楊宇臣,季 淵,陳文棟,穆廷洲,張春燕,冉 峰
面向數(shù)字驅(qū)動(dòng)式硅基微顯示器的雙幀分權(quán)融合掃描
楊宇臣,季 淵*,陳文棟,穆廷洲,張春燕,冉 峰
上海大學(xué)微電子研究與開發(fā)中心,上海 200444
當(dāng)microLED處于正向工作區(qū)時(shí),難以精確調(diào)節(jié)它們的電壓來獲得不同的發(fā)光亮度;且當(dāng)microLED/OLED工作時(shí),會(huì)較長時(shí)間處于閉合狀態(tài),導(dǎo)致人眼觀察到的圖像顯示亮度變差。為解決以上問題,本文提出一種雙幀分權(quán)融合掃描策略,通過調(diào)節(jié)microLED/OLED導(dǎo)通時(shí)間來獲得不同亮度。該方法先對(duì)數(shù)據(jù)位重新分權(quán),使導(dǎo)通時(shí)間分散插入到閉合時(shí)間內(nèi),然后將分權(quán)后的各數(shù)據(jù)位權(quán)值進(jìn)行雙幀融合,最后重新定義數(shù)據(jù)位的掃描順序。并根據(jù)所提出的掃描策略設(shè)計(jì)了一款面向數(shù)字驅(qū)動(dòng)式硅基微顯示器的掃描控制器。結(jié)果表明:本文提出的雙幀分權(quán)融合掃描策略可以精確調(diào)節(jié)microLED/OLED的發(fā)光亮度,提高人眼觀察到圖像顯示亮度。該掃描策略與其它掃描策略相比,掃描效率提升至93.75%,場(chǎng)頻提升至2040 Hz,掃描時(shí)鐘頻率為102.36 MHz,且同時(shí)減小了掃描數(shù)據(jù)帶寬。最后通過測(cè)試證明了掃描控制器的可行性。
發(fā)光亮度;雙幀分權(quán)融合;數(shù)字驅(qū)動(dòng)式硅基微顯示器;掃描控制器;掃描效率
MicroLED和OLED是當(dāng)下兩種前沿的顯示技術(shù)。與傳統(tǒng)LED技術(shù)相比,microLED/OLED為自主發(fā)光器件,具有更高的光源利用率和更高的對(duì)比度。microLED和OLED發(fā)光材料都可以生長在硅基上制作成硅基微顯示器。該類微顯示器具有功耗低、響應(yīng)快等特點(diǎn),主要應(yīng)用于近眼顯示設(shè)備和虛擬顯示設(shè)備。
硅基微顯示器的灰度產(chǎn)生方式主要有模擬幅值調(diào)制和數(shù)字脈寬調(diào)制兩種調(diào)制方式[1]。模擬幅值調(diào)制是通過DAC將數(shù)字信號(hào)轉(zhuǎn)換成模擬信號(hào),通過調(diào)節(jié)microLED/OLED兩端的電壓值來獲得不同的亮度值。其主要面臨著DAC精度、速度以及面積開銷等方面的問題,不適用于高灰度級(jí)和高分辨率微顯示器。數(shù)字脈寬調(diào)制方式是指通過脈沖寬度調(diào)制(pulse width modulation, PWM)來控制microLED/OLED發(fā)光的時(shí)間進(jìn)而產(chǎn)生不同的灰度等級(jí)。一種實(shí)現(xiàn)方式是在芯片中集成由比較器和計(jì)數(shù)器組成的PWM發(fā)生器,通過內(nèi)部控制PWM發(fā)生器產(chǎn)生PWM信號(hào),從而控制microLED/OLED的導(dǎo)通時(shí)間來獲得不同程度發(fā)光亮度[2-3]。另一種方式是在芯片外部直接產(chǎn)生PWM信號(hào)來控制microLED/OLED的導(dǎo)通時(shí)間,不需要在芯片內(nèi)集成PWM發(fā)生器[4-8]。數(shù)字調(diào)制方式具有精度和靈活性高、對(duì)電路特性要求低等特點(diǎn)。由于microLED/OLED伏安特性類似于p-n結(jié),當(dāng)其處于正向工作區(qū)時(shí),電流曲線斜率很大,難以通過調(diào)節(jié)電壓來精確地調(diào)節(jié)電流進(jìn)而得到不同的亮度[9-11],因此本文選取數(shù)字脈寬PWM調(diào)制方式。傳統(tǒng)的PWM調(diào)制會(huì)使microLED/OLED長時(shí)間處于閉合狀態(tài),影響人眼觀看的圖像顯示亮度[12-14]。本文將基于第二種數(shù)字脈寬調(diào)制方式提出一種雙幀分權(quán)融合掃描策略。該掃描策略能夠精確調(diào)制微顯示器的灰度等級(jí)和改善人眼觀看圖像顯示亮度,減少掃描數(shù)據(jù)帶寬,提高掃描的效率和幀頻。最后使用FPGA完成雙幀分權(quán)融合策略控制器的設(shè)計(jì),并能驅(qū)動(dòng)硅基微顯示器正常工作。
傳統(tǒng)的8位二進(jìn)制數(shù)據(jù)PWM調(diào)制[15]產(chǎn)生的有效高電平如式(1)所示。我們通過調(diào)節(jié)每個(gè)PWM周期中的值來獲得不同的亮度,即灰階。
