An instrument

Contents of this post

• Introduction

• The instrument

• Models of the world of light

• Variation

• An experiment with Powerpoint

• A thought experiment

• Odds and ends

• Conclusions

• References

• Annex: abstract of subject paper

Contents of the subject paper

Introduction

This post is the product of reading some of the paper from 1942 at reference 1. A paper which I lighted upon in the course of looking into the dimensionality of colour, on which I shall be posting further in due course.

In what follows we are interested in the experience of colour. Not in all the other stuff that human visual systems do. The instrument which will be described reduces that experience to two half discs of colour, one of which the observer can adjust to try and match the other. Two half discs in a bland background, this last filling rest of the visual field. There is nothing else to see. A diagram of what the observer sees, using just the one eye, is snapped above. The other eye is patched over.

So very little to distract the observer from the business of colour matching – this despite the strong interest of brains in any departure from the regular, from what is expected. Brains are very much on the lookout for such. So, hopefully, our observer is not very likely to start thinking that one of the half discs is actually a rather poor representation of a dog, a saucepan or anything else. Or wondering what the little speck in the top left of the pale blue field is. 

The instrument to be more fully described below, includes one main source of light and two colour filters and the appearance of the two half discs in the figure above is a function of the proportion in which light from those two filters are mixed. For each half disc this proportion is the function of the angle of a special prism and the instrument includes two thumb wheels which are used to vary the angles of these two prisms. The experimenter has access to one thumb wheel and sets the target colour. The observer has access to the other thumb wheel which he uses to get the best match possible of his colour with the target colour. Once the instrument has been set up and the experimenter has set his prism, the observer usually has 50 goes at matching the target.

I have yet to find how his prism is reset between goes, although the titles of Tables IV and V suggest that it might, in those case where one filter is near white, be set back to white. So perhaps the observer’s prism is reset to one end of its range.

The instrument also includes two dials, with verniers, so that the experimenter can read off the angles of the two prisms, which he then converts to CIE xyY tuples. CIE, of reference 4, being the international organisation which busies itself with these matters. One tuple for the target and one tuple for each go at matching the target – with a total of some 500 sets of 50, or 25,000 goes in all for the principal observer. 

Around 100 different filters were used, chosen so as to give good coverage of the CIE chromaticity diagram reproduced below. Hereafter abbreviated to CCD.

I get the impression that there was a fair amount of fiddling with the instrument and its associated materials as the work proceeded. It was not the case that it was all set up for a clear run at all the observations.

We are not told how long all this took – or at least if we are told, I have failed to find where. Guessing, of the order of a year.

The instrument

An instrument from the days when laboratories made and worked up their own instruments. Maybe not the brown wood, glass and brass of the 19th century, but not so far from it. Plenty of precision optical components, that is to say lenses and prisms. Perhaps with lenses and prisms cemented together. Computation was time consuming and difficult – enough so that in this case they made their own slide rule to help with it.

Given time, even a non-specialist can work some of it out, but the figure above might speed things up a bit. In which A, B, C and D suggest the four stages of the original diagrams. Illumination right, omitted from the original diagrams, observer left, eye to the left hand hole in the separately illuminated globe.

Let us call the two filters of stage A, filter X and filter Y. These filters are made of small pieces of coloured gelatine film sandwiched between two microscope slides and there are around 100 of them. For around half of the observations, one of these filters is near white and the other is quite close to the spectral line of the CCD, for which see below. Observations which look at our perception of colour purity, also called saturation. The other half of the observations look at our perception of colour in the immediate neighbourhood of some nominated colour. Neighbourhood in the sense of that same CCD.

Let us call the output half discs disc E (the one under experimenter control) and disc O (the one under observer control). The designer of the instrument has gone to a lot of bother to arrange it so that the two output half discs have the same luminosity, the same brightness, a quantity which is known to have an effect on the perception of colour differences. Y in the xyY coding scheme mentioned above.

The polariser splits the inbound beams into two components, one polarised one way, one the other. With the result that the output from one filter is polarised one way, the output from the other filter is polarised the other way. To do this the polariser uses a special prism, called a Wollaston prism.

