This study defines measurements of three-dimensional rigid-body shapes by using a fiber optic Lloyd’s mirror. A fiber optic Lloyd's mirror assembly is basically a technique to create an optical interference pattern using the real light point sources and their images. The generated fringe pattern thanks to this technique is deformed when it is projected on an object's surface. The introduced surface profilometry algorithm depends on a multi-step phase shifting process. The deformed fringe patterns containing information of the object's surface profile are captured by a digital CCD camera. While each frames are captured, required π∕2 phase shifts for interference fringe pattern are obtained by mechanically sliding the Lloyd assembly via an ordinary micrometer stage. Some preprocess algorithms are applied to the frames and are processed with an algorithm to accomplish 3D topographies. Finally, the continuous data determines the depth information and the surface topography of the object. The experimental setup is simple and low cost to construct, and is insensitive to the ambient temperature fluctuations and environmental vibrations that cause unwanted effects on the projected fringe pattern. Such a fiber optic Lloyd’s system which provides an accurate non-contact measurement without contaminating and harming the object surface has a wide range of applications from laser interference based lithography in nano-scale to macro-scale interferometers.
This study defines measurements of three-dimensional rigid-body shapes by using a fiber optic Lloyd’s mirror.
A fiber optic Lloyd's mirror assembly is basically a technique to create an optical interference pattern using real light
point sources and their images. The generated fringe pattern thanks to this technique is deformed when projected on an
object's surface. The deformed fringe pattern containing information of the object's surface profile is captured by a digital
CCD camera. The two-dimensional Fourier transformation is applied to the image, which is digitized with a frame
grabber card. After applying a band-pass filter to this transformed data in its spatial frequency domain, the twodimensional
inverse Fourier transform is applied. Using the complex data obtained by the inverse Fourier transform, the
phase information is determined. A phase unwrapping algorithm is applied to eliminate discontinuities in the phase
information and to make the phase data continuous. Finally, the continuous data determines the depth information and
the surface topography of the object. It is illustrated for the first time that the use of such a fiber optic Lloyd's system
increases the compactness and the stability of the fringe projection system. Such a fiber optic Lloyd’s system which
provides an accurate non-contact measurement without contaminating and harming the object surface has a wide range
of applications from laser interference lithography (LIL) in nano-scale to macro-scale interferometers.
Ways of calculating phase shifts between laser beams propagating through atmospheric turbulence can give us insight towards the understanding of spatial diversity in Free-Space Optical (FSO) links. We propose a new geometrical model to estimate phase shifts between rays as the laser beam propagates through a simulated turbulent media. Turbulence is simulated by filling the propagation path with spherical bubbles of varying sizes and refractive index discontinuities statistically distributed according to various models. The level of turbulence is increased by elongating the range and/or increasing the number of bubbles that the rays interact with along their path. For each statistical representation of the atmosphere, the trajectories of two parallel rays separated by a particular distance are analyzed and computed simultaneously using geometrical optics. The three-dimensional geometry of the spheres is taken into account in the propagation of the rays. The bubble model is used to calculate the correlation between the two rays as their separation distance changes. The total distance traveled by each ray as both rays travel to the target is computed. The difference in the path length traveled will yield the phase difference between the rays. The mean square phase difference is taken to be the phase structure function which in the literature, for a pair of collimated parallel pencil thin rays, obeys a five-third law assuming weak turbulence. All simulation results will be compared with the predictions of wave theory.
Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.
It is well known that optical signals propagating through the atmosphere are subject to random fluctuations in phase
and amplitude. These fluctuations are caused by random temperature distributions in the atmosphere, which
manifests themselves as a random index of refraction changes along the propagation path. We introduce a simulation
method for modeling atmospheric turbulence effects, which is based on a split-step approach to numerically solve
the parabolic wave equation. Atmospheric turbulence effects are modeled by a number of phase screens. These
phase screens are generated on a numerical grid of finite size, which corresponds to a narrow spatial area of
atmospheric turbulence.
Strong turbulence measurements that are taken using real time optical wireless experimental setups are valuable
when studying the effects of turbulence regimes on a propagating optical beam. In any kind of FSO system, for us to
know the strength of the turbulence thus the refractive index structure constant, is beneficial for having an optimum
bandwidth of communication. Even if the FSO Link is placed very well-high-above the ground just to have weak
enough turbulence effects, there can be severe atmospheric conditions that can change the turbulence regime.
