An 11-sample triangle window is defined by $w0=(1,2,3,4,5,6,5,4,3,2,1)$. If we average the three windows with a relative shift of one sample, the resultant window becomes Display Formula
$w=w0+w\pi 3+w2\pi 3=(1,3,6,9,12,15,16,15,12,9,6,3,1).$(13)
If we describe the phase shift by $\alpha i=\pi (i\u22127)/3$, for $i=1,2,\u2026,13$, the sampling amplitudes for the denominator and the numerator of the new algorithm are given by $wi$$cos\u2009\alpha i$ and $wi$$sin\u2009\alpha i$, respectively. The resultant algorithm is obtained as Display Formula$\theta =arctan\u20093(3I2+6I3\u221212I5\u221215I6+15I8+12I9\u22126I11\u22123I12)2I1+3I2\u22126I3\u221218I4\u221212I5+15I6+32I7+15I8\u221212I9\u221218I10\u22126I11+3I12+2I13,$(14)
where $Ii$$(x,y)$ is the intensity of the $i$’th interference fringes.