sensors Article

A 3D Optical Surface Profilometer Using a Dual-Frequency Liquid Crystal-Based Dynamic Fringe Pattern Generator Kyung-Il Joo † , Mugeon Kim † , Min-Kyu Park, Heewon Park, Byeonggon Kim, JoonKu Hahn and Hak-Rin Kim * School of Electronics Engineering, Kyungpook National University, Daegu 41566, Korea; [email protected] (K.-I.J.); [email protected] (M.K.); [email protected] (M.-K.P.); [email protected] (H.P.); [email protected] (B.K.); [email protected] (J.H.) * Correspondence: [email protected]; Tel.: +82-53-950-7211; Fax: +82-53-940-8622 † These authors contributed equally to this work. Academic Editor: Gonzalo Pajares Martinsanz Received: 23 September 2016; Accepted: 24 October 2016; Published: 27 October 2016

Abstract: We propose a liquid crystal (LC)-based 3D optical surface profilometer that can utilize multiple fringe patterns to extract an enhanced 3D surface depth profile. To avoid the optical phase ambiguity and enhance the 3D depth extraction, 16 interference patterns were generated by the LC-based dynamic fringe pattern generator (DFPG) using four-step phase shifting and four-step spatial frequency varying schemes. The DFPG had one common slit with an electrically controllable birefringence (ECB) LC mode and four switching slits with a twisted nematic LC mode. The spatial frequency of the projected fringe pattern could be controlled by selecting one of the switching slits. In addition, moving fringe patterns were obtainable by applying voltages to the ECB LC layer, which varied the phase difference between the common and the selected switching slits. Notably, the DFPG switching time required to project 16 fringe patterns was minimized by utilizing the dual-frequency modulation of the driving waveform to switch the LC layers. We calculated the phase modulation of the DFPG and reconstructed the depth profile of 3D objects using a discrete Fourier transform method and geometric optical parameters. Keywords: optical surface profilometry; interference; phase modulation; liquid crystal; dynamic fringe pattern generator

1. Introduction Recently, the demand for acquiring 3D information has increased, accompanied by improvements in several 3D applications like 3D displays, 3D printing technologies, 3D medical or dental imaging systems, and 3D vision modules for robot or vehicle applications [1–6]. For these applications, 3D depth information together with conventional 2D images is critically needed, and cannot be obtained with conventional 2D vision systems. Optical 3D vision systems can measure 3D information for an object with a wide scope in a relatively short time because they obtain the 2D coordinate information together with the depth information optically in parallel using a Charge-Coupled Device (CCD) or Complementary Metal Oxide Semiconductor (CMOS) image sensor. The optical 3D surface profilometer can optically measure the surface morphology of an object and compute the depth information without direct contact. In general, optical surface profilometers, which extract 3D depth information from distortions of the projected optical beam patterns, need an optical beam pattern generator module to utilize several structured beam. To measure a surface profile of 3D objects, N-bits of binary-coded stripe patterns could be projected [7], where the number of the binary-coded projection beam patterns needed to be increased to improve the measurement Sensors 2016, 16, 1794; doi:10.3390/s16111794

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resolution. By utilizing gray-level beam patterns, the number of projection patterns could be effectively reduced [8], but this approach needs more complex spatial light modulators (SLMs) with a higher pixel resolution and a larger pixel density to generate the gray-level patterns. To effectively reduce the measurement time, a one-shot scanning method using periodic grid patterns was proposed [9]. Using a coherent light source, interference fringe patterns could be projected [10–14]. To avoid the optical phase ambiguity from the fringe patterns distorted by the surface morphology, multiple sets of interference patterns were needed, and phase unwrapping or geometrical parameter methods were applied to reconstruct surface depth profiles. The depth extraction method based on the geometrical parameters could provide the depth and position value informations in the absolute coordinate system without the phase unwrapping process [10]. These optical techniques do not damage the surface morphology of an object even for a soft surface. In most cases of optical surface profilometries, to acquire more precise 3D depth information, several sets of specific beam patterns are needed. These are generated by beam pattern projecting modules such as mechanically moving wedge plates [15], tunable gratings [16], switchable gradient index lenses [17], polymer dispersed liquid crystal (LC) techniques [18,19], and several types of phase modulators using SLMs [20,21]. Recently, to obtain color information of an object in addition to the 3D depth information, time-sequential projection of structured and RGB-colored beam patterns was also proposed using fast switching digital light processing (DLP) projectors [22]. However, conventional projection units based on commercial SLMs and DLP are too bulky and not cost-effective for industrial field applications, especially dental imaging, which needs an elaborate and complex semiconductor manufacturing process for the preparation of backplanes to control the 2D phase or intensity patterns with matrix driving schemes [23–25]. In this study, we propose an LC-based dynamic fringe pattern generator (DFPG) for a more compact 3D optical surface profilometer system, which can generate multiple fringe patterns to enhance the 3D depth extraction and avoid the optical phase ambiguity in analyzing the 3D depth profile from distorted fringe patterns induced by the surface morphologies. Sixteen interference patterns are generated with four-step phase shifting and four-step spatial frequency varying schemes by the proposed LC-based DFPG without a mechanically moving part. In our DFPG, the 16 sets of fringe patterns can be generated by a single, compact LC cell, which has one common slit operated by an electrically controllable birefringent (ECB) LC mode and four switching slits operated by a twisted nematic (TN) LC mode. Four different moving fringe patterns are controlled by the phase value of the ECB LC layer behind one common slit. The interferometric fringe patterns with four different spatial frequencies are controlled by electrically selecting one of the switching slits operated by the TN mode. The switching time of the DFPG module, required for projecting the 16 sets of fringe patterns, is minimized by utilizing the dual-frequency-based LC switching scheme. We present the optical and material design of the LC-based DFPG and its manufacturing process obtaining multiple sets of fringe patterns using a compact module with a fast switching time. The electrical switching properties of the phase modulation and the slit spacing controls for the interference patterns of the DFPG are characterized and the 3D depth profile reconstruction from the distorted fringe patterns using the discrete Fourier transform (DFT) method and geometric optical parameters is presented. 2. Operation Principle of the DFPG and the Theory of Depth Extraction 2.1. Schematic and Operation Principle of the DFPG 2.1.1. Schematic of the DFPG In this study, the DFPG was designed to develop a 3D optical surface profilometer that can exhibit multiple sets of interference fringe patterns with four steps of the spatial frequency and four steps of the phase shifting properties without any mechanical translation stages. As shown in Figure 1, the DFPG consists of a multi-directional LC alignment layer on the top substrate to provide the ECB LC and TN LC modes for the phase-shifting common slit and four switching slits, respectively. On the other side

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of the multi-alignment layer of the top substrate, five Al slits were fabricated by the lift-off process. The indium tin oxide (ITO) tin layer under multi-directional alignment alignment layer waslayer also was patterned lift-off process. The indium oxide (ITO)the layer under the multi-directional also using photolithography to control one ECB LCone layer and TN LCfour layers by applying patterned using photolithography to control ECB LCfour layer and TNindividually LC layers individually appropriate voltages to them. The positions thepositions patterned patterned LC alignment by applying appropriate voltages to them.of The ofITO the layer, patterned ITO layer, patternedlayers, LC alignment layers,precisely and Al slits werewith precisely withalignment each othermarks. with alignment marks. The and Al slits were aligned each aligned other with The spacings between spacings between onethe common slitmode with the mode and the other switching slits with the TN one common slit with ECB LC andECB theLC other switching slits with the TN LC modes were modes 200,µm. 400,The 600, and 800 µm.AlThe ofpatterned the Al slits and the patterned ITO ∆gLC = 200, 400,were 600, Δg and=800 widths of the slitswidths and the ITO electrodes were 52 and electrodes were 52 and 50 µm, respectively. A uni-directionally rubbed LC alignment layer was 50 µm, respectively. A uni-directionally rubbed LC alignment layer was prepared on the non-patterned prepared on the non-patterned ITO glass substrate as polarizers the bottom were substrate. Parallel ITO glass substrate as the bottom substrate. Parallel attached on polarizers both sideswere of the attached on both sides of the two substrates. two substrates.

Figure 1. 1. Schematic patterngenerator generatorfor forprojecting projecting multiple sets Figure Schematicofofthe theLC-based LC-baseddynamic dynamic fringe pattern multiple sets of of interference patternswith withphase-shifting phase-shiftingand and spatial-frequency-varying spatial-frequency-varying properties. interference patterns properties.

