The effect of the change in the wavelength of the incident field is studied. In Chapter VI an experimental study of the scattering of light from cylinders is reported.
CHAPTER I REFERENCES
The coefficients are function of the wavelength (A), the radius of the cylinder (a), the scattering angle ($) and the distance p. 3.6) The total electric field is the superposition of the incident field and the scattered field, i.e. The main features of the scattered field pattern are the same as those for the parallel polarization case.
The scattered field from the conducting and the dielectric cylinders, represented by infinite arrays of the same shape.
CHAPTER IV
A formula is derived for the fringe spacings of the scattered field and this is compared to the rigorous solution. When the diameter of the cylinder is large compared to the wavelength, we expect that physical optics solutions for the scattered field will be appropriate. As the radius of the cylinder becomes larger relative to the wavelength, the diffraction field becomes narrower and more intense (1).
The diffraction field depends mainly on the size and shape of the object and not on its composition or the nature of the surface. So the diffracted crack field will have the same amplitude as that for the strip with a phase difference of n. The edge spacings of the modified bar have the same value as the cylinder ones, but they do not disappear.
Thus, the modified stripe-diffracted field is a good approximation for the cylinder in the range of edge existence. The fields generated by the surface current can be derived exactly using Maxwell's equations and by integration over the surface of the cylinder. From the geometry of the cylinder, when P is in the far zone, we obtain el Z €I2 E @, and.
CHAPTER V
Van Blade1 investigated the effect of the dielectric constant on the resonances of the scattering cross section(8). In section 5.2, a study of the field at @ = O0 as a function of the variation of the wavelength is reported to show the resonances of the scattered field. The incident field polarization considered here is the case when the incident field is polarized parallel to the axis of the cylinder.
Inside the cylinder, the fields bounce back and forth between the inner surfaces of the cylinder. When the diameter of the cylinder becomes an integer multiple of half-wavelengths, the permeability of the field becomes maximum and resonance occurs, and the frequency is the resonant frequency (13'14). Another thing we can see in the diffuse intensity pattern is that it is modulated by a low frequency function which.
This function also depends on the parameters of the cylinder in its period, and the period decreases with an increase in the diameter of the cylinder. 3 The effect of the resonances on the scattered intensity pattern In Chapter I11 we studied the scattered field pattern as a function of the angle @ for a different range of diameters and refractive indices. Figure 5 shows the scattered intensity plotted as a function of the angle @ at points a, b, c, d and e.
D EGI
The main lobe and the first and second side lobes decrease in amplitude as we move from at-resonance to off-resonance at the peak. The main difference noted between the five intensity patterns is in the envelope that modulates the patterns. At resonance, the envelope has larger variations in its amplitude than that at outer resonance, exhibiting this behavior at both the peak and trough.
135O, in the second part there is a very clear difference between the at-resonance and off-resonance cases; in the at-resonance patterns the intensity has a large variation in amplitude, while in off-resonance the intensity varies greatly. a bit around average. The average of the at-resonance and off-resonance intensity is virtually the same in this range. The intensity value in each of these patterns is the same because we are illuminating the cylinder with the same incident field of amplitude.
So, when the field is in resonance, the intensity will be centered around Q, = 0°, which will decrease the intensity in the interval 45O 5 Q, 5 180° to balance for the whole intensity value. And the main difference between the peak and trough intensity pattern is in the amplitude of the main and first sidelobes, as shown earlier. So the resonances of the fields are affecting the distributed intensity pattern in the way it is formed in different regions of the angle Q,.
CHAPTER V REFERENCES
Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt.
EXPERIMENTS
RS ROTARY STAGE SM STEPPING MOTOR
FH FILM HOLDER
BEAM
EXPANDER IRIS
MOTOR
1 CONTROLLER I
MICROCOMP. CONVERTOR
The movie's HD curve is fitted using a polynomial, which is used to convert density to intensity data. However, we preferred to use the photodiode system for the overall advantages, such as its reliability and ability to obtain a direct recording of the intensity. 6.4(a), the density curve of the film recorded for the intensity pattern of a dielectric cylinder in the region 45O 5 I$ 5 90° is plotted.
