Dimension being tested

ABSOLUTE THRESHOLD OF VISION

(one type of absolute threshold)

A classic study by Hecht, Shlaer and Pirenne (1942)

1) This chapter describes the factors that guided the selection of the fixed

stimulus dimensions: wavelength, size, duration, along with the retinal

location and the subject’s adaptation level

2) Analysis to examine the effects of fluctuations in the amount of light

presented on each trial

3) The results of the study led to the conclusions that -

a) a single quantum of light is sufficient to activate a single rod

b) 6 – 10 quanta must stimulate rods within a brief time period to produce the

perception of light.

4) Other studies have found that cones have a higher threshold (~5 quanta

activating 2 cones)

Important Stimulus Dimensions

intensity

wavelength

size

exposure duration

frequency

shape

relative locations of elements of the stimulus

cognitive meaning

In addition,

location on the subject’s retina

light adaptation of the subject’s visual system

Dimension being tested

Remained constant during testing









Making threshold measurements requires choices about the values to select for the stimulus dimensions that are not being measured

Five needed special care in their selection:

Wavelength, size, and duration are three characteristics of the stimulus.

Two characteristics related to the observer also had to be selected with care:

The retinal location that was stimulated and

The adaptive state of the observer’s eye

Only the stimulus intensity was altered from trial to trial

Retinal Location

Retinal Location

They aimed the spot of light 20 degrees temporal on the retina

Eccentricity From Fovea (mm)

-20 -15 -10 -5 0 5 10 15 20

Cells/mm2

0

50,000

100,000

150,000

200,000

Eccentricity From Fovea (deg)

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70O

ptic

Ner

ve H

ead

Blin

d S

pot

Rods

Cones

NasalTemporal

The density of rod photoreceptors determined the retinal location thatwas stimulated

Distribution of rods and cones along the horizontal meridian in a human retina.Data provided by Dr. Christine Curcio.

Fig. 2.1

Wavelength

400 nm 500 nm 600 nm 700 nm

The wavelength of the stimulus was a very narrow (10 nm wide) band

of wavelengths. The band was centered at 510 nm

Peak rod spectral sensitivity determined the stimulus wavelength

Fig. 2.2

Left eye, temporal retina

They used “monochromatic” light – but what wavelength to use to get lowest threshold?

Wavelength

400 nm 500 nm 600 nm 700 nm

|

|

Stimulus

Size

10’ (minutes of arc) = 1/6th of a degree

Any bigger would have “wasted” light

Spatial summation limited the stimulus size

Wald (1938) had found that the threshold (measured in the number

of quanta of light) for detection of a low intensity flash of light was

independent of size for spots less than about 15' of arc in diameter

when the stimulus was presented 5 or more from the fovea.

Photograph of rod (small) and cone (large) outer segments in a human retina 5 mm temporal to the fovea, in the approximate region stimulated by Hecht et al. This photograph shows a region approximately 40 m wide by 25 m high. The 10’ of arc spot used by Hecht et al. would have covered a slightly larger area (about 46 m in diameter). Potentially, all the rods shown in the photograph might converge onto a single bipolar cell so that activation in the rods can summate spatially. (Reproduced with permission from (Curcio et al., 1990).)

The light quanta may be thought of as “drops of rain” falling upon the

retina. Some of the light quanta are absorbed by the rods, which are

connected through bipolar cells to form the receptive-field centers

of retinal ganglion cells. In this part of the retina, a typical ganglion

cell could have a receptive-field center diameter of around 15' of arc.

Fig. 2.3

Photons that are absorbed anywhere within a small region (<15 min. of arc) will add together

Photons that are absorbed outside a certain size area do not add together

This is because of the wiring of the retina – which produces the “receptive field” of cells

The receptive field of a neuron is the region on the retina where light can produce a response from the cell

Receptive field (center) of on bipolar is the diameter of the single cone that connects to it

(Not concerned here with the R-F “surround” because: dark adapted & very low stimulus levels)

Receptive field of this bipolar is the diameter of the all the cones that connect to it

Receptive field of this ganglion cell is the diameter of all the cones that connect to it through the bipolar cells

Spatial summation (defined as: the adding together of events that occur in spatially different photoreceptors) will occur regardless of where the quanta fall within that receptive-field center.

