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