{"title": "Silicon Retina with Adaptive Filtering Properties", "book": "Advances in Neural Information Processing Systems", "page_first": 712, "page_last": 718, "abstract": null, "full_text": "Silicon  Retina with Adaptive Filtering \n\nProperties \n\nComputation and Neural Systems \n\n136-93 California Institute of Technology \n\nShih-Chii Liu \n\nPasadena, CA  91125 \nshih@pcmp.caltech.edu \n\nAbstract \n\nThis  paper  describes  a  small,  compact  circuit  that  captures  the \ntemporal and adaptation properties both of the photoreceptor and \nof the laminar layers  of the fly.  This  circuit  uses  only six  transis(cid:173)\ntors and two capacitors.  It is operated in the subthreshold domain. \nThe circuit maintains a  high transient gain by using adaptation to \nthe  background intensity  as  a  form  of gain  control.  The  adapta(cid:173)\ntion time  constant of the circuit  can be  controlled via an external \nbias.  Its temporal filtering  properties change with the background \nintensity or  signal-to-noise conditions.  The frequency  response  of \nthe  circuit  shows  that in  the  frequency  range  of 1 to  100  Hz,  the \ncircuit response goes from  highpass filtering under high light levels \nto lowpass filtering  under low  light levels  (Le.,  when  the signal-to(cid:173)\nnoise  ratio is  low).  A  chip  with  20x20 pixels  has  been fabricated \nin  1.2J.Lm  ORBIT CMOS  nwell technology. \n\n1  BACKGROUND \n\nThe  first  two  layers  in  the  fly  visual  system  are  the  retina  layer  and  the  laminar \nlayer.  The  photo receptors  in  the  retina  synapse  onto  the  monopolar  cells  in  the \nlaminar layer.  The photoreceptors adapt to the background intensity,  and use  this \nadaptation  as  a  form  of gain  control  in  maintaining  a  high  response  to  transient \nsignals.  The laminar layer  performs  bandpass filtering  under  high  background in(cid:173)\ntensities,  and  reverts to low pass filtering  in the case  of low  background intensities \nwhere the signal-to-noise  (SIN)  ratio is  low.  This adaptive filtering response in the \ntemporal domain is  analogous to the spatial center-surround response of the bipolar \ncells  in the vertebrate retina. \n\n\fSilicon Retina with Acklptive Filtering Properties \n\n713 \n\nFigure  1:  Circuit  diagram  of retino-Iaminar  circuit.  The  feedback  consists  of a \nresistor implemented by a  pFET transistor,  Q1.  The conductance of the resistor is \ncontrolled by the external bias, Vm . \n\nVr \n\niin \n\nga \n\nCdI  CI \n\n-\n\nVI \n\n~ \n\nFigure  2:  Small  signal  model  of the  circuit  shown  in  Figure  1.  Cr  is  the  parasitic \ncapacitance at the node,  Vr . \n\nThe Delbriick silicon  receptor circuit  (Delbriick,  1994)  modeled closely the step re(cid:173)\nsponses and the adaptation responses of the biological receptors.  By including two \nadditional transistors, the retino-Iaminar  (RL)  circuit described  here  captures \nthe properties of both the  photoreceptor layer  (Le.,  the  adaptation  properties  and \nphototransduction)  and  the  cells  in  the  laminar layer  (Le.,  the  adaptive filtering). \nThe time constant of the circuit is controllable via an external bias, and the adapta(cid:173)\ntion behavior of the circuit over different background intensities is more symmetrical \nthan that of Delbriick's  photoreceptor circuit. \n\n2  CIRCUIT DESCRIPTION \n\nThe  RL  circuit  which  has  the  basic  form  of Delbriick's  receptor  circuit  is  shown \nI  have  replaced  the  adaptive  element  in  his  receptor  circuit  by  a \nin  Figure  1. \nnonlinear  resistor  consisting  of a  pFET  transistor,  Q1.  The  implementation  of a \nfloating, voltage-controlled resistor has been described earlier by (Banu and Tsividis, \n1982).  The  bias  for  Q1,  Vb,  is  generated  by  Q3  and  Q4.  The  conductance  of Q1 \nis  determined  by the output voltage,  Vi,  and an external bias,  Vm .  