Digital approximation to extended depth of field in no telecentric imaging systems

Transcription

1 Journl of Physics: Conference Series Digitl pproximtion to extended depth of field in no telecentric imging systems To cite this rticle: J E Meneses nd C R Contrers 0 J Phys: Conf Ser View the rticle online for updtes nd enhncements This content ws downloded from IP ddress on 0/0/08 t 04:40

2 XVII Reunión Iberomericn de Óptic & X Encuentro de Óptic, Láseres y Aplicciones IOP Publishing Journl of Physics: Conference Series 74 ( doi:0088/ /74//0040 Digitl pproximtion to extended depth of field in no telecentric imging systems J E Meneses nd C R Contrers Grupo de Óptic y Trtmiento de Señles, Escuel de Físic, Universidd Industril de Sntnder AA 678 Bucrmng Colombi Emil: jimen@uiseduco Abstrct A method used to digitlly extend the depth of field of n imging system consists to move the object of study long the opticl xis of the system nd different imges will contin different res tht re shrp; those imges re stored nd processed digitlly to obtin fused imge, in tht imge will be shrp ll regions of the object The implementtion of this method, lthough widely used, imposes certin experimentl conditions tht should be evluted for to study the degree of vlidity of the imge finl obtined An experimentl condition is relted with the conservtion of the geometric mgnifiction fctor when there is reltive movement between the object nd the observtion system; this implies tht the system must be telecentric, which leds to reduction of the observtion field nd the use of expensive systems if the ppliction includes microscopic observtion This pper presents technique tht mkes possible to extend depth of filed of n imging system non telecentric; this system is used to relize pplictions in Opticl Metrology with systems tht hve gret observtion field Introduction The opticl systems tht re constructed with conventionl lens hve limited depth of field nd only the regions tht re inside of depth of field (DOF will pper in focus in the finl imge Thus the regions of the object surfce tht re out of DOF will pper out of focus on the cquired imge Physicl optics estblishes tht the diffrction pttern dimeter of pupil imging system defines the DOF of the imging system The dimeter of this centrl spot, in experimentl situtions is of the order of tenths of micron, while tht the digitl cmers hve micro-sensor dimensions of some microns Thus, diffrction-relted effects s predicted by physicl optics re not significnt, since the sptil resolution of most sensor rrys is quite below tht of the diffrction limit It implictes tht the geometricl optics defines the depth of field of digitl imging system like CCD or CMOS According to geometricl model of thin lenses, if the sensor plne does not coincide with the focl plne, the imge of punctul object will be circle for circulr pupil of the imging system nd known s circle of confusion The dimeter of the circle confusion is clculted from the prmeters of the opticl system nd the defocus distnce, displcement from sensor plne to focl plne Thus, the PSF cn be pproximted to cylindricl function of brightness constnt, filtering high frequency informtion However, due to lens berrtions, diffrction nd noise, the brightness decreses grdully to brim Frequently is suggested two-dimensionl Gussin function s PSF model of the opticl system In this wy defocused imging system is considered s low pss filtering system Thus blurry imge hve ttenuted informtion of high frequency, without imge detils nd Published under licence by IOP Publishing Ltd

