From 92550c0132752d7d91f361760e8b04ee65c8551f Mon Sep 17 00:00:00 2001 From: Edward Emelianov Date: Thu, 24 Mar 2022 23:57:28 +0300 Subject: [PATCH] add 2nd additional lecture 4 SFedU --- Komp_obr_SFedU/additional/01.pdf | Bin 1698659 -> 984033 bytes Komp_obr_SFedU/additional/01.tex | 129 +---- Komp_obr_SFedU/additional/02.pdf | Bin 0 -> 2606917 bytes Komp_obr_SFedU/additional/02.tex | 463 ++++++++++++++++++ .../additional/pic/Airy_vs_gaus.pdf | Bin 0 -> 7532 bytes Komp_obr_SFedU/additional/pic/Z1000frame.jpg | Bin 0 -> 292105 bytes Komp_obr_SFedU/additional/pic/airy.jpg | Bin 0 -> 40855 bytes Komp_obr_SFedU/additional/pic/difff.jpg | Bin 0 -> 147531 bytes Komp_obr_SFedU/additional/pic/fitting.jpg | Bin 0 -> 34557 bytes Komp_obr_SFedU/additional/pic/fwhm.pdf | Bin 0 -> 21966 bytes .../additional/pic/growth_curves.png | Bin 0 -> 92316 bytes Komp_obr_SFedU/additional/pic/moffat.png | Bin 0 -> 42054 bytes Komp_obr_SFedU/additional/pic/photcurves.png | Bin 0 -> 77823 bytes 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+ \Delta_N^{bright},$$ + $m(x)$~-- Ú×ÅÚÄÎÁÑ ×ÅÌÉÞÉÎÁ ÎÁ ÁÐÅÒÔÕÒÅ~$x$. +\end{block}\vspace*{-1em} +\img[0.45]{fwhm} +\end{blueframe} + +\begin{frame} +\only<1>{ +\begin{columns} +\column{0.45\textwidth} +\img{starphotom} +\column{0.52\textwidth} +\begin{block}{íÏÄÅÌØ ÁÐÅÒÔÕÒÎÏÊ ÆÏÔÏÍÅÔÒÉÉ} +ðÁÒÁÍÅÔÒÙ Ú×ÅÚÄÙ: ÕÒÏ×ÅÎØ ÓÉÇÎÁÌÁ, ËÏÏÒÄÉÎÁÔÙ ÃÅÎÔÒÁ, ÐÏÌÕÛÉÒÉÎÁ. + +ðÁÒÁÍÅÔÒÙ ÆÏÎÁ: ÓÒÅÄÎÉÊ ÕÒÏ×ÅÎØ ÓÉÇÎÁÌÁ, $B$. + +ðÁÒÁÍÅÔÒÙ Ó×ÅÔÏÐÒÉÅÍÎÉËÁ: Ë×ÁÎÔÏ×ÁÑ ÜÆÆÅËÔÉ×ÎÏÓÔØ, ÛÕÍÙ. + +òÁÄÉÕÓÙ ÁÐÅÒÔÕÒ: $r_1$, $r_2$, $r_3$. + +$$m = \C -2.5\lg(N_{star}-N_{sky}).