傳統(tǒng)8位數(shù)據(jù)位寬的LED灰度調(diào)制是將一幀的顯示時(shí)間按照27: 26: 25:…: 20行權(quán)值分割,數(shù)據(jù)位越高對(duì)應(yīng)的權(quán)值越大。各數(shù)據(jù)位的值可為1或0,分別表示LED導(dǎo)通或關(guān)閉狀態(tài),因此8 bit數(shù)據(jù)可以表示256個(gè)不同的值即256階灰度。在極短時(shí)間內(nèi)LED的發(fā)光亮度與導(dǎo)通時(shí)間可以近似看作一種線性關(guān)系,導(dǎo)通時(shí)間越長LED亮度越大。由于microLED/OLED都為自主發(fā)光型器件,不需要背光。為滿足人眼的正常觀看,需對(duì)microLED/OLED的亮度進(jìn)行調(diào)節(jié),也就是調(diào)節(jié)它們的導(dǎo)通時(shí)間。
圖1為在相同亮度下傳統(tǒng)LED導(dǎo)通時(shí)間演變?yōu)閙icroLED導(dǎo)通時(shí)間的示意圖,其中高電平持續(xù)時(shí)間表示發(fā)光材料的導(dǎo)通時(shí)間,低電平持續(xù)時(shí)間為關(guān)閉時(shí)間。由于電光轉(zhuǎn)化效率的不同,相同亮度下microLED所需的導(dǎo)通時(shí)間小于LED。人眼觀察亮度是動(dòng)態(tài)積分過程,關(guān)閉時(shí)間過長會(huì)導(dǎo)致人眼觀察到微顯示器圖像亮度變差。為了改善顯示效果,本文提出了雙幀分權(quán)融合掃描策略。該掃描策略是先基于傳統(tǒng)的PWM調(diào)制算法將數(shù)據(jù)位的權(quán)值重新分權(quán),然后將分權(quán)之后的權(quán)值進(jìn)行雙幀融合,最后將經(jīng)過融合之后各數(shù)據(jù)位的掃描順序重新排列。對(duì)于8位數(shù)據(jù),可將式(1)作式(2)變換:
圖1 LED導(dǎo)通時(shí)間與microLED導(dǎo)通時(shí)間對(duì)比
式(2)將數(shù)據(jù)位8、7和6權(quán)值變?yōu)樵瓉淼?/4,出現(xiàn)頻率為原來的4倍,但數(shù)據(jù)位的總權(quán)值和占空比與式(1)相比沒有發(fā)生變化。該變換可以理解為將原變化的導(dǎo)通時(shí)間平均分為四份插入到總的時(shí)間之內(nèi),使人眼觀察到連續(xù)的閉合時(shí)間變短,改善了因長時(shí)間閉合導(dǎo)致人眼觀察的圖像顯示亮度變差的問題。數(shù)據(jù)位的權(quán)值重新定義為2:1:1/2:1:1/2:1/4:1/8:1/16。在實(shí)現(xiàn)過程中當(dāng)數(shù)據(jù)位權(quán)值小于1時(shí),掃描期間需要通過額外的消隱操作來實(shí)現(xiàn),因此會(huì)存在一定的時(shí)間冗余使得掃描效率降低和損失亮度。雙幀融合是指將兩幀圖像相同比特位的子場(chǎng)融合為同一個(gè)子場(chǎng),利用上一幀子場(chǎng)的消隱冗余時(shí)間進(jìn)行下一幀的子場(chǎng)掃描,將兩幀中不足一個(gè)基本場(chǎng)時(shí)間長度的子場(chǎng)權(quán)值合并,進(jìn)行兩幀的子場(chǎng)融合調(diào)制。人眼觀察到的數(shù)據(jù)位實(shí)際顯示亮度不會(huì)發(fā)生變化。本文在常見的60 Hz基礎(chǔ)上,在原一幀的時(shí)間內(nèi)將一幀視頻源數(shù)據(jù)重復(fù)讀取兩次,等效于兩幀。具體操作是將分權(quán)之后權(quán)值為1/2的6和4進(jìn)行融合并放在第一幀內(nèi),第二次讀取的6和4權(quán)值變?yōu)?,放入第二幀內(nèi)。同理,將其他權(quán)值小于1的數(shù)據(jù)位也同樣進(jìn)行融合,放入一個(gè)幀內(nèi),另一幀內(nèi)相應(yīng)的權(quán)值也變?yōu)?。雙幀融合的示意圖如圖2所示,其中Bit7對(duì)應(yīng)8,Bit6對(duì)應(yīng)7,以此類推。
融合之后,我們將數(shù)據(jù)劃分為高數(shù)據(jù)位(HDB)和低數(shù)據(jù)位(LDB)。由式(2)可以看出高數(shù)據(jù)位8、7和6的權(quán)值縮小為原來的1/4但出現(xiàn)的頻率變?yōu)樵瓉淼?倍。再打散融合后的掃描順序,將低數(shù)據(jù)位依次分別插入放置于高數(shù)據(jù)位之后。由于融合以后兩幀的權(quán)值都會(huì)發(fā)生變化且變得不同,因此分別對(duì)兩幀的掃描順序進(jìn)行排列,最后排列方式如圖3所示。
由雙幀融合后權(quán)值可知,第一幀的HDB0包含數(shù)據(jù)位8、7和6,第二幀的HDB1包含數(shù)據(jù)位8和7。這種排列方式的優(yōu)點(diǎn)在于各數(shù)據(jù)位的總權(quán)值和占空比沒有發(fā)生變化的情況下提高了視覺刷新率,充分減少了人眼觀看microLED/OLED微顯示器時(shí)接收到兩次光刺激的間隔時(shí)間。在掃描過程當(dāng)中,本文提出的算法每幀的掃描數(shù)據(jù)帶寬也從8個(gè)bit減小到6個(gè)bit或者5個(gè)bit值,掃描效率(可以為看作為各bit位總導(dǎo)通時(shí)間所占總時(shí)間的百分比)為93.75%。場(chǎng)頻表示顯示器每秒顯示圖像的次數(shù),本文所提算法在原一幀時(shí)間內(nèi)共掃描34次畫面,故場(chǎng)頻為2040 Hz。其中場(chǎng)頻越大,圖像刷新的次數(shù)越多,圖像顯示的閃爍就越小,畫面質(zhì)量越高,但場(chǎng)頻還影響著掃描時(shí)鐘頻率,故不是越高越好,因此需綜合看待。
