Comparative Analysis of SNR for Image Sensors with Enhanced Dynamic Range David X. D. Yang, Abbas El Gamal Information Systems Laboratory, Stanford Un

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1 Comparaive Analysis of SNR for Image Sensors wih Enhanced Dynamic Range David X. D. Yang, Abbas El Gamal Informaion Sysems Laboraory, Sanford Universiy ABSTRACT Dynamic range is a criical figure of meri for image sensors. Ofen a sensor wih higher dynamic range is regarded as higher qualiy han one wih lower dynamic range. For CCD and CMOS sensors operaing in he inegraion mode he sensor SNR monoonically increases wih he signal. Therefore, a sensor wih higher dynamic range, generally, produces higher qualiy images han one wih lower dynamic range. This, however, is no necessarily he case when dynamic range enhancemen schemes are used. For example, using he well capaciy adjusing scheme dynamic range is enhanced bu a he expense of subsanial degradaion in SNR. On he oher hand, using muliple sampling dynamic range can be enhanced wihou degrading SNR. Therefore, even if boh schemes achieve he same dynamic range he laer can produce higher image qualiy han he former. The paper provides a quaniaive framework for comparing SNR for image sensors wih enhanced dynamic range. We inroduce a simple model o describe he sensor oupu response as a funcion of he phoogeneraed signal, dark signal, and noise for sensors operaing in inegraion mode wih and wihou dynamic range enhancemen schemes. We use he model o quanify and compare dynamic range and SNR for hree sensor operaion modes, inegraion wih shuering, using he well capaciy adjusing scheme, and using muliple sampling. Keywords: CMOS Image sensor, CCD, Wide Dynamic Range, APS, Pixel level, ADC 1. INTRODUCTION Dynamic range, defined as he raio of he larges nonsauraing signal o he sandard deviaion of he noise under dark condiions, is a criical figure of meri for image sensors. I is ofen regarded as synonymous o sensor qualiy a sensor wih higher dynamic range is generally believed o produce higher qualiy images han one wih lower dynamic range. Several approaches have been proposed o enhance he dynamic range of a sensor. For CCD and CMOS sensors operaing in he inegraion mode, hree such schemes have been proposed. The firs is o adjus well capaciy during inegraion, using a laeral overflow gae, o compress he sensor illuminaion o charge ransfer curve. 1, The second scheme is o capure muliple samples a differen inegraion imes and hen o combine he samples o synhesize a high dynamic range image. Nakamura e al. 3 describe an implemenaion of dual sampling using a CMD image sensor. Yadid-Pech e al. 4 describe a clever implemenaion of dual sampling in a CMOS APS. Yang e al. 5 show ha pixel level ADC is ideally suied for implemening muliple sampling, since he pixel oupus are available o he ADCs a all imes. The hird scheme for enhancing dynamic range involves local shuering. 6 Even hough his scheme is concepually appealing i requires a large number of ransisors per pixel o implemen, and a considerable amoun of pos processing o reconsruc he image. For CMOS sensors operaing in insananeous curren readou mode, 7, a differen approach is used. Here he phoocurren is fed ino a device wih logarihmic response, e.g. a diode conneced MOS ransisor o compress he sensor ransfer curve. Alhough his scheme can achieve very wide dynamic range, he resuling image qualiy is generally poor due o low SNR. In his paper we argue ha using dynamic range as a measure of image sensor qualiy, alhough well jusified for CCD and CMOS sensors operaing in he inegraion mode, can be misleading when dynamic range enhancemen schemes are employed. When operaing in he inegraion mode, he sensor signal-onoise raio (SNR) monoonically increases wih he signal. Therefore, a sensor wih higher dynamic range, Oher auhor informaion: dyang@isl.sanford.edu, abbas@isl.sanford.edu; Telephone: ; Fax:

