Emre Coşkun

Optical phase distribution evaluation by using an S-transform

An experimental study of the use of an S-transform to evaluate the phase distribution from a two-dimensional fringe pattern by introducing the carrier frequencies in two spatial directions, x and y, is presented. The phase distribution is extracted from the optical fringe pattern by using an S-transform gradient and S-transform phase methods. The experimental result for the Fourier transform profilometry algorithm is compared with the results of the S-transform analysis.

Determination of birefringence dispersion in nematic liquid crystals by using an S-transform

An analysis of the transmittance signal of the 5CB-coded nematic liquid crystal by using an S-transform is presented. The transmittance spectrum of this liquid crystal is acquired in the 1.26-2.22 microm(-1) region at room temperature. The dispersion curve of birefringence is obtained for 5CB by this analysis, and data are fitted to the Cauchy formula, whereby the dispersion parameters are extracted. The result is found to be in favorable accordance with the Merck catalog value.

Generalized Morse wavelets for the phase evaluation of projected fringe pattern

Generalized Morse wavelets are proposed to evaluate the phase information from projected fringe pattern with the spatial carrier frequency in the x direction. The height profile of the object is determined through the phase change distribution by using the phase of the continuous wavelet transform. The choice of an appropriate mother wavelet is an important step for the calculation of phase. As a mother wavelet, zero order generalized Morse wavelet is chosen because of the flexible spatial and frequency localization property, and it is exactly analytic. Experimental results for the Morlet and Paul wavelets are compared with the results of generalized Morse wavelets analysis.

Paul wavelet algorithm for the determination of birefringence dispersion of a liquid crystal cell

The Paul wavelet algorithm was prepared as a method to obtain the birefringence values continuously for a liquid crystal sample by using the transmittance spectrum in visible and near-infrared regions at room temperature. The obtained results determined from the Paul wavelet algorithm are harmonious with the 5CB-coded liquid crystal catalog value and the results determined from the fringe counting method. The controlling on the resolution of the working space is possible with the Paul wavelet, and the presented work attempts to depict the importance of control. Noise effect and absolute errors of the presented method and the fringe counting method are also studied and compared.

Determination of the refractive index of a dielectric film continuously by the generalized S-transform

The generalized S-transform was improved as a method to determine the refractive index of a dielectric film continuously by using the transmittance spectrum, and the applicability of the method was demonstrated on mica. The result determined from the generalized S-transform method was compared with the results determined from the S-transform and the fringe counting methods and published values. The advantage of the proposed method was explained, and the absolute error of the presented method was also calculated.

An improved method for the determination of birefringence dispersion of liquid crystal cell: A simulation study

An improved approach to determine the birefringence dispersion of a liquid crystal cell was presented. Using the local maxima or minima of the transmittance spectrum of liquid crystal cell is a very convenient method for this aim with the proviso that at least one birefringence value must be known in advance from which the interference orders corresponding to maxima or minima are determined. Presented approach overcomes this problem. The improved method was based on the minimizing procedure leading to the determination of interference order and Cauchy parameters accurately. It was tested on a theoretically generated transmittance spectrum of liquid crystal cell and the details of the fitting procedure were discussed.

Profile measurement of objects by using stockwell and continuous wavelet transforms

In this study, 3D profile measurements of objects are tested with integral transforms by using a standard fringe projection technique consisting of a CCD (charge-coupled device) camera and a projector. The surface profile of a rough object is studied experimentally with crossed optical axes geometry. A two dimensional fringe pattern by introducing the carrier frequencies in two spatial directions, x and y, is analyzed with S-transform and continuous wavelet transform based on Morlet wavelet algorithms. Phase gradient and phase methods are presented for continuous wavelet transform (CWT) and S-transform of the fringe pattern. At the end, results of experimental application of these techniques are compared.

S-transform analysis of projected fringe patterns

3D profile measurement of an object is studied experimentally by using a standard fringe projection technique consisting of a CCD camera and a digital projector. The height profile of the object is calculated through the phase change distribution of the projected fringes with two dimensional fringe pattern by introducing the carrier frequencies in two spatial directions, x and y. The phase distribution is extracted from the optical fringe pattern by using S-transform gradient and S-transform phase methods. Experimental result for the Fourier transform profilometry algorithm is compared with the results of the S-transform analysis.

Optical phase distribution evaluation by using zero order Generalized Morse Wavelet

When determining the phase from the projected fringes by using continuous wavelet transform (CWT), selection of wavelet is an important step. A new wavelet for phase retrieval from the fringe pattern with the spatial carrier frequency in the x direction is presented. As a mother wavelet, zero order generalized Morse wavelet (GMW) is chosen because of the flexible spatial and frequency localization property, and it is exactly analytic. In this study, GMW method is explained and numerical simulations are carried out to show the validity of this technique for finding the phase distributions. Results for the Morlet and Paul wavelets are compared with the results of GMW analysis.

A simulation study for determination of refractive index dispersion of dielectric film from reflectance spectrum by using Paul wavelet

In this work, the Continuous Wavelet Transform (CWT) with Paul wavelet was improved as a tool for determination of refractive index dispersion of dielectric film by using the reflectance spectrum of the film. The reflectance spectrum was generated theoretically in the range of 0.8333 - 3.3333 μm wavenumber and it was analyzed with presented method. Obtained refractive index determined from various resolution of Paul wavelet were compared with the input values, and the importance of the tunable resolution with Paul wavelet was discussed briefly. The noise immunity and uncertainty of the method was also studied.