Optics MST2

5 steps in the optical design process

1. Specification - what is the object you want to take an image from? What is the brief?

2. Thin lens design – as a first approximation

3. Aberration reduction - choose material & shapes

4. Thicken the lenses

5. Set manufacturing tolerances

what kind of info is included in the specification

1. Transverse mag

2. Throw

3. aperture stop at the lens

4. numerical aperture in image space

5. field size

Gaussian optics

• powers

• length

• position of conjugate planes

• magnifications

• pupils

• FOV

image quality and aberration

• resolving power

• all the different kinds of aberrations

ergonomical factors

environmental factors

7 design steps

1. Calculate thin lens powers & separations

2. Choose aperture stop (position & size)

3. Choose field of view

4. Trace paraxial marginal ray & paraxial pupil ray - determines how wide our lens needs to be

5. Determine aperture radii for each surface radius (p) = |h| + |h bar| (for condition of no vignetting)

6. Check the product |pF| for each surface (p = radius) - needs to be less than 1 i think

7. Check field of view values T for

   1. vignetting just beginning and

   2. vignetting just becoming complete

Magnification equations (4) and lens equation

Magnification equations

M = - Fe/Fo (negative)

M = - fo/fe (negative)

M = l’/l

M = entrance pupil diameter/exit pupil diameter

Transverse magnification equation

M = (nl’)/(n’l)

M = nu/n’u’

lens equation

F = 1/l’ - 1/l

Single lens system - from specification to design

1. determine l and l’ through magnification equation and throw (will need to rearrange)

• M = l’ / l

• throw (d between image and object) = l’ - l (remember l should usually be negative otherwise we will have a virtual image)

2. Calculate thin lens power, using the lens equation

• F = 1/l’ - 1/l

3. Determine object space angle through the numerical aperture numerical aperture = n’sin(u’)

4. find the object space angle u with the transverse magnification

• M = (nu / n’u’)

5. Trace the PMR to find height at lens

• PMR = determined image height at lens

• PMR = determines image plane - on axis object, top of AS

• PPR = determines image height - off axis object, middle of AS

6. trace PPR to find image height

• PPR to find image height

• goes thru centre without angle change. (same angle on both sides)

• draw triangle and calc.

7. Find aperture radius (p) row

• p = h + h(hat) (for no vignetting)

8. Confirm that the aperture radius can be made

• product = pF

Ray tracing steps

• ACTUALLY, JUST FOLLOW THE TRIANGLES ITS CHILL

• opening equation h = -ul

• paraxial refraction equation: n’u’ - nu = -hF

• paraxial transfer equation: h’ = h + u’d

• closing equation: h=-u’l’

calculation for product (to check that the aperture radius can be made)

product = pF

• rowF - needs to be in METERS

• aperture radius x power

• >1 is NOT POSSIBLE - lens will be too thick

what does numerical aperture determine - don’t worry i don’t think

can trace back numerical aperture to get PMR (on axis ray)

what problems can a 2 lens system solve? Example - surgeon

if we require the object and the image to be in the same spot, can’t use one lens, because then the lens would have to be on the object.

• 2 lens can solve this problem and magnify

• if you put the 2 lenses closer together, you will need MORE AND MORE power differences between the two lensees!!! (rlly pos and rlly neg for example)

2 lens power equation (2 thin lens system)

• F1 generally from object side I think

• F2 from image

• P = h1/h2 = Mlv/lv’

(magnification x object distance) / image distance

height 1/height 2 of lens i think…

what is this in DIOPTERS

+35D

2 lens system. From specification to

1. Get mag

2. get image distance

3. get object distance

• from lens closest to eye

4. solve for P (Mlv/lv’)

5. Find F1 and F2 (from new equations)

6. set aperture stop size + position

7. set Field of view size

• step 6 and 7 enable us to:

8. Trace PMR + PPR

9. Determine diameters of each lens

describe what a telephoto lens does.

a 2 lens replacement for a long focal length objective lens to shorten an optical system

• similar to Galilean telescope, but instead of columnated rays coming out, it forms a real image.

• what negative lens does is make the rays less strongly convergent (but they are still convergent!)

A telephoto pair uses a strong positive lens followed by a negative lens to behave like a long focal length lens, but with a shorter physical length.

