Intro to Light and Quantum Optics

Light Theory

• The primary characteristic of light that supports the wave theory is its ability to exhibit diffraction, interference, and superposition.

Quantum Mechanics

• The field of study that deals with the behavior of light at an atomic and subatomic level is Quantum Mechanics.

Photometry

• The branch of science that deals with the measurement of the intensity of light is Photometry.

Wave-Particle Duality

• The fundamental concept that challenges the classical wave theory of light is the concept of wave-particle duality, which suggests that light can behave as both waves and particles.

Classical Wave Theory

• The underlying assumption of classical wave theory of light is that light is a continuous, wave-like disturbance that travels through space.

Fundamentals of Optics

• Optics is the study of the behavior and properties of light, including its interactions with matter.
• The visual system is a critical application of optics, involving the human eye and its functions.

Optical Elements and Sign Conventions

• Optical elements include objects, images, distances, and angles, which are crucial in understanding optical systems.
• A sign convention is used to describe the orientation and direction of light rays, with a Cartesian coordinate system.
• Distances and heights are measured in meters (m) or centimeters (cm), while angles are measured in degrees or radians.
• Magnitudes of optical elements are described using quantities such as focal length, object distance, and image distance.

Properties of Images and Optical Elements

• Images can be real or virtual, upright or inverted, and magnified or reduced, depending on the optical element.
• Graphical approaches, such as ray tracing, and analytical approaches, such as lens equations, can be used to analyze optical systems.
• Optical elements can produce a range of images, including real, virtual, upright, inverted, magnified, and reduced images.

Ophthalmic Lenses for Refractive Errors

• Ophthalmic lenses are used to correct refractive errors, such as myopia (nearsightedness), hyperopia (farsightedness), and astigmatism.
• The power of an ophthalmic lens is measured in diopters (D), which describes the degree of correction needed.
• Different types of ophthalmic lenses, including spherical, cylindrical, and aspheric lenses, are used to correct specific refractive errors.

Nature of Light

• Light is a travelling electromagnetic wave with wavelength (distance between two peaks) and frequency (number of times per second the two consecutive peaks hit one point in space)
• Light can also be described as a particle (photon) travelling through space

Reflection, Refraction, Interference, Diffraction, and Polarisation

• Reflection can be explained using waves and particles
• Refraction can be explained using waves and particles
• Interference can be explained using waves only
• Diffraction can be explained using waves only
• Polarisation can be explained using waves only

Electromagnetic Spectrum

• The electromagnetic spectrum consists of different waves, with greater frequency or shorter wavelength corresponding to more energetic radiation (higher energy photons) and potentially more danger to health
• The spectrum includes: Radio waves → Microwaves → Infrared waves → UV waves → X-ray → Gamma-ray

Optical Spectrum

• Wavelength (nm): 1 nm = 1 x 10^-9 m
• Regions of the spectrum relevant to optometrists:
  • Infrared: 700-400 nm
  • Optical: 400-700 nm
  • UV: 1-400 nm
• UVA wavelength penetrates right into the dermis and is associated with ageing
• UVB wavelength penetrates the dermis
• UVC wavelength only penetrates the epidermis and is associated with burning

Light as Waves

• Light travels on a straight path but bends (refracts) when travelling through a transparent object
• Light can be reflected, scattered, absorbed, or transmitted (e.g., sunglasses absorb visible light and reduce transmission)

Properties of Light

• A wave is a disturbance that transfers energy from one point of a medium to another without the medium itself moving noticeably
• Speed of light in a vacuum (C) = 300,000 km/s or 300,000,000 m/s
• In media other than a vacuum, the speed of light is slowed down (v < C)
• Refractive index (RI) of a medium affects the speed of light propagation
• RI is 1 in a vacuum and >1 everywhere else

