近代光信息处理-第6章课件.ppt

1、第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-71第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-74第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-75第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-76-W()()W()(-第第1 1

2、节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-77-第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-78-第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-79第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-712(17)引入参数引入参数a，b，第第

3、1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-715第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-716 )abx(ha1)x(h b,a )b(g)ab(ha1dx)x(g)abx(ha1)x(g),x(h)x(gW*b,ab,a 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-717)2texp()t2iexp(21)t(h

4、 220 )abt(ha1)t(h n,m 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-718 )a2texp()at2iexp(21a1)t(h 20220000,1 )2taexp()ta2iexp(21a/11)t(h 22200000,1 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-719第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6

5、 6章章2022-12-720)a(H)b2iexp(adx)x(h)x2iexp()x(H b,ab,a d)(G)b2iexp()a(Ha)x(gW *b,a 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-724第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-725第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-728 )

6、43t(2rect)41t(2rect)t(h 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-729 /)cos(1)iexp(i 2)(H vvvv 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-730 )2texp()t2iexp()t(h 20 )(2exp)(2exp2)(H 202202 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6

7、6章章2022-12-731第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-732 )2texp()t1()t(h 22 )2exp(4)(H 222 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-733第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-734 3231),(2)1(第第1 1节节第第2 2节节第第3 3节节第第

8、4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-735 3231),(2)2(d)21t(2cos)(sin2)t(h 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-736 a/a/)xx(h)x(gW xjjiij a/a/)xx(hW)x(s ijjjiij 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-737第第1 1节节第第2 2节节第第3 3节节第第4 4节节

9、第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-738图14-10柱面透镜图14-11柱面透镜成像柱面透镜水平剖面与凸透镜的剖面相同，在这个平面内，对光线有会聚作用；而竖直剖面与平板玻璃剖面相同，对光线没有会聚作用。所以，一个点光源经过此柱面透镜所成的像为一条竖直的直线。第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-739第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-740第第1

10、 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-741 )M,2,1,m()a,a(agW mma,am gW a,am),a(H mu第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-742)b(g)ab(ha1dx)x(g)abx(ha1)x(gW*b,a dd),(ab,abhaa1 )b,b(ab,abhaa1)y,x(W yyxx*yxyxyyxxyxb,b,a,ayxyx dd),(ab,abha1)y,x(W

11、yx*b,b,ayx 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-743 d)dbb(2iexp),()a,a(HaaW yxyx*yxb,b,a,ayxyxvuvuvuvu第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-744 d)dbb(2iexp),()a,a(HaaW yxyx*yxb,b,a,ayxyxvuvuvuvu)y,x(W yxyxb,b,a,a 第第1 1节节第第2 2节节第第3 3节节第第4

12、 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-745 mdxrectdxcomb*xrectd1)x(t m 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-747第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-748 dycomb*yrectdxcomb*xrectd1)y,x(t 2 dy,dxcombd1)y,x(t 2 第第1 1节节第第2 2节节第第3 3节节第第

13、4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-749 d1)nf,mf(d1 )dd(comb*)()(mnn,m2mnoo2 vuvu,vu,vu,第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-750 e)nf(a),mf(aH)(F mn)qp(2omom*nm vuvuvu,第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-751 mnqb,pb,a,amn2mnn

14、ymxnnymmxmn2mn)qb()pb(2inm*mn2)qb()pb(2ioomnonom*2yx)y,x(WCd1 )qb,pb(aqb,apbhCd1 dde),()a,a(HCd1 dde)nf,mf()nf(a),mf(aHd1)b,b(nymxnmnymxnymxvuvuvu vuvuvuvuvu第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-752第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-75

