%APN3_PROCEEDINGS_FORM%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % TEMPLATE.TEX -- APN3 (2003) ASP Conference Proceedings template. % % Derived from ADASS VIII (98) ASP Conference Proceedings template % Updated by N. Manset for ADASS IX (99), F. Primini for ADASS 2000, % D.Bohlender for ADASS 2001, and H. Payne for ADASS XII and LaTeX2e. % % Use this template to create your proceedings paper in LaTeX format % by following the instructions given below. Much of the input will % be enclosed by braces (i.e., { }). The percent sign, "%", denotes % the start of a comment; text after it will be ignored by LaTeX. % You might also notice in some of the examples below the use of "\ " % after a period; this prevents LaTeX from interpreting the period as % the end of a sentence and putting extra space after it. % % You should check your paper by processing it with LaTeX. For % details about how to run LaTeX as well as how to print out the User % Guide, consult the README file. You should also consult the sample % LaTeX papers, sample1.tex and sample2.tex, for examples of including % figures, html links, special symbols, and other advanced features. % % If you do not have access to the LaTeX software or a laser printer % at your site, you can still prepare your paper following the % instructions in the User Guide. In such cases, the editors will % process the file and make any necessary editorial adjustments. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \documentclass[11pt,twoside]{article} % Leave intact \usepackage{adassconf} % If you have the old LaTeX 2.09, and not the current LaTeX2e, comment % out the \documentclass and \usepackage lines above and uncomment % the following: %\documentstyle[11pt,twoside,adassconf]{article} \begin{document} % Leave intact %----------------------------------------------------------------------- % Paper ID Code %----------------------------------------------------------------------- % Enter the proper paper identification code. The ID code for your % paper is the session number associated with your presentation as % published in the official conference proceedings. You can % find this number locating your abstract in the printed proceedings % that you received at the meeting or on-line at the conference web % site; the ID code is the letter/number sequence proceeding the title % of your presentation. % % This will not appear in your paper; however, it allows different % papers in the proceedings to cross-reference each other. Note that % you should only have one \paperID, and it should not include a % trailing period. % % EXAMPLE: \paperID{O4-1} % EXAMPLE: \paperID{P7-7} % \paperID{P5-6} %%%% ID=P5-6 %----------------------------------------------------------------------- % Paper Title %----------------------------------------------------------------------- % Enter the title of the paper. % % EXAMPLE: \title{A Breakthrough in Astronomical Software Development} % % If your title is so long as to fill the page header when you print it, % then please supply a short form as a \titlemark. % % EXAMPLE: % \title{Rapid Development for Distributed Computing, with Implications % for the Virtual Observatory} % \titlemark{Rapid Development for Distributed Computing} % \title{Shadow Bands Observed During the Total Solar Eclipse of 4 December 2002, by High-Resolution Imaging.} \titlemark{Shadow Bands During the Total Solar Eclipse of 4 Dec 2002} %----------------------------------------------------------------------- % Authors of Paper %----------------------------------------------------------------------- % Enter the authors followed by their affiliations. The \author and % \affil commands may appear multiple times as necessary (see example % below). List each author by giving the first name or initials first % followed by the last name. Authors with the same affiliations % should grouped together. % % EXAMPLE: \author{Raymond Plante, Doug Roberts, % R.\ M.\ Crutcher\altaffilmark{1}} % \affil{National Center for Supercomputing Applications, % University of Illinois Urbana-Champaign, Urbana, IL % 61801} % \author{Tom Troland} % \affil{University of Kentucky} % % \altaffiltext{1}{Astronomy Department, UIUC} % % In this example, the first three authors, "Plante", "Roberts", and % "Crutcher" are affiliated with "NCSA". "Crutcher" has an alternate % affiliation with the "Astronomy Department". The fourth author, % "Troland", is affiliated with "University of Kentucky" \author{Szymon Gladysz, Michael Redfern} \affil{Experimental Physics Department, National University of Ireland, Galway, Ireland} \author{Barrie W. Jones} \affil{Physics and Astronomy Department, The Open University, Milton Keynes, MK7 6AA, UK} %----------------------------------------------------------------------- % Contact Information %----------------------------------------------------------------------- % This information will not appear in the paper but will be used by % the editors in case you need to be contacted concerning your % submission. Enter your name as the contact along with your email % address. % % EXAMPLE: \contact{Dennis Crabtree} % \email{crabtree@cfht.hawaii.edu} % \contact{Szymon Gladysz } \email{Szymon.Gladysz@NUIGalway.ie } %----------------------------------------------------------------------- % Author Index Specification %----------------------------------------------------------------------- % Specify how each author name should appear in the author index. The % \paindex{ } should be used to indicate the primary author, and the % \aindex for all other co-authors. You MUST use the following % syntax: % % SYNTAX: \aindex{Lastname, F. M.