The multi-spatial frequency properties of the interference fringe patterns were achieved by The multi-spatial frequency properties of the interference fringe patterns were achieved by applying a turn-on voltage on one of the switching slits prepared with the TN LC mode. The fourapplying a turn-on voltage on one of the switching slits prepared with the TN LC mode. The four-step step phase shifting properties were developed by controlling the applied voltage through the ECB phase shifting properties were developed by controlling the applied voltage through the ECB LC LC mode layer used for the common slit. As a result, the DFPG can generate 16 sets of the multiple mode layer used for the common slit. As a result, the DFPG can generate 16 sets of the multiple fringe fringe patterns that exhibit four different spatial frequencies together with four-step phase-shifted patterns that exhibit fourselected different spatial frequencies together with four-step phase-shifted fringe fringe patterns for each spatial frequency. patternsThe forDFPG each selected spatial frequency. was fabricated with a dual-frequency LC (MLC-2048, Merck Ltd., Seoul, Korea) to The DFPG was fabricated with a dual-frequency LC (MLC-2048, Merck Ltd., Seoul, Korea) enhance its switching response time required for generating the 16 sets of fringe patterns. The to enhance its switching response time required for generating the 16 sets of fringe patterns. The inversion inversion frequency of the dielectric anisotropy of MLC-2048 is 50 kHz. Its dielectric anisotropy frequency ofΔε the dielectric anisotropy MLC-2048 kHz. Its =dielectric values values are = 3.2 at the low frequencyofAC driving ofis1 50 kHz and Δε −3.4 at theanisotropy high frequency ACare ∆εdriving = 3.2 atofthe low frequency AC driving of 1 kHzindex and ∆ε = −dual-frequency 3.4 at the high LC frequency driving 100 kHz. The extraordinary refractive of the is 1.7192,AC and the of ordinary 100 kHz.refractive The extraordinary refractive indexthe of cell the gap dual-frequency 1.7192, and the ordinary index is 1.4978. Therefore, of the DFPG LC wasiscalculated as 2.48 µm to realize over 3π/2 phase modulation LCgap layer. We DFPG dropped a mixture of an refractive index is 1.4978. Therefore, of thethe cell of the was calculated as optical 2.48 µmadhesive to realize polymer (NOA modulation 65, Norland of Products, NJ, USA) with ball the four polymer edges over 3π/2 phase the LC Inc., layer.Cranbury, We dropped a mixture of anspacers opticalon adhesive of the substrate, and the top wasball covered with electrode (NOA 65,patterned Norland ITO/Al Products, Inc., Cranbury, NJ,substrate USA) with spacers onthe thebottom four edges of the substrate. The ball spacers uniformly supported the cell gap of the DFPG required for reliable phase patterned ITO/Al substrate, and the top substrate was covered with the bottom electrode substrate. modulation. our DFPG,supported the cell gap 4 µm. The empty DFPG was filled MLCThe ball spacersInuniformly thewas cellabout gap of the DFPG required forcell reliable phasewith modulation. by the capillary forcewas overabout the nematic-isotropic phase transition temperature NI = 106.2 °C) of In 2048 our DFPG, the cell gap 4 µm. The empty DFPG cell was filled with(TMLC-2048 by the the LC. After slowly cooling the LC cell to room temperature, the LC layer was well aligned ◦ C) ofmulticapillary force over the nematic-isotropic phase transition temperature (TNI = 106.2 the LC. directionally along the patterned rubbing directions of the alignment layer of the top substrate, After slowly cooling the LC cell to room temperature, the LC layer was well aligned multi-directionally showing the two LC domains of the ECB and TN LC modes. along the patterned rubbing directions of the alignment layer of the top substrate, showing the two LC domains of the ECB and TN LC modes. 2.1.2. Operation Principle of the DFPG

2.1.2. Operation Principle of theofDFPG The operation principles our DFPG and field-dependent LC orientations on each patterned slit are shown in Figure 2, where the projected fringe patterns, which were measured under the farThe operation principles of our DFPG and field-dependent LC orientations on each patterned slit field interference conditions using a CCD camera, are co-plotted according to the applied voltage are shown in Figure 2, where the projected fringe patterns, which were measured under the far-field conditions. As shown in Figure 2, the common slit is aligned with the ECB LC mode that can interference conditions using a CCD camera, are co-plotted according to the applied voltage conditions. modulate the phase shifting and the four switching slits are aligned with the TN LC mode that can Asmodulate shown inthe Figure 2, the commonofslit aligned with the ECB LC mode polarizer that can modulate spatial frequencies theisfringe pattern. Under the parallel condition,the the phase LC

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shifting and the four switching slits are aligned with the TN LC mode that can modulate the spatial frequencies of the fringe pattern. Under the parallel polarizer condition, the LC alignment direction of Sensors 2016, 16, 1794 4 of 18 the bottom substrate is parallel with the transmission axes of the top and bottom polarizers. Therefore, thealignment incident polarization state after the bottomispolarizer doesthe nottransmission change irrespective of the direction of the bottom substrate parallel with axes of the topapplied and voltage within the ECB LC mode. The incident beam passing through the ECB LC layer bottom polarizers. Therefore, the incident polarization state after the bottom polarizer doesalways not transmits the top polarizer after passing though the common slit without intensity loss irrespective change irrespective of the applied voltage within the ECB LC mode. The incident beam passing of thethrough appliedthe voltage. ECB LC layer always transmits the top polarizer after passing though the common slit However, the polarization states incident beams passing through the TN LC layers, initially without intensity loss irrespective of of thethe applied voltage. polarized by the bottom polarizer,states are rotated 90◦ owing the polarization rotating effect of the However, the polarization of the by incident beamstopassing through the TN LC layers, initially polarizer, are rotated by 90° owing the polarization effect twisted LCpolarized structureby inthe thebottom field-off state. Thus, the beams after fourtoswitching slits arerotating blocked by the of thepolarizer twisted LC structure the field-off state. Thus, the beams afterscheme. four switching slits are anisotropy blocked second without an in applied voltage in our parallel polarizer The dielectric polarizer without an ourfrequency parallel polarizer scheme. The dielectric of by thethe LCsecond used in our experiment is applied positivevoltage under in low AC driving conditions, and the anisotropy of the LC usedthe in applied our experiment is positiveWhen underalow frequency AC driving LCs are reoriented along field direction. voltage sufficient to fullyconditions, reorient the and the LCs reoriented the applied fieldto direction. a voltage to fully reorient LCs along theare vertical fieldalong direction is applied the TN When LC layer undersufficient one of the switching slits the LCs along the vertical field direction is applied to the TN LC layer under one of the switching by the patterned ITO electrode, the LC molecules in the selected local area can be fully reoriented to by the patterned ITO electrode, the LCinmolecules in the selected local area can be fully reoriented theslits vertically aligned geometry, as shown Figure 2a,b. Thus, the beam passing through the selected to the vertically aligned geometry, as shown in Figure 2a,b. Thus, the beam passing through the switching slit can be transmitted through the second polarizer. Therefore, depending on the applied selected switching slit can be transmitted through the second polarizer. Therefore, depending on the voltages of the patterned ITO electrodes under the four switching slits, the distance between two applied voltages of the patterned ITO electrodes under the four switching slits, the distance between interference slits can be controlled, which enables four different spatial frequencies of the projected two interference slits can be controlled, which enables four different spatial frequencies of the fringe patterns, as shown in Figure 2a,b. In Figure 2a,b, the fringe patterns measured under the shortest projected fringe patterns, as shown in Figure 2a,b. In Figure 2a,b, the fringe patterns measured under and the longest slit distances in our DFPG are shown for the example cases of the lowest and the the shortest and the longest slit distances in our DFPG are shown for the example cases of the lowest highest spatial frequencies of the projected fringe patterns, respectively. By using and the highest spatial frequencies of the projected fringe patterns, respectively. Bythese usingmethods, these themethods, multi-spatial frequency schemes were developed in the DFPG without any mechanical translation the multi-spatial frequency schemes were developed in the DFPG without any mechanical stage part. stage part. translation

Figure 2.2.Operation principlesofofthe theDFPG DFPG switched by field-induced patterned LC orientations Figure Operation principles switched by field-induced patterned LC orientations and and resulting projected patterns. (a,b) the LC orientations spatial frequency thethe resulting projected fringefringe patterns. (a,b) show theshow LC orientations and spatial and frequency variations variations of the fringe projected fringe patterns the selected switching slit with (a) applied of the projected patterns by control of by the control selectedof switching slit with applied voltages: Δg voltages: (a)slit ∆gspacing = 200 µm = 800 (c,d) µm slit spacing; (c,d) show LC theorientations field-induced = 200 µm andslit (b)spacing Δg = 800and µm(b) slit∆g spacing; show the field-induced LCand orientations andfringe the moving fringe patterns the phase shifting at the slit with the moving patterns by control ofby thecontrol phase of shifting at the common slitcommon with applied voltages under the fixed spacing condition (Δg = 200(∆g µm=slit applied voltages under theslit fixed slit spacing condition 200spacing). µm slit spacing).

