## Abstract

A method is presented that can be applied to phase-step interferometry to locate the regions within which integral multiples of π should be added to the wrapped phase that results from arctangent calculations. Unlike previous methods, this one is immune to the noise-related errors that confuse simple phase-unwrap schemes. It makes use of the fact that the noise-related errors occur at fixed locations in the phase map, whereas the location of the wrap regions depends on the way in which the arctangent is calculated.

© 1996 Optical Society of America

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### Figures (3)

Fig. 1

Plot of 11 phase values calculated from Eqs. (2a) and (2c) with the same data.

Fig. 2

(a) Plot of half the difference of the values in the upper and lower plots in Fig. 1 (dashed line). The solid line plots these values converted to a staircase function for unwrapping, (b) Plot of the average of the values in the upper and lower plots in Fig. 1 (dashed line). The solid line plots the unwrapped phase values obtained by adding the staircase function from Fig. 2(a). Note that the transition greater than π between the third and fourth points has been preserved.

Fig. 3

Two-dimensional array of phase-wrap regions calculated by subtracting phase values calculated with Eqs. (2a) and (2c) and dividing by 2. The filled circles indicate values of π/2, the open circles −π/2.

### Equations (5)

$ϕ ( x , y ) = arctan ( n / d ) ,$
$ϕ 0 ( x , y ) = arctan ( n / d ) ,$
$ϕ 90 ( x , y ) = arctan ( d / − n ) ,$
$ϕ 180 ( x , y ) = arctan ( − n / − d ) ,$
$ϕ 270 ( x , y ) = arctan ( − d / n ) ,$