. Inoducion Design of compac join ansfom coelao Chao Fan College of Infomaion Science and Engineeing, Henan Univesiy of Technology, Zhengzhou 45000, China Received: 4..06 Absac. To impove he qualiy of images aken wih spaial cameas, we measue sub-pixel shifs beween wo adjacen images, using a join ansfom coelao (JTC). Fis we descibe he pinciples of measuemens of he image shifs based on he JTC. Then, consideing discee pixel-like sucues of a CCD and a spaial ligh modulao, we discuss elaionships among he paamees of JTC componens, issuing fom he sampling heoem and he Fouie opics pinciples. Following fom hese poins, we selec he devices needed and design he Fouie lens o consuc a compac JTC. Finally, we build he expeimenal plafom and esimae he efficiency of measuemens of he image shifs. The esuls show ha sub-pixel image shifs can be measued vey accuaely, wih he eos being less han 0. pixel unde condiion ha he image shifs ae wihin pixel. Keywods: join ansfom coelao, image shifs, opical measuemens, compac design PACS: 4.5.Eq UDC: 535.8 Wih inceasing esoluion of emoe sensing cameas, image shifs become a majo faco ha affecs he image qualiy. Because of complex woking condiions associaed wih saellies, he image shifs ae andom and eveal almos no egulaiy. To decease hese shifs, he aiude of a saellie is equied o be conolled in a vey sable manne. This educes he vibaions of he saellie bu inceases lagely he cos and complexiy of he appaaus. As a esul, vaious image sabilizaion mehods have been exensively sudied. They can be divided ino wo kinds, a digial image mehod and an opical sabilizaion one [, ]. No mae which of he mehods is being used, he measuemens of he image shifs epesen a fis sep and a key pocedue. Being accompanied by he ecen evoluion of spaial ligh modulaos (SLM) and CCD cameas, join ansfom coelaos (JTCs) have evolved fom a puely opical sysem owads a hybid compue-conolled phooelecic sysem. Now JTCs eveal a numbe of meis of he opical pocessing, e.g. fas paallel pocessing, lage capaciy and high speed, and can also be pogammed convenienly. JTCs have been widely used in he image ecogniion and age deecion [3 5]. In he pesen sudy, we use a JTC o measue he image shifs. Ou idea is o inpu sampled adjacen sequenial images ino he JTC and compue he appopiae coelaions basing on he disances beween he acual coss-coelaion peaks and he heoeical ones. The image shifs can be accuaely obained in his way. The ouline of his aicle is as follows. Fis he pinciples of measuemens of he image shifs based on he JTC ae given. Then, consideing a discee pixel-like sucue of CCD and SLM, we discuss he elaionships among he paamees of hese devices, issuing fom he Fouie opics fundamenals. Then a miniauized JTC is designed and an expeimenal plafom is buil. Finally, we veify he measuemen efficiency and he accuacy achieved fo he image shifs. Uk. J. Phys. Op. 07, Volume 8, Issue 55
Chao Fan. The measuemen pinciple of he image shifs based on JTC The sucual scheme of an opoeleconic JTC suggesed by us is displayed in Fig.. To make he sucue of ou JTC simple and compac, we employ he JTC consuced using a single Fouie lens (FL) and a single SLM. The efeence image (x, y) and he age image (x, y) ae loaded along an x diecion in a plane P. Thei cenes ae locaed a he poins (b, 0) and ( b, 0). Compaed wih he efeence image, he scene in he age image is moved some disances x and y along he x and y diecions, especively. Then he inpu of he JTC is given by E( x, y) ( x b, y) ( x x b, y y ). () Fig.. Sucual scheme of ou opoeleconic JTC. Afe ansfomaion pefomed by he FL, one can calculae he