We introduce a new method, based on Fresnel diffraction of light from a step, for the study of correlation properties (temporal and spatial) of optical fields. The method renders to measure wavelength, coherence length, and coherence width by recording the visibility of the diffraction fringes versus optical path difference and spacing of the interfering beams. In addition, the method permits to specify the spectral line shape, particularly, of lights with short coherence lengths and the spatial coherence behavior of the lights with short coherence widths. Since, in the introduced method the optical path difference can be varied by changing the light incident angle, practically, in an interval of 90º, a large volume of data is acquired which leads to reliable and accurate study of the subject. The method can be applied easily using modest equipment. We have applied the method to the study of correlation properties of the lights emitted by LED, incandescent bulb, and Hg lamp.
When the emitted light from a small object illuminates a rough interface, the image of the object is formed in reflection if the incident angle of the light is larger than a threshold angle. The threshold angle is the angle beyond which the specularly scattered light acquires a coherent component. The threshold angle depends on interface roughness and light wavelength. In transmission mode, the incident angle on the rough interface has an upper limit for image formation. The latter angle depends also on the refractive indices of the media surrounding the rough interface. We have determined the threshold angles and corresponding roughness for three different wavelengths using rough sheet-glass surfaces that were prepared by grinding sheet-glass surfaces by powders of different grain size. The roughnesses obtained by this method are in good agreement with those obtained by other methods. Our experimental studies also show that the threshold angle is practically independent of the illumination intensity. The presented method has the potential to be used in process measurement due to simplicity of the required optical system.
It is generally accepted that mirage is formed when temperature of the ground surface, in a flat area like desert, is higher
than the temperatures of the over ground air layers. In this case, light emerging from a distant object makes total internal
reflection in the air layers and forms the image of the object that is called mirage. Our investigation on mirage formation
in desert indicates that there is no meaningful relation between mirage formation and temperature change over the
ground. In addition, we show that, the interference of the lights reflected from different air layers destroys the coherency
of the image forming light. This happens because the temperature change occurs in an interval larger than a wavelength.
In the second part of the report we demonstrate theoretically and experimentally that flat rough surfaces behave like
mirrors at very large incident angles. We show that there is a threshold incident angle for observation of image in a rough
surface that depends on the surface roughness and light wavelength. The shortest distance between observer and the
image is determined by the threshold incident angle. Mirage is such an image. Image formation is studied in rough sheet
glass surfaces that prepared by grinding with powders of different sizes.
When two similar gratings are superimposed, the transmission function of them varies with the displacement of one
grating with respect to the other. The transmitted light intensity versus displacement is proportional to the autocorrelation
of the transmission function of the gratings. In this paper, it is shown by measuring the latter function for gratings of
pitches in order of a fraction of millimeter, submicron displacements can be measured. More precision is easily available
by increasing the area of gratings and the detector gain. The presented technique is not expensive, complicated and
sensitive to environmental vibrations.
Specification of vibration modes, amplitudes, and damping coefficients of structures are crucial issues in civil and mechanical engineering. Several techniques have been used for this kind of studies, including holographic interferometry, speckle interferometry, and moiré technique. But, for a large-scale structure, the modal analysis technique is usually used. We use the time-averaged digital image of a sinusoidal pattern fixed on a vibrating 6-m iron I-beam to study in-plane vibration. The study includes specification of vibrating modes, amplitudes, and damping coefficients. Using a wide-angle high-resolution digital camera, successive images of the vibrating pattern are recorded in exposure times much longer than the vibration period and much shorter than the relaxation time. The visibility measurement along the images leads to the specification of the mentioned parameters.
A nondestructive technique, based on Fresnel diffraction from phase objects, is proposed for specifying the refractive indices of optical fibers without requiring index matching liquid. The method involves measurement of normalized intensity distribution on the Fresnel diffraction pattern of a monochromatic plane wave diffracted from a fiber, and evaluation of the fiber core refractive index from the intensity distribution by the least-square method. It is also shown that for the case of an unknown fiber core radius, by fitting a suitable theoretical intensity distribution on the corresponding experimental intensity distribution, the core radius and refractive index can be obtained with reasonable accuracy. Simulation and experimental studies show that the technique is reliable and quite sensitive to refractive index change.
