TWI877795B - A kind of improved dihedral corner reflector array and its application in stereolithography method and apparatus. - Google Patents
A kind of improved dihedral corner reflector array and its application in stereolithography method and apparatus. Download PDFInfo
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現有的雙角反射鏡陣列(DCRA),自發明以來大部份運用於浮空投影顯示方面;其部份原因是因為其鬼影的產生;難以消除。本發明從理論方面深入分析其產生原因,並提出有效方法加以防治。然後運用其浮空投影的特點,運用於光固化式的(積層製造設備)3D印表機系統之中,可以大幅加快其列印速度及增加精度。當前的光固化式3D印表機,運作起來非常緩慢,經常一個工件要列印要等上2~3小時,令人心急,經常中途列印失敗,不能穩定工作,令人卻步。究其原因,普通的光固化式3D印表機是緊貼著LCD做曝光的,每當曝光完畢,工件必須脫璃曝光區,讓工件不產生沾黏,讓新鮮的溶劑流入曝光區。脫離的過程產生溶劑的搖晃擾動,造成工件品質非常不穩定;列印完沾黏的殘渣更是麻煩無限,每一次都需要更換耗材。改善鬼影效應之後的雙角反射鏡陣列,可以浮空成像在溶劑之中,可以快速連續列印,沒有沾黏問題,使得整個列印時間可以縮短到只有傳統方法的1/5。 Since its invention, the existing dual-angle reflector array (DCRA) has been mostly used in floating projection display. Part of the reason is that it produces ghost images, which are difficult to eliminate. The present invention analyzes the causes of its generation from a theoretical perspective and proposes effective methods to prevent and control it. Then, using its floating projection characteristics, it is applied to the light-curing (layer-by-layer manufacturing equipment) 3D printer system, which can greatly speed up its printing speed and increase its accuracy. The current light-curing 3D printer operates very slowly. It often takes 2 to 3 hours to print a workpiece, which makes people anxious. Printing often fails in the middle and cannot work stably, which makes people hesitate. The reason is that ordinary light-curing 3D printers are exposed in close contact with the LCD. After each exposure, the workpiece must be deglazed in the exposure area to prevent the workpiece from sticking and allow fresh solvent to flow into the exposure area. The deglazing process causes the solvent to shake, resulting in very unstable workpiece quality; the sticky residue after printing is even more troublesome, and the consumables need to be replaced every time. The double-angle reflector array after improving the ghosting effect can float in the solvent, allowing for fast and continuous printing without sticking problems, so that the entire printing time can be shortened to only 1/5 of the traditional method.
浮空投影裝置的發明,2006年前川聰在SPIE(國際光電工程協會)發表論文,利用雙角反射鏡陣列(DCRA),可以形成浮在空中的高品質影像如第1圖。整個系統,含物方110,DCRA元件100及成像方120。物方110與DCRA 元件100有45°夾角,DCRA元件100與成像方120有45°夾角,物方110與成像方120有相互成90°夾角的特徵。僅管實際的成品還有鬼影及低光利用效率的缺點;但其解析度仍然遠遠勝過以往使用傳統光學元件做成的效果。目前經過多年的改良,其做成的浮空投影顯示器已有成功的商業運用。唯鬼影的消除仍然不夠完美,以致於限制了其它的用途。 In 2006, Chuan Cong published a paper in SPIE (International Society of Photoelectric Engineering) on the invention of the floating projection device. By using the double-angle reflector array (DCRA), a high-quality image floating in the air can be formed as shown in Figure 1. The entire system includes an object space 110, a DCRA element 100 and an imaging space 120. The object space 110 and the DCRA element 100 have a 45° angle, the DCRA element 100 and the imaging space 120 have a 45° angle, and the object space 110 and the imaging space 120 have a 90° angle with each other. Although the actual finished product still has the disadvantages of ghosting and low light utilization efficiency; its resolution is still far better than the effect made by using traditional optical elements in the past. After years of improvement, the floating projection display made by it has been successfully used in business. However, the ghost removal is still not perfect enough, which limits its other uses.
關於DCRA的鬼影問題,經過大量的實驗結果,可以發現從物方來的光線,經過DCRA之後,只有一部份變成了有效的成像光線;總括來說;如第2圖,在YZ平面上來看,有大於45度部份的光線140,此部份的光線,無法入射到DCRA中雙角反射面的任何一面;變成雜光被DCRA中的黑色檔光層中吸收消失。有小於45度的光線150,但是可以入射到DCRA中雙角反射面的一個面,但是無法入射到DCRA中雙角反射面的另外一個面,這部份的光線會成像在成像區,變成鬼影光線;有小於45度的光線160,但是都可以連續入射到DCRA中雙角反射面的兩個面,這部份的光線會清楚成像,是我們需要的光線;這三部分的光混雜再一起,變成我們所看到的影像;過去有一些論文提及改變光源的角度分布可以減少鬼影情況,但是當光源的強度增加,人眼仍然能察覺其存在,本發明將從理論及改進設計的觀點,徹底消除鬼影,擴展其在其他成像光學方面的應用。 Regarding the ghosting problem of DCRA, after a large number of experimental results, it can be found that only a part of the light from the object side becomes effective imaging light after passing through DCRA. In summary, as shown in Figure 2, on the YZ plane, there is a part of light 140 greater than 45 degrees. This part of the light cannot be incident on any side of the double-angle reflective surface in DCRA; it becomes stray light and is absorbed by the black light layer in DCRA and disappears. There is light 150 less than 45 degrees, but it can be incident on one side of the double-angle reflective surface in DCRA, but it cannot be incident on the other side of the double-angle reflective surface in DCRA. This part of the light will be imaged in the imaging area and become ghost light; there is light 160 less than 45 degrees, but it can be incident on both sides of the double-angle reflective surface in DCRA continuously. This part of the light will form a clear image, which is the light we need; these three parts of light are mixed together to become the image we see; in the past, some papers mentioned that changing the angular distribution of the light source can reduce the ghost situation, but when the intensity of the light source increases, the human eye can still perceive its existence. The present invention will completely eliminate ghosts from the perspective of theory and improved design, and expand its application in other imaging optics.