本文使用的數(shù)字驅(qū)動(dòng)式硅基微顯示器系統(tǒng)主要分為兩部分:第一部分是微顯示器驅(qū)動(dòng)芯片,主要包括行、列驅(qū)動(dòng)電路以及像素驅(qū)動(dòng)電路;第二部分為掃描控制器,掃描控制器會(huì)處理從視頻源出來的數(shù)據(jù)信號(hào)和產(chǎn)生控制微顯示器工作的控制信號(hào)??傮w系統(tǒng)結(jié)構(gòu)圖如圖4所示。
微顯示器芯片接收來自接口模塊的數(shù)據(jù)信號(hào)和控制信號(hào),通過移位寄存器對(duì)輸入的數(shù)據(jù)信號(hào)進(jìn)行串行移位,再將移位后的所有數(shù)據(jù)存入鎖存器中以保證數(shù)據(jù)傳輸?shù)耐瑫r(shí)性,最后使用能夠增加驅(qū)動(dòng)能力的緩存器,將數(shù)據(jù)信號(hào)傳輸至像素驅(qū)動(dòng)電路中。芯片中的列驅(qū)動(dòng)控制微顯示器的每一行,實(shí)現(xiàn)從左到右、從上到下逐行掃描。本論文可以使用的數(shù)字驅(qū)動(dòng)式硅基微顯示芯片由本課題組自行研發(fā),各芯片參數(shù)如表1所示。其中一些數(shù)字驅(qū)動(dòng)式硅基芯片如圖5所示。
圖2 雙幀融合示意圖
圖3 數(shù)據(jù)位權(quán)值排列順序
圖4 數(shù)字式硅基微顯示器整體系統(tǒng)結(jié)構(gòu)
為驅(qū)動(dòng)數(shù)字式硅基微顯示器,本文將根據(jù)第2節(jié)所提出的雙幀分權(quán)融合掃描策略設(shè)計(jì)一款控制器。整體結(jié)構(gòu)如圖6所示。
當(dāng)視頻源數(shù)據(jù)輸入進(jìn)來后,需要將其按照一定的方式處理,例如圖像縮放、伽馬矯正等,然后再將數(shù)據(jù)傳輸給RAM模塊。RAM模塊起到一個(gè)數(shù)據(jù)存儲(chǔ)前的緩沖數(shù)據(jù)的作用,當(dāng)輸入至RAM的緩存數(shù)據(jù)滿足SDRAM的突發(fā)長度時(shí),便將數(shù)據(jù)輸入給SDRAM模塊。SDRAM模塊則作為幀緩存的外部存儲(chǔ)器,緩存根據(jù)掃描策略重新排布數(shù)據(jù)。掃描控制模塊接收SDRAM模塊傳輸來的數(shù)據(jù),然后產(chǎn)生控制微顯示器所需的時(shí)序。RAM模塊和SDRAM皆采用乒乓操作的處理方式工作。最后輸出模塊是用來配置FPGA和芯片上的LVDS接口,然后將控制器產(chǎn)生的控制信號(hào)和處理后的數(shù)據(jù)信號(hào)通過接口傳輸至微顯示器進(jìn)而顯示圖像。
表1 數(shù)字式硅基微顯示器各性能參數(shù)
圖5 (a) 硅基OLED芯片;(b) 硅基microLED芯片
圖6 控制器整體構(gòu)圖
控制器中的掃描控制模塊是根據(jù)幀分權(quán)融合掃描策略進(jìn)行設(shè)計(jì)。scan_enable模塊接收由FIFO輸出的同步模塊標(biāo)志信號(hào)rdusedw和rdempty,判斷scan_ctrl是否需要工作。當(dāng)scan_ctrl模塊工作時(shí),產(chǎn)生使能信號(hào)輸入至field模塊作為讀取子場(chǎng)的請(qǐng)求。Field模塊中存儲(chǔ)的是雙幀融合掃描策略所對(duì)應(yīng)的子場(chǎng)個(gè)數(shù)、順序以及子場(chǎng)對(duì)應(yīng)的權(quán)值。由于frame_1和frame_2的輸入數(shù)據(jù)是相同的,將融合后的frame_2掃描順序直接放置融合后的frame_1的掃描序列之后。Command產(chǎn)生硅基微顯示器的控制信號(hào),data為數(shù)據(jù)通路,輸出經(jīng)延時(shí)處理的數(shù)據(jù)信號(hào)。其結(jié)構(gòu)圖如圖7,其中g(shù)_1和g_2分別代表列驅(qū)動(dòng)電路里的鎖存器使能信號(hào)和行驅(qū)動(dòng)電路里的行觸發(fā)器使能信號(hào)。Edff為列驅(qū)動(dòng)電路中移位寄存器的使能信號(hào)。Start_en為scan_ctrl模塊的使能信號(hào),其值由scan_enable模塊輸出。Next_field_en為讀取field模塊中子場(chǎng)的標(biāo)志信號(hào),field_work為輸出的當(dāng)前子場(chǎng)信息的輸出信號(hào),ctrl[9:0]為輸入給行驅(qū)動(dòng)電路的控制信號(hào),dout[31:0]為輸出給列驅(qū)動(dòng)電路的數(shù)據(jù)信號(hào),即像素點(diǎn)的邏輯值。