• aka the equivalent power of the telephoto lens system is the same of the single lens its replacing

what is the problem with having 2 conjugate planes (ex. retina and pupil imaged to the clinican)

• patient’s retina is imaged to the clinician

• patient’s pupil should also be imaged to the clinician’s pupil

• When only one pair of conjugate planes is specified, lens separation (d) can be chosen freely. But once a second pair of planes is also specified, d is no longer free.

what ray tells you HEIGHT AT LENS and which ray tells you IMAGE HEIGHT

HEIGHT AT LENS = PMR

IMAGE HEIGHT = PPR

GOT UP TO SLIDE 53 on thin lens design

🙂

Equations for telescopes with what kind of lenses are identical?? WHY?

1. two thin lenses

2. one thick lens

Why?

• because F1 and F2 for thin lens = thin lens powers

• because F1 and F2 for thick lenses = surface powers

THE equation is the same but because the medium between the components are NOT air then you have to multiply by the refractive index

What determines the lens diameter?

the steepest radius of curvature. In keplarian telescopes the F is too high and curvature is too small - not possible to make.

Only possible to make a Galilean telescope with one thick lens.

General telescope trends (M, d, + vs -)

• If thickness d increases, required surface powers decrease.

• If magnification M increases, required surface powers increase.

• The sign of M matters a lot.

• Positive M gives a Galilean-style system and is usually more practical.

• Negative M gives a Keplerian-style system and often requires very high powers.

Simple version:

To make the curvatures less extreme, make the lens thicker.
To get more magnification, you need stronger curvatures.

what is spectacle magnification? what application?

spectacle magnification: size of sharp (corrected) image / size of blurred (uncorrected) image

• aniseikonia = different retinal image sizes between the L and R eyes which cause perceptual effects.

Problem with a normal thin lens (glasses) for someone with aniseikonia?

SM = 1 / (1 − hₑF) - for a single thin lens system

Where:

• SM = spectacle magnification

• hₑ = distance from the eye’s entrance pupil to the lens/back principal plane***

• F = lens power

How can we control magnification?

There are only two obvious options:

1. Change F
   But that is the patient’s prescription, so you generally cannot change it.

2. Change hₑ
   You can adjust vertex distance somewhat with frame fit, or use contact lenses.

Key point:

With a thin lens, there is limited ability to control magnification independently of prescription.

How to solve magnification problem with Px with aniseikonia?

Can change the magnification without changing the F (prescription), by putting an afocal thick lens (telescope) immediately in front

• another magnification equation here but i don’t think (i hope) we don’t need to know

• just know that the equation for mag is in terms of equivalent power F but spectacles are measured from the back vertex.

• BUT this is ok cause we are not changing the F so its all freaking good. back vertex power remains unchanged . Can use back vertex power in the equation😛

example of a 3 lens system

Keplarian telescope with a field lens!

• field lens placed at intermediate image plane to steer the beam into the eyelens and through the exit pupil

what is the effect on eye relief when a field lens is placed in the intermediate image plane?

• exit pupil moves closer to the eye lens

• AND stays the same size

Why might we split single components in a multiple lens system?

1. to ease the condition pF

• splitting one lens into two equal lenses means:

  • power is halved in each

  • therefore pF is halved

2. aberrations

• more power in a single lens = more aberration.

• splitting = reduces dis 🙂

3. achromatic doublets

• if we’re working over multiple wavelengths, we want them to all be in focus together.

• multiple lenses reduces this difference.

what is the condition/product??? (pF)

How big a specific lens has to be to fit all the rays through. To find this you have to trace the PMR and PPR to find the aperture radius….

remember: p = h + hbar

• a condition or product of more than 1 is NOT possible

• for a multi-lens system, would have to check for each lens separately. THE WORST/HIGHEST value is of concern!

what does the telephoto ratio tell you?

how much you’ve shortened the optical system by adding telephoto lens

physical length/effective focal length

smaller = more compact

what is the difference between incandescent and luminescent light sources? Give examples:

1. Incandescence: visible light is emitted from objects if they have a high enough temp

examples (about 1500C)

• sun, flames (some), tungsten filament lamp

2. Luminescence: Light produced by non-thermal processes, such as electrical, chemical, or light-driven (photo) excitation.