15、3 eHaaeHaaHaa1 RHaa)(F mn)qp(2mnnm)qp(2*mnnm2*mn2n2mmn2mn*mnnmnmnm vuvuvu,)e()aa(Haa mn)qp(2nm*nmnm vuvu,v u,mnqb,pb,a,amnnymxnnymmx)qb()pb(2imnnm*nmyx)y,x(W )qb,pb(aqb,apbh dde),()a,a(Haa)b,b(nymxnmnymxvuvuvuvu(18)eHaaeHaaHaa1 RHaa)(F mn)qp(2mnnm)qp(2*mnnm2*mn2n2mmn2mn*mnnmnmnm vuvuvu,第第1 1节节第第2 2节

16、节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-757第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-758第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-759 2yxexp)yx(221)y,x(h 2222 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-76

17、0第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-761 ),(ay,axga21-dd),(ay,axga21-dd),(ay,axha1 )y,x(ay,axha1W 22*y,x,a第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-762 a2yxexpay,axg 222 ),(ay,axga21-W 2y,x,a 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第

18、第7 7节节第第6 6章章2022-12-763第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-764第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-765(d)I=24,a=0.08(e)I=24,a=0.15(c)I=24,a=0.05(f)I=24,a=0.20(a)待处理图像(b)小波函数图像 第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6

19、6章章2022-12-767第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-768 vuvuvu,vuvuvu,vuvudde)a,a(H)(aW dde)a,a(H)(aW)yx(2i*y,x,a)yx(2i*y,x,aa=la=2第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-771第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-

20、12-772第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-773第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-777第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-778旁瓣旁瓣H(v)频率窗恰频率窗恰恰开在旁瓣恰开在旁瓣第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7

21、节节第第6 6章章2022-12-779第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-780-1+1+1-1第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-781第第1 1节节第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-783 dd),(ab,abh)b,b(yxyx dd),(ab,abha1 W yx*b,b,ayx 第第1 1节节

22、第第2 2节节第第3 3节节第第4 4节节第第5 5节节第第6 6节节目目 录录第第7 7节节第第6 6章章2022-12-788 11J o 0001P 1000P 111121P 45SLMyxJ J J10 111000JP J01 110001JP /4-ooo表为表为方向的偏振分析器，可方向的偏振分析器，可放置沿一放置沿一前前入信号入信号方向的线偏振光。在输方向的线偏振光。在输和和”分别是沿”分别是沿和和”及及掩掩模模板板的的制制作作。编编码码技技术术实实现现了了，这这样样一一来来，我我们们就就用用的的相相位位差差为为方方向向的的偏偏振振光光，它它们们和和分分别别是是沿沿和和”及及变

23、变成成振振分分析析器器，部部分分的的光光波波，再再经经过过偏偏及及经经过过掩掩模模中中Haar 13545J J J1121 10111121JP J1121 01111121JP 1-1 oo-4/4/Application of the wavelet transform to edge detection is discussed in general.To propose two new wavelet transforms for edge detection:Modified Haars wavelet transform(MHWT)and Haar-Gaussian wavele

24、t transform(HGWT).To analyze the performance of MHWT and HGWT for edge detection in both space and frequency domains.Application for lead inspection of surface mount devices(SMD)in electronic industry by using MHWT and HGWT is presented in detail.Keywords:Wavelet transform,Machine vision&automatic i

25、nspection,Edge detection,Lead inspection,Surface mount devices(SMD)1.INTRODUCTIONAn image generally contains some slowly varying areas andsharply varying regions.Sharp varieties,singularities often carryinteresting and important information.EDGE DETECTION(I)Edges of an image are generally localized

26、by singularities and irregularities.Edge detection is one of the basic operations of all artificial,computer,robotic,or machine vision systems.Gradient estimations are classical models which give satisfactory results in thecases of slightly noisy images.For Noisy images a low-pass filter should be i

27、ncluded.However,its performanceis greatly dependent on the smoothing scale factor of the impulse response.If theedge to be detected is sharp,one can choose a small impulse response.EDGE DETECTION(II)But if the edge is smooth,a large impulse response will give moresatisfactory results.Therefore,singl