This output goes into the tuner which can vary the mix of output light according to polarity, effectively according to filter. So, in principle at least, the output can be filter X light, filter Y light or anything in between, in the sense of a straight line on the CCD. To do this the tuner uses a pair of special prisms, call Rochon prisms, one for half disc E and one for half disc O.

Tuning is rotating these prisms, setting their angles in the range 0° to 90°. These angles can be read off from vernier equipped dials. Angles which can then be converted, with the help of the special slide rule mentioned above, into points on the CCD.

The idea is that the experimenter sets his half disc to a colour. The observer then has fifty goes at matching his half disc to that colour. The fifty readings have a standard deviation, standard deviations which via Table II and Table III of the original paper, feed into the line graphs and ellipses illustrated below. Move onto next colour.

Models of the world of light

We have a reasonable grip on what is going on in the outside world, with packets of light arriving at the eye, being integrated over small amounts of time and space and somehow becoming the conscious experience of colour. There are, no doubt, lots of unconscious goings-on too, but these are not of present concern. 

Natural world packets of light tend to have fairly smooth spectra. Not at all like the three narrow bands of tri-stimulus colour which can be generated mechanically.

That aside and leaving polarity aside, a packet can be more or completely specified by a non-negative real valued function on the unit interval, corresponding to the range of visible light, say 400nm to 750nm. Now the space of functions from [0, 1] to [0,1] is very large, an infinite dimension vector space, even if we restrict consideration to continuous functions, although we can get that right down if we require all the derivatives to exist and to be globally bounded.

CIE have reduced that space to a number of much smaller spaces, the one of present interest being the 1931 model, snapped above, clean right and annotated left, and introduced at reference 3. A snap which can be thought of as a horizontal slice through a three dimensional model, with the missing dimension being brightness, considered to be the single most important property of one of our packets of light. Think how much can be done with a black and white photograph or a black and white film.

Any packet of light can be mapped to a unique position in this CIE space. Which means that lots of quite different packets get mapped to the same position, a phenomenon known as metamerism.

This model is continuous and it is not at all clear how the space, even the two dimensional version snapped above, can be cut up into, can be translated into discrete colours which we can discriminate, name and talk about.

Furthermore, interpretation of the distance between two points or of the direction from one point to another on a CCD is difficult. This point is covered in the first section of the present paper.

The CCD and the CIE are described more fully, for example, at references 3 and 4.

Issues with continuity are avoided by the discrete Munsell colour system, with its 500 odd samples of colour, represented, at least originally, by pieces of carefully painted card. A system which arranges its samples in a very approximately spherical arrangement, not so different in its organising principles from the CIE model.

So viewed from above, we have the circle of hues, left in the snap above, based on the five basic hues of red, yellow, green, blue and purple. Then each hue has a leaf, of which we have a sample left. As it happens, for a hue intermediate between two of those shown left. The open squares signify colours which exist in theory but which cannot yet be achieved in dye or pigment.

In the leaf, saturation, or purity, runs from low left to high right. While value, or brightness, runs from low bottom to high top. Again, values N0 and N10 exist in theory but cannot yet be achieved in dye or pigment.

Described more fully, for example, at references 5 and 6.

So one way or another, we have ways of talking about colour. We know quite a lot about how colour is processed in the eye: we know, four example, that the eye does not transmit RGB tuples – of the sort to be found in Microsoft’s Powerpoint – to the brain, rather something much closer to CIE tuples. We know much less about what the brain does with that information, about how, for example, the brain decides that two colours are the same, something that it is quite good at if the two colours are presented side by side. A decision making process which seems to be more or less unconscious. All that gets to consciousness is the decision as to how alike the two colours are.

To make things a little more concrete, consider the figure above. Suppose we have the two colours A and B which our observer can distinguish, one being a yellow the other a green-blue. T is somewhere in the middle of the line AB which, given the law of addition, can be represented as T = αA + βB where α and β are non-negative and α + β = 1. Clearly, when β = 0, then T is A. But what is important for present purposes is that as β approaches 0, there will come a point where our observer cannot distinguish T from A. In the context, they are to all intents and purposes the same colour. A quite different matter from the metamerism mentioned earlier.

