**Measurement** **Velocity** **by** **the** **CCD** **Linear** **Image** **Sensor** **Operating** in **the**TDI Mode.Ludě k Kejzlar, Jan FischerCzech Technical University, Dept. of **Measurement**, Technicka 2,166 27, Prague 6, Czech Republic, kejzlal@feld.cvut.cz, fischer@feld.cvut.czSUMMARYThis paper is devoted to description, analysis andpractical verification of a new method of control of**CCD** linear image sensor working in TDI (TimeDelay Integration) mode. TDI mode of operation isused when objects observed **by** **CCD** sensor move in**the** direction of sensor line. The results of experimentswith test patterns moving with different velocities arediscussed. Conclusions and hints applicable forfinding velocity of movement are also included in **the**paper.Keywords: **CCD** linear image sensor, TDI, velocitymeasurementSubject category: Physical sensors (non-magnetic)**CCD** LINEAR IMAGE SENSOR MODELSThe **CCD** linear image sensor physical structure ison Figure 1. This structure could **by** described **by** **the****CCD** linear sensor signal model, which is on Figure 2.Photo-sensitive elementsShift registerTransfer gateShutter gateΦ XΦ SΦ t1Φ t2SiO 2ElectrodesSemiconductor PDepeletion AreaFigure 1. **CCD** linear image sensor physical structureThe colours in Figure 2 correspond with colours inFigure 1 and describe **the** same parts of sensor. Thephotosensitive element is modelled as convector E/Qwith accumulator (green). The transfer gate ismodelled as N switches controlled **by** one signal (red).Two-phase shift register is represented **by** delay linewith delay T t (blue). The shutter gate is represented asN switches that are connected to ground (yellow).The signal model was used to develop **the**simulation program for **CCD** linear sensor. Thesignal model was used for ma**the**matics descriptiontoo.Φ SΦ XΦ tE/QΣΣD -Tt**Image** of object1 2 3 NE/Q E/QE/QΣΣD -TtΣΣD -TtΣΣD -TtPhoto sensitiveelementsK rShutterTransfer gateShift registerOutputFigure 2. **CCD** linear image sensor signal model**CCD** linear sensor principle diagram is on Figure3 this scheme will **by** used to explain **the** TDIoperation mode.Φ SΦ XΦ tq 1photo sensitiv elementsq itransfer gateTxcharge transp. registerq NOutputUoutFigure 3. **CCD** linear image sensor principle diagramPRINCIPLE OF CONTROLLING THE **CCD**LINEAR CAMERA IN TDI MODETDI mode is a mode of **the** **CCD** linear sensorcontrol. In this case **the** TDI mode is implemented inline. In this mode a value of each output pixel isdetermined from values of all N active pixels incorresponding times.The principle of **the** TDI mode lies in repetition ofa cycle (described below) during control **the** sensoroperation.During **the** first phase of operation **the** charges areintegrated in **the** **CCD** photo-elements (’’pixels’’) (q i ),during **the** time T Xef .q 1v IMv CHq iN**Image**q NΦ XUoutFigure 4. a) Principle of **CCD** linear image sensorworking in TDI ; second cycle - second phase

In **the** second phase (after **the** end of integration)**the** charges are transported to **the** charge shift registervia **the** transfer gate controlled **by** signal Φ X (seeFigure 4 a)). Transported charges are added to **the**charges, stored in shift register from **the** previouscycle.In **the** third phase **the** charges in shift register aremoved **by** one position via control signal Φ t (withfrequency f Φt ). Step three of this cycle overlaps with**the** step one of **the** next cycle (see Figure 4 b).q 1v IMv CHq iN**Image**q NΦ tUoutFigure 4 b) Principle of **CCD** linear image sensorworking in TDI ; first cycle - third phase andsecond cycle - first phaseIn **the** TDI mode **the** charges in **the** shift registershifts with velocity v CH , determined **by** **the** multiple of**the** pixel pitch of **the** photo elements d PIX [m] and **the**control frequency of shift register f Φt [Hz] (**the** controlfrequency of shift register f Φt correspond withtime T X ).vCH=dTXd=2fΦ tWhen **the** velocity of charge v CH is equal to **the**velocity of image of object v IM , coherent accumulationof charges occurs and sharp image of **the** object isobtained. The equation ( 1) describes chargeintegrated in photosensitive element i for integrationtime T X .this equation correspond with **the** colours of blocks in**the** signal model (Figure 2).SPECIAL **CCD** LINEAR CAMERAThe TDI mode of operation was realised in special**CCD** linear camera, we designed. Its block diagram isin Figure 5. There is used **the** DSP (Digital SignalProcessor) to control **the** **CCD** linear sensor.PCRS232ControlRAMDSPADSP2115Signal or DataLensA/D**CCD**VideoFigure 5. Special **CCD** linear camera block diagramAdvantage of this solution is possibility to changeor adjust **the** control algorithm. This camera can workin many special modes like standard mode, TDImode, FIR mode and so on.PRINCIPLE OF MEASURING VELOCITY BYTHE **CCD** CAMERA WORKING IN TDI MODEThe special **CCD** linear camera working inTDI mode is observing **the** moving object (test tapewith black and white stripes). The measuring set-upwe used for velocity measurement is described inFigure 6.**CCD**Lensdv CHv IMMM = d Dv Oq i(nT t) = k c∫ E i ( t ) dt0T Xef» k cE i( nT t)T Xef( 1),where **the** E i (t) is i-th pixel radiant intensity (constantfor time T X ), k r represents conversion constant (pixelarea, conversion of watts to coulomb, ...), n is timeindex and T t is **the** charge shift time T t = 2 / f Φt .The Equation ( 2) describes output voltage of **the****CCD** linear image sensor working in TDI mode.u OUT(i) =( 2)+ N Q( O )k rN( q i( t-i·T t) )i = 1where **the** q i (t) is charge integrated in i-th pixel attime t, **the** T t = 2 / f Φt , **the** N is number of active pixelcells of **the** sensor and **the** Q 0 represents **the** parasiticcharges generated in charge shift register. Colours inDMoving test tapeFigure 6 Set-up of experimentv o= v IMMChoice of coherency criterion is basic for correctfunction of this method. We used **the** criteriondescribed **by** **the** following equation (mean varianceof **the** image signal):Kef1=NN∑12( s − EX )i( 3) ,where s i are samples of image signal and EX is meanvalue of image signal. When **the** velocity ofcharge v CH and **the** velocity of image v IM are equal,**the**n coherency criterion has its maximum value. Thiscriterion was verified using simulation program wedesigned.

In Figure 7 a) is simulated curve of coherencycriterion and in Figure 7 b) is measured curve ofcoherency criterion. The curve is measured(simulated) when **the** test tape has a constantvelocity v O and **the** shift time T t is changed. For everyobtained frame (with different T t ) criterion K ef ( 3 ) iscalculated. The graph in Figure 7 b) represents **the**result of calculation i.e. K ef as a function of v CH , whichitself is calculated **by** Equation ( 4 ).0,1K ef[ - ]v CH / v IM [ - ]0,00,5 1 1,5 2Figure 7. a) Simulated coherency criterion curveBoth of **the** curves are obtained using test tapewith periodically repeated black and white stripes.The test tape has 16 black stripes in camera angle ofview (see Figure 8. a)).6050403020100K ef[ - ]v CH / v IM [ - ]0,5 1 1,5 2Figure 7. b) Measured coherency criterion curveThe detection of maximum of coherence criterionis not easy as **the** curve is non-monotonous (seeFigure 7 a). This fact should be respected **by** a properdesign of **the** measurement algorithm.20010001 251 501 751 1001 1251 1501 1751 2001samplesFigure 8. a) Strip test static frame (standard mode)Frame in **the** Figure 8 a) is obtained as static **by****CCD** linear camera working in standard mode. Youcan compare this frame with frame in Figure 8 b)where is **the** same scene obtained **by** **CCD** linearcamera working in TDI mode and **the** test tape moves**by** velocity v O = 0,92 m/s.200CALCULATING A VELOCITY FROM THECHARGE SHIFT TIME T t**Velocity** of test tape movement can be calculatedfrom Equation ( 4 ).vdT t= PIX( 4) ,Ot OMwhere d PIX is pixel pitch, T t is **the** charge shift time forwhich **the** criterion had maximum value, t 0 is aresolution of T t and M is magnification of lens.Equation ( 5) found **by** differentiation of ( 4)shows that **the** resolution of this method depends on**the** measured velocity and magnification of lens.dPIX∆vMmin=2tOM Tt1∆Tt( 5).RESULTS AND PARAMETERS OF VELOCITYMEASUREMENTFigure 9 shows **the** measured transfercharacteristic of this method. The linearity error isequal to δ L =0,06% and maximal relative error ofvelocity v CH is δ CH = 0,13%.4321v O[ m/s ]v CH[ m/s ]00 0,1 0,2 0,3 0,4Figure 9. The dependence of v O on v CH for M = 0.1060,10%0,05%0,00%-0,05%-0,10%δv O[ % ]0 0,1 0,2 0,3 0,4v CH [ m/s ]Figure 9. **Linear**ity error of **the** function on Figure 9For measured velocity of test tape v O = 1.518 m/sfor time 15 min **the** maximum relative error of thisvelocity was δ v CH = 0.86% (see Figure 10).Measuring range was 1 : 10 of integrating timedue to **the** limitations of used camera.1,531,521,51v [ m/s ]01 251 501 751 1001 1251 1501 1751 2001samplesFigure 8. b) Strip test dynamic frame (TDI mode)1,501,491,48t [ m/s ]Figure 10. StabilityVo [ m/s ]Vch [ m/s ]

0,4%0,2%0,0%-0,2%-0,4%δv CH[m/s]t [ - ]Special**CCD** linearcameraRS 232to PCFigure 10. Stability errorLensLIMITATION OF METHOD WHEN ONLY ONE**CCD** LINEAR SENSOR IS USEDA basic condition is movement in **the** direction ofline sensor axis. For **the** movement under some smallangle with respect to sensor axis only projection of**the** measured velocity vector to **the** axis can be found.The next basic condition for correct function isscanning scene **the** objects of which fulfil **the** samecoherency criterion. When this is not true moresensors must be used and **the**ir output signals shouldbe compared.The next condition of correct function of thismethod is constant or slowly varying illumination of**the** measured scene. When **the** deviation of velocityshould be measured a constant illumination isnecessary.EXAMPLES OF APPLICATIONExample of measuring test tape velocity is inFigure 11. The velocity v O is measured **by** IRC sensorand **the** velocity v CH is measured **by** **CCD** linearcamera working in TDI mode.1,761,741,721,71,681,661,64v [ m/s ]Vm v CH [ [ m/s m/s ] ]Vt v O [ m/s [ m/s ] ]Figure 11. Curves of test tape velocityt [ - ]IRC**Sensor**V OStepmotorMovingtest tapeFigure 12. **Measurement** set-upThe result of this experiment is in Figure 11.There are two graphs, first represent velocity v Omeasured **by** IRC sensor and second representsvelocity v CH measured **by** **CCD** linear camera workingin TDI mode. There is apparent correlation between**the**se curves. The v CH differ from v O in multiplicationconstant, because of **the** magnification of lens.The method can **by** used for:- Contact-less measurements of velocity- Regulation and monitoring of velocity- **Measurement** of velocity deviation from correctvelocity valueThe described method is related to **the** correlationbased velocity measurement.ACKNOWLEDGEMENTThis work has been supported **by** **the** researchproject MSM 210000015 „Research of New Methodsfor Physical Quantities **Measurement** and TheirApplication in Instrumentation“.1,0%0,5%0,0%-0,5%δvCH[ % ]Figure 11. Centred velocity v CH errort [ - ]REFERENCES[ 1 ] E. Wagner, R. Dändliker, K. Spener ; SENSORSA Conmprehensive Survey, Volume 6, Opticalsensors ; Weinheim , New York 1992 ; pp 234 -252[ 2 ] Chamberlain, S.,G., Washkurak W.,D.,‘ HighSpeed, Low Noise, Fine Resolution TDI **CCD****Image**rs‘, in 252 SPIE Vol. 1242 Charge CoupledDevices and Solid State Optical **Sensor**s, 1990http://measure.feld.cvut.cz/groups/videometry