experiment 8 - aberrations

Question 1

what is spacial resolution limited by ?

Answer 1

spatial resolution is limited by diffraction , higher order aberrations and scattered light

Question 2

what happens to rays close to the axis ?

Answer 2

rays close to the axis focus at the paraxial region

Question 3

what happens as we increase aperture size?

Answer 3

rays no longer focus in the paraxial image plane

Question 4

why do we need a spherical ideal wave front ?

Answer 4

• the paraxial rays which originate very close to axis they appear to be part of a spherical surface which is paraxial wave front
• only a spherical surface sends all the rays to the same point because they are simply radii of curvature and they all point to centre of sphere

Question 5

what happens when increase ray height ?

Answer 5

• we move from the paraxial wavefront to the real wavefront , the two no longer coincide
• the real wavefront is displaced with respect to paraxial wavefront
• when object is on axis the real wavefront is displaced symmetrically

Question 6

what is the wavefront aberration function ?

Answer 6

𝛿W(x,y) maps the difference between the ideal wavefront surface ( which is always a perfect sphere ) and the actual wavefront surface( which encodes the aberrations in the lens)

Question 7

what does the distortions you have on real wavefront surface compared to ideal wavefront surface encode ?

Answer 7

• the distortions you have on real wavefront surface compared to ideal wavefront surface encode all the aberrations

Question 8

what should 𝛿W be for every point if system is aberration free ?

Answer 8

• if system is free from any aberrations then 𝛿W ( wavefront )for every point should be zero
• real wavefront matches ideal wavefront and you end up with ideal image formation

Question 9

how do astronomers probe the universe ?

Answer 9

by getting the best possible image with optical instruments

Question 10

what does presence of spherical aberration do in terms of spacial resolution ?

Answer 10

the presence of spherical aberrations reduces spacial resolution that can be achieved in the absence of aberration

Question 11

what are the key parameters affecting optical aberrations ?

Answer 11

1- (β ) object field angle - if object is on axis , object field angle will be 0 and image will be on axis

2- (θ )specifies meridian in exit pupil plane

3-(h) specifies ray height in exit pupil plane

Question 12

what are the key parameters affecting optical aberrations ?

Answer 12

1- (β ) object field angle - if object is on axis , object field angle will be 0 and image will be on axis

2- (θ )specifies meridian in exit pupil plane

3-(h) specifies ray height in exit pupil plane

Question 13

what is spherical aberration ?

Answer 13

• proportional to the 4th power of ray height
• b determines how much spherical aberration you have
• no β - which means that spherical aberration is a large on axis as off axis
• spherical aberration independent of object field angle
• big aperture = lot of spherical aberration

Question 14

what is coma ?

Answer 14

• proportional to object field angle
• proportional to value of cosine of angle θ
• when object is on-axis , the coma will be 0
• absent on axis

Question 15

what is astigmatism ?

Answer 15

• proportional to the square of object field angle
• proportional to β so no on-axis astigmatism
• off axis

Question 16

what is field curvature ?

Answer 16

• best plane for off-axis object point is closer to the lens
• quality of image isn’t affected by field curvature

Question 17

what is distortion ?

Answer 17

• quality of image point is not affected by distortion
• images generated are no longer geometrically similar to objects that generate those images
• proportional to the third power of object field angle

Question 18

what does b1,b2,b3,b4,b5 means ?

Answer 18

• constants that determine the size of each aberration term

Question 19

what are the effects of primary seidel aberrations ?

Answer 19

. expanded size for a point image ( spherical aberration ,coma and astigmatism ) as they affect the quality of the image

. curved image plane ( field curvature )

. extended images are no longer geometrically similar to the object ( distortion )

Question 20

what kind of effect does aberration have ?

Answer 20

aberrations are geometric effects which reveal the way rays are refracted through optical surfaces which are symmetrical with respect to the axis

Question 21

what happens if we increase ray height in spherical aberration ?

Answer 21

• the quality of image isn’t good
• the paraxial image rays has curved
• the distribution of rays in paraxial image plane is no longer symmetrical

Question 22

what is the only aberration that is on-axis ?

Answer 22

spherical aberration

Question 23

explain the lab equipment designed to illustrate effects of aberration ?

Answer 23

• light source - small dot object that is very bright
• light goes through lens
• single lens with variable size iris
• goniometer which allows you to rotate the lens on horizontal and vertical plane

Question 24

what happens once we use the equipment which illustrates the effects of spherical aberration ?

