Download presentation
Presentation is loading. Please wait.
Published byPhillip Sullivan Modified over 9 years ago
1
Lecture #8 Sensitivity Land + Nilsson ch3 end 2/19/13
2
Topics for today Challenges for high resolution 1)Contrast 2)Diffraction 3)Low light levels Sensitivity
3
Vertebrate spatial frequencies: best case scenarios AnimalMax resolvable spatial freq Inter-receptor angle Eagle8000 cycles/rad0.0036 deg Human41750.007 Cat5730.05 Goldfish4090.07 Rat570.5
4
Resolution problem #1) What if there is less contrast? Contrast If I min = 0 then contrast is maximum = 100% White vs black
5
Contrast I maxI minC White/Black100%0% White/gray100%20% Lt gray / gray70%30% Med gray / med gray 50%
6
Contrast I maxI minC White/Black100%0%1.0 White/gray100%20%0.66 Lt gray / gray70%30%0.4 Med gray / med gray 50% 0.0
11
T
12
T
13
T
14
Problem #2) What if there is diffraction Diffraction causes angular spreading Width of central interference peak is w = λ / D D w
15
Diffraction Resolution is limited - can’t resolve anything smaller than this angle D w
16
Detectable grating frequency Max frequency that can be detected depends on diffraction v co is max cut-off frequency w is width of diffraction peak (radians) λ is wavelength D is aperture
17
Detectable grating frequency - Humans Max frequency that can be detected depends on diffraction λ is wavelength500 nm D is pupil aperture2 mm w = 500 x 10 -9 m / 2 x 10 -3 m = 0.00025 rad v co = 4000 cycles / rad
18
Diffraction in optical systems blurs images This decreases contrast This makes gratings even harder to detect http://www.microscopyu.com/tutorials/java/mtf/spatialvariation/index.html Lp/mm = line pairs/mm Contrast I max I min
19
Diffraction decreases contrast and contrast ratio Contrast of image decreases compared to contrast of object = contrast ratio More loss of contrast with higher frequency grating Spatial freq is normalized to diffraction limited cutoff, v CO Land and Nilsson fig 3.3
20
Contrast sensitivity function Contrast sensitivity Frequency Fall off due to blurring by lens and diffraction from pupil Diffraction limit, v CO Hi contrast Lo contrast
21
Diffraction decreases contrast and contrast ratio Contrast of image decreases compared to contrast of object = contrast ratio More loss of contrast with higher frequency grating Spatial freq is normalized to diffraction limited cutoff, w=D/λ Land and Nilsson fig 3.3
22
Contrast sensitivity function Contrast sensitivity Frequency Fall off due to blurring by lens and diffraction from pupil Diffraction limit, v CO Hi contrast On low frequency side size of neurons matter
23
Contrast sensitivity decreases with age
24
Contrast sensitivity test
26
Problem #3) Low light levels limit detection Random arrival of photons at each receptor Very low light levels cause image to be less certain
27
Seeing object - high light levels Land & Nilsson fig 3.8 Black object on bright background
28
Seeing object - low light levels Land & Nilsson fig 3.8 Black object on dim background
29
Seeing object at low light level Land & Nilsson fig 3.8 Very few photons At light detection threshold Photoreceptor detecting light
30
Seeing object at low light level Land & Nilsson fig 3.8 10x more light - more receptors detect photons
31
Seeing object at low light level Land & Nilsson fig 3.8 10x 100x 1000x
32
Photon counting At low light levels, rod will “count” the number of photons, n Photon arrival is a poisson process Uncertainty in photon arriving goes as √n Fewer photons means more uncertainty n √n 100 10 10 3.3 1
33
Photon counting Uncertainty in photons arriving √n is 1 standard deviation = 66% of variation 2 √n is 2 standard deviations = 95% of variation So if 9 photons arrive on average in 1 s, for any particular second 9 ± 6 photons will arrive with 95% confidence
34
Contrast detection The bright / dark stripe of a grating falls across two receptors Contrast I max is intensity of brighter stripe I min is intensity of darker stripe ΔI is difference between these two Average intensity, I = 1/2 (I max + I min )
35
Contrast detection To detect stripes as being different, average number of photons must be greater than uncertainty in photon number 95% confidence So contrast in terms of photon number is
36
Contrast detection To detect stripes as being different, average number of photons must be greater than uncertainty in photon number 95% confidence So contrast in terms of photon number is Detectable contrast
37
How many photons are needed? To detect contrast, C Contrast is between 0 and 1. n will be greater than 1
38
How many photons are needed to detect contrast? # photons needed n >1/C 2 Contrast# photons# detected photons/s #photons needed/s 100%11030 50%440120 10%10010003000 1%10000100,000300,000
39
How many photons are needed to detect contrast? # photons needed n >1/C 2 Contrast# photons# photons detected/s #photons needed/s 100%11030 50%440120 10%10010003000 1%10000100,000300,000 Takes rod 0.1s to detect light so rate = # photons / 0.1s
40
How many photons are needed to detect contrast? # photons needed n >1/C 2 Contrast# photons# photons detected/s #photons needed/s 100%11030 50%440120 10%10010003000 1%10000100,000300,000 Only detect 30% of photons that arrive at eye so need 3x more
41
