geometry between of everyknife adjacentnose radius paths. and The path scallop interval. is an error It would induced induce by the larger roughness.geometry ofThe knife relation nose radius of scal andlop path height, interval. path It interval, would induce and radius larger roughness.of knife nose The can be expressedrelation of as scallop the following height, path equation interval, [37]: and radius of knife nose can be expressed as the following equation [37]: √ ∆y =∆y =8rε√8𝑟𝜀 (5) (5) wherewhere ∆∆yy is is the the path interval,interval,r ris is the the nose nose radius radius of theof the microshaper, microshaper, and ε andis the ε scallopis the scallop height.height. The The path path interval ∆∆yy is is deﬁned defined in in programming programming the CNCthe CNC machine machine cutter cutter path path (∆y)2 ∆ planning.planning. Therefore,Therefore, the the scallop scallo heightp height can be estimated:can be estimated:ε = . Therefore,ε= . thereTherefore, would there 8r wouldbe larger be roughnesslarger roughness in path intervalin path direction interval (directiony-direction). (y-direction).

Figure 6. Scallop will happen between machined path intervals.

FigureIn 6. thisScallop study, will a happen planoconvex between lens machined array was path designed intervals. and manufactured. The profile height Z (Figure3) was used to determine the height of the microshaper in the cutting path (FigureIn this4b). study, To fabricate a planoconvex the microlens lens array, array a three-axis was designed vertical and CNC manufactured. machine (CPV-750, The profile heightCampro Z (Figure Precision 3) Machinery was used Co., to Ltd.,determine Taichung, the Taiwan) height withof the a resolutionmicroshaper of 1 µinm the was cutting pathused. (Figure A 1-mm-thick 4b). To polymethyl fabricate methacrylatethe microlens (PMMA) array, substrate a three-axis was used vertical to manufacture CNC machine (CPV-750,the microlens Campro on this Precision substrate Machinery due to its good Co., optical Ltd., properties.Taichung, TheTaiwan) CNC with programming a resolution of 1 elaboratesμm was used. on Appendix A 1-mm-thickA. polymethyl methacrylate (PMMA) substrate was used to manufacture3. Results and the Discussions microlens on this substrate due to its good optical properties. The CNC programmingThe microlens elaborates array wason Appendix. successfully fabricated, as displayed in Figure7. Figure7a reveals the array of 5 × 6 micro spherical lenses of 4-mm radius of curvature. It costs about 3.an Results hour and and half Discussions to manufacture the array of 5 × 6 micro spherical lenses by CNC machine withThe cutter-path microlens planning. array wasFigure successfully7b, c illustrates fabricated, the cross as section displayed of a 1-mm in Figure and 4-mm7. Figure 7a revealsradius ofthe curvature array of microspherical 5 × 6 micro lens spherical respectively. lenses The of radii 4-mm of curvature radius ofR ofcurvature.Figure7b,c It costs aboutcalculated an hour from and Equation half to (1) manufacture are 1.07 and the 4.04 array mm. Theyof 5 × agreed 6 micro the spherical design values lenses well. by CNC Figure8 illustrates the image of the cross section observed on microscope with scale grid machine with cutter-path planning. Figures 7b and c illustrates the cross section of a on eyepiece. We add an arc of a circle to compare the profile of the machined convex 1-mmsurface. and It 4-mm shows radius the profiles of curvature of the micro microspherical surface is enveloped lens respectively. by the arcs. FigureThe radii9a,b of cur- vatureshow theR of profiles Figure of 7b machined and c calculated surface compares from Equation with the theoretical (1) are 1.07 profiles and calculated4.04 mm. They agreedfrom Equation the design (1). values From the well. results, Figure it shows 8 illust thatrates the the profiles image of crossof the sections cross section machined observed onby microscope micro shaper with agree scale well grid with on the eyepiece. design profiles. We add an arc of a circle to compare the profile of the machined convex surface. It shows the profiles of the micro surface is enveloped by the arcs. Figures 9a and b show the profiles of machined surface compares with the theoretical profiles calculated from Equation (1). From the results, it shows that the profiles of cross sections machined by micro shaper agree well with the design profiles.

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(a)

(b)

(c) FigureFigure 7. Microlens7. Microlens array array fabrication fabrication results, (a results,) the array (a of) the 5 × array6 micro of spherical 5 × 6 micro lenses, spherical (b) cross section lenses, of the(b) fabricated cross microlenssection withof theR =fabricated 1 mm and (microlensc) cross section with of theR = fabricated 1 mm and microlens (c) cross with sectionR = 4 mm. of the fabricated microlens with R = 4 mm.