Answer 24

• initially we have small dot image
• we start by increasing the size of iris
• as you increase aperture size you get spreading of rays in image plane suggesting its spherical aberration

Question 25

explain spherical aberration in a concave mirror ?

Answer 25

- in concave mirror you have a distant object with rays parallel to optical axis and all the rays are not focusing at same focal point - rays closer to paraxial region will focus at same point

Question 26

how to overcome spherical aberrations in mirror ?

Answer 26

- by making the surfaces aspherical so that all rays image at the focal point - this is what happens in astronomical telescope

Question 27

what is the difference in lens power between the marginal and the paraxial focal planes in spherical aberration ?

Answer 27

the difference in lens power between the marginal and the paraxial focal planes is proportional to the square of ray height (h^2)

Question 28

what does the disc of least confusion divide in spherical aberration ?

Answer 28

the disc of least confusion divides the distance between marginal and paraxial foci in the ratio 1:3 for large aberration

Question 29

what happens to mean wave aberration function as pupil size increases ?

Answer 29

- the larger the pupil size the larger the mean wave aberration function

Question 30

what happens in pupil size of less than 3mm ?

Answer 30

- good eye is aberration free

Question 31

explain what happens in coma in the lab ?

Answer 31

- use aperture size of a bout 2.5 cm ( medium size aperture ) - tilt the lens by about 20deg - intermediate image size coma increases with field angle and therefor zero on axis - rays perpendicular to the wavefront surface generate a distribution of intensity in the image of a point that has a comet like appearance

Question 32

what is the effect of coma on wave front aberration function ?

Answer 32

- on axis and pupil size small we end up with ideal wavefront surface - the real wavefront is behind the ideal wavefront

Question 33

what happens if object is on-axis for astigmatism ?

Answer 33

we have no astigmatism

Question 34

how are the tangential plane and sagittal plane produced in astigmatism ?

Answer 34

- take a line from object point that passes through the axis so that line and the axis form a plane which is the tangential image plane - if we rotate point , every single point will have a different projection to axis and a different tangential and sagittal plane

Question 35

where is sagittal image line ?

Answer 35

-sagittal image line is in tangential image plane

Question 36

where is tangential image line ?

Answer 36

tangential image line is in sagittal plane

Question 37

what is difference in circle focus between tangential image line and sagittal image plane ?

Answer 37

tangential image line= circles are sharp in focus | sagittal image line = circles are blurred

Question 38

what happens to line that passes through axis the further out you go ?

Answer 38

- the line that passes through axis becomes more and more blurred the further out you go because the amount of astigmatism is proportional to the square field angle - further out you are = the larger object field angle

Question 39

which focal line is closer to lens in astigmatism ?

Answer 39

- tangential focal line which is in sagittal plane is closer to the lens

Question 40

what happens if aberration is zero in astigmatism ?

Answer 40

- rays are imaged as a line ( sagittal focal line )

Question 41

where is best focus ?

Answer 41

between sagittal and tangential image plane

Question 42

describe astigmatism as wavefront aberration ?

Answer 42

- the tangential or meridian plane (θ=0) has the largest aberration whilst the sagittal plane (θ=90) has no aberration - the dioptric difference in power between the tangential and sagittal focal lines increases with the square of the field - in symmetrical optical systems astigmatism is absent on axis when β=0 deg - astigmatism in the eye is often caused by a significant difference in the curvature of the cornea in one meridian

Question 43

what is astigmatism cause by ?

Answer 43

- caused by difference in power from rays originating in one meridian compared to other meridian -

Question 44

what does we have on axis in astigmatism ?

Answer 44

we have astigmatism caused by change in curvature of corneal surface in one meridian with respect to orthogonal meridian

Question 45

why are we not concerned with oblique astigmatism in the eye ?

Answer 45

in human eye we are not concerned with oblique astigmatism because its in the periphery of visual field where our visual acuity is poor

Question 46

how do we correct astigamtism?

Answer 46

by using toroidal lenses which have specific power which cancel out increase power in astigmatic meridian

Question 47

describe field curvature as a wavefront aberration ?

Answer 47

1. field curvature represents a variation in focusing distance that varies with the square of the field 2. field curvature is an advantage given the shape of imaging surface 3. field curvature increases with the square of the object field angle and ray height 4. field curvature can be combined with astigmatism to ensure that the best astigmatic image plane forms a flat surface

Question 48

what are the two types distortion?

Answer 48

- image with negative or pincushion distortion | - image with positive or barrel distortion

Question 49

when do monochromatic aberration arise ?

Answer 49

arise as a natural consequence of refraction and reflection in symmetrical optical systems