Intensity discrimination is the process of distinguishing one stimulus intensity from another

Intensity Discrimination

Two types:

Difference thresholds – the two stimuli are physically separate

Increment thresholds – the two stimuli are immediately adjacent or superimposed

Fig. 1.1

Increment

Difference

LLTLLT

L T = L + L L T = L - L

L

LT=L+L

LT=L-L

+L

-L

0

A B

Luminance

Fig. 1.2

Task: find the threshold ΔL

Quantum fluctuations provide a theoretical lower limit for

intensity discrimination by an “ideal” observer

Theory and Practice of Increment Thresholds

Theory:

Number of Quanta in a Flash

0 5 10 15 20 25 30

0.0

0.4

Probability that thenumbers of quantaon the x-axis will occur in any given flash

Mean = 1

Mean = 2

Mean = 4

Mean = 8

Mean = 16

Fig. 2.7

To distinguish a flash with a mean of 8 from a flash with a mean of 9 quanta is impossible! The distributions overlap almost completely

1 6

11 16 21 26 31 36

S1

0

0.05

0.1

0.15

Series1

Series2

Mean of 8, vs. mean of 9

Just based on the number of photons in the two distributions, there is too much overlap for it to be possible to detect 9 vs. 8

1 6

11 16 21 26 31 36

S1

0

0.05

0.1

0.15

Series1

Series2

Mean of 8, vs. mean of 12

1 6

11 16 21 26 31 36

S1

0

0.05

0.1

0.15

Series1

Series2

Mean of 8, vs. mean of 16

1 6

11 16 21 26 31 36

S1

0

0.05

0.1

0.15

Series1

Series2

Mean of 8, vs. mean of 20

In a Poisson distribution, the variance is equal to the mean.

The standard deviation (SD) is the square root of the mean.

In a two-alternative forced-choice task, to reach threshold (75% correct), LT must differ from L by 0.95 SD. (e.g., threshold L = 0.95 SD)

1 6

11 16 21 26 31 36

S1

0

0.05

0.1

0.15

Series1

Series2

Mean of 8 photons, SD = √8 = 2.8

0.95 x 2.8 = 2.7

Can just detect 11 photon flash as different from 8 at threshold

1 6

11 16 21 26 31 36

S1

0

0.05

0.1

0.15

Series1

Series2

Moreover, as L increases, the minimum L needed to reach threshold also increases with the

Lbecause the variance in a Poisson distribution equals the mean, so the SD changes with the square root of the mean

deVries-Rose Law (deVries, 1943;Rose, 1948):

KLL

where L is the threshold luminance difference, L is the

background, or reference, luminance and K is a constant.

An “ideal” observer would follow the

Theory and Practice

In practice:

at low background intensities, human observers behave as an ideal detector (follow the deVries-Rose Law)

L (milliLamberts)

L (milliLamberts)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Fig. 3.1

deVries-Rose Law holds

Line = DeVries-Rose law prediction

Circles = data

At higher intensity levels, the intensity discrimination

threshold is higher than expected from an ideal detector

(e.g., Weber’s Law holds)

The constant proportional relationship between the increment

threshold and the reference or background level is called

Weber’s law, which is mathematically expressed as:

KLL where L is the threshold luminance difference, L is thebackground, or reference, luminance and K is a constant.

Weber’s Law

L (milliLamberts)

L (milliLamberts)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Fig. 3.1

Weber’s Law holds

the fraction: threshold L divided by the reference luminance,

L is called the “Weber fraction” (threshold L / L)

You always can determine the Weber fraction, even when Weber’s Law does not hold

L (milliLamberts)

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

L/L

0.0

0.2

0.4

0.6

0.8

1.0

Weber’s Law holds

Weber’s Law does NOT hold(L/ L rises as L decreases)

Fig. 3.2

The x-axis is the same as in Fig. 3.1 but now the y-axis is the Weber fraction

Both the deVries-Rose and Weber’s laws fail to account

The increment threshold data of a rod monochromat (circles) plotted alongwith the theoretical lower limit (deVries-Rose, dotted line) and the predictions of Weber’s

