basic visual science core · 2018. 10. 3. · basic visual science core absolute and increment...

BASIC VISUAL SCIENCE CORE

Absolute and Increment Thresholds

Ronald S. Harwerth

Fall, 2018

1. Psychophysics of Vision

2. Light and Dark Adaptation

Michael Kalloniatis and Charles Luu

The Neuron Doctrine for Perception

• The neural basis for

behavior - there should be a

correlation between

psychophysically

determined functions and

neurophysiology.

• An early example - Hartline

proposed that lateral

inhibition, similar to that

measured in a Limulus eye,

could account for Mach

bands.

Mach Bands

Mach Bands

Limulus Eyes

• The lateral eyes of Limulus

(Horseshoe crab) are faceted.

• The visual receptors (ommatidia) are

connected by lateral neurons.

• The lateral interactions between

ommatidia are inhibitory.

A: Limulus lateral eye. Dark spots in

photograph are individual ommatidia.

Width of eye ∼1 cm.

B: Schematic drawing of an ommatidium

in the lateral eye. l, lens; a, aperture; b,

rhabdomere; r, retinular cell; p,

pigment cell; e, eccentric cell; i,

synaptic sites of self and lateral

inhibition; x, site of spike generation.

Diameter of ommatidium ∼250 μm.

C: Functional diagram of optical and

neural mechanisms operating in the

lateral eye that transform visual

scenes into patterns of optic nerve

activity, or neural images.

Limulus Eyes

Passaglia, et al., J Neuro Physiol 1998;80:1800-1815.

http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=hctN_L7CoGnXnM&tbnid=bVgymsiRdi3gfM:&ved=0CAgQjRwwAA&url=http://jn.physiology.org/content/80/4/1800/F1.expansion&ei=DRJwUvbhIaWF2gXsn4FA&psig=AFQjCNH8xggObb5HIBrC67r5OsZRLjbJpw&ust=1383162765585690http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=hctN_L7CoGnXnM&tbnid=bVgymsiRdi3gfM:&ved=0CAgQjRwwAA&url=http://jn.physiology.org/content/80/4/1800/F1.expansion&ei=DRJwUvbhIaWF2gXsn4FA&psig=AFQjCNH8xggObb5HIBrC67r5OsZRLjbJpw&ust=1383162765585690

Lateral Inhibition in Limulus Eyes

Log intensity falling

on inhibiting spot

Distance between inhibiting

and inhibited facets

De

cre

as

e in

fre

qu

en

cy

(im

pu

lse

s p

er

se

c)

• Lateral inhibition in the Limulus eye is directly proportional

to the intensity of the inhibiting stimulus and inversely

proportional to the distance of the inhibiting ommatidium.

Lateral Inhibition and Mach Bands

•

• Based on the

neurophysiology of the

Limulus eye, the lateral

inhibition from receptors to

the left of the green spot will

be greater than the inhibition

from the receptors to the

right.

• The lower figure shows

recordings from an

ommatidium as an edge

moves across the eye with

either, all other ommatida

occluded (triangles) or

illuminated (circles).

• The activity of a single nerve cell and influences

of other cells is a complete enough description

for understanding the nervous system.

• The sensory system is organized to achieve as

complete representation as possible with the

minimum number of active neurons.

• The frequency of neural impulses codes

certainty: a high impulse frequency corresponds

to a high degree of certainty that the cause of

the percept is present.

The Neuron Doctrine for Perception:

Barlow’s Dogma

Barlow, HB. Perception 1972;1:371 – 394.

Definitions:


Response continuum

Stimulus continuum

R0

S0

• Absolute threshold - the lowest energy level (S0 ) that can be

perceived (R0).

• Increment threshold (differential threshold) - the lowest

amount of energy which must be added to an existing

stimulus intensity in order to see a change in the stimulus.

• Increment thresholds often follow the predictions of Weber’s

law (I / I = K) or Fechner’s law (R = K * log(S)).

R1

S1

R2

S2

I I


Weber’s Law

• I / I = K

• Log transformation

log(I) = log(I) + log(K)

• Weber’s law predicts a

linear relationship between

the log threshold intensity

and log background

intensity with a slope = 1

and y-intercept = K.