關於DCRA做為成像元件應用其他領域;DCRA自從發明以來,因為其卓越的解析度特性,引起許多人的關注,但是令人困擾的鬼影問題,難以擴展其應用;如果能消除鬼影,DCRA將有比傳統成像光學元件更具優勢的應用;比如曝光顯影用的成像鏡頭。傳統的成像鏡頭為了消除球差及畸變;必須堆疊非常多的鏡片組以消除像差,另外是必需做精準位移控制,才能獲 得大面積的精密影像成像;如果加上其必需是在浸潤式的情況成像;鏡頭的工作距離必需足夠,這造成鏡頭設計及製造需克服許多困難,成本也極高。本發明方面走另外的途徑,利用DCRA簡單而且高解析度的特質,設法從理論層次去解析及改變設計,消除鬼影。並且引入到積層製造(3D列印)方面的運用。 Regarding the application of DCRA as an imaging element in other fields; since its invention, DCRA has attracted the attention of many people due to its excellent resolution characteristics, but the annoying ghost problem makes it difficult to expand its application; if ghosting can be eliminated, DCRA will have more advantageous applications than traditional imaging optical elements; such as imaging lenses used for exposure and development. In order to eliminate spherical aberration and distortion, traditional imaging lenses must stack a lot of lens groups to eliminate aberrations, and precise displacement control is required to obtain large-area precision imaging; if it is added that it must be imaged in an immersion situation, the working distance of the lens must be sufficient, which causes many difficulties to be overcome in lens design and manufacturing, and the cost is also extremely high. This invention takes a different approach, using the simplicity and high-resolution characteristics of DCRA to analyze and change the design from a theoretical level to eliminate ghosting. It also introduces the application of multi-layer manufacturing (3D printing).
DLP光固化式積層製造設備,如第3A圖,第3B圖是DLP式的光固化式積層製造設備(以下簡稱3D印表機)200,利用燈泡(或LED)產生的UV光220,將芯片210上的影像,經由220投影鏡頭投影到240光固化溶劑槽240中工件的所在位置250;顯示出切片畫面。在高分子感光溶液中,曝光顯影,凝結成型。然後再移動升降機構裝置260進行下一層切片的投影,曝光成型。這個系統的缺點是,做為光學放大的鏡頭基本上在週邊會產生畸變像差,造成工件變形;解析度品質方面,中心與週邊不一致;往往中心區域解析度可以,週邊會變形及模糊;另外是如圖3C,鏡頭的邊緣光束270,在廣角的情況下,光固化溶劑的濃度會變,導致遠近成像位置280,290會有些微改變,造成成像的大小會變化。這對於越廣角的鏡頭,誤差越嚴重。因此不能太廣角的結果,造成製造的面積沒有辦法很大,而且高品質的光學成像鏡頭價格,也極為昂貴難以接受。
DLP photocuring type multilayer manufacturing equipment, as shown in FIG. 3A and FIG. 3B, is a DLP type photocuring type multilayer manufacturing equipment (hereinafter referred to as 3D printer) 200, which uses
LCD光固化式積層製造設備,如第4A圖,第4B圖是LCD式的光固化式積層製造設備(以下簡稱3D印表機);利用單色LCD面板320及UV LED背光板310;在光固化溶劑槽330中,顯示切片畫面,透過離形膜在高分子感光溶液中,密接曝光凝結成型。此方法的優點是,製造面積可以比較大,解析度高,中心與週邊解析度平均。缺點如第4C圖,顯示,300A,300B,300C是三種工作狀態,密接曝光,脫離,回復定位點之示意圖,一開始升降機350控制
340工件,與LCD上的離型膜320密接曝光,溶劑凝結成型。然後進行脫離,與離形膜撕裂,(否則無法進行下一層切片製造)。等新的溶濟流入,然後再度與LCD上的離形膜密接,進行下一層切片曝光成型。這裡面LCD面板上的離型膜的作用至為關鍵;一個有400個切片的立體工件,離形膜要能承受分離的撕裂力量而且不留殘渣;(因此經常失敗),離形膜成為必要更換的耗材;品質極為關鍵。另外用使用離形膜,系統必須在切片畫片曝光完之後要分離,讓感光溶液流入曝光區及等待溶液靜止;因此速度上很慢;如果垂直移動的軸承不穩定,會造成列印的工件歪斜扭曲。因此LCD式的光固化式3D印表機僅管成本較低;但仍然被視為低階機種;其列印品質及速度仍然需要大幅改進。
LCD photocuring lamination manufacturing equipment, as shown in Figure 4A, Figure 4B is an LCD-type photocuring lamination manufacturing equipment (hereinafter referred to as 3D printer); using a single-
關於下一代用於3d列印的成像元件,綜合以上所述,下一代用於3d列印的成像元件,其必要的條件為: Regarding the next generation of imaging components for 3D printing, based on the above, the necessary conditions for the next generation of imaging components for 3D printing are:
(1)要能有足夠長的工作距離,可以在液體中成像 (1) It must have a sufficiently long working distance to be able to image in liquids
(2)最好是像方遠心成像,也就是稍微改變距離也不影響成像大小 (2) It is best to use telecentric imaging, which means that a slight change in distance will not affect the image size.
