The analysis of polarization evolution in a tunable fiber laser in a ring configuration is presented, an interferometer was used to tune the laser and was manufactured with thin-core fiber (Thin-Core Fiber, TCF). The interferometer was achieved by splicing a segment of thin-core fiber (Thin-Core Fiber, TCF) between two segments of single-mode fiber SMF-28 (Single-Mode Fiber). Single and double and triple line emissions were obtained by means of the angular micrometric deflection in the TCFMI (Thin-Core Fiber Modal Interferometer) interferometer section, as well as depending on the position of the polarization controller plates (PC1 and PC2). Also, a uniform tuning was achieved, depending on the polarization state of the pumping source and the position of the plates of the second polarization controller (PC2), which started at 1534.70265 nm and moved to the left side to 1531.65142 nm and the evolution of the polarization state in this tuning range was observed. A tuning range of 1527.01738 to 1553.66363 nm was also achieved by means of the angular micrometric deflection in the TCFMI interferometer section.
We describe a simple and precise experimental procedure for the detection of the transverse fluorescence emitted by
excited ions in erbium-doped fibers. The modulation of the optical pump (980 nm) power allows distinguishing between
transverse fluorescence and pump radiated modes in the measured optical signal using a broadband InGaAs detector.
In this work we present an experimental evaluation of the twist-induced birefringence changes measured in straight
samples of commercial single-mode erbium-doped fibers. The five commercial samples studied showed a significant
asymmetric response to right and left twists, a result different to that previously measured in standard telecom fibers. We
found similar birefringence responses measured for fibers with different erbium concentrations, developed by the same
manufacturer; while fibers made by different manufacturers presented a non-similar response. Since absorption is an
important characteristic of erbium-doped fibers, we have considered the possible influence of hybrid (linear and circular)
dichroism. Therefore, we calculated the 4×4 Mueller matrix required to predict the induced birefringence taking into
account refractive and absorption anisotropies.
Photonic crystal optical fibers have much more degrees of freedom concerning the geometries and index contrasts than
step-index fibers; therefore, the theoretical analysis of their performance is usually based on the finite element method.
In this work, taking advantage of the similarities observed for twisted single-mode fibers: standard (SMF-28 and SMF-
28e) and hexagonal photonic fibers, we propose that in regard with polarization performance, photonic fibers can be
described using a simpler model based on classical polarization optics. The main advantages of the matrix model we
propose lie in its accuracy and generality: for each one of the selected wavelengths and input states of polarization, it
allows a precise prediction of the output polarization state. The comparison of the experimental results measured for
standard and photonic fibers with the theoretical model predictions indicates that in both cases, twist induced
birefringence is produced not only by the medium's photoelasticity, but also by the waveguide (cladding/core structure
and asymmetry) modification. In addition, for the photonic fiber, the non-symmetrical response to right and left twist
allowed the identification of an initial twist as part of the residual elliptical birefringence.
An analytic method based on Mueller matrix formalism and the Poincaré sphere is used to evaluate the birefringence
dispersion in hexagonal photonic fibers with circular air-holes when the hexagonal symmetry is modified. This
evaluation has been performed in the wavelength range from 1520 to 1570 nm, using monochromatic signals.
In this work, the birefringence response of two commercial single-mode erbium-doped fibers to right and left twist is
reported. The evolution of the output polarization state for a variable twist (0 to ±8π) was mapped on the Poincaré sphere
and analyzed considering the specific variation of each one of the Stokes parameters. These fibers were studied over the
wavelength range from 1520 to 1570 nm. We found that the contributions of photo-elastic effect and torsion introduced
during the fiber fabrication modify twist induced birefringence in erbium-doped fibers.
Polarization devices developed for fiber optic systems are pigtailed. These pigtails, built with standard single-mode
optical fiber (~1 m long) modify the input and output characteristics of the signal's polarization state. Even though this
contribution is negligible when the fibers are kept straight, it increases when they are wound up to form compact
systems. In this work, we used Mueller calculus and experimental results to analyze the polarization performance of
helically wound single-mode fibers. These results have been used to propose the cascaded helical structures we have
built. Using linear and circular input polarization states and the Poincaré sphere it is shown that to control the total
birefringence the relative orientation of the symmetry axes of these helices must be varied. The experimental results
obtained for the birefringence of these structures demonstrates that it is possible to minimize their birefringence
contribution within a limited spectral bandwidth.
