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In this study, the determination of the surface morphology of red blood cell (RBC) from interferogram image obtained by quantitative phase imaging (QPI) method is presented. QPI, is an optical measurement method fre-quently used in recent years, allows to obtain quantitative data for different samples (cell, thin film surface, etc.). Many measurement setups at the micrometer level and with nanometer precision have been designed for quantita-tive surface determination. Among these, white light diffraction phase microscopy (WDPM) is a design that combines the advantages of off-axis holography-specific speed and phase sensitivity associated with common path interferometry. Interferogram image of RBCs have been formed by the WDPM setup. Analysis of this image has been carried out by Fourier transform. As a result of this analysis, three-dimensional (3D), dynamic (observable from all angles) and height-known profiles of RBCs have been created. From the height profiles, the parameters related to the morphology of RBCs as the projected surface area (PSA), diameter (D), mean corpuscular volume (MCV) and total surface area occupied by the cell (SA), have been determined quantitatively. In addition, two-dimensional images, obtained by examining blood samples with light microscopy and scanning electron micros-copy (SEM), have been compared with the data achieved by WDPM. The advantages and disadvantages of WDPM and light microscopy and SEM, which are commonly used in biomedical measurements, are discussed through the results. In this way, it was possible to see the difference between QPI and traditional methods used to imaging the cell surface.

The zero order generalized Morse wavelet was proposed as a method to determine the refractive index and extinction coefficient dispersions of an absorbing thin film in the visible and near infrared regions at room temperature. The generalized Morse wavelet has two degree of freedom and the advantages and disadvantages of additional degree of freedom were discussed in the simulation works. The simulation studies were based on the mean relative error and Cauchy coefficients comparisions, and accuracy of the calculated refractive index was improved by the presented method, were compared with the Morlet wavelet and Paul wavelet. Also, the noise immunity of the method was discussed. The experimental validity of the method was tested on a cadmium sulfide absorbing thin film and the calculated refractive index were cross checked with the value of envelope method and literature.

In this study, the white light diffraction phase microscopy and the generalized Morse wavelet are proposed to achieve practical and precise measurement of a thin film surface. The white light diffraction phase microscopy provides low speckle noise and single-shot measurement, and thus it has been used to produce an image with interference fringes from the surface of a thin film. Relying on produced interferogram, quantitative phase information of the thin film surface has been obtained using the continuous wavelet transform. In the calculation of the quantitative phase, in many studies the continuous wavelet transform method with different wavelets is preferred. The Morlet wavelet is a commonly used one with a fixed resolution. An alternative approach is proposed using the generalized Morse wavelet capable of controlling the resolution. It has an additional advantage of varying the two parameters, thus improving the sensitivity of phase calculation. Results of the generalized Morse wavelet were compared with the Morlet and Paul wavelets which also have one varying parameter. For the determination of the thin film surface profile, besides the white light diffraction phase microscopy, surfaces have been investigated by a Dektak stylus profilometer and a scanning electron microscope. In this way, it was possible to observe the difference between the most commonly used methods with regard to the imaging of thin film surfaces. The application of the white light diffraction phase microscopy with the generalized Morse wavelet was compared with the common microscopy techniques for studying thin film surfaces, and experimental results were discussed at the end of the study. © 2021 Polish Academy of Sciences. All rights reserved. 120F325 This work was supported by the Tekirda? Nam?k Kemal University Scientific Research Project Commission (NKUBAP.01.GA.18.148) and the Turkish Scientific and Technical Research Council (TUBITAK-MFAG No 120F325). This work was supported by the Tekirdağ Namık Kemal University Scientific Research Project Commission (NKUBAP.01.GA.18.148) and the Turkish Scientific and Technical Research Council (TUBITAK-MFAG No 120F325).

The Generalized Morse Wavelet (GMW) algorithm was adapted to determine the refractive index of dielectric film from the reflectance spectrum. A theoretically generated reflectance spectrum in the range of 300-1200 nm wavelength was analyzed by the Continuous Wavelet Transform (CWT) and the refractive index dispersion was obtained by the mentioned method. In addition, a noisy reflectance spectrum was analyzed to show the advantages of the CWT method. Refractive index dispersions calculated by the Morlet and the Paul wavelet were compared to GMW at the end of the study. Turkish Scientific and Technical Research Council (TUBITAK-MFAG) [115F168] This work was supported by the Turkish Scientific and Technical Research Council (TUBITAK-MFAG no: 115F168). This study was evaluated from Erhan Tiryaki's doctoral dissertation.

The present study focuses on the quantitative phase imaging of erythrocytes with the aim to compare the morphological differences between epilepsy patients under antiepileptic treatment, who have no other disease which may affect the erythrocyte morphology, and the healthy control group. The white light diffraction phase microscopy (WDPM) has been used to obtain the interferogram of the erythrocyte surfaces. The continuous wavelet transform with Paul wavelet has been chosen to calculate the surface profiles from this interferogram image. For the determination of alteration in morphology, besides WDPM, erythrocyte surfaces have been investigated by light microscope and scanning electron microscope. In this way, it has been possible to see the difference in terms of precision and implementation between the most commonly used methods with regard to the quantitative phase imaging. Erythrocytes from all the samples have been examined and displayed in both two- and three-dimensional way. We have observed that erythrocytes of patients with effective antiepileptic blood levels were more affected in morphology than healthy subjects. When we compared the erythrocyte morphological changes of patients who received monotherapy or polytherapy, no difference was observed. In conclusion, antiepileptic drugs (AEDs) cause red blood cell (RBC) morphological changes and a combined usage of WDPM with Paul wavelet and light microscopy methods are very convenient for studying the erythrocyte morphologies on multiple patients.

