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Lecture 6: Wave aberrations (Wave aberration in Optical systems (Quality…
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
wave front for only 1 field point
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
Tilt of wavefront
deltaW = n
y_p
theta < 0
linear in y_p
the usual description of distortion
Defocussing of wavefront
deltaW >0
W对y_p: quadratic shape
Wave Aberration Criteria
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:
RMS included
All shapes of wavefronts can be considered.
Special cases of Wave Aberrations
axial color and field curvature --> defocussing term
Zernike C4
distortion and lateral color--> tilt term
Zernike C2, C3
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
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