2 generally, produces higher qualiy images han one wih lower dynamic range. This, however, is no necessarily he case when dynamic range enhancemen schemes are used. SNR does no increase monoonically wih he signal. For example, using he well capaciy adjusing scheme, widening dynamic range comes a he expense of subsanial degradaion in SNR. On he oher hand, he muliple sampling scheme, if properly used, can widen dynamic range wihou degrading SNR. Therefore, even if boh schemes achieve he same dynamic range he laer can produce higher image qualiy han he former. The purpose of his paper is o make hese argumens clear. To dosowe use a simplified model o find he sensor oupu response as a funcion of he phoogeneraed signal, dark signal, and noise for sensors operaing in currenegraion mode wih and wihou dynamic range enhancemen schemes. We use he model o quanify dynamic range and SNR for hree sensor operaion modes. In secion we find SNR and dynamic range for a sensor operaing in inegraion mode wih shuering. We show ha for a fixed inegraion ime, dynamic range is a good measure of sensor qualiy. We show ha shuering has lile effec on dynamic range and SNR. In secion 3 we analyze SNR and dynamic range when he well capaciy adjusing scheme is used. In his case we see ha as dynamic range is enhanced SNR degrades. In secion 4 we analyze dynamic range and SNR when muliple sampling is used. We find ha dynamic range can be increased wihou degradaion in SNR.. DYNAMIC RANGE AND SNR IN THE INTEGRATION MODE We are concerned wih CCD and CMOS image sensors ha operae in currenegraion mode wih and wihou dynamic range enhancemen. As depiced in Fig 1, in his mode of operaion phoocurren i ph and dark curren i d are inegraed on a capacior, and he accumulaed charge is hen read ou. We assume hroughou ha boh he phoocurren i ph A, and he dark curren i d A are consan over inegraion ime Λ. We also assume ha he sensor has a finie charge capaciy > elecrons. In Figure we plo he colleced charge vs. ime for wo phoocurren values. i ph i ph + i d C d + i d C Figure 1. Inegraion mode. The lef figure depics direcegraion where curren is inegraed on he phoodiode capacior. The righ figure depics direc injecion, where curren is inegraed on a separae capacior. In his secion we inroduce a simplified phoocurren o oupu volage sensor model, and use i o analyze dynamic range and SNR for sensors operaing in inegraion mode wihou dynamic range enhancemen. In he nex wo secions we use he same model o analyze dynamic range and SNR when dynamic range enhancemen schemes are employed. The model is depiced in Figure 3. The curren source I s () represens he sho noise due o phoo and dark currens, and is modeled as a whie Gaussian noise process wih double sided power specral densiy q(i ph + i d ). The accumulaed charge Q a he end of inegraion is a funcional f[:] of he curren I() over he inegraion ime»». When he sensor is operaing R in in inegraion mode wihou dynamic range enhancemen f[:] is simply minf I()d; q max g y. Choosing f[:] as a general funcional, as we see laer, enables us o model he sensor operaion when dynamic range enhancemen schemes are used. We assume linear charge-o-volage amplifier(s) wih oal amplificaion g. The added charge Q r represens he noise due o he readou circuis z, including inpu referred amplifier noise, and rese noise for Λ In he paper, lower case leers will indicae consan values, e.g. random variables. mean of a signal, and upper case leers will indicae y This assumes ha he min is always posiive, which is rue wih high probabiliy, since wih high probabiliy he inegraed sho noise is much less han he signal charge (including dark curren). z Quanizaion noise can also be included in Q r.

3 Charge high illuminaion low illuminaion Time Figure. Charge colleced vs. ime. CMOS APS. We assume ha i is zero mean and has average power ff r. To simplify he model we ignore fixed paern noise (FPN). i d I s () Q r g i ph I() f[i();»» T ] Q V Figure 3. Sensor model. i d N i ph i f (i) Q Figure 4. Sensor model afer combining he noise sources. Using his model we can now define dynamic range (DR) and signal o noise raio (SNR). Dynamic range is he raio of he sensor's larges nonsauraing inpu signal, i.e. inpu signal swing, o is smalles deecable inpu signal. The inpu signal in our case is he phoocurren i ph. For inegraion ime, he larges nonsauraing inpu signal is given by, i max = qmax i in d. The smalles deecable signal, i min, is no as well defined. Clearly, i mus be large enough so ha i can be discriminaed from i ph =. The convenion, which isvery opimisic, is o assume ha i min is equal o he sandard deviaion of he inpu referred noise when no signal is presen. To find he sandard deviaion of he inpu referred noise we redraw our model as shown in Figure 4. Here he noise is combined ino a single zero mean random variable N, which is he sum of Q r and he oupu referred noise due o sho noise Q s, and f (i) = f[i;»» T ], where i = i ph + i d, i.e. f[:] when I s () = for»» T. For a sensor operaing in he inegraion mode f (i) =minfi ; g. This is ploed in Figure 6. Now,

