4Sensitivity and response

subjective detection threshold magnitude is reached. At this threshold, all intensities are regarded as being equally strong for the subject.

This psychophysical sensitivity is influenced by many conditions, relating specifically to the test subject, such as whether the person is awake and alert, whether adapted to the situation, interested in the task and concentrated, or whether easily distracted or tired. Even after taking all such factors into account, psychophysical measurements of thresholds display a variable degree of uncertainty for each individual as well as differences between individuals. Both types of data tend to have a Gaussian distribution.

Absolute visual sensitivity is given as the inverse energy, or the smallest number of photons that gives a light impression. This requires that the person be completely dark-adapted (see below) and that stimulation is applied to that part of the retina which has the highest absolute sensitivity.

It is also valuable to compare stimuli directly with each other with respect to their effectiveness in evoking a visual impression, with or without a reference stimulus. In Figure 4.1 the left half, A, is a reference light with a certain wavelength o, and an

Figure 4.1 A bipartite photometric field can be used to compare a stimulus B with a reference stimulus A. I denotes intensity and wavelength.

intensity Io. In the right half field, B the wavelength is changed from o to , and the intensity, I, is varied until field B looks as bright as field A. Making such comparisons for wavelengths in the entire spectrum, relative to the same reference ð o, Io), leads to the derivation of the eye’s relative sensitivity to spectral lights. The method can, for instance, be used to determine the effectiveness of every wavelength in the spectrum in evoking the same impression of brightness in the dark-adapted eye. This procedure is used to determine a spectral luminous efficiency function, V0 , of humans in the dark, which has a maximum sensitivity at 507 nm (Figure 4.2). When the eye is darkadapted we see no colors. In this condition it is therefore possible to achieve complete equality between fields A and B. The sensitivity of the light-adapted eye, however, needs to be determined in a different manner because color differences make it impossible to achieve equality between two wavelengths (see section on Photometry, p. 165).

The sensitivity to differences between two similar stimuli, for instance to increments or decrements in reflectance on a gray scale, is also an example of a visual

V′λ

Wavelength λ (nm)

Figure 4.2 The scotopic luminous efficiency curve of the dark adapted human eye. Maximum sensitivity is at 507 nm.

threshold. Yet another example is the smallest wavelength difference, , that can be detected as a color difference at a specified spectral location. The experimental setup of Figure 4.1 can also be used for these tests. In the latter case, one starts with the wavelength o in both fields A and B and after a complete color match has been achieved, the wavelength of field B is changed to o until a color difference is barely detected. To avoid wavelength discrimination being contaminated by lightness differences, this experiment should be carried out with equiluminant stimuli, where isoluminance is determined in a separate experiment.

The results of such experiments tell us how good we are in discriminating between physical stimuli, i.e. it gives us charactersitics about ourselves as measuring devices. In the case of wavelength differences, Figure 4.3 shows that we discriminate the smallest difference in the yellow part of the spectrum, around 570 nm. Under optimal conditions, a person can distinguish different yellow nuances for wavelengths differing by a single nanometer.

∆λ (nm)

Wavelength λ (nm)

Figure 4.3 The ability to discriminate between colors in the spectrum. is the smallest wavelength difference that can be discerned as a chromatic difference when luminance is constant.

Vision in daylight and in the dark

The retina can adjust its operating range to very different levels of illumination and lighting conditions. The notation adaptation is used both for the process of adjustment (‘to adapt to a new condition’) as well as for the end state (‘to be adapted to a condition’). During the adaptation process, the visual system changes its sensitivity to light over time. Depending on the light level, we might talk about adaptation to light and photopic vision, or about adaptation to the dark and scotopic vision. After being adapted to a bright light, it may take about an hour or so to become completely dark-adapted, whereas the adaptation from darkness to daylight takes only a few seconds. The size of the pupil plays only a minor role in this process, which operates over more than 10 log units of light intensity.

An important feature of photopic vision is chromatic adaptation, a process of adjustment to the prevailing color. The visual system can compensate and neutralize chromatic changes in illumination such that the perceived color of a reflecting surface is fairly constant. White surfaces, for instance, look white even if the illumination changes from bluish daylight to yellowish incandescent light indoors (but try taking pictures under both conditions with the same roll of film). Owing to chromatic adaptation, the color of illuminated objects changes less than one would expect from the spectral distribution of their reflected light. This is called color constancy, and it serves a practical purpose in that it aids the recognition of objects by means of color under a wide variety of illuminations. The mechanisms behind the different adaptation processes are still not fully known (see the Chapter 5).

