Use of computers in education and research has completely changed the way things were made before. For example, a lecture to the students or the presentation of a paper to a Congress are completely different with respect to those of only a few decades ago, when blackboard, transparencies or photographic slides were used. There are many positive aspects of using computers, for example making a talk very attractive. However, there are also negative aspects. In this paper an analysis is presented of advantages and disadvantages I experienced and of consequences of using computers.
Three different histograms of the instantaneous Stehl ratio, measured from three adaptive optics telescopes, were recently published (J Opt. Soc. Am, November 2010) by Gladysz et al., in a paper on the use of the probability density function (PdF) of adaptive optics for exoplanets detection. Their PdFs present values of the skewness coefficients of different signs. Surprisingly they are the same kind of histograms that we found many years ago, measuring the time evolution of the intensity at the focus of a large lens collecting an atmospherically degraded laser beam, many years ago. We describe the explanation we gave of our results (Ciolli, Consortini et al., Applied Optics, May 1977) and suggest here a similar one.
Wandering of a laser beam in the atmosphere is due to fluctuations of the refractive index of the atmosphere and, having
a strong dependence on the path length, is very useful to investigate random or continuous changes of the refractive
index during time. First, we describe methods we developed and applied to locally investigate the parameters of
turbulence (inner scale, outer scale and structure constant) based on our previous theory of propagation of "thin" beams.
Then we describe use of thin beams to investigate the evolution of the refractive index gradient and show experimental
results including non stationary and non isotropic conditions.
We present a way to use a Research Laboratory for training students to learn about simple measurements. In most cases, doing research and training students imply conflicting requirements, for instance in a Research Laboratory everything is aligned, some equipment cannot be moved and so on; therefore research and training laboratories are separated. Sometimes however, there is the possibility of using a part or the complete research equipment by the students, without "consequences". As an example, here we describe the way we used a research set up of wave propagation through atmospheric turbulence, devoted to long lasting statistical measurements, to train students in making position measurements and experiments at different levels, starting from beginners up to advanced and PhD students.
The refractive index gradient, averaged over short horizontal paths, in the atmosphere was experimentally investigated by using a method we developed, based on the use of thin parallel laser beams. Horizontal and vertical components of the gradient were shown to be directly related to the corresponding lateral displacements of the beams at the end of the path. The method is here described and results of measurements made in different locations and conditions are presented. Some cases of strong anisotropy were also found, which can be related to the local air convective movements from the ground.
We recently developed a method1 to measure the gradient of the refractive index of the atmosphere, by using the lateral fluctuations of thin laser beams along a given path. We showed that the horizontal and vertical instantaneous fluctuations of a ray on a screen, at the end of a path of length L, are related to the horizontal and vertical components, averaged along the path, of the refractive index gradient, respectively.
Our method, which is based on the geometrical optics approximation, requires that the beams are "thin", that is that their transverse dimension be not larger than the dimensions of the smallest inhomogeneities of the atmosphere (inner scale of turbulence). In practice, it allows "local" measurements, that is measurements over short horizontal paths, even few meters' paths. Experiments were made in the open air.
Here we describe the method and present results of measurements made in different locations and conditions, at near ground levels. Temperature and transverse wind velocity were also measured and some correlation of these quantities to the refractive index gradient will be presented. Some cases of strong vertical anisotropy are also shown, which can be related to the local air convective movements from the ground.
We recently developed method for estimating the outer scale of tmospheric turbulence based on the correlation functions of lateral displ cements of thin beams propagating horizont lly over short paths.Here,the method is briefly summerized and comparison between the results of the method obtained by using the von Karman and
Hill-Andrews models of turbulence is presented.
Use of fractional moments of low order, recently proposed by Consortini and Rigal for investigating probability density functions (PDF's) in laser scintillation statistics through atmospheric turbulence, is here proposed for overcoming the saturation effects of the electronics due to low dynamics acquisition systems.
Optics students' need for statistical knowledge is investigated. By statistics I mean both probability and statistics. By starting with a simple interferometer some different cases are presented where, from no need for statistical knowledge, one reaches cases where simple probability is needed and finally cases that require profound knowledge of statistics.
Use of fractional moments of low order is here proposed for processing data of intensity fluctuations from optical atmospheric propagation measurements. In this paper we check the accuracy of low order moment estimation and their ability to discriminate which one, among a number of candidate theoretical distributions, better represents the experimental histograms of intensity. The comparison method is tested by sampling sets of data from three popular distributions, that is Ln, LnME and K distribution. Applications to experimental sets of data are also presented.
In atmospheric and astronomical optics, as well as in applications involving optical propagation through the atmosphere, atmospheric turbulence plays an important role in deterioration of information. Recently, adaptive systems allow correction of aberrations produced by turbulence. In all cases knowledge is necessary of atmospheric turbulence and its characteristic parameters, i.e. inner scale, outer scale and the so called structure constant.