4 i d N i i ph I f (I) Q Figure 5. Sensor model wih inpu referred noise. for i sufficienly below qmax, wih high probabiliy, Q s = R I s ()d, which has zero mean and variance q(i ph + i d ). Since Q s and Q r are uncorrelaed, he oal average noise power ffq = q(i ph + i d ) + ffr. To find he equivalen zero mean inpu referred noise N i we redraw he model again as shown in Figure 5. We assume ha ff Ni is very small compared o he signal i, and herefore f (i + N i ) ß f (i) +N i f(i) evaluaed a i (in mean square), provided he derivaive exiss. Thus, he average power of he equivalen inpu referred noise ff N i = f ff Q Q ff = (i) : in Seing i ph o zero, we ge i min = 1 p qid + ff r, and he sensor dynamic range DR = i max = p : (1) i min qid + ffr f (i) i Figure 6. f (i) vs. i. We define he signal o noise raio SNR(i ph ), which is a funcion of i ph, as he raio of he inpu signal power i ph o he average inpu referred noise power ff N i. For he sensor in inegraion mode we ge (i ph ) SNR(i ph )=, for i q(i ph + i d ) + ffr ph» i max : () Noe ha we do no define SNR for i ph >i max, i.e. afer he sensor sauraes. Of course disorion can be used o exend he SNR definiion beyond i max as is cusomarily done in he ADC lieraure. 9 Inroducing

5 disorion, however, would complicae our already complex formulas wihou offering any addiional insigh. Equaion is ploed in Figure 7 for a sensor wih = 1:5 1 5 elecrons, ff r = elecrons, and inegraion ime = 3ms for hree differen dark currens i d = 1fA, 5fA, and 15fA. Noe ha even hough he average noise power increases wih i ph, SNR monoonically increases, firs a a rae of dbs per decade when read noise dominaes, and ulimaely a 1dBs per decade as sho noise dominaes. Also noe ha he sensor wih he highes dynamic range, i.e. he one corresponding o i d = 1fA, is also he one wih he highes SNR. Thus, if we consider SNR o be a good measure of image qualiy, high dynamic range, which is a single number, can be equally regarded as a good measure of qualiy. As we will show in he following wo secions his is no necessarily he case when dynamic range enhancemen schemes are employed = 15 ff r =e =3ms 3 1 1fA 5fA 15fA Figure 7. SNR vs. i ph. Shuering is commonly used o adjusegraion ime o he scene's dynamic range. A fas shuer speed, i.e. shoregraion ime, is used for a brigh scene o avoid well sauraion, whereas a slow shuer speed is used for a dark scene o increase he image SNR. Equaions 1, can be readily used o analyze he effec of shuering on dynamic range and SNR. For example o find ou he effec of shuering on dynamic range we plo dynamic range vs. inegraion ime in Figure. For small, boh i min and i max are inversely proporional o and dynamic range does no change. For large,however, dark curren i d, decreases i max and is sho noise increases i min, resuling in dynamic range roll off. Thus, shuering does no maerially affec a sensor's dynamic range. I merely maches he dynamic range o he scene's range of illuminaion as illusraed in Figure ENHANCING DYNAMIC RANGE BY ADJUSTING WELL CAPACITY The well capaciy adjusing scheme described by Knigh 1 and Sayag and implemened by Decker 1 compresses he sensor's curren versus charge response curve using a laeral overflow gae, e.g. he rese ransisor gae in a CMOS APS. The volage applied o he overflow gae deermines he well capaciy. During inegraion well capaciy is monoonically increased o is maximum value. The excess phoogeneraed charge is drained via he overflow gae. For example, assume ha well capaciy isadjused only once a ime 1 from o full capaciy. Figure 1 plos he average colleced charge versus ime for wo inpu phoocurren values. Noe ha when he colleced charge reaches, e.g. he high illuminaion case in he figure, he oupu charge is clipped unil ime 1.

6 DR (db) = 15 ff r =e i d =1fA Inegraion ime (sec) Figure. Dynamic range vs. inegraion ime = 15 ff r =e i d = 5fA 4ms ms 1ms 5ms Figure 9. SNR vs. i ph a four inegraion imes.

