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LMS colour space

The LMS colour space is a practical implementation of trichromatic colour theory that enables the full range of human observable colours to be specified by measuring the responsiveness of the L, M and S cones to each wavelength of light within the visible spectrum.

  • The LMS colour space was one of the first systematic demonstrations of trichromatic colour theory.
  • LMS describes how the three types of cone photoreceptors (L, M and S cone types) in a human eye respond given any particular light stimuli.
  • The method used in the development of the LMS colour space produced a generalized representation of human colour perception.
  • The underlying principle was that any colour can be described in physiological terms by measuring the response of the L, M and S cone cells in the human eye’s retina to different wavelengths of light.
  • The initial source of data for the LMS colour space was taken from experiments that compared the spectral sensitivity of subjects with normal sensitivity with other subjects experiencing forms of colour blindness.
  • A more recent technique used to collect data for LMS belongs to the field of visual psychophysics and is known as heterochromatic flicker photometry. It provides extensive and accurate spectral sensitivity data obtained from cellular material removed from the eye.
  • The LMS colour space describes human observable colours using three parameters, known as tristimulus colour values, each component of which corresponds with the response of the L, M and S cone types.
Tristimulus colour values
  • Tristimulus colour values have three components corresponding with the response of the L, M and S cone types. Each response is measured against a scale with values between 0 and 1.
  • LMS tristimulus colour values for a monochromatic red, green and blue stimulus might appear as follows:
    • Red: wavelength  = 635 nanometres: L = 0.3278612, M = 0.0444877, S = 0.0
    • Green: wavelength = 520 nanometres:  L = 0.6285647, M = 0.8166012, S = 0.02920317
    • Blue: wavelength= 450 nanometres: L = 0.04986433, M = 0.08705225, S = 0.9553885
    • Data from: https://cie.co.at/datatable/cie-2006-lms-cone-fundamentals-2-field-size-terms-energy
  • Tristimulus colour values can be thought of as colour-matching functions. If you know a tristimulus colour value then you can predict the corresponding colour experience.
Limitations of the LMS colour space
  • The LMS colour space provides an accurate physiological description of human colour perception but has limitations related to the fact that some colours in the visible spectrum appear brighter than others.
  • Whilst the achievements of the research that produced the LMS colour space underpin much of the subsequent developments within the field, LMS has been superseded by the CIE (1931) XYZ colour space.
  • The CIE (1931) XYZ colour space addresses the limitations of the LMS colour space by sacrificing physiologically accurate measurements of colour perceptions in favour of a solution better suited to everyday colour management..
  • The XYZ tristimulus colour parameters replace the LMS tristimulus colour parameters
  • XYZ is a more convenient representation and the CIE XYZ colour plot defines all the possible colours a human observer can see. For a given luminance Y, the XZ value specifies all possible chromaticity values one can see.
  • There is a simple linear transformation, via a 3 x 3 matrix, between LMS and XYZ.
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Tangent

A tangent to a circle is a straight line that touches the circle at exactly one point and is perpendicular to the radius drawn to that point.

In geometry, a tangent (or tangent line) to a curve is a straight line that touches but does not intersect the curve. It can be defined as a line through a pair of infinitely close points on a curve.

If you zoom in to the point of tangency on the curve, the curve starts to look more and more like a straight line, and the tangent line becomes indistinguishable from the curve itself.

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Tangent

A tangent to a circle is a straight line that touches but does not intersect the circle and is at right angles to a radial line drawn from  the centre of the circle.

  • In geometry, a tangent (or tangent line) to a curve is a straight line that touches but does not intersect the curve. It can be defined as a line through a pair of infinitely close points on a curve.

https://en.wikipedia.org/wiki/Tangent

Temperature

All objects with a temperature above absolute zero emit electromagnetic radiation, and the amount of radiation emitted at each wavelength depends on the temperature of the object.