A figure which brings home the additive property of the CCD, the fact that you can add up a mixture of A and B to get the sum T lying on the line AB. Otherwise Grassman’s laws of reference 7. Laws which follow from the human eye having three sets of colour receptors, human colour perception being essentially three dimensional, laws which I dare say are generally true but probably break down a bit at the margins.

From where I associate to the fact that the octaves on concert pianos are not uniform across the keyboard, getting stretched at the right and squeezed at the left. Octaves are not as basic as at might first appear. See reference 8, from which the figure above is taken.

Pianos aside, it seems likely that these matters will vary across the CIE colour space and between individuals. And individuals probably change over time, probably mostly for the worse. Variation across the CIE colour space for one individual, one Mr. Perley G. Nutting, Jr., is the subject of the present paper.

Variation

We start with the observation that repeated precision measurements of a physical quantity, such as a temperature or a pressure, will usually yield a series of slightly different values. A series with a mean and a standard deviation, quite possibly near enough normally distributed, fully specified by mean and standard deviation. And on a good day the mean will be close to the true value, without bias one way or the other.

The same sort of thing will happen with measurements of physiological quantities, not least because it is harder to control the state of a person than that of a machine, even a complicated one. You are unlikely to get exactly the same reading twice. A difficulty compounded with quantities like the concentration of this or that chemical in the blood, which may well vary with time, perhaps time of day or time of month. They may well vary with the place from which the sample is taken, the posture of the subject and what he has been up to in the period leading up to the time in question.

In the present case, we are making lots of measurements of colour matches, in groups of 50, and there will be within group variation. This is summarised in the figure above.

Starting with the right hand panel, the instrument has been set up with filters A and B and the experimenter has selected target T. By turning his thumb wheel, the observer moves the colour of his half disc O back and forth along a short segment of the line AB. This being a consequence of the additive property of the CCD mentioned above. The variation is so controlled or constrained. It is one dimensional. Things are kept simple. The observer is not wandering around some more or less circular neighbourhood of T, as suggested by the cloud icon.

Moving to the panel top left, the observer does his 50 best matches to the target, resulting in a cluster of dots around the point T on the line AB, with the dots being specified in terms of the angle of his prism, that is to say between 0° and 90°.

This results in the approximately normal distribution suggested in the panel bottom left, a normal distribution hopefully centred on the target and with a low standard distribution. In this panel, we have used prism angles for the x axis along the bottom. In the experiment proper, angles are converted into distances from the target, that is to say along the line AB on the CCD.

The subject paper is all about how this standard deviation varies with the position chosen for the line AB and the position of the target T on it. With the argument being that these standard deviations are a good indicator of the colour discriminating power of the eye in the immediate neighbourhood of T. An indicator which turns out to vary in a systematic way with both position of the point T and the orientation of the line AB.

In these experiments, there always is a matching colour. The instrument has been set up with just the one pair of filters so that there is always a setting of the observer thumb wheel so that there is an exact match to the setting of the experimenter thumb wheel – assuming here that the relevant gears were indeed set up deliver smooth motion. It would be interesting to know what would happen if the instrument was modified to include two pairs of filters so that there could be settings for which there was not an exact match.

The figure above attempts to summarise what tables II (left) and III (right) are about. The two large blocks of observations.

All the lines in a group on Table II use the same pair of filters. So the lines AB and BC above left each correspond to such a group of lines. On the first, longer page of Table II, one of the two filters (23) is close to white and what changes is purity. How does standard deviation vary with purity? 

The observer turning his thumb wheel moves him along the line AB.

All the lines in a group on Table III use the same chromaticity, that is to say the same pair of xy values. So the lines through the point D above right correspond to a group of lines on Table III, all targeting the same chromaticity, but each with their own pair of filters. How does standard deviation vary with angle of attack?

The observer turning his thumb wheel moves him along one of the lines through D.

Table III and the cluster of lines on point D above reminding us that there are many ways of making up any one colour in the interior of the CCD.