Log background intensity

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Background

Test

field


Fechner’s law• R = K * log(S)

• Fechner’s law predicts a

linear relationship between

the response magnitude and

log background intensity

with a slope = K and y-

intercept = 0.


Resp

on

se m

ag

nit

ud

e

Background

Test

field



I0

The form of empirical data

follows the form:

I = (IB2 + ID

2) 0.5

where

I = increment threshold

IB = background intensity

ID = intrinsic noise

IB

ID

The Classic Experiments of

Hecht, Shlaer and Pirenne

• Experiments designed to determine the absolute

minimum intensity of light needed for vision.

• The results provided important data to answer two

basic questions.

1. Is there an absolute threshold for seeing?

2. What is the minimum number of neural

impulses required for seeing?

Hecht, Shlaer, & Pirenne, J Gen Physiol. 1942;25:819–840.



1. Is there an absolute threshold for seeing?

• The psychometric or

“frequency-of-seeing”

function is an ogive or “S-

shaped” curve (black line),

not a step function (green

line) that would be predicted

for a system with and

absolute threshold.

• The shape of the function

indicates that there is noise

in the measurement.



2. What is the minimum number of neural impulses

required for seeing?

• Light has a quantum nature

(E = h).

where:

E = energy of a quantum

h = Plank’s constant

= the frequency of light

• The number of quanta at

threshold = the number of

rhodopsin isomerizations =

the number of neural

impluses generated.


The critical parameters for empirical measurements of

absolute thresholds:

• There are three peaks in the

absorption spectrum of

rhodopsin.

• The action of light on

rhodopsin causes a shift in

the absorption peak in visible

light (. peak).

• The absorption spectrum also

represents the probability of

absorption of a quantum of

light.

1. The wavelength of the test stimulus (510 nm).




• After correction for pre-retinal

light losses, the spectral

sensitivity of the dark adapted

eye matches the absorption

spectrum of rhodopsin.

• The optimal wavelength - the

highest probability for

absorption of quanta - will be

close to the peak absorption

of rhodopsin at 505 nm.

1. The wavelength of the test stimulus (510 nm).




• The density of cones

and rods varies

across the retina.

• The optimal stimulus

location will be the

eccentricity with the

highest density of

rod photoreceptors -

about 20 deg, on

temporal retinal to

avoid the optic nerve

head.

2. The retinal area for the test stimulus (20 deg, temporal retina).




• Diagram of fixation and test

field.

2. The retinal area for the test stimulus (20 deg, temporal retina).




• The visual threshold

decreases with time in the

dark (dark adaptation).

• The absolute threshold cannot

be measured until the time of

the final rod threshold.

3. The state of adaptation (30 - 40 min of dark adaptation).

Cone phase

Rod phase

Rod - cone break

Final rod

threshold

Time in the dark (min)




• The visual threshold

decreases with time in the

dark (dark adaptation).

• The time of the rod-cone

break and the final rod

threshold depend on the

amount of light adaptation

prior to dark adaptation.

• The final rod threshold will

occur after 30 - 40 min of

dark adaptation, even after

intense rhodopsin bleaching.

3. The state of adaptation (30 - 40 min of dark adaptation).

Time in the dark (min)




• Bloch’s law (I * t) = k for t < tc,

I = k for t > tc, where

I = threshold intensity

t = time

k = constant

• For stimulus duration of less

than 80 - 100 mesc, threshold

is determined by total energy

(I * t).

• For stimulus duration greater

than a critical duration (tc),

threshold is determined by

stimulus intensity (I = k).

4. The duration of the stimulus (1 msec).

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Log stimulus duration (msec)

-1 0 1 2

tc

(I * t) = k

I = k




• Bloch’s law (I * t) = k for t < tc, I

= k for t > tc, where


t = time

k = constant

• The plotted data show the

product I * t as a function of t

for central and peripheral

stimuli, to illustrate the

constant integration across

the retina.

4. The duration of the stimulus (Bloch’s law).

Log time




• Ricco’s law (I * a) = k for a < ac,

I = k for a > ac, where


a = area

k = constant

• The ac depends on the retinal

eccentricity - at an eccentricity

of 20 deg the reciprocity for

area and intensity holds for

stimulus diameters up to

about 1 deg.

• For foveal vision, ac is about 5

min diameter.

