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 logI =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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