28、e smoothing scale of impulse response is ofteninsufficient in many applications,and multi-scale or variable impulseresponse for edge detection is very attractive.WAVELET TRANSFORM Mallat 1 suggested that the wavelet transform is very closely relatedto a multi-scale impulse response for edge detectio

29、n.An attractive feature of the wavelet transform is that it can well localizethe regularity of signals in both space and frequency domains.Byvarying its dilation parameter,the wavelet transform accordinglychanges its smoothing scale factor automatically.2.NEW WAVELET TRANSFORMS Haars wavelet is cons

30、tructed by two rectangular functions as expressed inEq.(1)and shown in Fig.1.432412xrectxrectxh .(1)where rect(x)is defined as2/1|02/1|1xxxHAAR WAVELET Its Fourier transform is )2(,cos12iieH,It has a zero dc component.Fig.1.Haars wavelet(a)and its spectrum(b)xh(x)1(b)H().(a)TWO NEW WAVELETS We propo

31、sed two new wavetes:Modified Haars wavelet and Haar-Gaussianwavelet,4,5,defined as:)0(qssqxrectsqxrectxhs,(3)0(expexp22qssqxsqxxhs (4)q:offset parameter s:dilation factor Modified Haars wavelet and Haar-Gaussian wavelet are both anti-symmetric asshown in Fig.2.With an additional offsetparameter q,mo

32、dified Haarswavelet and Haar-Gaussianwavelet are very powerful innoisy edge detection andfeature extraction.Fig.2.Modified Haars wavelet(solid line)and Haar-Gaussian wavelet (dashed line)-qq3.NOISY EDGE DETECTION Mathematical model of edge function is expressed in Eq.(5)21tan1xxf,(5)Width of edge is

33、given by.(6)The edge function isdepicted in Fig.3.Fig.3.Model of an edgewith width .NOISY EDGE FUNCTION(I)Noisy edge function is further simulated as follows.rndxxxxf221112sin2sin21tan,(7)Last three terms represent the sinusoid interference and random noise.Simulated noisy edge function is depicted

34、in Figs.4(a),(b),(c)and(d),together withthe Haar-Gaussian wavelets of various dilations s.The vertical lines(dashed)specify the spatial windows of the wavelet.(a)s=0.63(b)s=0.42NOISY EDGE FUNCTION(II)Fig.4.Noisy edge function and Haar-Gaussian wavelets with various dilations.(a)s=0.63,2s =9.5;(b)s=0

35、.42,2s =6.4;(c)s=0.10,2s =1.6;(d)s=0.053,2s =0.8 2s :width of the spatial window,is defined as follows.2/12,2xhxhxhxxhs,(8)where(f,g)represents the inner product of functions f and g.(c)s=0.01(d)s=0.053HAAR-GAUSSIAN WAVELET TRANSFORM OF THENOISY EDGE FUNCTION(I)Haar-Gaussian wavelet transform(HGWT)o

36、f the noisy edgefunction f(x)is a correlation of the signal with the wavelet:dsxhfxhxfxfWss)(*,(9)HGWT for different dilations s(which is equivalent to thesmoothing scale of impulse response discussed previously)aredepicted in Fig.5.Maxima of the WT indicatethe location of the edge.Fig.5.HGWT of the

37、 noisy edgefor different dilation s:(a)s=0.63(curve with thebroadest peak),(b)s=0.42(curve with the lessbroad peak),(c)s=0.10(curve with narrowpeak and small ripples),and (d)s=0.053(curve with severeripples).HAAR-GAUSSIAN W AVELET TRANSFORM OF THENOISY EDGE FUNCTION(II)Characteristic dimension of th

38、e noise is given as:2.0/1,(10):the frequency of the sinusoidal noise.s:dilation of W T 2s :width of spatial windows :characterized noise dimension.W hen the width of the spatial window is close to the characteristicdimension of the noise multiple maxima are found in the wavelettransforms and the fal