7 Charge high illuminaion low illuminaion 1 Time Figure 1. Charge vs. ime for well capaciy adjusing scheme. In his case he funcional in he model R in >< I()d if» i ph < qmax i 1 d f[:] = + R q Id >: 1 if max i 1 d» i ph < qmax(1 ) 1 oherwise. In order o compue SNR and dynamic range, we need o compue he inpu referred noise power ff Q x. I is imporan o noe ha he inpu referred noise power is no simply ff Q in i and Q is nonlinear. In his case >< i f (i) = + i( 1 ) >: if i d» i< qmax 1 q if max» i< qmax(1 ) 1 1 oherwise, since he relaionship beween This is ploed in Figure 11. Noe ha he slope decreases beyond i = i 1 = qmax 1, which resuls in he compression of he response. I can be easily shown ha ff Q = ( q(i ph + i d ) + ff r q(i ph + i d )( 1 )+ff r if» i ph < qmax 1 if 1» i ph < qmax(1 ) 1 ; and >< if i d» i< qmax f(i) 1 = q 1 if max >: 1 oherwise:» i< qmax(1 ) 1 Therefore x There is an addiional noise of» pkt C associaed wih he overflow gae, where» is he subhreshold gae efficiency parameer. This noise can be incorporaed in read noise Q r.

8 f (i) 1 i 1 = qmax 1 (1 ) 1 i Figure 11. f (i) vs. i for he well adjusing scheme. < SNR(i ph )= : i ph in q(i ph +i d )+ff r i ph (in 1) q(i ph +i d )( 1)+ff r if» i ph < qmax 1 if 1» i ph < qmax(1 ) 1 : Now, i max = qmax(1 ) i in 1 d, and i min is he same as before. Thus, for small i d, dynamic range is enhanced by a facor DRF = : A i 1, assuming ha sho noise dominaes, SNR(i ph ) dips by a facor DIP = (1 1 ); which is inversely proporional o he dynamic range enhancemen facor DRF. This is illusraed in Figure 1, where SNR is ploed versus i ph using he same sensor parameers as before, and assuming ha i d = 1fA, = 7, and 1 = In his case DRFß 3, and DIPß, i.e. around 4 dbs The analysis can be exended o any numberofwell capaciy adjusmens k. In his case le < i < 1, 1» i» k be he resuling fracions of he well capaciy corresponding o he adjusmens, and < i <, be he adjusmen imes. I can be shown ha dynamic range expands by DRF = (1 k ) i in k d 1 ß k i in d 1 k ; and >< SNR(i ph )= >: i ph (in ) q(i ph +i d )( )+ff r i ph (in 1) q(i ph +i d )( 1)+ff r. i ph (in k 1) q(i ph +i d )( k 1 )+ffr i ph (in k) q(i ph +i d )( k )+ffr if» i ph < qmax 1 1 if qmax( 1 ) 1» i ph < qmax( 1) ( 1) if qmax( k 1 k ) k 1 i k d» i ph < qmax( k k 1 ) k i k 1 d if qmax( k k 1 ) k i k 1 d» i ph < qmax(1 k) i in k d :

9 = 15 ff r =e =3ms i d = 1fA Figure 1. SNR vs. i ph for he well capaciy adjusmen scheme. Dynamic range is enhanced by a facor of 3 Noe ha as dynamic range is increased, he final SNR(i max ) degrades by he same facor 1 k relaive o peak SNR when no dynamic range enhancemen is used. Moreover, he sum of he SNR dips, expressed in dbs, is approximaely j1 log 1 (1 k )j, which isalways greaer han DRF expressed in dbs. In paricular he difference, expressed in dbs, beween he sum of he SNR dips and half of DRF is equal o he SNR(i max ) degradaion facor expressed in dbs. In Figure 13 we plo SNR versus i ph for k = capaciy adjusmens. The capaciy levels i = i and 1 adjusmen imes i =1 1 for 1Λ i 1 i =1; ;:::; are chosen so ha he resuling average charge f (:) vs. i ph curve assumes an A-law companding shape. Dynamic range is increased by DRFß 56, i.e. 4 db. The sum of he SNR dips is ß 31dBs, and he SNR(i max ) degrades by 7dBs. 4. ENHANCING DYNAMIC RANGE VIA MULTIPLE SAMPLING Dual sampling has been used o enhance he dynamic range for CCD sensors, CMD sensors, 3 and CMOS APS sesnors. 4 A scene is imaged wice, once afer a shoregraion ime and anoher afer a much longer inegraion ime, and he wo images are combined ino a high dynamic range image. Concepually, he shoregraion ime image capures he high illuminaion areas before he well sauraes and he long inegraion ime image capures he low illuminaion areas afer adequae inegraion ime. Two images, however, may no be sufficien o represen he areas of he scene ha are oo dark o be capured in he firs image and oo brigh o be capured in he second. Yang e al. 5 show ha pixel level ADC is ideally suied for implemening muliple sampling in general. The paper considers he implemenaion of muliple sampling for an exponenially increasing inegraion imes. In his case, dynamic range is enhanced by a facor of k and he combined image has a floaing poin resoluion wih exponen k. In his secion we use our sensor model o analyze SNR and dynamic range when muliple sampling is used. We firs invesigae dual sampling a in a and, for a>1. Figure 14 plos he average colleced charge versus ime for hree illuminaions. Noe ha by sampling a in a, he moderae illuminaion signal can be sampled before he sensor sauraes. For dual sampling i can be shown ha he funcional in our model