How many photons are out there? Bright sun is 10 20 photons / m 2 sr s But a photoreceptor is only 5 μm 2 Collection angle is 0.0003 sr Land&Nilsson Table 2.1
42
Measuring incident light (lecture 3) Irradiance Light flux on a surface - from all directions Photons /s m 2 Radiance Irradiance Radiance Light flux on a surface: from a particular direction and angle Photons /s m 2 sr
43
Light arriving at one photoreceptor - Bright sun
44
How many photons arrive at one photoreceptor Light levelPhoton flux photons / m 2 /sr/s Photon rate Photons/s Bright sun10 20 1.5 x 10 5 Room light10 17 150 Moon light10 14 0.15 Star light10 12 0.0015
45
How many photons are needed to detect contrast? Contrast# photons needed/s Light# photons arriving/s 100%30Moon light0.15 50%120Room light150 10%3000 1%300,000Bright sun150,000
46
How many photons are needed to detect contrast? Can only detect high contrast in bright sun Contrast# photons needed/s Light# photons arriving/s 100%30Moon light0.15 50%120Room light150 10%3000 1%300,000Bright sun150,000
47
Some caveats In dark, rods gang together so you get a larger area of light collection to increase photon #s and so ability to detect contrast To maximize ability to resolve fine detail requires high light levels Gets worse with age
48
Eye sensitivity Sensitivity tells how well photoreceptors detect light Sensitivity = # photons (n) caught per receptor for standard radiance
49
What impacts eye sensitivity? D
50
Eye sensitivity S = n/R = # photons / radiance (W/m 2 sr s) (photons m 2 sr ) Fig 3.11 D = diameter of pupil Δρ = receptor acceptance angle P abs = probability photon is absorbed
51
Human sensitivities Human S=0.62 D 2 Δρ P abs Daytime: D=2 mm = 2000μm Δρ=1.2x10 -4 rad P abs =0.3 S = 0.62 (2000 μm) 2 (1.2x10 -4 rad) 2 (0.3) Note: D must be in μm and Δρ in radians
52
Human sensitivities Human S=0.62 D 2 Δρ P abs Daytime: D=2 mm = 2000μm Δρ=1.2x10 -4 rad P abs =0.3 S = 0.01 μm 2 sr
53
Example sensitivities cones rods S in μm 2 sr
54
Sensitivity correlates with light regime Diurnal or surface dwelling S < 1 Crepuscular or mid water S = 1-100 Nocturnal or deep sea 100-10000
55
How do you increase sensitivity and not change resolution? Sensitivity S = 0.62 D 2 Δρ 2 P abs Resolution, 1/Δρ = f/d focal length / receptor diam
56
Pupil aperture Pupil aperture changes Sensitivity goes as D 2 Change in D x4 gives change in S x 16 Day Night 2 mm 8 mm
57
Nocturnal animals Pupil opens almost to full eye size After this, must increase eye size to get bigger aperture
58
How can you increase P abs (probability absorb photon)? A=1-T=1-e -αl Pack in more pigment Make photoreceptors longer Have light do a double pass through the retina by adding reflector at back
59
Large eyes = good eye sight Good resolution Humans hawks dragonflies
60
Large eyes = good eye sight Good sensitivity Cats owls moths
61
Large eyes = good eye sight Both resolution and sensitivity Blue whale : 12-15 cm eye Giant squid : 40 cm eye (16 inches)
62
Blue whale Blue whale : softball sized eye 12-15 cm
63
Giant squid eyes http://www.youtube.com/watch?v=JSBDoCoJTZg
64
Another way to think about sensitivity F# = f /D F/#=focal length / aperture D f
65
F# = focal length / aperture Short focal length Long focal length For constant aperture
66
F# = focal length / aperture Short focal length Small f/# Long focal length Big f/# For constant aperture
67
F# = focal length / aperture Big aperture Small aperture For constant focal length
68
F# = focal length / aperture Big aperture Small f/# Small aperture Big f/# For constant focal length
69
F# = focal length / aperture If focal length = aperture F/# is 1
70
F # of eye F # = Eye focal length Pupil diameter = f/D Humans (daytime) F# = 16 mm / 2 mm = 8 D f
71
F number, F# = f / D SpeciesF# Humans - day 8 Humans - night 2 Bees 2 Fish / nocturnal verts 1 Arthropods0.5
72
Sensitivity in terms of F/# Sensitivity, S=0.62 D 2 Δρ P abs So how should an eye’s sensitivity be increased? Δ ρ =d/f F# = f / D
73
F number As F# goes down, sensitivity increases to second power SpeciesF#Sensitivity = Relative brightness Humans - day 8 1 Humans - night 2 16 Bees 2 16 Fish / nocturnal verts 1 64 Arthropods0.5 256
74
To optimize resolution and sensitivity, eyes get large CharacterOptimizesEquation Long focal length, fMinimum resolvable angle Maximum sampling frequency Δρ=d/f ν s =f/2s
75
A good eye is large - resolution and sensitivity CharacterOptimizesEquation Long focal length, fMinimum resolvable angle Maximum sampling frequency Δρ=d/f ν s =f/2s Wide aperture, DMinimize diffraction High optical cut-off frequency w=λ/D ν co =1/w=D/λ R e s o lu t i o n
76
A good eye is large - resolution and sensitivity CharacterOptimizesEquation Long focal length, fMinimum resolvable angle Maximum sampling frequency Δρ=d/f ν s =f/2s Wide aperture, DMinimize diffraction High optical cut-off frequency w=λ/D ν co =1/w=D/λ Wide aperture, DIncrease light to eye Good contrast detection S=0.62D 2 Δρ 2 P abs C>1/√n SensiSensi tivity
77
Conclusions Resolution is best for high contrast, minimal diffraction, and high light intensities Sensitivity and resolution are inversely correlated Next few lectures - aquatic and terrestrial examples
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.