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(a)

(b)

FigureFigure 8. Cross 8. Cross section section observed observed on microscopemicroscope with with scale scale grid grid on eyepiece.on eyepiece. (a) R (a=) 1R mm. = 1 mm. (b) R (=b 4) mm.R = 4 mm. To observe whether the micro lens can focus light or not, the lens is put in front of a He-Ne laser as shown in Figure 10. The lens focus of the laser in Figure 10. As shown in Figure7b,c, it reveals that the microlens successfully focused light. This verified the focusing ability of the lens. Machining properties would also affect the optical properties of microlenses. To evaluate the properties of material scraping by the microshaper, a surface roughness (SJ-310, Mitutoyo, Kanagawa, Japan) was used to measure the roughness of lens surface. The roughness measured is arithmetic mean deviation roughness. The roughness in feed direction (x-direction) is 116 nm. And the roughness in path interval direction (y-direction) is 462 nm. After machined by using CNC, the roughness of the microlenses is large. Therefore, the microlenses needs furthermore polished. To reduce the roughness, a simple and not expensive method is used. Spreading the toothpaste on soft cloth and rubbing the PMMA substrate, the microlenses can be polished by the abrasive containing in toothpaste. After polishing, using water to wash out toothpaste, the roughness reduces to moderate values of 43 nm and 56 nm in feed direction and path interval direction respectively. Comparing with specific method of thermal radiation induced local reflow (TRILR) [43] for reducing roughness of PMMA, this roughness value is acceptable.

(a)

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(a)

(b) Figure 8. Cross section observed on microscope with scale grid on eyepiece. (a) R = 1 mm. (b) R = 4 Micromachines 2021, 12, 244 mm. 9 of 15

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(a)

(b) FigureFigure 9. 9. ComparisonComparison of machinedmachined curved curved surface surface proﬁles prof withiles with theoretical theoretical conic section conic section proﬁles profiles calculatedcalculated from from Equation. (a ()aR) R= 1= mm.1 mm. (b) (Rb=) R 4 mm.= 4 mm.

To observe whether the micro lens can focus light or not, the lens is put in front of a He-Ne laser as shown in Figure 10. The lens focus of the laser in Figure 10. As shown in Figure 7b and c, it reveals that the microlens successfully focused light. This verified the focusing ability of the lens.

(a)

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(b) Figure 9. Comparison of machined curved surface profiles with theoretical conic section profiles calculated from Equation. (a) R = 1 mm. (b) R = 4 mm.

To observe whether the micro lens can focus light or not, the lens is put in front of a Micromachines 2021, He-Ne12, 244 laser as shown in Figure 10. The lens focus of the laser in Figure 10. As shown in 10 of 15 Figure 7b and c, it reveals that the microlens successfully focused light. This verified the focusing ability of the lens.

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(a)

(b) (c) Figure 10. (a)The He-Ne laser is focused by using the microlens. (b) The light spot of laser beam without passing through lens projects on screen. (c) The light spot of laser beam passing through lens projects on screen.

Machining properties would also affect the optical properties of microlenses. To evaluate the properties of material scraping by the microshaper, a surface roughness (SJ-310, Mitutoyo, Kanagawa, Japan) was used to measure the roughness of lens surface. The roughness measured is arithmetic mean deviation roughness. The roughness in feed direction (x-direction) is 116 nm. And the roughness in path interval direction (y-direction)(b is) 462 nm. After machined by using CNC, the roughness (c) of the microlenses is large. Therefore, the microlenses needs furthermore polished. To reduce the roughness, Figure 10. (a)Figure The He-Ne 10. (a)The lasera simpleHe-Ne is focused and laser not by is expensive focused using the methodby microlens. using is used.the microlens. ( bSpreading) The light the(b) spot toothpasteThe oflight laser onspot beamsoft of cloth laser without and beam passing through lens projectswithout on screen. passing (c) Therubbing through light the spot lens PMMA of projects laser substrate, beam on screen.the passing microlenses (c) throughThe can light be lens polishedspot projects of laserby the onbeam abrasive screen. passing containing through lens projects on inscreen. toothpaste. After polishing, using water to wash out toothpaste, the roughness reduces to moderateFigure values 11 displaysof 43 nm and setup 56 nm ofin fe theed direction focal length and path measurement, interval direction re- where A is a screen for Machiningspectively. properties Comparing would with also specific affect method the of optical thermal propertiesradiation induced of microlenses.local reflow To observing(TRILR) [43] for the reducing image, roughnessB is the of microlens, PMMA, this roughness and C is value a light is acceptable. with a luminous flux of 1000 lm as evaluate the propertiesbeingFigure the 11 objectof displays material expressed setup scrapi of the in focalng Figure by length 4the. Initially,measurement, microshaper, the where distance a Asurface is a between screen roughness for the screen A and light (SJ-310, Mitutoyo,Cobserving is fixed.Kanagawa, the Thenimage, Japan)moveB is the the microlens,was microlens used and to C measure is to a findlight with the the twoa roughnessluminous conjugate flux of of lens positions1000 lmsurface. for observing clear The roughnessas measured being the object is arithmetic expressed in Figuremean 4. deviation Initially, the roughness. distance between The the roughness screen A and in feed imagelight C is projecting fixed. Then move on screen the microlens as displaying to find the intwo Figure conjugate 12 positions. The distance for observ- of the two conjugates is direction (x-direction)measureding clear image is used projecting116 vernier nm. on screen caliper.And asthe displa roughnessying in Figure in 12. Thepath distance interval of the twodirection (y-direction) isconjugates 462 nm. is After measured machined used vernier by caliper. using CNC, the roughness of the microlenses is large. Therefore, the microlenses needs furthermore polished. To reduce the roughness, a simple and not expensive method is used. Spreading the toothpaste on soft cloth and rubbing the PMMA substrate, the microlenses can be polished by the abrasive containing in toothpaste. After polishing, using water to wash out toothpaste, the roughness reduces to moderate values of 43 nm and 56 nm in feed direction and path interval direction respectively. Comparing with specific method of thermal radiation induced local reflow (TRILR) [43] for reducing roughness of PMMA, this roughness value is acceptable. Figure 11 displays setup of the focal length measurement, where A is a screen for observing the image, B is the microlens, and C is a light with a luminous flux of 1000 lm as being the object expressed in Figure 4. Initially, the distance between the screen A and light C is fixed. Then move the microlens to find the two conjugate positions for observ-