join specum G(, ) in he Fouie plane as G(, ) R(, )exp[ i b ] T (, )exp i[( b x) y], () whee R(ξ, η) and T(ξ, η) ae he Fouie ansfoms of (x, y) and (x, y), especively. Thee is a CCD camea in he Fouie plane, which ecods he inensiy disibuion: G(, ) R(, ) T (, ) R(, ) T *(, )exp i [( b b x) y], (3) T (, ) R *(, )exp i[( b b x) y] whee he symbol * implies complex conjugaion. Conolled by a digial pocessing and conol uni (see Fig. ), he powe specum is loaded o he SLM and ansfomed again by he FL. The complex ampliude disibuion in he oupu plane of he sysem hen eads as C( x, y) ( x, y) ( x, y) ( x, y) ( x, y) ( x, y) ( x, y)* ( x b b x, y y), (4) ( x, y) ( x, y)* ( x b b x, y y) whee he symbols * and now denoe especively convoluion and coelaion, and implies he Dela funcion. The fis wo iems ae auo-coelaions and he las wo coss-coelaions. As eviden fom Eq. (4), when he efeence image and he age image conain he same infomaion, wih a sligh shifs x and y, hese shifs can be measued by finding he displacemens beween he acual coss-coelaion peaks and he elevan ideal poins [±(b +b ), 0]. 3. Analysis of elaionships among he paamee of JTC componens Meanwhile, no consucion paamees of he sysem componens, such as he SLM, he lens and he CCD, have been consideed. In any pacical siuaion, boh he SLM and he CCD conain 56 Uk. J. Phys. Op. 07, Volume 8, Issue
Design of compac discee pixels ha affec he image paen accoding o he sampling heoem. Theefoe we should sudy he elaionships among he consucion paamees of hese componens. Because he efeence and age images ae displayed along he hoizonal diecion on he SLM, we discuss only a single x diecion fo simpliciy. We suppose ha, fo he SLM shown in Fig., he disance beween he pixels is equal o d and he widh of he anspaen zone is w. Fo he image loaded o he SLM, he sampling ineval is given by he sampling heoem as d. Then he maximum spaial fequency which can be disinguished by he SLM eads as max. (5) d Fig. The pixel sucue of SLM The sampled inpu image g(x ) can be descibed in he plane P as [6] x x g( x ) E( x ) ( x md) ec ec, (6) m w Lx whee L x is he oal SLM widh in he x diecion and he inege m coesponds o he m-h ode sampling. Supposing ha hee ae N pixels in he x diecion, we obain L x = N d. If he plane P is illuminaed by a coheen plane-wave wave wih he uni ampliude and a ansfomaion is done by he FL, we ge he fequency funcion G(ξ) in he oupu plane P: ( ) ( ) m G E w sinc( w ) L sinc( ) x L x, (7) d m d whee ξ = x /(λf) and x denoes he x coodinae in he plane P. Accoding o Eq. (7), he specum of he inpu image is peiodic because of he discee sampling by he SLM pixels, wheeas he ineval of he cycles is (λf)/d following fom he diffacion pinciple. The widh and he powe disibuion of he highe-ode speca ae simila o hose of he zeo-ode specum, wih he diffeence ha hei ampliudes ae modulaed wih he funcion sinc(w ξ). The lae induces a apid decease in he specal powes wih inceasing ode m. Accoding o he diffacion specum shown in Fig. 3 and Eq. (7), he cenal spo epesens a socalled diffacion poin spead funcion of he Fouie ansfom sysem. Is widh is λf/(n d ), so ha we have N d f, (8) d whee N d is he CCD widh along he x diecion. As a esul, we obain he inequaliy Uk. J. Phys. Op. 07, Volume 8, Issue 57 Ndd f. (9)