Law (solid line). Luminance values are in cd/m2 . (Redrawn from Hess et al. (1990)

Log Background Intensity, L (cd/m2)

-6 -4 -2 0 2 4 6

Log Increment Threshold, L

-6

-4

-2

0

2

4

6

Predicted by DeVries Rose Law

Predicted by Weber's Law

Fig. 3.3

for thresholds at high light intensities

The Weber Fraction is affected by stimulus size, duration,

wavelength, and retinal location (eccentricity from the fovea)

More practical issues:

How changes in other stimulus dimensions affect the Weber fraction

Log Background Intensity, L (cd/m2)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3

Log Weber Fraction, L/L

-3

-2

-1

0

1

2

121'55'18'10'4'

Test Field DiameterFig. 3.4

#1 Stimulus size: the Weber fraction is lower (smaller) for larger test stimuli

Log Background Intensity, L (cd/m2)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3

Log Weber Fraction, L/L

-3

-2

-1

0

1

2

121'

4'Test Field Diameter

More practical issues: Is a target visible under certain conditions?

Is a spot with a particular luminance, relative to background, visible? It depends on its size.

This is the target’s Weber fraction. It is NOT a threshold

If the target is 121’, it is visible

If 4’, it is not visible

Need to distinguish between the Weber fraction of a target vs. the threshold of a viewer.

For a subject or patient viewing a target, if the subject’s Weber fraction is below a line, then the subject’s threshold is better (smaller).

If the Weber fraction of a target is below the line, the target is NOT visible to someone whose threshold is on the line.

The “dinner plate” example:

121’ plate with luminance (LT) of 0.0102 footlamberts. Background is 0.01 footlamberts

The Weber fraction for the plate is: L/L

L is (LT – L) = 0.0102 – 0.01 = 0.0002

L is 0.01

Target’s Weber fraction - L/L = 0.0002/0.01 = 0.02 (plate is 2% more intense than the background)

Plot this on Fig. 3.4 – Is this going to be visible?

Need to compare actual plate Weber fraction with human Weber fraction.

Log Background Intensity, L (cd/m2)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3

Log Weber Fraction, L/L

-3

-2

-1

0

1

2

121'55'18'10'4'

Test Field Diameter

.

Target ΔL/L is less than the human threshold for a 121’ stimulus, so target is not visible.

Log Background Intensity, L (cd/m2)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3

Log Weber Fraction, L/L

-3

-2

-1

0

1

2

121'

4'Test Field Diameter

More practical issues: Is a target visible under certain conditions?

Is a spot with a particular luminance, relative to background, visible? It depends on its size.

Plate’s Weber fraction

Threshold Weber

fraction for 121’ objects

On Figure 3-4, can see that this is not visible.

The target’s Weber fraction is less than an average person’s threshold

Note: in lab, when you plot the value of YOUR threshold ΔL/L and it is below the 121’ line, that means YOU can have a lower threshold than that group of people.

The Weber Fraction is affected by stimulus size, duration,

wavelength, and retinal location (eccentricity from the fovea)

More practical issues:

How changes in other stimulus dimensions affect the Weber fraction

#2 Short-duration flashes are harder to see (are less discriminable) than long-duration flashes

That is, the threshold L increases as flash duration becomes shorter.

Continuing: How changes in other stimulus dimensions affect the Weber fraction

#3 Threshold L varies with eccentricity from the fovea

At low luminance levels, threshold is lowest (sensitivity is highest) about 15-20 degrees from fovea and the fovea is “blind”

At high luminance levels, threshold is lowest at the fovea

Continuing: How changes in other stimulus dimensions affect the Weber fraction

Sensitivity = 1/threshold

Increment threshold as a function of eccentricity from the fovea for several luminance levels. The top line shows the threshold when the background luminance (L) is very low (0 apostilbs). The bottom line shows the threshold for a background L of 1000 apostilbs. Note, on the Y-axis, that lower thresholds (higher sensitivities) are upwards on the graph. (Modified from (Lynn, Felman & Starita, 1996).)