• LED, laser, neon tube etc. not hot.

what is a black body?

an ideal or perfect incandescent source. Must be a perfect absorber (aka black).

• Actual objects are not perfect (even if black). may absorb a high % but may be reflecting parts of the spectrum that we can’t see (ex. soot about 98% black)

What are the names of the properties of the perfect black body radiator? (3 laws)

1. Wien’s displacement law

• TELLS you where the peak is

• The peak wavelength decreases with increasing temperature (see pic)

• hotter = emit radiation at smaller wavelengths (shift toward blue)

2. Planck’s law

• Predicts the whole curve as temp increases. Curve changes shape

3. Stefan-Boltzman law

• This law says total radiation emitted varies with the fourth power of temperature:

• aka if temp increases, emitted power increases a lot

What is colour temperature? (exam q)

Real sources emit less radiation than an ideal black body sources at the same temperature (because they’re not perfect absorbers!! THey are grey)

Colour temperature means

• what temperature would a black body need to be to produce the observed output spectrum (colour)

• This is NOT the actual temperature of the object, it ONLY describes the shape of the spectrum

example: A torch or screen might have a colour temperature of 6000 K, but it is obviously not physically 6000 K.

what would an object with a lower colour temperature vs higher colour temperature appear?

Lower colour temps: warmer/redder

• candle, tungsten bulb, warm indoor light

Higher colour temps: cooler, bluer

common examples of luminescence. How are they different and how are they similar?

Electro-luminescence

Photo-luminescence: Fluorescence and phosphorescence

Chemi-luminescence

• different in how the ‘excited state’ gets generated, but the relaxation process is generally the same

how does electroluminescence work? (what is the extra step for fluorescent tubes?) - exam q

Electroluminescence means light caused by electrical activity.

• Electrical energy excites electrons to higher energy state (collides w gas atoms)

• when it drops it emits a photon with wavelength λ = hc / ΔE

• the energy CHANGE determines the wavelength of the photon

• larger energy change = shorter wavelength, more energetic light

• so blue violet light is more energetic than red light (UV is even more)

• λ = hc / ΔE = hc / ΔE

example; gas discharge tubes, gas lasers, solid-state sources

• fluorescent tubes do this but also have a phosphor coating… They use mercury and get so excited that UV light is emitted (not visible, highly excited). BUT fluorescent tubes have a phosphor coating which emits visible light. this is photoluminescence.

what is a discrete emission spectrum? example:

discrete emission spectrum.

That means it does not emit a smooth rainbow of wavelengths. It emits strong lines at specific wavelengths

• discrete energy transitions

Laser produce light by 2 types of processes. What are these, what is it called, and how it work? EXAM

electroluminescence and photoluminescence

Stimulated emission: Electrical energy starts the excitation, but photons then stimulate further photon emission.

• pump energy into laser

• electrons move to higher NRG states and excite atoms

• atoms spontaneously emit photons

• mirrors reflect photons back and forth

• photon catalyse electron transitions, more atoms excited

• emitted photons match the stimulating photon

• chain reaction builds up

one mirror is transparent, so laser beams out

Electroluminescence + photoluminescence - fluorescent tube: which one of these is a more efficient light source?

TOP. Discrete = more efficient

• lower curve = lower light output. but filling out whole spectrum.

• trade off: The bottom will look whiter and may be nicer but less efficient

Fluorescence/Photoluminescence: what can quantum dots do?

Main idea:

• short wavelength light goes in

• longer wavelength light comes out

• emitted wavelength depends on dot size

** Combined with phosphors, any spectrum shape can be achieved

• very efficient

what is Chemiluminescence

chemiluminescence: a chemical reaction creates an excited product, and when it relaxes back down, it emits light. The decay from an excited state is the same as for other types of luminescence.

light is emitted in the same physical way. However, getting to the excited state happens chemically

• example: bioluminescence (glow worms, fireflies)

fluorescent vs bioluminescent animal

bio-luminescent: animal generates light via a chemical reeaction (chemi-luminescent)

fluorescent: animal absorbs light and re-emits at a longer wavelength (photo-luminescent)

• glow fish illuminated with a UV light, fish absorb this and emit longer wavelength red light 🙂

what is scattering?

when light (electromagnetic radiation) interacts with matter, energy is taken from the incident wave and some of that energy is re-emitted, often in different directions. WILL oscillate with it if it can….