10 = 15 ff r =e =3ms i d = 1fA DRF= Figure 13. SNR vs. i ph for he well capaciy adjusmen scheme. Dynamic range is enhanced by a facor of 56 Charge high illuminaion moderae illuminaion low illuminaion a Time Figure 14. Charge vs. ime for dual sampling.

11 f (i) a a i Figure 15. f (i) vs. i for dual sampling. >< f[:] = >: R in I()d R a I()d if qmax if» i ph < qmax i in d» i ph < aqmax i in d ; oherwise; and < f (i) = : i i a if i d» i< qmax if qmax» i< aqmax in oherwise: Figure 15 plos f (i) versus i. Noe ha, unlike he previous cases, f (:) is no a one-o-one funcion. The average noise power ρ q(iph + ffq i d ) + ffr = q(i ph + i d ) in a + ff r if qmax if» i ph < qmax in i d» i ph < aqmax i in d : We can now compue >< SNR(i ph )= >: i ph in q(i ph +i d )+ff r i ph ( a ) q(i ph +i d ) a +ff r if» i ph < qmax if qmax» i ph < aqmax : Since i max = aqmax and i min is he same as before, he dynamic range enhancemen facor DRF = a in i d ß a; for small i d : As in he case of well capaciy adjusing, SNR dips in he middle. For he same DRF, however, he dip is smaller. Moreover, he final SNR(i max ) is always equal o he peak SNR wihou dynamic range enhancemen.

12 = 15 ff r =e =3ms i d = 1fA Figure 16. SNR vs. i ph example for he dual sampling. Dynamic range is enhanced by a facor of 3. Figure 16 plos SNR vs. i ph for a = 3, = 3ms, and assuming he same sensor parameer values as before. The analysis can be exended o muliple sampling in general. For k + 1 samples a in k, k 1, :::, in, ), we ge DRF = k i in d ß k ; i in d and >< SNR(i ph )= >: i ph in q(i ph +i d )+ff r i ph (in=) q(i ph +i d )=+ffr. i ph (in=k 1 ) q(i ph +i d )= k 1 +ffr i ph (in=k ) q(i ph +i d )= k +ffr if» i ph < qmax if qmax. if k if k 1» i ph < qmax» i ph < k 1» i ph < k : This is ploed in Figure 17 for k = and assuming = 3ms, and he sensor parameer values in he previous examples. Dynamic range is enhanced by DRFß 56 as expeced. 5. CONCLUSION We have shown ha using he well adjusing scheme SNR degrades as dynamic range is increased. On he oher hand using he muliple sampling scheme, dynamic range can be widened wihou degrading SNR. To demonsrae his, in Figure 1 we compare he case of a single well capaciy adjusmen o dual sampling by combining he SNR vs. i ph plos for he examples in Figures 1, and 16. Boh schemes achieve DRF= 3. Dual sampling, however, exhibis beer SNR for large i ph s.