Colour

• The human eye perceives light as different colours
• Colour depends on the length of the light wave
• Wavelengths of red (longest), green, and violet (shortest) light
• Colour properties → hue, colourfulness, and brightness
• Chroma = colourfulness relative to brightness
• Lightness = relative brightness
• Saturation = colourfulness of an area judged in relation to its brightness
• Primary additive colours → red, green, and blue: mixing all gives us white
• Primary subtractive colours → cyan, magenta, and yellow: mixing all gives us black

Nature of Light

• Light is a travelling electromagnetic wave with wavelength (distance between two peaks) and frequency (number of times per second the two consecutive peaks hit one point in space)
• Light can also be described as a particle (photon) travelling through space

Reflection, Refraction, Interference, Diffraction, and Polarisation

• Reflection can be explained using waves and particles
• Refraction can be explained using waves and particles
• Interference can be explained using waves only
• Diffraction can be explained using waves only
• Polarisation can be explained using waves only

Electromagnetic Spectrum

• The electromagnetic spectrum consists of different waves, with greater frequency or shorter wavelength corresponding to more energetic radiation (higher energy photons) and potentially more danger to health
• The spectrum includes: Radio waves → Microwaves → Infrared waves → UV waves → X-ray → Gamma-ray

Optical Spectrum

• Wavelength (nm): 1 nm = 1 x 10^-9 m
• Regions of the spectrum relevant to optometrists:
  • Infrared: 700-400 nm
  • Optical: 400-700 nm
  • UV: 1-400 nm
• UVA wavelength penetrates right into the dermis and is associated with ageing
• UVB wavelength penetrates the dermis
• UVC wavelength only penetrates the epidermis and is associated with burning

Light as Waves

• Light travels on a straight path but bends (refracts) when travelling through a transparent object
• Light can be reflected, scattered, absorbed, or transmitted (e.g., sunglasses absorb visible light and reduce transmission)

Properties of Light

• A wave is a disturbance that transfers energy from one point of a medium to another without the medium itself moving noticeably
• Speed of light in a vacuum (C) = 300,000 km/s or 300,000,000 m/s
• In media other than a vacuum, the speed of light is slowed down (v < C)
• Refractive index (RI) of a medium affects the speed of light propagation
• RI is 1 in a vacuum and >1 everywhere else

Colour

• The human eye perceives light as different colours
• Colour depends on the length of the light wave
• Wavelengths of red (longest), green, and violet (shortest) light
• Colour properties → hue, colourfulness, and brightness
• Chroma = colourfulness relative to brightness
• Lightness = relative brightness
• Saturation = colourfulness of an area judged in relation to its brightness
• Primary additive colours → red, green, and blue: mixing all gives us white
• Primary subtractive colours → cyan, magenta, and yellow: mixing all gives us black

Quantum Optics

• Ephoton (E) = hv, where h is Planck's constant (6.63 x 10^-34 J/s) and v is the frequency of light in hertz
• Transitions between energy levels generate light of specific wavelengths (UV or visible)
• Quantum theory: light energy is quantized and transferred in small parcels called quanta (photons)
• Photons have properties like frequency, wavelength, and energy

Emission Spectrum

• Atomic emissions produce discrete spectra (e.g., fluorescent lighting)
• Thermal emissions produce continuous spectra (e.g., incandescent light)

Radiometry and Photometry

• Radiometry: measures physical quantities of EM radiation (independent of human vision)
• Photometry: measures the part of radiant power that is perceived by humans (visible light)
• Each radiometric unit has a corresponding photometric magnitude/unit

Measurement Units

• Radiant power or flux (W) depends on wavelength
• Luminous power or flux (lumens) = radiant flux * luminous efficiency
• Steradian (Sr): solid angle subtended by a unit area on a unit sphere
• Radiant intensity (W/sr): power emitted in a solid angle by a point source
• Luminous intensity (Candela, lm/sr) = power emitted within the visible range in a specific direction
• Radiance (W/sr/m2): radiant intensity per unit of projected area of an extended source
• Luminance (candela/m2): luminous intensity in a solid angle or extended source perceived by humans
• Irradiance (W/m2): amount of radiation reaching a surface
• Illuminance (lm/m2): amount of lumens reaching a surface

