Optics and Rod and cone vision 1

Andrew Stockman Outline Fundamental Optics of the Eye and Rod and Cone vision Andrew Stockman Light Revision Course in Basic Sciences for FRCOphth...
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Andrew Stockman

Outline

Fundamental Optics of the Eye and Rod and Cone vision Andrew Stockman

Light

Revision Course in Basic Sciences for FRCOphth. Part 1

400 ‐ 700 nm is important for vision

The eye Visual optics Image quality Measuring image quality Refractive errors Rod and cone vision differences Rod vision is achromatic How do we see colour with cone vision?

The retina is carpeted with light‐ sensitive rods and cones

An inverted image is  formed on the retina

Optics and Rod and cone vision

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Andrew Stockman

Retinal cross-section Cornea – Clear membrane on the front of the eye. Crystalline Lens – Lens that can change shape to alter focus. Retina – Photosensitive inner lining of eye Fovea – central region of retina with sharpest vision. Optic Nerve – bundle of nerve fibers that carry information to the brain.

Visual optics

Jim Schwiegerling

Image formation Cornea

Crystalline lens

Jim Schwiegerling

Optics and Rod and cone vision

Openstax College Physics

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Andrew Stockman

Jim Bowmaker dissecting an eye… 

Retinal cross-section

BBC Horizon: Light Fantastic (2006)

Retina 200 

Accommodation to target distance

LIGHT

Accommodation

Distant target, relaxed ciliary muscles

Near target, accommodated eye, constricted ciliary muscles.

Larry Thibos

Optics and Rod and cone vision

Relaxed ciliary muscle  pulls zonules taut an  flattens crystalline lens.

Constricted ciliary muscle  releases tension on zonules and crystalline lens bulges.

Jim Schwiegerling

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Andrew Stockman Point spread function

Optical systems are rarely ideal. Optical System

scene

image

Point spread function of Human Eyes

Image quality

 x 

point source

Optical System

PSF  x  point spread function

Input

PSF

Point spread function (PSF)

If we know the Point Spread Function (PSF) or  the Line Spread Function (LSF), then we can  characterize the optical performance of the eye.

Point in visual space

From Webvision, Michael Kalloniatis

Optics and Rod and cone vision

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Andrew Stockman

6/60

Measuring image quality psychophysically

6/30

Smallest resolvable black and white target. Many different types of tests are available , but the letter chart introduced by Snellen in 1862 is the most common.

6/21 6/15 6/12 6/9

1. Visual acuity measures

6/60

6/30 6/21 6/15 6/12 6/9 6/7.5 6/6 NORMAL ACUITY

Optics and Rod and cone vision

Snellen defined “standard vision” as the ability to recognize one of his optotypes when it subtended 5 minutes of arc. Thus, the optotype can only be recognized if the person viewing it can discriminate a spatial pattern separated by a visual angle of 1 minute of arc. A Snellen chart is placed at a standard distance, twenty feet in the US (6 metres in Europe). At this distance, the symbols on the line representing "normal" acuity subtend an angle of five minutes of arc, and the thickness of the lines and of the spaces between the lines subtends one minute of arc. This line, designated 20/20, is the smallest line that a person with normal acuity can read at a distance of twenty feet. The letters on the 20/40 line are twice as large. A person with normal acuity could be expected to read these letters at a distance of forty feet. This line is designated by the ratio 20/40. If this is the smallest line a person can read, the person's acuity is "20/40."

6/7.5 6/6

6/60

6/30 6/21 6/15 6/12 6/9 6/7.5 6/6

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Andrew Stockman Visual Acuity: four standard methods Can the subject correctly identify the letter or the letter orientation?

Letter  acuity (Snellen)

Grating  acuity

2‐line  resolution 2‐point  resolution

vs. vs.

Orientation resolution acuity

Detection acuity

Can the subject see two lines or points rather than one? Arthur Bradley

Spatial frequency

Measuring image quality psychophysically

2. Spatial contrast sensitivity  measures

Optics and Rod and cone vision

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Andrew Stockman Harmonics of a square wave 3

1

5

7

Image of line

PSF

Steven Lehars

1+3+5 Spatial MTF

1 3 5

What would the results for a perfect lens look like?