• energy can be dissipated as heat (prob don’t need to know this)

What does polarisation describe?

The direction in which the electric field of a light wave oscillates.

4 types of polarized light states, and what do they describe, and give examples - WILL BE EXAM QUESTION

1. Plane/linear polarized light

• Light where the electric field oscillates in one fixed direction or plane.

2. Unpolarised/randomly polarized light

• light where the electric field direction varies randomly over time, so there is no single preferred polarisation direction.

• ex. blackbody (sun)

3. partially polarized light

• A mixture of unpolarised light and light with a bias toward one polarisation direction.

• ex. gas discharge lamps.

4. elliptically polarized light (can be circular)

• Light where the electric field vector rotates so its endpoint traces a circle as the wave travels.

What are three ways light can become polarised?

Filtering, reflection, and small particle scattering.

Polarisation by filtering: What is the difference between extinction axis and transmission axis?

The extinction axis is the absorbed direction; the transmission axis is the direction that passes through.

top = absorbed (extinction)

bottom = transmitted

Polarisation by filtering: If the strands in a polarising filter are horizontal, what polarisation passes through?

Vertically polarised light passes through.

How much unpolarised light passes through a perfect polariser?

50%.

• can determine how much light gets thru with Malus’s Law

• equation involving the angle between the polariser axes

What happens when two polarisers are crossed at 90°?

Complete extinction; ideally no light passes through.

How do polarizing sunglasses work?

Sunglasses designed to absorb horizontally polarized light

This matters because glare from horizontal surfaces, such as water or wet roads, is often mainly horizontally polarised.

How can polarisation be used in stereopsis tests?

Different polarised images are shown to each eye, creating binocular disparity that can be fused into depth.

What did polarisation help reveal about light?

Light is a TRANSVERSE wave, meaning its oscillations are perpendicular to its direction of travel. (can travel in all directions) idk

• before noticing the calcite crystal, it was thought that light was a LONGITUDINAL wave (aka oscillations traveling in the same direction as travel)

What type of surface commonly produces polarised reflected light?

Dielectric/non-conducting surfaces, such as water, glass, paper, and wet roads.

What is Brewster’s angle?

he angle of incidence where the reflected and refracted rays are 90° apart and reflected p-polarised light is zero.

• KNOW that at Brewster’s angle, reflected light becomes STRONGLY POLARISED

tan θB = nt / ni

p-polarised light

Electric field vibrates in the page/screen plane.

s-polarised light

Electric field vibrates out of the page/screen plane.

Why is glare from water often horizontally polarised? why can sunglasses reduce this glare?

Reflection near Brewster’s angle from a horizontal surface produces reflected light dominated by horizontal polarisation.

They reduce reflected glare from the water surface, allowing more transmitted light from below the surface to be seen.

• sun is vertical and high…. we want a horizontal filter to block out

what are the 2 types of scattering?

Rayleigh scattering

Mie scattering

What is Rayleigh scattering?

Scattering by particles much smaller than the wavelength of light, such as oxygen and nitrogen molecules.

What is Mie scattering?

Scattering by larger particles, such as dust or water droplets.

• creates veiling luminance (overlays an imate and reduces contrast)

What is the key wavelength relationship in Rayleigh scattering? EXAM Q FOR SHO

Rayleigh scattering is proportional to 1/λ⁴.

• This means shorter wavelengths scatter much more strongly than longer wavelengths.

• blue light scatters more!

Why is Earth’s sky blue?

Small atmospheric molecules Rayleigh-scatter short wavelengths, especially blue, much more strongly than long wavelengths.

Why are sunsets red/orange?

At low sun angles, light travels through more atmosphere, so short wavelengths are scattered out of the direct beam, leaving more red/orange light.

How does Mie scattering differ from Rayleigh scattering?

Mie scattering is caused by larger particles, is less wavelength-dependent, and is more forward-directed.

• bigger particles than wavelength of light, scattering affects equal wavelengths across the visible spectrum (achromatic)

Why is Mars’ sky not blue like Earth’s?