Under the fixed spatial frequency attained by selecting the switching slit of one TN LC layer, the four-step phase-shifting schemes can be achieved by applying voltages to the ECB LC layer of the

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Under the fixed spatial frequency attained by selecting the switching slit of one TN LC layer, the common slit for an appropriate phase difference with the phase of the selected switching slit. The four-step phase-shifting schemes can be achieved by applying voltages to the ECB LC layer of the phase shift is decided by the optical path length difference between the ECB LC layer and the fieldcommon slit for an appropriate phase difference with the phase of the selected switching slit. The phase applied TN LC layer under two slits of one common slit and the selected switching slit, respectively. shift is decided by the optical path length difference between the ECB LC layer and the field-applied Figure 2c,d show the initial and the relatively moved fringe patterns according to the applied voltages TN LC layer under two slits of one common slit and the selected switching slit, respectively. Figure 2c,d in the ECB LC layer for the same selected switching slit condition, where the spatial frequencies of show the initial and the relatively moved fringe patterns according to the applied voltages in the two fringe patterns maintain each other. The effective refractive index of the ECB LC layer can be ECB LC layer for the same selected switching slit condition, where the spatial frequencies of two varied by applying voltages because the incident polarization is parallel to the rubbing direction of fringe patterns maintain each other. The effective refractive index of the ECB LC layer can be varied the LC alignment layer, and the LC layer operated with the ECB LC mode, which has a fieldby applying voltages because the incident polarization is parallel to the rubbing direction of the LC dependent tilting redistribution of the LC layer, does not exhibit any LC twisting distortion alignment layer, and the LC layer operated with the ECB LC mode, which has a field-dependent irrespective of the applied voltages. Thus, the optical path length passing though the common slit tilting redistribution of the LC layer, does not exhibit any LC twisting distortion irrespective of the can be modulated according to the voltage applied to the ECB LC layer. For 3D depth extraction from applied voltages. Thus, the optical path length passing though the common slit can be modulated the projected fringe patterns, which are distorted by an object, four-step phase shifting, especially according to the voltage applied to the ECB LC layer. For 3D depth extraction from the projected fringe over 3π/2 phase shifting, is needed, and the thickness of the DFPG LC cell is designed considering patterns, which are distorted by an object, four-step phase shifting, especially over 3π/2 phase shifting, the birefringence of the LC used in our experiment. is needed, and the thickness of the DFPG LC cell is designed considering the birefringence of the LC used in our experiment. 2.1.3. Fabrication Process of the DFPG 2.1.3.To Fabrication Process ofthe the spatial-frequencies DFPG electrically control and phase modulation of the fringe patterns, the ITO To electrodes were patterned by a photolithography chemical etchingofprocess, as shown in electrically control the spatial-frequencies andand phase modulation the fringe patterns, Figure The first were step for developing patterned ITO electrodes was etching the spin-coating of ashown positive the ITO3a. electrodes patterned by athe photolithography and chemical process, as in photoresistor (GXR-601, AZ Electronic Materials Co., Wiesbaden, Germany) on the ITO glass Figure 3a. The first step for developing the patterned ITO electrodes was the spin-coating of a positive substrate. The(GXR-601, GXR-601 AZ photoresistor was coated under the conditions of 2500 rpm forglass 5 s, 3500 rpm photoresistor Electronic Materials Co., Wiesbaden, Germany) on the ITO substrate. for 30 s, and 2500 rpm for 5 s. After the spin-coating process, the coated ITO glass was heated to 90 The GXR-601 photoresistor was coated under the conditions of 2500 rpm for 5 s, 3500 rpm for 30 s, and ◦ °C on a hotplate for 90 s. Then, the coated photoresistor was projected through the photo-mask 2500 rpm for 5 s. After the spin-coating process, the coated ITO glass was heated to 90 C on a hotplate pattern ultraviolet light and was etched the photoresistor developer (AZ300, Electronic for 90 s. by Then, the coated photoresistor was with projected through the photo-mask pattern AZ by ultraviolet Materials Co.) for 18 s. light and was etched with the photoresistor developer (AZ300, AZ Electronic Materials Co.) for 18 s.

Figure 3. Fabrication process of the top substrate for the multiple slits and the aligned ITO patterns of the LC-based DFPG device: (a) ITO electrode patterning and (b) Al slit array patterning using the lift-off process.

The patterned patterned photoresistor photoresistor coated coated on on the the ITO ITO glass glass was was heated heated again again on on the the hotplate hotplate at at 120 120 ◦°C The C for 3 min. Finally, to define the ITO electrode pattern, the ITO electrode was etched by the ITO etchant for 3 min. Finally, to define the ITO electrode pattern, the ITO electrode was etched by the ITO etchant (LCE-12K, Cyantek Co., Fort Worth, TX, USA) for 20 min and the photoresistor, which might have remained on the substrate, was removed by an acetone cleaning process.

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(LCE-12K, Cyantek Co., Fort Worth, TX, USA) for 20 min and the photoresistor, which might 6have Sensors 2016, 16, 1794 of 18 remained on the substrate, was removed by an acetone cleaning process. To generate generate the the interference interference patterns, patterns, the the Al Al slits slits were were prepared prepared on on the the backside backside of the patterned To glass substrate. substrate. In this study, the Al slits slits were were fabricated fabricated using the metal lift-off ITO surface of the glass method to avoid chemical damage on the ITO patterns during our Al slit manufacturing prepared at patterning process, the patterned ITO glass glass substrate substrate was turned turned the same substrate. For the Al slit patterning over and and the thephotoresist photoresistwas waspatterned patternedwith witha aphoto-mask, photo-mask, shown Figure The slits must over asas shown in in Figure 3b.3b. The Al Al slits must be be aligned precisely the patterned ITO electrodes to each control slit independently. The aligned precisely withwith the patterned ITO electrodes to control slit each independently. The positions positions of the patterned ITO electrodes Al slits werewith aligned with the alignment A of the patterned ITO electrodes and the Aland slitsthe were aligned the alignment marks. A marks. negative negative photoresist (AZ-5214, AZ Electronic Materials Co.) wasfor used slit patterning, which photoresist (AZ-5214, AZ Electronic Materials Co.) was used thefor Althe slitAl patterning, which was was suitable formetal the metal lift-off process. After the process of the negative photoresist pattering, suitable for the lift-off process. After the process of the negative photoresist pattering, thethe Al Al layer deposited using vacuum thermal evaporation equipment with a 500 thickness. layer waswas deposited using vacuum thermal evaporation equipment with a 500 nmnm thickness. TheThe Al Al slit patterns were defined clearly by removing the photoresist acetone. To protect Alfrom slits slit patterns were defined clearly by removing the photoresist with with acetone. To protect the Althe slits a physical damage, SiOwas 2 layer was deposited on the Al patterned layer as a afrom physical scratchscratch damage, the SiO2the layer deposited on the patterned layer as Al a passivation passivation with a 500 nm thickness. layer with a layer 500 nm thickness. Torealize realizethethe optical 3D surface profilometry system any without any mechanical stage, we To optical 3D surface profilometry system without mechanical stage, we implemented implemented analigned orthogonally aligned LC the sample, where the two LC alignment directions were an orthogonally LC sample, where two LC alignment directions were precisely aligned precisely with regionsslitofand the four common slit and fourThose switching Those were with two aligned regions of thetwo common switching slits. were slits. also aligned with also the aligned with patterned electrodes, in Figures and 4. 4, Asthe shown in Figure 4, the patterned ITOthe electrodes, as ITO shown in Figuresas1 shown and 4. As shown in1 Figure orthogonally aligned orthogonally aligned LC sample was the implemented usingmethod the multi-rubbing method on the patterned LC sample was implemented using multi-rubbing on the patterned ITO/Al substrate. ITO/Al substrate. rubbing the LC with alignment withcloth a softattached rubbingon cloth on rubbing the rollAfter rubbing the After LC alignment layer a soft layer rubbing theattached roll-based based rubbing thecan LCbemolecules can be aligned unidirectionally on the LC alignment machine, the LCmachine, molecules unidirectionally on the LCaligned alignment surface along the surface along the rubbing direction owing to the rubbing-induced surface morphology and rubbing direction owing to the rubbing-induced surface morphology change and thechange alignment the alignment effect of the LC-interactive side chains of the LC alignment surface material [26]. effect of the LC-interactive side chains of the LC alignment surface material [26]. However, with this However, with this conventional rubbing process, the multi-directional patterned required LC alignment conventional rubbing process, the multi-directional patterned LC alignment condition, in our condition, required in our LCand modes of the LC the TN LC DFPG for coexisting two LCDFPG modesfor of coexisting the ECB LCtwo mode the TN LCECB mode inmode singleand LC cell, cannot mode in single LC cell,the cannot obtained. To develop the withwe thesuggested multi-directional be obtained. To develop DFPGbewith the multi-directional LC DFPG alignment, two stepsLC of alignment, suggested two by steps the rubbing process supported therubbing photolithography the rubbingwe process supported theofphotolithography process betweenby each step. First, process between each step.PI, First, the LC alignment layerIndustries (polyimide, SE-5811, Nissan the LC alignment layerrubbing (polyimide, SE-5811, Nissan Chemical Co.,PI, Tokyo, Japan) was Chemical Industries Co., Tokyo, Japan) was spin-coated on theofpatterned under the spin-coated on the patterned ITO electrode under the conditions 1000 rpm ITO for 5electrode s, 3000 rpm for 30 s, conditions of 1000 and 1000 rpm for 5rpm s. for 5 s, 3000 rpm for 30 s, and 1000 rpm for 5 s.