The graphical derivatives in the original paper of the scheme suggested in the previous figure: samples of Figures 8 thru 21 (left) and Figures 23 thru 47 (right) in that paper.

The circles on the solid line left corresponding to the lines in two opposing groups on Table II. That is to say 66-23 and 23-17 with the filter 66 being approximately 476nm, 23 approximately white and 17 approximately opposite at 576nm (there called μm or millimicrons rather than nm or nanometres). Say AB and BC on the previous figure. Note that the Δs of the vertical scale is a standard deviation of distance, while the s of the lower horizontal scale is a distance on the CCD, corresponding to the percentage on the upper horizontal scale.

The numbers at the ends of the lines right are the numbers of the relevant filters, as displayed in Fig. 1 and listed in Table I. All in all, a neat and attractive view of the world, expressed in summary in the figure which follows.

The figure left tends to cover more space on the CCD than the figure right. A larger scale view.

The argument of the present paper is that these standard deviations are good measure of the colour resolving power of the human eye. That the variation in matching colours is a good proxy for the ability to distinguish colours. Variation which can conveniently expressed as ellipses on the CCD, ellipses which have a short axis, a long axis and an orientation, quantities derived from the standard deviations of the groups of observations concerned. With each ellipse corresponding to a group of half a dozen lines or so of Table III, all focussed on the same target point of the diagram.

One of the conclusions is that there is systematic variation in shape and orientation of these ellipses as one moves around the CCD.

Another is that trying to organise things mathematically so that equal distances on the diagram mean equal resolving power is not worth it. It all gets too complicated. Better to stick with the CCD.

An experiment with Powerpoint

Playing with Microsoft’s Powerpoint on a laptop computer with its coloured pixels is not the same as using an optical device, with the device in question here producing a more or less natural image. Nor can one eliminate visual – and other – distractions to anything like the same degree.

Nevertheless, the six rectangles above, using four shades of green suggest that the visual experience of a mismatch relies on the appearance of a line between the two rectangles. If one is conscious of a line, then we have a mismatch. If one cannot make out a line, then we have a match. One’s experience of colour is mediated by one’s experience of line. Perhaps it is not as easy to isolate colour as at first appeared?

With this experiment weakened by the absence of near misses.

Here we vary the two rectangles top right in the first snap, by varying the green element of the Microsoft RGB value – expressed by triplets of numbers in the range 0 thru 255. And on this laptop the story seems to be that differences of two or more are detectable while a difference of one is not, although if one works at it one can get a suggestion of a line. Hard to know whether this is bottom-up or top-down processing. Top-down being made possible by my knowing the answer, which the observer in the experiments described above would not.

For most observers, I would guess that the process of deciding whether or not two colours were the same was largely unconscious – while consciousness is at a low level. But the decision is reported to consciousness, when consciousness moves to a high level. And that decision is translated into action: no match then continue fiddling with the thumb screw; match then stop. Maybe, for an experienced observer the whole process is more or less unconscious. Half his mind can be on planning the evening or the meal to come. Maybe, rather in the way that we can arrive at our destination with no idea about how we got there, about what happened on the way, the experienced observer can get through his 50 observations with no idea about that.

One might, of course get different results in different parts of the palette, perhaps with much smaller green values, these being near the maximum.

However, it is all change when we tell Powerpoint to give the rectangles their boundary lines back. The sense of discrimination between nearby colours is much weakened, dominated by the boundary lines, and with the five numbered rectangles all looking much the same. A change complicated by that weakening interacting with the distance from which and with the angle at which one looks at the screen of the laptop.

In the case of the instrument described above, the last element in the optical train is a biprism and I do not know what that does with the centre line between the two half discs E and O – and I do not think that we are told. The sort of experimental detail which this paper is a bit light on by modern standards.

Another difference is that, with the instrument, the observer is trying to get a match, not searching for the colour which is nearest to that of the target while still being different from it. The genius of the author and his collaborators at Eastman Kodak being to devise an instrument which allowed continuous variation of the observer colour, the colour of half disc O, not possible at my level of Powerpoint. An instrument which demonstrated to the author’s satisfaction that the standard deviation of the best match was a more reliable indicator of colour discrimination than the standard deviation of the best non-match.