(3)能做大面積成像 (3) Capable of large-area imaging
(4)成像元件的成本要低,結構不要太敏感複雜。從以上的條件來看,改進後的DCRA實為最佳的候選元件。 (4) The cost of the imaging element should be low and the structure should not be too sensitive or complex. Based on the above conditions, the improved DCRA is the best candidate element.
本發明針對雙角反射鏡陣列(DCRA)做光線路徑理論的分析,提出一種在輸入光線平面處,設立禁止區,以限制一次反射之無效光線進入單元內的方法;(實務上是將禁止區塗黑),因此可以取出純淨的二次反射之有效光,以消除鬼影。本發明亦藉由理論計算提出,成像解析度與單元大小之數學關係,也就如果能定義希望得到的解析度,便可以依此計算出所需的單元 大小。另外,本發明提出可以將去除鬼影後的雙角反射鏡陣列(DCRA),應用於浸潤式曝光機之方法,並且設計出其架構。另外進一步,本發明提出可以將去除鬼影後的雙角反射鏡陣列(DCRA),應用於光固化積層製造(3D印表機)之方法,並且設計出其架構。新式的光固化積層製造(3D印表機),比傳統形式精準,而且因為可以連續列印,速度相對較快。 The present invention analyzes the light path theory of the dual-angle reflector array (DCRA) and proposes a method to set up a forbidden area at the input light plane to limit the invalid light of the first reflection from entering the unit; (in practice, the forbidden area is painted black), so that the pure effective light of the second reflection can be extracted to eliminate ghosting. The present invention also proposes the mathematical relationship between imaging resolution and unit size through theoretical calculation, that is, if the desired resolution can be defined, the required unit size can be calculated accordingly. In addition, the present invention proposes a method to apply the dual-angle reflector array (DCRA) after ghosting is removed to an immersion exposure machine, and designs its structure. Furthermore, the present invention proposes a method of applying the dual-angle reflector array (DCRA) after ghost removal to photocuring laminated manufacturing (3D printer) and designs its structure. The new photocuring laminated manufacturing (3D printer) is more accurate than the traditional form, and because it can print continuously, the speed is relatively fast.
100:雙角反射鏡陣列(DCRA)平板 100: Double-angle reflector array (DCRA) plate
110:物方在顯示器位置 110: Object is at the display position
120:像方在浮空投影顯像之位置 120: The image side's position in the floating projection display
130:DCRA之單元 130: DCRA Unit
140:與中軸線夾角超過45度之光線,只能打到雙角反射鏡之一面 140: Light that is at an angle of more than 45 degrees to the center axis can only hit one side of the double-angle reflector.
150:與中軸線夾角小過45度之光線,但只能打到雙角反射鏡之一面 150: Light with an angle less than 45 degrees to the central axis can only hit one side of the double-angle reflector
160:與中軸線夾角小過45度之光線,可以打到雙角反射鏡的兩個面 160: Light with an angle less than 45 degrees with the central axis can hit both sides of the double-angle reflector.
170:與中軸線夾角小過45度之光線,可以打到雙角反射鏡之第二面的邊緣點G 170: Light rays with an angle less than 45 degrees with the central axis can hit the edge point G of the second surface of the double-angle reflector.
131:光線進入DCRA之處,在GFEH平面上之點A 131: Where the light enters DCRA, point A on the GFEH plane
132:光線發生第一次反射之處,點B 132: The first reflection of the light, point B
133:光線發生第一次反射之處,點C 133: The first reflection of the light, point C
134:光線離開DCRA之處,點D 134: Where the light leaves DCRA, point D
130A:光線在A’之處入射DCRA單元之一,在ZX平面上之投影 130A: The projection of the light incident on one of the DCRA units at A’ on the ZX plane
130B:光線在A’之處入射DCRA單元之一,在ZX平面上之投影 130B: The projection of the light incident on one of the DCRA units at A’ on the ZX plane
130R:一個DCRA的單元,光線射入角度為正的情況 130R: A DCRA unit with a positive incident angle of light
131R:光線在單元130R內的射入點A’
131R: The incident point A’ of the light in
132R:光線在單元130R內的第一反射點B
132R: The first reflection point B of the light in
133R:光線在單元130R內的第二反射點C
133R: The second reflection point C of the light in
134R:光線在單元130R內的出射點D
134R: The light exit point D in
135R:光線在單元130R內的射入點,延伸到EH邊上之交會點為A
135R: The light enters the
130L:一個DCRA的單元,光線射入角度為負的情況 130L: A DCRA unit with a negative incident angle of light
131L:光線在單元130L內的射入點A’
131L: The incident point A’ of the light in
132L:光線在單元130L內的第一反射點B
132L: The first reflection point B of the light in
133L:光線在單元130L內的第二反射點C
133L: The second reflection point C of the light in
134L:光線在單元130L內的出射點D
134L: The light exit point D in
135L:光線在單元130L內的射入點,延伸到EH邊上之交會點為A
135L: The light enters the
