Thresholds for Seeing

Question 1

Could cats possibly be more sensitive to light than human beings?

Answer 1

In practise no one has ever measured visual sensitivity in cats and people with the same apparatus, under the same viewing conditions, using the same protocols, with the same definition of seeing and the same units of measurement, so there is no way of comparing them.

Question 2

What is the absolute threshold for vision?

Answer 2

the absolute minimum amount of light that a person can see.
Hecht et al aimed to determine the value of the absolute threshold of human vision and arbitrarily defined this as the minimum number of photons that observers could detect 60% of the time for the purpose of their studies.

Question 3

How is light sensitivity measured?

Answer 3

its measured in terms of contrast threshold which is the minimum difference between light and dark in an image that can be detected; as this is a difference threshold it is not relevant in the context of absolute thresholds.

Question 4

How is light intensity measured?

Answer 4

ESSI units, the intensity of a luminous surface can be measured in candelas per meter squared. This refers to the luminous power in watts or joules per second per unit solid angle emitted by a point light sources in a particular direction, weighted by the spectral sensitivity of the human visual system.
1 candela corresponds to what a single candle looks like to an observer.
candelas are a measure of flux and denote the number of photons per unit area per unit time.
Intensity in candelas per meter squared is not the same thing as number of photons.

Question 5

What is it to see?

Answer 5

Seeing is a property of the whole system, not just the eye.
It depends on the properties of the eye, the photoreceptors, ganglion cells and the primary visual cortex as well as the ability or inclination of the observer to respond.
A stimulus may elicit a response in neurons at every level of the visual system but the observer still has the option of reporting not having seen it.
In Hecht et al.’s experiments, seeing was arbitrarily defined as correctly detecting the stimulus on 60% of the trials.

Question 6

what are the properties of light?

Answer 6

Light is a form of electromagnetic radiation that can be considered as a wave and as indivisible particles or packets of energy or quanta.
Light refers to the visible part of the electromagnetic spectrum as it can be detected with our eyes. This encompasses the wavelengths from 400nm-700nm.
The visible spectrum is perceived as bluish at the short wavelengths through to reddish at long wavelengths.
A photon is a quantum of light. It represents the smallest amount of energy at a given wavelength.

Question 7

What was the experimental procedure in Hecht et al.’s (1942) absolute threshold studies?

Answer 7

Apparatus is used to present brief faint flashes of light one at a time to one eye of the observer whilst the other eye is covered.
On each trial, the observer must report whether they saw the flash or not. The experimenter adjusts the intensity of the flashes until the observer reports seeing them 60% of the time.
As they wanted to measure the absolute threshold, they had to optimise various factors to ensure that the observer’s eye was as sensitive to light as it could possibly be.
These factors included: dark adaptation, the position of the test light on the retina, wavelength of test light, size of test light and the duration of the flash.

Question 8

What is dark adaptation?

Answer 8

When stepping from bright sunlight to a dark room, vision is temporarily lost as eyes gradually adjust.
The pupil dilates to allow more light into the eye, however the diameter of the pupil and the size of the eye is unlikely to allow for anything more than a 16 fold increase in light capture.
This is less than the range of light intensities in the environment by several orders of magnitude.
Hecht controlled for changes in pupil size by placing an artificial pupil of fixed aperture in front of the observers eye.
Dark adaptation is largely to due to the properties of photoreceptors.
Rods and cones contain stacks of light sensitive photopigments which change shape in the presence of a photon. This releases energy which opens ion channels and hyperpolarises the receptor cell membrane and the photopigment is ‘bleached’.
The bleached photopigment molecule is then actively reset so that it is available to capture another photon but this requires time and energy.
At a given constant light intensity, the proportion of photopigment molecules in the bleached state is determined by the balance between the rate of photon capture and the rate of photopigment regeneration.
the sensitivity of photoreceptors is auto-calibrated to the ambient light levels.
Thresholds fall and sensitivity increases with time during dark adaptation and reaches its minimum threshold after 40 minutes.
The range of vision at lowest light levels is scotopic and only rod cells contribute as rhodopsin is very sensitive to light.
Hecht et al. wanted to measure the absolute threshold for vision under scotopic conditions so needed to optimise other factors in the experiment to favour rod vision.

Question 9

How are rods and cones distributed in the retina?