Figure 4. Schematic of the multi-rubbing process for two domains of the initial LC alignments on Figure 4. Schematic of the multi-rubbing process for two domains of the initial LC alignments on patterned ITO substrates to enable the ECB LC mode on the common slit for the phase changing of the patterned ITO substrates to enable the ECB LC mode on the common slit for the phase changing of interference patterns and the TN LC mode on the switching slits for changing the spatial frequency of the interference patterns and the TN LC mode on the switching slits for changing the spatial frequency the projected fringes: (a) spin-coating of the LC alignment layer; (b) the first rubbing process over the of the projected fringes: (a) spin-coating of the LC alignment layer; (b) the first rubbing process over whole area; (c) the second rubbing process after the formation of the patterned passivation layer with the whole area; (c) the second rubbing process after the formation of the patterned passivation layer photoresistor where the rubbing direction is orthogonal to the first rubbing direction; and (d) the final with photoresistor where the rubbing direction is orthogonal to the first rubbing direction; and (d) multi-rubbed LC alignment layer for the top substrate of the DFPG device, prepared after removing the final multi-rubbed LC alignment layer for the top substrate of the DFPG device, prepared after the passivation layer. removing the passivation layer.

The coated PI layer was baked at 230 °C for 30 min and then it was uni-directionally rubbed with the roll-based rubbing machine at a roller speed of 300 rpm and a substrate speed of 10 mm/s in the horizontal direction, as shown in Figure 4b. Before the second rubbing process, the rubbed PI layer

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The coated PI layer was baked at 230 ◦ C for 30 min and then it was uni-directionally rubbed with the roll-based rubbing machine at a roller speed of 300 rpm and a substrate speed of 10 mm/s in the Sensors 2016, 16, 1794 7 of 18 horizontal direction, as shown in Figure 4b. Before the second rubbing process, the rubbed PI layer was protected by the photoresist (GXR-601)(GXR-601) layer, and itlayer, was partially by thepatterned photolithography was protected by the photoresist and it patterned was partially by the process using the photo-mask, as shown in Figure 4c, where the LC alignment layer for the photolithography process using the photo-mask, as shown in Figure 4c, where the LCprepared alignment layer ECB LC mode operation common slit was locally protected for the protected second rubbing prepared for the ECB LCunder mode the operation under the common slit was locally for theprocess. second With the partially passivated PI layer, the uncovered PI surface was rubbed orthogonal to the first rubbing process. With the partially passivated PI layer, the uncovered PI surface was rubbed rubbing direction, the residual GXR-601 layer was completely removed as orthogonal to the and firstthen rubbing direction, and then the residual GXR-601 layerusing was acetone, completely shown in Figure 4d, which schematically shows the final LC alignment directions of the top substrate removed using acetone, as shown in Figure 4d, which schematically shows the final LC alignment of our DFPG, which two orthogonal LC alignments LC domains of the ECB and TN LC directions of the tophas substrate of our DFPG, which has for twotwo orthogonal LC alignments for two LC modes. two domains of LC alignment, photoresist process and its removing processprocess should domainsFor of our the ECB and TN LC modes. For ourthe two domains of LC alignment, the photoresist not degrade the LC capability degrade producedthe by LC the first rubbing process. andphysio-chemically its removing process should notalignment physio-chemically alignment capability Thus, the types of photoresist and their etchants should be carefully chosen, as mentioned in our produced by the first rubbing process. Thus, the types of photoresist and their etchants should be experimental procedure. carefully chosen, as mentioned in our experimental procedure. Figure and the the Al Al slit slit patterning patterning process, process, Figure 5a,b 5a,b show show the the photo-mask photo-mask used used for for the the ITO ITO etching etching and respectively. In Figure Figure 5a, 5a,five fivewide wideITO ITOpatterns, patterns,directly directlyconnected connected each ITO line pattern, respectively. In toto each ITO line pattern, cancan be be seen, which were prepared for the wire-bonding process to control the electro-optic properties seen, which were prepared for the wire-bonding process to control the electro-optic properties of the of the common five switching slits individually thesignals. drivingFigure signals. Figurethe 5c finally shows common slit andslit fiveand switching slits individually with the with driving 5c shows the finally implemented topofsubstrate ofwith the DFPG with theITO patterned ITOand electrodes andarrays. the AlThe slit implemented top substrate the DFPG the patterned electrodes the Al slit 2 in our sample implementation. The size of the actual area, 2 arrays. The substrate size was 15 × 20 mm substrate size was 15 × 20 mm in our sample implementation. The size of the actual area, which which optically as the DFPG, was almost 8 ×2. 1 mm2 . optically acts asacts the DFPG, was almost 8 × 1 mm

(a)

(b)

(c)

Figure 5. 5. CAD CAD images images of of photo-lithographic photo-lithographic masks masks with with the the alignment alignment marks marks for for (a) (a) ITO ITO patterning patterning Figure and (b) Al slit patterning; (c) Image of the fabricated DFPG device. and (b) Al slit patterning; (c) Image of the fabricated DFPG device.

2.2. Theory of Depth Extraction 2.2. Theory of Depth Extraction 2.2.1. Calculation Calculation of of the the Phase Phase Modulation Modulation 2.2.1. When using using our our four-step four-step phase-shifting phase-shifting scheme scheme for for the the 3D 3D depth depth extraction, extraction, the the phase-shifting phase-shifting When in our DFPG according to an applied voltage to the common slit needs to be precisely measured. The in our DFPG according to an applied voltage to the common slit needs to be precisely measured. optical set-up of the modulation measurement is shown in Figure 6a. The6a. coherent light source The optical set-up ofphase the phase modulation measurement is shown in Figure The coherent light of a He-Ne laser (λ = 632.8 nm) was used to generate interference fringe patterns and to measure the source of a He-Ne laser (λ = 632.8 nm) was used to generate interference fringe patterns and to measure field-dependent phase modulation of the LC layer operated by the ECB LC mode. The speckle noise the field-dependent phase modulation of the LC layer operated by the ECB LC mode. The speckle and high fringefringe visibility couldcould be minimized to beto a negligible levellevel as shown in Figures 2 and noise and order high order visibility be minimized be a negligible as shown in Figures 2 6 because the coherence length of the He-Ne laser used in our experiment was 20 cm that was much and 6 because the coherence length of the He-Ne laser used in our experiment was 20 cm that was smallersmaller than than thosethose of coherent light sources used interference much of coherent light sources usedfor forconventional conventional holographic holographic interference experiments. The fringe visibility of the dynamic fringe patterns was about 0.9 in our system. This experiments. The fringe visibility of the dynamic fringe patterns was about 0.9 in our system. This fringe visibility was enough to obtain the 3D depth extraction with our four-step phase-shifting and fringe visibility was enough to obtain the 3D depth extraction with our four-step phase-shifting and four steps steps of of multi-spatial multi-spatial frequency frequency scheme scheme [21]. [21]. The The beam beam from from the the He-Ne He-Ne laser laser was was expanded expanded by by four a beam expander and was passed through an iris to reduce the optical noise so that a suitable spot a beam expander and was passed through an iris to reduce the optical noise so that a suitable spot size with with aauniform uniformbeam beamintensity intensitycan cancover cover five slits. light polarized the xsize allall of of thethe five Al Al slits. TheThe light polarized withwith the x-axis axis polarizer was passed through the DFPG. DFPG generated fringe patterns polarizer was passed through the DFPG. The The DFPG generated fringe patterns fromfrom two two slitsslits andand the the fringe patterns expanded by a projection lens were projected on a flat-panel screen. The projected fringe patterns on the flat-panel screen were captured by a CCD (FL2-14S3H, Pointgrey, Richmind, BC, Canada) with 4.4 µm pixel pitch and the field of view (FOV) of the CCD lens module was 12°. We used the DFT method to measure the phase modulation. The fringe pattern by the DFPG was calculated using the equation Mphase = angle[X(pN/Λ + 1)], as explained in our previous study, obtained using a mechanical moving slit system [21]. The values of the phase modulation were

