week 10

what is a fresnel zone plate

optical device that acts like a flat lens which has a pattern of concentric, alternating opaque (blocks light) and transparent (allows light through) rings that work together to manipulate incoming wavefronts and generate a focal point through diffraction

how does a Fresnel zone plate focus light compared to a traditional spectacle lens

traditional lens uses refraction which is the bending of light by changing its speed through curved surfaces of varying thickness whereas Fresnel uses diffraction which forces light waves to bend, spread and interfere with each other as they pass through narrow slits

how can the angle of diffraction be increased

reducing slit width or increasing wavelength of light waves

why must the concentric rings of Fresnel zone plate become progressively narrower and tighter together moving from the center out to the edge

to decrease slit width toward the periphery. this increases the angle of diffraction at the edges forcing outer light rays to bend sharply enough to hit the exact same central focal point as the inner rays

why does the spacing between the slits in a Fresnel zone plate decrease from the center to the edge

to continually increase the angle of diffraction for the outer light rays to ensure that all wavefronts arrive completely in phase at exact same focal point

what major optical drawback occurs when a manufacturer drastically reduced the zone plate spacing to achieve higher focusing power

less overall light transmission since the slits are narrower which reduces image brightness and quality

what phase state must all the diffracted light wavefronts be in when they reach the focal point of a Fresnel zone plate

all be in phase to allow the overlapping light waves to constructively interfere, reinforcing each other to create a single, sharp focus

how do diffractive ophthalmic lenses divide the workload between distance vision and reading power

distance vision is provided by the traditional refraction through central curved surface of the lens whereas reading add via diffraction is provided by a Fresnel zone plate integrated into the lens

what is the primary visual complaint that causes poor patient acceptance and unpopularity for diffractive contact lenses

ghosting of images which occurs because the patient’s pupil area covers multiple diffractive zones at once causing light to focus at different points simultaneously

besides pupil size changes, what two dynamic ocular surface factors negatively impact the visual quality of a diffractive contact lens

fluctuations in the tear film and buildup of contact lens deposits

how do diffractive-refractive IOLs implanted after cataract surgery separate distance and near focal points

distance vision is provided by the refractive central zone of the intraocular lens whereas the reading add is provided by the diffractive peripheral zone surrounding the center

what four physical factors determine how light waves interfere with each other when passing through a thin film

thickness and refractive index of film, wavelength of light relative to the film’s thickness and angle of incidence of incoming light

when an oil film sits on water, why does the thickness λ/2 result in constructive interference for the reflected light ​

the path travels distance down and back through the film equals one full wavelength. when combined with phase changes at the boundaries, the light waves reflected from the air-oil interface and the oil-water interface one up perfectly in phase, reinforcing each other

how can a thin film that is currently causing constructive interference suddenly switch to causing destructive interference

changing wavelength of incoming light (changing its colour) or by changing the angle of incidence at which the light strikes the film surface which alters the optical path length and shifts the waves out of phase

why must a single layer ar coating have a physical thickness of exactly one quarter wavelength

because light must travel down and back through the coating and the thickness forces the light wave reflecting off the back surface to travel a total extra distance of half a wavelength, placing it perfectly out of phase with the front reflection causing destructive interference

does an ar coating absorb light energy it cancels out through destructive interference/? what happens to that light?

no absorption happens, the light energy cancelled by destructive interference is redirected in the forward direction which directly increases overall light transmission through the ophthalmic lens to the eye

what is the mathematical relationship required between the refractive index of the film and the lens substrate for a single layer arc to completely eliminate reflections

the ideal film index must equal the square root of the lens index

what are the primary benefits of magnesium fluoride as an arc material and what is its refractive index

n=1.38 and good adhesion to lens surface, abrasion-resistant and relatively inexpensive

why is a magnesium fluoride coating nf=1.38 ideal for high-index glass lenses nl=1.90 but less effective on standard plastic lenses nl=1.50

because the square root of nl=1.90 is approximately 1.38 making magnesium fluoride a match for 1.90 high index whereas for nl=1.50, the value is lower than nf=1.38

why do single layer magnesium fluoride coatings produce a distinct purple residual reflection on the lens

the single layer thickness is optimised perfectly for the center of the visible spectrum at ~550nm creating a v-shaped reflection curve which because the reflection is higher at the outer blue and red ends of the spectrum, the combined remaining reflections looks purple

under what two optical conditions does a single layer arc fail to work efficiently

when the refractive index of the film does not match the mathematical ideal relative to the lens and for wavelengths of light where the physical coating thickness is not exactly quarter of a wavelength such as short wavelength blue or long wavelength red

why can a single layer arc never reduce reflections to 0% on a standard polycarbonate lens n=1.58

polycarbonate requires a arc material with refractive index of approximately 1.22 to work perfectly and no durable, stable coating material exists in nature with a refractive index that low

what is the typical minimum reflection percentage per surface achievable by a standard single-layer arc due to material index mismatches