In this work we present experimental results of the twist-induced birefringence changes for a single-mode erbium-doped
fiber with uniform residual birefringence. Two polarimetric methods were used in this study. Both discern evolution of
the azimuth and ellipticity angles of the output polarization state. According to these results when the initial residual
birefringence is elliptical, the modified optical anisotropy does not enhance its optical activity.
In this work we derive the birefringence matrix of a twisted nematic liquid crystal using Jones matrix formalism. It is
assumed that due to the shape of the molecules and negligible absorption each plane slice of a liquid crystal cell exhibits
a uniform intrinsic birefringence (linear or elliptical). Under this scope, it is shown that the anisotropy of the twisted nematic liquid crystal is described by an inhomogeneous birefringence matrix. A polarimetric procedure to verify this result is also proposed.
KEYWORDS: Polarization, Birefringence, Wave plates, Poincaré sphere, Single mode fibers, Indium oxide, Fiber characterization, Linear polarizers, Signal attenuation, Jones calculus
In this work we present the theoretical basis of two methods applied to the birefringence characterization of single--mode
optical fibers and devices. Both methods are based on classical polarization optics and make use of the geometric
properties of the Poincare sphere. One of them, used to identify the dominant polarization characteristics, is based on the
wavelength scanning technique; i.e. assumes that wavelength dependence can be neglected. The second one, with a
higher accuracy, avoids the uncertainty introduced by birefringence dispersion using a monochromatic linear signal to
determine the polarization eigenmodes for that specific wavelength. The results obtained for some common cases are
presented and discussed.
The characterization of the residual birefringence of erbium-doped fibers using the Poincare sphere requires a careful
alignment of the polarimetric set up. It is necessary to define the reference frame and then, to measure the input and
output polarization states. The procedure is time consuming when the sample and the prism polarizer are removed and
repositioned manually. In this work we present an automatic polarimetric set up that takes advantage of the geometric
properties of the Poincare sphere and the polarization optics of homogeneous retarders. The measurement procedure has
been modified to improve the measurement precision and to shorten the time required to perform the spectral
birefringence characterization of these laser fibers. We discuss the fundamental limitations of this evaluation procedure
comparing it with the wavelength scanning method based on Jones calculus, often used to characterize the birefringence
of optical fibers.
Erbium-doped monomode optical fibers are widely used to build amplifiers, lasers, incoherent light sources and sensors. Since the performance of these devices can be modified by its spectral birefringence, it is important to characterize it. In the case of an elliptical retarder the determination of the sign of the linear birefringence and the relative value of the linear and circular distributed birefringence is not obvious. In this work we analyze the anisotropic response of erbium fibers assuming that they are uniform and behave as a distributed retarder with linear and circular birefringence. Taking advantage of the geometric properties of the Poincare sphere it is possible to separate the linear birefringence contribution from that of the circular birefringence and to determine their signs and relative values.
In this work we present a polarimetric method that uses a polarization description based on the Poincare sphere. The erbium fiber is modeled assuming that it is uniform and behaves as a distributed retarder with linear and circular birefringences. We show that taking advantage of the geometric properties of the Poincare sphere it is possible to separate the linear birefringence contribution from that of the circular birefringence while the measurement precision is optimized. The experimental procedure here presented provides reproducible results for the measurement of the linear and circular distributed birefringences in erbium-doped fibers.
Optics in Mexico has had a fast growth for the last two decades, sustained basically by academic goals on education and research, and for a large electronic engineering students enrollment. The current socioeconomical demands creates conditions where more applied optical skills are favored.
The refractive index is the parameter used to describe the physical medium through which light propagates. It is considered that for homogeneous and isotropic materials it has a unique value at any point; hence a material border is represented by a step index function. This description assumes that the physical properties of the materia at the surface are the same as those of the bulk. From the physics of surfaces we know that in the case of a solid, the interaction between the atoms of the solid and its surroundings are responsible of processes such as adsorption, desorption, etc. In this work we present two basic models that can be sued to characterize, in terms of gradient index profiles, the physical properties of the interface. These models were developed within the physical chemistry of solids to describe the interfacial state, and we have translated them to refractive index profiles following recent results reported for optical wave-guides. The ray tracing equations obtained for light traveling through such refractive index profiles predict Goos-Hanchen effect and satisfy the reflection laws.
