생리현상에 대한 공학적해석 10: The Eye as a Transducer ABSTRACT
• Visible light; 380nm~825nm : lens, retina • Cone cell; at the foveola(center of the eye) : 3um in diameter, 0.7' visual angle • Amplitude range : 4500:1(cone) ; 7 min dark adaptation time : 22:1(rod); 30 min dark adaptation time • Photoreceptors : generate graded potential : proportional to logarithm of visual stimulus
1 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer ABSTRACT • Retina; five layers 1. photoreceptors; receptor potential 2. bipolar cells ; subtraction 3. horizontal cells; gather receptor potentials → local value 4. ganglion cells; translate to APs 5. amacrine cells; detection of illuminance change
• Cones 1. red cones; 65%, respond maximally to yellow 2. gg;reen cones; 33%, resppygond maximally to green 3. blue cones; 2%, respond maximally to indigo
2 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer ABSTRACT
• SbjtiSubjective sensati on; sat urati on & &h hue
: depend on the ratio red: green: blue(CR:CG:CB) :white: white =(CR :C: CG :C: CB) = 90:45:1 • Standard chromaticity diagram
: 0.9 log CR + 0.1log CB -log CG ↔ log CG -log CB - topologically similar to standard diagram : 3-D map in visual cortex; 2-D color map + illuminance : chromaticity diagram for color blindness • Contrast enhancement : B&W enhancement, color enhancement : hypothetical retinal model
3 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Charac ter is tics o f the Eye
• Viibllihisible light; e lectromagnet ic wave : 825nm(3.6×1014Hz)~380nm(7.9 ×1014Hz) : atoms & molecules act like tiny antennas • Why sensitive to only this small range? : only this range reach to the earth from sun : for some radiowave, reach through, -but much to small to act as a antenna : phthotorecept or cell ; organi c compoun d(hdd(rhodops i)in) - visible light → receptor potential - by electrochemical cycles
4 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
Cross section of Human eye
• Lens; squeeze using accommodation muscle • Normal; - relaxed lens; looking at distant object on retina - 10yrs old; change focal length by 2.3mm (focus an object 8cm away) - 70yrs-old; change focal length by 0.22mm (sufficient for an object 1m away)
5 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
5 layers in Retina
Fig.50-11
6 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
5 layers in Retina • Reversed direction -wrong evolution direction & not able to turn back - photoreceptor; require high oxygen tension : closer to blood supply • Light → ganglion → amacrine → bipolar → horizontal → photoreceptor - essentially transparent • Optic disk - optic nerve through the hole in the retina -15° toward nasal side → blind spot - blend in with surroundings
7 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
Foveola
• Central area for "looking at" an object : 34,000 photoreceptors : 0.6mm in diameter : each receptor - 3um= 3000nm = 3.6 × wavelength of red light → visual acuity - (3um/15000um) × (360° /2π) = 0.011° = 0.7’ ≅ 1' → limiting resolving power of the eye • 1' for a TV screen? - minimum viewing distance? - (screen height/495) ×(360' × 60/2π) = 7 × height
8 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
Photoreceptors • Rod - rod shape, sensitive to dim light, free of color - maximally sensitive to 512nm(green; dark gray) - no rod in fovea; increase away from the fovea - maximal visual acuity; 7% of cone - high sensitivity sacrificing resolution • Cone - cone shape - dominate & inhibit rods under "daylight" condition - color vision
9 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
Relative Time Response
• Lux : SI unit f or ill um inance : power : 1 lux = 1 lumem/m2 • √lux : measure of amplitude : 33020 √lux ~ 0. 0032 √lux → 100,000:1(107 for ear)
10 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
Relative Time Response
• Cone photoreceptor : from 320 to 0. 5 : sudden decrease from maximal tolerable white to black : pupil start to open; - opening slowly increase to maximum in 7 min. - 0.07 √lux ; completely absence of light - some chemical & neural change occur • RdRod p hthotorecep tor : 0.07 √lux; cones cease to inhibit the rods : start to increase sensitivity : due to slow chemical & neural factor : 0.0032 √lux after 30 min from the 320 √lux level
11 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Retinal Responses to Steady Light