~1.4%

what is the primary optical advantage of using a multilayer arc stack (3-5+ layers) instead of a single layer coating

reduces surface reflections across a wide range of wavelengths spanning the entire visible spectrum rather than optimising for just one central wavelength

how do the multiple layers of an arc stack work together to systematically eliminate reflections

the layers vary in thickness and refractive index which creates destructive interference for multiple individual wavelengths simultaneously, while forcing light reflecting off the different boundary interfaces to destructively interfere with each other

describe the shape of the reflection curve for a multilayer arc and identify the wavelengths where reflections is reduced the most

features a w-shaped reflection curve and maintains low reflection across the entire visible spectrum with absolute greatest reductions occurring at 450nm blue light and 670nm red light

why do lenses with multilayer arc coatings exhibit a pale green/green-yellow residual reflection

because the w-shaped curve reduces blue and red reflections heavily, leaving a relatively higher though still very low reflectance right in the middle of the spectrum

which materials are used on the outermost surface of a multilayer stack for durability and what high/low index materials are alternated beneath them

magnesium fluoride or silicon dioxide for outer and high index titanium dioxide and low/medium index aluminium oxide of varying thickness

what does the acronym QHQ stand for in a common three layer arc design and what does it describe

stands for quarter half quarter and describes using three layers of different optical materials stacked in thickness of quarter, half, and quarter wavelength

to what absolute minimum percentage can a high-performing precision multilayer arc reduce surface reflections across most of the visible spectrum

below 0.1%

how are refractive indices arranged in a qhq stack and what specific materials are preferred for the outermost layer

internal structure comprises alternating layers of both low and high refractive index and the outer layer is typically made of MgF2 or SiO2 because they are structurally robust and high resistant to abrasion

what is the primary cosmetic benefit of an arc coating ad for which lens type is this effect most dramatic

reduction in surface reflections which allows people to see the wearer’s eyes and most significant for high-index lenses which naturally reflect more light

by how much does a standard arc increase overall light transmission through a spectacle lens and how much is this gain divided

~7% which is achieved by recovering about 3.5% of lost light transmission from each of the two lens surfaces

what debilitating visual phenomenon occurs due to internal reflections within an uncoated lens and how does an arc fix it

ghosting of images which is the spurious internal reflections that create faint double images especially noticeable at night with headlights which the arc eliminates these internal reflections

what is the function of a dichroic filter in ophthalmic equipment and how does it achieve this

manages the reflection and transmission of light for specific target wavelengths and works by regulating constructive and destructive interference through thin film layers to selectively allow certain colours/wavelengths to pass through while reflecting others which acts as a beam splitter

name a retinal image instrument used daily in optometry that relies entirely on the principle of light interference

optical coherence tomography which uses low-coherence interferometry to compare light reflected off retinal tissue layers against a reference mirror creating micrometer resolution cross sectional scans of the eye

what is unpolarised light in terms of its electric field oscillations

it is a light beam consisting of waves with their electric fields oscillating in multiple directions that are all perpendicular to the direction the light is travelling (the axis of propagation)

why physical tool is used to transform unpolarised light into polarised light and what material is it typically made of

polarising filters also called polarisers which are made of specialised thin plastic sheets

what is plane polarised light or linearly polarised light

light consisting of waves that oscillate in only a single plane or with a single uniform spatial orientation

how does a polariser decide which light waves to let through and which to block

only allows light waves that are oscillating parallel to its transmission axis to pass through. it completely blocks all other light waves oscillating in non-parallel directions

how much total incident unpolarised light does a perfect polariser transmit versus block and what causes the blockage

transmits exactly 50% and blocks the other 50% which is lost due to absorption by the filter material

in a polarised optical system, what is an analyser

second polariser placed downstream from the first polariser and is used to analyse, further transmit or completely block the polarised light emerging from the first filter by changing its orientation

define each variable in Malus’ Law (I, I0 and theta)