The volution of the state of polarization along an out-of- plane trajectory has been widely studied for monomode optical fibers. To demonstrate the validity of our proposal we compare the results predicted by our model with experimental result obtained for helically wound optical fibers and the conoscopic patterns obtained for GRIN lenses when oblique illumination is used.
The relative insensitivity of erbium doped fiber amplifiers to the state of polarization of the input signal is considered as an advantage when these devices are used within communication networks. On the other hand, in order to use them in combination with interferometric optical fiber sensor, they should be able to maintain the input polarization state. In this work we presented the results obtained for the performance characterization of an EDFA built with a helically wound monomode erbium fiber. The use of a regular winding allows the control of the evolution of the state of polarization of the optical signal to be amplified. We include results of the geometrical and birefringence characterization of two helices built with tow different commercial erbium fibers. The amplification of polarized signals has been evaluated for the C band. It presents a high gain for small as well as for saturated signals. In regard with the noise due to the amplified spontaneous emission, it was evaluated also for small as well as for saturated signals. The values we measured are below the theoretical predictions based on typical EDFAs built with an irregularly wound erbium fiber.
In this work we apply a simple, non-destructive method we developed for the birefringence characterization of helically wound passive fibers to monomode erbium-doped optical fibers. This method is based on the Jones matrix model developed by JN Ross for helically wound optical fibers. In the case of passive fibers Ross model is correct if the polarization evolution of light is measured with respect o an input local reference frame defined by the helix geometry; but in order to use a fixed reference frame it is necessary to consider the rotation of the plane of polarization introduced by parallel transport along the fiber. The use of Poincare's method and Mueller calculus simplifies the physical interpretation of the results. The birefringence properties of two helically wound erbium fibers are tested in the neighborhood of the amplification band showing that in this case the spectral response has a much stronger variation than in the case of passive step- index monomode fibers. Despite the topological contribution due to the parallel transport of the reference frame, with method where presented provides an easy way to measure the total linear retardation induced by the fiber curvature and the total circular retardation indued by the fiber torsion. Experimental results obtained for two commercial EDF are presented.
In a helically wound single-mode fiber the mode degeneracy is lifted by the geometric form and the photo-elastic effect. Fiber bending induces linear birefringence' and the presence of torsion is responsible for circular birefringence.2 Considering the geometrical properties of a helix and using Jones calculus, it has been shown3 that a helically wound fiber can be described as the combination of two distributed homogeneous retarders: a linear retarder and a circular retarder. Since linear and circular retardation can be easily followed on the Poincaré sphere, we use Mueller calculus to describe the polarization optics of helical fiber structures.4 Because of the strong absorption and the subsequent emission that active fibers present within the amplification band, the signal becomes depolarized and it is not possible to characterize the birefringence properties of active fibers at these wavelengths. In this work, the birefringence performance of active fibers is evaluated in the neighborhood of the amplification band, using signals with a high signal to noise ratio at the active fiber output. We present the birefringence characterization of a helically wound erbium fiber. This helical fiber structure was built with a commercial fiber. Since the birefringence parameters we measured agree with the values predicted by the theoretical model, we propose that we can make use of this model to design the helix structure and, to select the input polarization states of the pump and the signal that can be used to control the polarization evolution of the amplified signal as it propagates along the fiber.
The polarization optical properties of single mode fibers are important in those applications based on the use of coherent polarized light, such as fiber optic interferometric sensors and coherent communication systems. Various birefringence mechanisms and combinations of them have been developed to control the polarization evolution of light along the fiber. Since 1977 when A.Papp and H.Harms1 suggested the application of helical core fibers for this purpose, their polarization properties have been studied by several authors.24 In I 984 J.N. Ross2 showed that helically wound monomode fibers behave as the combination of a distributed linear retarder and a distributed circular retarder. Since linear and circular retardation can be easily followed on the Poincaré sphere, this representation of polarized light results adequate for helical fibers. In this work the non-destructive evaluation of the equivalent optical activity and the equivalent linear retardation of a fiber helix are performed using the trajectory described on the Poincaré sphere when the orientation of the linearly polarized light at the input rotates 360°. The results we obtain are compared with the values determined for the linear and circular retardation using Ross model and an input circular or linear polarization. We present preliminary results obtained for the birefringence characterization of two helically wound fibers built with .-l4m and —27m of a telecommunications fiber ( I 550nm).