Adaptation to darkness

The time course of dark adaptation depends on the intensity and duration of the previous light adaptation. If you are starting from low light levels, complete dark adaptation is relatively fast, whereas a light-adapted eye needs more time to ‘get used to’ the dark. The rod-free fovea has only a very limited capacity for dark adaptation, and the foveal dark adaptation process as a function of time is characterized by a single monophasic curve. For stimuli that are large enough to also stimulate rods during central fixation, dark adaptation goes through an initial fast phase attributed to the cones. When the cone sensitivity has reached a maximum, or a little before that, threshold will be determined by the slower adapting rods (Figure 4.4).

In Figure 4.4, relative thresholds are plotted instead of relative sensitivity (the inverse of thresholds). Whether the physical parameter varied is adaptation luminance, retinal illuminance or quantum flux does not matter for the shape of these curves because for the same stimulus, these units are proportional to each other. In determining such adaptation curves, the experimenter changes the stimulus magnitude I, and the only task of the subject is to say yes or no, meaning seen or not seen.

(a)

Time (min)

(b)

Time (min)

(c)

Time (min)

Figure 4.4 (a) The threshold luminance for the detection of light as a function of time in the dark. The first rapid phase, lasting between 5 and 10 min, is due to the dark adaptation of cones and is followed by dark adaptation of rods. The exact form of the curve depends on the level of light adaptation before the experiment started. (b) Dark adaptation curves after different levels of initial light adaptation. Curve 1 is for light adaptation to 400 000 td, curve 2 for adaptation to 40 000 td, 3 for 2000 td, 4 for 4000 td, and 5 for 260 td. (c) The shaded curve indicates dark adaptation curves for persons with no rods and who therefore suffer from night blindness. N is the normal curve.

The threshold criterion can for instance be defined as that intensity of the stimulus that results in yes more frequently than no, say in 55 or maybe 75 percent of all the presentations. The curve in Figure 4.4 (a), showing how thresholds depend on time in the dark, was obtained using short-wavelength, violet light. The light intensity at detection threshold was measured in terms of relative luminance. As time passes, the

subject is able to detect spots of increasingly lower light intensity, and threshold decreases to reach a minimum value. Dark adaptation is rapid during the first few minutes, and in the first minutes [the branch to the very left of Figure 4.4(a)], the subject can see a violet hue at threshold. After a few minutes in total darkness the curve flattens out, and after another minute or so, the threshold again starts to fall rapidly with time. Now the chromatic impression has disapeared, and the light has no hue. The first phase can last for 5–10 min, depending on the foregoing light adaptation; this branch of the curve is ascribed to the activity of cones. After this initial phase, the rods take over as the most sensitive, threshold-determining elements. Achieving maximum sensitivity in the dark takes between 30 min and 1 h, depending on the level of light exposure before starting dark adaptation.

After exposure to strong light, a significant amount of the rod rhodopsin photopigment will be broken down (bleached). With a lower concentration of pigment, fewer light quanta will be absorbed, and the sensitivity will be reduced. This process of changing the concentration of rhodopsin in the rods is called photochemical adaptation. In normal daylight the rods are non-functioning, with sensitivity being low owing to significant bleaching; their output signals are not modulated by normal variations in retinal illuminance, and they cannot transmit information about contrasts. If most of the rhodopsin has been broken down by light exposure, it takes about 45 min to regenerate it fully and to obtain maximum sensitivity. When rods are shielded from light, retinal returns to the outer receptor segment from the pigment epithelium and contributes to the regeneration of rhodopsin.

Figure 4.4(b) shows the course of dark adaptation after preadaptation to different retinal illuminances, measured in photopic troland (td).

troland ¼ A L ðtdÞ

where troland is the unit for retinal illuminance, A is the area of the pupil in mm2 and L is the luminance of the object in cd/m2. One sees from the curves of Figure 4.4 that the cone branch disappears at about 0.1 photopic troland. This is also regarded as the absolute threshold value for the cones. Below this value cones are non-functioning. In addition to the slow adaptation of the photoreceptors, illustrated here over a span of about 4 log units of light intensity, there is also a fast neural adaptation that is important under normal lighting conditions. It will be described later.

The dark adaptation curve of a subject suffering from night blindness is shown as a hatched curve in Figure 4.4(c). When, as in this case, night blindness is caused by the absence of rods in the retina, sensitivity will depend on cones only. Anomalies in the dark adaptation curve may also result from vitamin A deficiency.

The time course of dark adaptation is different for young and old as illustrated in Figure 4.5. While older subjects are less sensitive than younger ones at all light levels, the difference is greater for dark-adapted eyes. In this particular case, using shortwavelength light, the difference between old and young can be between 1:100 and 1:1000.

n = 240

Time (min)

Figure 4.5 Dark adaptation curves for different age groups using short-wavelength light. The curves show relative threshold luminance as a function of time in the dark. Older persons are less sensitive to light than younger ones, and the difference is largest for the dark-adapted eye. A darkadapted 20-year-old is about 200 times more sensitive than an 80-year-old (the latter needs about 200 times more light at threshold).