Laws

• Inverse square law for illuminance: illuminance decreases with the square of the distance
• Lambert's cosine law of illumination: illuminance reduced by cosine of the angle with the perpendicular

Filters and Transmittance

• Neutral density filters reduce all wavelengths
• Coloured filters remove specific wavelengths
• Not all coloured filters work perfectly

Vergence (L)

• Definition: reciprocal of the radius of curvature of the wavefront (1/metre, Diopter)
• Convergent wavefront: +ve vergence
• Divergent wavefront: -ve vergence
• Planar wavefronts: image at optical infinity (~6-10m)
• Measuring from the wavefront to the centre:
  • Object space: -ve (against direction of light)
  • Image space: +ve (with direction of light)

Calculating Vergence

• Vergence = L = 1/r(metre) Diopter
• Reduced vergence L = n/r(metre) Diopter (n>1, for media other than vacuum)

Objects, Images, and Blur

• Primary light source: creates light it emits
• Secondary light source: reflects light from a primary source
• Point source: distance > 5 times the largest dimension of the object
• Extended source: consists of many point sources
• Shadows: umbra (point source) and penumbra (extended source)
• Blur circles: image plane, aperture, and screen position affect blur circle size

Eye and Vision

• Light converges on the retina = image position
• Emmetropia: light converges on the retina
• Ametropia: converging light does not focus on the retina (blurred image)
• Types of ametropia:
  • Hyperopia (long-sightedness): image falls behind the retina
  • Myopia (short-sightedness): image falls before the retina
• Pinhole camera: produces real and inverted images

Quantum Optics

• Ephoton (E) = hv, where h is Planck's constant (6.63 x 10^-34 J/s) and v is the frequency of light in hertz
• Transitions between energy levels generate light of specific wavelengths (UV or visible)
• Quantum theory: light energy is quantized and transferred in small parcels called quanta (photons)
• Photons have properties like frequency, wavelength, and energy

Emission Spectrum

• Atomic emissions produce discrete spectra (e.g., fluorescent lighting)
• Thermal emissions produce continuous spectra (e.g., incandescent light)

Radiometry and Photometry

• Radiometry: measures physical quantities of EM radiation (independent of human vision)
• Photometry: measures the part of radiant power that is perceived by humans (visible light)
• Each radiometric unit has a corresponding photometric magnitude/unit

Measurement Units

• Radiant power or flux (W) depends on wavelength
• Luminous power or flux (lumens) = radiant flux * luminous efficiency
• Steradian (Sr): solid angle subtended by a unit area on a unit sphere
• Radiant intensity (W/sr): power emitted in a solid angle by a point source
• Luminous intensity (Candela, lm/sr) = power emitted within the visible range in a specific direction
• Radiance (W/sr/m2): radiant intensity per unit of projected area of an extended source
• Luminance (candela/m2): luminous intensity in a solid angle or extended source perceived by humans
• Irradiance (W/m2): amount of radiation reaching a surface
• Illuminance (lm/m2): amount of lumens reaching a surface

Laws

• Inverse square law for illuminance: illuminance decreases with the square of the distance
• Lambert's cosine law of illumination: illuminance reduced by cosine of the angle with the perpendicular

Filters and Transmittance

• Neutral density filters reduce all wavelengths
• Coloured filters remove specific wavelengths
• Not all coloured filters work perfectly

Vergence (L)

• Definition: reciprocal of the radius of curvature of the wavefront (1/metre, Diopter)
• Convergent wavefront: +ve vergence
• Divergent wavefront: -ve vergence
• Planar wavefronts: image at optical infinity (~6-10m)
• Measuring from the wavefront to the centre:
  • Object space: -ve (against direction of light)
  • Image space: +ve (with direction of light)