Having a successful theory that will cover all regimes will give us the chance of directly processing the image in
existing or using an additional hardware thus deciding on the optimum bandwidth of the communication line at
firsthand.
For this purpose, Strong Turbulence data has been collected using an outdoor optical wireless setup placed about 85
centimeters above the ground with an acceptable declination and a path length of about 250 meters inducing strong
turbulence to the propagating beam. Variations of turbulence strength estimation methods as well as frame image
analysis techniques are then been applied to the experimental data in order to study the effects of different
parameters on the result. Such strong turbulence data is compared with existing weak and intermediate turbulence
data. Aperture Averaging Factor for different turbulence regimes is also investigated.
Simulation of beam propagation through turbulent media has always been a tricky subject when it comes to
moderate-to-strong turbulent regimes. Creating a well controlled turbulent environment is beneficial as a fast and a
practical approach when it comes to testing the optical wireless communication systems in diverse atmospheric
conditions.
Turbulent media is created using multiple phase screens each having controlled random variations in its frequency
and power while the propagated beam is calculated using Fresnel diffraction method. The effect of the turbulent
media is added to the propagated beam using modified Von Karman spectrum. Created scintillation screens are
tested and compared with the experimental data which are gathered in different turbulence regimes within various
atmospheric conditions. We believe that the general drawback of the beam propagation simulation is the difference
in terms of spatial distribution and sequential phase textures. To overcome these two challenges we calculate the
Aperture Averaging Factors to create more realistic results. In this manner, it is possible create more viable turbulent
like scintillations thus the relationship between the turbulence strength and the simulated turbulence parameters are
distinctly available.
Our simulation gives us an elusive insight on the real atmospheric turbulent media. It improves our understanding on
parameters that are involved in real time intensity fluctuations that occur in every wireless optical communication
system.
The performance of free space optical (FSO) links in a clear atmosphere is affected by the non-ideal characteristics of
the communication channel. Atmospheric turbulence causes fluctuations in the received signal level, which increase the
bit errors in a digital communication link. In order to quantify performance limitations, a better understanding of the
effect of the intensity fluctuations on the received signal at all turbulence levels is needed. Theory reliably describes the
behavior in the weak turbulence regime, but theoretical descriptions in the intermediate and strong turbulence regimes
are less well developed. We have developed a flexible empirical approach for characterizing link performance in strong
turbulence conditions through image analysis of intensity scintillation patterns coupled with frame aperture averaging on
an FSO communication link. These measurements are complemented with direct measurements of temporal and spatial
correlation functions. A He-Ne laser beam propagates 106 meters in free-space over flat terrain about a meter above the
ground to provide strong atmospheric turbulence conditions. A high performance digital camera with a frame-grabbing
computer interface is used to capture received laser intensity distributions at rates up to 30 frames per second and various
short shutter speeds, down to 1/16,000s per frame. A scintillometer is used for accurate measurements of the turbulence
parameter Cn2. Laboratory measurements use a local strong turbulence generator, which mimics a strong phase screen.
Spatial correlation functions are measured using laterally separated point detectors placed in the receiver plane.
Correlations and captured image frames are analyzed in Labview to evaluate correlation functions, Cn2, and the aperture
averaging factor. The aperture averaging results demonstrate the expected reduction in intensity fluctuations with
increasing aperture diameter, and show quantitatively the differences in behavior between various strengths of
turbulence. This paper will present accurate empirical data in the strong turbulence regime. Such results can help build
upon existing empirical data and lead to the development of new theories.
Intensity fluctuations at the receiver in free space optical (FSO) communication links lead to a received power variance that depends on the size of the receiver aperture. Increasing the size of the receiver aperture reduces the power variance. This effect of the receiver size on power variance is called aperture averaging. If there were no aperture size limitation at the receiver, then there would be no turbulence-induced scintillation. In practice, there is always a tradeoff between aperture size, transceiver weight, and potential transceiver agility for pointing, acquisition and tracking (PAT) of FSO communication links. We have developed a geometrical simulation model to predict the aperture averaging factor. This model is used to simulate the aperture averaging effect at given range by using a large number of rays, Gaussian as well as uniformly distributed, propagating through simulated turbulence into a circular receiver of varying aperture size. Turbulence is simulated by filling the propagation path with spherical bubbles of varying sizes and refractive index discontinuities statistically distributed according to various models. For each statistical representation of the atmosphere, the three-dimensional trajectory of each ray is analyzed using geometrical optics. These Monte Carlo techniques have proved capable of assessing the aperture averaging effect, in particular, the quantitative expected reduction in intensity fluctuations with increasing aperture diameter. In addition, beam wander results have demonstrated the range-cubed dependence of mean-squared beam wander. An effective turbulence parameter can also be determined by correlating beam wander behavior with the path length.
