Generalized Morse wavelet for the determination of the birefringence of a liquid crystal cell

Abstract

The generalized Morse wavelet (GMW) was improved as an alternative tool to determine the birefringence dispersion of a liquid crystal (LC) material by using the transmittance spectrum. The GMW has two degrees of freedom and the advantage of this additional degree of freedom was clearly exhibited in the simulation study. The validity of the presented method was shown by using the transmittance spectrum of the ZLI-6000 coded nematic LC and the acquired results were compared with the results of other methods. The noise immunity and uncertainty of the presented method were also studied.

Determination of phase from the ridge of CWT using generalized Morse wavelet

“…In table 1, uncertainties for some β and γ values of GMWs are compared to Morlet and Paul wavelets. It can be seen that GMWs has the minimum uncertainty as 0.50 for β = 3, 5, 7, 10 and γ = 3, and their concentration is comparable to or greater than that of Morlet wavelet which satisfies the uncertainty as 0.5 [30]. The mth order Paul wavelet produces uncertainty as (1/2)[(2m + 1)/(2m − 1)] (1/2) [14,31].…”

“…is Euler number, β and γ are two varying parameters which provide two degrees of freedom. β and γ parameters affect the resolution on x and α domains, and this property has an important role for the analysis [26,29,30]. The analyzing wavelet is localized around the point {x c , α c } of the pixel frequency plane, where x c and α c are the center of GMW in x and α domain respectively.…”

“…This process is repeated for γ = 3, 5, 7 and 10 when β = 3, 5, 7, 10. At these γ and β values, GMWs satisfy the minimum uncertainty [30]. For four different pixel numbers, the absolute phase errors, which are equal to the difference between the test and calculated phases, were determined and given in table 2.…”

The generalized Morse wavelet method to determine refractive index dispersion of dielectric films

“…where k c 0 and x c 0 are the center of the GMW in k 0 and x 0 domain, respectively. Resolution of the GMW, calculated as the multiplication of the variance in both domains, is changed with β and γ parameters [20]. Because of the degrees of freedom, the GMW provides a good alternative when better localization is needed.…”