Space

Spatial Frequency All frequencies

One frequency

Increasing spatial frequency

Spatial frequency gratings

Increasing contrast

Optics and Rod and cone vision

Source: Hans Irtel

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Andrew Stockman Spatial MTF

The apparent border between visible and invisible modulation corresponds to your own visual modulation transfer function.

Increasing contrast

Spatial frequency in this image increases in the horizontal direction and modulation depth decreases in the vertical direction.

Increasing contrast

Spatial MTF

Increasing spatial frequency

2. Grating Contrast Sensitivity

Contrast Sensitivity Function (CSF)

Increasing contrast sensitivity

Peak CS

High SF cut‐off

Peak SF

low

Example of grating contrast sensitivity test using printed gratings

medium

Optics and Rod and cone vision

Increasing contrast

high

Spatial Frequency (c/deg)

Increasing spatial frequency

Contrast Sensitivity  (1/contrast threshold)

“Bandpass”

Increasing spatial frequency

Arthur Bradley

Arthur Bradley

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Andrew Stockman

Spatial CSFs

Refractive errors

What happens as the visual system light adapts?

Aberrations of the Eye Perfect optics

PSFs for different refractive errors

Imperfect optics

Nearsighted

Farsighted

Larry Thibos

Optics and Rod and cone vision

From Webvision, Michael Kalloniatis

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Andrew Stockman

Corrective lenses Light

Myopia

Hyperopia

Lens

Focal plane

Emmetropia (normal)

Myopia (nearsightedness)

Hyperopia (farsightedness)

Presbyopia (aged)

Presbyopia (age related far-sightedness)

Rods and cones: why do we have two types of photoreceptor?

Optics and Rod and cone vision

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Andrew Stockman

Our vision has to operate over an enormous range of   1012 (1,000,000,000,000) levels

Rods that are optimized for low light levels Cones that are optimized for higher light levels

Sunlight

Moonlight

Typical ambient light levels

Sunlight

Moonlight

Starlight

Typical ambient light levels Indoor lighting

Starlight

Indoor lighting

Visual function Visual function Absolute rod threshold

Cone threshold

Rod saturation begins

Absolute rod threshold

Damaging levels

To cover that range we have two  different types of photoreceptor...

Sensitive ROD SYSTEM Lower range

Cone threshold

Rod saturation begins

Damaging levels

Less sensitive CONE SYSTEM Upper range

Two systems Sunlight

Moonlight

Rod vision

Typical ambient light levels Indoor lighting

Starlight

Photopic retinal illuminance (log phot td)

-4.3

-2.4

-0.5

1.1

2.7

Scotopic retinal illuminance (log scot td)

-3.9

-2.0

-0.1

1.5

3.1

SCOTOPIC

Visual function

Absolute rod threshold

Scotopic levels (below cone threshold)  where rod vision  functions alone. A range of c. 103.5

MESOPIC

Cone threshold

Rod saturation begins

Mesopic levels where rod and cone  vision function  together. A range of c. 103

Optics and Rod and cone vision

4.5

6.5

8.5

4.9

6.9

8.9

 Achromatic  High sensitivity  Poor detail and no  colour

Cone vision  Achromatic and chromatic  Lower sensitivity  Detail and good colour

PHOTOPIC

Damage possible

Photopic levels (above rod saturation) where cone vision  functions alone. A range of > 106

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Andrew Stockman

ROD AND CONE DIFFERENCES

Differences in the number and distribution of cone and rod photoreceptors

Rod and cone distribution

Facts and figures There are about 120 million rods. They are absent in  the central 0.3 mm diameter area of the fovea,  known as the fovea centralis. There are only about 6 to 7 million cones. They are  much more concentrated in the fovea.

0.3 mm of eccentricity is  about 1 deg of visual angle

Optics and Rod and cone vision

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Andrew Stockman

Rod density peaks at about 20 deg eccentricity

During the day, you have to look at  things directly to see them in detail

Cones peak at the  centre of vision at 0 deg

At night, you have to look  away from things to see  them in more detail

Cone distribution and photoreceptor mosaics

Original photograph

The human cone visual system is a foveating system Simulation of what we see when  we fixate with cone vision…

Credit: Stuart Anstis, UCSD

Optics and Rod and cone vision

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Andrew Stockman

The foveal region is magnified in the cortical (brain) representation

Visual acuity gets much poorer with eccentricity

Credit: Stuart Anstis, UCSD

Rod vision is more sensitive than cone vision

Optics and Rod and cone vision

Rod and cone differences can be demonstrated  using tests of visual performance.

