Trough

A trough is a 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 the lowest point in the wave cycle, where the water displacement is furthest down from its rest position. A crest, on the other hand, is the highest point where the displacement is furthest up.
  • For electromagnetic waves, which have electric and magnetic fields, a trough on either axis represents the point where the field reaches its minimum value in the downward direction. A crest represents the point of maximum value in the upward direction.

Tristimulus colour values

 

Human eyes perceive colour through three types of cone cells: L (long-wavelength sensitive), M (medium-wavelength sensitive), and S (short-wavelength sensitive). Tristimulus values quantify colour by representing the levels of stimulation in these three types of cone cells when exposed to a particular colour. These values form the basis for various colour models and are essential in applications such as colour science, colour matching, and colour management.

  • Tristimulus values are fundamental to colour measurement, whether in terms of the physiological response of the human eye to light or within systems used for precise colour matching and management in digital and physical media.
  • Tristimulus values are often linked to the CIE XYZ colour space, which is a standard in colour science for translating cone cell responses into numerical values that represent colour.
  • The notation for tristimulus colour values is typically represented using the three values X, Y, and Z in the CIE XYZ colour space. These values correspond to the quantified response of the L, M, and S cone cells, but they aren’t direct measurements of those responses. Instead, they are transformed to represent human vision in a way that can be standardized across various applications.
  • Tristimulus values serve as the foundation for converting physical light and colour into numerical formats used in digital displays, photography, and printing.

Trichromatic colour vision

Trichromatic colour vision, also known as normal colour vision, allows humans and some other animals to distinguish a wide range of colours due to the presence of three types of cone cells in the retina. Each types of cone cells is sensitive to a different range of wavelengths of light, corresponding roughly to blue, green, and red. The brain interprets the signals from these cones to create the perception of different colours.

  • Each types of cone cells is sensitive to a different range of wavelengths of light, corresponding roughly to blue, green, and red.
  • The brain interprets the signals from these cones to create the perception of different colours.
  • There are three different types of cone cells in the human retina:
    • S-cones: Most sensitive to short wavelengths (blue light)
    • M-cones: Most sensitive to medium wavelengths (green light)
    • L-cones: Most sensitive to long wavelengths (red light)
  • When light enters the eye, it stimulates these cone cells according to the wavelengths it contains. The brain then receives signals from these cones and interprets their combination as specific colours.

Trichromatic colour theory

The foundation of the trichromatic colour theory lies in understanding the physiological basis for the subjective experience of colour. It seeks to explain how our eyes and brains work together to create the rich world of colour we see around us.

  • Contemporary versions of trichromatic colour theory developed from several parallel lines of research:
    • One crucial discovery involved experiments around 1850. In these experiments, people were able to match a variety of coloured swatches by adjusting the intensity of three coloured lights – one red, one green, and one blue. This research showed that by carefully adjusting the intensity of these three coloured lights, a person could match a wide variety of colours. This led to the conclusion that any colour within the visible spectrum could be produced by mixing these three specific colours of light.
    • Another important line of research, beginning in the early 19th century, focused on understanding the structure of the human eye. This research revealed 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).

Trichromacy

Trichromacy is the form of colour vision (trichromatic colour vision) possessed by human beings and other trichromats. It involves three different types of cone cells and one type of rod cell within the retina of the eye. Three independent channels convey 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 and enable trichromatic colour vision.
    • 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 how colour information is produced across the entire surface of the retina of both eyes is encoded onto separate channels.

Triboluminescence

Triboluminescence is the emission of light caused by mechanical stress applied to a material. This stress can be from actions like rubbing, crushing, breaking, or scratching.

  • When a material is subjected to mechanical stress, it creates a separation of electric charges within the material. As the material reunites, the separated charges can recombine. This recombination releases energy in the form of a burst of visible light.
  • Not fully understood: While the basic mechanism is understood, the exact process of charge separation and recombination isn’t fully established and varies depending on the material.

Transverse wave

A transverse wave is a wave that oscillates up and down, left and right, or in any direction perpendicular to the direction it travels.

  • A transverse wave is a type of 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 waves on a string, water ripples, and certain types of seismic waves.
  • Note that light and other electromagnetic waves are transverse waves that can travel through a vacuum.
  • Transverse waves exhibit specific properties, including wavelength, frequency, amplitude, and wave speed.

Transmission

Transmission refers to the process of electromagnetic radiation passing through a medium. When electromagnetic waves move through a material without being absorbed or reflected, we say they are transmitted. If no radiation is reflected or absorbed at all, the material achieves 100% transmission.

  • When electromagnetic waves move through a material without being absorbed or reflected, we say they are transmitted.
  • If no radiation is reflected or absorbed , the material achieves 100% transmission.
  • Transmittance meanwhile is a way to measure how well a material allows light or other forms of radiation to be transmitted through it. It is essentially the fraction of incoming radiation that gets transmitted through the material.
  • A high transmittance value indicates the material allows most radiation to pass through, while a low transmittance indicates most radiation is absorbed or reflected.

Thermoluminescence

Thermoluminescence is the emission of light from a material when it is heated, following previous exposure to ionizing radiation.