本文選取表1中所述的數(shù)字式OLED硅基微顯示器來進(jìn)行控制器的驗(yàn)證。它的灰度等級(jí)為256級(jí),分辨率為1280×1024,幀頻為60 Hz。在此硬件基礎(chǔ)下,本文所提出的雙幀分權(quán)掃描算法的性能參數(shù)與其他算法的比較,如表2所示。
本文提出的雙幀分權(quán)融合算法其線性度為100%,掃描效率為93.75%,場(chǎng)頻可以達(dá)到2040 Hz,掃描時(shí)鐘頻率為102.36 MHz。所使用的硬件系統(tǒng)實(shí)物圖和示波器測(cè)試結(jié)果圖如圖8所示。
圖8(a)展示的為本課題組自行設(shè)計(jì)的控制器實(shí)物圖,圖8(b)為控制器控制數(shù)字驅(qū)動(dòng)式硅基微顯示器的點(diǎn)亮圖,圖8(c)為列驅(qū)動(dòng)測(cè)試圖,圖中顯示的是BL和BLN信號(hào),該信號(hào)為BUFF模塊輸出至像素電路的數(shù)據(jù)信號(hào)。由于所使用的像素驅(qū)動(dòng)電路存儲(chǔ)部分為SRAM雙穩(wěn)態(tài)鎖存結(jié)構(gòu),因此需要輸入相反的雙通道數(shù)據(jù),圖中為所測(cè)的BL和BLN通道信號(hào)是相反的,說明所設(shè)計(jì)的控制器能夠控制列驅(qū)動(dòng)電路正常工作。圖8(d)表示的是行選信號(hào)WL,在掃描時(shí)打開一行的開關(guān)使數(shù)據(jù)傳輸至像素電路,然后再關(guān)閉,下個(gè)掃描信號(hào)來以后再次打開,故圖8(d)表明行驅(qū)動(dòng)電路在正常工作。以上實(shí)驗(yàn)結(jié)果圖說明本文所設(shè)計(jì)的控制器可以控制數(shù)字驅(qū)動(dòng)式硅基微顯示器正常工作。
圖7 掃描控制模塊
表2 各算法性能參數(shù)
圖8 (a) 控制器實(shí)物圖;(b) 硅基微顯示器點(diǎn)亮圖;(c) 列驅(qū)動(dòng)測(cè)試圖;(d) 行驅(qū)動(dòng)測(cè)試圖
本文提出了一種雙幀分權(quán)融合掃描策略,該掃描策略可以精確調(diào)制微顯示器不同的灰度等級(jí),且改善了因microLED/OLED長時(shí)間閉合而導(dǎo)致人眼觀察圖像顯示亮度變差的現(xiàn)象。與其它掃描策略相比較,該掃描策略降低了掃描數(shù)據(jù)帶寬,同時(shí)將掃描效率提升至93.75%,場(chǎng)頻提升至2040 Hz,掃描時(shí)鐘頻率為102.36 MHz,并使用FPGA實(shí)現(xiàn)掃描控制器的設(shè)計(jì),通過片外FPGA給出數(shù)據(jù)信號(hào)和控制信號(hào)來控制數(shù)字驅(qū)動(dòng)式硅基微顯示器工作。
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Dual-frame decentralized fusion scanning for digital drive on-silicon microdisplays
Yang Yuchen, Ji Yuan*, Chen Wendong, Mu Tingzhou, Zhang Chunyan, Ran Feng
Microelectronic Research & Development Center, Shanghai University, Shanghai 200444, China
Data bit weight order
Overview:MicroLEDs and OLEDs are the two leading edge display technologies. Compared to conventional LED technology, microLED has higher luminance and luminous efficiency, and lower power consumption at the same brightness. Both microLED and OLED luminescent materials can be grown on a silicon substrate to form an on-silicon microdisplay. When the microLED is in the forward working direction, it is difficult to precisely adjust its voltage to obtain different brightness. Moreover, the microLED/OLED will be in a closed state for a long time during working, resulting in deterioration of the brightness of the image observed by the human eye. In order to solve these problems, this paper proposes a dual-frame decentralized fusion scanning strategy to achieve different brightness by adjusting the