  • Hot objects emit more electromagnetic radiation at shorter wavelengths.
  • Cold objects emit more electromagnetic radiation at longer wavelengths.
  • The temperature of an object is related to the wavelength at which the object emits the most radiation, which is known as the peak wavelength.
  • The relationship between the temperature of an object and the peak wavelength of its emitted radiation is described by Wien’s displacement law, which states that the product of the temperature and the peak wavelength of radiation emitted by a black body is a constant.
  • A black body is an idealized object that absorbs all incoming radiation and emits radiation at all wavelengths. Real objects are not perfect black bodies, but they still emit electromagnetic radiation according to their temperature.
About colour & temperature

The surface colour of objects and their thermal temperature can be distinguished as follows.

Surface colour
  • The surface colour of an object seen by an observer is dependent on:
    • The light that falls upon it.
    • The sensitivity of the human eye to the range of wavelengths that correspond to the colours of the visible spectrum.
    • The physical and chemical properties of an object, so its material composition. These determine how it interacts with incident light, including how it absorbs, reflects or scatters light.
  • In terms of the difference between surface colour and thermal radiation, an apple that appears red at 5 degrees Celsius will still appear red at 85 degrees Celsius, but the thermal radiation it emits will be different at the two temperatures.
Thermal radiation
  • Thermal radiation is a measure of the electromagnetic radiation emitted by an object due solely to its temperature, in the absence of incident light.
  • The colour and brightness of most objects that we see in daily life are due to the reflected light such as sunlight or artificial light.
  • Reflected light is typically much brighter than the thermal radiation emitted by the same object at room temperature.
  • The amount of thermal radiation emitted by an object at room temperature is relatively low compared to the amount of radiation it will emit at higher temperatures.
  • However, the amount and distribution of thermal radiation emitted by an object can be affected by factors such as the composition of the object, the properties of its surface, and the ambient temperature and humidity of the surrounding environment.
  • The concept of thermal radiation typically encompasses a broad range of wavelengths across the electromagnetic spectrum, including infrared radiation, visible light, and ultraviolet radiation.
  • At room temperature, most objects emit low levels of thermal radiation in the infrared region of the electromagnetic spectrum.
  • An iron rod would need to be heated to a temperature of around 1000 to 1200 degrees Celsius to emit thermal radiation that is visible to the human eye.
    • At this temperature, the rod would glow red, and the colour of the glow would become brighter and shift towards yellow and then white as the temperature increases further.
    • It’s worth noting that the precise temperature at which an iron rod starts to emit visible thermal radiation can vary depending on  the specific rod and its environment.
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Thermonuclear fusion

Thermonuclear fusion is the process of combining two atomic nuclei to form a heavier nucleus, releasing a vast amount of energy in the process.

  • There are two forms of thermonuclear fusion:
    • Uncontrolled fusion is the process in which the atomic nuclei combine spontaneously, releasing an enormous amount of energy uncontrollably. It occurs naturally in most stars and is the principle behind thermonuclear weapons.
    • Controlled fusion is the process in which atomic nuclei are combined in a controlled environment to release energy for constructive purposes.
  • The energy released during fusion can take various forms, including light.
  • During fusion, gamma rays are released, which are high-energy photons that belong to the electromagnetic spectrum.
  • These gamma rays can interact with matter and produce other forms of light, such as visible light, which we can see with our eyes.
  • In stars, fusion occurs at their cores where hydrogen atoms combine to form helium, releasing a large amount of energy, including light.
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Thermonuclear fusion

Thermonuclear fusion involves atoms fusing together. Thermonuclear fusion requires immense pressure and heat.

  • There are two forms of thermonuclear fusion:
    • Uncontrolled fusion, in which the resulting energy is released in an uncontrolled way, as it is in thermonuclear weapons (“hydrogen bombs”) and in most stars.
    • Controlled fusion, where the reaction takes place in an environment allowing some or all of the energy released to be harnessed for constructive purposes.

Tone

In the field of colour theory tone describes the darkness of a colour or hue.