136:DCRA單元靠近物方之平面,光線射入端 136: DCRA unit close to the object plane, light incident end
137:DCRA單元靠近物方之平面,光線射出端 137: DCRA unit close to the object plane, light emission end
138:DCRA單元靠近物方平面,左側之禁止線,靠左需途黑,是禁止區 138: The DCRA unit is close to the object plane, the prohibited line on the left side, the road to the left must be black, it is a prohibited area
139:DCRA單元靠近物方平面,右側之禁止線,靠右需途黑,是禁止區 139: The DCRA unit is close to the object plane, the prohibited line on the right side, the road to the right must be black, it is a prohibited area
161:光線之入射點A’ 161: Light incident point A’
162:光線之第一個反射點B 162: The first reflection point of light B
163:光線之第二個反射點C 163: The second reflection point of light C
164:光線之出射點D 164: Light emission point D
171:光線之入射點A’ 171: Light incident point A’
172:光線之第一個反射點B 172: The first reflection point of light B
173:光線之第二個反射點C 173: The second reflection point of light C
174:光線之出射點D 174: Light emission point D
180:光路徑向量在YZ平面上之投影 180: Projection of the light path vector on the YZ plane
190:光路徑向量在ZX平面上之投影 190: Projection of light path vector on ZX plane
200:一個使用DLP作為主要成像元件的3D列印機 200: A 3D printer using DLP as the main imaging element
210:DLP芯片 210:DLP chip
220:DLP照明系統 220:DLP lighting system
230:DLP光機之投影鏡頭 230:DLP optical engine projection lens
240:光固化溶劑槽 240: Light-curing solvent tank
250:列印的工件 250: Printed workpiece
260:升降機構裝置 260: Lifting mechanism device
270:曝光投影之邊緣光束 270: Edge beam of exposure projection
280:因溶劑濃度改變,投影距離變長,導致成像面積變大 280: Due to the change in solvent concentration, the projection distance becomes longer, resulting in a larger imaging area
290:因溶劑濃度改變,投影距離變短,導致成像面積變小 290: Due to the change in solvent concentration, the projection distance becomes shorter, resulting in a smaller imaging area
300:一個使用LCD作為主要成像元件的3D列印機 300: A 3D printer using LCD as the main imaging element
310:UVLED光源 310: UVLED light source
320:LCD面板,上面覆蓋一層離型膜 320: LCD panel, covered with a layer of release film
330:光固化溶劑槽 330: Light-curing solvent tank
340:列印的工件 340: Printed workpiece
350:升降機構裝置 350: Lifting mechanism device
300A:工件與LCD上的離型膜密接曝光成型 300A: Exposure molding of the workpiece and the release film on the LCD in close contact
300B:工件與LCD上的離型膜撕裂脫離 300B: The release film on the workpiece and LCD is torn and separated
300C:工件回復到原定位點與LCD密接,LCD顯示下一切片層畫面 300C: The workpiece returns to the original position and is in close contact with the LCD, and the LCD displays the next slice layer screen
500:一個使用改進後之DCRA於3D印表機系統 500: A 3D printer system using improved DCRA
510:經過準直化的UV光源 510: Collimated UV light source
520:不帶光源的LCD面版 520: LCD panel without light source
530:經過改進後,塗黑處理的DCRA平板 530: Improved DCRA flat panel with black finish
540:成像位置,光固化劑凝結之處 540: Imaging position, where the light curing agent condenses
550:光固化劑溶劑槽 550: Light curing agent solvent tank
560:光固化之成品工件 560: Finished workpiece of light curing
570:工件之夾持機構 570: Workpiece clamping mechanism
500A:一個使用改進後之DCRA於3D印表機系統,在初始列印階段示意圖 500A: A schematic diagram of the initial printing stage using the improved DCRA in a 3D printer system
500B:一個使用改進後之DCRA於3D印表機系統,在中途列印階段之一示意圖 500B: A schematic diagram of a 3D printer system using the improved DCRA at a mid-printing stage
500C:一個使用改進後之DCRA於3D印表機系統,在中途列印階段之二示意圖 500C: A schematic diagram of the second printing stage using the improved DCRA in a 3D printer system
500D:一個使用改進後之DCRA於3D印表機系統,在最後列印階段示意圖 500D: A schematic diagram of a 3D printer system using the improved DCRA at the final printing stage
600R:x>0情況下,虛線處為二次反射之有效光線範圍 600R: When x > 0, the dotted line is the effective light range of secondary reflection
610R:x>0情況下,<1曲線範圍 610R: x > 0, <1 Curve Range
620R:x>0情況下,2-tan(x+)<曲線範圍 620R: x > 0, 2-tan( x + )< Curve range
630R:x>0情況下,0<x<曲線範圍 630R: x >0, 0< x < Curve range
600L:x<0情況下,虛線處為二次反射之有效光線範圍 600L: When x <0, the dotted line is the effective light range of secondary reflection
610L:x<0情況下,<1曲線範圍 610L: x <0, <1 Curve Range
620L:x<0情況下,2-tan(x+)<曲線範圍 620L: When x <0, 2-tan( x + )< Curve range
630L:x<0情況下,-<x<0曲線範圍 630L: x <0, - <x<0 curve range