Atmospheric turbulence may have strong impact on astronomical imaging, aerial surveying, terrestrial geodesy, optical ranging, and wireless optical communication. Major effects are beam broadening, irradiance fluctuations (scintillation), and angle-of-arrival (AA) fluctuations. The interesting effects of atmospheric turbulence for optical propagation studies are the variation (gradient and fluctuations) of refractive index. The corresponding refractive- index structure constant, Cn2, is the parameter most commonly used to describe the strength of atmospheric turbulence. Besides, the Modulation Transfer Function of the atmosphere is measurable by Cn2. Good image quality requires Cn2 being as small as possible. In this work we present an easily applicable and accurate method, based on moire technique, for the measurement of Cn2 and its profile in the ground level atmosphere. In this method from a low frequency sinusoidal amplitude grating, installed at certain distance from a telescope, successive images are recorded and stored in a computer. By rotating one of the image by +θ, say 4°, and multiplying its transmission function by the transmission functions of the other images which have been rotated by -θ, a large number of moire patterns are produced. By finding the traces of the moire fringes in the patterns, the fluctuations of the image grating lines are obtained. Which correspond to AA fluctuations distribution. From the AA fluctuations distribution in successive patterns, Cn2 and its profile in vertical direction are deduced. This technique renders to measure some other atmospheric parameters which are discussed in the report.
The turbulence of the atmosphere puts an upper limit on the quality of the image of a ground object obtained by long-exposure photography from low or high altitudes in the atmosphere or in the space. By using good optics and high resolution film or CCD and a stable platform, this limit could be approached but not exceeded. A useful quantity for indicating the magnitude of this limit is the integral of the modulation transfer function (MTF) associated with the turbulence. In this work, we introduce a new method for measuring the MTF of the atmosphere in the surface layer, based on moire technique. In this technique, from a low frequency Ronchi grating, installed at a certain distance from a digital camera equipped with a tele lens, successive images are recorded and then transferred to a PC. By rotating each image by θ/2 and -θ/2, say ±3°, and superimposing them, a large number moire patterns are produced. The average transmittance function of the superimposed image gratings is measured in a moire fringe interval. The latter function is measured by scanning the moire pattern by a slit parallel to moire fringes. It is shown theoretically that from the Fourier transform of the latter function the MTF of the atmosphere can be deduced, if the MTFs of the imaging system and the grating are given or their effects are negligible. The atmospheric MTFs have been measured at different turbulence conditions. Also, we have studied the behavior of the atmospheric MTF respect to exposure time.
The refractive index profile of fiber preform is determined by using shearing interferometry and the fringe analyzing by phase-step method. The experimental results for two different shearing are presented.
A nondestructive technique for determining the refractive indices of the core and the cladding of step index
optical fibers is presented. This method involves diffraction of plane wave from an optical fiber and application
the iterative method on Fresnel-Kirchhoff integral, the refractive indices of the core and the clad obtained by
this method are in good agreement with the results of other techniques.
In glass casting or shaping processes, some times wavy and distortion defects are developed in glass sheets. Specifying the locations of these defects and measuring the deflections they cause are significant parameters in many applications. There are several techniques for observing and measuring these defects, but the technique we introduce in this work is more simple and flexible and can be easy installed in production line for quality controlling purposes. The presented deflectometer functions in the following way. The imaging system of the device forms an image of large-scale low frequency linear periodical pattern painted on a vertical plane on a transmission grating. The distance between the object grating (painted pattern) and the second grating is so that the frequencies of the image grating and the second (probe) grating are practically the same. There is a small angle between the lines of the latter gratings to form moire fringes. A CCD camera transfers the moire fringes to a PC. By applying phase shifting technique, which is realized by shifting the probe grating in definite steps in its plane in a direction perpendicular to its lines, the phase distribution due to imprecations in optical system and gratings, are specified, At this stage the defected sheet glass is installed between the object grating and the imaging system and the distorted moire pattern is processed as described before. The difference between two-phase distributions is the phase distribution caused by the defects in the glass, which can be easily converted into the required ray deflections. All the processes are carried out automatically in a time less than 30 seconds and the accuracy of the measurement is of the order of 20 arc seconds.