5. The size of the stimulus (10 min diameter).

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Log stimulus diameter (deg)

-2 -1 0

ac

(I * a) = k

I = k




• Ricco’s law (I * a) = k for a < ac,

I = k for a > ac, where


a = area

k = constant

• The psychophysical

thresholds as a function of the

diameter of the stimuli for

foveal and peripheral stimuli

illustrate the differences in

integration of central and

peripheral retina.

5. The size of the stimulus (Ricco’s law).

Log radius




6. The psychophysical method for determining

thresholds.

1. The method-of-adjustment - The subject adjusts the

intensity of the stimulus to a “just-seen” (or “not

seen”) level.

2. The method-of-limits - Stimuli intensities are decreased

(or increased) in discreet steps to determine the

threshold.

3. The method-of-constant stimuli - Stimuli of fixed

intensities are presented in random order to determine

the frequency-of-seeing for each intensity level.


The results: Method-of-limits measurements

• For the three observers, 54 -148 quanta, at the cornea, were

necessary for seeing. How many quanta were absorbed by

rhodopsin?

• Approximate values for the major losses of light

1. The cornea reflects 4% of the light.

2. The crystalline lens absorbs 50% of light at 505 nm.

3. 80% of the light passes between the rod receptors.

• The threshold intensities represent 5 - 14 quanta absorbed

by the photopigments.

• Conclusion - the threshold for seeing is determined by a

small number of rods, each absorbing a single quantum,

within a certain area and time.


The results: The absolute threshold

1. A single quantum is sufficient to activate a rod.

• At the 20 deg eccentricity, the 10 min diameter test stimulus

covered approximately 500 rods, therefore, the probability

of “double hits” for a single receptor is extremely small.

2. A single quantum is insufficient for seeing.

• A threshold of a single quantum is incompatible with

Ricco’s law or probability summation.

• At the retinal area of stimulation, Ricco’s law predicts

pooling of signals from over 17,000 rods.

3. If there is an absolute threshold for seeing, why is there

a finite slope for psychometric functions?


The results: Method-of-constant stimuli

1. Further evidence for an absolute threshold was derived

by modeling their psychometric functions.

Log average number of quanta per flash-1 0 1

• The Poission distribution

pn = an / ea n!

• The Poission probability

distribution is a binomial

distribution that is valid for

a situation where there is a

large number of possible

events, but a very few

actually occur.

n = 1



1. The family of Poission probability distributions represent templates to describe the psychometric function for each

value of n.

2. The shape of the function

will be constant,

regardless of its location

on the abscissa because of

the logarithmic coordinate.



1. The templates for 5 - 7 quanta matched the psychometric

functions for the three investigators.

2. The model is compatible with an absolute threshold.

For example, Subject S.H. reported “seen” any time 6,

or more, quanta were absorbed and never said “seen” if

less than 6 quanta were absorbed.



3. If the quantum efficiency is 1.0, then S.H. saw the light

every time that 6 neural impulses were generated.

4. If there is an absolute threshold, then the noise in the

threshold measure must arise from non-biological sources,

probably the variability of the stimulus.


Further considerations: Is there an absolute threshold?

1. The experiments did not consider criterion effects on

threshold measurements. For the data shown, the subjects

all used a very conservative criterion for saying “seen”

because the false alarm rate for each psychometric

function is zero.

Is there an absolute threshold?

1. In Sakitt’s experiments

(“Counting Every

Quantum”), the subjects

were trained to scale the

apparent brightness of test

stimuli seen at near

threshold intensities.

2. She found that some

subjects could reliably

detect a single quantum

and discriminate between

intensity increments of

one quantum - there was

no absolute threshold.

Sakitt, B. J Physiol. 1972;233:131-150


1. In more recent

experiments, Teich, et al.,

investigated the effect of

criterion on the absolute

threshold.

2. They confirmed the

results of HS&P if they

instructed their subjects

to use a strict criterion for

reporting “seen” (< 5%

false alarm rate).

Teich, MC. et al., J Opt Soc Am. 1982;72:419-431


3. With a more lax response

criterion, the subject’s

false alarm rates were

elevated, but the

psychometric functions

still demonstrated a

systematic relationship to

the intensity of the

stimulus.

4. An absolute threshold

(60% correct) of 1 quantum

is possible, if a false alarm

rate of 55% is acceptable.

Teich, MC. et al., J Opt Soc Am. 1982;72:419-431

Frequency of seeing curves for subject using a lenient criterion (diamonds), to progressively more strict criteria (squares),

(triangles), and (circles).

After adjusting for the non-zero false positive rate 1the curves for the two most lenient criteria, collapse onto each other, indicating

no net benefit to detection.

Solid curves are nonlinear least-squares Weibull fits to the frequency of seeing data.

The Absolute Threshold for Cone Vision

Koeing, D & Hofer, H. Jvis. 2011, 11

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3671617/#FD1

Is there an absolute threshold for

photopic vision?

1. The photopic system is most

often studied under light

adapted conditions because it

is a high resolution, color

system - not ordinarily

operating in a quantum limited

environment.

2. An absolute threshold with dark

adaptation has been measured.

Under optimal conditions

(small, short, foveal test target),

the absolute threshold is about

1000 quanta - statistically

compatible with 5 - 7 quanta

absorptions per cone, with

pooling over about 40 cones.

Is there an absolute threshold for

photopic vision?

1. The more recent analyses of

the slopes of psychometric

functions and spatial

summation functions under

dark and light adaptation

have provided evidence

against a multiple hit

hypothesis.

2. The higher threshold for

photopic vision may be

caused by higher intrinsic

noise in cones than rods.

cones rods

Donner, K. Vision Res. 1992;32:853-866

Brightness Discrimination

(increment-threshold spectral sensitivity)

Adaptation field

Test field

Methods:

1. White or chromatic adaptation

field (background) to obtain static

photopic state.

2. Threshold - the smallest

perceptible light increment (I of

the monochromatic test field

added to the adapting

background (I).

3. Sensitivity = log (1 / threshold

intensity).

Distance

Inte

nsit

y

I

I

Increment threshold studies of visual

function.

1. The increment threshold as a

function of background

intensity is commonly known

as a tvi (threshold-versus-

intensity) function.

2. The three independent

variables of tvi functions are

• the absolute threshold (a)

• the intrinsic noise (Id)

• the slope of the adaptation

portion of the function (b)

(It)

(Ib)

The tvi relationship is

It = a (Ib + Id) b

b

Ida


function.

1. A common paradigm for

increment thresholds is to

determine the least perceptible

amount of light that must be

added to a stationary

background as a function of the

intensity of the background.

Background field

500 nm

Test field

580 nm


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10 deg parafoveal

function -

500 nm background

580 nm test

Stiles, WS. Proc Nat Acad Sci USA., 1959;45:100-114.

Subjective methods of defining

the cone fundamentals

• Stiles’ two-color, increment-threshold

spectral sensitivity.

• Assumptions:

1. In any area of the retina there are

several different photopigments, but

the one with highest sensitivity will

determine the visual threshold.

2. Photopigments that differ in their

spectral locations will adapt at

different rates for a given wavelength

of the background.

3. Cone mechanisms can be identified

by “threshold-versus-intensity” (TVI)

functions.

Background Intensity

Stiles’ TVI functions

• With the correct choice of test

field and background

wavelengths, the color vision

mechanisms can be isolated

and their spectral sensitivities

investigated.

• The example shows two

independent color vision

mechanisms, one more

sensitive to the 480 nm test

field at absolute threshold and

which adapts more rapidly to

the 540 nm background field.

Stiles’ TVI functions

• Measurements of TVI

functions across

wavelengths provides

data to derive the

spectra response

function for each

mechanism.

• Initially, Stiles called

the functions cone

photopigments, but

later called them the “pi

mechanisms.”

Stiles’ pi mechanisms

• Stiles presented data for 5

independent photopic mechanisms

and 1 scotopic mechanism.

0 - rod photopigment

1 - SW mechanism

2 - SW & MW mechanism

3 - SW mechanism

4 - MW mechanism

5 - LW mechanism

Human Cone Spectral Sensitivities

• Cone spectral sensitivities based on measurements in

normal trichromats, dichromats, and monochromats.

Cone Sensitivities by Objective Methods

Wavelength (nm)

• The spectral sensitivities of

the three cone types in the

primate retina.