Chao Fan Usually, a join powe specum (JPS) can be bee deeced by he FL wih a longe focal lengh. Hence, we selec he focal lengh of he FL as Ndd f. (0) On he ohe hand, he JPS is fomed by inefeence among he same poins coming fom he age and efeence images. The spaial fequency of he finge is (b +b )/(λf), accoding o he inefeence heoy. When he JPS is deeced wih he CCD, he spaial esoluion of he lae should be highe han ha of he JPS, i.e. we have he condiion o b b, () f d f Nd b b. () d Eq. () descibes he elaionships among he disance beween he age and efeence images, he pixel size of he CCD, he focal lengh of he FL, and he wavelengh of he lase. The JPS sampled by a pixel of he CCD can be descibed as follows: d f f P( ) G( ) n *ec ec. (3) m f d Nd Then, conolled by a compue, he JPS is e-inpu ino he SLM. I can be wien as d f f P( ) G( M ) n ec ec. (4) m f d Nd Hee ξ is he spaial fequency coodinae of he JPS displayed a he SLM, ξ = ξ/m, M = d /d is a scaling faco inoduced by he diffeence in he pixel sizes of he CCD and he SLM, and N d is he JPS widh a he SLM. Because he N d value is much lage han w, he diffacion effec can be ignoed wheneve he SLM is illuminaed by a paallel lase beam. Afe Fouie ansfoming by he lens, he opical field disibuion in he oupu plane is given by [7] Hee Fig. 3. Diffacion paen caused by a discee pixel-like sucue of ou SLM. ( ) sinc n f f d C( x ) n x d C x w w x. (5) 58 Uk. J. Phys. Op. 07, Volume 8, Issue
Design of compac ( ) ( ) x x x x C x G M ec ec M WM M WM x x x x ec ec M WM M WM, (6) x x x x ec ec M WM M WM x M b b x x x x x M b b M WM M WM ec ec whee W is he widh of each inpu image. Noe ha he consan faco /M 4 in Eq. (6) is ignoed. I is seen fom he above equaions ha, since he JPS is ecoded by he CCD and is eloaded ino he SLM again, he muli-level diffacion is induced in he oupu plane and he opical field is disibued peiodically. In Fig. 4, a dashed line epesens he modulaion effec of he funcion sinc(w x /λf) in Eq. (5), whose fis zeo poins ae locaed a ±λf/w, and he cuve inside each dashed ecangle is deemined by he funcion C(x ), which denoes he oupu of each level coelaion. The cenes of each level coelaions ae locaed a (nλf)/d, whee n = 0, ±, ±,. The coesponding inensiy deceases quickly wih inceasing n, and he disance beween he wo adjacen coelaion peaks λf/d is deemined by he pixel size of he SLM. Only a zeo-level coelaion peak is deeced if one measues he image shifs by ecoding he locaions of he coelaed peaks. ' C x ( ) f w f d M ( b b ) M ( b b ) f d f x w Fig. 4. Oupu spaial disibuion of he coelaion signal. Accoding o Eq. (6), hee ae fou ems in he zeo-level coelaion. The fis and he second ones ae auo-coelaion peaks, boh of hem being ovelapped a he oigin, wih he widh MW. The hid and he fouh ems ae coss-coelaions elaed o he image shifs, which should be deeced accuaely. Thei cenes ae locaed a ±M(b +b ) and he widh of each is also equal o MW. To avoid ovelapping among he auo-coelaions and coss-coelaions, one has o mee he condiion o M ( b b ) MW, (7) Uk. J. Phys. Op. 07, Volume 8, Issue 59 b b W. (8) The coss-coelaions of he zeo and fis levels should also be avoided:
Chao Fan Since we have M = d /d, he above equaion can be ewien as f M ( b b ) MW. (9) d f b b W. (0) d Compaing Eqs. () and (0), one can see ha he sum (b + b ) saisfying Eq. (0) is enough. Because he pixel sizes of he SLM and he CCD used in he JTC ae esiced by he manufacuing echnology, hey canno be seleced a andom. To saisfy he elaionship deduced above, he ohe paamees (i.e., he focal lengh of he FL, he widh of he inpu image, and he disance beween he age and efeence images) mus be adjused popely basing on he above equaions. 