Mars’ atmosphere is dominated by dust particles causing Mie scattering, plus absorption of shorter wavelengths by dust, giving a yellowish/reddish sky.

• note: If the dust did not absorb any sunlight, the Martian sky would appear whitish, since all wavelengths would be scattered to similar degree

What are aberrations?

Aberrations cause the rays in a beam to depart from their ideal (i.e. paraxial) paths

What are the five main monochromatic aberrations? - be prepared to draw each of these on the final exam!

1. Spherical aberration

2. coma

3. (oblique) astigmatism

4. field curvature

5. distortion.

What is the difference between monochromatic and chromatic aberrations?

Monochromatic aberrations occur even with one wavelength; chromatic aberrations depend on wavelength differences in polychromatic light.

Which monochromatic aberration can occur for both on-axis and off-axis object points?

Only spherical aberration.

• everything else is only for off-axis object points

Which monochromatic aberrations occur only for off-axis object points?

Coma

(oblique) astigmatism - (for spherical surfaces)

field curvature

distortion.

• everything but spherical aberration

Which monochromatic aberrations do not give point-to-point imagery?

Spherical aberration, coma, and oblique astigmatism.

• everything but field curvature and distortion

Which monochromatic aberrations still give point-to-point imagery? where do they not give point-to-point imagery?

1. Field curvature - but NOT in the paraxial image plane

2. Distortion, but NOT in paraxial position

What is spherical aberration?

• An aberration where rays from one object point focus at different positions depending on ray height, producing blur rather than one point image.

• Higher ray = further from paraxial image point X

  • I think with positive lens, higher ray = closer to lens, and opposite for negative (but confirm)

• form concentric rings

Does spherical aberration require spherical surfaces?

No. It can occur even with a plane glass plate if rays at different angles are refracted differently.

What is coma aberration?

An off-axis aberration where a point image becomes cone/comet-shaped because ray cones form non-concentric circles in the image plane.

• main difference = spherical aberrations are concentric (look more like a bullseye)

What is oblique astigmatism? What are the two line foci called? DRAW

An off-axis aberration where tangential and sagittal ray fans focus at different positions, producing two perpendicular line foci rather than one point.

The beam can be thought of as two perpendicular sets of ray fans:

• tangential fans

• sagittal fans

These focus at different positions:

• tangential focus = T

• sagittal focus = S

Between the two line foci is the circle of least confusion, where blur is more circular/even.

not to be confused with clinical astigmatism

What is field curvature? What is the curved image surface called?

It gives point-to-point imagery, but the point image is not located in the flat paraxial image plane.

• Instead, the sharp image points lie on a curved surface called the Petzval surface.

• So if you had a flat sensor or flat image plane, off-axis points may appear blurred because their best focus is actually in front of or behind that flat plane.

What is distortion (aberration). What are the 2 types.

• It gives point-to-point imagery, and the point is in the paraxial image plane, but it is not at the expected paraxial position.

(so it converges in the image plane but strikes at a different point (Qbar’ not Q’)

• So the image is sharp, but spatially warped.

• positive distortion = pincushion

• negative distortion = barrel (square ish)

Why do we need to quantify aberration levels

When we design/assess optical system, we need to know how to: • determine which aberrations are present, and at what levels • minimize aberrations to below minimum values tolerable

What are four common ways to quantify ray aberrations?

1. Transverse aberration

2. longitudinal aberration

3. angular aberration

4. wave aberration.

• these are all based on paths of individual rays

• focus on transverse and longitudinal!

Longitudinal vs transverse aberrations:

• know how to sketch (esp for meridonal ray) - there is another flashcard on this

1. longitudinal

• displacement along the optical axis

2. transverse

• displacement along the image plane?

What is a meridional ray? - draw longitudinal vs transverse aberration for meridional rays

A ray that intersects the optical axis.

Picture: showing longitudinal vs. transverse aberrations for meridional rays.

• Longitudinal = [O’G]

• Transverse = [O’H]

What is a skew ray?

Skew rays are rays that do not intersect the optical axis or the central ray of the beam.

