The Contrast Sensitivity Function

Prepared by Peter Wenderoth

Imagine that you are driving a car in a very thick fog. Objects which are normally easily seen, like black writing on a white billboard, will be hard to see because the black writing and the white background will both be greyish. That is the difference between whites and blacks - contrast - will be reduced. Some objects may not be visible at all because their contrast is too low (the invisible objects are said to be below threshold contrast). It is also very important that you are able to see the overall shapes of big things (cars, trucks etc) as well as fine details like the writing on signposts etc. Fortunately, your visual system has brain cells some of which are designed to process big things, others which process very small things and still others which process in between sized objects. For this driving scenario, it is important to know if all these differently sized objects become just visible (just above threshold) at the same contrast or whether differently sized things require different amounts of contrast to be just visible. So the question of interest here is how much contrast - how much difference between light and dark parts of objects - do we need to just see objects of various sizes. In the laboratory, it is more convenient not to use cars, trucks and signposts but to use black and white bars of different thicknesses.

The top of the figure below shows a black-white edge. Black has low intensity (properly called "luminance") and white has high intensity or luminance.The graph below the edge shows a way of representing the edge graphically. The X axis is space or distance; the Y axis is intensity or luminance. The graph shows that the left side is all low luminance and then there is a step up to high luminance on the right hand side.

The next picture (below) shows - on the left - how a similar graph can be drawn for a series of repeating bars (called a "grating"). This left hand grating is a high contrast grating because the light bars have a very high intensity and the dark bars have a very low intensity, as the graph below the grating shows. The right hand grating has lower contrast because the light bits are not very light and the dark bars are not very dark. The dashed horizontal lines show that both gratings have the same average intensity or luminance. Your TV set has a control for average intensity (usually this is called "brightness") and another for contrast (usually called "contrast" or sometimes "picture").Changing average intensity makes the average luminance - everything - either lighter or darker; changing contrast leaves the average the same but makes the blacks blacker and the whites whiter.

The gratings shown above and on the left below graph like square waves - the graph lines go straight up and down and are flat on top - so they are called square wave gratings. As shown by the graph underneath the right hand grating below, it changes gradually in luminance over space. In fact luminance changes in sine wave fashion so it is called a sine wave grating.

The picture below shows three sine wave gratings of different contrast but the same average luminance. Contrast decreases from left to right. The grating on the right is hardest to see because - as you can see from the sine wave trace below it - the difference between its whitest white and its blackest black is very small. That is the sine wave here is almost a straight horizontal line. Another way to say this is that the difference between its peak luminance and its trough luminance is tiny. If we call its peak luminance LMAX (for maximum luminance) and its trough luminance LMIN (for minimum luminance), we can say that (LMAX - LMIN) is biggest for the grating on the left, next biggest for the middle grating and smallest for the grating on the right.

The true definition of contrast is in fact (LMAX - LMIN) ÷ (LMAX + LMIN). If the sine wave on the right above were just a horizontal line there would be no contrast at all, the so-called grating would just be a homogeneous grey, LMAX would be the same as LMIN and contrast would be zero because (LMAX - LMIN) would be zero. If, on the other hand, the black bars were very black and the white bars were very white, (LMAX - LMIN) ÷ (LMAX + LMIN) might be (1000 -1) ÷ (1000+1) - these are just made up numbers - but it is clear that maximum contrast you can ever have is 1.0.

The picture on the left above shows a sine wave grating and contrast decreases as the picture goes up. At a certain point the contrast is too low to see the grating and you just see homogeneous grey. The picture above on the right is exactly the same except that the bars of the grating go from being very thick on the left to being very thin on the right. Notice that the very thick and very thin bars are harder to see than the middle thickness bars - you lose the very thick and very thin bars at a quite high contrast. You need less contrast to see the middle thickness bars which is why you see them going higher up the page. Your visual system is more sensitive to middle thickness bars than to very thick or very thin bars.

The thickness of bars in a grating is called spatial frequency - how frequently bars occur across space. If lots and lots of bars occur across a particular distance the grating has very thin bars and is said to have high spatial frequency, as on the right side of the right hand picture above. If very few bars occur across the same distance, the grating has very thick bars and is said to have low spatial frequency, as on the left side of the right hand picture above. Now you will realise that any grating will look to have differently sized bars depending upon whether it is close to you or far away so we need to talk about spatial frequency not in the world but on the back of your eye, on the retina. The size of an object on the back of your eye is measured by the size of the angle it subtends (called visual angle) and the picture (left) below shows that an object 1 cm tall at a distance of 57 cm subtends a visual angle of 1°. The picture also shows that many combinations of different sizes and distances will subtend the same visual angle e.g. an object 2 cm high at 114 cm as shown. Because your arm is about 57 cm long and your fingernail is about 1 cm in diameter, your fingernail at arm's length subtends about 1°. In a grating, one black bar and one white bar is called one cycle. The right hand picture below shows a fingernail at arm's length into which fits one cycle of a grating. The spatial frequency of that grating is therefore one cycle per degree of visual angle. A grating with bars half that size would fit two cycles (four bars) on your nail and so would have a frequency of two cyles per degree. Now look back to the above picture on the right which showed that you are most sensitive to middle frequencies and quite insensitive to very low and very high frequencies. This produces the upside-down U-shaped sensitivity curve that you see. But which frequencies exactly?

The picture below shows you the answer. This shows the upside-down U-shaped curve of sensitivity. The top X axis is spatial frequency in cycles per degree. The right-hand Y axis is sensitivity. The peak sensitivity - the highest point of the visibility curve - is between 1 and 10 cycles per degree. Many experiments have shown that you are most sensitive to spatial frequencies between 1 and 10 cycles per degree.