4. The design of miniauized JTC 4.. Selecion of he componens Accoding o ou design pocedue, he SLM and he CCD ae seleced fis of all since, as menioned above, hei paamees ae esiced by he manufacuing echnique. An elecically addessed device TFT-LCD XGA3 made by he Foh Dimension Displays Co. Ld, England, has been used as an SLM. Is spaial esoluion is 04 768, he pixel pich 8 8 μm, he pixel dimensions 3 0 μm, and he whole size 8.5 3.9 mm. We have used a device EL-400ME made by DTA Co. Ld, Ialy, as a CCD. Is esoluion is 768 5, he pixel dimensions 9 9 μm, and he oal size 6.9 4.6 mm. A He-Ne lase wih he wavelengh λ = 0.638 μm has been used as a monochome ligh inefeence souce. Then he focal lengh of FL can be calculaed wih Eq. (0): Ndd 76898 f 96.6 mm. () 0.638 Since he SLM should be compleely illuminaed by a paallel lase beam, he apeue of he lens should be no less han he lengh of he SLM diagonal: whee D is he apeue of he FL. 4. The design of Fouie lens D 8.5 3.9 3 mm () To make he consucion of JTC compac, we use a long-disance Fouie ansfom lens consising of a posiive lens and a negaive lens (see Fig. 5). Since he above lenses ae sepaaed in he opical sysem, he main plane of he lae is shifed in he fowad diecion. Then he woking disance is less han he focal lengh, which can efficienly shoen he oal size of he FL. Assume ha he focal lenghs of he lenses L and L ae equal especively o f and f, he focal lengh of he FL is f, he disance beween L and L is, and he disance fom L o he CCD (i.e., o he focal plane) is. Since, accoding o Eqs. () and (), we have f = 96.6 mm and he apeue D 3 mm, we le he lae paamee o be D = 5 mm. Applying a simple geomeical opics, we obain, (3) f f f f f f f, (4) 60 Uk. J. Phys. Op. 07, Volume 8, Issue
Design of compac L L D Fig. 5. Schemaic diagam of a long-disance opical sysem. L, (5) Based on Eqs. (3) and (4), we expess he paamee as f ( f ). (6) f To make he JTC shoe, we subsiue Eq. (6) ino Eq. (5) and use he condiion dl/d = 0: f min f, (7) f f f ( min f ). (8) f f Fig. 6 illusaes he elaionships among he woking disance and he focal lenghs f and f, which follow fom he above equaions fo he paicula case f = 96.6 mm. If we have f = 40 mm, Eqs. (7) and (8) esul in = = 57.8 mm, f = 80.84 mm, D = 5 mm and D = 7.9 mm. Hence, he elaive apeues of L and L ae equal o : 3. and : 5.5, especively. If he focal lengh of L is adjused and f = 00 mm, he e-calculaed woking disances ae = 80.34 mm and = 38.67 mm. Then he oal lengh of he FL becomes L 80.34 38.64 8.98 mm. (9) Fig. 6. Illusaion of elaionships among he woking disance and he paamees f and f. Uk. J. Phys. Op. 07, Volume 8, Issue 6
Chao Fan Finally, he apeue of he lens L hen eads as D f 00 80.34 D 5 5 mm f 00 (30) Afe adjusing popely, he elaive apeues become D /f = : 4 and D /f = : 8. Alhough he oal lengh is now a lile longe, he elaive apeues of he lenses L and L ae impoved significanly, which is of benefi fo he lens design. Wih he above paamees, he angle of he field of view of he FL is given by y 6.9 4.6 acan acan., (3) f 96.9 whee y is he lengh of he CCD diagonal and f he focal lengh of he FL. The esuling paamees of he long-disance FL calculaed as explained above ae lised in Table. Table. Paamees calculaed fo ou long-disance Fouie lens. Paamee Fouie lens sysem Lens L Lens L Focal lengh, mm 96.6 00 40 Apeue, mm 5 5 5 Relaive apeue /8 /4 /8 Some posiional = 80.34, = 38.64, L = 8.98 (oal lengh) paamees, mm Field of view angle ω =.º Since we use a lase in ou JTC, we have no need in consideing chomaic abeaion coecions. On he ohe hand, he spheical abeaion and he sine condiion ae sill essenial because he opical sysem of he FL has a lile field-of-view angle and a lage apeue. Then a double can be used fo he lens L, hus benefiing he abeaion coelaion. Similaly, a lase beam-expansion sysem can also use he idenical long-disance lens. The final sucue of he opical sysem of ou compac JTC is shown in Fig. 7. The oal lengh of he JTC is given by L JTC = 8.98 + 8.98 + 40 = 77.96 78 mm. Even hough some exensions can be compomised, he oal lengh is no longe han 300 mm, which educes efficienly he oal size of he JTC. Fig. 7. Geneal schemaic diagam of ou miniauized JTC. 6 Uk. J. Phys. Op. 07, Volume 8, Issue