700:將600L及610L合併之結果。此時-18.43°<x<18.43° 700: The result of combining 600L and 610L. At this time, -18.43 ° < x <18.43 °
800:將700加上<曲線範圍之結果,此時-11.3°<x<11.3° 800: add 700 < The result of the curve range is -11.3 ° < x <11.3 °
900:一個使用DCRA的浸潤式曝光機系統 900: An immersion exposure system using DCRA
910:經過準直化的UV光源 910: Collimated UV light source
920:不帶光源的LCD面版 920: LCD panel without light source
930:DCRA平板 930:DCRA flat panel
940:光固化溶劑槽 940: Light-curing solvent tank
950:工件之光成像面 950: Light imaging surface of the workpiece
960:夾持工件機構 960: Workpiece clamping mechanism
圖1 雙角反射鏡陣列(DCRA)系統圖 Figure 1 Dual-corner reflector array (DCRA) system diagram
圖2 進入DCRA的光線之分類示意圖 Figure 2 Schematic diagram of the classification of light entering DCRA
圖3A 一個使用DLP作為主要成像元件的3D列印機之正面示意圖 Figure 3A A schematic diagram of the front view of a 3D printer using DLP as the main imaging element
圖3B 一個使用DLP作為主要成像元件的3D列印機之立體示意圖 Figure 3B A 3D schematic diagram of a 3D printer using DLP as the main imaging element
圖3C 一個使用DLP作為主要成像元件的3D列印機之原理圖 Figure 3C Schematic diagram of a 3D printer using DLP as the main imaging element
圖4A 一個使用LCD作為主要成像元件的3D列印機之正面示意圖 Figure 4A Schematic diagram of the front view of a 3D printer using LCD as the main imaging element
圖4B 一個使用LCD作為主要成像元件的3D列印機之立體示意圖 Figure 4B A three-dimensional schematic diagram of a 3D printer using LCD as the main imaging element
圖4C 一個使用LCD作為主要成像元件的3D列印機之三種工作時的狀態 Figure 4C Three working states of a 3D printer using LCD as the main imaging element
圖5A 光線進入DCRA單元路徑向量之立體示意圖 Figure 5A 3D schematic diagram of the path vector of light entering the DCRA unit
圖5B 光線進入DCRA單元路徑向量之YZ平面分量示意圖 Figure 5B Schematic diagram of the YZ plane component of the path vector of the light entering the DCRA unit
圖5C 光線進入DCRA單元路徑向量之ZX平面分量示意圖 Figure 5C Schematic diagram of the ZX plane component of the path vector of the light entering the DCRA unit
圖6 不同位置光線進入DCRA單元之ZX平面示意圖 Figure 6 Schematic diagram of the ZX plane of light entering the DCRA unit at different positions
圖7 光線向量在ZX平面示意圖,射入角度為正的情況 Figure 7 Schematic diagram of the light vector in the ZX plane, when the incident angle is positive
圖8 當光線射入角度為正,路徑為一次反射及二次反射之解範圍示意圖 Figure 8 Schematic diagram of the solution range when the incident angle of the light is positive and the path is a single reflection and a double reflection
圖9 光線向量在ZX平面示意圖,射入角度為負的情況 Figure 9 Schematic diagram of light vector in the ZX plane, when the incident angle is negative
圖10 當光線射入角度為負,路徑為一次反射及二次反射之解範圍示意圖 Figure 10 Schematic diagram of the solution range when the incident angle of the light is negative and the path is a single reflection and a double reflection
圖11 無論光線射入角度為正或負,路徑為一次反射及二次反射之完整解範圍示意圖 Figure 11 Schematic diagram of the complete solution range for a single reflection and a double reflection path, regardless of whether the incident angle of the light is positive or negative.
圖12 設定P/W範圍及x範圍後,可得純粹之二次反射有效光線解之範圍示意圖 Figure 12 After setting the P/W range and x range, the range diagram of the pure secondary reflection effective light solution can be obtained
圖13 設定P/W範圍及x範圍後,可得純粹之二次反射有效光線解之光線路徑值曲線圖 Figure 13 After setting the P/W range and x range, the light path value curve of the pure secondary reflection effective light solution can be obtained
圖14 一個使用DCRA的浸潤式曝光機系統 Figure 14 An immersion exposure system using DCRA
圖15 在DCRA單元上設立禁止區之立體視圖 Figure 15 3D view of setting up a prohibited area on a DCRA unit
圖16A 在DCRA單元靠近物端,左側設立禁止區之內,有效光線射入,射出光線圖 Figure 16A: Effective light entering and exiting the prohibited area on the left side of the DCRA unit near the object end
圖16B 在DCRA單元靠近物端,左側設立禁止區之外,無效光線射入,射出光線圖 Figure 16B shows the DCRA unit near the object end, with invalid light entering and exiting the forbidden area on the left side.
圖17A 在DCRA單元靠近物端,右側設立禁止區之內,有效光線射入,射出光線圖 Figure 17A: Effective light entering and exiting the prohibited area on the right side of the DCRA unit near the object end
圖17B 在DCRA單元靠近物端,右側設立禁止區之內,無效光線射入,射出光線圖 Figure 17B shows the DCRA unit near the object end, with invalid light entering and exiting the prohibited area on the right side.
