Quantitative Study of High Dynamic Range Sigma Delta-based Focal Plane Array Architectures

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1 Quaniaive Sudy of High Dynamic Range Sigma Dela-based Focal Plane Array Archiecures Sam Kavusi, Hossein Kakavand and Abbas El Gamal Deparmen of Elecrical Engineering, Sanford Universiy, Sanford, CA ABSTRACT The paper invesigaes he suiabiliy of Σ modulaion based FPA readou schemes for use in Verically Inerconneced Sensor Arrays requiring ulra high dynamic range and frame rae. I is shown ha he exended couning scheme is capable of achieving he DR and frame rae requiremens bu a he expense of high power consumpion. Exended couning is also shown o ouperform several oher HDR schemes in erms of SNR a he ulra high DR and frame rae. Keywords: IR focal plane array, ROIC, high dynamic range, verical inegraion, sigma-dela, exended couning 1. INTRODUCTION Several mehods for exending focal-plane-array (FPA) dynamic range have been developed in recen years. 1 3 In [4], a mehodology for comparing hese schemes based on heir SNR was proposed. Using idealized readou circui models, his mehodology was used in he paper and in a subsequen uorial 5 o compare several HDR schemes. Moivaed by he adven of verical inegraion, a recen paper 6 invesigaed four high fideliy, HDR schemes, namely, ime-o-sauraion, muliple-capure, asynchronous self-rese wih muliple capure, and synchronous self-rese wih residue readou. The schemes were again compared based on heir SNR, bu assuming more realisic circui models. Implemenaion and power consumpion issues were also discussed. 2, 3, 7 In his paper we exend our earlier work o sudy Σ modulaion based FPA readou. This exension is moivaed by he ulra high dynamic range (120dB or more) and high frame rae (up o 1000 frames/sec) requiremens of he Verically Inerconneced Sensor Array projec. 8 We firs show ha Σ modulaion based schemes such as firs-order 7 and sampled free-running oscillaor 2 exend dynamic range a he high end, bu a he expense of reducion in dynamic range a he low end. We hen invesigae he exended couning scheme inroduced in [9]. We show ha i is capable of achieving ulra-high DR a high frame rae wih accepable fideliy, bu a he expense of high power consumpion. In he nex secion we provide he background needed. In Secion 3, we discuss he Σ based schemes. In Secion 4, we compare he exended couning scheme o he schemes discussed in [6] based on heir SNR assuming he aforemenioned ulra-high dynamic range and high frame rae requiremens. 2. BACKGROUND AND PREVIOUS WORK To be self conained, we repea here some of he background on he operaion of convenional sensors, DR and SNR definiions, and he general readou archiecure model for HDR schemes appeared in [6]. Background: Each phoodiode in a convenional image sensor convers phoon flux ino phoocurren. Since his process is linear, is a good measure of he inciden phoon flux. The resuling phoocurren is ypically oo small o measure direcly, and hus i is inegraed ino charge. Afer inegraion ime in,he charge is convered linearly o a volage and subsequenly digiized and read ou. Dark curren and addiive noise corrup he oupu signal charge. Ignoring dark curren, noise can be expressed as he sum of four independen componens: (i) inegraed sho noise, which has zero mean and average power in /q elecron 2, where q is he elecron charge, (ii) rese (ktc) noise, (iii) readou circui noise (including quanizaion noise) wih zero mean and average power σreadou 2, and (iv) offse and gain FPN due o phoodeecor and device mismaches. Correspondence: skavusi@sanford.edu, abbas@isl.sanford.edu; Telephone: ; Fax: Infrared Technology and Applicaions XXX, edied by Bjørn F. Andresen, Gabor F. Fulop, Proc. of SPIE Vol (SPIE, Bellingham, WA, 2004) X/04/$15 doi: /

