Lecture 13 and 14 - Waves diffraction and interference Flashcards
What is interference
is superposition of 2 or more waves producing a resultant disturbance that is the sum of the overlapping wave contributions
What is total constructive interference ?
they are precisely in phase the resultant is the sum of the 2 wave height values
The result is that the two waves add up to give a wave having twice the amplitude of of the individual waves.
What does it mean when they waves are in phase?
they are at exactly the same point in their cycle – the peak of one wave coincides with the peak of the other wave, and hence the trough of one also coincides with the trough of the other.
-The peaks of the waves represent a positive disturbance above the zero point, and since the disturbances will add when when the waves combine, the result is an even bigger positive disturbance.
Similarly, the troughs a negative disturbance – will add up to give an even deeper (i.e. more negative) trough.
What is total destructive interference ?
When the phase difference reaches 180 degrees , waves will cancel each other.
What does it mean when waves are out of phase?
therefore the peak of one wave coincides with the trough of the other. If the waves have equal amplitudes (which would be the case if the beamsplitter in Figure 20.1 split the light by half) then the positive disturbance to the electro-magnetic field represented by a peak exactly cancels out the negative disturbance represented by the trough, the result is no disturbance, and hence no wave. There is no light on the screen since the light waves have cancelled each other out
What happens to light that goes through a geometrical point in a opaque screen?
The beam of light will go through the aperture or hole
- either light goes through or not
- the light that goes through is unaffected by the aperture- the aperture has no effect on the rays that go through.
What are parallel rays- in wave optics?
plane wavefronts that are coming from an infinitely distant object
What is diffraction?
the property of light that causes the wavefront to no longer be plane but slightly bent on the extremes of the wavefront .
- Here as light is squeezing through the aperture some of the light deviates from the straight light trajectory and there is bending of the wavefront.
- HAPPENS at the boundary or the edge of the wavefront
Why is there no refraction ?
due to the fact that light behaves in this way when it is squeezing through an aperture
-Some of the light going through this aperture is travelling at a different angle
What happens in reflection or refraction in geometrical optics?
only reflection or refraction can change the direction of the beam
What does the circular beam look like going through an aperture (FRONT VIEW) ?
- in geometrical optics this aperture will remain circular and it doesnt matter how far this beam goes- it does not change its shape- however this not happen
- -When zooming in you see a fringing effect occurring at the edges of the beam
- It is no longer a smooth beam
- the beam is changing direction in a peculiar way
- diffraction happens at the edge of the beam
- where a beam of light is being cut down by a certain aperture
- no lenses involved.
What does diffraction depend on?
size of aperture
What is diffraction significant ?
for a small aperture compared to a large aperture.
What happens for a large aperture ?
the centre of the beam is quite far from the edge of the beam , so it becomes shielded on the effect of diffraction.
- it is far enough from the edges so as it is unaffected by the perturbation introduced by the edge.
- Therefore a large part of the wavefront is still plane and only a small region close to the edges of the wavefront has been affected by diffraction.
What happens as the beam travels further away from the aperture in geometrical optics?
the effect becomes greater, further away it will effect the centre of the wavefront as well
What relationship does diffraction have with aperture size?
diffraction has an inverse relationship with aperture size
Why does diffraction have an inverse relationship with aperture size?
since the smaller the aperture the larger the amount of diffraction, and vice versa.
What happens as the beam travels further away from the aperture in geometrical optics?
however in geometrical optics it doesnt matter how far the beam has travelled it will have no effect on the beam
What happens as the beam travels further away from the aperture in wave optics?
this perturbation will affect the whole beam
What effect does the beam travelling have on forming images in a optical system? - in geometrical optics
What will give a perfect point image in a gemoertical optics?
wavefront after going through lens are spherical in shape.
What happens as light goes through an aperture?
edge of beam undergoes the effect of diffraction
the wavefront is no longer spherical
A wavefront that is not spherical would give us an image that is affected by diffraction
What gives us perfect images?
spherical wavefronts
What is an airy disk ?
the image of a point object due to effect of diffraction
- no optical system is ideal so any point object will look like an airy disk .
What will give an airy disk?
case of optical system with no aberrations
-the wavefronts after refraction by the lens are no longer spherical due to diffraction will give an image like an airy disk
What does the airy disk look like?
slightly blurred image point with a series bright and dark concentric rings around it that get fainter and fainter.
How do we quantify how good our images?
look a size of central lobe and ignore rings around central point
- need expression
What is the equation for diffraction of an airy disk?
d= 2.44(wavelength)(z)/ D
How does wavelength affect airy disk size?
the longer the wavelength (e.g red than blue) the larger the. airy disk hence more diffraction
What is z?
the distance of the image from the exit pupil of an optical system.
What is D?
the size and diameter of the exit pupil
and has a reciprocal relationship - the larger the aperture the less the diffraction- smaller airy disk- image achieved is clearer as less aberrations
What does it mean when there is a small aperture size?
the bigger the diffraction and the bigger the airy disk
What is used to minimise to diffraction ?
- Photographer - use large lenses - clearer picture
- ground based telescope - less diffraction- image achieved is clearer
- human eye and ophthalmic instruments .
What is PSF ?