microLED/OLED on-time. Firstly, the method de-weights the data bits and inserts their on-times into the closed time. Then the data bit weights are double-frame fused after decentralization. Finally, the scanning order of the data bits is redefined. According to the proposed scanning strategy, we designed a scanning controller to drive digital on-silicon microdisplay. The results show that the dual-frame decentralized fusion scan proposed in this paper can accurately adjust the luminance of microLED/OLED and improve the brightness of the image observed by human eyes. Compared with other scanning strategies, the scanning strategy improves the scanning efficiency to 93.75%, the field frequency is increased to 2040 Hz, the scanning clock frequency is 102.36 MHz, and the scanning data bandwidth is reduced. The digital drive on-silicon microdisplay system used in this paper is mainly divided into two parts. The first part is the microdisplay driver chip, which mainly includes row, column and pixel driver circuits. The second part is the scan controller, which will process the data signal from the video source and generate the control signal to control the operation of the microdisplay. When the video source data is entered, we need to process it in a certain way, such as image scaling, gamma correction, etc., and then transfer the data to the RAM module. The RAM module functions as a buffered data before data storage. When the cached data input to the RAM satisfies the burst length of the SDRAM, the data is input to the SDRAM module. The SDRAM module acts as an external memory for the frame buffer and rearrange the data according to the scanning policy. The scan control module receives the data transmitted by the SDRAM module and generates the timing required to control the microdisplay. Both RAM module and SDRAM are operated by ping-pong operation. Finally, the output module is used to configure the LVDS interface on the FPGA and the chip, and then transmit the control signal generated by the controller and the processed data signal to the microdisplay through the interface to display the image. The scan controller proved to be feasible by testing at last.
Citation: Yang Y C, Ji Y, Chen W D,. Dual-frame decentralized fusion scanning for digitaldrive on-silicon microdisplays[J]., 2020,47(11): 190366
