Zernike Analysis (Optional); General - OCULUS Easygraph 70620 Instruction Manual

Zernike polynomials are normally used to describe
wavefronts. The diagram below shows a parallel
wavefront passing through a refractive surface L.
Every light ray consists of a sinusoidal oscillation.
Locations of equal phase within the total array of
sinusoidal oscillations
perpendicular to the direction of propagation on the
refractive surface (green).
wavefronts, which are oriented parallel to each other,
are deformed, in the ideal case resulting in spherical
waves which meet precisely in the focus F (in the
diagram above the wavefronts are shown as red
concentric circular arcs around F).
This ideal case is virtually never encountered in
practice because real wavefronts show deviations from
a perfect spherical wave after passing through the
refractive surface (difference area represented by gray
squares in the second diagram). The smaller this
deviation or aberration is, the higher is the quality of
the refractive system, be it a telescope, a microscope,
the cornea or the entirety of refractive media comprised
by the human eye.
The Dutch physicist and Nobel Prize winner Frits
Zernike (1888-1966, inventor of the contrasting phase
Instruction Manual Easygraph

7.5.2.5 Zernike Analysis (optional)

7.5.2.5.1 General

form planar wavefronts
Here the incident
microscope) succeeded in mathematically representing
the deviations of a real wavefront from an ideal one by
means of a sum of polynomials. Each polynomial is
named according to the image defects it represents
(e.g. astigmatism, comatic
aberration). Zernike polynomials are also known as
circular polynomials because they refer to a circle
with radius 1 and are expressed in terms of polar
coordinates.
Mathematically speaking, each Zernike polynomial is
characterized by a power series in the radial variable,
ρ, and a Fourier-like series in the angular variable, θ.
In its
Z n,±m, n gives the degree of the polynomial in the
radial variable, while m gives the frequency of the
angle θ per 360°. Polynomials with an even n and m=0
are always rotationally symmetrical, while all others are
dependent on the angle.
The first Zernike polynomials bear the following
designations:
Z 0,0 height constant, average height of surface
Z 1,±1 tilt (+1 in x-direction, -1 in y-direction)
Z 2,0 focus, resp., surface in the shape of a conic
section
Z 2,±2 astigmatism
Z 3,±1 coma
Z 3,±3 trefoil
Z 4,0 spherical aberration
Z 4, ±2 higher (4
th
) order astigmatism
Z 4, ±4 four-lobed defect
Z 5, ±1 higher (5
th
)order coma
Z 5, ±3 higher (5 th
) order trefoil
Z 5, ±5 five-lobed defect
Z 6,0 higher (6th) order spherical aberration
Z 6, ±2 higher (6
th
) order astigmatism
Z 6, ±4 higher (6 th
) order four-lobed defect
Z 6, ±6 six-lobed defect
The exact mathematical formula of each Zernike
polynomials are stored in the file:
C:\TOPO\ZERNEKE.TXT
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effect or spherical
general form,