I am reminded of advice, given me a long time ago by a snagging painter with whom I was working at the time. He said that when doing a patch the trick was to ensure that the edges of the patch were ragged, as that way the eye would not pick them out. Put in a nice neat, rectangular patch and the eye would pick it up straight away. And this would still be true if you were painting a patch, rather than sticking on a bit of wallpaper. So, maybe, it is not that the brain is good at colour, rather than it is good at projecting straight lines onto the material it is presented with.

I am also reminded of a much more recent incident, when I was lazy enough to take wine from the china/pottery mug from which I usually drink tea, having gone so far as to rinse it first, naturally. The wine tasted very odd, rather unpleasant in fact, with a taste which reminded me of washing machines and disinfectant. The same wine tasted fine the following evening, when taken from a glass. The present relevance being that the sense of taste is clearly all mixed up with other senses, other goings on in the brain. Just like colour.

While remembering that few people drank their wine out of glasses until relatively recently. Cups made of horn, metal, pottery or porcelain yes; glass no.

A thought experiment

Let us update the instrument slightly. So one eye is put to the eyepiece, the other eye is hooded. One hand works the thumb screw. We add a button to say that the observer has reached a match and that readings can be taken and the instrument reset for the next reading. When the button is pressed, the two half discs are replaced by something irrelevant. Perhaps a textured red disc oscillating in some way or another. We add an audible signal telling the observer that he can start again.

Then one hand works the thumb screw, the second hand is and remains idle. The brain decides it has the match and the hand, or at least the first finger moves to the button and presses it. The two half discs are replaced by the oscillating red disc. Observer relaxes, maybe pays attention to the disc maybe not. Whatever the case, at the audible signal, the E disc now has the target colour and the O disc has been set to the zero end of its range. The observer starts matching.

The setup is monetised in the sense that the observer is paid by results. The smaller the standard deviation, the more he gets paid. This is intended to stop him losing interest, getting lazy and generally slacking off. Does reward improve performance? One might also add a time limit.

My contention is that after a while, the observer will learn to do this while paying hardly any conscious attention at all. Perhaps fully able to conduct a conversation about his last expedition to the mountains or his last baking festival while doing the observations. Perhaps just pausing the conversation from time to time when he has a more tricky than usual match.

Maybe the point of consciousness in this context is to provide a bit of supervision. A place where interrupts requiring more serious thought than a reflex can be raised and where they will reasonably reliably be acted upon. A feature which most computers manage without aspiring to consciousness at all.

Note that ‘hardly any conscious attention’ is not the same as being asleep. The common locution ‘I could do that in my sleep’ is usually fairly wide of the mark, with a sleeping person not able to actually do very much at all. While I grant that a sleeping person can think, at least after a fashion, in the sense that, for example, one can go to sleep on a problem and wake to its rapid resolution. Something does seem to have been going on in the meanwhile. But that does not help in the present case.

Odds and ends

I failed to work out what Tables IV and V were about, the word ‘step’ not being used elsewhere in the paper – beyond suspecting that it was part of the absence of experimental detail of which I am complaining.

The instrument described in this paper is obsolete to the extent that the observer experience would be easy enough to replicate on a computer screen, perhaps adapted to include a suitable hood – but whether one would get the same results using pixels and three colours as one gets with optics and chemical dyes is another matter. In which connection, the author makes the point that what he is doing is probably reasonably close in terms of spectrums to what happens out in the real world.

Then while there are lots of observations and plenty of standard deviations in the tables and in the figures, there is very little of the statistical material one would expect to see in a paper of this sort written now. Not much about the experimental procedures, about how exactly all these sets of 50 observations were made, about why most of the work was done with just one observer and not much in the way of fancy statistics with tests of this and that, significance or p-values. Dr. Bayes is not even mentioned. This, for me, is both a plus and a minus. A plus because I can’t usually understand the statistics; a minus because one feels there ought to be some!

