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Lecture #13. Non simple eyes Mirrors and multifacets (compound) 3 / 7 / 13 (Not on midterm). Homework. Do you want me to post the equations from 10-11 HW I have electronically? Do folks mind having their HW posted?. Today. Mirrored eyes Compound eyes Apposition Superposition - PowerPoint PPT Presentation
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Lecture #13
Non simple eyesMirrors and multifacets (compound)
3/7/13(Not on midterm)
Homework
• Do you want me to post the equations from 10-11 HW I have electronically?
• Do folks mind having their HW posted?
Today
• Mirrored eyes• Compound eyes
AppositionSuperposition
How well can they see?What are they good for?
How many eye designs?
Fig 1.9
Mirror
Mirrors occur in eyes all the time• Tapetum lucidum –
reflecting structure behind photoreceptors
• Have light do a double pass through the retina by adding reflector at back
Tapetum – reflecting platelets
• Usually high index platelets (guanine) in lower index matrix
• Anchovy rod outer segments (ros) surrounded by reflecting layer
Fig 6.13
Scallop: mirrors as optical elements
60-100 eyes - 1 mm
Scallop eye - closeup
Eye contains a lens sitting right on top of retina
Fig 6.2b+c
Eye does form an image!
Fig 6.3
Mirror will form an image
r=radius of curvature
object
image
f=r/2 lens focal length
Image of far off object forms at distance f which is half radius of curvature
Mirascope – creating a real image
Light passes through retina 2x: 1st time unfocused, 2nd time focused
Fig 6.4 Lens even has correction for spherical aberration
Fish also use mirrors
Spookfish, Dolichopteryx longipes
Lives at 1000m
Upward pointing tubular eyes
Downward pointing mirror eyes
Two retina and two collecting elements: 1 lens
and 1 mirrorLooking up
Looking down
“diverticulum” eye with m = mirror
Mirror has slanted reflectors
Light is focussed by this diverticulum
Deep sea bioluminescence
Bristlemouth Lanternfish
anglerfish
How many eye designs?
Fig 1.9
Apposition
Superposition
Two kinds of compound eyes
Apposition Superposition
Diurnal insects Nocturnal insectsDeep sea crustaceans
Photoreceptor
Lens
Aperture
Focal Length
The Compound Eye
Modification 1
Modification 2
Modification 3
Modification 4
Apposition eyes• Each ommatidium points in different
direction• Views different part of image
Fig 7.3
Leeuwenhoek’s experiment - a hundred points of light
• Viewed candle flame through the compound insect cornea
Each lens of compound cornea produced a focused inverted image
What does the insect see? Fig 8.2
Apposition eyes
• AppositionLight through each lens goes to all cells of rhabdomImage is not resolved by 8 cellsEach lens views different part of image
Fig 7.4
Resolution in terms of sampling frequency is same in compound and simple eyes
• Sampling angleΔΦ = D / r = Δρ
D = receptor diameterr = lens radius of curvature
Same as d/f in camera eye
• Resolution = 1/ΔΦ = r/D
Fig 7.1
Compound
Simple
Resolution is not too bad in compound eyes
Bee ommatidiumUV B G
Bee’s eye view
A. Human viewB. Photo through UV
transmitting lens
Dr. Adrian Dyer, Monash Univ
Bee’s eye view
A. Human viewB. Photo through UV
transmitting lensC. False color and
lower resolution to account for ommatidium acceptance angle
D. What bee’s brain might do to process image
Dr. Adrian Dyer, Monash Univ
Pixelation
B-EYE view
Organismal diversity
• Apposition - Diurnal insectsBees, grasshoppers, water fleas, crabs
• Neural superposition True (two winged) flies
Dipterans - true two winged flies• Horse fly, picture
wing, hoverfly
• Use neural superposition
Apposition eyes
• AppositionLight through each lens equally detected by all 8 receptors
• Neural superposition7 receptors in ommatidium are spaced further apart“Resolve image” of different locations in space Fig 7.4
Neural superpositionSome overlap in view of neighboring ommatidia
Certain receptors view same part of space
These then sum together so get more signal for same part of image Increase sensitivity for same resolution!
What strategies could insects use to collect light?
• Focal length – curvature, thickness, index of refraction
• Vertebrates change shape - ????• Aperture – let in more light• Alter index across the lens
Different kinds of apposition lenses
Fig 7.5a
• Easiest way to make an image is with curved cornea
• Get image about 4r behind lens
Different kinds of apposition lenses
Fig 7.5b
• For water bugs, normal cornea is useless
• Use high index plus lower indexCorrect spherical aberration?
