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Nijboer–Zernike Aberration

An optical aberration is a departure of the performance of an optical system from the predictions of paraxial optics. The analysis by Nijboer and Zernike describes the intensity distribution close to the optimum focal plane.

The Zernike term depends on the azimuthal frequency index, azimuthal angle and the radius.

Formula

QuantityVariable[Subsuperscript["Z", "n", "m"], "Unitless"] == (((1 + (-1)^QuantityVariable["m", "Unitless"])*Cos[QuantityVariable["m", "Unitless"]*QuantityVariable["ϕ", "Angle"]])/2 + ((1 + (-1)^(1 + QuantityVariable["m", "Unitless"]))*Sin[QuantityVariable["m", "Unitless"]*QuantityVariable["ϕ", "Angle"]])/2)*ZernikeR[QuantityVariable["n", "Unitless"], QuantityVariable["m", "Unitless"], QuantityVariable["r", "Unitless"]]

symbol description physical quantity
Znm Zernike term "Unitless"
m azimuthal frequency index "Unitless"
ϕ azimuthal angle "Angle"
n radial order "Unitless"
r radius "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Nijboer\[Dash]Zernike Aberration"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Nijboer\[Dash]Zernike Aberration"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Nijboer\[Dash]Zernike Aberration"], {QuantityVariable[ "\[Phi]","Angle"] -> Quantity[45, "AngularDegrees"], QuantityVariable["n","Unitless"] -> 6}]
Out[3]=

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