Dual-frame decentralized fusion scanning for digital drive on-silicon microdisplays
Yang Yuchen, Ji Yuan*, Chen Wendong, Mu Tingzhou, Zhang Chunyan, Ran Feng
Microelectronic Research & Development Center, Shanghai University, Shanghai 200444, China
When the microLED is in the forward working direction, it is difficult to precisely adjust its voltage to obtain different brightness. Moreover, when the microLED/OLED is turned on, they will be in a closed state for a long time, causing the image display brightness to be deteriorated by the human eye. In order to solve these problems, this paper proposes a dual-frame decentralized fusion scanning strategy to achieve different brightness by adjusting the microLED/OLED on-time. Firstly, the method de-weights the data bits and inserts their on-times into the closed time. Then the data bit weights are double-frame fused after decentralization. Finally, the scanning order of the data bits is redefined. According to the proposed scanning strategy, we designed a scanning controller to drive digital on-silicon microdisplay. The results show that the dual-frame decentralized fusion scan proposed in this paper can accurately adjust the luminance of microLED/OLED and improve the brightness of the image observed by human eyes. Compared with other scanning strategies, the scanning strategy improves the scanning efficiency to 93.75%, the field frequency is increased to 2040 Hz, the scanning clock frequency is 102.36 MHz, and the scanning data bandwidth is reduced. The feasibility of the scan controller is proved by testing at last.
luminance; dual frame decentralized fusion; digital drive on-silicon microdisplay; scan controller; scanning efficiency
TN27
A
楊宇臣,季淵,陳文棟,等. 面向數(shù)字驅(qū)動(dòng)式硅基微顯示器的雙幀分權(quán)融合掃描[J]. 光電工程,2020,47(11): 190366
10.12086/oee.2020.190366
: Yang Y C, Ji Y, Chen W D,Dual-frame decentralized fusion scanning for digital drive on-silicon microdisplays[J]., 2020, 47(11): 190366
2019-06-28;
2019-11-29
國家自然科學(xué)基金資助項(xiàng)目(61674100,61774101);軍民融合項(xiàng)目(2019-jmrh1-kj37)
楊宇臣(1994-),男,碩士研究生,主要從事集成電路設(shè)計(jì)和顯示技術(shù)的研究。E-mail:625965240@qq.com
季淵(1980-),男,博士,副研究員,主要從事OLED微顯示器的研究。E-mail:jiyuan@shu.edu.cn
Supported by National Natural Science Foundation of China (61674100,61774101) and Civil-military Integration Project(2019-jmrh1-kj37)
* E-mail: jiyuan@shu.edu.cn