Optics - Final

Stehl ratio. What it tells us? What is the ideal ratio?

gives us information about PSF

Stehl ratio = height of PSF measured/height of PSF in ideal case

• closer to one = better

• ideal case = limited by diffraction only

What causes chromatic aberration?

Dispersion: refractive index varies with wavelength, so different wavelengths are refracted by different amounts

What is dispersion?

Variation in refractive index with wavelength

how does wavelength and refractive index vary. What happens to refractive index when wavelength increases?

short wavelengths are refracted more strongly. Aka the refractive index/lens power increases as wavelength decreases (and vice versa).

Short wavelength/blue light has higher n, travels slower, bends more, and focuses closer to the lens.

what is optical path length? what can it be used to measure

will travel slower

OPL = n x distance

• n is higher for short wavelength light

• OPL will be greater

when light enters a new (higher) medium, what changes

• frequency

• wavelength

• speed

• frequency stays constant

• wavelength decreases

• speed decreases

v=c/n

v=f/λ

How many types of chromatic aberrations are there? What are they called and describe them.

1. Longitudinal chromatic aberration

• different colours focus at different planes.

• since power increases with decreasing wavelengths, different wavelengths focus at different axial distances.

Longitudinal chromatic aberration occurs for what kind of object point?

mainly described for an on-axis object point

What is transverse chromatic aberration?

Different wavelengths focus at different heights

Longitudinal chromatic aberration occurs for what kind of object point?

mainly described for off-axis object points.

What ray trace would differ in longitudinal chromatic aberrations?

what ray would differ in transverse chromatic aberrations?

1. Longitudinal

• PMR (cross axis at different points)

2. Transverse

• PPR (rays at different heights)

What is dispersion measured as? (important) What do higher/lower values mean.

Abbe V-value describes dispersion (variation in refractive index with wavelength)

related to the difference in power ΔF between hydrogen blue & red wavelengths is related to V-value by the equation

• lower v-value = more dispersion (more chromatic aberrations)

• higher v-value = less dispersion (more aberration)

if the aperture stop is at the lens would you get chromatic aberration?

no transverse chromatic aberration when the AS is at the lens!

when the AS is infront of the lens do you get chromatic aberrations?

YEW

AS in front = positive transverse chromatic aberrations

positive = blue lower

when the AS is infront of the lens do you get chromatic aberrations?

AS behind the lens = Negative transverse chromatic aberration

Key aperture stop rule for chromatic aberration?

LCA not really affected by stop position; TCA depends strongly on stop position

What is an achromatic doublet? How does it work?

Two lenses, usually different materials and powers, combined to reduce chromatic aberration.

• ·         two thin lenses in contact (F1 + F2 = F)

Uses materials with different Abbe V-values and lens powers so chromatic aberrations partly cancel.

What signs of lenses are often combined in an achromatic doublet?

a positive and negative lens combination to cancel out and control aberrations.

Does an achromatic doublet remove all chromatic aberration?

no, there is still some residual chromatic aberration. This technically only fully reduces red and blue because these are how the abbe value is calculated

sign of chromatic aberration (longitudinal and transverse) depends on what?

longitudinal

• always the lens power

  • keplarian = positive

  • galilean = negative

transverse

• depends on:

  • aperture stop position

  • lens powers

in a keplarian telescope, does it have transverse and longitudinal aberrations? Where do they come from?

Transverse aberrations are ONLY COMING FROM THE EYE LENS

• objective stop is the AS!!

• positive chromatic aberrations

Does the human eye have chromatic aberration?

Yes. The eye has both longitudinal and transverse chromatic aberration

what is the MTF?

The modulation transfer function describes how well an optical system transfers contrast from object to image as a function of spatial frequency

photon energy, wavelengths and frequency

shorter wavelengths have higher frequency and higher photon energy

snell’s law

describes how much light bends when it crosses from one medium to another

how will light bend/change speed from:

low n → high n?

slower, bend toward normal

how will light bend/change speed from:

high n → low n?

faster, bend away from normal

Optical path length

Optical path length (OPL) = n x distance

Fermat’s principle, Snell’s law link?

The path taken must be the path with the least travel time

Snell’s law follows from Fermat’s principle because light bends at a boundary to minimise/stabilise optical travel time.

critical angle

the angle of incidence where the refracted ray bends so much that it travels along the boundary between the two media

it only happens when light travels from:

higher refractive index → lower refractive index

At the critical angle:

θr=90∘

Total internal reflection

Total internal reflection occurs when light travels from a higher refractive index medium to a lower refractive index medium and the angle of incidence exceeds the critical angle

angle of incidence > critical angle

describe what happens to light:

1. below the critical angle

2. at the critical angle

3. above the critical angle

• Below critical angle
  Some light is refracted out into the second medium, and some is reflected.

• At critical angle
  The refracted ray bends to 90°, so it travels along the boundary.

• Above critical angle
  No refracted ray exits into the second medium. The light is totally internally reflected back into the original medium.

apply critical angle and TIR to telecommunication

Critical angle is important in optical fibres.

Light travels through a high refractive index core surrounded by lower refractive index cladding.

