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Optics > lecture 17 - monochromatic aberrations > Flashcards

lecture 17 - monochromatic aberrations Flashcards

1
Q

what are the key parameters affecting monochromatic aberrations ?

A

. object field angle ( βo) - when we are dealing with extended objects they can be far away from the optical axis and each point location within the object will have a different object field angle

. ray height which is determined by aperture size (D )of the optical system

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2
Q

what is ideal optical system ?

A
  • generates a spherical wave front surface
  • this can be for object off axis or on axis
  • every ray that originates from one object point passes through the conjugate image point
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3
Q

what happens if rays appear to come from a spherical surface ?

A
  • all the rays will pass through the centre of curvature of the surface and will meet at a single point
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4
Q

what ideal image formation ?

A
  • lens produces a perfectly spherical wavefront surface
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5
Q

how to restore an image back to original object in ideal image formation ?

A
  • magnification is the only parameter needed to restore image to original object
  • this requires that images must be geometrically similar except for the magnification to object
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6
Q

what happens in real optical systems ?

A
  • real optical systems do not produce spherical wavefront surfaces
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7
Q

what happens in a real optical system to wave front surface ?

A

wave front surface deviates from the paraxial wave front surface and the amount by which it deviates depends on the height of ray with respect to axis

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8
Q

what is wave front aberration function ?

A

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

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9
Q

explain the concept of wavefront aberration ?

A

the rays are always perpendicular to the wavefront surface , but the latter varies locally in curvature and is no longer part of a single spherical surface

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10
Q

what are ‘ primary ‘ or ‘seidel’ aberrations ?

A
  • the possible distortions to the wavefront when light passes through symmetrical optical system
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11
Q

what are the 5 seidel aberrations terms ?

A
  • spherical aberration
  • coma
  • astigmatism
  • field curvature
  • distortion
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12
Q

what are the variables used to define the wavefront aberration function ?

look at the slides

A
  • ( β )object field angle - what we consider when dealing with extended objects
  • (θ) meridian in exit pupil plane
  • (h) ray height in exit pupil plane
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13
Q

what is the expression for spherical aberration ?

A

b1 h^4

  • proportional to the fourth power of ray height in the pupil plane
  • doesn’t depend on object field angle
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14
Q

what is expression for coma ?

A
  • b2 h^3 βcosθ
  • proportional to the third power of ray height
  • also proportional to the object field angle and cosine of angle theta
  • this means that coma is absent when the object is on axis , when objet field angle is 0
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15
Q

what is expression for astigmatism ?

A
  • b3 h^2 β^2 cos ^2 θ
  • proportional to the square of object field angle
  • off-axis
  • depends on square of ray height and square of the cosine angle theta
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16
Q

what is expression for field curvature ?

A
  • b4 h^2 β^2
  • increases with the square of ray height and the square of the object field angle
  • doesn’t cause a distortion in the quality of the image but shifts the image plane
  • off-axis image plane will be pulled towards the lens
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17
Q

what is expression for distortion ?

A
  • b5 h β^3 cos θ
  • proportional to the third power of object field angle
  • only the first power of aperture
  • distortion causes a change in the shape of the image
  • distortion is large when object field angle is large
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18
Q

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

A
  • they are constants that determine the size of the corresponding seidel aberration
  • able of optical design is to minimise these coefficients as much as possible to reduce the size of these aberrations
19
Q

what are the effects of the primary seidel aberrations ?

A
  • expanded size for a point image
  • curved image plane
  • extended images are no longer geometrically similar to the objects
20
Q

what is the effect of primary seidel aberrations

?

A
  • expanded size for a point image ( spherical aberration , coma and astigmatism )
  • curved image plane ( field curvature )
  • extended images are no longer geometrically similar to the objects ( distortion )
21
Q

what happens when you increase aperture size in spherical aberration ?

A
  • rays distribute
  • symmetrically around the paraxial image point but they move away from the paraxial image plane so we end up with two image planes paraxial image plane and marginal image plane.
  • no object field angle in this expression
  • If we use a small object height- centre paraxial region- end up with a very good image point (with small amount of spherical aberration)
  • if look off-axis, the object point is effected by the remaining aberrations which depend on the object field angle .
22
Q

what are the two extreme image planes formed by spherical aberration ?