We  give  a  brief \ndescription of the circuit operation here;  details are described in  (Delbriick,  1994). \nThe receptor node,  Vr ,  is clamped to the voltage needed to sink the current sourced \n\n\f714 \n\ns-c. Liu \n\nFrequency (Hz) \n\nFigure 3:  Frequency plot of the RL circuit over five  decades of background intensity. \nThe number next to each curve corresponds to the log intensity of the mean value; \na log corresponds to the intensity of a  red LED.  The plot shows  that,  in the range \nof 1 to 100 Hz,  the circuit is  a  bandpass filter  at high light levels,  and reduces to a \nlowpass filter  at low  light levels. \n\nby Q6,  which is  biased by an external voltage, Vu.  Changes in the photo current are \namplified by the transistors, Q2  and Q6,  resulting in a change in Vi,  This change in \nVi  is  capacitively  coupled through the capacitive divider,  consisting of Cl  and Cd, \ninto Vp1 ,  so  that Qs  supplies the extra increase in photocurrent. \nThe feedback transistor,  Qs,  is  operated in  subthreshold so that v;.  and Vi  is  loga(cid:173)\nrithmic  in  the  photocurrent.  A  large  change in  the  photocurrent  resulting from  a \nchange in  the  background intensity,  leads  to  a  large  change  in  the  circuit  output, \nVi. Significant  current then flows  through Ql, thus charging or discharging Vp1 . \n\n3  PROPERTIES  OF  RL  CIRCUIT \n\nThe  temporal  responses  and  adaptation  properties  of this  circuit  are  expounded \nin  the following  sections.  In  Section  3.1,  we  solve  for  the  transfer function  of the \ncircuit  and in  Section  3.2,  we  describe  the  dependence  of the  conductance  of Ql \non  the  background  intensity. \nIn  Sections  3.3  and  3.4,  we  describe  the  temporal \nresponses  of this  circuit,  and  compare the  adaptation response  of RL  circuit  with \nthat of Delbriick's circuit. \n\n3.1  TRANSFER FUNCTION \n\nWe  can solve for  the transfer function  of the RL circuit in  Figure  1 by writing the \nKCL  equations of the small-signal model shown in Figure 2.  The transfer function, \n~, is given  by: \n'.n \n\n-= - -\ngrnS \nlin \n\n(1) \n\n\fSilicon Retina with Aooptive Filtering Properties \n\n715 \n\n17 \n\n~ \n.~ \n\nB .: .. . ~ \nj \n\nI 2 0~--::1l'::-2 ----::0':-.4  ----::0:';-.6  ----::0:'::-.8 - - - !  \n\n.. \n\nTime (sec) \n\nFigure 4:  Temporal responses of the circuit over five  decades of background inten(cid:173)\nsity.  The input stimulus is  a square-wave-modulated red LED of contrast 0.15.  The \ncircuit acts as  a  high pass filter  (that is,  a  differentiator)  at high  intensities,  and as \na  lowpass filter  as the intensity drops. \n\nwhere  Aamp =  9~2, gm  is  the transconductance, and gd  is  the output conductance \nof a transistor.  We  define the time constants, TI,  TT'  and Tid,  as follows: \n\nCd \nTI  =  - ;T r  =  --;Tld = --, \ngm2 \n\nCl \ngm2 \n\nCr \ngm5 \n\nwhere ga  is the output conductance of Ql  and Cr is the parasitic capacitance at the \nnode,  Yr' \nThe frequency response curves in  Figure 3 are measured from  the fabricated circuit \nover  five  decades  of background  intensity.  We  obtain  the  curves  by  using  a  sine(cid:173)\nwave-modulated red LED source.  The number next to each curve is the log intensity \nof the  mean  value;  0  log  is  the  intensity  of a  red  LED.  We  obtain the  remaining \ncurves  by interposing neutral density filters  between the LED  source  and the chip. \nFigure  3  shows  that,  in  the  range  of 1  to  100  Hz,  the  circuit  is  a  bandpass  filter \nat  high  light  levels,  and  reduces  to  a  lowpass  filter  at  low  light  levels.  For  each \nfrequency  curve,  the gain  is  flat  in  the  middle,  and is  given  by  Ad  =  CI~~d.  The \ncutoff frequencies  change with  the background intensity; this change is  analyzed in \nSection 3.2. \n\n3.2  DEPENDENCE OF CIRCUIT'S  TIME CONSTANT ON \n\nBACKGROUND INTENSITY \n\nThe cutoff frequencies  of the circuit  depend on  the  conductance,  ga,  of Ql .  Here, \nwe  analyze the dependence of ga  on the background intensity.  