the zero frequency method
For such a case the above code can be slightly modified to do the Zero Crossing calculation. This pattern is captured in real time as a function of exposure at specific time intervals, then is digitized and transferred to a personal computer [15]. Initial monomer volume fraction for PVA compositions analyzed. A full fringe shift is equal to a radians variation in the phase shift. H. J. Coufal, D. Psaltis, and G. T. Sincerbox, A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,”, G. Manivannan and R. A. Lessard, “Trends in holographic recording materials,”. The recording material is perpendicularly oriented with respect to the interferometer axis in order to simplify the analysis of the interferometric results: at an oblique incidence we should take into account both the Fresnel coefficients at the interface and the increase of distance in the propagation across the layer. In this sense, it is important to obtain a precise estimation of the initial volume fraction of the monomer present in the layer [13, 27, 28]. • Change the slope of the sketch at this point to account for the new dynamics: -1 for pole, +1 for zero, -2 for double poles, . We have tested photopolymers with different TEA concentrations, with different concentrations of BMA, and different dyes. In our case, 48 hours after the layer deposition, the initial monomer volume fraction reaches the values presented in Table 3. Depending on the sense of movement of the fringes (indicated by the arrow in the Figure 1) we can deduce if the exposed zone is shrinking or swelling with respect to the nonexposed one. In these materials the absence of cover plate will lead to two types of cross membrane diffusion taking place: oxygen across the boundary [26] and water in and/or out (due to heating or absorption). The cross-correlation produces a clear peak [15–17]. This value is in good agreement with the value of 0.5, usually assumed for photopolymers with low viscosity [12, 17]. The solution (100 mL) was sonicated in an ultrasonic bath, heated, mixed with a magnetic mixer, and deposited between two glass plates each 2 mm thick. The solutions, whose compositions can be seen in Table 1, with water as solvent, and PVA as binder (Mw = 130000 a.m.u., hydrolysis degree = 87.7%) are deposited, using the force of gravity over a glass. The setup has two arms with an angular separation of 14°, one to expose the recording material, whereas the second arm is the interferometer used to measure, in real time, the phase-shift.
It is important to note that for low values of the parameter γ the nonlinearity is increased. As the velocity of the reaction is very slow, after 1000 s the material continues changing in compositions A, E, and D (compositions without crosslinker). In Table 2 we described the composition of different layers analyzed at zero spatial frequencies. We can observe that the maximum shrinkage is around 3% for compositions B, C, and D. This shrinkage is large enough to store reflection diffractive elements using the relief variations [35]. Once the interference pattern has been stored, we can measure the shift with respect to the initial pattern obtained for the unexposed layer. Therefore, we have changed the AA by sodium acrylate, NaAO, in order to obtain a higher environmental compatibility. Your email address will not be published. To make the calculus more accurate it is possible to measure the exact concentration of each component at the end of zero spatial frequency recording by additional methods. This volume fraction it is more complicate to calculate in noncover-plated PVA materials, because PVA water absorption from the environment depends on the humidity. frequency and phase estimator based on simple estimates of the zero-crossing times of the observation. Furthermore, if the quantities of different compounds are known, it is possible to obtain the polymer refractive index using Lorentz-Lorenz equation [28].
Following the same steps presented in [15–17] we can obtain the polymerization rate as a function of the experimental values of the phase shift during recording, , and the phase of saturation, : A microscope objective is used to amplify the interference pattern onto a CCD camera. 0000000016 00000 n In our opinion the viability of these three types of photopolymers for diffractive and holographic application has been demonstrated. 0000019605 00000 n The H-PDLC photopolymer is composed of dipentaerythritol penta/hexa-acrylate (DPHPA) as monomer and binder, N-vinylpyrrolidone (NVP) as crosslinker, ethyl eosin (YEt) as dye, and N-methyl diethanolamine (NMDETA) as radical generator. There are many types of photopolymers that may be differentiated by the type of binder, since this component determines to a great extent the choice of monomer, dye, and initiator used in the photopolymer. Since a sine wave crosses the x-axis twice during each cycle, we can simply count the number of crossings and divide it by two and again divide it by the observation window size, giving us the frequency … To calculate the value of γ in PVA/NaAO materials we exposed the material to two different exposure intensities 0.5 and 1 mW/cm2 for composition type A and we calculated the polymerization rate value in each experiment using (4). 0000047904 00000 n In this sense values of around 0.5 are associated to high fluid systems and for very dry systems values are near to 1 [12, 17]. The invention discloses a method for detecting zero crossing time, frequency and phase difference of power sinusoidal signals. This photopolymer have been studied for many groups in many different cases [19–23]. We note that there may appear reflection gratings generated by Fresnel boundary reflections.