A

marginal image plane - most peripheral raise

paraxial image plane

23
Q

what are the properties of spherical aberration ?

A
  • spherical aberration is absent on axis because it doesn’t depend on the object field angle
  • spherical aberration remains constant over the field
  • spherical aberration is very large in the human eye - important because the only
  • only aberration on-axis is spherical aberration and highest resolving power is in the central vision - so it is important in affecting our visual performance
24
Q

where is the best image plane formed in spherical aberration ?

A

the best image plane corresponds to the disc of least confusion . the location of this plane divides the distance between marginal and paraxial foci in the ratio

25
Q

what is the relationship between the marginal focal plane and paraxial focal plane in spherical aberration ?

A
  • the disc of least confusion divides the distance between the marginal and paraxial foci 1:3
  • the difference in lens power between the marginal and the paraxial focal planes is proportional to the square of ray height ( h^2 )
  • 𝛿F - h^2
26
Q

how does wavefront aberration relate to the size of pupil ?

A
  • small pupil sizes (3mm) - no wave front aberration - system is diffraction limited
  • as the pupil size increase the wavefront aberration increases which affects the quality of the retinal image
27
Q

what is residual wavefront aberrations ?

A
  • measure of the size of the deviations over the whole of the wavefront surface
28
Q

what are the effects of coma ?

A
  • off-axis-
  • but as you increase object field angle you get more coma with more asymmetric distribution of rays as indicated
  • coma increase with third power of ray height-
29
Q

why is coma off-axis ?

A
  • because its proportional to object field angle so when object field angle is 0 there is no coma
30
Q

how does coma get a comet appearance ?

A
  • rays perpendicular to the wavefront surface generate a distribution intensity in the image of a point that has a comet like appearance
31
Q

describe astigmatism ?

A
  • off axis because astigmatism is proportional to the square of the object field angle
  • when object is on - axis there is no astigmatism
  • proportional to the square of ray height
  • astigmatism increase with both the square of the ray height and with square with object field angle
32
Q

what happens in the sagittal plane in astigmatism ?

A
  • object with circular symmetry will be blurred in the sagittal image plane
  • sagittal line that passes through the axis will be imaged sharply in focus in the paraxial image plane
  • circle rotates in paraxial image line
33
Q

what happens in the tangential image plane in astigmatism ?

A
  • doesn’t blur circle as much as sagittal line

- circle in object plane will be imaged with good spatial resolution whilst a line

34
Q

what are the two components of astigmatism ?

A
  • sagittal image plane

- tangential image

35
Q

what is the difference between sagittal plane and tangential plane in astigmatism ?

A
  • the tangential plane ( θ=0) has the largest aberration while sagittal plane (θ=90) has no aberration
  • the dioptric power between tangential and sagittal focal lines increases with the square of the field
36
Q

what is oblique astigmatism ?

A

in symmetrical optical systems , astigmatism is absent on axis when β=0

37
Q

how is astigmatism is caused in eye ?

A
  • astigmatism in eye is often caused by a significant difference in the curvature of the cornea in one meridian . when this happens astigmatism will be observed for on-axis objects
38
Q

describe field curvature ?

A
  • field curvature represents a variation in focusing distance that varies with the square of the field
  • increases with the square of object field angle and the square of the aperture size
39
Q

how is field curvature an advantage in the eye ?

A

field curvature is an advantage because when field curvature is negative it can combined with astigmatism to ensure that the best astigmatic image forms a flat surface

40
Q

how to minimise the effects of field curvature ?

A
  • use a curved image surface as in the human eye
  • when plane image field is essential one can reduce field curvature using a combination of negative and positive lenses
  • minimise the effects of astigmatism by introducing an appropriate amounts of field curvature
41
Q

what is distortion ?

A
  • proportional to the third power of object field angle
  • distortion represents a displacement of focus for each image point in a radical direction that increases with the third power of the field.
    distortion is unavoidable in wide angle lenses
42
Q

what is cause of distortion ?

A
  • the chief ray which passes through centre of lens and edge of aperture doesn’t end up at corresponding position in the image plane and this deviation can cause distortion of extended object
43
Q

what are the two types of distortion ?

A
  • image with negative or pincushion distortion

- image with positive or barrel distortion

44
Q

why do monochromatic aberration arise ?

A

arise as natural consequences of refraction and reflection in symmetrical optical systems

Optics (34 decks)

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