Lecture 6: Wave aberrations

Ray-Wave Equivalent


Wave is purely geometrical and has no diffraction properties

Law of Malus-Dupin

equivalence of rays and wavefronts
both are orthonormal
identical information

Condition: No caustic of rays

Fermat Principle

Optical path length

Optical path difference

Relation between wave aberrations, transverse
aberrations and longitudinal aberrations

Wave aberration in Optical systems

Definition

Pupil sampling

Quality assessment of wave aberrations

peak valley value(PV)

rms value, area average

Zernike decomposition for detailed analysis

sign and reference

relative to reference sphere
choice of offset value：
center where chief ray passing through

sign of W:
W>0: stronger convergence

Wave Aberration Criteria

Tilt of wavefront

Defocussing of wavefront

deltaW = ny_p theta < 0
linear in y_p

the usual description of distortion

deltaW >0

W对y_p: quadratic shape

Special cases of Wave Aberrations

axial color and field curvature --> defocussing term
Zernike C4

distortion and lateral color--> tilt term
Zernike C2, C3

wave front for only 1 field point

Afocal system:
exit pupil in infinity
plane wave as reference

Telecentric system: chief ray parallel to axis
Choose the position of pupil plane and the corresponding center of the reference sphere

Polynomial expansion of Wave aberrations

Taylor expansion of the primary aberrations(monochromatic aberrations)

Zernike Polynomials

Mean quadratic wave deviation(rms)

Peak valley value W_pv

General case with apodization

Rayleigh Criterion: |W_pv|<=lambda/4

beginning of destructive interference of partial waves

diffraction limited(definition)

different limiting values for aberration shapes and definitions(Seidel, Zernike,...)

Marechal criterion

Rayleigh criterion corresponds to
W_rms<lambda/14 in case of defocus

Generalization of W_rms< lambda/14 for all shapes of wave fronts

Corresponds to Strehl ratio D_s>0.8(in case of defocus)

More useful:

  1. RMS included
  2. All shapes of wavefronts can be considered.

Typical variation of Wave Aberrations

RMS of the wavefront changes with field position scaled in lambda

wavelength and field position dependent

Zernike calculation on distorted grids

Zernike coefficients for change of radius

Zernike expansion of local deviation

Measurement of wave aberrations

Direct phase measuring techniques

Indirect measurement by inversion of the wave equation

Indirect measurement by analyzing the imaging conditions

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