  • In the context of additive colour models such as RGB or HSB, a darker tone of a hue is produced by reducing its colour brightness. The result is a desaturated, muted version of the original colour.
  • In the context of subtractive colour models such as CMY and RYB, A darker tone (or shade) of a colour is achieved by adding black to it. The result is a desaturated, muted version of the original colour.
  • In photography, tone refers to the different shades of grey that can be produced, ranging from pure white to pure black.
  • In the context of a greyscale, tone is used to describe the relative darkness or lightness of a specific shade of grey.
    • A greyscale is the result of removing hue from a range of colours leaving their saturation and brightness unaffected.
    • Whilst yellow appears to have a very light tone when converted to greyscale, blue appears to have a very dark tone.
  • Tone is closely related to the term value.
    • Value refers to the amount of light reflected from a surface or emitted by a computer screen.
    • White has a high value while black has a low value.
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References

https://en.wikipedia.org/wiki/Lightness
https://en.wikipedia.org/wiki/Grayscale

Total internal reflection

Total internal reflection occurs when incoming light travelling through a medium strikes the boundary with a second medium at angles greater than a certain critical angle with the result that no light crosses the boundary and so all the light is reflected back into the medium.

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Transmission

Transmission occurs when any form of electromagnetic radiation passes through a medium.

  • Transmission refers to the passage of any form of electromagnetic radiation through a medium.
  • If no electromagnetic radiation is reflected or absorbed as it passes through a medium, then it is considered to have achieved 100% transmission.
  • The transmittance of a material describes how well it transmits radiant energy and is calculated as the fraction of incident electromagnetic power that is transmitted through the material.
  • The opposite of transmission is absorption, where electromagnetic radiation is absorbed by a medium and converted into other forms of energy, such as heat.
  • The degree of transmission of electromagnetic radiation through a material can depend on factors such as the wavelength of the radiation, the thickness and composition of the medium, and the angle of incidence of the radiation.
  • The degree of transmission can also vary depending on the type of electromagnetic radiation. For example, materials that transmit visible light well may not transmit ultraviolet light or infrared radiation as effectively.
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Transverse wave

A transverse wave oscillates (vibrates) from side to side at a right angle to the direction of propagation.

  • A transverse wave is a type of mechanical wave in which the particles of the medium oscillate (vibrate) perpendicular to the direction of wave propagation.
  • Transverse waves can be observed in various phenomena, such as light waves, electromagnetic waves, and certain types of seismic waves.
  • Transverse waves exhibit specific properties, including wavelength, frequency, amplitude, and wave speed.
  • The motion of a transverse wave can be represented graphically using a sine wave or cosine wave, illustrating the peaks and troughs of the wave.
  • Transverse waves can be polarized, meaning the oscillations are confined to a particular plane or direction, which has important implications in optics and other fields.
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Trichromacy

Trichromacy (or trichromatism) is the form of colour vision possessed by human beings and other trichromats that features three different types of cone cells and one type of rod cell within the retina of the eye and uses three independent channels for conveying colour information to subsequent visual processing centres and towards the visual cortex of the brain.

Trichromatic colour theory of human vision explores various aspects of trichromacy, including:

  • The functions, differences, and connections between the three types of cone cells (and the one type of rod cell) and other types of neurons within the human retina.
  • The sensitivity of the three types of cones to three overlapping ranges of wavelengths of light that make up the visible spectrum.
  • The sensitivity and function of rod cells in low levels of lighting.
  • The role of rods and cones in encoding colour information in anticipation of subsequent stages of visual processing.
  • The details of the way in which colour information is produced across the entire surface of the retina of both eyes is encoded onto separate channels.
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Trichromatic colour model

Trichromatic colour model

Trichromatic colour models (and the trichromatic colour theory that underpins them) provide methods for visually matching and mixing colours from combinations of three primary colours – red, green and blue ( or cyan, magenta and yellow). The information about how much of each primary colour is needed to produce a target colour is stored as tristimulus values. Tristimulus values are simply codes that can be used to record and pass on colour information.

The LMS colour model (long, medium, short), is a trichromatic colour model that represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths. It is used to systematize the response of the three types of cones of the human eye to different visual stimuli, that is, different wavelengths of light. The strength of the LMS colour model is its concern for the connection between the physiological aspects of vision and the everyday visual experience of an observer. L M and S refer to the bands of wavelengths that each cone type within the retina responds to.

Let’s look more carefully at this connection between trichromacy and tristimulus systems of which the RGB colour model provides a good example.

We start with the premise that trichromatic processing within the retina reduces all colours an observer sees to responses corresponding with the spectral biases of L, M and S cone cells.