Calculating Vergence

• Vergence = L = 1/r(metre) Diopter
• Reduced vergence L = n/r(metre) Diopter (n>1, for media other than vacuum)

Objects, Images, and Blur

• Primary light source: creates light it emits
• Secondary light source: reflects light from a primary source
• Point source: distance > 5 times the largest dimension of the object
• Extended source: consists of many point sources
• Shadows: umbra (point source) and penumbra (extended source)
• Blur circles: image plane, aperture, and screen position affect blur circle size

Eye and Vision

• Light converges on the retina = image position
• Emmetropia: light converges on the retina
• Ametropia: converging light does not focus on the retina (blurred image)
• Types of ametropia:
  • Hyperopia (long-sightedness): image falls behind the retina
  • Myopia (short-sightedness): image falls before the retina
• Pinhole camera: produces real and inverted images

Refraction on Flat Surfaces

• Refraction is the decrease in speed of light when traveling in a medium other than vacuum/air.
• The decrease in speed depends on the medium and is quantified using the refractive index (RI): n = c/v.
• When light travels in a medium other than vacuum/air, its wavelength decreases and the distance between wavefronts decreases.
• The wave slows down, and the wavefronts become closer together, similar to moving from concrete to grass.

Refraction at an Interface

• When light rays travel perpendicular to the interface, there is no change in direction.
• When light rays do not travel perpendicular to the interface, the change in speed (refraction) causes the light rays to bend.
• The light path is reversible.

Laws of Refraction

• The 1st law of refraction states that the incident and refracted rays and the normal are on the same plane (perpendicular to the refractive surface).
• The 2nd law of refraction, Snell's law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, which is equal to the ratio of the refractive indices of the media.
• The change in direction depends on the angle of incidence and the ratio of the refractive indices (n vs n').

Snell and Dispersion

• For non-normal incidence, the deviation of refracted rays depends on the change in speed of light, which depends on the refractive index (n).
• In a medium other than vacuum, the speed of light decreases more for shorter wavelengths.
• Shorter wavelengths (blue) deviate more than longer wavelengths (red).

Refraction vs Reflection

• The angle of the refracted ray increases with the angle of incidence.
• As the angle of incidence increases, the intensity of the refracted ray decreases, while the intensity of the reflected light increases.
• There is an angle of incidence for which there is no light refracted, and for larger angles, all the light is reflected.

Critical Angle and Total Internal Reflection (TIR)

• For all angles greater than the critical angle (the angle of incidence for which the angle of refraction is 90 degrees), all light is reflected back into the first medium, resulting in total internal reflection.
• TIR only occurs when light travels to a medium with a lower refractive index: sin(θ) is always less than or equal to 1.
• To find the critical angle, divide the refractive index of the second medium by the refractive index of the first medium, then take the inverse sine of that number.

Anatomy of the Cornea

• The cornea is the anterior 1/6 of the globe, comprising 5 layers: epithelium, Bowman's layer, stroma, Descemet's membrane, and endothelium.
• It merges with the sclera and conjunctiva in a transitional region called the limbus.

Dimensions of the Cornea

• The cornea has an oval appearance anteriorly, measuring 11.7mm horizontally and 10.6mm vertically.
• Posteriorly, it is circular, with a diameter of approximately 11.7mm.
• The cornea is thinnest centrally, with a thickness of approximately 550 μm, increasing to 700 μm in the periphery.
• The radius of curvature averages 7.7mm anteriorly and 6.9mm posteriorly.

Optical Zones

• Only the central optical zone (central 3-4mm) is responsible for image formation.
• The remainder is for mechanical support and peripheral vision with a dilated pupil.
• The central zone is mostly spherical, while the paracentral zone is generally spherical but flatter than the central zone.
• The peripheral zone flattens significantly, and the limbal zone transitions into the sclera and conjunctiva.