圖18 在DCRA陣列上做部分塗黑之XZ平面方向視圖 Figure 18: XZ plane view of partially blackening the DCRA array
圖19 一個使用改進後之DCRA於3D印表機系統之立體視圖 Figure 19 A stereoscopic view of a 3D printer system using the improved DCRA
圖20A 一個使用改進後之DCRA於3D印表機系統之側面視圖 Figure 20A A side view of a 3D printer system using the improved DCRA
圖20B 一個使用改進後之DCRA於3D印表機系統之正面視圖 Figure 20B A front view of a 3D printer system using the improved DCRA
圖21 一個使用改進後之DCRA於3D印表機系統進行連續列印示意圖 Figure 21 A schematic diagram of continuous printing using the improved DCRA in a 3D printer system
DCRA的光學路徑方程(Optical Path Equation) Optical Path Equation of DCRA
以下我們使用光學路徑方程(Optical Path equation)來分析DCRA的有效光線問題,並且提出解決辦法;我們考慮光線有x,y,z的向量,如第5A圖是一道光線入射進DCRA的路徑立體圖及其對應的座標系;進入的點是130,A點,然後打到第一個反射面的140,B點,再打到第二個反射面的150,C點,最後從160,D點出射。整個光向量可以考慮成由如第5B圖之Y平面向量170與如第5C圖之XZ平面向量180組成。XZ平面是DCRA下方的一個菱形的區域,參考第6圖不同光線射入DCRA之XZ平面位置示意圖130A,130B。以130A為例,光線從161,A’點射入,經過162,B點反射,再經過163,C點反射,從164,D點射出。A’B點可以延伸到EH邊線找到交叉點A。以130B為例,光線從171,B’點射入,經過172,B點反射,再經過173,C點反射,從174,D’點射出。CD’點可以延伸到GH邊線找到交叉點D。
Below we use the optical path equation to analyze the effective light problem of DCRA and propose a solution; we consider that light has x, y, z vectors, such as Figure 5A is a three-dimensional diagram of the path of a light incident on DCRA and its corresponding coordinate system; the entry point is 130, point A, then hits the first reflection surface 140, point B, then hits the second reflection surface 150, point C, and finally exits from 160, point D. The entire light vector can be considered to be composed of the Y plane vector 170 in Figure 5B and the
以下我們分析DCRA單元的光學路徑方程如下:假設進入DCRA的光線起點為A’,可以延伸到EH線上之A點。光線先入射到EF反射面,再遇到FG反射面。(先入射到FG,再遇到EF也是一樣的情況) Below we analyze the optical path equation of the DCRA unit as follows: Assume that the starting point of the light entering the DCRA is A’, and it can be extended to point A on the EH line. The light first enters the EF reflective surface, and then encounters the FG reflective surface. (The same situation applies if it first enters FG and then encounters EF)
假設x是光線與X軸夾角,我們將所有經過A點的光線,分成兩群來討論; Assuming x is the angle between the light and the X-axis, we divide all the light rays passing through point A into two groups for discussion;
(1)第一群光線,如第7圖:光線從131R,A’點射入(延伸到EH邊線為135R,A點),在132R,B點反射,在133R,C點反射,從134R,D點射出。
(1) The first group of light rays, as shown in Figure 7: The light rays enter from
假設: Assumptions:
其中我們假設菱形邊長EF=FG=GH=HE為W,AH為p。 Here we assume that the side length of the rhombus EF = FG = GH = HE is W and AH is p .
因此進入菱形區域內的光線,經過兩次反射之後,離開菱形區域之總長度為:OPE(x)=AB+BC+CD------------(3) Therefore, after entering the diamond area, the total length of the light leaving the diamond area after two reflections is: OPE ( x ) = AB + BC + CD ------------(3)
其中可以達成兩個面都反射的條件為CG>0。(這裡CG<0,表示光線無法遇到第二個反射面) The condition for achieving reflection on both surfaces is CG > 0. (Here CG < 0 means that the light cannot encounter the second reflection surface)
反射兩次條件
此處我們處理一下三角函數以簡化方程
總光程可以化簡為:AB=WT 3-pT 3-----------(18) The total optical path can be simplified as: AB = WT 3 - pT 3 -----------(18)
=W(T 2-T 3)+pT 3-------------(20) = W ( T 2 - T 3 )+ pT 3 -------------(20)
反射兩次條件(13)可重寫成:
綜合(29)及(1)(2)式,我們以做圖法解析x解的範圍如第8圖。 Combining (29) and (1)(2), we use graphical method to analyze the range of solutions for x as shown in Figure 8.
第8圖之630R以(1)式表示,610R為(2)式表示,620R為(29)式表示 In Figure 8, 630R is represented by formula (1), 610R is represented by formula (2), and 620R is represented by formula (29)
(2)第二群光線如第9圖:此時光線從131R,A’點射入(延伸到EH邊線為135R,A點),在132R,B點反射,在133R,C點反射,從134R,D點射出。
(2) The second group of light rays is shown in Figure 9: At this time, the light rays enter from
此時的反射兩次條件為:
仿照之前的推導方法,可以推導出下式
我們以X座標代表x(光線與菱形區域中的X軸夾角),以Y座標代表,由以上方程式(2)及(30)(32),可作圖如第10圖 We use the X coordinate to represent x (the angle between the light and the x-axis in the diamond area) and the Y coordinate to represent , from the above equations (2) and (30)(32), we can draw a graph as shown in Figure 10
第10圖之630L以(30)式表示,610L為(2)式表示,620L為(32)式表示綜合第8圖及第10圖的結果,綜合結果x的範圍700如第11圖所示;虛線的部份是二次反射,有效光線的範圍,從第11圖來看,如果想要得到純粹的二次反射,有效光線,必須同時限制值及x值的範圍。 630L in Figure 10 is expressed by equation (30), 610L is expressed by equation (2), and 620L is expressed by equation (32). The combined results of Figures 8 and 10 are shown in Figure 11. The range of the combined result x is 700. The dotted part is the range of secondary reflection and effective light. From Figure 11, if you want to obtain pure secondary reflection and effective light, you must limit The range of values and x values.