Point spread function
What is the point spread function?
image any optical system gives when an object is a point.
t he image of a point source produced by an optical system
-diffraction limited case (PSF)
= no aberrations are present
- not ideal but if diffraction was small- it is the best image we can achieve
What is diffraction always?
always present as it is a property of light
What is the PSF good for?
way of assessing how good an optical system is.
- may be large, distorted, asymmetric
- the particular shape of the PSF can tell us about the diffraction and aberrations present in the optical system
what is the paraxial region ?
. special region where everything works well
. this would be an ideal lens one that behaves following the paraxial approximation
. these rays carry information about the object , the lens will converge the information to a point to form an image
. by restricting our self to the paraxial region we can use the fundamental paraxial equation and equivalent thins lens
what happens when we go outside the paraxial region ?
.rays don’t meet at one point
. the further the rays are from the optical axis , the worse they behave , they refract more and cross at an earlier point , this means that the information coming from object is being transferred over a larger area creating a blur , the image is more spread out
what is a real system ?
. there is a range on optical axis where rays are crossing this is a real system
. it is typical of any system to to introduce imperfections or aberrations
how to convert from rays to wavefronts ?
. rays intersect wavefronts at 90 deg
what do ideal system give us ?
ideal systems give us spherical wave fronts , its the only way rays will meet at one point
what happens in real lens with aberrations ?
wave fronts will no longer be spherical
what is the way to distinguish between ideal spherical wavefront and non ideal ?
ideal = spherical / reference wave front
actual , non-ideal = spherical wave front
how do we know how aberrated an wave front is ?
the wave front that can come out of any optical system can have any shape and the departures are differences from the spherical or reference wave front will provide a measure of how aberrated it is and type of aberration present in optical system
what happens to PSF in diffraction limited case when no aberration are present ?
. the PSF is an airy disk
what happens to PSF is affected by spherical aberration ?
. this disperses light into a larger region of space
what is the PSF for astigmatism ?
. vertical rays cross at a point and horizontal points cross at a different point
. the distance along the optical axis between both meridians is a measure of the aberration
. the middle position between these two lines of focus is circle of least confusion and is the only part that is symmetric
what is astigmatism ?
. different refractive power along different meridians
what is the DLC ?
. the distance along the optical axis between both meridians is a measure of the aberration
. the middle position between these two lines of focus is circle of least confusion and is the only part that is symmetric
how does the best image look like in a coma ?
in a coma the best image is distorted like a comet
what is PSF a combination of ?
. PSF is a combination of the effect of both aberration and diffraction
how are aberration and diffraction different ?
. diffraction can only be discussed using wave optics
. . aberrations are due to the imperfect shape of optical systems ( difficult to get rid of but possible )
e.g. parabolic shapes and under certain circumstances spherical mirrors can be aberration free
what matters here is that under certain conditions we can have optical systems with no aberrations
. diffraction is always present
. they both effect the image and make it worse , less imperfect image point
. both take a spherical wavefront and make it no longer spherical
what shape is typical in aberrations ?
this is an optical system which has significant aberrations which are very asymmetric in shape this is typical of aberrations and diffraction is always present
what are aberrations ?
. aberrations are non-ideal behaviour of the paraxial rays
what happens when aperture size is largest and what happens when that aperture size decreases ?
. when the apertures is largest the PSF is dominated by aberrations with a very asymmetric PSF
. as the aperture size decreases , the new paraxial rays are removed , at the end the aperture is very small , there are no aberrations and only diffraction is present
. this is the same optical system which has gone from being dominated by aberrations to being dominated by diffraction
what is an airy disk ?
. airy disk is symmetric pattern and in aberrations the PSF appears asymmetric in shape
. asymmetry disappears and then it becomes more secular which is the diffraction limited case
what gives us the best image diffraction or aberration ?
. compromise between aberrations and diffraction
somewhere in between where we get the best image
is aberration present in human eye ?
. this is particular case of human eye , the human eye suffers from many aberrations , high order aberrations are very common in the eye
what size is pupil ?
the pupil can vary in size between 27 mm in size
when is the best image for the eye ?
when pupil size is 3.5 mm
what is effect of dilating drops ?
. you don’t see very well because a large pupil has a lot of aberration
. smaller aperture is affected by diffraction so usually the best case is somewhere in between the the largest and smallest aperture in size
how can we describe an optical system
. we can think of optical system as a point object , and the image of that point is the point spread function
. the input is a point object and and the PSF is the image of that point
. an object can be made up of many points
. the PSF tells us what happens to a single point , we can then extend or extrapolate for the entire object
. if image of a point is aberrated , the collection of these points is a blurred image
. if we replace every object point with a copy of the point spread function we end up with a blurred image
. the larger the PSF the more blurred an image is
. the PSF tells us how to obtain the output from the input
what is an object ?
object is anything an optical system is looking at
can be a collection of points
what happens in a case of large aperture ?
. every point of object is being replaced by an asymmetric PSF
. the PSF of every single point affects how the whole image looks like
what happens in a medium size aperture ?
this shows a tradeoff between diffraction and aberrations
. every point of object is being replaced by its PSF
. the PSF is less asymmetric and blurring is less
what happens in a smaller size aperture ?
we only have diffraction and image becomes more blurry