Specification of vibrational modes and amplitudes of structures are crucial issues in civil and mechanical engineering. Several techniques have been used for this kind of studies, including holographic interferometry, speckle interferometry and moire technique. But, for large-scale structures modal analysis technique is usually used. In this work we have used time averaging moire technique to study in plane vibrations of large structures. The study includes specification of vibrating modes and amplitudes of structures. The technique is applied by painting a suitable size linear sinusoidal reflectance pattern on the lateral surface of the structure. As the structure is put into vibration, using a wide-angle high-resolution digital camera, the image of vibrating pattern is recorded in an exposure time much larger than the vibration period. The visibilities of the image along a line parallel to the painted pattern line are derived by processing the reflectance distribution. By dividing the resulted visibilities by the visibility of the image of the static pattern we get the normalized visibility curve. The number of normalized visibilities equal to 1 provides the number of vibrational modes and the magnitudes of the visibility minima or the locations of the zero visibility give the amplitudes of vibration.
In this paper we will present determination of refractive index profile of an ion exchanged planar waveguide using wedge technique. The sample preparation, data analysis and experimental results will be presented.
Due to finite width of a spectral line, the visibility of the more fringes, formed by a grating and the image of another similar grating, produced by self-imaging technique, reduces by the increase of the image order. This effect has been exploited to specify the line shape, by taking Fourier transform from the visibility curve of the more fringes. The technique also renders to specify the non symmetric spectral line shapes, which are very difficult to determine by interferometric techniques. When a dispersive material, liquid or solid, is held between the gratings the visibility curve changes. It is shown that by comparing the Fourier transforms of the visibility curves obtained with and without sample, the dispersion function of the latter can be specified.
It is shown that when a part of a wave-front bears a sharp change in its phase, the Fresnel diffraction becomes noticeable. To change the phase sharply, one can reflect the wave-front from a step or transmit it through a transparent medium having a sharp change in its thickness or refractive index. The visibility of the corresponding diffraction fringes depends on the amount of phase change and can be varied from zero to one. Since the phase change can be accomplished by various means, the effect renders to measure phase change, refractive index change, displacement, and so on. Here, the change of visibility is the measurement criterion, therefore the fluctuations of the source intensity do not affect the measurement precision. In this paper Fresnel diffraction from one dimensional step, circular step, and single strip are studied, and some of its applications are briefly discussed.
3D analysis of intensity distribution in the interference field of two interfering waves enables one to reconstruct the corresponding wave-vectors at each point in space. This has been exploited to specify the lens parameters, radii of curvatures, refractive index and the thickness of the lens. The technique is very suitable for lenses of small diameters and short focal lengths.
In this work we have introduced a new interferometric technique for measuring the nonlinear refractive index in different samples. Adopting a holographic point of view we have developed a mathematical theory for this technique which is based on the propagation of a Gaussian wave through a small phase aperture.
Fresnel diffraction from a step, in reflection and transmission modes is studied. The study shows that the resulting diffraction pattern is similar to that of a semi- infinite obstacle, but the intensity distribution near the step edge is very sensitive to the step height and is a periodic function of the height. Therefore the effect can be exploited for measuring the heights and optical path differences of the coated films, strips, and small displacements.
When a transparent plane parallel plate is coated by a transparent film, the interference pattern of light in the plate is changed. This change has been exploited to measure the growth rate, the optical thickness, and the refractive index of the film. Using CCD, this technique enables to measure these quantities at each point on the plate, therefore, it provides a good mean for studying the homogeneity of overgrowth distribution and the change of refractive index in growth process. By this technique a quarter-wave thickness can be monitored very precisely, and also film thickness of many wavelengths can be measured. The technique easily can be applied, there is no need for calibration, and precision is quite good.
A new approach to the fringe formation in the interference of light incident on a plane parallel plate is introduced. It is shown that for a particular angle of incidence, which depends only on the refractive index, the interfringes are minimum. It is proved that in an angular interval of few arc degrees around this particular incident angle the interfringes are equal to a high accuracy. It is shown that this feature can be exploited to produce an interference grating with an arbitrary transparent-to-opaque groove ratio, and to measure the wavelength of light and the fine structures of a spectrum with a precision considerably higher than can be obtained in the other similar interferometric methods.
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