對DCRA同時做及x值的範圍做限制以濾除無效光線,如果我們限制了0<< DCRA and x values to filter out invalid light. If we limit 0< <
從(29),(32)式,tan(x+)<,tan(-x+)< From (29), (32), tan( x + )< ,tan(- x + )<
我們可以得到:x<0.063π=11.34°;11.34°<x<0,綜合以上:我們可以得到限制-11.34°<x<11.4°,x值範圍,800如第12圖顯示之虛線區域,可以得到純粹的二次反射光線。 We can get: x <0.063 π =11.34 ° ; 11.34 ° < x <0, combining the above: we can get the limit -11.34 ° < x <11.4 ° , x value range, 800 as shown in the dotted area in Figure 12, we can get pure secondary reflected light.
光學路徑方程(Optical Path Equation)與DCRA的解析度問題,從(3)及(18)(20)(25)式可以整理出完整的光線路徑方程如下:OPE(x)=AB+BC+CD Optical Path Equation and DCRA resolution problem. From (3) and (18)(20)(25), the complete optical path equation can be obtained as follows: OPE ( x ) = AB + BC + CD
此時0<x<, At this
(x)這個函數,是一個平滑遞增變化的函數。在x接近情況下,函數值會接近無窮大。其物理意義是,光線無法入射到DCRA的第一個反射鏡,是無效的光線。 ( x ) is a smoothly increasing function. In this case, the function value will approach infinity. Its physical meaning is that the light cannot enter the first reflector of DCRA and is invalid light.
考慮之前的分析,0<<及-11.34°<x<11.34°;可以求出(x)邊界值如下;假設0<x<0.063π;相當於1.414<T 2<1.803,
如第13圖,顯示RPE(x)在不同的的值情況下的變化圖,其變化量不是很大。 As shown in Figure 13, RPE ( x ) is different in The change graph under the value of , the change amount is not very large.
在情況下;
在情況下;
綜合(37)(38)式可以得到
從(39)式,我們可以得到, From (39), we can get,
△OPE(x)<0.354W---------------(40) △ OPE ( x )<0.354 W ---------------(40)
此值代表DCRA產生的畫素成像的誤差值。 This value represents the pixel imaging error value generated by DCRA.
也就是DCRA產生的畫素成像為W+0.354W=1.354W That is, the pixel image produced by DCRA is W + 0.354 W = 1.354 W.
一般來說,假設我們原始的顯示器之單一畫素邊長為p;則經過DCRA平板之後,最後顯示的邊長p'
一個DCRA用於微影光學方面之實施案例:從以上的分析;我們提出一個DCRA用於微影光學方面之實施案例如下:假設我們使用一個手機使用的5.6inchOLED面板;尺寸為151.3*70.1mm;解析度為1080P(2220X1080pixels)的OLED面板;pixel size 68*65um.取最大畫素邊長68um;如果我們希望得到的影像接近原始的OLED面板水準,68um,根據公式(41)(1+0.354)W=68um A practical example of DCRA for lithography: Based on the above analysis, we propose a practical example of DCRA for lithography as follows: Assume that we use a 5.6-inch OLED panel used in mobile phones; the size is 151.3*70.1mm; the resolution is 1080P (2220X1080 pixels); the pixel size is 68*65um. The maximum pixel side length is 68um. If we want to obtain an image close to the original OLED panel level, 68um, according to formula (41)(1+0.354) W = 68 um
W=50um W =50 um
關於DCRA在微影光學的應用,我們都知道,在微影光學中,一個非常高解析度的鏡頭成像裝置是至為關鍵的一部份;為了消除像差及畸變,其結構也變得極為複雜昂貴。我們認為DCRA的單元更微小化之後,以及經過消除鬼影處理,其有潛力可以做為微影光學的成像裝置應用。DCRA可以做浮空投影的特質甚至可以在浸潤式的微影裝置上使用。如第14圖,一個浸潤式的曝光機系統900中,使用了DCRA的示意圖,其中910是UV光源,920是光罩,930是DCRA元件,940是水或是油等折射率介質,950是曝光顯影的工件,960是夾持工件的機構。因為DCRA有足夠的工作距離,因此可以在液體中做曝光顯影的製程。
Regarding the application of DCRA in lithography, we all know that in lithography, a very high-resolution lens imaging device is a critical part; in order to eliminate aberrations and distortions, its structure becomes extremely complex and expensive. We believe that after the DCRA unit is miniaturized and ghosting is eliminated, it has the potential to be used as an imaging device in lithography. The DCRA's ability to perform floating projection can even be used in immersion lithography devices. As shown in Figure 14, a schematic diagram of the use of DCRA in an
對DCRA做遮罩處理,達成對值的限制。 Masking is performed on DCRA to achieve Value restrictions.