Different kinds of apposition lenses
Fig 7.5c
• Limulus must function in water and on land
• Has graded index lens
Different kinds of apposition lenses
Fig 7.5d
• Graded index lens with 15 um x 5 mm long light guide
• Helps camouflage the eye
• Phronima
Different kinds of apposition lenses
Fig 7.5e compare to 7.5a
Image forms inside crystalline coneGraded lens cylinder which makes light parallel and directs to rhabdom
Resolution actually determined by acceptance angle and diffraction
• Ommatidia geometry determines resolutionBee Δρ = 1.9°
• But diffraction can degrade resolution set by geometry
Fig 7.6
To improve bee resolution• For bee to have
human resolutionv =1/ 2Δρ = 60 cycle / degree
• Δρ = 0.00014 rad
• To not be limited by diffraction: D = 2 mm
• So r = D /Δρ which is 13.8 m
Fig 7.6
To improve bee resolution• If bees had
human resolution, eye would have to be 27 m in diameter
Fig 7.7
To improve bee resolution• If bees had
human resolution, eye would have to be 27 m in diameter
• If let resolution vary with angle then only 1 m diameter
Fig 7.7
Resolution and sensitivity
• Human resolution >> BeeDifficult to increase resolution in apposition eye without making eye bigger
• Sensitivity is similar though bee is betterS = 0.62 D2Δρ 2 Pabs
Dhuman>>Dbee
Δρhuman <<Δρbee
Shuman < Sbee
Sensitivity
Adapting to different environments
• Callinectes: Shallow water blue crab
• Cirolana: Deep water isopod
• Photoreceptor diameters differ
Fig 7.8
Adapting to different environments
• Callinectes: Shallow water blue crab
• Cirolana: Deep water isopod
• Cirolana is 4000x more sensitiveBut Δρ= 47° instead of 2°
Fig 7.8
Adapting to different light levels
a) Variable pupilb) Radial migration of pigmentc) Change in rhabdom diameterd) Change in lens focal length
Fig 7.9
S = 0.62 D2Δρ2 Pabs
Pseudopupil
Fig 7.10
Optical effect - light absorbed along axis of rhabdome
Shows how resolution changes across the eye
Measure ommatidial distances
Regions of high resolution – camera eye (aside)
• Can’t have too many ganglion cells6.5 x 106 cones120 x 106 rodsIf one ganglion cell for every receptor, optic nerve would be 25 mm thick
• Put ganglion cells where they are needed most1.2 x 106 ganglion cellsOptic nerve ≈ 2mm
Regions of high resolution – Vertebrate fovea
• Fovea centralis1° spotPrimates ganglion density in fovea =
150,000 / mm2
Similar to photoreceptor density so 1 ganglion cell / cone
So put ganglion cells where they are most needed - distribution
• Visual streakHigh density of ganglia along lineVision dominated by horizon
1000’s cells / mm2
So put ganglion cells where they are most needed - distribution
• Visual streakHigh density of ganglia along lineVision dominated by horizon
• Area centralisRadially concentric ganglia density3D visual field (forest)1000’s cells / mm2
Birds can have 2 foveas• One for looking
out laterally• Other to image
their bill region Temporal spot
Invert eye designs for enhanced acuity
• Forward locomotion
• Acute zones important for predation or finding mates
• Stripes oriented to horizon
Flying bee – where is angular velocity greatest?
Bee speed V Speed of object moving by V
S distance to object
θ viewing angle
Angular speed of image moving across retina
Flying bee – where is angular velocity greatest?
Bee speed V Speed of object moving by V
S distance to object
θ viewing angle
10 ms response time of photoreceptor so image blur across 2.3 degrees
Forward locomotion• Large angular
motion at sidesNo point to have high resolution there
• No motion in frontHigh resolution
• Butterfly varies receptor spacing
Fig 7.14
Insect vision
More receptors in behaviorally important regions
• Flying insects
• Water surface insects
• Horizontal streak
Fig 7.16
Acuity zones - capture• If male and
female acuity same - capture of prey
• If male acuity > females then for capture mates
Fig 7.17
Resolution zones• Why are facets in high
acuity zone bigger?
• Overcoming diffraction limitResolutionDiff = D / λ
Fig 7.18
Most complex compound eye• Strepsipteran
Wasp parasites• 50 lenses
100 receptors behind each lens• Have neural wiring to recombine these into unified
image
Fig 7.21
Two kinds of compound eyes
Apposition Superposition
Diurnal insects Nocturnal insectsDeep sea crustaceans
What People Think Bugs See…
The Superposition Eye
Image formed by compound eyes
Apposition – many images Superposition – single image
Need strong optics to bend light by large angles to form single image
Fig 8.3
Image here
Tough to make light bend so much with single element lens
Three possible optical arrangements
Fig 8.4
Superposition – super light bendingeither with lenses or mirrors
Decopod shrimp• Mirrors reflect the light and direct onto retina
Decapod shrimp
Optical superposition eye
• Image produced on continuous retina
• Clear space between lenses and receptors
Fig 8.6
Resolution of superposition eye
Fig 8.7
Ommatidia layout Image formed
Sensitivity of apposition vs superposition eye