Changes

== Phase Shifting Technique ==

== Phase Shifting Technique ==

[[Image:framediff.jpg|thumb|A schematic of rotations]]

[[Image:framediff.jpg|thumb|A schematic of rotations]]

As noted in the introduction, the first phase-shifting algorithms were designed in the 1960's by Carre, Rowley and Harmon.  The essence of the phase shifting algorithm lies in the ability to gather the necessary phase information from (theoretically) three to (more realistically) five interference patterns, called frames, so that a nearly complete image may be rendered of the surface in question.

As noted in the introduction, the first phase-shifting algorithms were designed in the 1960's by Carre, Rowley and Harmon.  The essence of the phase shifting algorithm lies in the ability to gather the necessary phase information from (theoretically) three to (more realistically) five interference patterns, called frames [[#References|[1]]], so that a nearly complete surface topology may be rendered.

In recent years combinations of spatial and temporal methods have been combined and thus form a subcategory of the phase-shifting method, known as "self calibrating [sic] spatio-temporal algroithms." Among these methods are the Fourier Method, the Lissajou ellipse fitting method, the interferogram correlation method and others.  Each of these have their high points and low points, mostly stemming from either the type of surface they best work for or the the number of frames required.  

In recent years combinations of spatial and temporal methods have been combined and thus form a subcategory of the phase-shifting method, known as "self calibrating spatio-temporal algroithms" [[#References|[1]]].  Among these methods are the Fourier Method, the Lissajou ellipse fitting method, the interferogram correlation method and others.  Each of these possess strengths and weaknesses, mostly stemming from either the type of surface they best work for or the the number of frames required.  

In his paper, Larkin proposes a method mentioned in the previous paragraph that utilizes a "truly isotropic 2-D Hilbert-Fourier demodulation algorithm" or "vortex algorithm" as a solution to the problem of overcoming discontinuities in un-processed fringe patterns.  Larkin's algorithm initially eliminates the presence of the offset term a(x,Y) in the general fringe-pattern equation and follows by introducing a weighting function that depends on the frequency of the fringe oscillation.  Thus, higher frequency modulations are weighted closer to zero, while those that are closer to DC recieve a higher weight.  This tactic, when combined with the vortex transform, gives one the ability to link different frames to analyze a fringe pattern, with as little as three separate images.

In his paper, Larkin proposes a method mentioned in the previous paragraph that utilizes a "truly isotropic 2-D Hilbert-Fourier demodulation algorithm" or "vortex algorithm" as a solution to the problem of overcoming discontinuities in un-processed fringe patterns.  Larkin's algorithm initially eliminates the presence of the offset term a(x,Y) in the general fringe-pattern equation and follows by introducing a weighting function that depends on the frequency of the fringe oscillation.  Thus, higher frequency areas of the pattern are weighted closer to zero, while those that are closer to DC recieve a higher weight.  This tactic, when combined with the vortex transform, gives one the ability to link different frames to analyze a fringe pattern, with as little as three separate images [[#References|[1]]].

== Fourier Analysis Method ==

== Fourier Analysis Method ==