Design of compac 5. Image shif measuemens based on he JTC Ou expeimenal plafom has been buil using he componens descibed above wih he pupose of checking he effeciveness of he sysem and he measuemen accuacy. In ou expeimen, an iniial sub-image wih he size of 56 56 is exaced fom he emoe sensing image, afe being inepolaed and down-sampled. The age image wih he sub-pixel shifs and he efeence image ae hen obained, wih he same sizes 8 8. Then he boh images ae inpu ino he SLM. Accoding o he elaionships deived in Secion 3, he disance beween he images is 00 pixels (see Fig. 8a). The oupu associaed wih he coelaion of hese wo images is shown in Fig. 8b. The auo-coelaions and he wo coss-coelaions epesen lage dispese spos sepaaed some disance fom each ohe. This is simila o he paen shown in he cenal slashed ecangle in Fig. 4. I is eviden ha he measuemen eo is lage han pixel if he image shif is diecly measued fom he oupu. Fo impoving he measuemen accuacy one has o weaken he auo-coelaion powe, which makes he coss-coelaions shink ino lile bigh poins. Thee ae many pocessing mehods fo his aim, which allow finding he appopiae cenoids easily [8 ]. Afe having done a lo of expeimens, we have found ha he measuemen accuacy becomes he highes when he powe speca of he age and efeence images ae fis subaced fom he JPS. Then he subaced powe specum is binaized wih a zeo heshold, as shown in Fig. 8c. A lo of sips ae conained in he powe specum, which means ha he JPS epesens an inefeence paen fomed by numeous idenical poins coming fom he age and efeence images. Thei inensiies ae modulaed by he diffacion of he age image (o he efeence image). Afe being subaced, he inefeence sips ha conain he infomaion on he image shifs ae only emained in he JPS. The pocessed JPS is again Fouie ansfomed by he FL and he coelaion oupu is caugh by he CCD, as shown in Fig. 8d. Now we find ha he coss-coelaions shink ino wo lile spos wih moe disinc edges and highe powes, if compaed wih Fig. 8b. This allows fo deemining he cenoids of he coss-coelaions peaks easily. As a consequence, he image shifs can be measued wih noable highe accuacy. (a) Inpu of he JTC (b) Oupu of he JTC wih no pocessing (c) Subaced and binaized JPS Fig. 8. Illusaions of inpus and oupus of ou JTC. (d) Oupu of he JTC afe pocessing Uk. J. Phys. Op. 07, Volume 8, Issue 63
Chao Fan Basing on ou expeimenal plafom, we have sudied he measuemen pefomances of he JTC on he examples of 00 diffeen sub-images, whose sizes ae 56 56. Afe ha, he iniial and shifed images have been inepolaed and meged wih sofwae o fom he age image and he efeence image wih he same sizes 8 8. The image shif beween hem is less han pixel. We have inpu hese sub-images ino ou JTC and he image shif has been measued. The esuls analyzed using sandad mahemaical saisics have demonsaed ha he image shifs can indeed be measued vey accuaely and he mean measuemen eo fo all of he images emains less han 0. pixel. 