2 The oupu charge from a pixel can hus be expressed as Q( in )= 1 q ( in + Q Sho + Q Rese + Q Readou + Q FPN ) elecron, provided Q( in ) Q max, he sauraion charge, also referred o as well capaciy. Assuming ha correlaed-double-sampling (CDS) is performed, we can eliminae Q Rese and he offse par of Q FPN. If we also assume ha gain FPN is negligible compared o sho noise, SNR is given by ( in ) 2 SNR( )= q in + q 2 σreadou 2, for qq max. in Noe ha SNR increases wih, firs a 20dB per decade when readou noise variance dominaes, and hen a 10dB per decade when sho noise variance dominaes. SNR also increases wih in. Thus i is always preferred o have he longes possible exposure ime. Sauraion and change in phoocurren due o moion, however, makes i impracical o make inegraion ime oo long. Image sensor DR is defined as he raio of he larges nonsauraing phoocurren o he smalles deecable phoocurren, ypically defined as he sandard deviaion of he noise under dark condiions. Assuming he above sensor model, i max = qq max / in and i min = qσ Readou / in and dynamic range is given by DR = i max = Q max. i min σ Readou Readou Archiecure Model: To unify he analysis of he high dynamic range schemes, we use he concepual sensor readou archiecure proposed in [6] shown in Figure 1. I comprises a curren modulaor ha convers ino a waveform s() and possibly a discree (in ime and value) sequence. The waveform s() is hen digiized by an a one or more ime insances and he oupu is filered o produce an esimae of. The modulaor is ypically implemened per pixel, while he and filer are implemened per group of neighboring pixels. Since he overall sysem aemps o reproduce he signal, i has uniy gain. Thus we can refer he noise o he oupu when compuing he sysem SNR. Modulaor s() Sample & Digial Samples Binary Sequence Figure 1. General block diagram. For a convenional image sensor, he modulaor is simply an inegraor ha sauraes when he inegraed charge exceeds he well capaciy Q max. The oupu of he modulaor is sampled a = 0 (for CDS) and = in. The /filer perform he subracion for CDS, scaling, and digiizaion. Reference Sensor: As in [6], we use an opimized convenional sensor, which we refer o as a reference sensor for comparison. We denoe is average readou noise power as σreadou Ref 2, is minimum nonsauraing curren as i min Ref, and is DR as he reference DR. We assume ha σreadou Ref 2 is no limied by quanizaion noise and ha analog readou circui noise is minimized, and herefore σreadou Ref 2 and i min Ref are a heir pracical minimums (for a given in ). We also assume ha gain FPN can be ignored wihin he reference DR. 3. EXTENDED COUNTING Σ We firs discuss he firs order Σ readou scheme and is variaions. In Subsecion 3.2, we analyze he exended couning scheme. 342 Proc. of SPIE Vol. 5406

3 3.1. Firs Order Incremenal Σ The block diagram of he firs order single-bi Σ 7 is shown in Figure 2. A each clock cycle, he inegraor oupu is compared o he hreshold value /2. If he comparaor flips, /2 is subraced off, hus prevening sauraion of he inegraor. The subracion is ypically implemened using a swiched capacior circui. A filer, which can be as simple as a couner, is used o esimae he phoocurren from he binary comparaor oupu sequence. In incremenal Σ, 10 he inegraor is rese a he beginning of each frame. Such reseing improves SNR, 11 because, unlike he free-running case, he inegraor value a he beginning of each frame is known. We, herefore, focus on incremenal Σ. Frame rese + - Vmax/2 Binary Sequence CLK Modulaor (a) V max v Vmax/ (b) Figure 2. Single-bi Σ block diagram. To quanify he SNR and DR achieved by incremenal Σ, we use he equivalen inegraor oupu ramp shown in Figure 3. Noe ha he oupu sequence from he Σ modulaor is idenical o he sequence generaed by comparing he equivalen ramp o he cumulaive sum of he sequence, scaled by and biased by /2. Assuming ha a couner is used for decimaion, hen a he end of inegraion ime, he couner value is n couner ( )= 2 in /C. Now, assuming ha he /4 bias in he couner readou is compensaed for, and ha quanizaion noise is signal independen and uncorrelaed wih oher noise sources, he sandard deviaion of he effecive readou noise is approximaely given by (C ) σ Readou eff = 2 48q 2 + n couner ( )σswich 2 + σ2 Rese, where, σ Swich is he noise due o charge subracion and σ Rese is he rese noise. The firs erm in σ Readou eff corresponds o quanizaion noise 2 /12 wih = /2. Therefore, he minimum deecable signal is given by i min = qσ Readou eff / in C /4 3 in. In smar emperaure sensors, he incremenal archiecure is also used for he same reason. 12 Proc. of SPIE Vol

