Generalization
The phase shifting method was first introduced in 1966 [5], when P. Carré invented this processing method for the interferential comparator of the BIPM (International Office for Weights and Measurements).
This technique has the advantage that it doesn't require any intervention from an experimentalist after the interferograms have been registered. This is actually the reason why this method is widely used in some commercially available devices: Fizeau interferometer, interferential microscope, fringe pattern projection, shearography, etc. Phase shifting algorithms usually assume that the fringe pattern has a sinusoidal profile characteristic of two-wave interferences. The interferogram can thus be written, in a general way:
where
is "the phase shift ", and where the spatial and possibly temporal dependencies have been implied. Using this simple expression, which contains three unknowns,
, or possibly four with
depending on the degree of knowledge of
, one needs at least three equations to determine all variables. Thus, if
takes successively N values, one will obtain a system of N equations with three (or four) variables which can be solved.
The main advantages of phase shifting are the follwing:
-
a small sensitivity to stationary noise in the range on which
varies; for example, for temporal phase shifting the algorithm is insensitive to the nonuniformity of a and b and to the variation of detector sensitivity from one pixel to another. -
the algorithms can be used with poorly contrasted fringe patterns.
-
the uncertainty on the result is limited by the signal to noise ratio of the fringe pattern; systematic errors can be sufficiently reduced so that the noise will be the factor limiting the uncertainty.
-
the analysis process of the fringe pattern can be fully automated.
-
the optical phase
is determined at each point of the interferogram. -
spatial resolution is high since the number of points for which the phase is measured coincides with the number of pixels of the acquisition sensor.
-
the high computation power available today (PC included) enables calculation of times smaller than 1s.
In fact, the main limitation of these algorithms is that the phase is calculated modulo
. Moreover, the smallest fringe period in the camera acquisition plane must be larger than 2 pixels.
Phase shifting algorithms can be classified using several criteria. We will use a classification in two groups: the larger group will bring together the algorithms that we will call "generic", obtained by a systematic processing. The second group will contain the so-called "specific " algorithms, for which the previous hypothesis are non valid and Δφ cannot be the result of direct systematic processing [6].
For this lesson, we will focus on generic algorithms.