The presence of contaminants in optical interfaces modifies their optical properties. In the presence of contaminants, the organization of the molecules within the medium is no longer the same for the interior and the surface. Such an interface becomes a region of some finite thickness in which there is a gradual change of physical properties. In this case, a step refractive index profile cannot be used to describe this region, as is generally used in refractometry. In general, the refractive index at a surface or an interface should be presented as a gradient. The profile of the refractive index distribution at an interface is defined by the physical-chemical properties of the base medium and the contaminant. From the thermodynamic models developed for interfaces, a refractive index distribution can be proposed. The description of the interface in terms of a refractive index profile allows the use of optical testing methods developed for the characterization of optical materials. In particular, geometrical and interferometric testing procedures can be used. Ray tracing is required become the analysis of interferograms and light distribution in the outcome of geometrical test relays on an a-priori knowledge of the optical path followed by light. In this work we propose refractive index distributions based on the thermodynamic potentials of typical interfaces. Making use of the mathematical forumlism based on Fermat's principle, the ray tracing equation associated to each case is presented. The information about these light trajectories is necessary to determine the thickness, concentration, as well as the type of contaminant in the contaminated region.
Several models have been developed to describe the interaction between neighboring ions in heavily doped erbium fibers. All of them are based on the anomalous saturation of the pump power. In this work we present experimental results of the anomalous behavior of the gain saturation in an EDFA, induced by the signal's power. This additional information shows us that energy migration is also induced by phonons.
In this work we discuss the possibility of using an optical fiber laser constructed by two Bragg grating as a temperature sensor. The device is based on measurement of the power transmitted through the Bragg gratings when the temperature of one of these gratings is changed. Changes on the temperature results in a shift of reflection wavelength of the Bragg grating and therefore change the transition coefficient. The resulting change of the power at the laser output can be used for simple and exact measurement of the temperature.
In this work we present an analysis of the birefringence effects induced by external fields on passive fibers and, on the basis of this information, we propose an explanation for some effects observed in active fibers. To modify the passive fiber birefringence we have used external forces. The photo-elastic description of the birefringence induced by simple stresses is verified for short circuit cylindrical samples of silica glass (step-index and GRIN). Phase and polarization changes of light transmitted through these samples were studied using holographic interferometry and polarimetry. Using these results, a proposal is made to understand the polarization sensitivity of EDFAs. In the case of active fibers its birefringence was altered changing its geometrical shape. The amplifying performance of an EDFA built with a helically-wound active fiber was compared with that of an EDFA built with an irregularly wound erbium fiber.
The polarization dependent performance of EDFA has been explained in terms of polarization hole burning, considering that the erbium sites in the silica matrix preserve its random nature. Although typical EDFAs are built with an erbium fiber longer than 10 m (hence the active fiber is necessarily wound) the influence of the bending has not been included in the investigation of this effect. To verify the relevance of bending induced birefringence, a helically- wound active fiber has been used to build an EDFA. The characterization of this helically-wound optical amplifier has shown that the polarization dependent performance was enhanced. The stronger link between the states of polarization of the signal wave, the pump wave and the active fiber birefringence axes was used to show that a selective excitation of the erbium ions by a polarized pump and a selective de-excitation of those ions by a polarized signal are the origin of the polarization dependent performance of EDFAs.
New digital demodulation algorithm for recently announced twin-grating fiber-optic sensor is presented. The sensor is built with two short, identical, low reflectance, closely spaced Bragg gratings imprinted in a telecommunications fiber. Because of such a design the reflection spectrum of this sensor is a sinusoidal wave within an envelope of the reflection spectrum of a single Bragg grating. Similar to traditional sensor based on Bragg gratings, the change of the temperature or strain leads to a shift of the reflection spectrum along the wavelength axis. However the reflection spectrum of the twin-grating sensor has more complicated structure and instead of measuring the position of gravity center of the spectrum we use more sophisticated algorithm to evaluate the measurands. Two computational methods are used to estimate the shift of the spectrum: evaluation of the phase of the sinusoidal wave and calculation of the position of the envelope. This combination of two different methods provides high accuracy of temperature or strain measurements. The ability of this sensor to provide simultaneous measurement of both temperature and axial strain is also demonstrated using computer simulation of twin-grating sensor in a Hi-Bi fiber.