4 /2 0 1 k M-1 SEQ N CMP (Vmax/2) Figure 3. Equivalence of Σ oupu sequence (SEQ) o he sequence obained by comparing he equivalen ramp (solid line) o he cumulaive sum (CMP) of he sequence scaled and biased by /2. Now from Figure 3, he maximum non-sauraing signal is given by i max = C /2 clk. Therefore, he maximum achievable dynamic range for a given in is given by DR = 2 3 in clk. In order o derive SNR, we need o consider he variaion in charge subracion, which ranslaes ino gain FPN. Denoing he sandard deviaion of charge subracion by σ Offse, we obain SNR( )= ( in ) 2 q in +(qσ Readou eff ) 2 +(n couner qσ Offse ) 2. Figure 4 plos SNR versus and compares i wih SNR of he reference sensor. Noe ha wih he same Q max and in he DR of his scheme is shifed o he righ wih respec o he reference sensor DR, ha is, his scheme has very poor low signal performance. Also noe ha SNR a he low end is quanizaion limied, whereas a he high end, i becomes gain FPN limied. The reason for he SNR degradaion a he low end is he coarseness of he single-bi quanizaion and he filer used. Reducing he size of he inegraing capacior or lowering may improve low end performance. However, hese soluions increase σ Offse, which would degrade SNR a he high end. SNR a he low end can also be improved by using more sophisicaed filers such as riangular, zoomer, 13 recursive, 14 opimal, 15 ec. To demonsrae he exen of possible SNR improvemen, in Figure 5 we compare he performance using a couner o ha using he opimal filer. 15 Noe ha subsanial improvemen in SNR is possible, bu a he expense of higher circui complexiy and power consumpion. As discussed, SNR a he high end is limied by he gain FPN due o variaion in charge subracion. The sampled free-running oscillaor archiecure inroduced in [2] eliminaes charge subracion (see Figure 6). As shown in he figure, he inegraed phoocurren value is compared o. When he comparaor flips he inegraor is rese and a pulse wih period clk is produced by he monosable. The binary sequence generaed by sampling v mon is hen filered o esimae he phoocurren. I can be shown ha in he ideal case, his scheme produces a binary sequence ha is idenical o a single-bi Σ wih wice he well capaciy. Even hough his scheme eliminaes charge subracion, i suffers from larger σ Offse due o sensiiviy o comparaor offse. The exended couning scheme we discuss in he following secion solves he coarse quanizaion problem of he single-bi Σ schemes by quanizing he residue a he end of inegraion, v( in ), using a muli-bi. 344 Proc. of SPIE Vol. 5406

5 80 70 Reference Example 1 Example 2 60 SNR (db) (A) Figure 4. SNR versus for single-bi Σ. The reference assumes Q max = 625, 000e, in = 1msec, clk = 0.1µsec, σ Readou =40e, σ Swich = 127e and achieves DR= 83dB. Example 1 assumes σ Offse =76e and achieves DR= 80dB. Example 2 assumes σ Offse = 610e and achieves DR= 80dB Reference Couner Opimal 60 SNR (db) (A) Figure 5. SNR versus for single-bi Σ wih couner and opimal filer. The reference assumes Q max = 625, 000e, in =1msec, σ Readou =40e and achieves DR= 83dB. Σ examples assume Q max =625, 000e, in = 1msec, clk =0.1µsec, σ Offse =76e, σ Swich = 127e and achieves DR= 80dB. Proc. of SPIE Vol

6 Vmax Rese Monosable Sample CLK Modulaor v (a) v V max V max sa v mon v mon Low Ligh (b) High Ligh Figure 6. Sampled free-running oscillaor block diagram Exending Couning A block diagram of he exended couning scheme 3 is shown in Figure 7. Excep for he addiional residue sep, he archiecure is idenical o he single-bi Σ archiecure wih a couner, discussed in he previous secion. The couner value a he end of he inegraion ime and he digiized residue are combined o esimae he phoocurren as î ph = qq max in ( 1 2 n couner + v( ) in). by In order o calculae DR and SNR, we noe ha he sandard deviaion of he effecive readou noise is given σ Readou eff = σ 2 Readou + n couner( )σ 2 Swich + σ2 Rese, where, σ Readou is he quanizaion noise, σ Swich is he swiched capacior noise due o charge subracion, σ Rese is he rese noise and n couner ( ) is he couner oupu a he end of in. Thus, he minimum deecable and maximum non-sauraing signals are i min = qσ Readou eff / in = q σ Readou 2 + σ2 Rese / in, and i max = C /2 clk. 346 Proc. of SPIE Vol. 5406