Sums were done with books of tables and with slide rules rather than with computers. Again, both a plus and a minus. A plus in that computers, for these purposes, are quick and easy. A minus because it makes it all too easy for the experimenter not to look at the data.

The presentation also reflects what could be managed in the 1940’s. The graphics and the figures are relatively crude. 

After starting with this paper on the screen, I found it helpful to work from a printed copy. Partly because it takes one away from the screen for a bit, partly because I find it easier to scribble on hard copy than on the screen – although my version of Acrobat does include scribbling capability of a sort; a capability which comes with pluses and minuses. All, I suppose, a reflection of my age. 

Conclusions

A period piece. What we have here is what, at the time, was a relatively novel way of looking at the colour discrimination powers of the human eye. A novel way which appears to have stood the test of time.

Of present interest both from the point of view of the history of science and of what happens when the conscious experience is cut right back. When the stimulation from the outside world is cut down to a few essentials, leaving the brain with plenty of free power to concentrate on the matter at hand.

It would also be interesting to know if anyone has attempted to replicate this work using a computer, which would probably not achieve the same optical verisimilitude as this instrument, but which would be a lot easier to build and use – no need, for example, to build you own slide rule to help with the sums. And much easier to use a proper sample of observers rather than mostly relying on just the one.

It would also be interesting to know if there had been any work on the organisation of the ellipses snapped above. Could it all be explained by the shapes of the various response curves involved? It seems that the present author concluded that trying to transform the CCD to make the ellipses into circles was not worth the candle. Better to stick with what we then already had.

References

Reference 1: Visual Sensitivities to Color Differences in Daylight – David L. MacAdam – 1942.

Reference 2: https://www.nvcuk.com/technical-support/view/what-did-david-macadam-do-15. An introduction to reference 1 which is a bit more accessible than the original. 

Reference 3: https://en.wikipedia.org/wiki/CIE_1931_color_space. 

Reference 4: https://cie.co.at/. CIE was once known as ICI and is not to be confused with the once large chemical company. Probably, as it happens, also interested in colour.

Reference 5: https://munsell.com/.

Reference 6: https://www.munsellcolourscienceforpainters.com. 

Reference 7: https://psmv5.blogspot.com/2022/01/on-grasssmann.html. 

Reference 8: https://en.wikipedia.org/wiki/Piano_tuning. A digression!

Annex

The abstract provided for reference 1, the subject paper: An apparatus is described which facilitates the presentation of pairs of variable colors without variation of luminance. With this instrument, various criteria of visual sensitivity to color difference have been investigated. The standard deviation of color matching was finally adopted as the most reproducible criterion. The test field was two degrees in diameter, divided by a vertical biprism edge, and was viewed centrally with a surrounding field of forty two degrees diameter uniformly illuminated so as to have a chromaticity similar to that of the I.C.I. Standard Illuminant C (average daylight). The luminance of the test field was maintained constant at 15 millilamberts, and the surrounding field was 7.5 millilamberts. These fields were viewed monocularly through an artificial pupil, 2.6 mm in diameter. Over twenty-five thousand trials at color matching have been recorded for a single observer, and the readings are analyzed in detail and compared with previously available data. The standard deviations of the trials are represented in terms of distance in the standard 1931 I.C.I. chromaticity diagram. These increments of distance are represented as functions of position along straight lines in the chromaticity diagram, and also as functions of direction of departure from points representing certain standard chromaticities. Such representations are simpler than the traditional representations of wavelength thresholds and purity thresholds as functions of wave-length, and the accuracy of the representations is improved by this simplicity. Chromaticity discrimination for non-spectral colors is represented simultaneously and on the same basis as for spectral colors. Small, equally noticeable chromaticity differences are represented for all chromaticities and for all kinds of variations by the lengths of the radii of a family of ellipses drawn on the standard chromaticity diagram. These ellipses cannot be transformed into equal-sized circles by any projective transformation of the standard chromaticity diagram. The consistency of these data with the results of other investigators is exhibited in terms of the noticeabilities of wave-length differences in the spectrum and of the noticeabilities of purity differences from a neutral stimulus, as functions of dominant wave-length.