The composition E, with PRF as a dye, the shrinkage is around 0.25 μm, nevertheless we cannot extract any significant information because the dye crystallizes during exposition. These compositions are designed to keep the liquid volume constant. In this sense, radical polymerization models could be used to know the exact concentration of monomer and dye after illumination [31–33]. In the first arm, the exposure beam provided by a solid-state Nd-YVO4 Verdi laser with a wavelength of 532 nm (at this wavelength the dye presents the maximum absorption) is expanded and collimated using a spatial filter and a lens, obtaining a beam with 1 cm of radius.
A review,”, M. Ortuño, E. Fernández, S. Gallego, A. Beléndez, and I. Pascual, “New photopolymer holographic recording material with sustainable design,”, M. R. Gleeson, J. V. Kelly, C. E. Close, F. T. O'Neill, and J. T. Sheridan, “Effects of absorption and inhibition during grating formation in photopolymer materials,”, S. Gallego, C. Neipp, M. Ortuño, A. Beléndez, E. Fernández, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,”, S. Gallego, M. Ortuño, C. Neipp et al., “3-dimensional characterization of thick grating formation in PVA/AA based photopolymer,”, S. Liu, M. R. Gleeson, J. Guo, and J. T. Sheridan, “Optical characterization of photopolymers materials: theoreticalandexperimental examination of primary radical generation,”, D. Sabol, M. R. Gleeson, S. Liu, and J. T. Sheridan, “Photoinitiation study of Irgacure 784 in an epoxy resin photopolymer,”, S. Liu, M. R. Gleeson, J. Guo, and J. T. Sheridan, “High intensity response of photopolymer materials for holographic grating formation,”, S. Gallego, A. Márquez, M. Ortuño et al., “Surface relief model for photopolymers without cover plating,”, S. Gallego, A. Márquez, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Relief diffracted elements recorded on absorbent photopolymers,”, J. V. Kelly, F. T. O'Neill, J. T. Sheridan, C. Neipp, S. Gallego, and M. Ortuno, “Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions,”. The distance between the two orders is more than 1 cm, so as to eliminate the influence of the monomer diffusion in the polymerization process. As can be seen in this figure, the presence of CL molecules produces a decrease in phase shift. As discussed in my previous post Instantaneous Frequency (IF) is nothing but the rate of change of phase. Photopolymers are useful for different holographic applications such as holographic data storage or diffractive optical elements.
K. Curtis, L. Dhar, L. Murphy, and A. Hill, J. T. Sheridan and J. R. Lawrence, “Nonlocal-response diffusion model of holographic recording in photopolymer,”, M. R. Gleeson, S. Liu, and J. T. Sheridan, “The production of primary radicals in photopolymers during holographic exposure,”, I. Naydenova, E. Mihaylova, S. Martin, and V. Toal, “Holographic patterning of acrylamide-based photopolymer surface,”, G. Zhao and P. Moroulis, “Extension of diffusion model of holograhic photopolymer,”, J. V. Kelly, M. R. Gleeson, C. E. Close et al., “Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model,”, S. Gallego, A. Márquez, D. Méndez, S. Marini, A. Beléndez, and I. Pascual, “Spatial-phase-modulation-based study of polyvinyl-alcohol/acrylamide photopolymers in the low spatial frequency range,”, S. Gallego, A. Márquez, D. Méndez et al., “Real-time interferometric characterization of a polyvinyl alcohol based photopolymer at the zero spatial frequency limit,”, S. Gallego, A. Márquez, D. Méndez et al., “Analysis of PVA/AA based photopolymers at the zero spatial frequency limit using interferometric methods,”, S. Gallego, A. Márquez, M. Ortuño, S. Marini, and J. Francés, “High environmental compatibility photopolymers compared to PVA/AA based materials at zero spatial frequency limit,”, A.J.
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