  • Exposure to Radiation: When a material (usually a crystalline solid) is exposed to ionizing radiation (like X-rays, gamma rays, or cosmic rays), some electrons within the material get trapped in imperfections within the crystal structure.
  • Heating and Light Emission: When the material is heated, these trapped electrons gain enough energy to escape their traps. As they return to their original energy state, they release energy in the form of visible light.

Thermodynamics

The two laws of thermodynamics are fundamental principles that govern the behaviour of energy in the universe. They provide us with essential insights into how energy behaves and is transformed.

  • The First Law of Thermodynamics:
    • This law is a statement of the principle of conservation of energy. It states that energy can neither be created nor destroyed but only transferred from one form to another.
    • The total amount of energy in a closed system (one that does not exchange energy with its surroundings) remains constant.
  • The Second Law of Thermodynamics:
    • This law deals with the concept of entropy, a measure of disorder in a system.
    • A system with high entropy is more disordered than a system with low entropy. The second law states that in an isolated system (one that does not exchange matter or energy with its surroundings), entropy always increases over time.
    • This means that usable energy tends to disperse over time into less usable forms, leading to a gradual increase in disorder.
    • Entropy can be understood as a measure of how spread out or disorganized the energy in a system is. Over time, energy tends to disperse from concentrated usable forms to more spread-out unusable forms, increasing the overall disorder.

Thermal radiation

Thermal radiation is a form of electromagnetic radiation emitted by any object with a temperature above absolute zero (-273.15°C or 0° Kelvin). It’s a result of the movement of charged particles within the matter.

  • When charged particles change energy states, they release energy in the form of electromagnetic waves.
  • The frequency and intensity of this radiation depend directly on the object’s temperature.
  • All matter consists of atoms and molecules in constant motion. This motion has kinetic energy, which is associated with the temperature of an object.
  • As temperature increases, the motion of the particles becomes more agitated. This causes charged particles within the matter (like protons and electrons) to accelerate and change their energy states.
  • Thermal radiation covers a wide range of the electromagnetic spectrum. However, much of it falls within the infrared region, which we experience as heat. Hotter objects emit more thermal radiation and a higher proportion of radiation in the visible light spectrum. This is why very hot objects can start to glow red or white.

Temperature

Temperature is closely linked to how objects emit electromagnetic radiation, the energy form that includes light, heat, and radio waves.

  • All objects with a temperature above absolute zero (the coldest possible temperature) emit this type of energy.
  • The key thing to understand is that the temperature of an object influences the wavelength of the radiation it emits the most.
    • Hot objects: Emit more electromagnetic radiation at shorter wavelengths. Imagine a hot fire burning bright with blue hues. Similarly, hot objects emit a higher proportion of their energy at shorter wavelengths, which often appear bluish.
    • Cold objects: Emit more electromagnetic radiation at longer wavelengths. Think of a dimmer fire glowing red. Colder objects emit more radiation at longer wavelengths, which tend to be perceived as redder.
  • The relationship between temperature and the peak wavelength of an object’s radiation is described by Wien’s displacement law. This law states that the product of an object’s temperature and the peak wavelength of the radiation it emits is a constant.

Total internal reflection

Total internal reflection occurs when light travelling through a denser medium strikes a boundary with a less dense medium at an angle exceeding a specific critical angle. As a result, all the light is reflected back into the denser medium, and no light transmits into the second medium.

  • Total Internal reflection only takes place when the first medium (where the light originates) is denser than the second medium.
  • The critical angle is the angle of incidence above which total internal reflection occurs.
  • The critical angle is measured with respect to the normal.
    • The normal is an imaginary line drawn in a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.

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.

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

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.

Thermonuclear fusion

Thermonuclear fusion, also known as nuclear fusion, is a powerful process where atomic nuclei combine to form a heavier nucleus. This process releases enormous amounts of energy, millions of times greater than what we get from traditional chemical reactions like burning fossil fuels.

  • There are two forms of thermonuclear fusion (nuclear fusion):
    • Uncontrolled Fusion: This is the process where atomic nuclei merge spontaneously and release a tremendous amount of uncontrollable energy.
    • It is the natural process happening within stars and the principle behind thermonuclear weapons.
    • Controlled Fusion: Scientists are actively researching ways to achieve controlled fusion, where atomic nuclei are combined in a controlled environment.
    • This would allow us to harness the immense energy released for constructive purposes like generating clean and sustainable power, reducing reliance on fossil fuels, and potentially powering future space exploration endeavours.

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.

  • There are two main contexts to consider:
    • Circles: A tangent to a circle is a straight line that touches the circle at exactly one point – like a line just brushing against a ball. There’s also a special property – the radius drawn from the centre of the circle to the point of touch is always perpendicular (at a 90-degree angle) to the tangent line.
    • General Curves: A tangent line can also be applied to any smooth, curved shape. Here, the concept gets a bit more mathematical. We can define a tangent as a straight line that intersects the curve at exactly one point, but if we could zoom in infinitely close to that point, the curve would begin to resemble a straight line, and the tangent line would become indistinguishable from the curve itself.