Answer 9

It is not a uniform distribution.
All the cones are centred around the fovea to about 10’ of eccentricity so is specialised for photopic vision.
All the rods are found in the periphery, beyond 10’ of eccentricity from the fovea so is specialised for scotopic vision.
Rods are most dense at 20’ of eccentricity where the eye is more sensitive to dim light (scotopic conditions) than anywhere else.
Hecht et al. positioned test stimuli at 20’ of eccentricity on the temporal side of the retina as this optimises scotopic vision while avoiding the blind spot where there are no photoreceptors.

Question 10

How did Hecht control for wavelength of light.

Answer 10

Probability that a photon will be captured by a photopigment depends on the photons wavelength.
Most photopigments will capture photons from a wide range of wavelengths but tend to have a characteristic preference or peak sensitivity.
Rhodopsin is most sensitive to photons with wavelength 510nm.
Hecht et al. used wavelength 510nm in their experiment.

Question 11

How did Hecht et al. control the diameter of the test flash?

Answer 11

The distinction between the number of photons in a flash and the intensity of a flash is important.
Intensity is the number of photons per unit area per unit time. A fixed number of photons presented in a larger area has a lower intensity than the same number of photons presented in a smaller area.
Hecht et al. are concerned with measuring the minimum number of photons.
Up to an area of 10 minutes of visual angle, the threshold number of photons does not change.
As the diameter of light exceeds that, the threshold number of photons increases so more photons must be added to the test flash in order for it to be seen.
In line with Ricco’s law.
Hecht et al chose to use a test spot of 10 minutes of visual angle.

Question 12

What is Ricco’s law?

Answer 12

Ricco’s law uses the principle of summation to explain the critical area up to which the threshold number of photons remains unchanged from the absolute minimum.
In humans this an area of 10 minutes of visual angle.
The responses elicited by photons in rods that fall within the same receptive field are pooled.
As long as a sufficient number of rods with a RF are activated, the flash will be detected.
As long as the diameter of the test flash is small enough to fit within one RF diameter will not effect results.
If it does exceed this then the threshold for that RF will not be met and can only be met if more photons are delivered to the RF.
The more the diameter exceeds the critical value, the more photons must be delivered.
Spatial summation increases as ambient light intensity falls causing spatial acuity to degrade.

Question 13

How what the duration of the flash controlled?

Answer 13

The threshold number of photons doesn’t change up to a duration of 10ms
once the duration exceeds this value more photons need to be delivered in the test flash for it to be seen.
In line with Bloch’s law.
Hecht et al chose a test flash duration of 1 ms.

Question 14

What is Bloch’s law?

Answer 14

Denotes the critical duration at which the minimum number of photons can be seen, in humans this approximately 10ms.
When a photon interacts with a rhodopsin molecule, it causes the membrane potential of the rod to become hyperpolarised.
it takes a while for the membrane potential to return to its resting state.
If two or more rods are hyperpolarised simultaneously, their responses will be summed postsynaptically.
if a threshold number of responses are summed the flash will be seen.
the critical duration of bloch’s law implies that as a long as a threshold number of hyperpolarisations occur within a time period determined by how long it takes for the membrane potentials to return to their resting values, the threshold will be reached.
Temporal summation increases as ambient light levels fall and temporal acuity falls.

Question 15

What were the test conditions?

Answer 15

observers adapted for 40 minutes to maximise rod sensitiivity.
Artificial pupil used to control diameter.
Test flash optimised for rod vision by being presented at 20’ of visual eccentricity in the temporal retina where rod density is at its maximum.
Used wavelength 510nm which corresponds to the peak rod spectral sensitivity.
Diameter was set to 10 minutes of visual angle with the critical diameter for Ricco’s law
duration set to 1 ms within the critical duration of Bloch;s law.