7 Frame rese + - /2 Binary Sequence Couner Linear CLK Modulaor (a) v v /2 /2 clk Low Ligh High Ligh (b) Figure 7. Exended couning block diagram. Therefore, he maximum achievable dynamic range for a given in is given by DR = Q max in. 2 σ Readou 2 + σ2 Rese clk In order o derive SNR, noe ha any variaion of charge subracion, σ Offse will ranslae o gain fixed paern noise. Thus SNR is given by SNR( )= ( in ) 2 q in +(qσ Readou ) 2 +(n couner qσ Offse ) 2. SNR is ploed versus signal in Figure 8. Remarks: (i) DR a he low end is improved over he single-bi Σ using he residue digiizaion, which reduces σ Readou eff. However, σ Readou eff is larger han he readou noise of he reference sensor σ Readou Ref because CDS canno be performed in his archiecure. (ii) DR a he high end is direcly relaed o clk and Q max. To avoid sauraion during charge subracion caused by comparaor and charge subracion offses, one needs o se he comparison volage higher han /2, which reduces DR a he high end. (iii) DR can be increased by reducing clk. To undersand he impac of increasing clock speed, consider he ypical inegraor/ charge subracion implemenaion using capaciive ransimpedance amplifier (CTIA) and swiched capacior shown in Figure 9. Noe ha decreasing clk requires reducing he amplifier imeconsan, because for a given SNR he charge subracion circui seling ime dicaes he required gain bandwidh produc. As a resul, amplifier power consumpion increases. Thus, assuming he MOS squarelaw, amplifier power needs o increase as he square of he facor of increase in DR. Proc. of SPIE Vol

8 80 70 Reference Example 1 Example 2 60 SNR (db) (A) Figure 8. SNR versus for exended-couning. The reference assumes Q max =625, 000e, in =1msec, clk = 0.1µsec, σ Readou =40e, σ Swich = 127e and achieves DR= 83dB. Example 1 assumes σ Offse =76e and achieves DR= 154dB. Example 2 assumes σ Offse = 610e and achieves DR= 154dB. Noe ha he maximum curren of he swich in Figure 9 mus be conrolled o avoid large changes in he deecor bias. Conrolling he swich curren and saisfying he seling ime requiremen makes i necessary o increase he required amplifier bias. C sub C in V ref v inv V bias Figure 9. Schemaic of he inegraor and he subracion mechanism (digial-o-analog-converer) in each pixel. (iv) SNR in he exended range is limied by σ Offse, which is mainly due o (a) mismach 16 in he inegraing and subracing capaciors shown in Figure 9, (b) variaion in he pedesal error caused by swiching (also mismach if dummy swiches are used), (c) variaion in V ref roued o all pixels, (d) variaion in he seling ime of he swiched capacior, and (e) finie dc gain of he amplifiers. (v) The dominan source of power consumpion in his scheme is he CTIA. 4. COMPARISON OF HDR SCHEMES In his secion we compare he exended couning scheme o he four schemes discussed in [6] for very high dynamic range (120 db) and high speed (1000 frames/sec) applicaions. We assume ha verical inegraion is used in he implemenaion of hese schemes, since i would be difficul if no impossible o achieve he desired DR and frame rae using planar echnologies wih reasonable size pixels. Verical inegraion enables he inegraion of more circuis a he each pixel, reducing noise coupling and device mismach, and eliminaing he column readou speed and power dissipaion bolenecks. 348 Proc. of SPIE Vol. 5406