3 XVII Reunión Iberomericn de Óptic & X Encuentro de Óptic, Láseres y Aplicciones IOP Publishing Journl of Physics: Conference Series 74 ( doi:0088/ /74//0040 degrded imge qulity As result, limited DOF poses significnt problem when utomtic nlysis of imges is desired Severl methods hve been proposed to increment DOF of clssicl imging system Bsiclly the increment of the depth of field cn be crry out: ( physiclly djusting the PSF of the opticl system without post-cpture digitl tretment, ( digitlly mking digitl tretment on cquired imges nd (3 combintion of the previous methods: physiclly introducing externl devices to the trditionl systems (pltforms of movement, phse msks, etc nd computtionlly mking restortion opertion through digitl tretments Severl methods hve been proposed to extended-dof [-7] A method used frequently nd used in the most commercil systems with E-DOF consists in to cquire severl imges for severl positions on the opticl xis Thus if N imges of m n pixels hs been cquired, ech pixel hs n intensity vector of N vlues corresponding to N different xil positions In order to extrct the intensity vlue corresponding to focused xil position for ech pixel, function or mthemticl criterion must be defined to evlute the focus qulity, clled focus mesure Severl methods hve been proposed to define the focus mesure (locl vrince, grdient, wvelet trnsform, Fourier trnsform, etc All of them rely on the fct tht focused imge hs high contents of higher frequencies with higher locl vritions of intensity vlues Thus, for ech pixel the focus mesure (FM is evluted nd the intensity tht produces the mximum vlue of FM is extrcted nd used to generte fused imge with E-DOF The procedure described bove for E-DOF imposes the condition tht the N intensity vlues correspond to the sme surfce point nd imged in the sme pixel ( i, j for ech xil position Thus, if the imging system is non-telecentric, the mgnifiction fctor chnges nd the surfce point is imged in different pixels ccording to the xil position Additionlly lterl displcement in the perpendiculr direction of the opticl xis produces the sme problem: Intensity vector for pixel ( i, j does not correspond to the sme surfce point on the object In this work we propose new method to Extended DOF for non-telecentric imging system The focus mesure of specific pixel is evluted using the Tenengrd method with the pproprited correction in order to reduce the non-telecentric influence A mthemticl correction is proposed to extrct from ech imge the coordintes in pixels tht correspond to the sme surfce point E-DOF for non-telecentric system Figure shows the imges of surfce point projected by non-telecentric system In the figure P xyz,, +Δ z the imges of these points pper hs coordintes ( xyz,, while P hs coordintes ( locted in x nd x respectively; P nd P correspond to sme surfce point for two xil positions The reltive displcement in the xil direction between object nd opticl system is Δ z It is evident the problem becuse the system is non-telecentric: the sme surfce point locted on the object hs two different positions in the imge spce, these points re x nd x respectively The solution of this problem is to find the corrected pixel position in ech cquired imges which corresponds to the sme surfce point nd it is used to evlute the FM In the non-telecentric condition the lterl displcement between x nd x depends on opticl system prmeters, object distnce nd z vlue of surfce point A mthemticl structure is proposed in order to eliminte the z vlue influence using first order pproximtion in the compute of x - x distnce From figure cn be deduced tht, vx x = u xtnθ ( Now for x, tht is the position of the point P in the imge spce, is obtined,

4 XVII Reunión Iberomericn de Óptic & X Encuentro de Óptic, Láseres y Aplicciones IOP Publishing Journl of Physics: Conference Series 74 ( doi:0088/ /74//0040 x vx u x tn θ Δ z ( Figure Imging for no telecentric system Generlly cn be demonstrted tht for the nth movement Δ z, is obtined, uvx x n = uv n Δ z x + v ( ( tnθ uvy y n = uv n Δ z x + v ( ( tnθ (3 (4 The equtions (3 nd (4 enble to clculte the coordintes in the imge spce of specific surfce point for ech cquired imge in non-telecentric system The problem lies in these equtions is the influence of unknown vlues z nd θ However if is tke into ccount the pproximtion θ θ nd tht θ = θ (see figure, then, x x tn θ, = z +Δ z x x= ztn θ, (5 (6 x θ = (7 u tn It is possible to express x in terms of opticl system prmeters, 3