The development of a new fiber Bragg grating multiplexing technique is reported. The technique is based on a twin Bragg grating sensor configuration and exploits a combination of wavelength- and frequency-domain multiplexing. We demonstrate that very weak Bragg gratings with reflexivity of approximately 0.5 percent or less can be efficiently used by this technique. Experimental results presented in the paper and theoretical estimates indicate that the interrogation of more than 100-element serial array sensor system is feasible.
Many different schemes of Bragg grating based quasi-distributed and multiplexed sensors have been reported.1 Most of them utilize wavelength division multiplexing and detect the resonant wavelength for sensor interrogation
A method of interrogation of a quasi-distributed sensor in the frequency domain is discussed. The sensor consists of a series of pairs of the identical Bragg gratings imprinted in the fiber core along its length. Each pair of the Bragg gratings performs as a low reflective Fabry-Perot interferometer producing a cosine modulated reflection spectrum within a grating's main lobe. The detector signal represents the superposition of the modulated reflection spectra which can be decomposed using the fast Fourier transform.
The operation of distributed polarimetric fiber-optical sensors using wavelength scanning technique is discussed along with algorithms for processing of a signal coming form the sensor to retrieve the information about the distribution of external force and field along the fiber. The principle of the sensor operation is based on a change of spectral and polarization characteristics of broad-band radiation, propagating in the fiber, caused by the external influence. The distribution of the external force along the fiber is determined by the computer processing of the output spectrum. The analysis of such sensor and the results of our experiments demonstrate high spatial resolution and sensitivity.
The operation of new quasi-distributed interferometric sensor is discussed. The sensor is based on the array of unbalanced interferometers formed by point polarization couplers along birefringent fiber. Simultaneous interrogation of the sensing interferometers was achieved by using spectroscopic methods and a simple signal processing. Results of investigation of sensor performance and analysis of cross-talk problem are presented.
Refractive index changes induced by twisting, bending, and compressing samples of multimode fibers were investigated using holographic interferometry and conoscopic examination in a polarimeter. Observations have been made utilizing a non-expanded laser beam traveling through short samples of silica and plastic fibers.
We demonstrate experimentally two regimes of an enhanced beam amplification in photorefractive waveguide. Enhancement is achieved by matching the optical activity and the reflections of the beams in waveguide. Beam amplification is assisted by stimulated photorefractive scattering.
In this work we analyze a feasibility to use non-resonant polarization mode coupling in birefringent fiber for simultaneous strain and temperature quasi-distributed measuring. The method employs white light and a two-mode fiber containing in-fiber sensing interferometers. This technique allows us to interrogate local sensors and demultiplex output signals using a compact grating spectrometer. First experimental results are presented.
We describe a technique for investigation of beam coupling in photorefractive materials. We used a probe beam which partly erases the recorded hologram in a small region of the crystal. This erasure changes the coupling between the beams, then the output intensities of these beams are changed. We show by numerical simulations that these changes give us information about coupling coefficient along the length of the photorefractive sample. We compare the numerical results with experimental data of two-beam coupling in an optical active BTO waveguide-like crystal.
We report the observation of self-pulsing behavior in a linear cavity Er-doped fiber laser pumped by a 980 nm laser diode. Stable self-pulsing is observed for both continuous-wave and low frequency chopped pumping. By measuring the time evolution of the transmitted pump light, we were able to observe a long build-up time (around 5 ms) for lasing action to take place. While the self-pulsing behavior of similar lasers has been recently reported, the long laser build up times have not been reported before. A numerical model for the time and space dependance of the excited state populations of the Er-ions reproduces some of the observed features.
This paper describes a method for measuring modal birefringence in optical fibers. It combines an interferometric technique with wavelength scanning and allows a high precision, nondestructive measurement of the birefringence along different sections of a long optical fiber. The experimental results for hi-bi fibers, 10-meters and 100-meters long, are presented. An accuracy of about 0.1% is achieved in the spectral range of 600 - 850 nm.