This premise can be demonstrated experimentally by positioning an observer in front of three different light torches, each covered with a red, green or blue filter, that project light onto the same area of a neutrally coloured surface. The effect of each filter is to block all wavelengths except one. If the three torches project light at equal intensities the surface appears white. If the intensity of light or the colours of the filters are not exactly matched a colour cast will be apparent. If one light is turned off, then a secondary colour appears. Depending on which colour is absent the result will be cyan, yellow or magenta.

The reason the surface appears white to the observer in this experiment when all three torches are turned on is that each of the three cone types in their retina is being triggered evenly. This means that each of these types of photosensitive neurons are registering the presence of the wavelengths of light they are tuned to.

In the second part of the demonstration, a calibrated dial is used to alter the intensity of each torch. By setting each dial to a component of a tristimulus value for a known colour, it is possible to test whether the resulting stimulus causes the observer to see the intended colour.

This experiment corresponds directly with the way all RGB devices such as TVs, computer monitors, phone screens and projectors work in so far as tristimulus RGB values are used to stimulate the L, M and S cone cells on the retina to produce the intended experience of colour.

Opponent processing does not play a determining role in this experiment. We know from opponent-processing theory that after trichromatic processing takes place, the signals will be processed based on whether the cone responses indicate that the stimulus is bright or dull, more red-or-green, and at the same time, more blue-or-yellow. The output of this process will be fed into the million-or-so fibres of each optic nerve encoded into two channels of chromatic information and one dealing with the perception of brightness.

Experiments by several generations of scientists and artists have confirmed the connection between trichromacy and tristimulus systems. Opponent-processing cannot be demonstrated quite so directly but visual illusions and unexpected consequences of different attributes of colour perception have been used experimentally to unravel what is going on with extraordinary success.

One of the outcomes of research into tristimulus systems is the requirement, when choosing primary colours, that two of them cannot be combined to produce the third. Each must be unique so far as the human eye is concerned.
Research into the opponent-process has established that there are in fact four unique colours, red, green, blue and yellow, each of which shows no perceptual similarity to any of the others.

The implications of the fact that human vision can be stimulated by three distinct colour inputs are:

  • In normal conditions, any particular colour seen by an observer is produced by complex patterns of different wavelengths and intensities of light from across the visible spectrum as they enter the eye and are absorbed by cone cells within the retina in real-time.
  • The complex pattern of wavelengths and intensities of light being emitted by a light source at any moment is called its spectral power distribution. A spectral power distribution can be plotted on a graph and always appears as a wavy line with red at one end and violet at the other. The profile of the plot rises for high and falls for low intensities of light.
  • The colour notation used to record tristimulus values can, in principle, describe any human colour sensation.
  • If tristimulus values corresponding with the full range of human observable colours are plotted on a graph, with three axes drawn perpendicular to one another, they can produce an inclusive representation of colour perception in the form of a 3-dimensional colour solid.
  • The three axes correspond with the range of responses of the three cone types and so can be labelled L, M and S. A scale along each axis can be added to correspond with a minimum cone response at one end and a maximum at the other. This is the basis of the LMS colour model, which is one of a number of colour models devised to quantify human colour vision.
    Colour models such as RGB colour and the Munsell colour system also use tristimulus notation to record colour information. The implications are that LMS, RGB and Munsell are all grounded in the trichromatic nature of human vision and take advantage of the resulting opportunities in terms of systems that use additive colour.
    Other colour models such as HSB colour, HSV colour and HSL colour which are all variants of RGB colour do not use forms of notation that correspond directly with tristimulus value.

Trichromatic colour theory

The foundation of trichromatic colour theory lies in understanding the physiological basis for the subjective experience of colour.