If the angle of incidence at the core-cladding boundary exceeds the critical angle, total internal reflection occurs, so light is guided along the fibre with minimal loss over long distances.

apply critical angle and TIR to telecommunication

Critical angle/TIR can be relevant to light guiding in retinal structures, especially photoreceptors/Müller cells acting partly like optical waveguides. This helps direct light toward photoreceptor outer segments.

refracted and reflected ray will be on what side of the normal to the incident ray?

Opposite side of the normal

filters can alter light beams in which way

1. intensity

2. spectral distribution (ex. spectral filters transmitting specific wavelengths)

define scattering

Scattering is the redirection of light after interaction with particles, molecules or structures

Rayleigh scattering. What is scattering intensity proportional to?

happens when light is scattered by tiny particles/molecules smaller than the wavelength of light (e.g. N2 & O2)

• Scattering intensity is proportional to: 1/λ^4​

• this is why blue light gets scattered more!

Rayleigh scattering and polarisation

In Rayleigh scattering, the degree of polarisation depends on scattering angle. Light scattered at 90° to the incident beam is maximally polarised, while light scattered directly forward or backward is unpolarised.

Mie scattering

Mie scattering occurs with particles larger than the wavelength (dust, water droplets) and is less wavelength-dependent

• light sprays in all directions

why is the sky blue and black in space

• in space, no particles smaller than wavelength so no rayleigh scattering of blue wavelengths

• sky blue because blue gets scattered most

why are sunsets red

• At noon: sunlight travels through less atmosphere, so only some blue is scattered away. The sun still looks yellow-white.

• At dawn/dusk: sunlight travels through much more atmosphere, so much more blue/short-wavelength light is removed from the beam.

Sunsets look red because the blue light has been scattered out of the direct beam before it reaches you.

mars atmosphere (yellow/brown). Why?

looks yellow/brown due to mie scattering through fine dust

scattering (including absorption) of sunlight by dust in the atmosphere account for this colour

what is polarisation? (important)

Polarisation describes the direction of oscillation of the electric field in a transverse light wave.

states of polarised light (4) (important)

• plane

• unpolarised

• partially-polarised

• elliptically polarised

• arrows in these pictures depict the electric field strength and direction

describe plane polarized light

the electric field vector is confined to a single plane

describe unpolarized light and give example

light that’s electric field is randomly oriented in any direction

• e.g. sun

describe partially-polarised light and give an

• mix of unpolarised and plane polarised light

What does it mean that light is an electromagnetic wave?

Light is a transverse electromagnetic wave made of oscillating electric and magnetic fields. The electric and magnetic fields are perpendicular to each other and both are perpendicular to the direction of propagation. The wave can be described by wavelength, frequency, amplitude and phase.

what is reflected unpolarised light?

partially polarised!

• bias toward one direction

• light is rarely perfectly polarised or unpolarised.

what is elliptically polarized light?

the electric field direction rotates as the light travels, and the tip of the electric field traces an ellipse.

Luminous flux

Luminous flux is the total visible light output of a source, measured in lumens (F)

luminous intensity

Luminous intensity is luminous flux emitted per unit solid angle, measured in candela

candela = lumens/steradian (I)

Illuminance

illuminance is luminous flux that falls upon a surface per unit area

Luminous flux / m2

measured in lux (E)

Unit: lm/m²

Illuminance = flux /area

Luminance

Luminance describes the visible light emitted or reflected from an extended surface in a particular direction per unit area.

luminance = luminous flux (lumens) / (steradian x metre²)

cd/m²

(luminous intensity/m²)

inverse squared relationship - illuminance

illuminance = luminous intensity / d²

A POINT SOURCE IS ASSUMED

compare real and virtual images

✅ Real image

• image is on the opposite side of the optical sysetm to the object

• rays converge after leaving the system

• image can be seen on a screen

 

❌ Virtual image

• on the same side of the optical system as the object

• image can’t be seen on screen

• rays diverging after leaving the system

Vergence

Vergence describes whether light rays are diverging, converging or parallel at a given point

Aperture stop

The component that limits the amount of light entering the system

• decreasing the AS → decreases image brightness

vignetting

the blocking of rays by a surface other than the aperture stop (or field stop), typically occurring at the edge of a field.

Entrance pupil (draw real / virtual)

image of the AS as seen from object space

field stop definition and effects

Field stop = limiting aperture placed at an intermediate real image plane or final image plane → limits field of view with a sharper cut-off.

2 main things that reduce the field of view in a telescope?

1. vignetting

2. field stop

define pupil matching

Pupil matching means placing the observer’s eye pupil at the instrument’s exit pupil to maximise field of view and light collection.