In curves of dark adaptation measured with long-wavelength red light there is no evidence of a rod-branch (see Figure 4.12). Consequently, using long-wavelength red light of moderate intensity in the dark-adapted eye allows for L-cone vision, without disrupting the state of dark adaptation for the rods. White light has about the same dark-adaptation curve as yellow light. The difference in sensitivity between the rods and cones is dependent on the state of dark adaptation and has been denoted the photochromatic interval (Lie, 1963).

Maximum sensitivity

Maximum absolute sensitivity for detection of light is found between 10 and 20 to the side of the fovea, where the density of rods is the highest. The minimum energy that gives rise to light detection in the dark for a young eye is close to the physical limit, namely the simultaneous absorption of a single quantum of light by each of only a few rods. The lowest energy that can be recognized as light in a dark-adapted eye (at 507 nm, at which the rods are the most sensitive) was found to be between 3.3 and 6:6 10 17 J measured at the cornea (Pirenne, 1967). At 507 nm, the energy, E ¼ h , of a light quantum is 3:92 10 19 J. This means that between about 50 and 150 quanta reach the cornea at absolute threshold. Let us assume that (i) about 50 percent of the light is absorbed in the eye media before it reaches the retina (see Figure 3.2), and that (ii) so many of the incoming quanta are lost between the rods

that only 20 percent of the quanta reaching the receptor level are absorbed. This means that only between 5 and 15 quanta are actually absorbed at absolute threshold. Early data and statistical methods, based on the comparison of experimentally determined ‘frequency of seeing’ curves and summated Poisson distributions, gave five to seven quanta as the best estimate (Hecht et al., 1942). With so few quanta absorbed, the likelihood of the same rod being hit by two quanta simultaneously is vanishingly small. Therefore, we must assume that one quantum absorbed in each of between 5 and 15 rods is a sufficient condition for light detection. This is said to compare to perceiving the light of a candle in absolute darkness at a distance of 20–25 km.

Light adaptation and contrast

In practical life it is more interesting to know a subject’s sensitivity to contrast at daylight levels than the absolute threshold intensity. Contrast sensitivity can be determined with stimuli arrangements like those in Figure 4.6 for measuring

(a) (b) (c)

Figure 4.6 Different configurations of stimuli used to measure a difference threshold, I. Thresholds can be measured relative to a comparison field with or without a surround (a, b), or relative to a background of intensity I (c). The ratio I=I is called the Weber ratio or the Weber fraction.

difference thresholds. One can, for instance, measure the smallest detectable intensity change, I, in a field of intensity I, or one can measure the smallest detectable intensity difference between a reference field of intensity I and a test field of intensity I I. Thresholds determined relative to a light background (Figure 4.6(c)), give relative sensitivities resembling those of Figure 4.7. In this case one measures the increment threshold, L ¼ L LB, relative to a steady background with the luminance LB. The ratio L=LB is called the ‘Weber ratio’ (after the German physiologist E. H. Weber, 1795–1878). The index ‘B’ for background is often omitted, and the ratio is simply written L=L. The inverse ratio, L= L, is taken as a measure of the relative sensitivity, i.e. the increment sensitivity for a particular background of luminance L.

Figure 4.7 demonstrates that the sensitivity for discriminating small light increments on a background increases as the background luminance, L, increases up to

Sensitivity ∆L

L

Adaptation luminance (cd/m2)

Figure 4.7 Threshold sensitivity (the inverse Weber ratio) plotted as a function of background luminance L. Increasing adaptation luminance leads to a smaller Weber fraction and a higher sensitivity, up to about 50 cd/m2. For a higher luminance, up to about 10 000 cd/m2, the Weber ratio is constant.

about 50 cd/m2. As luminance increases up to this level, we are able to distinguish weaker and weaker contrasts. For higher luminance levels, the Weber ratio at threshold stays constant for a relatively large range of luminance. It is in this range, between 50 and 10 000 cd/m2, that we are able to distinguish the smallest contrasts. Here Weber’s law holds that:

L=LB ¼ constant:

Weber’s law says that the Weber ratio is constant at threshold, and we see from Figure 4.7 that the value of this constant is about 0.02. This means that L is proportional to L over a large range of daylight luminance levels. The value of 2 percent contrast refers to a particular experiment and a medium test field size. We shall later take a closer look at how contrast sensitivity depends on stimulus size.

Weber’s law behavior is assumed in many sensory domains. It was originally a psychophysical finding, and only in recent years has it been possible to relate it to electrophysiological measurements of receptor responses. In a later section, ‘Adaptation of Cones’ (p. 160), we shall see that the responses of cones give a physiological foundation for Weber law behavior in photopic vision.

Purkinje’s phenomenon

Purkinje’s phenomenon illustrates the gradual transition from cone to rod vision as the eye becomes dark adapted. Let the fields A and B in Figure 4.1 be two isoluminant monochromatic lights viewed in a dark room, with A being about