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fringe patterns expanded by a projection lens were projected on a flat-panel screen. The projected fringe patterns on the flat-panel screen were captured by a CCD (FL2-14S3H, Pointgrey, Richmind, BC, Canada) with 4.4 µm pixel pitch and the field of view (FOV) of the CCD lens module was 12◦ . We used the DFT method to measure the phase modulation. The fringe pattern by the DFPG8 was Sensors 2016, 16, 1794 of 18 calculated using the equation Mphase = angle[X(pN/Λ + 1)], as explained in our previous study, obtained using a mechanical moving slit system The of thevoltage phase with modulation wereofrepeatedly repeatedly calculated depending on the [21]. change of values the applied an increase 0.01 V per calculated depending on the of the applied voltage withwas an increase As step. As shown in Figure 6b,change the phase modulation over 3π/2 achievedofat0.01 5.6 V V.per Thestep. voltage shown 6b, the phase was achieved at 3.8, 5.6 V. The the values in forFigure the four-step phase modulation modulation over were3π/2 measured as 2.1, 3.1, and 5.6voltage V, eachvalues for thefor phase four-step phase were measured as 2.1, 3.1, 3.8,inand 5.6 V,6b. each the step phase of ∆φ =the 0, shift of Δφ = 0, modulation π/2, π, and 3π/2, respectively, as shown Figure Forfor each ofshift increasing π/2, π, and 3π/2, respectively, as shown in Figure 6b. For each step of increasing the applied voltage applied voltage to the common slit, the projected fringe patterns with the same spatial frequency to the common slit, the projected fringe with theofsame were moved spatially were moved spatially by a quarter of patterns the periodicity the spatial fringe frequency patterns, as shown in the inset by a quarter of the6b. periodicity of the fringe patterns, as shown in the inset picture of Figure 6b. picture of Figure

(a)

(b)

Figure 6. (a) Optical system for measuring phase modulation values of the common slit according to Figure 6. (a) Optical system for measuring phase modulation values of the common slit according to an applied voltage and their moving fringe patterns; (b) Measured phase modulation curve according an applied voltage and their moving fringe patterns; (b) Measured phase modulation curve according to an applied applied voltage voltage and and the thefringe fringe patterns patternscaptured capturedunder under∆φ Δφ== 0, 0, π/2, π/2, π, and 3π/2 3π/2 conditions. to an π, and conditions.

Figure 7 shows the time sequence of the driving waveforms applied to the common slit part and Figure 7 shows the time sequence of the driving waveforms applied to the common slit part and four switching slit parts used for our DFPG. The driving waveforms for the common slit were four switching slit parts used for our DFPG. The driving waveforms for the common slit were changed changed every 200 ms and the amount of the applied voltage was increased to 2.1 V, 3.1 V, 3.8 V, and every 200 ms and the amount of the applied voltage was increased to 2.1 V, 3.1 V, 3.8 V, and 5.6 V 5.6 V at 1 kHz to achieve phase shifting of Δφ = 0, π/2, π, and 3π/2, respectively, as shown in Figure at 1 kHz to achieve phase shifting of ∆φ = 0, π/2, π, and 3π/2, respectively, as shown in Figure 6. 6. At a given phase-shifting amount condition, four-step spatial-frequency-varying fringe patterns At a given phase-shifting amount condition, four-step spatial-frequency-varying were were projected by applying dual-frequency-driving waveforms to the TN LCfringe partspatterns individually projected dual-frequency-driving waveforms to the TN LC parts individually operated operated by by applying the four patterned ITO electrodes. The turn-on waveform for each TN LC part of the by the four patterned ITO electrodes. The turn-on waveform for each TN LC part of the switching switching slits was applied with 5 V of the applied voltage at 1 kHz for 50 ms, and then the turn-off slits was applied with 5 Vwith of the applied 1 kHz for 50 ms, and waveform waveform was applied 5V of the voltage appliedatvoltage at 100 kHz forthen 150the ms.turn-off These frequencywas applied with 5 V of the applied voltage at 100 kHz for 150 ms. These frequency-modulating modulating AC waveforms were applied in sequence to the ITO electrode pattern of each switching AC applied sequence to the ITO electrode of spatial each switching slit When every slit waveforms every 50 mswere to obtain fourinsets of fringe patterns with fourpattern different frequencies. 50 ms to obtain four sets of fringe patterns with fourAC different spatial applying applying the turn-off waveform with high frequency driving to thefrequencies. switching slitWhen IV, the voltage the turn-off waveform with high frequency AC driving to the switching slit IV, the voltage required required for the next step of the phase-shifting was applied to the ECB LC layer of the common slit for the next step of the phase-shifting was applied to the ECB LC layer of the common slit and then, and then, frequency-modulating waveforms were sequentially applied to the four TN LC layers to frequency-modulating waveforms were sequentially applied to patterns. the four TN LC layers to select four select four different spatial frequencies of the projected fringe In this manner, the whole different spatial frequencies of the projected fringe patterns. In this manner, the whole scanning time scanning time required for the four-step multi-spatial frequencies and four-step phase shifting required for thebefour-step multi-spatial four-step shifting couldcan be schemes could completed in less thanfrequencies 800 ms. Thisand means that thephase optical surfaceschemes profilometry completed in less than 800 ms. This means that the optical surface profilometry can capture 16 sets capture 16 sets of fringe patterns distorted by an object in less than 800 ms. Our profilometry using of patterns distorted by fast an object in less than 800 ms. Our profilometry using the DFPG can thefringe DFPG can exhibit quite scanning and capturing speeds suitable for hand-held dental exhibit quite fast scanningwith and capturing speeds suitable hand-held compared applications, compared our previous study of for a 3D optical dental surfaceapplications, profilometry system constructed with a mechanically moving optical element [21].

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with our previous study of a 3D optical surface profilometry system constructed with a mechanically 9 of 18 [21].

Sensors 2016, 16, 1794 moving optical element

Figure 7. Driving waveforms of voltages applied to the LC layer on each slit of the DFPG utilizing the Figure 7. Driving waveforms of voltages applied to the LC layer on each slit of the DFPG utilizing dual-frequency modulation for projecting 16 fringe patterns with the four different multi-spatial the dual-frequency modulation for projecting 16 fringe patterns with the four different multi-spatial frequencies and the four-step phase shifting within the fast switching time. frequencies and the four-step phase shifting within the fast switching time.

2.2.2. Theory of 3D Depth Extraction 2.2.2. Theory of 3D Depth Extraction Figure 8a shows the optical setup used to reconstruct a 3D depth profile with the DFPG device. Figure 8a shows the optical setup used to reconstruct a 3D depth profile with the DFPG device. The multiple sets of fringe patterns generated by the DFPG were projected though the projection lens The multiple sets of fringe patterns generated by the DFPG were projected though the projection lens onto the surface of an object. The fringe patterns distorted by the object surface were captured by a onto the surface of an object. The fringe patterns distorted by the object surface were captured by a CCD. Figure 8b shows the geometrical parameters used to calculate the depth and position CCD. Figure 8b shows the geometrical parameters used to calculate the depth and position information information from the CCD images. The optical system is composed of the DFPG, projection lens, CCD from the CCD images. The optical system is composed of the DFPG, projection lens, CCD camera, camera, and testing object. The DFPG and CCD are on the y-z plane. The center points of the and testing object. The DFPG and CCD are on the y-z plane. The center points of the projection lens, projection lens, CCD, and object are defined by (yM, zM), (yC, zC) and (yPOI, zPOI), respectively. The fringe CCD, and object are defined by (yM , zM ), (yC , zC ) and (yPOI , zPOI ), respectively. The fringe patterns are patterns are expanded through the projection lens, and the projected fringe patterns are distorted expanded through the projection lens, and the projected fringe patterns are distorted depending on the depending on the surface profile of an object. The optical axis of the DFPG is parallel to the z-axis, surface profile of an object. The optical axis of the DFPG is parallel to the z-axis, and the optical axis of and the optical axis of the CCD is tilted at an angle of φC to the z-axis. A point of interest (POI) on the the CCD is tilted at an angle of φC to the z-axis. A point of interest (POI) on the object is expressed object is expressed using geometrical parameters. As shown in Figure 8, a POI on the object is defined using geometrical parameters. As shown in Figure 8, a POI on the object is defined as (yPOI , zPOI ). as (yPOI, zPOI). The line between the center of the projection lens and the POI is tilted at an angle of α The line between the center of the projection lens and the POI is tilted at an angle of α with respect to with respect to the optical axis of the DFPG. The line between the center of the CCD and the POI is the optical axis of the DFPG. The line between the center of the CCD and the POI is tilted at an angle tilted at an angle of θPOI with respect to the optical axis of the CCD. In this case, the triangular method, of θPOI with respect to the optical axis of the CCD. In this case, the triangular method, defined by the defined by the geometrical parameters, leads to the following relationships: geometrical parameters, leads to the following relationships:



 



zPOI  zC   yPOI  yC cot C POI and z POI − zC = − (y POI − yC ) cot (φC − θPOI ) and z  y

z

y

 cot 

(1) (1)

POI M M z POI − zM = (yPOI POI − y M ) cotα

(2) (2)

 yC  yM    zC  zM  tan   z zPOI= (yC − y M ) − (zC − z M ) tanα and z POI tan −tan tan(φ CC −θ tanα  ) +C zC and POI POI

(3) (3)

From From Equations Equations (1) (1) and and (2): (2):

yPOI 

z

C

 zM    yC  yM  cot 

cot   cot  C  POI 

 yC

(4)

are obtained. Finally, Equations (3) and (4) show the depth and position information of the object calculated from the geometrical parameters [21].