I=intensity of light transmitted through the analyser, I0=intensity of polarised light incident on the analyser and theta=angle between the transmission axis of the polariser and the transmission axis of the analyser

according to Malus’ law, what happens to the transmitted light intensity I when the analyser is aligned perfectly parallel to the polariser theta=0 degrees

transmitted intensity is at its macixum and since cos(0)² is 1, all of the incident polarised light passes through the analyser

according to Malus’ Law, what happens to the transmitted light intensity I when the analyser’s axis is oriented perpendicular to the polariser theta=90 degrees

transmitted intensity drops to zero I=0 which is known as the crossed polarisers condition and since cos(90)²=0, the analyser completely blocks all incoming light

how does unpolarised light from the sun or a lightbulb become naturally polarised without passing through a plastic filter

becomes polarised via specular reflection when it bounces off smooth, non-metallic surfaces

wha are two common everyday examples of smooth surfaces that cause natural polarisation via specular reflection

surface of water like lakes, oceans, puddles and smooth non-metallic surfaces like roads or glass windows

when unpolarised light reflects off a flat, horizontal surface like a wet road or lake, what is the dominant orientation os the resulting polarised light

horizontally polarised which the human eyes perceive as blinding glare

what is Brewster’s angle

specific angle of incidence at which unpolarised light when reflecting off a smooth, non-metallic surface becomes 100% completely polarised

what happens to the polarisation of reflected light if it strikes a surface at an angle either greater than or less than Brewster’s angle

reflected light will not be completely polarised, only partially. complete polarisation only occurs exactly at Brewster’s angles

what is the precise geometric relationship between the reflected ray and the refracted ray when light hits a surface exactly at Brewster’s angle

reflected and refracted ray are perpendicular to each other

how are s-polarised and p-polarised light waves defined relative to the plane of incidence

p-polarised light is where the electric field vibrates parallel to the plane of incidence whereas in s-polarised light, the electric field vibrates perpendicular to the plane of incidence

what happens to reflection amplitudes of p-polarised vs s-polarised light exactly at Brewster’s angle

in p-polarised light, the reflected wave completely disappears (drops to zero amplitude) whereas in s-polarised light, the reflected wave does not diminish and its reflection continuously increases as the incident angle grows

what material and chemical dopant are polarising sunglasses made of

polarising film of polyvinyl alcohol plastic with iodine doping

what manufacturing step causes the PVA molecular chains to align in one particular direction

stretching the plastic sheet during manufacture forces the long chain PVA molecules to physically align parallel to each other in one direction

why does light polarised parallel to the aligned molecular chains of the PVA sheet get blocked (absorption axis)

light waves with an electric field aligned parallel to the molecular chains easily transfer their energy to the electros in the plastic medium and this energy transfer causes the light to the completely absorbed

why does light polarised perpendicular to the aligned molecular chains pass through the lens (transmission axis)

light waves with an electric field perpendicular the molecular chains cannot transfer energy to the electrons and becuase there is no energy exchange, the light passes straight through and is transmitted

if a perfect polariser transmits 50% of unpolarised light, how do sunglasses achieve a darker, safer transmission of around 25%

manufacturers add a secondary, non-polarisation-specific absorber (tint) which means only ~50% of the total light absorption is actually polarisation specific and the rest is standard tint

in what direction is the transmission axis oriented in standard polarising sunglasses and why

oriented vertically meaning absorption axis is horizontal. this is chosen because glare reflecting off horizontal surfaces consists of horizontal electric vectors which the horizontal absorption axis blocks

in optical terms, how do polarising sunglasses act as an analyser for a wearer outdoors

act as an analyser because the environment naturally polarises light horizontally via reflections. the sunglasses evaluate this incoming light, systematically blocked the horizontal glare component

under what theoretical condition do polarising sunglasses work at their absolute best to eliminate reflections

when unpolarised light reflects off a flat, horizontal specular surface exactly at Brewster’s angle. at this angle, the reflected glare becomes 100% horizontally polarised allowing the vertical transmission axis of the glasses to block it completely

what is the primary optical benefit of polarising sunglasses and what are four common outdoor activities where they are highly recommended

drastic reduction of blinding reflected glare, good for fishing, water activities, skiing and other outdoor sports

what is the clinical function of diffractive elements inside modern contact lenses and intraocular lenses (iols)

they create a multifocal effect by splitting incoming light into two or more simultaneous focal points, allowing the patient to see clearly at both distance and near planes

what is the difference between a polarizer and an analyser in a laboratory or clinical optical setup

a polarizer restricts random light into a single linear plane of vibration, while an analyser is a second polarizing element used to measure, control, or block the orientation of that polarized light beam

what are the three primary clinical benefits of adding an anti-reflective (ar) coating to a spectacle lens

it increases total light transmission to the eye, eliminates distracting internal ghost images, and removes external cosmetic reflections so the wearer's eyes are clearly visible to others