  • Contemporary versions of trichromatic colour theory developed from several parallel lines of research:
    • A crucially important strand of research produced experimental evidence around 1850 that a test subject could produce a match for various different colour swatches by adjusting the intensity of three monochromatic light sources: one in the red, one in the green, and one in the blue part of the spectrum. This research concluded that if the correct wavelength was selected for each of the three lights, then any colour within the visible spectrum could be produced.
    • Research began in the early 19th century into the structure of the human eye, revealing the function of rod and cone cells, along with other types of neurons found within the eyeball.
    • Systematic research into the relationship between the stimulation of the retina by different wavelengths of light and the corresponding subjective experience of colour reached maturity during the 1920s.
  • The discovery that mixtures of red, green, and blue light at different levels of intensity could be used to stimulate the L, M, and S cone types to produce any human observable colour provides the underpinning for almost every form of colour management in practice
  • The outcome of this inquiry into trichromacy was the LMS colour model and the CIE (1931) XYZ colour space (among others).
Cone cells
  • Trichromatic colour theory established that there are three types of cone cells in the human eye that carry out the initial stage of colour processing, ultimately producing the world of colours we see around us.
  • Cone cells are daylight photoreceptors, which means they can convert light into electrical charges through a process called photo-transduction.
  • The sensitivity of cone cells was established using spectroscopy which measures which wavelengths are absorbed and which are reflected.
  • The three types of cone cells were identified along with the range of wavelength they absorbed:
    • L = Long (500–700 nm)
    • M = Medium (440 – 670 nm)
    • S = Short (380 – 540 nm)
  • Each of the three cone types was found to absorb with a bias towards a favoured range of wavelengths of light within the visible spectrum.
    • L = Sensitive to the red region of the visible spectrum (biased towards 560 nm).
    • M =  Sensitive to the green region (biased towards 530 nm).
    • S = Sensitive to the blue region (biased towards 420 nm).
  • It  became clear that the three types of cone cells work in combination with one another to enable the human eye to respond to all wavelengths of the visible spectrum and produce the fine gradation of colours we see across the visible spectrum.
  • Some research suggested that the sensitivity of these biological processes enables us to distinguish between as many as seven million different colours.
Cone cell biases
  • A closer look at the biases of the L, M and S cone cells detailed above reveals a complicated picture. There is a certain amount of overlap in the range of wavelengths that rods and three types of cones are receptive to:
    • L cones: Respond to long wavelengths so to a region that includes red, orange, green and yellow but with a peak bias between red and yellow.
    • M cones: Respond to medium wavelengths so to a region of sensitivity that includes orange, green, yellow and cyan but with a peak bias between yellow and green.
    • S cones: Respond to short wavelengths so to a region of sensitivity that includes cyan, blue and violet but with a peak bias between blue and violet.
    • Rods: Rod cells which come into their own in low-level lighting, are most sensitive to wavelengths around 498 nanometres, with a peak sensitivity towards green-blue, and are insensitive to wavelengths longer than about 640 nanometres.
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Trichromatic colour vision

Trichromatic colour vision (Trichromacy)

Photo-transduction by cone cell receptors is the physiological basis for trichromatic colour vision in humans. The fact that we see colour is, in the first instance, the result of interactions among the three types of cones, each of which responds with a bias towards its favoured wavelength within the visible spectrum. The result is that the L, M and S cone types respond best to light with long wavelengths (L =biased towards 560 nm), medium wavelengths (M =biased towards 530 nm), and short wavelengths (S = biased towards 420 nm) respectively.

Tristimulus colour values

Tristimulus colour values are numerical representations of colour perception, describing the responses of three types of cone cells (L, M, and S) in the human eye to different wavelengths of light.

These values serve as the foundation for various colour spaces, such as LMS and XYZ, and are essential for accurately measuring, representing, and matching colours in the field of colour science, colour matching, and colour management.