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y POI =

(zC − z M ) − (yC − y M ) cotα + yC cotα + cot (φC − θPOI )

(4)

are obtained. Finally, Equations (3) and (4) show the depth and position information of the object calculated from Sensors 2016, 16, 1794the geometrical parameters [21]. 10 of 18

Figure 8. 8. (a) (a)Optical Opticalset-up set-uptotoreconstruct reconstructthe the depth profile a 3D object with DFPG device; Figure depth profile of of a 3D object with the the DFPG device; (b) (b) Geometrical parameters of the 3D vision system used for 3D depth extraction. Geometrical parameters of the 3D vision system used for 3D depth extraction.

3. Experimental ExperimentalResults Resultsand andDiscussion Discussion 3. 3.1. Dynamic Dynamic Phase Phase Changing Changing and and Multiple Multiple Spatial Spatial Frequency 3.1. Frequency Modulation Modulation Properties Properties of of the the DFPG DFPG In our our DFPG DFPG for for 3D 3D optical optical surface surface profilometry, profilometry, the the two two polarizers polarizers and and In the transmission transmission axes axes of of the the rubbing direction of the LC alignment layer of the bottom substrate are aligned to be parallel to the rubbing direction of the LC alignment layer of the bottom substrate are aligned to be parallel to each other. other. In In this configuration, Figure Figure 9a 9a shows shows the the polarization polarization optical optical microscope microscope (POM) (POM) each this device device configuration, images of the DFPG cell measured with applying the turn-on voltage to one of the TN LC layers used images of the DFPG cell measured with applying the turn-on voltage to one of the TN LC layers used for switching the switching slits with varying the spacing for two beam interference, ∆g = 200, 400, 600 for switching the switching slits with varying the spacing for two beam interference, Δg = 200, 400, and and 800 µm. As shown in Figure 9a, the9a, beam through the common slit, which used as 600 800 µm. As shown in Figure the transmitted beam transmitted through the common slit,iswhich is one beam spot for two-beam interference, is always under the turn-on state without intensity variation. used as one beam spot for two-beam interference, is always under the turn-on state without intensity However, the spacingthe between thebetween two slits the for interference be controlled applied voltage variation. However, spacing two slits forcan interference canby bethe controlled by the conditions of theconditions TN LC layers under switching slits. In all cases, three slit areas, applied voltage of the TNthe LCfour layers under the four switching slits.switching In all cases, three which were not selected by were the turn-on voltage, a dark texture without light transmittance. switching slit areas, which not selected by showed the turn-on voltage, showed a dark texture without observe the field-dependent birefringence change in the ECB LC layer under the common light To transmittance. slit, POM imagesthe of the DFPG cell were obtained between crossed after detaching the To observe field-dependent birefringence change the in the ECB polarizers LC layer under the common parallel polarizers from the DFPG cell, as shown in Figure 9b. In this measurement, the POM images slit, POM images of the DFPG cell were obtained between the crossed polarizers after detaching the ◦ with were captured by rotating rubbing bottom substrate of the DFPGthe cellPOM by 45images parallel polarizers from thethe DFPG cell, direction as shownof inthe Figure 9b. In this measurement, respect to the crossed polarizers. On thedirection commonofslit area, lightsubstrate transmittance a color change were captured by rotating the rubbing the bottom of theor DFPG cell by 45°could with be observed owing to a variation of the phase modulation with increasing applied voltage to the ECB respect to the crossed polarizers. On the common slit area, light transmittance or a color change could LCobserved layer. be owing to a variation of the phase modulation with increasing applied voltage to the ECB

LC layer.

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Figure POM images Figure 9.9. POM images depending depending on on applied applied voltage voltage conditions conditions at at each each slit. slit. (a) (a) POM POM images images measured measured between between the the parallel parallel polarizers polarizers with with varying varying selected selected switching switching slits slits for for interference, interference, which which creates creates fringe fringe patterns patterns with with four four different different spatial spatial frequencies; frequencies; (b) (b) POM POM images images showing showing the the four-step four-step phase phase shifting shifting of of the the LC LC layer layer on on the the common common slit slit captured captured between between the the crossed crossed polarizers polarizers to to show show field-dependent birefringence variation. field-dependent birefringence variation.

It is is important important to to obtain obtain the the fast fast response response property property of of the the DFPG DFPG required required in in projecting projecting 16 16 sets sets of of It multiplefringe fringepatterns. patterns. The depth profile is calculated from the 16pattern fringeimages patterndistorted images multiple The 3D 3D depth profile is calculated from the 16 fringe distorted surface morphology. The fasttime response of each LC slit is positively necessarythe to by surfaceby morphology. The fast response of eachtime LC slit is positively necessary to improve improve the operating time of the 3D vision system. In this study, the dual-frequency LC was used operating time of the 3D vision system. In this study, the dual-frequency LC was used to improve to improve response time of the LC layer A switching. A dual-frequency the frequencythe responsethe time of the LC layer switching. dual-frequency LC exhibitsLC theexhibits frequency-dependent dependent dielectricwhere anisotropy where Δε is positive the low frequency operation andunder Δε is dielectric anisotropy ∆ε is positive under the lowunder frequency operation and ∆ε is negative negative under the high frequency operation. That means that the LC molecules are reoriented along the high frequency operation. That means that the LC molecules are reoriented along the applied field the applied field underoperation, the low whereas frequency whereas the LC molecules are direction under thedirection low frequency theoperation, LC molecules are reoriented perpendicular reoriented perpendicular to the applied field direction under the high frequency operation. to the applied field direction under the high frequency operation. The response response times times of of the the DFPG DFPG were were measured measured by by electro-optic electro-optic characterization characterization equipment equipment The (LCMS200, Sesim Sesim Photonics Photonics Technology Technology Co. Co. Ltd., Ltd., Uiwang, Uiwang, Korea). Korea). The The common common slit slit was was blocked blocked to to (LCMS200, measure the response times of the switching slits operated by the TN LC mode. Figure 10a shows measure the response times of the switching slits operated by the TN LC mode. Figure 10a shows that the the turn-on turn-on response response time switched by the low Hz operation of 5 V at 1 kHz was about 1.6 ms, that sufficient for for projecting projecting multiple multiple fringe fringe patterns. patterns. However, the the turn-off turn-off response response time, time, measured measured by by sufficient the field-off condition, showed a relatively slow response with a value of about 36.1 ms, as shown in the showed a relatively slow response with a value of about 36.1 ms, as shown Figure 10b. The natural field-off LC in Figure 10b. The natural field-offLC LCrelaxation relaxationtotothe theinitial initialTN TNstate state is is supported supported only only by the LC elastic property and the LC surface anchoring, which was too slow to be used in our optical surface elastic property and the LC surface anchoring, which was too slow to be used in our optical surface profilometry system. In the switching slitslit was improved by profilometry Inour ourexperiment, experiment,the theturn-off turn-offresponse responseofof the switching was improved applying thethe high frequency operating fieldfield to obtain the field-driven turn-off property instead of the by applying high frequency operating to obtain the field-driven turn-off property instead natural field-off LC relaxation. FigureFigure 10c shows that the turn-off response was improved to about of the natural field-off LC relaxation. 10c shows that the turn-off response was improved to 8.1 ms8.1 byms applying a high afrequency AC field offield 5 V atof100 Consequentially, the total response about by applying high frequency AC 5 VkHz. at 100 kHz. Consequentially, the total time of the TNofslit 9.7about ms. As Figurein7,Figure the dual-frequency modulation scheme response time thewas TNabout slit was 9.7shown ms. Asinshown 7, the dual-frequency modulation was used to switch four switching slits in sequence at a given phase-shifting amount of the common scheme was used to switch four switching slits in sequence at a given phase-shifting amount of the slit. common slit.

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Figure LCLC layer of of thethe DFPG. (a) (a) Field-on response time; (b) Field-off Figure10. 10.On/Off On/Offresponse responsetimes timesofofthe the layer DFPG. Field-on response time; (b) Fieldresponse timetime obtained by the natural relaxation of the LCLC layer due to to thethe surface alignment off response obtained by the natural relaxation of the layer due surface alignmenteffect effect without applying any electric field; (c) Off response time obtained by applying a high frequency field without applying any electric field; (c) Off response time obtained by applying a high frequency field totothe anisotropy. theLC LClayer layerutilizing utilizingthe thefrequency frequencyinversion inversioneffect effectofofthe theLC LCdielectric dielectric anisotropy.