• no exit pupil in galilean telescope (pupil is the AS limiting the rays) To get the widest field of view, place the eye as close to the eye lens as possible to reduce vignetting

Pupil size

Pupil size affects image quality by changing the balance between light throughput, aberrations, depth of focus and diffraction

paraxial marginal ray

PMR = ray from an on axis object point, that touches the edge of the aperture stop, and intersects the optical axis at the image plane

• determines image position

paraxial pupil ray

PPR = ray from the edge of the object field, passing through the centre of the AS, and finally intersecting the paraxial image plane at Q’

• determines image height

exit pupil (real and virtual)

the image of the AS as seen from image space

Field stop

The field stop limits the extent of the field of view by restricting off-axis rays

Paraxial ray

rays that are very close to the optical axis

• ray angles are very small

• ray heights are very small

because the angles are small sin(0.1) = 0.1

• can remove the sign

i think good to study cause less aberration

different between degrees and radians

angle: 2 intersecting lines deviating from one another

radian: portion of a circumference of a circle

ray tracing

1. opening equation to find h at first surface

2. paraxial refraction equation to find angle of refraction (u’)

3. transfer equation to find h’

4. paraxial refraction equation to fine (u’’)

when using the paraxial approximation do you express in radians or degrees

radians

surface power. what is it determined by?

Surface power is the refracting power of one surface, determined by the radius of curvature and refractive index change

F = C(n’-n)

C = 1/r

Paraxial refraction equation

The paraxial refraction equation describes how a ray’s angle changes at a refracting surface depending on refractive index, surface power and ray height.

Transfer equation

The transfer step describes how ray height changes as a ray travels a distance through space or a medium

Equivalent power

Equivalent power is the overall vergence-changing power of a lens or optical system

Vertex power

Vertex power is lens power referenced to a physical front or back vertex of the lens

Principal planes

Principal planes are conjugate planes used as reference planes when treating a thick lens as an equivalent thin lens

Focal points

Focal points are points where parallel rays focus, or from which rays must appear to originate to emerge parallel

what points coincide in thin lens?

• vertex points

• principal points

• nodal points

because lens thickness is ignored

keplarian v galilean

• image orientation

• magnification

• length

• intermediate image

• real exit pupil

• AS

• field of view

• eye positioning

• main limitation

Image orientation	Inverted	Upright
Magnification	Negative sign, about 2.25×	Positive sign, about 2.25×
Length	Longer	Shorter
Intermediate image	Yes	No
Real exit pupil	Yes	No
Aperture stop	Objective lens (usually)	Real eye pupil
Eye positioning	Easier due to exit pupil	More sensitive
Field of view	Usually wider	Usually narrower
Main limitation	Inverted image, longer	No pupil matching. Vignetting, no real exit pupil

positive v negative field lens

• positive field lens → increased field of view, decreased eye relief

• negative field lens → decreased field of view, increased eye relief

Why is Galilean field of view more limited?

It has no real intermediate image plane or real exit pupil to match to the eye, so field is more sensitive to eye position and vignetting.

myopia

Myopia occurs when distant rays focus in front of the retina because the eye is too long or too powerful

Hyperopia

Hyperopia occurs when distant rays would focus behind the retina without accommodation because the eye is too short or underpowered

what does one degree correspond to on the retina? What about 3 degrees

0.3 mm on the retina

linear relationship:

3 degrees = 0.9 mm on retina

what is optical design

Optical design involves choosing components to achieve required image position, magnification, field of view, system length and image quality

simplest eye model (model 1)

thin lens in air

• the whole eye is replaced by one thin lens

Emsley reduced eye

still a single refracting surface but takes into account that the back of the eye is essentially water (vitreous)

n = 1.33 (4/3)

where would the nodal point be on emsely reduced eye

centre of rotation of the spherical cornea

• normally the nodal points coincide with principle and vertex points for a thin lens in air, but because the n is different on opposite sides it is different

how to find focal length

F = n/f

• so for emsely n = 1.33 and for air n = 1

6 limitations of thins lens models? how to address these?

1. does not distinguish between cornea and crystalline lens

2. ignores refractive indices of the ocular media

3. does not consider accommodation

4. will give inaccurate measure of aberrations

5. note easy to use with biometry data from actual eye (corneal curvature, axial length)

to address these limitations, we introduce models with multiple refracting surfaces

two more complicated eye models. How many surfaces

1. Gullstrand simplified (No. 2) - 3 surfaces

2. Gullstrand exact (No. 1) - 6 surfaces

gullstrand exact eye model

6 surfaces

• cornea has thickness = 2 surfaces

• lens has thickness = 4 surfaces

  • lens is made of two zones (the nucleus and the cortex)

where would we stick a thin lens in gullstrands exact eye model

P’ !!

great strength of Gullstrand’s exact eye model. Limitations?

explains accommodation

• still does not predict real aberrations and real optical performance

Why is the full accommodation in model change in 11D but the change in power of lens actually 14D irl?

becuse this is measuring the change in vergence at the cornea. Actually bigger change in power at lens position, but when measured from further away account for this.

• placement matters

what did the more precise (Liou and Brennan) models account for?

1. aspheric surfaces

• prolate ellipsoid (steeper in the centre than periphery)

2. gradient refractive index of the lens

3. decentred pupil

4. angle alpha (fovea not exactly on the optical axis) - 5deg

Nodal points

Nodal points are points on the optical axis where the nodal ray appears to cross. The nodal ray enters and exits the system at the same angle to the optical axis.