• Retina : Basic sense of light : 2 layer - photoreceptor - ganglion cell : 3 more layers Fig. 10-3 - enhance contrast - signal motion • Simple Circuit : for steady state input : excluding - motion detection
12 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Signa l Process ing in Re tina
• Photoreceptor(P) -coppypge with the 600:1 dynamic input range - measure average intensity - i/o characteristics can be changed by " chemical & neural changes" - transfer function for average light intensity : lateral communication between cones : feedback from horizontal(H) cell : constant saccadic motion - wander within a field randomly - 50 cone diameter in 4s : eachllifftdbllh cell is affected by local average
13 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Signa l Process ing in Re tina
• Compressifion of output : 600:1 : w/o compression - 20Hz for minimum, 12,000Hz for maximum → ? : with compression - 20~12,000 → 20~500Hz AP frequency • Color dependent : only weakly to brightness : extract ratio(red/green , blue/green.. ) : logarithm + subtraction : red(270), green(135); log270 - log135 = 5. 60 - 491=0694.91 = 0.69 : red(27), green(13.5); log27 - log13.5 = 3.29 - 2.60 = 0.69 (same hue)
14 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
• Logarithmic compression : transfer fn . changes as average intensity change
: VP = 16 + 5 log(LZ/LZ0) - valid 0.0408 < LZ/LZ0 < 24.5 → 0.0408:24.5=600:1 - LZ0 = average of local light intensity -VP = cone's output potential -LZ = input light intensity : maximum value = 16 + 5 log(24.5) = 32mV : minimum value = 16 + 5 log(0.0408) = 0mV : input: local average
VP = 16 + 5 log(LZ/LZ0 ) =16mV
15 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Idea lize d Neura l • P cells Model - respond to light - logarithmic compression • H cells - wired uppg to measure average • B cells - excited by P cell Fig. 10-3 - inhibited by H cell - contrast enhancement
: VB=VP-0.5VH - spherical bipolar structure : up & down • A cells - concerned with motion • G cells - convert GP to AP
16 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
CtContrast • Visual scene presentation
Enhancement : resulting bipolar cell output; VB
: average input light intensity (LZ0) = 50 • First Experiment : dark background except for a bright center
: VP; 16mV(background), 32mV(saturation) Fig. 10-5 : VH; 21mV(center) to 16mV(peripheral) - remote H cell; attenuation of long dendrite
-VH is biased for nearest cone neighbors -r² : ΔVH = (ΔVP/π) e ; Gaussian model -r² -r² : ΔVH = (16/π) e → VH = 16 + 5.093 e
:V: VB = VP - 05V0.5VH
- at center; VB=32-0.5(21.093)= 21.45mV
-far away; VB =16 - 0.5(16) = 8mV
17 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer CtContrast tEh Enhancement
• Step transition -black(2.04; 0mV) → white(97.96;19.36mV) → 19mV jump Fig. 10-7 - VP: step function
-VH = (ΔVP/2)( 1+ erfc x )
-VB = VP -0.5VH : 0mV[left] → -4.84mV → 14.52mV(19mV jump) → 9V9.7mV[i[righ h]t]
18 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer
Contrast Enhancement
Fig. 10-8
• 5 vertical gray strips - differences in subject and actual intensity variation - effect of large contrast change
19 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer CtContrast tEh Enhancement • Incorrect assessment of small area brightness
- medium gray(30:VP=13.45) : in dark gray
(10: VP =7.95) : in bright gray
(90: VP=18.94mV) Fig. 10-9 - strips are narrow → not seen by the H cell
-VB = VP -0.5VH : VB= 9.47mV(left) : VB = 3.98mV((gright ) : left strip looks brighter than right one
20 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer CtContrast tEh Enhancement
• Sinusoidal gratings - 0.2 cycles, 1 cycle/unit - compression of high intensity : spatial harmonics -H cell
: smooth out the VP variation : DC + fundamental component
-VH0 =14.88mV 2 - VH1 =VP1exp(-w /4) : VH1 = - 2.695cos(1.257x) mV : VH1 = - 0.0002cos(6.283x) mV (H cell doesn't see horizontal gratings)
-VB =8.3mV(lower f.), VB =11mV(higher f.) : more sensitive to higher freq.(smaller object)
21 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer CEhContrast Enhancement
• Ramp transition
: VP = 16 + 5 log(LZ/50)
: cusp in VB of enhanced contrast Fig. 10-11 : more slope discontinuity : enhancement is less in high brightness
22 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer MhBdMach Bands