3.2. 3.2.Depth DepthExtraction Extractionfrom from3D 3DOptical OpticalProfilometry Profilometry Figure the photographic photographicimage imageofofthe theobject object used depth extraction Figure11a 11ashows shows aa the used forfor thethe 3D 3D depth extraction with with the presented 3D optical surface profilometry system, which was deliberately chosen to have the presented 3D optical surface profilometry system, which was deliberately chosen to havea a continuously surface together with an abrupt change from the background continuouslyslanted slanted surface together with an depth abrupt depthdiscontinuity change discontinuity from the reference surface. The smallest at the abrupt edges of the object was over 40 mm, background reference surface.height The smallest height side at the abrupt sideslanted edges of the slanted object was which was much higher than the optical wavelength used in our experiment. The regions marked with over 40 mm, which was much higher than the optical wavelength used in our experiment. The the dottedmarked red boxwith werethe reconstructed projecting multiple sets fringe patterns with ourofDFPG. regions dotted red after box were reconstructed afterofprojecting multiple sets fringe Figure 11bwith shows 16 sets of fringe distorted slanted object. Four sets laterally patterns ourthe DFPG. Figure 11b patterns shows the 16 setson of the fringe patterns distorted onof the slanted moved patterns were obtained by changing viaobtained the common slit control. At the a given ∆φ object. fringe Four sets of laterally moved fringe patterns∆φ were by changing Δφ via common condition, multiple fringe having four different spatial having frequencies sequentially projected slit control. At a given Δφpatterns condition, multiple fringe patterns four were different spatial frequencies by selecting the ∆gprojected conditionby ofselecting the switching Because there was a high discontinuity were sequentially the Δgslits. condition of the switching slits.depth Because there was a between the slanted surface and thethe background surface, bright (or dark) fringe lines on the high depth discontinuity between slanted surface andsome the background surface, some bright (or slanted surface were those on continuous the background optical phasesurface. ambiguity dark) fringe lines oncontinuous the slantedwith surface were withsurface. those onThis the background This could bephase solvedambiguity using the could four-step phase shifting scheme during theshifting depth reconstruction optical be solved using the four-step phase scheme during[21,27]. the depth

reconstruction [21,27].

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Figure 11. (a) Photographic image of the slanted object used for the 3D depth extraction; (b) CCD Figure Photographic image of the slanted object used depth extraction; CCD Figure 11.11. (a) (a) Photographic image of the slanted object used forfor thethe 3D3D depth extraction; (b)(b) CCD images of the distorted fringe patterns projected on the slanted object. images of the distorted fringe patterns projected slanted object. images of the distorted fringe patterns projected onon thethe slanted object.

The upper image of Figure 12a shows the enlarged CCD image of one of the projected fringe The upper image of of Figure 12a12a shows thethe enlarged CCD image of of one of of thethe projected fringe The upper Figure shows enlarged CCD image one projected fringe patterns, where image we can observe some optical noises within the fringe patterns, which might be patterns, where we can observe some optical noises within the fringe patterns, which might be be patterns, where we can observe some optical noises within the fringe patterns, which might produced by some particles from our optical components. However, the synthesized phase map produced byby some particles from our optical components. However, thethe synthesized phase map produced some particles from our optical components. synthesized phase map obtained after applying the four-step phase shifting algorithm,However, presented in the lower image of Figure obtained after applying the four-step phasephase shifting algorithm, presented in the lower image of image Figure of obtained after applying the four-step shifting algorithm, presented in the lower 12a, shows that this type of the background optical noise within the fringe patterns can be 12a, shows thisthat typethis of the of background opticaloptical noise noise within the fringe patterns cancan be be Figure 12a,that shows background within the fringe patterns successfully eliminated aftertype the 3D the depth reconstruction. successfully eliminated after the 3D depth reconstruction. successfully eliminated after the 3D depth reconstruction.

Figure 12. 12. (a) Original fringe optical pattern image (upper image) projected on the the slanted slanted surface surface of Figure Original fringe optical pattern image (upper image) projected Figure 12. (a) (a) Original fringe optical pattern image (upper image) projected on on the slanted surface of of Figure 11a 11a using using the the interference interference slit of ∆g Δg = = 200 µm and the the synthesized synthesized phase map (lower image) Figure of phase map (lower image) Figure 11a using the interference slitslit of Δg = 200200 µmµm andand the synthesized phase map (lower image) obtained using the four-step phase shifting algorithm; (b) Fictitious scanning pattern images obtained using the four-step phase shifting algorithm; (b) Fictitious scanning pattern images generated obtained using the four-step phase shifting algorithm; (b) Fictitious scanning pattern images generated from two spatial frequencies (Δg = 200 and 800 µm) of the projected fringe patterns (the from two spatial (∆g = 200(Δg and the projected patterns (thepatterns upper images) generated from twofrequencies spatial frequencies =800 200µm) andof800 µm) of thefringe projected fringe (the upper images) and four spatial frequencies (Δg = 200, 400, 600, and 800 µm) of the projected multiple andimages) four spatial = 200, 400, and400, 800600, µm)and of the multiple fringe patterns upper and frequencies four spatial (∆g frequencies (Δg600, = 200, 800projected µm) of the projected multiple fringe patterns (lower images). (lower images). fringe patterns (lower images).

In our depth reconstruction, the fictitious scanning pattern is generated through multiple spatial In our depth reconstruction, the fictitious scanning pattern is generated through multiple spatial frequencies of the interference fringes for the 3D depth reconstruction using the geometrical optical frequencies of the interference fringes for the 3D depth reconstruction using the geometrical optical

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In our depth reconstruction, the fictitious scanning pattern is generated through multiple spatial parameters In Figure 12b, thefor upper and the lower images show fictitious scanning frequencies [21,27]. of the interference fringes the 3D depth reconstruction using the the geometrical optical patterns generated from the two spatial frequencies of Δg = 200 and 800 µm and generated from full parameters [21,27]. In Figure 12b, the upper and the lower images show the fictitious scanning patterns sets of four spatial frequencies (Δg = 200, 400, 600, and 800 µm), respectively. Compared with the generated from the two spatial frequencies of ∆g = 200 and 800 µm and generated from full sets of four upper the fictitious scanning pattern in the lower image can make much peaks spatialimage, frequencies (∆g = 200, 400, 600, and shown 800 µm), respectively. Compared with thesharper upper image, owing to more sinusoidal sets of the spatial frequencies used in the synthesis of the fictitious scanning the fictitious scanning pattern shown in the lower image can make much sharper peaks owing to more pattern [21,27]. This in the enhanced depth resolution precision afterpattern the 3D [21,27]. depth sinusoidal sets of thecould spatialresult frequencies used in the synthesis of the and fictitious scanning reconstruction. This could result in the enhanced depth resolution and precision after the 3D depth reconstruction. Figure shows the the 3D 3Ddepth depthprofile profilereconstructed reconstructedfrom from the slanted object using 16 sets of Figure 13 13 shows the slanted object using thethe 16 sets of the the dynamic fringe patterns. Compared with conventional phase unwrapping methods [28], of dynamic fringe patterns. Compared with conventional phase unwrapping methods [28], oneone of the the merits of the depth reconstruction based on the geometrical optical parameters used in our merits of the depth reconstruction based on the geometrical optical parameters used in our experiment experiment is that the absolute values with the 2D positional values, not just the is that the absolute depth valuesdepth together withtogether the 2D positional values, not just the relative phase relative phase canasbe obtained, as shown values, can be values, obtained, shown in Figure 13. in Figure 13.

Figure13. 13.3D 3Ddepth depthprofile profilereconstructed reconstructed from from the the slanted slanted object. object. Figure

When When the the size size of of an an object object to tobe bemeasured measured with with projecting projecting the the dynamic dynamic fringe fringe patterns patterns and and to to be be reconstructed with the 3D depth extraction increases with approaching the values of the numerical reconstructed with the 3D depth extraction increases with approaching the values of the numerical aperture aperture (NA) (NA) of of the the projection projection lens lens and and the the FOV FOV of of the the CCD CCD lens lens module, module, the the calibrations calibrations of of the the fringe images captured by the CCD camera would be needed to reduce and to compensate the image fringe images captured by the CCD camera would be needed to reduce and to compensate the image distortions distortions which which might might become become more more severe severe especially especially in in the the captured captured image image boundaries boundaries owing owing to to like the vignetting effect of the lens-based projection and imaging system. In our experiment, like the vignetting effect of the lens-based projection and imaging system. In our experiment,the theNA NA of the projection projectionlens lenswas was the FOV the lens CCD lens module 12°. Considering the of the 0.40.4 andand the FOV of theofCCD module was 12◦ .was Considering the projection projection distance of 1 m, the object size which can be measured in our experiment would be about distance of 1 m, the object size which can be measured in our experiment would be about 25 × 25 cm2 . 2. However, our object size was limited under 2 because we had a problem in 25 × 25 cmour 20 × 20 cm However, object size was limited under 20 × 20 cm2 because we had a problem in enlarging the enlarging detectable object because of the highly fringe intensitythe with increasing detectablethe object size because ofsize the highly weakened fringeweakened intensity with increasing fringe pattern the fringe pattern size as shown in Figures 2 and 11. In our projection system, the much parts of the size as shown in Figures 2 and 11. In our projection system, the much parts of the incident optical incident optical beams were five slits and the intensity profiles projected by the beams were blocked by the fiveblocked slits andbythethe intensity profiles projected by the projection lens decrease projection lens decrease from the center to the image edges. We expect that this problems would be from the center to the image edges. We expect that this problems would be solved by improving the solved by improving the collimating projection lens part and by introducing the optical coupling collimating projection lens part and by introducing the optical coupling module between the light module between the lightslits source and the work. individual slits this in the future work. However, source and the individual in the future However, nonuniform intensity profilethis did nonuniform intensity profile did not affect the depth extraction process in our four-step phase not affect the depth extraction process in our four-step phase shifting and four steps of multi-spatial shifting andscheme four steps of multi-spatial frequency as shown Figure our experiment frequency as shown in Figure 12. In our scheme experiment set-up,inwe used12. theInsurface-distorted set-up, we used the surface-distorted dynamic fringe patterns captured by the CCD lens module dynamic fringe patterns captured by the CCD lens module without the positional image calibration for without the positional image calibration for the 3D depth extraction process. We checked the effect the 3D depth extraction process. We checked the effect of the image distortion by our lens system by of the image distortion by our lens system by placing a grid pattern at the object plane, the image placing a grid pattern at the object plane, the image distortion was negligible under our experimental distortion negligible our experimental conditions of 13, thethe FOV and the measurement conditionswas of the FOV andunder the measurement distance. In Figure measurement error in the distance. In Figure 13, the measurement error in the absolute value was less than 2 mm. This might originate from additional image distortions produced during the depth reconstruction process based on the geometric parameters, which are dependent on the perspective imaging condition expressed