Intensity scintillation and beam wander caused by atmospheric turbulence are two significant phenomena that affect free space optical (FSO) communication links. We have constructed an imaging system for measuring the effects of atmospheric turbulence and obscuration on FSO links. A He-Ne laser beam propagates over a range of 863 meters in atmospheric turbulence conditions that vary diurnally and seasonally from weak to strong. A high performance digital camera with a frame-grabbing computer interface is used to capture received laser intensity distributions at rates up to 30 frames per second and various short shutter speeds, down to 1/16,000s per frame. The captured image frames are analyzed in Labview to evaluate the turbulence index parameter, temporal and spatial intensity variances, and aperture averaging. The aperture averaging results demonstrate the expected reduction in intensity fluctuations with increasing aperture diameter, and show quantitatively the differences in behavior between various strengths of turbulence. This paper will present the most accurate empirical data to date for the weak and intermediate turbulence regime. Such results can help build upon existing empirical data and lead to the development of new theories. Aperture averaging of the received irradiance is also shown to be independent of the shape of the receiver aperture, and depends only on its area. This finding allows the use of refractive or catadioptric receivers, whichever is convenient, and the same amount of aperture averaging will be achieved for equal unobscured aperture areas. This can make the telescope design for an FSO receiver more compact.
Even after several decades of study, inconsistencies remain in the application of atmospheric turbulence theories to experimental systems, and the demonstration of acceptable correlations with experimental results. We have developed a flexible empirical approach for improving link performance through image analysis of intensity scintillation patterns coupled with frame aperture averaging on a free space optical (FSO) communication link. Aperture averaging calculations are invaluable in receiver design. A receiver must be large enough to collect sufficient power and reduce scintillation effects at a given range, but must also be of practical size. We have constructed an imaging system for measuring the effects of atmospheric turbulence and obscuration on FSO links. A He-Ne laser beam propagates over a range of 863 meters in atmospheric turbulence conditions that vary diurnally and seasonally from weak to strong. A high performance digital camera with a frame-grabbing computer interface is used to capture received laser intensity distributions at rates up to 30 frames per second and various short shutter speeds, down to 1/16,000s per frame. The captured image frames are analyzed in Labview to evaluate the turbulence parameter Cn2, temporal and spatial intensity variances, and aperture averaging. The aperture averaging results demonstrate the expected reduction in intensity fluctuations with increasing aperture diameter, and show quantitatively the differences in behavior between various strengths of turbulence. The reduction in scintillation with aperture size guides the selection of optimum receiver aperture. Spatial and temporal variance analyses within single frames and between frames are compared and show good agreement.
Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes the optical phasefront to become distorted from propagation through turbulent eddies of varying sizes and refractive index. Turbulence also results in intensity scintillation and beam wander, which can severely impair the operation of target designation and free space optical (FSO) communications systems. We have developed a new model to assess the effects of turbulence on laser beam propagation in such applications. We model the atmosphere along the laser beam propagation path as a spatial distribution of spherical bubbles or curved interfaces. The size and refractive index discontinuity represented by each bubble are statistically distributed according to various models. For each statistical representation of the atmosphere, the path of a single ray, or a bundle of rays, is analyzed using geometrical optics. These Monte Carlo techniques allow us to assess beam wander, beam spread, and phase shifts along the path. An effective Cn2 can be determined by correlating beam wander behavior with the path length. This model has already proved capable of assessing beam wander, in particular the (Range)3 dependence of mean-squared beam wander, and in estimating lateral phase decorrelations that develop across the laser phasefront as it propagates through turbulence. In addition, we have developed efficient computational techniques for various correlation functions that are important in assessing the effects of turbulence. The Monte Carlo simulations are compared and show good agreement with the predictions of wave theory.
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