• more common

what is a skew ray? What aberrations can a skew ray be split into

skew rays: rays that do not intersect the optical axis or the central ray of the beam

• THERE is not longitudinal aberrations for skew ray (because not on the optical axis)

• HOWEVER, the transverse aberrations can be split into 2 components

  • HORIXONTAL (x-axis)

  • VERTICAL

• will not be asked to sketch skew ray but prob understand the two components

What is an angular aberration?

Angular aberration measures the angular difference between where a ray actually travels and where it should have travelled.

When is angular aberration especially useful?

In afocal systems, where errors are naturally described by angles rather than positions in a finite image plane.

What is optical path length?

Optical path length is physical distance multiplied by refractive index:

OPL = n × distance

• important concept to understand how long a wave has travelled from an optical perspective. aka: how many wavelengths has it gone through?

• think fermats principle…. if we double the refractive index, we will double the cycles - ray travels at HALF the speed 🙂

What is wave/path length aberration? What is it dependent on?

A difference in optical path length (OPL) between an actual ray/wavefront and the ideal reference.

• how much extra optical path did the ray have to travel?

• dependence on: ray height (Y) at the pupil plane

• measuring the wave aberration W(y) in terms of optical path length - how many cycles has it gone?

In wave aberration, what is the reference sphere?

The ideal wavefront shape that would focus perfectly at the ideal image point.

• dashed line = reference sphere

For spherical aberration, what happens as ray height increases?

Wave aberration increases strongly; peripheral rays are usually more aberrated.

In the off-axis wave aberration setup, which ray is defined as aberration-free?

• PUPIL RAY

• this passes thru the middle of the lens… I think this is why but legit not sure

Factors affecting wave aberrations

1. aperture stop diameter.

• larger aperture stop means more peripheral rays pass thru

• peripheral rays are usually more aberrated

• does not impact distortion

1. distance off axis

• further = more aberrations

• impacts all except spherical aberration. spherical is impacted the MOST by aperture stop diameter (power of 4)

• just understand the trends tho

What is the point spread function?

The light distribution in the image of a point source.

How can spherical aberration be quantified using PSF? What does it depend on?

By the width/size of the PSF, which depends on

• bigger pupil diameter = wider point - more light in centre

how can coma aberration be quantified using PSF? what does this depend on?

quantify by width or length

• depends on aperture stop diameter and distance off-axis

What is the interval of Sturm? What aberration does it measure and what does it depend on?

The separation between the sagittal and tangential line foci in astigmatism aberration

• depends on distance off-axis but NOT pupil diameter - but AS still does impact blur…. prob not important

• expressed in Dioptres

How can field curvature be quantified?

By using the Petzval surface and measuring how far the curved best-focus surface lies from the Gaussian/paraxial image plane.

Effect of Aperture Stop size. How does it incluence aberrations? What aberrations aren’t impacted

• increasing aperture stop size does not change the aberration of a specific ray but it allows more peripheral rays to pass thru

• since peripheral rays are usually more aberrated, the PSF typically becomes larger.

• SO increase aberrations except for:

  • distortion

  • transverse chromatic aberration (don’t know this one yet)

• aka bigger pupil = increase aberration

Effect of distance of an off-axis object point (field position)

Moving the object point off-axis changes ray paths for all rays!!!!

Moving further off-axis affects each aberration except:

• spherical aberration (influenced by aperture stop size)

• longitudinal chromatic aberration

The magnitude of change depends on the aberration

Which monochromatic aberration is not mainly affected by moving off-axis?

Spherical aberration.

What are 5 factors affecting the level of aberrations?

1. Aperture stop diameter

2. Field position - distance of off-axis object point

3. lens shape (including surface asphericity)

4. position of conjugate points?

5. aperture stop position

Keplarian v Galilean telescope: objective lens, eye lens, image orientation, intermediate image, aperture stop,

Keplerian

• positive OL

• positive EL

• inverted image

• real intermediate image

• AS generally the objective lens

Galilean

• Positive OL

• Negative EL

• Upright image

• no intermediate image (negative lens intercepts rays before they create int im)

• no intrinsic AS… pupil is AS

  • aka AS is the exit pupil (so NO eye relief…….)

define vignetting

the blocking of rays by a surface other than the aperture stop or field stop

define aperture stop

element that limits width of beam from on-axis object point