5 XVII Reunión Iberomericn de Óptic & X Encuentro de Óptic, Láseres y Aplicciones IOP Publishing Journl of Physics: Conference Series 74 ( doi:0088/ /74//0040 Δz x = x + u (8 Moreover it is tking into ccount tht x = x, is obtin tht, u v vx Δz x = + u u (9 The eqution (9 cn be generlized s follows, vx Δz xn = ( n u + (0 Similrly for the Y coordinte, vy Δz yn = ( n u + ( vx vy However tking into ccount tht x = nd y = ; the equtions (3 nd (4 cn be expressed u u s ( Δz xn = x + n, ( nd ( Δz yn = y + n (3 The equtions ( nd (3 enble to clculte the position of specific pixel for ech imge cquired for non-telecentric system knowing Δ z 3 Experimentl evlution In order to evlute the proposed equtions non-telecentric imging system ws implemented A FUJINON HF35HA-B objective of focl distnce 35 mm nd f 6 ws used in CCD cmer ivc500 (640 pixels 480 pixels, 65 μ m 65 μ m A trnsltion stge of 0 μ m precision ws used to generte the reltive displcement between object nd CCD cmer An integrted circuit ws used s test object A set of 9 imges with Δ z = 050 mm ws cquired Figure shows the cquired imge for z = 000 mm Figure 3 shows the fused imge E-DOF procedure using the Tenengrd method with 5 pixels 5 pixels window to clculte the focus mesure From visul nlysis it is pprecited tht the fused imge qulity is poor becuse it does not consider tht specific pixel does not hs the sme position in ech cquired imge In the centrl zone of the imge the influence of non-telecentric condition is pprecibly smller thn exterior zone: The fused imge is severely degrded in the exterior zone Figure 4 shows the fused imge using the proposed method with the Tenengrd focus mesure for 4

6 XVII Reunión Iberomericn de Óptic & X Encuentro de Óptic, Láseres y Aplicciones IOP Publishing Journl of Physics: Conference Series 74 ( doi:0088/ /74//0040 window size of 5 pixels 5 pixels From visul nlysis it is evident tht the qulity imge is ugmented becuse equtions ( nd (3 correct the lterl displcement introduce by the nontelecentric condition Figure Acquired imge for z = 000 mm Figure 3 Extended depth of field imge using the Tenengrd method Figure 4 Extended depth of field imge using the proposed method From the E-DOF procedure it is possible to compute the xil position tht hs the mximum vlue of the FM This vlue is relted to 3D informtion of surfce object Figure 5 shows the tridimensionl 5

7 XVII Reunión Iberomericn de Óptic & X Encuentro de Óptic, Láseres y Aplicciones IOP Publishing Journl of Physics: Conference Series 74 ( doi:0088/ /74//0040 reconstruction The z vlue is obtined by using the nth position of the mximum focus mesure for xy, pixel of the imge ech ( Figure 5 Tridimensionl reconstruction 4 Conclusions In this pper hs been proposed method (bsed in the first order pproximtion tht enbles to extend the depth of field of non-telecentric imging system A non-telecentric imging system hs been designed nd implemented in order to evlute the performnce of proposed method The results obtined show tht this method enbles to extend the depth of field of non telecentric imging system It is showed tht is necessry to know certin opticl prmeters of the system Additionlly, it is possible to obtin tridimensionl informtion of the study object References [] R J Pieper nd A Korpel, Imge processing for extended depth of field, Appl Opt, (983 [] S A Sugimoto nd Y Ichiok, Digitl composition of imges with incresed depth of focus considering depth informtion, Appl Opt 4, (985 [3] S C Tucker, W T Cthey, nd E R Dowsky, Jr, Extended depth of field nd berrtion control for inexpensive digitl microscope systems, Opt Express 4, (999 [4] A G Vldecss, D Mrshll, J M Becerr, nd J J Terrero, On the extended depth of focus lgorithms for bright field microscopy, Micron 3, (00 [5] B Forster, D vn de Ville, J Berent, D Sge, nd M Unser, Complex wvelet for extended depth of field: new method for the fusion of multichnnel microscopy imges, Microsc Res nd Tech 65, 33-4 (004 [6] A Cstro, nd J Ojed-Cstñed, Asymmetric phse msk for extended depth of field, Appl Opt 43, (004 [7] J Meneses, M A Surez, J Brg, nd T Ghrbi, Extended depth of field using shpeletbsed imge nlysis, Appl Opt 47, (008 6