Chapter 17 – Aberrations PDF

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Chapter 17 – Aberrations Deviations from the optical system’s performance – aberrations.Seidel aberrations  If angle i is very small – then sin i = i – first order approximation since it only uses I to the power of 1.  If the angles of incidence of the object rays are not small – sin i = i no lon...

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Chapter 17 – Aberrations  Deviations from the optical system’s performance – aberrations. Seidel aberrations  If angle i is very small – then sin i = i – first order approximation since it only uses I to the power of 1.  If the angles of incidence of the object rays are not small – sin i = i no longer works:  sin i = i – (i3/6) – does not result in ideal imaging. We get: 1. Spherical aberration (SI) – axial aberration  Rays coming from an axial object point at infinity.  i increases as the ray is further away from the optical axis.  For the rays close to the optical axis – i is small.  Caused by spherical surfaces.  Amount of spherical aberration increases as a larger part of surface is used – spherical surface with a large curvature will suffer spherical aberration at distances closer to the optical axis.  Spherical aberration can be reduced by reducing the size of the AS – reduces effective beam diameter – eliminates region of the beam for which the rays deviate most from the ideal.  Rays closest to the optical axis meet furthest from the surface – while rays furthest from the optical axis meet closest to the surface – distance along the axis is Longitudinal Spherical Aberration (LSA).  For paraxial surface with no aberrations – LSA would have a value of 0 – LSA also small if AS is reduced.  Larger the amount of spherical aberration, the larger the distance covering all the rays at the image plane – this distance is called Transverse Spherical Aberration (TSA).

 Absence of aberration – rays intersect at the same point – TSA = 0. 2. Coma (SII)  An off-axis aberration – introduced when object is at an off-axis point.  Non-paraxial rays are creating a blurred and displaced image at this plane – further the rays are from the paraxial region – more blurred and displaced the image they form is – rays are circular in shape.  Further away from the paraxial region – the more serious the effect of aberration. Reducing AS size – reduce the amount of coma present. 3. Astigmatism (SIII)  Off-axis aberration.  Top view shows us rays approaching the plate’s surface in a symmetric fashion – independent of the angle at which the beam of light is approaching the plate.  Top view – observing rays contained in a plane that contains the horizontal axis – sagittal plane – two rays shown both refract by the same amount.  Side view – angle between the beam and the plate is observed as a tilt – tangential plane – rays are not symmetrically at the surfaces of the glass plate – one ray refracted more than the other one.  3D – beam starts off as circular beam converging towards a single point – as astigmatism is introduced through passage through the optical system off-axis – beam converges more rapidly along tangential direction than sagittal – changing beam profile to an elliptical one.  As tangential focus is reached – elliptical beam has now been squashed into a straight-line perpendicular to the tangential axis.

 Rays in tangential plane will start to diverge again – while sagittal plane are still converging until sagittal focus is reached – giving another straight-line focus.

 Toroidal surface – one which has different curvatures along different axes. 4. Field curvature (SIV)  If the object distance l is the distance from the axial object point to the principal point of the optical system – distance from the off-axis object point to the principle point must be larger than l.  l’ is the axial distance – location of the image – the more offaxis the object-image points are, the larger the discrepancy.  Leads to image plane being a curved image surface rather than a plane – field curvature. 5. Distortion (SV)  If the magnification increases as the object is more off-axis – end up with a distorted image – pincushion distortion.  If the magnification decreases with field angle – image is pushed in from the edges – barrel distortion. Wavefront representation of aberrations  Ideal unaerated optical system – if light is emitted from an object point – points that are in phase always form a spherical surface centred on the object point.  If light is converging towards a single image point – then wavefronts must also be spherical surfaces centred at the image point.  Spherical wavefront represents the ideal wavefront that gives an ideal point image. If light is either

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coming from or going to infinity – spherical wavefront becomes a plane wavefront. In the presence of aberration – wavefront is distorted from its ideal spherical surface to a non-spherical one. Reference surface – spherical wavefront that best approximates the wavefront being assessed. Distance between the real wavefront and its spherical wavefront – called wavefront aberration (W). W at any point can take positive or negative values depending on whether the wavefront lies in front or behind the reference surface.

 Toroidal lens has two meridians with different powers. Reference surface is the spherical surface centred on the CLC .  Meridian with higher power = wavefront converging to a point closer to the lens than CLC – first line focus – W positive everywhere.  Meridian with weaker power – wavefront converging to a point beyond CLC – W is negative.

Zernike polynomials  Zernike function takes in a value that represents the position in the pupil and gives out a value that represents the distance between the wavefront and its reference surface at that point  represents astigmatism. Chromatic aberration  If polychromatic light is present in an imaging system – different wavelengths of light will form images at slightly different planes....