Rods show even more convergence (larger receptive fields)

Fig. 2.3



Fig. 2.3



Fig. 2.3

For maximum effect (lowest threshold) want all of your photons to “count” – to add together

Hecht, Shlaer & Pirenne didn’t know about receptive-field sizes – the wiring of the retina had not been as thoroughly studied as it now has been.

What they did know was that the number of photons needed to reach threshold was a constant until a test spot became too large.

This is summarized as Ricco’s Law

The constant number of quanta required to reach threshold for flashes of

small area and fixed duration is expressed in

Ricco’s Law, which relates threshold luminance to stimulus area

(we call it a “law” even though it really is just a relationship)

Ricco's Law is written as:

CAL 2-1

where L is the threshold luminance of the stimulus, A is the area of the

stimulus and C is a constant.

Flash Area (deg2)

0.001 0.01 0.1 1 10 100 1000

Log Threshold Luminance(quanta/s/deg2)

3

4

5

6

7

8

9

Flash Duration = 0.0085 s

Log Background Intensity7.83 5.94 4.96 3.65 No Background

Fig. 2.4

The key to understanding that the decrease in threshold stimulus luminance

with area is the same as a constant number of quanta to reach threshold, is

to understand that

areaduration)wavelengthspecificaat(quanta

anceminlu

2-2

Combining equations 2-1 and 2-2 gives equation 2-2a.

Cx area area duration x

quanta 2-3

“Luminance” generally refers to lights that are on continuously and have

the dimensions of quanta/s . deg.2. When a flashed stimulus is used, the

flash automatically contains a fixed number of quanta (at least on average).

Thus, quanta/time is a fixed value, quanta in the threshold flash. This

reduces to:

Cx area area

flashthresholdtheinquanta 2-3b

Ricco’s law holds only for small stimulus areas and the maximum

stimulus area for which Ricco’s Law holds varies with retinal location.

In the parafoveal region (4 - 7 from the fovea) it holds for spot

diameters up to approximately 30 min of arc. It holds for spots up to

2 in diameter for stimuli presented at an eccentricity of 35 .

I won’t ask you for these numbers, but I suppose you should have a

general idea of them in case they show up on boards.

I f a s t i m u l u s i s s l i g h t l y l a r g e r t h a n t h e d i a m e t e r f o r w h i c h R i c c o ’ s l a w

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

d e c l i n e s w i t h i n c r e a s i n g s p o t a r e a , b u t a t a s l o w e r r a t e . T h e

r e l a t i o n s h i p i s d e s c r i b e d b y P i p e r 's L a w .

CAL 2 - 4

w h e r e L i s t h e t h r e s h o l d l u m i n a n c e o f t h e s t i m u l u s , A i s t h e a r e a o f

t h e s t im u l u s a n d C i s a c o n s t a n t .

Flash Area (deg2)

0.001 0.01 0.1 1 10 100 1000


3

4

5

6

7

8

9

Flash Duration = 0.0085 s


Fig. 2.4Ricco’s Law

Piper’s Law

Piper’s Law can apply for stimuli up to 24 in diameter in the

peripheral visual field, but often does not. For stimuli with large

areas, threshold depends solely on the luminance of the stimulus.

Again, I won’t ask you for these numbers, but I suppose you should

have a general idea of them in case they show up on boards.

Back to the parameters used by Hecht et al.

Location: 20 degrees temporal

Wavelength: 510 nm

Size: 10’ diameter

Duration:

Adaptation:

Stimulus duration

Temporal summation limited the stimulus duration

Hecht et al. set the flash duration at 1 ms by controlling the length of

time the shutter remained open. This value was selected because a

previous study had found the threshold (in quanta) did not change for

flash durations less than 100 ms.

Fig. 2.2

This invariance in threshold quanta with changes in stimulus duration

occurs through “temporal summation” within the receptive field center

of ganglion cells. Temporal summation is defined as: the adding

together of events that occur at slightly different times.

In the eye, temporal summation occurs within a limited time period of

up to approximately 10 - 100 ms. Fig. 2.3

Time (msec)







Time (msec)







Time (msec)







Time (msec)







Time (msec)

B loch ’s Law re la tes th resho ld lum inance to s tim ulus dura tion

B loch 's Law , is w ritten as:

CtL 2 -5

w here L is the th resho ld lum inance o f the s tim ulus, t is the duration of

the flash, and C is a constant .

Flash Duration (s)

0.001 0.01 0.1 1 10 100

4

5

6

7

8

9


Stimulus area = 0.011 deg2


Fig. 2.5

By the same logic used in the explanation of Ricco’s Law, as t (flash

duration) increases and L decreases, the threshold number of quanta

remains constant. Combining equation 2-2 with equation 2-4 gives equation

2-4a.