13 = 15 ff r =e =3ms i d = 1fA Figure 17. SNR vs. i ph example for muliple sampling. Dynamic range is enhanced by a facor of 56. In Figure 19 we compare well capaciy adjusing o muliple sampling by combining he plos of he examples in Figures 13 and 17. Boh schemes achieve DRF= 56. Noe ha muliple sampling achieves around 1dBs higher SNR. Moreover, he SNR for he well adjusing scheme dips by more han 1dB in he middle. This clearly demonsraes ha muliple sampling enjoys beer SNR han well capaciy adjusmen a he same DRF. In fac if we include fixed paern noise, well barrier hermal noise and quanizaion noise in our analysis, i can be shown ha he difference in SNR in favor of muliple sampling is even greaer. In he paper We used he SNR plos o compare he differen schemes. Ofen, i is more convenien o use a single SNR number insead. This can be done by compuing an average SNR wih respec o he desired illuminaion probabiliy densiy funcion p iph (:), SNR = R SNR(i ph )p iph (i ph )di ph. The plo, of course, provides a more complee descripion of SNR. In our definiion of dynamic range i min is he sandard deviaion of he noise under dark condiions. If we use SNR as a measure of image qualiy, his definiion is very opimisic. SNR around i min is close o zero db, which clearly resuls in unaccepable image qualiy. In his case i is more appropriae o define a minimum accepable SNR for image qualiy. For example if we define he minimum accepable SNR o be db, dynamic range may be severly reduced as demonraed in Figure which plos SNR vs. i ph for single well capaciy adjusmen scheme. Here dynamic range drops from 14dB o 3dB. The sensor model inroduced in his paper proved useful in formalizing he definiions of dynamic range and SNR. This model is general enough o describe sensor nonlineariy, and oher poenial dynamic range enhancemen schemes by properly defining he funcional f[:]. The model can also be readily exended o include FPN and inpu illuminaion ha varies during inegraion. ACKNOWLEDGEMENTS The work repored in his paper was parially suppored under he Programmable Digial Camera Program by Inel, HP, Kodak, Inerval Research, and Canon, and by ADI. REFERENCES 1. T. F. Knigh, Design of an Inegraed Opical Sensor wih On-Chip Preprocessing. PhD hesis, MIT, 193.

14 = 15 ff r =e =3ms i d = 1fA Figure 1. SNR vs. i ph for boh well capaciy adjusmen and dual sampling. DRF = = 15 ff r =e =3ms i d = 1fA Figure 19. SNR vs. i ph for boh well capaciy adjusmen and muliple sampling. DFR = 56

15 = 15 ff r =e =3ms i d = 1fA Minimum accepable SNR line (db) Figure. SNR vs. i ph for he well capaciy adjusmen scheme. Dynamic range is enhanced by a facor of 3. M. Sayag, Non-linear Phoosie Response in CCD Imagers." U.S Paen No. 5,55,667, Filed T. Nakamura and K. Saioh, Recen Progress of CMD Imaging," in 1997 IEEE Workshop on Charge Coupled Devices and Advanced Image Sensors, June O. Yadid-Pech and E. Fossum, Wide Inrascene Dynamic Range CMOS APS Using Dual Sampling," in 1997 IEEE Workshop on Charge Coupled Devices and Advanced Image Sensors, June D. Yang, A. El Gamal, B. Fowler, and H. Tian, A CMOS Image Sensor wih Ulra Wide Dynamic Range Floaing Poin Pixel Level ADC," in ISSCC Diges of Technical Papers, (San Fransisco, CA), February Submied o ISSCC S. Chen and R. Ginosar, Adapive Sensiiviy CCD Image Sensor," in Proc. SPIE, vol. 415, pp , (San Jose, California), February C. Mead, Analog VLSI and Neural Sysems, Addison Wesley, N. Ricquier and B. Dierickx, Acive Pixel CMOS Image Sensor wih On-Chip Non-Uniformiy Correcion," in 1995 IEEE Workshop on Charge Coupled Devices and Advanced Image Sensors, April R. V. D. Plassche, Inegraed Analog-o-Digial and Digial-o-Analog Converers, Kluwer Academic Publishers, S. Decker, R. McGrah, K. Brehmer, and C. Sodini, A 56x56 CMOS imaging array wih wide dynamic range pixels and column-parallel digial oupu," in ISSCC Diges of Technical Papers, pp , (San Fransisco, CA), February 199.

Comparative Analysis of SNR for Image Sensors with Enhanced Dynamic Range

Comparative Analysis of SNR for Image Sensors with Enhanced Dynamic Range David X. D. Yang, Abbas El Gamal Information Systems Laboratory, Stanford University ABSTRACT Dynamic range is a critical figure