Since Ql  is  operated \nin  subthreshold, the conductance depends on the current flowing  through Ql'  The \nI-V relationship for  Ql  can be written as \n\nI  =  2IoP(fh r p e(l-Itnltp)y e- Itnltp t!.V/2 sinh (.6Yj2) \n\n(2) \n\non \n\n=  lal~~-Itnltp )/ltn e(1-2ltn lt p)t!. V/2 sinh(~ Vj2) \n\n(3) \nlph  is  the  photo current ,  and  fa  = \nwhere  V \n2Iop (-f!: t p ((: ) (l-Itnltp)/ltn .  The exponential  relationship  for  Equations 2  and  3 \nis  for  a  FET transistor operating in subthreshold,  where  lop  is  the quiescent  leak(cid:173)\nage  current  of the  transistor,  and  K.  is  the  effectiveness  of the  gate  in  controlling \n\n\"l~VPI,  ~V  =  Vi  - Vp1 , \n\n\f716 \n\ns-c. Liu \n\n1.8 \n\n1 6 \n\n... \n\n1.2 \n\n~ \n\"0 \n~ \n:; \n9-\n5 \nti \nc \n. ~ \nb \nC . .\" \n~ \n\nTime (sec) \n\nFigure 5:  Plots of adaptation responses of the RL circuit and of Delbriick's circuit. \nThe  input  stimulus  is  a  red  LED  driven  by  a  square  wave  of contrast  0.18.  The \nbottom curve corresponding to Delbriick's  receptor  has  been  shifted  down  so  that \nwe  can compare the two curves.  The adaptation response of the RL  circuit is  more \nsymmetrical than that of Delbriick's circuit when the circuit goes from dark to light \nconditions and back. \n\nthe  surface  potential  of the  channel  of the  transistor.  Equation  3  shows  that  ga \nis  proportional to the  photocurrent,  I ph ,  hence,  the background intensity.  A more \nintuitive  way  of understanding  how  ga  changes  with  Iph  is  that  the  change  in  Vb \nwith a fixed  change in the output, Vi,  depends on the output level of Vi.  The change \nin  Vb  is  larger for  a  higher  DC  output,  Vi,  because of the increased  body  effect  at \nQ4  due to its higher source voltage.  The larger change in Vb  leads to an increase in \nthe conductance,  gao \nAs  Iph  increases,  ga  increases, so the cutoff frequencies  shift  to the right, as seen in \nFigure 3.  If we  compare both the  \"0\"  curve and the  \"-1\"  curve, we  can see  that the \ncutoff frequencies  are approximately different by a factor of 10.  Thus, the exponent \nof Iph ,  (1- /'i,n/'i,p)//'i,n  :::::  1.  Since the  /'i,  values change with the current through the \ntransistor,  the  exponent  also  changes.  The  different  values  of the  exponent  with \nIph  can be  seen from  the different amounts of shifts in  the cutoff frequencies of the \ncurves. \n\n3.3  TEMPORAL RESPONSES \n\nThe  adaptive temporal  filtering  of the  circuit  over  five  decades  of background  in(cid:173)\ntensity can  also  be observed from the step response of the RL  circuit to  a  square(cid:173)\nwave-modulated  LED  of contrast 0.15,  as  shown  in  Figure 4.  The data in  Figure \n4  show  that the  time  constant of the circuit  increases  as  the light  level  decreases. \nThe  temporal  responses  observed  in  these  circuits  are  comparable to the contrast \nresponses recorded from  the LMCs by Juusola and colleagues (Juusola et aI.,  1995). \n\n3.4  ADAPTATION  PROPERTIES \n\nThe  RL  circuit  also  differs  from  Delbriick's  circuit  in  that  the  adaptation  time \nconstant can be set by an external bias.  In the Delbriick circuit, the adaptation time \nconstant is predetermined at the design phase and by process parameters.  In Figure \n5,  we  compare the adaptation properties of the RL  circuit with those of Delbriick's \n\n\fSilicon Retina with Atklptive Filtering Properties \n\n717 \n\n'\" \n\nV m..o.7l. 0.71. 0.8, 0.14. 0 .\u2022 7. 0.9 \n\n1.45 0 \n\n01 \n\n0.2 \n\n0 3 \n\n04 \n\n0.5 \n\n0.6 \n\nTime <sec) \n\nFigure  6:  Step  response  of the  RL  circuit  for  different  values  of Vm .  The  input \nstimulus is  a  square-wave-modulated red  LED  source.  The value  of Vm  was  varied \nfrom  0.73 to 0.9 V. The curve with the longest time constant of decay corresponds \nto the lowest  value of Vm . \n\ncircuit.  The input  stimulus  consists of a  square-wave-modulated LED  source  with \na  contrast  of about  0.18.  We  take  the  circuit  from  dark  to  light  conditions,  and \nback  again,  by  using  neutral  density  filters.  