C x duration area duration x

quanta 2-5

However, because the area value is fixed for all these flashes, quanta/area

is a fixed value quanta in the threshold flash. This reduces to:

C x durationduration

flashthresholdtheinquanta 2-5b

Bloch’s Law holds only over a limited range of stimulus durations

up to 100 ms under some conditions

often is less than 100 ms. The upper limit is called the “critical

duration”

For flashed stimuli with durations much longer than the critical

duration, threshold depends solely on the luminance of the stimulus.

Hecht, Shlaer and Pirenne (1942) decided to use a flash duration of

1 millisecond (ms)

The Adaptive State of the Subject’s Eye

A completely dark adapted eye has the lowest possible threshold (and the highest sensitivity)

Sensitivity is defined as: Threshold

ySensitivit 1 2-6

Based on the data available to Hecht et al. (1937) each subject for this study sat in a totally

dark room for at least 30 min before beginning the measurements.

Time in the Dark (min)0 10 20 30 40

log(Threshold Luminance)

2

3

4

5

6

7

8

9

Cone Branch

Rod Branch

Rod-Cone Break

Location: 20 degrees temporal

Wavelength: 510 nm

Size: 10’ diameter

Duration: 1 ms

Adaptation: 30 min in dark before starting

The Method of Constant Stimuli was used to measure the threshold

The Method of Constant Stimuli was used to measure the threshold

60% correct taken as threshold

The absolute threshold of vision was 54 to 148 quanta incident at the cornea

Log Mean Number of Quanta per Flash

1.25 1.50 1.75 2.00 2.25 2.50 2.75

Flashes Seen (%)

0

20

40

60

80

100 MHP DataMHP(Fitted curve, n=5)SH DataSH(Fitted curve, n=6)SS DataSS(Fitted curve, n=7)

Fig. 2.6

The last place Hecht, Shlaer & Pirenne could measure the amount of

light was at the front of the eye. Then they did calculations to

estimate how much light was lost inside the eye. This then gave them

an estimate of how many photons were absorbed by rods.

Fig. 2.2

Light loss reduced the number absorbed by rods to 5-14 quanta

100 x 0.96 x 0.5 = 48 quanta actually arrived at the retina. Of these,

Hecht et al. estimated that only 20% (10 photons) were actually

absorbed by the photopigment molecules. So, 54 – 148 at the cornea

becomes 5 - 14

This reduced the actual number of quanta that are needed to

produce the sensation of light to about somewhere between 5 and

14, roughly 10% of the quanta incident on the cornea.

Fig. 2.3

Thus, the energy from a pea (about 350 mg) dropped from a height of

1 cm, if converted to light energy, would provide every human that

ever lived with a faint impression of light!

Because the number of rods in the area stimulated by the flash was large in comparison to the number of quanta, the odds of two quanta being absorbed by one rod were small. Therefore, one quanta must be sufficient to stimulate one rod.

Figure courtesy of Diana Niculescu, PhD, DVM

One quantum can excite a rod

Responses of a rod outer segment from a toad to a series of forty consecutive very lowintensity flashes. Ten flashes were presented in each row. Each vertical mark on theabscissa indicates when the flash was presented. In most cases, the rod did notrespond. When rod hyperpolarization occurred, the response was either small (~ 1.5pA), or large (~ 3 pA), The flash response was quantized, Poisson-distributed and thequantal events resulted from a either a single or a pair of light quanta being absorbed bythe rod. (Reproduced with permission from Baylor et al., (1979)).

Fig. 2.10


1.25 1.50 1.75 2.00 2.25 2.50 2.75

Flashes Seen (%)

0

20

40

60

80


The data points are the actual data from Hecht, Shlaer and Pirenne. How did they come up with the psychometric functions that fit the data?

They used logic to come up with the “right” shape of function, based on the fact that there must have been variability in the number of quanta in each flash.

Suppose the subject’s threshold was perfect, but the number of quanta in a flash varied….


1.25 1.50 1.75 2.00 2.25 2.50 2.75

Flashes Seen (%)

0

20

40

60

80


How closely could they match this psychometric function just by stimulus variability? Assume a fixed threshold, but variability in the amount of light.