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Andrew Stockman

Rod and cone threshold versus intensity curves

Rods are about one thousand times  more sensitive than cones. They can be  triggered by individual photons. 

Rod‐cone break

Threshold versus target wavelength measurements Incremental flash

Rod and cone spectral sensitivity differences

Intensity

10-deg eccentric fixation

Space (x)

Optics and Rod and cone vision

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Andrew Stockman

Threshold versus target wavelength measurements

Threshold versus target wavelength measurements

Incremental flash

Incremental flash

10-deg eccentric fixation

Intensity

Intensity

10-deg eccentric fixation

Space (x)

Space (x)

Threshold versus target wavelength measurements

Rod and cone spectral sensitivity curves

Incremental flash

Plotted as “thresholds”  versus wavelength curves

Intensity

10-deg eccentric fixation

Space (x)

Optics and Rod and cone vision

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Andrew Stockman

Approximate dark‐ adapted photoreceptor  sensitivities.

Plotted as the more  conventional  spectral  “sensitivity” curve

4 3

-2

Log10 quantal sensitivity

Relative sensitivity (energy)

-1

-3

-4

-5

Rods

2 1

L

0

S

-1

M

-2 -3

Sensitivity = 1/threshold or log (sensitivity) = -log(threshold)

400

500

600

700

Wavelength (nm)

Spectral sensitivities and the Purkinje shift Peak rod sensitivity

Peak  overall cone (L&M) sensitivity

The Purkinje Shift

Log10 quantal sensitivity

0 -1 -2 -3

L

-4

Rods

S

-5

A change in the relative brightness  of colours as the light level changes  because of the difference in spectral  sensitivity between rod and cone  vision (e.g., reds and oranges  become darker as rods take over)

M Simulated: Dick Lyon & Lewis Collard at Wikimedia

400

450

500

550

600

650

700

Wavelength (nm)

Optics and Rod and cone vision

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Andrew Stockman

Suction electrode recording

Rod and cone temporal differences

Photocurrent responses

Highest flicker rates that can just be seen (c.f.f.)

FLICKER  INVISIBLE

Greater temporal integration  improves rod sensitivity (but  reduces temporal acuity)

Rods

Cones FLICKER  VISIBLE Photopically (cone) equated  scale

Optics and Rod and cone vision

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Andrew Stockman

Rod and cone visual acuities

König (1897) 1/1.6=.63

1/1=1

Rod and cone spatial differences (visual acuity) 1/.2=5

Rods

Rods

The acuity here is defined as  the reciprocal value of the  size of the gap (measured in  arc minutes) that can be  reliably identified.

Rod and cone visual acuities

König (1897)

Greater spatial integration  improves rod sensitivity  but reduces acuity The loss must be  postreceptoral because  the rods are smaller than  cones in the periphery)

Optics and Rod and cone vision

Rod and cone directional sensitivity differences Rods

Rods

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Andrew Stockman

Rod vision saturates – under most conditions cone vision does not. Stiles-Crawford effect

Rod threshold versus intensity (tvi) curves Failure of adaptation (saturation)

Weber’s Law I/I=k or logI =logI +c

Rod dark adaptation takes much longer than cone dark adaptation

Adaptation

Source: Barlow and Mollon, 1982

Optics and Rod and cone vision

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Andrew Stockman

Rod-cone dark adaptation curves

Rod-cone dark adaptation curves Cone plateau

Rod‐cone break

Rods take much longer to recover after a  bleach than cones

From Hecht, Haig & Chase (1937)

Cone vision is chromatic and rod vision is achromatic

The sensitivity loss during dark adaptation is much greater than the fraction of pigment bleached. For example, with a bleach of about 5% the sensitivity loss is more than 1000-fold. Rather than the lack of photopigment, it is the presence of a photoproduct that causes the sensitivity loss.

Optics and Rod and cone vision

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Andrew Stockman

Rod vision

Cone vision

 Achromatic  High sensitivity  Poor detail and no colour

 Achromatic and chromatic  Lower sensitivity  Detail and good colour

Rod vision is achromatic

Why?