The selection of wavelet is an important step in order to determine the phase from the fringe patterns. In the present work, a new wavelet for phase retrieval from the ridge of continuous wavelet transform (CWT) is presented. The phase distributions have been extracted from the optical fringe pattern by choosing the zero order generalized morse wavelet (GMW) as a mother wavelet. The aim of the study is to reveal the ways in which the two varying parameters of GMW affect the phase calculation. To show the validity of this method, an experimental study has been conducted by using the diffraction phase microscopy (DPM) setup; consequently, the profiles of red blood cells have been retrieved. The results for the CWT ridge technique with GMW have been compared with the results for the Morlet wavelet and the Paul wavelet; the results are almost identical for Paul and zero order GMW because of their degree of freedom. Also, for further discussion, the Fourier transform and the Stockwell transform have been applied comparatively. The outcome of the comparison reveals that GMWs are highly applicable to the research in various areas, predominantly biomedicine.

The main objective of this study was 3-dimensional (3D) profile measurements with standard fringe projection, consisting of a CCD and a projector. For obtaining height information of objects pixel by pixel, phases have to be calculated from the images taken by the fringe projection technique. In this study, the 2-dimensional continuous wavelet transform (2D CWT) phase method was used for phase extraction. 1D and 2D CWT analyses of noisy images were compared in simulations performed for a 2-dimensional fringe signal by introducing the carrier frequencies in two spatial directions, $x $ and $y$. Profile measurement of an object was made experimentally by cross optical axis geometry. Images, using fringes with two carrier frequencies, taken from this setup were analyzed with 2D CWT and 3D profiles of objects were obtained. Numerical simulations and actual experiments were carried out to show the validity of this technique for finding phase distributions from noisy images.

The continuous wavelet transform with Paul wavelet was proposed as a method for the simultaneous determination of physical thickness and refractive index dispersion of dielectric films in the visible and near infrared region. Transmittance spectrums, acquired at two different incident angles, were used for the calculations. By this way refractive index dispersion was obtained without knowing the film thickness. The method was tested with simulated data and experimentally applied to a sample of borosilicate glass. The obtained thickness and refractive index dispersion values were compared to the values obtained by the envelope method and the ones provided by the manufacturer.

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 phase distribution is extracted from the optical fringe pattern choosing zero order Generalized Morse Wavelet (GMW) as a mother wavelet. In this study, standard fringe projection technique is used for obtaining images. Experimental results for the GMW phase method are compared with the results of Morlet and Paul wavelet transform.

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.

The main objective of this study was 3-dimensional (3D) profile measurements with standard fringe projection, consisting of a CCD and a projector. For obtaining height information of objects pixel by pixel, phases have to be calculated from the images taken by the fringe projection technique. In this study, the 2-dimensional continuous wavelet transform (2D CWT) phase method was used for phase extraction. 1D and 2D CWT analyses of noisy images were compared in simulations performed for a 2-dimensional fringe signal by introducing the carrier frequencies in two spatial directions, x and y. Profile measurement of an object was made experimentally by cross optical axis geometry. Images, using fringes with two carrier frequencies, taken from this setup were analyzed with 2D CWT and 3D profiles of objects were obtained. Numerical simulations and actual experiments were carried out to show the validity of this technique for finding phase distributions from noisy images.

In this work an improved version of the method presented by Gandhi was presented for determination of refractive index of absorbing films. In this method local maxima of consecutive interference order in transmittance spectrum are used. The method is based on the minimizing procedure leading to the determination of interference order accurately by using reasonable Cauchy parameters. It was tested on theoretically generated transmittance spectrum of absorbing film and the details of the minimization procedure were discussed.

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.

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.

The continuous wavelet transform (CWT) method is a useful tool for the determination of refractive index dispersion of dielectric films. Mother wavelet selection is an important factor for the accuracy of the results when using CWT. In this study, generalized Morse wavelet (GMW) was proposed as the mother wavelet because of having two degrees of freedom. The simulation studies, based on error calculations and Cauchy Coefficient comparisons, were presented and also the noisy signal was tested by CWT method with GMW. The experimental validity of this method was checked by D263 T schott glass having 100 mu m thickness and the results were compared to those from the catalog value.

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.

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.

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.

A simulation study to evaluate phase distribution from 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 S‐transform gradient and S‐transform phase methods. Furthermore, a Gaussian white noise is added to the fringe pattern to test the noise immunity of S‐transform. The recovered phase distributions both by S‐transform gradient method and phase method are compared with the simulated one.

Transmittance spectra of 5CB and ZLI-6000 coded nematic liquid crystals were acquired in the 12600-22200 cm(-1) region at room temperature. The S-transform was applied to analyze the transmittance signal. Dispersion curves of the birefringence were obtained for 5CB and ZLI-6000 by this analysis and data were fitted to the Cauchy formula whereby the dispersion parameters were extracted. Results are found to be in favorable accordance with the published values.

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.

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.