Tristimulus colour values
  • Tristimulus values are the backbone of colour measurement whether in terms of the physiological response of the human eye to light or within the world of colour matching or colour management.
LMS tristimulus colour values
    • LMS tristimulus colour values form the foundation for measuring and representing colour perceptions within the LMS colour space. The system is based on the premise that any colour can be described physiologically by measuring the response of L, M, and S cone cells in the human eye’s retina to different wavelengths of light.
    • LMS tristimulus colour values have a genuine association with the range of colours that fall within the observable visible spectrum of a typical human observer.
    • LMS tristimulus colour values have three components corresponding to the response of the L, M, and S cone types. Each response is measured on a scale with values between 0 and 1.
XYZ tristimulus colour values
  • XYZ tristimulus colour values are equivalent to LMS colour values. The CIE (1931) XYZ colour space utilizes XYZ tristimulus colour values as the basis of the CIE colour system, which has become the global standard for conveying accurate colour information worldwide.
  • XYZ tristimulus colour values have a virtual correspondence with observable colours, meaning that some colours are hypothetical and require adjustments to account for variations in brightness. For instance, fully saturated yellow, green, or cyan may appear much lighter than red or blue.
  • XYZ tristimulus colour values correspond with the response of the L, M and S cone types.
  • Tristimulus colour values are colour-matching functions insofar as they allow you to predict the corresponding colour experience when you know a tristimulus value.
LMS tristimulus colour values & the human eye
  • The human eye with normal vision has three kinds of cone cells that sense light, having peaks of spectral sensitivity in:
    • Short wavelengths: S = 420 nm – 440 nm.
    • Middle wavelengths: M = 530 nm – 540 nm.
    • Long wavelengths: L = 560 nm – 580 nm.
  • Every human colour sensation can be explained in terms of the stimulus each cone type receives.
  • The LMS cone cells underlie human colour perception in conditions of medium and high brightness.
  • However, in very dim light, colour vision diminishes, and the low-brightness, monochromatic “night vision” receptors, known as “rod cells,” become effective.
  • The three parameters denoted as “S”, “M”, and “L” are represented in a 3-dimensional space known as the “LMS colour space,” which is one of many colour spaces designed to quantify human colour vision.
  • The LMS colour space was the subject of intense scientific study during the 1920s because it established a direct link between the subjective human experience of colour and wavelengths of the visible spectrum.
  • There were technical problems interpreting the LMS colour space, which led to the development of the CIE 1931 colour space. In the CIE 1931 colour space, LMS tristimulus values are denoted by X, Y, and Z tristimulus values.
  • One of the most important innovations associated with the CIE 1931 colour space is the CIE xy chromaticity diagram.
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Trivariance

Trivariance

The term trivariance is used to refer to this first stage of the trichromatic process. It refers to both the phototransductive response of the cone cells themselves and to the three separate channels used to convey their colour information forward to subsequent levels of neural processing.

Each channel conveys information about the response of one cone-type to both the wavelength of the incoming light it is tuned to and to its intensity. In both physiological and neurological terms this process is exclusively concerned with trivariance – three discernible differences in the overall composition of light entering the eye.

It is the separation of the signals produced on each channel that accounts for the ability of our eyes to respond to stimuli produced by additive mixtures of wavelengths corresponding with red, green and blue primary colours. But more of that later!

By way of summary, the rod and trivariant cone systems are composed of photoreceptors with connections to other cell types within the retina. Both specialize in different aspects of vision. The rod system is extremely sensitive to light but has a low spatial resolution. Conversely, the cone system is designed to function in stronger light. As a result, cones are relatively insensitive compared with rods but have a very high spatial resolution. It is this specialisation that results in the extraordinary detail, resolution and clarity of human vision.

Rod System Cone System
High sensitivity, specialized for night vision Lower sensitivity specialized for day vision
Saturate in daylight Saturate only in intense light
Achromatic Chromatic, mediate colour vision
Low acuity High acuity
Not present in the central fovea Concentrated in the central fovea
Present in larger number than cones Present in smaller number than rods

Caption

Trough

A trough is the point on a wave with the maximum value of downward displacement within a wave-cycle. A crest is the opposite of a trough, so the maximum or highest point in a wave-cycle.

  • On a wave at sea, the trough is a point where the displacement of water reaches a minimum. A crest is the opposite of a trough, so a crest is a point where the displacement of the water is at a maximum.
  • In the case of an electromagnetic wave which has an electric and a magnetic axis,  a trough on either axis refers to minimum displacement in the negative direction whilst a crest refers to maximum displacement.
  • Wavelength refers to a complete wave-cycle from one crest to the next, or one trough to the next.
  • Frequency refers to the number of wave-cycles that pass a given point in a given amount of time.
  • The amplitude of a wave is a measurement of the distance from the centre line (or the still position) to the top of a crest or to the bottom of a corresponding trough.
  • Amplitude is related to the energy a wave carries. The energy a wave carries is related to frequency and amplitude. The higher the frequency, the more energy, and the higher the amplitude, the more energy.
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