ing clear image projecting on screen as displaying in Figure 12. The distance of the two conjugates is measuredFigure 11. 11. Focal usedFocal length vernier length measurement measurement caliper. of the microlens, ofthe where microlens, A is the screen, where B is the A microlenses, is the screen, B is the microlenses, and C C is isthe the light light respectively. respectively.

Figure 11. Focal length measurement of the microlens, where A is the screen, B is the microlenses, and C is the light respectively.

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(a)

(b) Figure 12. Observe imageFigure projecting 12. Observe on image the scr projectingeen to find on the the screen two conjugates. to ﬁnd the two (a) conjugates. The position (a) The of position of ﬁrst first conjugate. (b) Theconjugate. position ( bof) Thethe positionsecond conjugate. of the second conjugate.

The measured focalThe length measured was focalcompared length waswith compared the designed with thevalues designed as shown values in as shown in Table1 and Figure 13. Table1 compares the focal lengths of the design and the measured Table 1 and Figure 13. Table 1 compares the focal lengths of the design and the measured results. In Table1, fm is the average value of focal length measured from the 5 × 6 micro results. In Table 1, sphericalfm is the lenses.average And value the standardof focal errorslength of measured the 30 lenses from for differentthe 5 × R6 aremicro also illustrated. spherical lenses. AndThe the largest standard error between errors of the the designed 30 lenses and measuredfor different focal R lengthare also is 2.9%. illus- The average trated. The largest errorerror is between 1.5%. These the errors designed may beand induced measured from machiningfocal length processes is 2.9%. and The measurement. average error is 1.5%.Due toThese reducing errors machining may be time, induced the cutter from offset machining often considered processes in traditional and milling measurement. Dueprocesses to reducing is ignored machining and there time is, nothe cutter cutter path offset compensation often considered in path planning.in tra- It would ditional milling processesalso induce is ignored error between and ther designe is and no measurementcutter path compensation focal length. And in from path the standard planning. It would errors,also indu thece measured error between uncertainty design is acceptable. and measurement As the cross focal section length. of microleses And shown in Figure7, the radii of curvature ( R) calculated from Equation (1) are 1.07 and 4.04 mm from the standard errors, the measured uncertainty is acceptable. As the cross section of respectively. Apply these values to Equation (3), the focal lengths calculated are 2.16 and microleses shown in Figure 7, the radii of curvature (R) calculated from Equation (1) are 8.24 mm respectively. They are larger than fd and fm. As shown in Figure 13, for different 1.07 and 4.04 mm respectively. Apply these values to Equation (3), the focal lengths calculated are 2.16 and 8.24 mm respectively. They are larger than fd and fm. As shown in Figure 13, for different radii of curvature (R), the measured focal lengths agree well with design focal lengths. The coefficients of the determination (r-squared,R2) is 0.9988. It

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shows that the microlenses made by microscraping with path planning having good focal Micromachines 2021, 12, 244 12 of 15 length precision.