• EitExperiments : 60 revolution/sec → smooth transition w/o flicker : 135° black ↔ 45° black : displays bumps at edges Fig. 10-12 - MhBdMach Band - white & black bands at edges : calibration ramps → location of equal brightness → estimate size of bumps : Mach Bands in low contrast case
23 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer MhBdMach Bands
• Difference from the out put of bi pol ar cell VB (1) rounded edge instead of sharp edge (()2) chang in g slo pe - small slope; no Mach Bands - increased slope; increased Mach Bands - vertical slope; decreased Mach Bands! (3) only in central region of eye(foveola) ↔ contrast enhancement is retina wide
• Mechanism for Mach band : interaction of reflectance & ambient light condition : unaware of sophisticated image processor
24 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer RtFlikdMtiResponse to Flicker and Motion
• Motion detection : detection of moving bug : rotating many bladed windmill - constant input for H cell : mudpuppy; large retina cells - microelectrode into the ganglion cell : center dot varied - stationary → active - slow rotation(()flicker) → inhibited - rapid rotation(no flicker) → active : large area change → inhibit transient ganglion : small change due to moving bug → fully seen if surrounding visual field is quiet
25 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer TitliiitTransient ganglion circuits
• Neural Model - F; flicker - BcellB cell → A cell, → G cell(steady state) → G cell(transient) - A cell: : receive flicker inputs - Transient Ganglion cell
: fTG = VBF -VA
26 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Flic ker ing Exper imen t
• Left : non-moving • Right: : flickering
• fTG : firing at a furious rate : aware of intense change
27 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Flic ker ing /Mov ing Do t
• Gray field + mov ing or flic ker ing do t - small change due to moving bug - fully seen in quiet background • Natural massive flicker - saccadic motion : insufficient to stimulate A cells - eye blinks, rapid eye scan, cloud moving in & out of the sun, leaves in the wind, • Amacrine cell - stimulation by large area flicker → inhibit ggganglion cell
28 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer SbjtiSubjective ClColor Charac ter itiistics • Cone & Color Characteristics - cones : red(65%), green(33%), blue(2%) - relative sensitivities : in lowest illuminance level with full color sensation Fig 10.17 : curves biby pigmen ts(PR,PG,PB) : cannot be directly measured (3um in diameter) : psychophisically obtained - 380um ~ 825nm - "ROYGBIV" : equal distance in log scale : wavelength ratio;1.089
29 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer SbjtiSubjective ClColor Charac ter itiistics • 3 "unsightly feature" 1) peak value; red cone(yellow), blue cone(indigo) - each cone is sensitive to all wavelengths - RGBR,G,B → white ; names for discovered 3 types 2) red cone & green cone - practically identical below 530nm → inefficient? 3) blue cone is muc h less sens itive → weak sensor receptor • If three evenlyyp spaced curves of e qual sensitivit y → improve SNR for color reception • 2% for Blue cone - save space for insensitive receptor - tritanope(blue blind); almost normal
30 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer SbjtiSubjective ClColor Charac ter itiistics
Cone Responses • LZ1 : light intensity at wavelength λ1
- response for intensity LZ2 : light intensity at wavelength λ2
: VP = 16 + 5 log (LZ/LZ0) PR1: red pigment response to λ1 - color response PR2: red pigment response to λ2
:C: CR = LZ1PR1 +LZ2PR2 PG1: ggpgpreen pigment response to λ1
PG2: green pigment response to λ2 : CG = LZ1PG1 +LZ2PG2 PB1: blue pigment response to λ1 : CB = LZ1PB1 +LZ2PB2 PB2: blue pigment response to λ2 - logarithm suppression C : total internal response of the red cone : VPR = log CR R CG : total internal response of the green cone :V: VPG =logC= log CG CB : total internal response of the blue cone :VPB = log CB