The intensity pattern measured using both systems is the same for all pattern characteristics. The accuracy of the intensity data is limited by the data is limited by: a) the non-linearity of the non-linearity of the film. The main feature of the model of the intensity of light scattered by a conducting cylinder, as shown in the photographs of Fig.
Both patterns are very similar in character, amplitude and edge position. The number of edges of the experimental plot is 110, while the theoretical plot has 108 edges. A comparison between theoretical and experimental results for the rest of the scattering angle range I$ is reported in Appendix D.
The sidelobes of the intensity pattern have distances that decrease with increasing Q to a minimum. E 60°, while the distances of the side lobes of the conducting cylinder have constant values as a function of. The intensity pattern of the dielectric cylinder has the same number of side lobes.
The field scattered by a conducting cylinder when the incident field is linearly polarized parallel to the axis of the cylinder is given by Eq. When the incident field is polarized normal to the axis of the cylinder, the scattered field is given by Eq. The intensity patterns for 5 different on-resonance and off-resonance wavelengths at the peak and limit of the resonance curve are shown in Figs.
In Chapter VI, photographs of the scattered intensity patterns for conducting and dielectric cylinders are shown in Figs. A comparison between the scattered patterns for the different polarizations of the incident field is shown in fig. So if m is slightly larger than ka, the summation of the series will give an exact value for the field.
Measurement of optical fiber diameter using the fast Fourier transform
Since the detected intensity is in the far zone, the scattered field is roughly the Fourier transform of the field at the fiber. The angular factors and the non-planar nature of the scatterer prevent this from being a precise relationship. Reading the edge distance frequency is greatly simplified if one uses the FFT of the recorded intensity, as shown in Figure 4.
If we model the intensity as where K is the local radian frequency of the intensity. To make the determination of the fiber diameter from the FF'F of the diffraction intensity, 2N log2N operations are needed on a digital computer for N data points.1°. Thus, it is possible to measure the diameter of the fiber in line as you take it out of the furnace.
In this appendix we show the H-D curve of the film as measured experimentally, and how it is curve fitted to enable us to convert the density data collected on the film from the scattered intensity pattern back to intensity data. To plot the characteristic curve of the film, the film is exposed using a uniform plane wave of laser light; and by changing the neutral density filters we can change the intensity of the field that exposes the film. The characteristic curve of the film as measured by the previous method is shown in Fig.
LOG [EXPOSURE]
5) we can determine the exposure knowing the density and r E and a of the film. In Chapter VI we have presented the experimental results obtained for models of intensity distributed by dielectric and conducting cylinders. The results are obtained for two different polarizations of the collision field parallel and normal to the axis of the cylinder.
In Chapter VI, we presented only parts of the scattered intensity patterns to demonstrate the experimental results and compare them with the theory. In this appendix, we present the rest of the scattered intensity patterns in the whole range of the angle 9. In each figure in this appendix, there are three different curves (except for dielectric cylinders with ka = 945): (a) a plot of the intensity pattern is obtained using the film/microdensitometer combination system following the same procedure as described in Chapter VI, (b) is a plot of the intensity pattern using the photodetector system, and (c) is a plot of the comparable theoretical results derived in one of the chapters I1 or 111.
1 to D.3, the polarization of the incident field is parallel to the acid triaxis of the cylinder. The intensity pattern plotted using the film/microdensitometer system has greater amplitude in the range lt; 4.5' and this is due to the non-linearity of the photographic film. The curves have comparable amplitudes of the side lobes and distances between the fringes.
PEG1
1 2 the scattered intensity pattern is plotted for the case when the incident field is polarized perpendicular to the axis of the cylinder. The fringes have a smaller contrast with respect to those in the parallel polarization, and there are the same number of fringes in the experimental and theoretical curves. 1 1 The scattered intensity pattern plotted for a dielectric cylinder with ka = 327 using (a) film/microdensitometer system, (b) photodetector system and (c) Eq.
17, the polarization of the incident field is parallel to the axis of the cylinder, while in Fig. This difference can be explained by the results from Chapter V, which show that the possible reason is that there is a small difference between the wavelength used in the calculations and that of the laser used in the experiment. The experimental curves obtained using the photodiode system are plotted in (a) and the theoretical curves are plotted in (b).
