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Wavefront Expansion

Excerpt from Field Guide to Geometrical Optics

The wavefront expansion is a power series expansion for thewavefront aberrations inherent to a rotationally symmetricoptical system. These aberrations are inherent to the design ofthe system. In order to satisfy the requirements of rotationalsymmetry, the expansion terms are H2, ρ2 and Hρ cosθ. The coefficient subscript encodes the powers of the corresponding polynomial term:


W = W020ρ2Defocus
+ W111Hρ cosθWavefront tilt

Third-Order Terms

+ W040ρ4Spherical aberration (SA)
+ W1313 cosθComa
+ W222H2ρ2 cos2 θAstigmatism
+ W220H2ρ2Field curvature
+ W311H3ρ cosθDistortion

Fifth-Order Terms

+ W060ρ6Fifth-order SA
+ W1515cosθFifth-order linear coma
+ W422H4ρ2cos2θFifth-order astigmatism
+ W420H4ρ2Fifth-order field curvature
+ W511H5ρcosθFifth-order distortion
+ W240H2ρ4Sagittal oblique SA
+ W242H2ρ4cos2θTangential oblique SA
+ W331H3ρ3cosθCubic coma
                      }   Elliptical coma
+ W333H3ρ3cos3θLine coma
+ Higher order terms 

The wavefront terms are denoted by the order of their rayaberration, which is one less than the wavefront aberrationorder. Terms with no pupil dependence, piston (W000) and field-dependent phase (W200,W400, etc.), are usually ignored.


J. E. Greivenkamp, Field Guide to Geometrical Optics, SPIE Press, Bellingham, WA (2004).

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