Corneal Epithelium

• The corneal epithelium is approximately 50-60 μm thick, consisting of 5 layers of cells centrally.
• It is a non-keratinized, stratified squamous epithelium with wing cells and columnar basal cells.
• The superficial cells are 2-3 layers thick, attached to each other by desmosomes, and have microvilli and microplicae on the outer surface to bind to the mucous component of the tear film.
• The wing cells have tight, lateral, intercellular junctions and multiple gap junctions, allowing for free communication between cells.
• The basal cells are a single layer of tall columnar cells sitting on a basement membrane, adherent to the membrane by anchoring complexes.
• The corneal epithelium has a complete turnover every 10 days, with the X, Y, Z hypothesis of corneal epithelial maintenance.

Basement Membrane

• The basement membrane is 40-100 nm thick, secreted by the epithelial cells, and composed of type IV collagen, laminin, heparin sulfate proteoglycans (HSPGs), and nidogens.
• It aids in binding the epithelium to the underlying Bowman's layer.

Bowman's Layer

• Bowman's layer is an acellular collagen fibril matrix, approximately 12μm thick, mainly composed of type I collagen, but also types III, V, and VI.
• The collagen fibrils are finer and more randomly arranged than in the stroma, and may be considered a modified superficial layer of the stroma.

Corneal Stroma

• The corneal stroma is a dense, regular connective tissue, comprising approximately 90% of the corneal thickness.
• It is composed of water, collagen arranged into lamellae, keratocytes between the lamellae, proteoglycans, and glycosaminoglycans (GAGs).
• The main collagen type is type I, with small amounts of types III, V, and VI.
• There are approximately 200-300 lamellae, with all fibrils in the same lamellae running in the same direction.

Stromal Cells

• Keratocytes (corneal fibroblasts) are flattened cells that lie between the lamellae, maintaining stromal collagen and ECM.
• They have large nuclei with minimal cytoplasm and communicate with each other via numerous long processes and gap junctions.

Proteoglycans and Glycosaminoglycans

• The four core proteoglycan proteins are decorin, lumican, keratocan, and mimican, with different distributions in the anterior and posterior stroma.
• The two types of GAGs found in the cornea are keratan sulfate (KS) and dermatan sulfate (DS), bound to a proteoglycan core protein.
• They attract and bind water, helping to maintain the precise spacing between collagen fibrils.

Descemet's Membrane

• Descemet's membrane is the basement membrane of the endothelium, composed of type IV collagen.
• It is approximately 5μm thick at birth and is produced throughout life, reaching approximately 15μm over a lifetime.
• It is divided into two laminae: the anterior lamina and the posterior lamina.

Corneal Endothelium

• The corneal endothelium is the innermost corneal layer, adjacent to the aqueous humor and anterior chamber.
• It is a single layer of flattened polygonal cells, approximately 20μm in diameter and 4-6μm thick.
• The cells have numerous mitochondria, a prominent endoplasmic reticulum, and a Golgi apparatus, and are involved in fluid production and transportation.
• The endothelial cells are not replenished and decrease with age.

Corneal Clarity

• The cornea is responsible for most of the refractive power in the globe.
• Corneal clarity is maintained by the regular collagen size, spacing, and lattice pattern, as well as the lattice fibril arrangement, which causes light to scatter off the fibrils and interfere destructively.

Nutrient Supply to the Cornea

• The cornea is avascular and receives nutrients by diffusion from the aqueous humor and limbal vessels.
• Oxygen is mainly obtained from atmospheric oxygen dissolved in the tear film, with some obtained from the aqueous or limbal capillaries.

Corneal Nerves

• The cornea is the most richly innervated body tissue, with approximately 160,000 nerve terminals/mm2.
• The sensory nerves are supplied by long ciliary nerves (ophthalmic branch of CN V) and form a unmyelinated plexus whose branches are mostly within the middle 1/3 of the stroma to Bowman's layer.