Table 1. Comparison of the measured and designed focal lengths, where R is radius of curvature, fd is radiithe designed of curvature focal (R), length, the measuredand fm is the focal measured lengths agreefocal length well with respectively. design focal lengths. The coefﬁcients of the determination (r-squared, R2) is 0.9988. It shows that the microlenses madeR (mm by microscraping) fd (mm with) pathf planningm(mm) havingStandard good focal error length of fm precision.(mm) Error (%) 1 2.04 2.10 0.04 2.9 Table 1.2 Comparison of4.08 the measured and4.14 designed focal lengths, 0.04where R is radius of curvature, 1.5f d is the designed3 focal length,6.12 and fm is the6.22 measured focal length respectively. 0.04 1.6

R 4(mm ) fd8.16(mm ) fm(mm8.20) Standard Error 0.09 of f m (mm) Error (%) 0.5 51 10.20 2.04 2.1010.41 0.04 0.08 2.9 2.0 62 12.24 4.08 4.1412.40 0.04 0.06 1.5 1.3 73 14.28 6.12 6.2214.15 0.04 0.08 1.6 −0.9 4 8.16 8.20 0.09 0.5 85 16.32 10.20 10.4116.67 0.08 0.08 2.0 2.1 96 18.36 12.24 12.4018.49 0.06 0.10 1.3 0.7 7 14.28 14.15 0.08 −0.9 108 20.40 16.32 16.6720.37 0.08 0.06 2.1 −0.1 119 22.44 18.36 18.4922.84 0.10 0.10 0.7 1.8 1210 24.48 20.40 20.3724.88 0.06 0.06 −0.1 1.6 11 22.44 22.84 0.10 1.8 1312 26.53 24.48 24.8827.13 0.06 0.10 1.6 2.3 13 26.53 27.13 0.10 2.3

f (mm) 15

10 designed focal length measured focal length 5

0 051015 R (mm)

Figure 13. Relation of focal length (f ) and radius of curvature (R). Figure 13. Relation of focal length (f) and radius of curvature (R). 4. Conclusions 4. ConclusionsA simple, easy, and inexpensive method to fabricate microlens array through nonsilicon- based micromachining by using microshaper on CNC machine with path-planning is devel- opedA andsimple, proved easy, to be and feasible. inexpensive The microlens method array to was fabricate successfully microlens fabricated. array The through proﬁle nonsilicon-basedof cross section micromachining of the microlens shows by a roundusing arcmicroshaper and agrees well on with CNC design curve.machine For with path-planningoptical properties, is developed the average and error proved between to designed be feasible. and measuredThe microlens focal lengths array was is 1.5%. success- fullyThe fabricated. coefﬁcients ofThe the profile determination of cross (r-squared) section forof designedthe microlens and measured shows focala round lengths arc and agreesis 0.9988 well for with micro-lens design arrayscurve. withFor optical 13 different properties, radii of the curvature. average The error measured between focal designed andlengths measured of the microlensesfocal lengths were is 1.5%. in agreement The coefficients with the designed of the determination focal lengths. The (r-squared) results for designedrevealed and that measured the microlens focal array lengths exhibited is 0.9988 good focusfor micro-lens ability. After arrays simple with polishing, 13 different the ra- roughness is 43 nm and 56 nm in feed direction and path interval direction respectively. dii of curvature. The measured focal lengths of the microlenses were in agreement with It shows the machining method developed in this work has good machining properties. theThe designed microlens focal array lengths. fabrication The methodresults usingreveal microshapered that the microlens mounted on array CNC exhibited machine good focus ability. After simple polishing, the roughness is 43 nm and 56 nm in feed direction and path interval direction respectively. It shows the machining method developed in

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with path-planning has good machining and optical properties. Therefore, the micro-lens manufacturing method developed in this work reveals nice results and has advantages for quick, simple, easy, and low cost prototypes manufacturing. Moreover, the results show the proﬁles of lens are precisely machined used this method. The method can be furthermore used in manufacturing aspheric microlens array or micro convex-concave lenses and stamps of nanoimprint.

Author Contributions: M.-J.L. conceived and designed the idea for this research. He also analyzed the data and wrote the paper. C.H.W. performed the device fabrication and measurements. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A Computer-aided manufacturing (CAM) uses software to control machine to manufacture work pieces. There are some commercial software can transform the computer-aided design (CAD) files to machining code of CAM. In this work, the cutter-path planning is executed by the software MATLAB. And the data is transformed to machining code (G-code). The file of machining code is then stored into the CNC machine. The procedures of the cutter-path planning executed in MATLAB is expressed as following. Procedures Define the coordinate frame (and the origin) and machining parameters (radius of knife radius, feeding rate, feeding line segment, R, lens diameter, etc.). Define the x- and y- coordinates of center of circle of each lens. Determine the path interval ∆y. Calculate number of steps of machining processes in x- and y-directions. Then calculate the x- and y- coordinates of each steps. Calculate the scraping depth z by Equation (1). When machining of this lens is finished, move the knife to beginning point of the next lens.

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