6. Conclusion To impove he qualiy of images aken wih high-esoluion spaial camea, we have suggesed using a specific JTC fo measuing he shifs beween he wo adjacen images. Consideing he miniauizaion equiemens, we have analyzed he elaionships among he paamees of he componens of ou opical sysem, basing on he Fouie opics pinciples. Afe having compleed hese sages, we have designed a compac JTC and buil a coesponding expeimen plafom. By employing ceain pocessing mehods associaed wih ou JPS, we have been in a posiion o deec easily he locaions of he coss-coelaion poins and so measue accuaely he elevan image shifs. The esuls obained have shown ha he measuemen eos do no exceed 0. pixel, wheneve he shifs beween he age and efeence images ae less han pixel. Acknowledgmens This wok is suppoed by he Science and Technology Suppo Pojec of he Sae Gain Adminisaion (No 04300), he China Scholaship Council (No 04084055) and he Naual Science Foundaion of Henan Povince (No 63004006). Refeences. Chiu C W, Chan P C and Wu D Y, 007. Opimal design of magneically acuaed opical image sabilize mechanism fo cameas in mobile phones via geneic algoihm. IEEE Tans. Magn. 43: 58 584.. Hyun Choi, Jong-Pil Kim, Myeong-Gyu Song, Wan-Chin Kim, No-Cheol Pak, Young-Pil Pak, and Kyoung-Su Pak, 008. Effecs of moion of an imaging sysem and opical image sabilize on he modulaion ansfe funcion. Op. Expess. 6: 3 4. 3. Thomas B, Miffe A, David G, Caiou J P, and Raioux P, 0. Remoe sensing of ace gases wih opical coelaion specoscopy and lida: Theoeical and numeical appoach. Appl. Phys. B. 08: 689 70. 4. Thomas B, David G, Anselmo C, Caiou J-P, Miffe A, and Raioux P, 03. Remoe sensing of amospheic gases wih opical coelaion specoscopy and lida: Fis expeimenal esuls on wae vapo pofile measuemens. Appl. Phys. B. 3: 65 75. 5. Elbouz M, Alfalou A, Bosseau C, Ben Haj Yahia N, Alam M S, 05. Assessing he pefomance of a moion acking sysem based on opical join ansfom coelaion. Op. Commun. 349: 65 8. 6. Michael J, 000. The influence of SLM pixel size and shape on he pefomance of opical coelaos and opical memoies. Poc. SPIE. 4089: 98 07. 7. Robe M Bunch, Jeffey A Davis, Don M Coell, Ehan A Meill, 005. Effecs of sampling and binaizaion in he oupu of he join Fouie ansfom coelao. Op. Eng. 9: 094 00. 64 Uk. J. Phys. Op. 07, Volume 8, Issue
Design of compac 8. Joewono W, 05. Noise-obus low-conas einal ecogniion using compession-based join wavele ansfom coelao. Op. Las. Techol. 74: 97 0. 9. Isha M, Sudheesh K R and Naveen K N, 04. Cypanalysis of an image encypion scheme based on join ansfom coelao wih ampliude- and phase-uncaion appoach. Op. Las. Eng. 5: 67 73. 0. Qian Yixian, Hong Xueing, Miao Hua, 03. Impoved age deecion and ecogniion in complicaed backgound wih join ansfom coelao. Opik. 4: 68 685.. Leonad I, Alfalou A, Alam MS, Anold-Bos A, 0 Adapive nonlinea finge-adjused join ansfom coelao. Op. Eng. 5: 0980. Chao Fan. 07. Design of compac join ansfom coelao. Uk.J.Phys.Op. 8: 55 65. Анотація. Для поліпшення якості знімків просторових камер ми вимірюємо субпіксельні зсуви між двома сусідніми зображеннями, використовуючи корелятор спільного перетворення (КСП). Спочатку ми описуємо принципи вимірювання зсувів зображень на основі КСП. Далі з урахуванням дискретної піксельно-подібної будови ПЗС і просторового модулятора світла обговорено зв язки між параметрами компонентів КСП, що випливають із теореми дискретизації та принципів фур є-оптики. На цій підставі обрано необхідні прилади і розраховано лінзу Фур'є для побудови компактного КСП. Нарешті, створено необхідну експериментальну базу і оцінено ефективність вимірювань зсувів зображень. Результати засвідчили, що субпіксельні зсуви зображень можна виміряти з досить високою точністю. Похибки є меншими за 0, піксель за умови, що зсуви зображень перебувають у межах до пікселя. Uk. J. Phys. Op. 07, Volume 8, Issue 65