The  top  curve  corresponds  to  the \nresponse  from  the  RL  circuit,  and  the  bottom  curve  corresponds to  the  response \nfrom  the  Delbriick  circuit.  The  RL  circuit  adapts  symmetrically,  when  it  goes \nfrom  light  to dark conditions  and  back.  In  contrast,  Delbriick's  circuit  shows  an \nasymmetrical adaptative behavior; it adapts more slowly when it goes from dark to \nlight conditions. \nThe  adaptation  time  constant of the  RL  circuit  depends  on  the  conductance,  ga, \nand the capacitors, CI  and Cd.  From Equation 3,  we  see that ga  is  dependent on h \nwhich is  set by the bias, Vm .  Hence, we  can change the adaptation time constant by \nvarying Vm .  The dependence  of the  time  constant on  Vm  is  further  demonstrated \nby  recording the  step  response  of the  circuit  to a  LED  source  of contrast 0.15  for \nvarious values of Vm .  The output data is  shown in  Figure 6 for  five  different  values \nof Vm .  The time constant of the circuit decreases as  Vm  increases. \nA  chip  consisting  of  20x20  pixels  was  fabricated  in  1.2l-tm  ORBIT  CMOS  nwell \ntechnology.  An  input  stimulus  consisting of a  rotating flywheel,  with  black  strips \non a white background, was initially presented to the imager.  The flywheel was then \nstopped,  and the  response  of the  chip  was  recorded  one  sec  after the  motion  was \nceased.  I  repeated the experiment for  two  adaptation time  constants  by  changing \nthe value of Vm .  Figure 7a shows the output of the chip  with the longer adaptation \ntime constant.  We  see  that the  image  is  still  present, whereas the image  in Figure \n7b has almost faded  away;  that is,  the chip has adapted away the stationary image. \n\n4  CONCLUSIONS \n\nI  have  described  a  small  circuit  captures  the  temporal  and  adaptation  properties \nof both the  photoreceptor and the laminar layers in the fly  retina.  By adapting to \nthe background intensity, the circuit maintains a high transient gain.  The temporal \nbehavior  of the  circuit  also  changes  with  the  background  intensity,  such  that,  at \nhigh  SIN  ratios,  the  circuit  acts  as  a  highpass  filter  and,  at  low  SIN  ratios,  the \ncircuit  acts  as  a  lowpass filter  to  average  out  the  noise .  The  circuit  uses  only  six \ntransistors and two capacitors and is compact.  The adaptation time constant of the \n\n\f718 \n\nsoc. Liu \n\n(a) \n\n(b) \n\nFigure  7:  Adaptation  results  from  a  two-dimensional  array of 20  x  20  pixels.  The \noutput  of  the  array  was  recorded  one  sec  after  cessation  of the  pattern  motion. \nThe experiment  was  repeated for  two  different  adaptation time  constants.  Figure \n(a)  corresponds to the longer  adaptation time constant.  The image is  still present, \nwhereas the image in  Figure  (b)  has almost faded  away. \n\ncircuit can be  controlled via an external bias. \n\nAcknowledgments \n\nI thank Bradley A.  Minch for  discussions of this work,  Carver Mead for  supporting \nthis work,  and the MOSIS foundation for  fabricating this circuit.  I also thank Lyn \nDupre for  editing this document.  This  work was supported in  part by the  Office of \nNaval Research, by DARPA,  and by the Beckman Foundation. \n\nReferences \n\nT.  Delbriick,  \"Analog VLSI  phototransduction  by  continous-time,  adaptive,  loga(cid:173)\nrithmic photoreceptor circuits,\"  eNS Memo  No.SO,  California Institute of Technol(cid:173)\nogy,  Pasadena, CA,  1994. \n\nM.  Banu and Y.  Tsividis,  \"Floating voltage-controlled resistors in  CMOS technol(cid:173)\nogy,\"  Electronics  Letters,  18:15, pp.  678-679,  1982. \nM.  Juusola,  R.O.  Uusitola,  and  M.  Weckstrom,  \" Transfer of graded  potentials  at \nthe  photoreceptor-interneuron synapse,\"  J.  of General  Physiology,  105,  pp.  115-\n148,1995. \n\n\f", "award": [], "sourceid": 1360, "authors": [{"given_name": "Shih-Chii", "family_name": "Liu", "institution": null}]}