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15 of 18 less than 2 mm. This might originate from additional image distortions produced during the depth reconstruction process based on the geometric parameters, which are dependent on by angle values of α condition and θPOI of Equations (4).values We expect thatθthe measurement accuracy thethe perspective imaging expressed by(3) theand angle of α and POI of Equations (3) and (4). can be further improved after calibration of these geometric parameters by using the periodic test We expect that the measurement accuracy can be further improved after calibration of these geometric patterns and the size of the measurable object can be enlarged after improving the projection parts parameters by using the periodic test patterns and the size of the measurable object can be enlarged and camera module. afterimproving improvingthe theCCD projection parts and improving the CCD camera module. Figure 14a shows the CCD thethe distorted fringe patterns projected on aon square box Figure 14a shows the CCDimages imagesof of distorted fringe patterns projected a square 3 object (80 × (80 80 ××8080 mm perspective view of theview 3D depth profile obtained afterobtained the 3D depth 3 ). The perspective box object × ).80The mm of the 3D depth profile after reconstruction is presented in Figure 14b with the absolute coordinate axis values. For each y, and the 3D depth reconstruction is presented in Figure 14b with the absolute coordinate axisx, values. zFor coordinate measurement errors of the extracted 3D depth were3D 1.6,depth 0.9, 1.2 mm, each x, y,axis, andthe z coordinate axis, the measurement errors of theprofile extracted profile respectively, slightly which different depending on the coordinate coordinatewere 1.6, 0.9, which 1.2 mm,were respectively, were slightly different depending axis. on theThis coordinate axis. dependent measurement error might originated in the different perspective viewing conditions This coordinate-dependent measurement error might originated in the different perspective viewing between thebetween projection part and the image-capturing CCD camera part in ourpart optical system as conditions thelens projection lens part and the image-capturing CCD camera in our optical shown the previous approaches, most of the optical profilometry systems are systemin asFigure shown8.inInFigure 8. In the previous approaches, most ofsurface the optical surface profilometry based on the phase unwrapping algorithm for the depth reconstruction [28–30] and need more systems are based on the phase unwrapping algorithm for the depth reconstruction [28–30] and complex optical elements like the time-sequentially switching multi-wavelength light sources [31,32], need more complex optical elements like the time-sequentially switching multi-wavelength light additional optical components [33,34], and a mechanical translation state [21,35] for the projection to sources [31,32], additional optical components [33,34], and a mechanical translation state [21,35] for generate multi-spatial-frequency or/and phase-shifting fringe patterns. Our optical surface the projection to generate multi-spatial-frequency or/and phase-shifting fringe patterns. Our optical profilometry system system based on the electrically switching single DFPG cancell generate dynamic fringe surface profilometry based on the electrically switching single cell DFPG can generate dynamic patterns in a fast switching time and can extract the depth and 2D positional information of 3Da fringe patterns in a fast switching time and can extract the depth and 2D positional informationa of object even for cases having large surface depth discontinuities. 3D object even for cases having large surface depth discontinuities.

Figure 14. 14. (a) (a) CCD CCD images images of of the the distorted distorted fringe fringe patterns patterns projected projected on on the the square square box box object; object; (b) (b) 3D 3D Figure depth profile reconstructed from the square box object. depth profile reconstructed from the square box object.

4. Conclusions Conclusions 4. 3D optical opticalsurface surfaceprofilometry profilometrysystems systemshave havebeen been applied measure depth profile 3D applied to to measure thethe depth profile of aof 3Da 3D object and their application fields are much growing recently. To enhance the accuracy of the object and their application fields are much growing recently. To enhance the accuracy of the 3D 3D depth extraction and/or to avoid phase ambiguity problem,multiple multiplesets setsof of fringe fringe pattern pattern depth extraction and/or to avoid thethe phase ambiguity problem, projections are essential in the optical surface profilometry system. We suggested a single LC cell DFPG projections are essential in the optical surface profilometry system. We suggested a single LC cell operated by a simple passive driving scheme, which can be fabricated into a compact optical module. DFPG operated by a simple passive driving scheme, which can be fabricated into a compact optical To project sets of16 dynamic fringe patterns having the optical of four-step phase shifting module. To16project sets of dynamic fringe patterns having thefeatures optical features of four-step phase and four different spatial frequencies without any mechanical parts and any complex and expensive shifting and four different spatial frequencies without any mechanical parts and any complex and SLM parts,SLM two types LC types modes—the LC mode andLC themode TN LCand mode—were included in the expensive parts,oftwo of LC ECB modes—the ECB the TN LC mode—were single LCincell preparing orthogonal LCorthogonal alignments onalignments one of theon LCone alignment Five included theby single LC celltwo by preparing two LC of the LClayers. alignment optical slits were prepared using photolithography and aligned with the patterned LC alignment layers. Five optical slits were prepared using photolithography and aligned with the patterned LC layer, where one common slitcommon with the slit ECBwith LC layer wasLC used for the alignment layer, where one the ECB layer wasfour-step used forphase-shifting the four-step control phase-

shifting control and four switching slits with the TN LC layers were used for the generation of four different spatial frequencies. Moreover, to improve the scanning time required for generating the 16 sets of dynamic fringe patterns, dual-frequency switching LC was employed, where the switching time—including the turn-on and the turn-off times—controlled by the frequency modulation

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and four switching slits with the TN LC layers were used for the generation of four different spatial frequencies. Moreover, to improve the scanning time required for generating the 16 sets of dynamic fringe patterns, dual-frequency switching LC was employed, where the switching time—including the turn-on and the turn-off times—controlled by the frequency modulation increased four-fold about four times compared with the switching time controlled by the conventional single frequency. As a result, the 16 sets of fringe patterns could be projected and captured within 800 ms. For the depth reconstruction procedures, the phase shifting in the common slit of the DFPG according to the applied voltages was accurately measured. The resolution of the depth reconstruction obtained by applying the DFT method and the optical geometric parameters was improved by using the four different sets of spatial frequencies of the dynamic fringe patterns. Our 3D optical surface profilometry system yields 3D depth profiles with respect to the absolute value 3D coordinates, not just the relative phase depth maps, even for objects with abruptly changing surface profiles. Owing to the compactness and fast switching properties of the DFPG, we expect that the presented 3D optical surface profilometry system can be applied to a hand-held 3D vision module, which can be widely used for several mobile applications requiring 3D depth information. Acknowledgments: This work was supported by ‘The Cross-Ministry Giga KOREA Project’ grant from the Ministry of Science, ICT and Future Planning, Korea. Author Contributions: Kyung-Il Joo and Mugeon Kim equally contributed to this paper. Hak-Rin Kim conceived and designed the experiments. Kyung-Il Joo and Mugeon Kim performed the optical experiments. Min-Kyu Park and Heewon Park prepared the LC device. Mugeon Kim and Byeonggon Kim designed the optical module and packaged it. Mugeon Kim, Kyung-Il Joo and Hak-Rin Kim analyzed the data and wrote the paper. JoonKu Hahn contributed the reconstruction algorithm. Hak-Rin Kim proofread and revised the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript: DFPG LC TN ECB ITO He-Ne Laser DFT POM FOV

Dynamic Fringe Pattern Generator Liquid Crystal Twisted Nematic electrically controlled birefringence indium thin oxide Helium-Neon Laser Discrete Fourier Transform Polarizing Optical Microscope Field of View

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