} % % where F is the first initial and M is the second initial (if % used). This guarantees that authors that appear in multiple papers % will appear only once in the author index. % % EXAMPLE: \paindex{Crabtree, D.} % \aindex{Manset, N.} % \aindex{Veillet, C.} % % NOTE: this information is also used to build the author list that % appears in the table of contents. Authors will be listed in the order % of the \paindex and \aindex commmands. % \paindex{Gladysz, S.} \aindex{Redfern, M.} \aindex{Jones, B. W.} % Remove this line if there is only one author %----------------------------------------------------------------------- % Author list for page header %----------------------------------------------------------------------- % Please supply a list of author last names for the page header. in % one of these formats: % % EXAMPLES: % \authormark{Lastname} % \authormark{Lastname1 \& Lastname2} % \authormark{Lastname1, Lastname2, ... \& LastnameN} % \authormark{Lastname et al.} % % Use the "et al." form in the case of seven or more authors, or if % the preferred form is too long to fit in the header. \authormark{Gladysz, Redfern, Jones} %----------------------------------------------------------------------- % Subject Index keywords %----------------------------------------------------------------------- % Enter a comma separated list of up to 6 keywords describing your % paper. These will NOT be printed as part of your paper; however, % they will be used to generate the subject index for the proceedings. % There is no standard list; however, you can consult the indices % for past proceedings (http://adass.org/adass/proceedings/). % % EXAMPLE: \keywords{visualization, astronomy: radio, parallel % computing, AIPS++, Galactic Center} % % In this example, the author noticed that "radio astronomy" appeared % in the ADASS VII Index as "astronomy" being the major keyword and % "radio" as the minor keyword. The colon is used to introduce another % level into the index. \keywords{image: processing, scintillation, atmospheric effects} %----------------------------------------------------------------------- % Abstract %----------------------------------------------------------------------- % Type abstract in the space below. Consult the User Guide and Latex % Information file for a list of supported macros (e.g. for typesetting % special symbols). Do not leave a blank line between \begin{abstract} % and the start of your text. \begin{abstract} % Leave intact % Place the text of your abstract here - NO BLANK LINES We present the results of comparison between characteristics of highly atypical shadow bands recorded during total solar eclipse of 4 December 2002 in Botswana and theory of Codona. For the first time the analysis was based on images of the phenomenon and not photometric data. Thanks to this, use was made of high spatial resolution and detailed plots of power spectra were obtained. The plots' shapes are in excellent agreement with the one predicted by theory. Due to the novel nature of the recording process, some noteworthy image processing techniques were used. \end{abstract} %----------------------------------------------------------------------- % Main Body %----------------------------------------------------------------------- % Place the text for the main body of the paper here. You should use % the \section command to label the various sections; use of % \subsection is optional. Significant words in section titles should % be capitalized. Sections and subsections will be numbered % automatically. % % EXAMPLE: \section{Introduction} % ... % \subsection{Our View of the World} % ... % \section{A New Approach} % % It is recommended that you look at the sample papers, sample1.tex % and sample2.tex, for examples for formatting references, footnotes, % figures, equations, html links, lists, and other special features. \section{Introduction} Shadow bands are natural phenomena that appear just before and just after totality during solar eclipses. They arise from the superposition of atmospheric speckle patterns from elements of an incoherent, extended line source (the remaining visible crescent of the Sun). They are linear patterns moving across the ground with typical speeds of a few m/s in the direction perpendicular to