Non-stationarity of atmospheric turbulence gives rise to some practical problems when one wants to determine the probability density function (PDF) of intensity fluctuations from laser atmospheric propagation experimental data. For strong fluctuations, the number of uncorrelated data that can be collected in stationary conditions is generally not enough to correctly evaluate intensity moments of order greater than two 1} . In the case of very strong fluctuations even the second order moment (and also variance) can not be estimated with accuracy [2] This is due to the fact that the stronger the fluctuations the longer is the tail of the distribution, which represents the main contribution in high order moment evaluation. If only integer moments are considered, information about intensity PDF that can be extracted from its moments is thus very poor because only a few of them are correctly estimated
The distributions of intensity fluctuations generally found in atmospheric optical scintillation measurements are characterized by a large range of intensity values, I, whose probability level, even if low, is not negligible. The range of I-values with a significant probability depends on the experimental conditions and can go from zero to several hundred times the mean value, < I <, of the distribution in the case of strong scintillation. In principle, an acquisition system should have dynamics able to cover the whole significant range of measured intensities. Of course, this requirement is not limited to scintillation measurements and the application of low order fractional moments we present here can be employed every time we face a measured quantity with a "long tail" distribution.
Intensity moments of any order are proposed and moments of low order (less than 2) are shown to be suitable for overcoming the problem of lack of data, due to turbulence non-stationarity, for correctly measuring higher order integer moments in atmospheric optical scintillation.
Measurement of atmospheric turbulence progressed though several stages in the last decades but has of recent seen little advance. Uses of lidars, ground based radar and intrusive techniques have all had limitations in their ability to measure the more fundamental atmospheric properties. Be it poor spatial or temporal resolution, difficulty in maintaining the sensor, or the requirement to use a preconceived atmospheric model, all have had shortcomings. Of the several physical atmospheric properties that can be quantified, the inner and outer scale sizes associated with the index of refraction, and hence the other atmospheric properties, are of high interest in the prediction of the performance of various adaptive optical sensors. In this paper, we will discuss a method based on a thin beam optical system to measure the inner and outer scales size that overcomes some of the limitations and assumptions in previous techniques. Based on research originally conducted at the University of Florence, we have extended the theory to optically thin layers that can account for real world design effects. Using this theory the paper will discuss the feasibility of using the technique to measure turbulence scale sizes in the upper atmosphere. Data from laboratory measurements will be shown.
Thin beam wandering through laboratory generated strong turbulence is experimentally investigated. In the case of small fluctuations and within the limits of geometrical optics, the transverse displacement variance is expected to follow a 3rd-power law dependence on distance. Here we describe the results of measurements made over a few meters path in the cases of strong turbulence.
An experiment to measure the enhancement factor of the transverse-displacement variance (wandering) of a narrow laser beam due to double passage of the beam through the same turbulence is described and the results reported.
Scintillation of waves is briefly reviewed, with particular attention to the problem of laser scintillation through atmospheric turbulence. An introductory description of turbulence, its model and relevant parameters, is given. Recent progress towards the solution of the problem of scintillation is reported, which includes modeling by means of numerical simulations and simultaneous measurements of both laser intensity fluctuations and all relevant parameters.
Mathematical needs for Diffraction and Fourier Optics are examined and some suggestions and examples given. The purpose is to suggest the mathematics needed by optics students for both understanding and working with Diffraction and Fourier Optics.
Results are described of recent contributions to the problem of optical scintillation in the atmosphere. Progress towards the solution of this very old problem is being made. It includes approximate modeling by means of numerical simulations, and simultaneous measurements of both laser intensity fluctuations and all relevant parameters.
The subject of coherent optical propagation and imaging through atmospheric turbulence, which was extensively investigated after the invention of the laser, has received renewed attention in recent years, both as a tool for investigating the physics of the atmosphere and in view of a number of applications in adaptive systems, in remote sensing and environmental applications. In the present paper some recent progress will be reviewed, with particular attention to double pass imaging and to the problem of laser scintillation. In double pass imaging, methods have been developed and tested whose aim is the production of images free from turbulence effects. Progress towards the solution of the problem of scintillation includes approximate theory, modelling by means of numerical simulations, and simultaneous measurements of both laser intensity fluctuations and all relevant parameters.
Angle-of-arrival fluctuations of a wave propagating through the atmosphere, as well as lateral fluctuations (wandering) of thin beams are phase-dependent quantities useful for sensing atmospheric turbulence, in particular for measuring structure parameter and inner and outer scale. Application to practical methods of measurement is described with some examples.
The effect of the inner scale of turbulence on the intensity fluctuations of laser radiation through the atmosphere has been measured. Intensity fluctuations, inner scale and structure parameter were simultaneously measured in conditions of homogeneous turbulence during a number of summer days, starting from very early morning, before sunrise, up to about noon. During the day the turbulence strength varied slowly and continuously, allowing measurements in condition of very low as well as intermediate and very high turbulence levels. Plots of intensity variance versus the structure parameter, for fixed ranges of inner scale values, allow the experimental determination of the role played by the inner scale, for the first time. They constitute a reference for comparison with results from theory or numerical simulations.
An attempt is made to answer the question of how much mathematics optics students should know, not only to understand optics, but also to be able to work with optics in the future. Fundamental optics and also some fields of application in optics or related disciplines are examined, in order to specify the mathematics required.
An optical method of measuring inner scale and refractive structure constant of atmospheric turbulence by laser radiation is described and a laboratory test presented. 1 -
An attempt to remove " large" uncorrelated noise from probability density histograms of measured intensity ir laser propagation through atmospheric turbulence is presented. L
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