Question 16

Results of Hecht’s study

Answer 16

60% seeing corresponds to a flash intensity of 5
This corresponds to 90 photons reaching the cornea of the eye
Of these it is estimated 3% were reflected off the cornea, 50% absorbed by the optic media, only 43 photons reach back of the eye. Only 20% of those 8-9 photons, were absorbed by rods.
At an eccentricity of 20’, a diameter of 10 minutes of visual angle on the retina corresponds to an area encompassing 350 rods.
Probability of a single rod absorbing more than one photon in a test flash is extremely small.
H et al. concluded that a single photon is sufficient to activate a rod and that 8-9 rods need to be activated to be seen,
The sensitivity of rods is as good as it is physically possible to be
No apparatus could be more sensitive than that

Question 17

Evaluation of Hecht’s studies

Answer 17

Implies that under optimal conditions the human visual system is as sensitive to light as it is physically possible to be
The graph of percentage flashes detected against the flash intensity (psychometric function) rises gradually in the form of an S shaped curve, rather than an abrupt step from 0-100% seeing
This s-shaped curve is characteristic of all psychometric functions and is though to be due to noise.
Theoretically: the noise could arise internally such as through spontaneous changes in the shape of photopigment molecules or spontaneous fluctuations in the firing rates of ganglion cells in the retina or could rise externally through quantal fluctuations in photon emission at the light source for example

Question 18

What potential sources of noise are there in Hecht’s studies?

Answer 18

H et al. assessed the role of external noise in theory experiment by modelling photon emission as cumulative poisson distributions
Poisson distribution: frequency distribution of sparse random events in which the variance is equivalent to the mean.
A cumulative poisson distribution is a plot of the area under the curve from left to right
H et al. plotted such curves with means of 4-10 and 14 as models of the psychometric functions of ideal observes with set thresholds corresponding to the mean
Overlay them over the graph of their own results: the % of flashes seen against the number of photons in the flash
Found that the best match was with the modelled threshold of 7 photons, which compared with an actual threshold of 8 photons
Concluded that most of the noise giving rise to the shape of the psychometric function in their case was due to fluctuations in photoemission from the external light source, and not internal to the observer’s visual system.
Ties in with their conclusion that a single photon can be detected by a single rod as it can only be the case if there were no internal noise to mask the detection of the single photons.
Note: 10 years lates psychophysical methods were developed which enabled researchers to test directly for the relative contribution of internal and external noise
In almost all detection experiments in which this has been applied, the noise is found to be due to internal sources.
These were available to H et al.

Question 19

What potential is there for response bias in Hecht’s studies?

Answer 19

Potential confound when measuring detection thresholds is response bias
The observer’s tendency to say yes irrespective of whether a test flash was presented or not.
If an observer tends to say yes more often regardless of whether the stimulus was presented or not, the response bias is ‘liberal’
This slides the entire psychometric function to the left which then yields a lower estimate of the threshold.
If the observer says yes less often their response bias is ‘conservative’ - slides to right, higher estimate of threshold
An experimenter can try to influence an observer’s response to bias to some extent e.g varying the payoffs for hits and false alarms or by varying the proportion of flash trials to non flash trials or by varying instructions
The extent to which bias is manipulated is beyond the experimenters control
The observer is able to set their own response bias so is able to influence the result of the experiment.
H et al presented a test flash on almost ebery trial
Tested for liberal response bias by including catch trials which are rare trials in which test flash is not presented
If the observer never responded yes in a catch trial, as was the case, we can be reasonably sure that the observer did not adopt a liberal response bias.
Does not test for conservative response bias
At best we can say that H et al. did not underestimate the threshold due to observers adopting a liberal response bias

Question 20

What is the issue with Hecht’s definition of seeing?

Answer 20

No point along the curb that corresponds obviously to the threshold as it is a smooth s-curve
H et al chose an arbitrary threshold of 60% seeing.
Concluded that a single photon could activate a single rod and that the pooled responses of 8 rods activated by a single photon each was sufficient for seeing
Threshold of 90% would be more realistic
Note: stimulus intensity is plotted on a log scale
The shape of the psychometric function allows the experimenter to choose a threshold that suits their purpose - experimenter is .’. In control of the results to a large degree.
Doesn’t imply cheating - results are valid but only for the specific conditions under which the measurements were conducted and for their specific arbitrary definition of seeeing
Limitations

Question 21

What can we conclude from Hecht’s studies?

Answer 21

H et al. experiments show that the visual system is extremely sensitive and noise free
Under optimal conditions, one photon is sufficient to activate one rod and the pooled responses of approx. 8 rods activated by single photons are sufficient for 60% seeing.
Dark adaptation involves adjustments in pupil diameter, photoreceptor auto calibration and trade offs between sensitivity and spatial and temporal acuity.
Measured thresholds can easily be confounded by observer’s response bias and the experimenter’s definition of seeing.