The number of quanta in each flash of a series of light flashes varies with predictable randomness

A “Poisson” distribution

The variance of a Poisson distribution is equal to the mean value

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

So, with a fixed threshold (for instance, 8 or more photons), the percent “yes” responses changes depending on how many quanta are in the flash, on average.

Remember, they did not know exactly how many quanta were in any one flash!

Number of Quanta in a Flash

0 2 4 6 8 10 12 14 16 18

Probability that a flashwill contain more thanthe number of quantashown on the x-axis

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Inverse cumulative distribution for a Poisson distribution with a mean of 8 quanta per flash.

Fig. 2.8

They worked out the shape of the psychometric function with a threshold of 8 or more and variation in the number of quant in each flash. Step 1: Use inverse cumulative distribution to find fraction of “yes” responses with threshold of 8 and mean of 8

Mean = 8 quanta0.547 (54.7%) of the flashes contain more than 7, so a subject with a threshold of 8 would see 54.7% of the flashes

Number of Quanta in a Single Flash

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Inversecumulativeprobability

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 Thresh

old >7 qua

nta

Mean Number of Quanta

2 4 6 8 10 12 14 16 1820

Fraction of"Yes"Responses

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Method of generating a theoretical Frequency of Seeing Curve (on the right) fromseveral inverse cumulative frequency distributions (on the left) assuming a threshold of 8quanta. The inset shows three such frequency of seeing curves for threshold values >4,>7, and >16, from left to right, respectively.

Fig. 2.9

Step 2: they generated a full psychometric function for threshold = 8 and flashes with various mean number of quanta

Mean = 8

Mean = 6

Mean = 4

Mean = 10

Number of Quanta in a Single Flash

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Inversecumulativeprobability

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 Thresh

old >7 qua

nta

Mean Number of Quanta

2 4 6 8 10 12 14 16 1820

Fraction of"Yes"Responses

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Method of generating a theoretical Frequency of Seeing Curve (on the right) fromseveral inverse cumulative frequency distributions (on the left) assuming a threshold of 8quanta. The inset shows three such frequency of seeing curves for threshold values >4,>7, and >16, from left to right, respectively.

Fig. 2.9

Step 3: they constructed different psychometric functions by assuming different thresholds

Mean = 8

Mean = 6

Mean = 4

Mean = 10

>4

>7

>16

>16>4


1.25 1.50 1.75 2.00 2.25 2.50 2.75

Flashes Seen (%)

0

20

40

60

80


Hecht et al. matched the shape of theoretical frequency of seeing curves

to the data by sliding the curve along the abscissa

The curves in the figure below were generated in that manner.

Based on the shape of the best fitting curves, Hecht et al. concluded that threshold was between 5 and 8 quanta.

They found the psychometric function that matched the shape of the real data

But remember, all this was assuming that there was NO subject variability.


1.25 1.50 1.75 2.00 2.25 2.50 2.75

Flashes Seen (%)

0

20

40

60

80



1.25 1.50 1.75 2.00 2.25 2.50 2.75

Flashes Seen (%)

0

20

40

60

80

100

MHP DataMHP(Fitted curve, n=5)SH DataSH(Fitted curve, n=6)SS DataSS(Fitted curve, n=7)

Because they felt that there had to be at least some subject variability, Hecht et al.’s conclusion was that between 6 and 10 quanta, rather than between 5 and 8 quanta, were required to reach threshold.

Fig. 2.6

Spatial and Temporal Summation are needed for a perceptual

response

The requirement that there be summation offers some protection

against “false alarms.”

False alarms could come from spontaneous isomerization of

rhodopsin; that is rare, but there are billions of rhodopsin molecules

in the retina, so it does happen

The threshold for “practical” vision is higher, but still very low

a white (e.g., broadband) test stimulus spread out over many degrees

on the retina and viewed by both eyes for a 15 s duration . The

threshold for detecting this stimulus was determined to be 0.75 x 10–6

cd/m2.

This is about 5%-30% of the luminance of the darkest night sky

measured by the National Physical Laboratory.

This threshold intensity corresponds to the illuminance provided by a

source of 1 candela illuminating a perfectly diffusing (white, matte

surface) object 650 m away from the source. This is the illuminance an

automobile headlamp could produce on the same surface from a

distance of 70 miles!

Any psychophysical measure of visual function must adhere to

the principles presented in this chapter (and Chapter 1) if it is to

provide accurate measures

(even if it isn’t obvious that it does so)

Documents

Dimension being tested