• The sensitivities were

determined over a 6 log unit

range.

• The MW and LW cone

sensitivities overlap across

the entire visible spectrum,

but the SW cone sensitivity is

more separated (max’s at

435, 535, & 570 nm).

Wavenumber (cm-1)


function - rod saturation.

Background field

580 nm

Test field

500 nm


(scotopic trolands)

9 deg parafoveal

function -

580 nm background

500 nm test

1. Aguilar & Stiles - Why do the

rods stop contributing to

vision at photopic adaptation

levels?

2. The rod response saturates at

about 100 scotopic trolands;

cone responses do not

saturate.

Aguilar, M, & Stiles, WS. Acta Optica 1954;1:59-65


function - Westheimer functions.

1. Westheimer functions - also called spatial interaction functions

or perceptive fields - are psychophysical measures of the center

(++) and surround (--) dimensions of retinal receptive fields.

2. The measurement

involves the increment

threshold for a small test

field (~ 5 arcmin) on a

background of variable size,

but with a constant

intensity.

+ +

- - -

- - -

Westheimer, G. J Physiol. 1967;190:139–154



1. The first measurement, without a background,

establishes the threshold of the receptive field without

interacting stimuli.

Diameter of background (deg)

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field

•

•

• ••

•• • •

1



2. Subsequent measurements involve increment

thresholds with a varying size background. When the

background is smaller than the receptive field center,

the increased noise causes an elevation of the

increment threshold.


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test

field

•

•

• ••

•• • •

1

•2



3. As measurements are made with larger backgrounds,

as long as the background is smaller than the receptive

field center, the elevation of the increment threshold is

proportional to the size of the background field.


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test

field

•

•

• ••

•• • •

1

2

3

•



4. The highest increment threshold will occur when the

size of the background matches the size of the receptive

field center. The portion of the Westheimer function

showing increasing threshold as a function of increasing

field size is called the desensitization limb.


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test

field

•

•

• ••

•• • •

1

•2

3

4 Desensitization

limb

Size of

receptive

field center



5. When the size of the background is larger than the

receptive field center, the opponent activity of the

surround reduces the noise induced by the center and,

thus, results in a relatively lower threshold .


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field

•

•

• ••

•• • •

1

•2

3

4

5



6. The reduction in the increment threshold intensity

continues with increasing field size, because the

background stimulation of the surround is more effective

in canceling the activity of the receptive field center .


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test

field

•

•

• ••

•• • •

1

•2

3

4

5

6



7. When the size of the background matches the size of the

surround of the receptive field, the field is maximally

effective in canceling the activity of the center by the

receptive field surround mechanism.


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test

field

•

•

• ••

•• • •

1

•2

3

4

5

6 7



8. Background sizes larger than the total size of the

receptive field do not cause changes in the increment

threshold intensity. The portion of the Westheimer

function showing decreasing threshold as a function of

increasing field size is called the sensitization limb.


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field

•

•

• ••

•• • •

1

•2

3

4

5

6 7 8

Sensitization

limb

Total size of

receptive field



The final result is a psychophysical measurement of the

center and surround sizes of the receptive field sizes at the

retinal location of the measurement.


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field

•

•

• ••

•• • •

1

2

3

4

5

6 7 8++

- - -

- - -

center center + surround



• Examples of Westheimer functions, under photopic

conditions, as a function of retinal eccentricity.

• The sizes of the center and surround increase as a function of

eccentricity, but a clear center-surround organization is

apparent at all eccentricities.



• Examples of Westheimer functions, under scotopic

conditions, as a function of retinal eccentricity.

• The size of the receptive field center increases as a function

of eccentricity, but under scotopic viewing the receptive

fields do not exhibit clearly the center-surround properties

of photopic functions.

The Neuron Doctrine for Perception

There should be a correlation between psychophysically determined functions and neurophysiology.

There are systematic relationships between stimulus parameters (size, duration, wavelength) that are based on

physiological properties.

The work of Hecht, Shlaer and Pirenne demonstrates the power of combining empirical data and modelling.

Studies of Westheimer functions have demonstrated relationships between the structure of receptive fields and

measures of vision function by increment thresholds.

basic visual science core · 2018. 10. 3. · basic visual science core absolute and increment...

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