Angular Distance From Fixation (deg)

-60 -45 -30 -15 0 15 30 45 60 75 90

Log Increment Threshold, L (Apostilbs)-4

-3

-2

-1

0

1

2

3

00.0010.010.11101001000

Backgroundluminance, LFig. 3.5

Note: threshold axis is “upside down”

Intensity discrimination can be limited at many places

within the visual system

But typically limitations originate in the retina

Sensory Magnitude Scales Revisited

Using the “just noticeable difference” (jnd) to create a scale for sensory magnitude vs. stimulus magnitude

L + threshold L = LT

LT is one jnd more intense than L.

LT + threshold L = LT2

LT2 is one jnd more intense than LT

And so on…

Stimulus Luminance, L (cd/m 2)

0 50 100 150 200

Sensory Magnitude

0

2

4

6

8

10

12

L

Stimulus Luminance, L (cd/m 2)

0 50 100 150 200

Sensory Magnitude

0

2

4

6

8

10

12

LT

L

L + threshold L = LT

LT is one “just noticeable difference” (jnd) more intense than L.

Stimulus Luminance, L (cd/m 2)

0 50 100 150 200

Sensory Magnitude

0

2

4

6

8

10

12

LT + threshold L = LT2

LT2 is one jnd more intense than LT

and 2 jnd’s larger than L

LT

L

LT2

Stimulus Luminance, L (cd/m 2)

0 50 100 150 200

Sensory Magnitude

0

2

4

6

8

10

12

When Weber’s Law holds, the threshold Ls keep getting larger, so 1 jnd is a larger increase in stimulus luminance

LT

L

LT2

LTnLTn+1

Stimulus Luminance, L (cd/m 2)

0 50 100 150 200

Sensory Magnitude

0

2

4

6

8

10

12

Fechner's Law: Log(L)

Fechner’s Law

F e c h n e r ’ s L a w r e l a t e s t h e m a g n i t u d e o f s e n s a t i o n t o t h e

i n c r e m e n t t h r e s h o l d

F e c h n e r ’ s l a w :

)log(k

w h e r e i s s e n s o r y m a g n i t u d e , i s a n a r b i t r a r y c o n s t a n t

d e t e r m i n i n g t h e s c a l e u n i t , a n d i s t h e s t i m u l u s m a g n i t u d e

Stimulus Luminance, L (cd/m2)

0 50 100 150 200

Sensory Magnitude

0

2

4

6

8

10

12

Stevens' Law: L0.15

Fechner's Law: Log(L)

Comparing Fechner’s Law with Stevens’ Power Law

Stevens’ Power Law resembles Fechner’s Law when the exponent is <1

Fig. 3.6

Increment threshold measures are important in clinical

vision testing

Measuring increment thresholds in patients is best done

under conditions where the Weber fraction is constant

(e.g., Weber’s Law holds)

Visual field testing represents a major clinical application forthe use of the increment threshold

Increment threshold as a function of eccentricity from the fovea for several luminance levels. The top line shows the threshold when the background luminance (L) is very low (0 apostilbs). The bottom line shows the threshold for a background L of 1000 apostilbs. Note, on the Y-axis, that lower thresholds (higher sensitivities) are upwards on the graph. (Modified from (Lynn, Felman & Starita, 1996).)

Angular Distance From Fixation (deg)

-60 -45 -30 -15 0 15 30 45 60 75 90

Log Increment Threshold, L (Apostilbs)-4

-3

-2

-1

0

1

2

3

00.0010.010.11101001000

Backgroundluminance, LFig. 3.6

Differential Light Sensitivity

Illustration of the “Hill of Vision”. The fovea corresponds to the region of greatest sensitivity(smallest increment threshold). Small and dim spots may be seen at this point, but largerand/or more intense spots are needed to reach threshold as the spot is presented further fromthe fovea. The black oval marks the optic disc where sensitivity is 0. In the usual plots of visualfields, this “hill” is represented on a two-dimensional plot at isopters or as a gray scale.Redrawn from Anderson (1987).