39、se response would occur.4.FREQUENCY DOM AIN ANALYSIS The edge detection based on the wavelet transform in space domain canbe analyzed in frequency domain as well.The frequency spectra of boththe noisy edge function and the Haar-Gaussian wavelet of differentdilations s are depicted in Fig.6(a)to(d).S

40、2s 0.633.00.422.00.100.500.0530.25 0.2Table 1 Fig.6.Spectra of noisy edge function(solid line),Haar-Gaussian wavelet (dashed line)and frequency filtering window(Vertical lines).(c)s=0.12(a)s=0.63(d)s=0.053(b)s=0.42FREQUENCY DOMAIN ANALYSIS(I)H aar-G aussianw avelet acts as alow frequencyband-pass fi

41、lterw ith no dccom ponent infrequency dom ain.T he spectrum of the ram p edge function consists of a high dccom ponent and a series of low frequency lobes.T he sharpest variationof the illum inant curve(the edge)contributes m ostly to the lowfrequency lobes.T he band-pass filter of the H aar-G aussi

42、an w avelet blocks the dccom ponent but passes the low frequency lobes belong to the edgesignal and thus enhances and extracts the edge transitioninform ation.F R E Q U E N C Y D O M A IN A N A LY SIS(II)FREQUENCY DOMAIN ANALYSIS(III)In Figs.6(a)and(b),the band-pass filter of the HGWT blocks the two

43、 high-frequency peaks of the sinusoid noise functions.These two peaks are farbeyond the cut-off frequency of the band-pass filter.Also,the spectrum of random noise is broadly spreading,having less influenceto the wavelet transform.(a)s=0.63(b)s=0.42In contrast to Fig.6(a)and(b),the frequencywindow o

44、f Fig.6(d)contains the noisecharacteristic frequency,which produces themulti-maxima in the space domain and mightresult in some fault locations in edgedetection.Fig.6(c)represents a criticalsituation where the peaks just locate atthe margin of the frequency window.Their contribution is insufficient

45、toimpact the edge detection.Fig.6(c)Fig.6(d)FREQUNCY DOMAIN ANALYSIS(IV)CONCLUTION The frequency domain analysis is in a good agreement with the space domain analysis.In the final analysis the random and sinusoidal noise have infinite extensions in space,but the wavelet transform localizes the signa

46、l in both space and frequency domains.Itis therefore insensitive to the noise and able to accurately indicate the location of theedge.5.APPLICATION TO LEAD INSPECTION OFSURFACE MOUNT DEVICES BACKGROUNDIn the last decade the volume production of surface mount device(SMD)has growntremendously and ther

47、e is a trend to replace the through-hole components by SMD.TH R O U G H-H O LE C O M PO N EN TS A N DSU R FA C E M O U N T D EV IC E(SM D)Surface m ount device(SM D)T hrough-hole device This new technology produces benefits in M iniaturization M uch larger integration cost reduction,and design flexi

48、bility.COPLANARITY,PITCH AND FOOT ANGLE OF SMD However,the following factors of SMD have put much stress on the productiontechnology:very finer pitch(0.5 mm)and much higher package lead counts(more than some hundreds leads per chip).To assure reliable solder contacts,it is required that the lead cop

49、lanarity andpitch should be 100 microns.The foot angle should be less than 10 deg.The IC manufacturers are responsible for accurately inspecting the 3-Dpositions of the leads for all outgoing components.CP Coplanarity(C),pitch(P)and foot angle()of SMDDUAL SHADOW TECHNIQUE FOR LEAD INSPECTIONSeveral

50、techniques have been proposed for the lead inspection on the productionline.The dual shadow technique 6 is cost-effective,reliable,and accepted bymost manufacturers.A schematic diagram of the lead inspection system is shown in Fig.7.An SMD is put on the pedestal.All its leads do not touch the top pl