their elongation. They align parallel to the tangent to the centre of the solar crescent (Marschall et al., 1984). It has been observed that shadow band spacing decreases and their contrast increases as totality approaches (Codona, 1986; Jones, 1996, 1999). \section{Obtaining The Data} Shadow bands were recorded during total eclipse of 4 December 2002 in Botswana. The imaging system consisted of a white, diffusely - reflective screen (surface was perpendicular to the line of sight to the eclipsed Sun) and a digital video recorder on a tripod in front of it. For the purpose of observation the aperture was locked fully open, exposure time was 1 ms (so that the phenomenon was "frozen"). The recorder was capturing 25 non-interlaced frames per second. The bands were also observed visually. They were weak and disorganized and resembled the surface of boiling water rather than linear patterns. \begin{figure} \epsscale{0.3} \plotone{P5-6_1.eps} \caption{A typical image of the screen. Shadow bands are of extremely low contrast.} \label{P5-6:screen} \end{figure} \section{Image Processing} \begin{itemize} \item Because we could not place the camera between the source and the screen there was a certain amount of perspective elongation that had to be removed from the images (Fig. 1). Perspective transformation arises if a planar object is viewed from a fixed point in space (Glasbey, Mardia, 1998): \begin{eqnarray} u & = & \frac{a_{10}x + a_{01}y + a_{00}}{c_{10}x + c_{01}y + 1}\;, \nonumber \\ & & \\ v & = & \frac{b_{10}x + b_{01}y + b_{00}}{c_{10}x + c_{01}y + 1} \nonumber \end{eqnarray} where x, y are the coordinates of a point in the object plane, and u, v are the coordinates of the same point in the image plane. The inverse transformation, (u, v) $\rightarrow$ (x, y), was applied to every image using the reciprocal formulae. The eight parameters $(a_{10}, a_{01}, a_{00}, b_{10}, b_{01}, b_{00}, c_{10}\ and\ c_{01})$ were found using known positions of the four corners of the screen before and after the transformation. This meant solving a system of eight linear equations with eight unknowns. Bi-cubic interpolation was used for image scaling. \item Subsequently images were flat-fielded using the ensemble-average as a flat-field. This is a simple variant of a technique proposed by Lindler et al. (1993) for Hubble Space Telescope's Faint Object Spectrograph and usually referred to as 'superflats'. The general decreasing (increasing) trend in overall brightness before (after) totality was removed by normalization. That produced images with the same intensity level as the first (last) image in the sequence. Background around the screen was cropped. \item The intensity values on the screen were in a very small range (30, 40 values on a 0-255 scale). We decided to enhance the contrast by applying Gaussian curve fixing algorithm to the histogram of intensity and this way determining the range that had to be widened (Fig. 2). Afterwards we transformed each value in the histogram to a corresponding new 'bin' between 0 and 255. Thanks to this we achieved values that subtended whole scale. \end{itemize} \begin{figure} \epsscale{0.4} \plottwo{P5-6_2.eps}{P5-6_3.eps} \caption{Typical intensity histogram with Gaussian curve fit (left). Histogram of an image after contrast enhancement (right).} \label{P5-6:histograms} \end{figure} \section{Results} Two batches of 1480 images (59.2 s) before and after totality were used for further analysis. Operations that could be used to detect shadow bands are: \begin{itemize} \item computation of the cross-correlation between two successive images to demonstrate the movement of coherent pattern between frames \item application of a FFT algorithm to a single image in order to find the shape of power spectral density function, psd(k), defined by Kay and Marple (1981), as predicted by Codona, and search for shadow bands' characteristic spatial frequencies. \end{itemize} Cross-correlation for different pairs of raw (without contrast enhancement) images revealed nothing but a peak at (0, 0) coordinates. This means that structure of the screen (hardly visible with an un-aided eye) is more pronounced than the shadow bands (meaning zero-shift between the images). Besides that, 25 fps means 40 ms between frames while coherence time (t0) for the atmosphere is usually not more than 10 ms (Monnier, 2003). Shadow bands change their shape too much from one image to another for the cross-correlation to detect them; the temporal-spatial approach was not useful in practice. The theory describing shadow bands is mostly based in the spatial domain, so the use of spatial approach in the analysis is more relevant. Power spectral density functions were more likely to reveal shadow bands as they are calculated in the spatial domain so that low fps limit of the digital video recorder played no role here. We recorded ambient noise at a low light level with the recorder (same settings as on the observation day), and calculated averaged and normalized psds for the resulting ensemble of images. The psd of an image is a two-dimensional function but for the purpose of this study a one-dimensional psd was calculated in order to make comparisons with Codona's plots. Power spectra for the pixel vectors at a right angle to the tangent to the crescent were calculated separately, added and averaged to produce a psd(k) plot. The psd of the noise was then subtracted from each psd of shadow bands. 60 such functions were computed before and after totality, setting the interval between measurements to 1 s. Smoothing with a rectangular window, 4 pixels wide, was used. The cut-off frequency was imposed by the Nyquist theorem. In some cases noise cancelled the signal in the very low frequency range, but that part of the plots was not significant for further analysis. \begin{figure} \epsscale{0.4} \plottwo{P5-6_4.eps}{P5-6_5.eps} \caption{Shadow bands' smoothed psd function (left), 41 s before second contact and Codona's (1986) prediction of a psd(k) shape (right).} \label{P5-6:psds} \end{figure} The qualitative resemblance between our power spectral density functions and the plot resulting from theoretical assumptions in Codona's paper is striking. According to Codona, shadow bands' psds display three characteristic scales. First characteristic scale is controlled by the geometry of the crescent and corresponds to the low-frequency peak in the spectrum. The next scale relates to the first minimum in the plots and is due to the first null of the source's spectrum. Third scale corresponds to the fast oscillating term in the analytic expression, called the "Fresnel filter" (starting at the second minimum in the plots). Which of them will be the dominant shadow band scale visible to the human eye depends on the distance of the atmospheric scattering layer from the observer and the time to totality. Codona derived formulae relating the height of the scattering layer, z, to the dominant spatial frequency of a psd plot. The derivation of the values of z is the goal of the next stage of the shadow bands' data analysis. %----------------------------------------------------------------------- % References %----------------------------------------------------------------------- % List your references below within the reference environment % (i.e. between the \begin{references} and \end{references} tags). % Each new reference should begin with a \reference command which sets % up the proper indentation. Observe the following order when listing % bibliographical information for each reference: author name(s), % publication year, journal name, volume, and page number for % articles. Note that many journal names are available as macros; see % the User Guide listing "macro-ized" journals. % % EXAMPLE: \reference Hagiwara, K., \& Zeppenfeld, D.\ 1986, % Nucl.Phys., 274, 1 % \reference H\'enon, M.\ 1961, Ann.d'Ap., 24, 369 % \reference King, I.\ R.\ 1966, \aj, 71, 276 % \reference King, I.\ R.\ 1975, in Dynamics of Stellar % Systems, ed.\ A.\ Hayli (Dordrecht: Reidel), 99 % \reference Tody, D.\ 1998, \adassvii, 146 % \reference Zacharias, N.\ \& Zacharias, M.\ 2003, % \adassxii, \paperref{P7.6} % % Note the following tricks used in the example above: % % o \& is used to format an ampersand symbol (&). % o \'e puts an accent agu over the letter e. See the User Guide % and the sample files for details on formatting special % characters. % o "\ " after a period prevents LaTeX from interpreting the period % as an end of a sentence. % o \aj is a macro that expands to "Astron. J." See the User Guide % for a full list of journal macros % o \adassvii is a macro that expands to the full title, editor, % and publishing information for the ADASS VII conference % proceedings. Such macros are defined for ADASS conferences I % through XI. % o When referencing a paper in the current volume, use the % \adassxii and \paperref macros. The argument to \paperref is % the paper ID code for the paper you are referencing. See the % note in the "Paper ID Code" section above for details on how to % determine the paper ID code for the paper you reference. % \begin{references} \reference Codona, C., 1986. Astronomy and Astrophysics, 164, 415 \reference Glasbey, C. A., Mardia, K. V., 1998. Journal of Applied Statistics, 25, 155 \reference Jones, B. W., 1996. Journal of Atmospheric and Terrestrial Physics, 58, 1309 \reference Jones, B. W., 1999. Journal of Atmospheric and Solar-Terrestrial Physics, 61, 965 \reference Kay, S. M., Marple, S. L., 1981. Proceedings of the IEEE, 69, 1380 \reference Lindler, D., Bohlin, R., Hartig, G., Keyes, C., 1993. FOS Instrument Science Report CAL/FOS-088 \reference Marschall, L. A., Mahon, R., Henry, R. C., 1984. Applied Optics, 23, 4390 \reference Monnier, J. D., 2003. Reports on Progress in Physics, 66, 789 \end{references} % Do not place any material after the references section \end{document} % Leave intact