Fig. 3.7

In kinetic perimetry an increment of constant size and intensity is moved

across the patient’s view until the patient can notice it, thus defining a

point on an isopter. A set of such points determined for a number

directions of target movement around the fixation point defines the

isopter for the target used.

Measuring the Visual Field: Perimetry

In static perimetry, the luminance of a threshold increment at specific

points in the visual field is measured. Computer-automated devices, such

as the Humphrey Field Analyzer, are typically used for static perimetry.

Automated Visual Field testers use multiple staircases with unequal down and up steps to “home in” on threshold very quickly

A classic example of psychophysical measurement procedures

Increment threshold as a function of eccentricity from the fovea for several luminance levels. The top line shows the threshold when the background luminance (L) is very low (0 apostilbs). The bottom line shows the threshold for a background L of 1000 apostilbs. Note, on the Y-axis, that lower thresholds (higher sensitivities) are upwards on the graph. (Modified from (Lynn, Felman & Starita, 1996).)

Angular Distance From Fixation (deg)

-60 -45 -30 -15 0 15 30 45 60 75 90

Log Increment Threshold, L (Apostilbs)-4

-3

-2

-1

0

1

2

3

00.0010.010.11101001000

Backgroundluminance, LFig. 3.6

The three main stimulus dimensions that are varied in visual perimetry are

Stimulus size

Stimulus intensity

Retinal locus

0° 45° 90°0°

45°

90°

Distancefrom fovea

0°45°90°0°

45°

90°

Direction from fovea

0°

10°

20°

30°

40°

50°

60°70°

80°90°100°110°

120°

130°

140°

150°

160°

170°

180°

190°

200°

210°

220°

230°

240°250°

260° 270° 280°290°

300°

310°

320°

330°

340°

350°

NASAL TEMPORAL

Isopters define points in the visual field with similarincrement thresholds

Fig. 3.8

Differential Light Sensitivity

Illustration of the “Hill of Vision”. The fovea corresponds to the region of greatest sensitivity(smallest increment threshold). Small and dim spots may be seen at this point, but largerand/or more intense spots are needed to reach threshold as the spot is presented further fromthe fovea. The black oval marks the optic disc where sensitivity is 0. In the usual plots of visualfields, this “hill” is represented on a two-dimensional plot at isopters or as a gray scale.Redrawn from Anderson (1987).

Fig. 3.7

The results of static perimetry and kinetic perimetry may differ

Patients may have a much greater sensitivity to the moving target

used in kinetic perimetry

Problem: there is substantial anatomical loss (ganglion cell

death) before visual field deficits are detected, so new and

better tests are needed

Perimetry is used to detect visual field loss caused by glaucoma

New and more efficient perimetric tests (visual field tests) are

being developed for early glaucoma detection & age-related

macular degeneration

SWAP (short wavelength automated perimetry) - yellow background

& blue test spot

Frequency doubling perimetry

Also developing pattern ERG (PERG) for early glaucoma detection

A “Glaring” Deficiency

Glare is ambient light that interferes with increment or difference threshold detections

Due to the effects of scattered light

Scattered light

Due to particles in the optical media

If small relative to the wavelength of light, the amount of scatter is inversely proportional to the 104 of the wavelength (Rayleigh scattering)

The sky is blue because of Rayleigh scattering

Scattered light

Due to particles in the optical media

If large relative to the wavelength of light, the amount of scatter independent of the wavelength (Mie scattering)

I think cataracts give Mie scattering

Lv = K (Eo/0) Eq. 3.4

where Lv = veiling luminance, K is a constant, Eo =

illuminance of the glare source, and 0 = the angle

between the glare source and the fixated target.

The Stiles Holladay formula

The amount of glare (Lv) goes down as the angle of the glare source goes up