31 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Sensati on of Whit e (a) Output of 3 curves for continuum of wavelength - area under the curve(90:45:1) - magic formula; not matter how it is gathered (b) Seven monochrome light(ROYGBIV) of equal intensity - 77:41:1(≅ 90:45:1) → impression of white (c ) With two monoc hroma tic beams - 90:45:1 combination - 650nm(red) +494nm(green) of correct intensity - 569nm(green)+450nm(indigo)of correct intensity - (650~569nm) + (450~494nm) - ggyenerate only limited color set : 587nm(orange) + 485nm(blue) : saturated orange → unsaturated orange → white → unsaturated blue → saturated blue 32 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Sensati on of Whit e
(d) com bina tion o f 3 monoc hrome : generate practically all colors(color TV, color photo) : 650nm(red), 520nm(green),450nm(indigo) : 372:130:86 → subjective sensation of white
Monochrome Beam Red Cone Green Cone Blue Cone λ Lz PR CR PG CG PB CB (1) 650nm 372 0.101 38 0.006 2 0 0 (2) 520nm 130 0.393 51 0.317 41 0.001 0.1 (3) 450nm 86 0.016 1 0.020 2 0.011 0.9 Total 90 45 1
33 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer The Standard Chromaticity Diagram
• 1931 by International Commission on Illumination - monochrome hue; edge of triangle - inside of triangle : mixture of hue plus white : 3 component for TV - tungsten filament heating curve : 1000K (red; 607nm) : 2000K(mixture of white & orange) : 3643K(melting temp) : 6000K (white) - linear combination : indistinguishable with monochromatic source of light : two points passing through white : 587nm → white → 485nm line
34 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Two-Dimens iona l Co lor Map
• Signal processing 1) color groups; 5000 in foveola
- CR:C: CG :CB; relatively constant over retina 2) 2-D map(similar with chromaticity diagram) - many thousands of maps(1000neurons/map) 3) ratios; invariant under 600:1 intensity change - logarithm + subtraction
-log CR -log CG,,g log CG -log CB
• 2-D chromaticity diagram with minor change
- H-axis; 0.9×log CR + 0.1×log CB - log CG
- V-axis; log CG - log CB
35 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Two-Dimens iona l Co lor Map
• Example - wavelength of 682nm(red)
: CR = 0.0144(VPR =14.18mV)
: CG = 0.000574(VPG =10.96mV) -8 : CB = 1.79 × 10 (VPB =0.58mV) - 090.9×14. 18 + 0. 1×0580.58 - 10. 96 = 1.86(H-axis) - 10. 96 - 0. 58 = 10. 38(V-axis) • calculation for "ROYGBIV" • linear combination of R&V((gright ed g)ge) • 45°rotation of chromaticity diagram : approximate agreement
36 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer Two-Dimens iona l Co lor Map Mo de l • 2-D color map model - zero potential depression - hue & saturation
-white; CR:CG:CB=270:135:3 : graded potential - (I) junction; threshold - input - (()jE) junction; input - threshold Fig 10.20 : 2-D map 5.04 2.16 9.36 16.56 2.24 0.96 4.16 7.36 0.56 0.24 1.04 1.84 3.36 1.44 6.24 11.04 - circular depression for the color(W) : 0dd0 graded potent ilWiial at W point : hue,saturation,intensity → 3-D
37 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer ClColor BlidBlindness
• deficiencyyg of photochemical pigment • red blindness(protanopia);
: H-axis; 0.9×logCR+0.1×logCB- logCG → meaningless : V-axis; logCG - logCB → 1-D line : ROY coincide on the 1-D map : red blindness; 2% of male green blindness(deuteranopia) • Fig 10.21 : lClogCR - lClogCB : similar with red blindness : G moves closer to ROY : green blin dness; 6% o f ma le : R/G blindness; 0.4% of female • blue blindness(tritanopia)
: logCR - logCG : confuse violet with green, otherwise normal : mostly unaware of their deficiency
38 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer ClColor Con tras tEht Enhancemen t
• Like monochrome contrast enhancement • Bright green in dark gray background → bright green in slightly reddish background • Center & surround are complementary each other • LGN(Lateral Geniculate Nuclei) of monkey - AP activity of single cell to a moving spot of light - maximum sensitivity to red, green, blue,or intensity - "green" neuron; inhibition on "red" surround • Microelectrode measurements - many LGN neuron can be turned off : on center - off surround : off center - on surround - increase of AP frequency if surround is illuminated : negligible response for broad illumination
39 서울대학교 대학원 의용생체공학 협동과정 생리현상에 대한 공학적해석 10: The Eye as a Transducer ClColor Con tras tEht Enhancemen t
• Hypothetical retinal circuit : for red & green - opponent - surround color receptive field : red center on - green surround off cell : green center on - red surround off cell
Fig. 10.22
40 서울대학교 대학원 의용생체공학 협동과정