9 Block diagrams of he four schemes discussed in [6] are depiced in Figure 10. Even wih verical inegraion, he only wo schemes ha can achieve he desired high dynamic range and high speed are synchronous self-rese wih residue readou and exended couning. As discussed in [6], synchronous self-rese suffers from low SNR a boh he high and low ends of DR. A he high end, i suffers from he underesimaion of charge and large gain FPN due o comparaor and self-rese offses. Exended couning does no suffer from charge underesimaion and has lower gain FPN, and as a resul i performs beer a he high end. A he low end, synchronous self-rese and exended couning perform exacly he same. Boh schemes underperform he reference sensor due o he fac ha rese noise canno be cancelled. Time-ramp sa C T-Ref Modulaor (a) Time-o-sauraion. Capure Clock (b) Muliple-capure. Rese Rese Linear V max V max Binary Sequence Couner Modulaor Modulaor CLK (a) Asynchronous self-rese wih muliple capure. (b) Synchronous self-rese wih residue readou. Figure 10. Block diagram of all of he sudied archiecures in he previous work. ACKNOWLEDGMENTS The work in his paper was parially suppored under DARPA Microsysems Technology Office Award No. N We wish o hank Professors B.A. Wooley, B. Gray and B. Wandell, Dr. D. Su, Dr. D. Yang, Dr. B. Fowler, A. Agah, H. Eloukhy, A. Ercan, S. Lee and K. Salama for helpful discussions. We also wish o hank Dr. L. McIlrah for providing he recursive decoder code. REFERENCES 1. S. Kleinfelder, S. Lim, X. Liu, and A. El Gamal, A 10,000 frames/s CMOS digial pixel sensor, IEEE Journal of Solid-Sae Circuis 36(12), pp , December L. McIlrah, A low-power low-noise ulrawide-dynamic-range CMOS imager wih pixel-parallel A/D conversion, IEEE Journal of Solid-Sae Circuis 36(5), pp , May C. Jansson, A high-resoluion, compac, and low-power suiable for array implemenaion in sandard CMOS, IEEE Transacions on Circuis and Sysems I 42(11), pp , November D. Yang and A. El Gamal, Comparaive analysis of SNR for image sensors wih enhanced dynamic range, in Sensors, Cameras, and Sysems for Scienific/Indusrial Applicaions, M.M.BloukeandG.M.W.Jr., eds., Proc. SPIE 3649, pp , April A. El Gamal, High dynamic range image sensors, Tuorial a Inernaional Solid-Sae Circuis Conference, February S. Kavusi and A. El Gamal, Quaniaive sudy of high dynamic range image sensor archiecures, in Sensors, Cameras, and Sysems for Scienific/Indusrial Applicaions, M.M.Blouke,G.M.W.Jr.,and R. J. Moa, eds., Proc. SPIE 5301, January B. Fowler, A. El Gamal, and D. Yang, A CMOS area image sensor wih pixel-level A/D conversion, IEEE Inernaional Solid-Sae Circuis Conference, pp , February Proc. of SPIE Vol

10 8. S. B. Horn, P. R. Noron, J. D. Murphy, and R. E. Clemen, Verically inegraed sensor arrays (VISA), SPIE Defense and Securiy Symposium (Invied Paper), April D. Seizer, G. Prezl, and N. A. Hamdy, Elecronic Analog-o-Digial Converers, Wiley, J. Rober, G. Temes, V. Valencic, R. Dessoulavy, and P. Deval, A 16-bi low-volage CMOS A/D converer, IEEE Journal of Solid-Sae Circuis 22(2), pp , April B. Fowler, CMOS Area Image Sensors wih Pixel Level A/D Conversion, Ph.D Thesis, Sanford Universiy, CA, M. Perijs, A. N. M. X. B., McKillop, and A. B. J. Huijsing, A CMOS emperaure sensor wih a 3σ inaccuracy of ±0.5 o Cfrom 50 o Co120 o C, IEEE Inernaional Solid-Sae Circuis Conference, pp , February S. Hein and A. Zakhor, Reconsrucion of oversampled bandlimied signals from sigma dela encoded binary sequences, IEEE Transacions on Signal Processing 42(4), pp , March L. McIlrah, A robus O(N log n) algorihm for opimal decoding of firs-order Σ sequences, IEEE Transacions on Signal Processing 50(8), pp , Augus H. Kakavand, S. Kavusi, and A. El Gamal, Opimal decoder for Σ modulaor, Inernal repor, Sanford Universiy, M. Pelgrom, H. Tuinhou, and M. Verreg, Transisor maching in analog CMOS applicaions, IEEE IEDM Technical Diges, pp , December Proc. of SPIE Vol. 5406