KEYWORDS: Wavefronts, Holography, Scattering, Light scattering, Laser crystals, 3D image reconstruction, Holograms, Holographic interferometers, Crystals, Signal to noise ratio
The design of a low-noise holographic interferometer applied to the study of diffusely scattering objects, is presented. This system is a dual-beam arrangement used for the reconstruction process, the anisotropic self-diffraction effect in Bi12TiO20 photorefractive crystals (PRC). It is shown both theoretically and experimentally that holographic recording and reconstruction of complex wavefronts in PRCs, is different from the case of a plane wavefront. This fact is taken into account to optimize the setup. The main optimization criterion is the enhancement of the signal-to-noise ratio (SNR) of the interferogram. Our theoretical predictions of SNR dependence on the recording beam intensities ratio, are verified by the experimental results here shown. An experimental approach to optimize a holographic interferometer with PRC is also presented.
A new technique for distributed fiber-optic sensors with polarization mode coupling is presented. The technique includes wavelength scanning and optical path compensation, allowing the user to choose the sensitive part at different positions along the fiber. A new digital processing procedure with birefringence dispersion data taken into account makes it possible to measure the coupling distribution along the sensitive part at more than 300 points simultaneously with a spatial resolution of 0.3 cm.
The measurement requirements of fifth-place refractometers based on the critical angle condition are analyzed. It is shown that the reference prism geometry limits the working interval of these instruments and that polarized light can be used to improve sensitivity.
Holographic interferometry is a differential technique used to detect small changes that can be translated to phase variations in the light transmitted or reflected by the object. Phase fluctuations are shown as interference fringes produced by the superposition of the wavefront in its original state, reconstructed by the hologram, and the modified wavefront coming from the real object. In order to reconstruct the original beam, the hologram is illuminated with the reference beam used to record it. Making the analysis ofthe resultant interference pattern is not easy. At first, a bidimensional mapping of the phase distribution along the interferogram must be performed. Then using fringe positions, the interference pattern must be interpreted. The detection of the phase in each point of the interferogram and the location of its individual position require a complicated detection system or a well trained operator. In this work we analyze the sensitivity of holographic optical correlation, a technique that gives a global evaluation of the changes in the object through the measurement of intensity variations in a single position. This technique combines the three-dimensional storage capacity ofholography with the integrated response given by the correlation of two wavefronts. Utilizing a Van der Lught type filtering system and a common path holographic interferometer the changes introduced in the object wavefront were studied. To do so, the reference object wavefront is recorded in the hologram. Afterwards the modified object wavefront is used to illuminate the hologram plate. Using a lens the intensity variations associated to the correlation of both object wavefronts is obtained in the direction of the reference beam used to record the hologram. The detector is positioned at the image point related with the collimated reference beam used to record the hologram. The intensity variations measured there give us a global evaluation of the changes in the object beam. Experimental results considering different objects and sources of change are shown.
Modern optical design requires measurement of the refractive index of optical glass to the sixth or the seventh decimal place. Reflectometry represents an interesting option to go beyond the fifth decimal place, since from the literature we know that this technique can work to the fifth decimal place. In addition to that, this method does not use a large area of the sample, a condition that helps to increase the contribution of systematic errors. The techniques used to determine the refractive index of optical materials include transmission and reflection methods. The highest accuracy transmission techniques used in refractometry are: minimum deviation and critical angle goniometry, moire deflectometry, and interferometry. The main systematic errors that limit the measuring accuracy of each of these techniques are mentioned. The techniques used for the determination of the refractive index of optical materials from measurements of the ratio of the reflectance coefficients of its surface are widely used. Many of these methods rest on simplifications of Fresnel equations at specific angles of incidence. The geometries used include: normal incidence, 45 degree(s), Brewster angle, and other angular positions related with the specific sample to be evaluated. The analyses reported in the literature contain just the parameters present in the simplified formulas obtained for the Fresnel coefficients of each specific configuration. In this work a more complete analysis of these techniques is presented.
The refractive index of an optical glass sample in the form of a wedge is measured by comparison with that of a reference liquid. This holographic technique can also be applied to the measurement of the refractive index of the immersion liquid, if the refractive index of the glass wedge is known. The accuracy ofthe method with respect to index matching, glass wedge preparation, and fringe position measurement on the interferogram is discussed.
An analysis of the measuring accuracy that can be obtained using critical angle refractometry as a direct and an indirect method is made. The working conditions required to get the highest accuracy are discussed.