這裡討論如何在實務上,將DCRA的值做限制;如第15圖;DCRA之一單元130,做了遮罩處理的示意圖(左邊是立體視角示意圖,右邊是塗黑區域相對於坐標系之示意圖),從途中可以看到下方光線進入的平面136進行了部分塗黑,上方出口的平面137不做處理)。這個處理方式來自於圖12的結果,對於做限制。
This article discusses how to apply DCRA in practice. As shown in Figure 15, a
也就是限制0<<的範圍,將<<1的部分(禁止線左方)做塗黑,以限制射入光線的範圍;如第16A圖,130L,考慮入射光與垂直軸的角度x=11.3入射底部平面136,從出口平面137射出,可以發現,左側的禁止線138在其中發揮了作用。在禁止線138右方0<<的入射光都成為有效光線,二次反
射後從出口平面137射出。如第16B圖,禁止線138也發揮了作用。在禁止線138左方<<1的一次無效入射光都被阻擋了。
That is,
如第17A圖,130R,考慮入射光與垂直軸的角度x=-11.3入射底部平面136,從出口平面137射出,可以發現,右側的禁止線139在其中發揮了作用。在禁止線139左方0<<的入射光都成為有效光線,二次反射後從出口平面137射出。如第17B圖,禁止線138也發揮了作用。在禁止線139右方<<1的一次無效入射光都被阻擋了。要注意的是禁止區域的塗黑只有在DCRA單元,面對入射光的平面136進行;出口平面137是不做處理的。
As shown in FIG. 17A, 130R, consider that the incident light is incident on the
如第18圖是把所有的DCRA單元都做禁止區域塗黑的示意圖;因為其區域很小很精細,在工藝上也需使用微影技術來實現。 For example, Figure 18 shows a schematic diagram of all DCRA units being blackened as prohibited areas; because the area is very small and fine, lithography technology is also required to achieve this in the process.
對DCRA的光源做處理,達成對x值的限制,從前面的分析,要抑制一次反射無效光線,必須要對入射光線做限制;這部分一般可以針對不同的光源,比如LED,做相對應的照明設計,使用準直器反射鏡或透鏡組,將光線角度分布縮小。 The DCRA light source is processed to limit the x value. From the previous analysis, in order to suppress invalid light from one reflection, the incident light must be limited. This part can generally be targeted at different light sources, such as LEDs, and corresponding lighting designs can be made, using collimators, reflectors or lens sets to reduce the angle distribution of light.
關於應用DCRA於光固化式積層製造設備,如上,改善之後的DCRA,可以應用於光固化式積層製造設備(3D印表機);其設計類似於第14圖的浸潤式的曝光機系統900;但是將工件夾持機構960,改成升降機構;可以做精密的垂直軸位移及定位,如第19圖是其立體視圖;並請同時參看第20A、20B圖所示;其結構是使用一個UV光源510,經由一個不帶背光板的LCD面板520,進入一個已做部分塗黑處理的DCRA平板530。然後
最後得到的成像影像540在液體槽550中,560是列印中的工件,570視工件夾持及精密升降裝置。如第20A圖是其側面視圖,第20B圖是其之正視圖;其工作方式是曝光,光固化凝結,升降機往上移位,然後重複曝光,光固化,移位的動作,如第21圖是進行連續列印時,從初始階段500A,到中途階段500B,500C,到最後完成品階段500D之示意圖。與之前提及的LCD形式3D印表機比較起來,因為此形式沒有撕開分離LCD離形膜的過程,可以直接列印,因此速度快很多。
Regarding the application of DCRA in photocuring lamination manufacturing equipment, as mentioned above, the improved DCRA can be applied to photocuring lamination manufacturing equipment (3D printer); its design is similar to the
500:一個使用改進後之DCRA於3D印表機系統 500: A 3D printer system using improved DCRA
520:不帶光源的LCD面版 520: LCD panel without light source
530:經過改進後,塗黑處理的DCRA平板 530: Improved DCRA flat panel with black finish
550:光固化劑溶劑槽 550: Light curing agent solvent tank
560:光固化之成品工件 560: Finished workpiece of light curing
570:工件之夾持機構 570: Workpiece clamping mechanism
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| Publication number | Priority date | Publication date | Assignee | Title |
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| TW202001344A (en) * | 2018-06-07 | 2020-01-01 | 財團法人國家實驗研究院 | Floating imaging display device including a display light source and at least one array type triangular mirror structure |
| US20210364818A1 (en) * | 2020-05-20 | 2021-11-25 | Hyundai Motor Company | Apparatus for displaying floating image and vehicular display module including the same |
| CN115769110A (en) * | 2020-05-15 | 2023-03-07 | 三星电子株式会社 | Reflection structure, reflection structure array including the same, and floating image display device |
| CN115917403A (en) * | 2020-06-03 | 2023-04-04 | 凸版印刷株式会社 | air display device |
| US20230288613A1 (en) * | 2022-03-09 | 2023-09-14 | Alps Alpine Co., Ltd. | Method for manufacturing optical element, optical element, aerial image display device, and spatial input device |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW202001344A (en) * | 2018-06-07 | 2020-01-01 | 財團法人國家實驗研究院 | Floating imaging display device including a display light source and at least one array type triangular mirror structure |
| CN115769110A (en) * | 2020-05-15 | 2023-03-07 | 三星电子株式会社 | Reflection structure, reflection structure array including the same, and floating image display device |
| US20210364818A1 (en) * | 2020-05-20 | 2021-11-25 | Hyundai Motor Company | Apparatus for displaying floating image and vehicular display module including the same |
| CN115917403A (en) * | 2020-06-03 | 2023-04-04 | 凸版印刷株式会社 | air display device |
| US20230288613A1 (en) * | 2022-03-09 | 2023-09-14 | Alps Alpine Co., Ltd. | Method for manufacturing optical element, optical element, aerial image display device, and spatial input device |
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