UNIVARIANCE Vision at the photoreceptor stage is relatively  simple because the output of each  photoreceptor is:

UNIVARIANT

Crucially, the effect of any absorbed photon is independent of its wavelength.

Rod

What does univariant mean? Once absorbed a photon produces the same change in photoreceptor output whatever its wavelength.

Optics and Rod and cone vision

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Andrew Stockman

UNIVARIANCE

UNIVARIANCE

Crucially, the effect of any absorbed photon is independent of its wavelength.

Crucially, the effect of any absorbed photon is independent of its wavelength.

Rod

UNIVARIANCE What does vary with wavelength is the probability that a photon will be absorbed.

This is reflected in what is called a “spectral sensitivity function”.

All the photoreceptor effectively does is to count photons.

Rod spectral sensitivity function (also known as the scotopic luminosity curve, CIE V)

Log relative sensitivity (energy units)

So, if you monitor the rod output, you can’t tell which “colour” of photon has been absorbed.

Rod

0

More sensitive

-1

Less sensitive

-2 -3

CIE V'

-4 -5 -6 -7 400

500

600

700

800

Wavelength (nm)

Optics and Rod and cone vision

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Andrew Stockman Rod spectral sensitivity function (V)

Linear sensitivity plot

0 -1

10V’

-2

CIE V'

-3

log(V)

-4 -5 -6

Much more detail at lower sensitivities

-7 400

500

600

700

800

Relative sensitivity (energy units)

Log relative sensitivity (energy units)

Logarithmic sensitivity plot 1.0

CIE V'

0.8 0.6 0.4 0.2 0.0 400

Wavelength (nm)

500

600

700

800

Wavelength (nm)

Log relative sensitivity (energy units)

Rod spectral sensitivity function (V)

In order of rod sensitivity:

0

> > > >

-1

> > > >

-2 -3

CIE V'

-4 -5 -6 -7 400

500

600

700

800

0 -1

So, imagine you have four lights of the same intensity (indicated here by the height)

-2 -3

The green will look brightest, then blue, then yellow and lastly the red will be the dimmest

CIE V'

-4 -5 -6 -7 400

500

600

700

Wavelength (nm)

Optics and Rod and cone vision

800

Log relative sensitivity (energy units)

Log relative sensitivity (energy units)

Wavelength (nm)

0 -1

We can adjust the intensities to compensate for the sensitivity differences.

-2 -3

When this has been done, the four lights will look completely identical.

CIE V'

-4 -5 -6 -7 400

500

600

700

800

Wavelength (nm)

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Andrew Stockman

UNIVARIANCE A change in photoreceptor output can be caused by a change in intensity or by a change in colour. There is no way of telling which.

Rod Colour or intensity change?? Changes in light intensity are confounded with changes in colour (wavelength)

A consequence of univariance is that we are colour-blind when only one photoreceptor operates…

Each photoreceptor is therefore ‘colour blind’, and is unable to distinguish between changes in colour and changes in intensity.

With three cone photoreceptors, our colour vision is chromatic…

Examples: SCOTOPIC VISION, cone monochromacy

Optics and Rod and cone vision

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Andrew Stockman

Cone spectral sensitivities Log10 quantal sensitivity

0

L

So, if each photoreceptor is colour‐ blind, how do we see colour?

M

-1

S -2

Or to put it another way: How is  colour encoded? -3 400

450

500

550

600

650

700

Wavelength (nm)

Colour is encoded by the relative cone outputs

Colour is encoded by the relative cone outputs

Blue light

Blue light 0

Log10 quantal sensitivity

Log10 quantal sensitivity

0

L -1

S

M

-2

-3

L -1

S

M Red light

-2

-3 400

450

500

550

600

Wavelength (nm)

Optics and Rod and cone vision

650

700

400

450

500

550

600

650

700

Wavelength (nm)

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Andrew Stockman Colour is encoded by the relative cone outputs Blue light

Colour is encoded by the relative cone outputs Blue light

Red light

Green light

Purple light

Yellow light

White light

Log10 quantal sensitivity

0

L -1

S

Green light

M

-2

Red light

-3 400

450

500

550

600

650

700

Wavelength (nm)

Rod vision  Achromatic  High sensitivity  Poor detail and no colour

Optics and Rod and cone vision

Cone vision  Achromatic and chromatic  Lower sensitivity  Detail and good colour

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