The refractive index of optical glass is typically measured using techniques based on the change of the direction light experiences after traveling through the sample; that is, using deflectoruetric methods such as: minimum deviation goniometry, critical angle procedures, moire deflectometry, etc. , (Ref.l) . On the other hand, interferometry has been used to evaluate the optical homogeneity of optical glass, as well as to determine the refractive index variation with temperature. In this work it is presented a method to measure the refractive index of optical glass samples using a holographic interferometer. This is an indirect technique in which the refractive index of the glass samples is measured by comparison with the refractive index of a reference liquid in which the sample is immersed. The presence of the reference fluid is used as well, to get higher values for the flatness tolerance on the working faces of the sample, and less precision in the measurement of the wedge angle. The values of the useful wedge angles depend on the fringe spacing value and the ruatching between the refractive index of the immersion fluid and the refractive index of the glass sample. The necessity of iaeasuring along a raininuirn distance given by the detector spacing and the accuracy needed for the measurement of fringe spacing, is discussed.
The degree of spatial variations of refractive index within a melt or blank is evaluated considering two paranieters: optical homogeneity and striae. The variations called striae correspond to strong inhoinogeneities of a very local nature. They produce a change on the propagation direction of light that is detected using schlieren techniques. Optical homogeneity corresponds to smooth spatial variations of the refractive index that produce negligible variations on the direction of propagation of light through the glass sample. Optical homogeneity is tested by transmission using classical interferomnetry (Ref . 1 , 2 , 3) . The wavefront transmitted through the sample is compared interferometrically with a reference wavefront. Hence conditions imposed on the quality of the optics used in these instruments are strong. The sample itself must be well polished or convenientely tested to separate its surface deformations from the contribution due to optical homogeneity. In this work it is presented the analysis of an holographic technique applied to the assessment of the honogeneity of optical glass plates. It is used an inunersion device to avoid the need for separating surface contributions. Optical homogeneity can be determined from a single interferogran, against the two (Ref . 3) , or four (Ref . 1 , 2) needed when using classical interferometry. It is shown here that this holographic interferornetry method has a higher accuracy.
In holographic interfeiometry nearly straight and equally spaced fringes can be produced by a lateral displacement of a diffuser plate. This fringes can be used as carrier fringes for visual inspection of interferograms when studying phase objects. 1. FIZEAU CARRIER FRINGES Several geometries have been used to produce Fizeau fringes as carrier fringes in holographic interferometry (Ref. 1 Nevertheless in many cases these fringes are not recommendable since the tilt introduced to generate them might produce non corresponding sections of the object wavefront to be under comparison. When this problem is present the results may include imperfections due to the optical components in addition to the changes under study. These unwanted variations might be comparable to the path differences under study since quality optics is not used. 2 . YOUNG FRINGES OBSERVATION GEOMETRY If a diffuser plate whithin an holographic interferometer is laterally displaced interference occurs just between homologous points. Straight and equally spaced fringes perpendicular to the displacement direction are observed. Using exact ray tracing it can be shown that the position of the m-th bright fringe is: r 2 a a rn 4R+2d -riL. '' I x '' [1+ ir d2m27''. 2 j (1) where d is the lateral displacement of the diffuser X the wavelength of light and a is the interference order (Ref. 3). Using Eq. 1 the positions of the fringes caii lie calculated
A holographic interferometry technique for the measurement of the refractive index of transparent liquid samples is presented. 1 . MEASURENT PROCEDURE. The liquid under study is within a tank with an optical glass wedge. The refractive index is determined by comparison withthat of the glass wedge. The immersion tank is illuminatcd with a collimated beam of light. A diffuser plate is used after the tank to avoid the noise produced by the out of focus images of the light source and the optical components before the tank (Fig. 1). After a hologram of the wavefront transmitted through the sample has been recorded the glass wedge is removed and equally spaced straight fringes (Fizeau fringes) are observed. The separation between these fringes depends on the welge angle and the refractive index difference between the sample and the immersion fluid. It is important to have a sample with a wedge angle value adequate to the index matching to obtain observable fringes. It can he shown (Ref. 1) that the refractive index of the liquid can be determined using: N x tan a where N'' is the refractive fringes associated with the this technique depends on determined. index of the glass wedge used as reference n the number of spacement AX and is the wedge angle. The accuracy of the accuracy with which the spacing between fringes is Fig. 1. Hologram interferometer diagram. In
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