$$ + +îÁÉÂÏÌÅÅ ÏÐÔÉÍÁÌØÎÙÍ ×ÁÒÉÁÎÔÏÍ ÂÕÄÅÔ ×ÙÂÒÁÔØ $2\cdot r_1$~ÒÁ×ÎÙÍ ÓÒÅÄÎÅÊ ÐÏ ÉÚÏÂÒÁÖÅÎÉÀ FWHM Ú×ÅÚÄ. +÷ ÌÀÂÏÍ ÓÌÕÞÁÅ, ÐÏÔÒÅÂÕÅÔÓÑ ÁÐÅÒÔÕÒÎÁÑ ËÏÒÒÅËÃÉÑ ÒÅÚÕÌØÔÁÔÏ×. +\end{block} +\end{columns} +}\only<2>{ +\begin{columns} +\column{0.33\textwidth} +\img{photcurves} +\column{0.62\textwidth} +\begin{block}{} +PASP, 1989 Steve B.~Howell: <>. + +íÁÓÛÔÁÂ: $0.4''/$ÐÉËÓÅÌØ. +ú×ÅÚÄÎÙÅ (ÉÎÓÔÒÕÍÅÎÔÁÌØÎÙÅ) ×ÅÌÉÞÉÎÙ: 14.2 (Ë×ÁÄÒÁÔ), 14.5 (ÔÒÅÕÇÏÌØÎÉË), 16.1 (ÐÕÓÔÏÊ Ë×ÁÄÒÁÔ). ðÏ +Â) ×ÉÄÎÏ, ÞÔÏ Õ ÓÌÁÂÏÊ Ú×ÅÚÄÙ ÐÌÏÈÏ ×ÙÒÁÖÅÎÎÙÅ ËÒÙÌØÑ, ÞÔÏ ÒÅÚËÏ ÕÍÅÎØÛÁÅÔ ÔÏÞÎÏÓÔØ ÐÒÉ Õ×ÅÌÉÞÅÎÉÉ +ÁÐÅÒÔÕÒÙ. îÁÉÂÏÌØÛÉÅ \SNR É ÔÏÞÎÏÓÔØ ÄÏÓÔÉÇÁÀÔÓÑ ÐÒÉ ÒÁÄÉÕÓÅ ÁÐÅÒÔÕÒÙ ÐÒÉÍÅÒÎÏ ÒÁ×ÎÏÍ FWHM/2. +\end{block} +\end{columns} +}\only<3>{\vspace*{-1em} +\begin{columns} +\column{0.37\textwidth} +\img{growth_curves} +\column{0.55\textwidth} +\begin{block}{ëÒÉ×ÙÅ ÒÏÓÔÁ} +ðÏÚ×ÏÌÑÀÔ ÏÐÒÅÄÅÌÉÔØ ÏÐÔÉÍÁÌØÎÙÊ ÒÁÄÉÕÓ. îÁ Á) ÐÏ ×ÅÒÔÉËÁÌÉ ÏÔÌÏÖÅÎÁ ÓÕÍÍÁ ÓÉÇÎÁÌÁ × ÄÁÎÎÏÊ +ÁÐÅÒÔÕÒÅ, ÄÅÌÅÎÎÁÑ ÎÁ ÅÅ ÐÌÏÝÁÄØ. ëÁË ÔÏÌØËÏ ÓÉÇÎÁÌ ÓÒÁ×ÎÉ×ÁÅÔÓÑ Ó ÆÏÎÏÍ, ËÒÉ×ÁÑ ÉÄÅÔ ×ÎÉÚ. +îÁ Â) ÜÔÉ ÖÅ ×ÅÌÉÞÉÎÙ × ÌÏÇÁÒÉÆÍÉÞÅÓËÏÊ ÛËÁÌÅ. + +ðÏ ÉÎÔÅÇÒÁÌØÎÏÊ ËÒÉ×ÏÊ ÒÏÓÔÁ (ÎÅ ÎÏÒÍÉÒÏ×ÁÎÎÏÊ ÎÁ ËÏÌÉÞÅÓÔ×Ï ÐÉËÓÅÌÅÊ) ÍÏÖÎÏ ÏÐÒÅÄÅÌÉÔØ ×ÉÄ +ÎÁÉÂÏÌÅÅ ÐÏÄÈÏÄÑÝÅÊ ÁÐÐÒÏËÓÉÍÉÒÕÀÝÅÊ ÆÕÎËÃÉÉ. îÁÐÒÉÍÅÒ, ÉÎÔÅÇÒÁÌØÎÙÅ ÆÕÎËÃÉÉ ÄÌÑ ÏÄÎÏÍÅÒÎÏÊ +ÇÁÕÓÓÉÁÎÙ É ÍÏÆÆÁÔÁ: +$$G(r)= 1 - \exp \Bigl(-\frac{r^2}{2\sigma^2}\Bigr),\quad \textrm{FWHM}=2\sigma\sqrt{2\ln2};$$ +$$M(r)= 1 - \Bigl(1+\frac{r^2}{\alpha^2}\Bigr)^{1-\beta},\quad \textrm{FWHM}=2\alpha +\sqrt{2^{1/\beta}-1}.$$ +\end{block} +\end{columns} +} + +\end{frame} + +\begin{frame} +\begin{block}{ïÓÎÏ×ÎÙÅ ×ÙÒÁÖÅÎÉÑ} +$S = F+B+Q+E$, ÇÄÅ $S$~-- ÎÁËÏÐÌÅÎÎÙÊ ÓÉÇÎÁÌ, $F$~-- ÓÉÇÎÁÌ ÏÔ Ú×ÅÚÄÙ, $B$~-- ÆÏÎ, $Q$~-- ÔÅÍÎÏ×ÏÊ +ÔÏË, $E$~-- bias. + +óÕÍÍÁÒÎÙÊ ÓÉÇÎÁÌ ÏÔ Ú×ÅÚÄÙ: $F_\Sigma = \sum F_i=\sum(S_i-[B_i+Q_i+E_i])$. + +ûÕÍ: $\sigma^2=F_\Sigma + N(\mean{B}+\mean{Q}+\sigma^2_{RO})+\sigma^2_{sky}$, $N$~-- ËÏÌÉÞÅÓÔ×Ï +ÐÉËÓÅÌÅÊ ÍÁÓËÉ Ú×ÅÚÄÙ, $\sigma^2_{RO}$~-- ÛÕÍ ÓÞÉÔÙ×ÁÎÉÑ. ðÅÒ×ÙÊ ÞÌÅÎ ÏÔÒÁÖÁÅÔ ÚÁ×ÉÓÉÍÏÓÔØ +ÐÕÁÓÓÏÎÏ×Á ÛÕÍÁ ÏÔ ÕÒÏ×ÎÑ ÓÉÇÎÁÌÁ. $\sigma^2_{sky}=N(\mean{B}+\mean{Q}+\sigma^2_{RO})/N_{sky}$, +$N_{sky}$~-- ËÏÌÉÞÅÓÔ×Ï ÐÉËÓÅÌÅÊ × ÍÁÓËÅ ÆÏÎÁ. + +$\SNR=F_\Sigma/\sigma$. þÅÍ ÓÌÁÂÅÅ Ú×ÅÚÄÁ, ÞÅÍ ÂÏÌØÛÅ ÕÒÏ×ÅÎØ ÆÏÎÁ, ÞÅÍ ÂÏÌØÛÅ~$N$ É +ÍÅÎØÛÅ~$N_{sky}$, ÔÅÍ ÈÕÄÛÉÍ ÂÕÄÅÔ \SNR. + +\vskip6pt + +ëÒÁÊÎÉÅ ÓÌÕÞÁÉ: <> É <>. SL: ÄÏÍÉÎÉÒÕÅÔ ÐÕÁÓÓÏÎÏ× ÛÕÍ +ÆÏÔÏÎÏ×, Ô.Å. $\SNR\approx N_\star/\sqrt{N_\star}=\sqrt{N_\star}\propto\sqrt{t_{exp}}$. +DL: ÄÏÍÉÎÉÒÕÅÔ ÛÕÍ ÓÞÉÔÙ×ÁÎÉÑ Ó×ÅÔÏÐÒÉÅÍÎÉËÁ $\SNR\approx N_\star/\sqrt{N\sigma^2_{RO}}\propto +N_\star\propto t_{exp}$. +\end{block} +\end{frame} + +\begin{frame} +\only<1>{ +\begin{columns} +\column{0.57\textwidth} +\img{starprofile} +\column{0.4\textwidth} +\begin{block}{ðÒÏÆÉÌÉ Ú×ÅÚÄ} +óÒÅÄÎÉÊ ÐÏ ÉÚÏÂÒÁÖÅÎÉÀ ÐÒÏÆÉÌØ ÐÏÚ×ÏÌÑÅÔ ÏÃÅÎÉÔØ ÒÁÄÉÕÓÙ ÁÐÅÒÔÕÒ. ôÁËÖÅ ÐÏÍÏÖÅÔ ÐÒÉ ÁÐÅÒÔÕÒÎÏÊ +ËÏÒÒÅËÃÉÉ. + +ïÛÉÂËÁ ÏÐÒÅÄÅÌÅÎÉÑ Ú×ÅÚÄÎÏÊ ×ÅÌÉÞÉÎÙ: $\sigma_m=1.0857/\SNR$. +\end{block} +\end{columns}} +\only<2>{ +\begin{columns}\column{0.6\textwidth} +\img[0.9]{Z1000frame} +\column{0.35\textwidth} +\begin{block}{} +ëÁÄÒ Ó ÆÏÔÏÍÅÔÒÁ-ÐÏÌÑÒÉÍÅÔÒÁ MMPP, Zeiss-1000, óáï òáî. +\end{block} +\end{columns} +} +\end{frame} + +\subsection{PSF--ÆÏÔÏÍÅÔÒÉÑ} +\begin{frame}{PSF--ÆÏÔÏÍÅÔÒÉÑ (æòô)} +\only<1>{\vspace*{-1em} +\begin{columns}\column{0.6\textwidth} +\img[0.9]{roboframe} +\column{0.35\textwidth} +\begin{block}{} +0.5-ÍÅÔÒÏ×ÙÊ ÔÅÌÅÓËÏÐ Astrosib, ÆÏËÕÓ îØÀÔÏÎÁ, óáï òáî. ðÏÌÅ ÐÒÉÍÅÒÎÏ $1.5\degr\times1.5\degr$. +\end{block} +\end{columns} +} +\only<2>{ +\vspace*{-1em} +\img{roboframepart}\vspace*{-1em} +\begin{block}{} +÷ ÔÅÓÎÙÈ Ú×ÅÚÄÎÙÈ ÐÏÌÑÈ ÎÅ×ÏÚÍÏÖÎÏ ÐÒÏÓÔÅÊÛÉÍ ÓÐÏÓÏÂÏÍ ×ÙÄÅÌÉÔØ ËÒÕÇÏ×ÕÀ ÁÐÅÒÔÕÒÕ ÆÏÎÁ ÏËÏÌÏ +Ú×ÅÚÄÙ. ÷ÁÒÉÁÎÔ 1: ÐÏ ÍÁÓËÅ ÉÓËÌÀÞÉÔØ Ú×ÅÚÄÙ É (ÎÁÐÒÉÍÅÒ, ÁÐÐÒÏËÓÉÍÁÃÉÅÊ B-ÓÐÌÁÊÎÁÍÉ) ÔÏÞÎÏ +×ÙÄÅÌÉÔØ ÆÏÎ. ÷ÁÒÉÁÎÔ 2: ÉÓÐÏÌØÚÏ×ÁÔØ PSF-ÆÏÔÏÍÅÔÒÉÀ (ÏÓÌÏÖÎÑÅÔÓÑ ÎÁ ÛÉÒÏËÉÈ ÐÏÌÑÈ, Ô.Ë. PSF ÓÉÌØÎÏ +ÍÅÎÑÅÔÓÑ ÐÏ ÐÏÌÀ). +\end{block} +}\only<3>{ +\begin{block}{} + áÐÐÒÏËÓÉÍÁÃÉÑ ÉÚÏÂÒÁÖÅÎÉÊ Ú×ÅÚÄ ÏÄÎÏÊ ÉÚ ÆÕÎËÃÉÊ ÆÉÔÉÒÏ×ÁÎÉÑ. ÷ ÏÂÝÅÍ ÓÌÕÞÁÅ ÄÌÑ ÕÓËÏÒÅÎÉÑ + ÚÁÄÁÞÉ + ÎÅÏÂÈÏÄÉÍÏ ÏÇÒÁÎÉÞÉÔØ ËÏÌÉÞÅÓÔ×Ï ÓÔÅÐÅÎÅÊ Ó×ÏÂÏÄÙ (ÎÁÐÒÉÍÅÒ, ÚÁÄÁÎÉÅÍ ÏÂÌÁÓÔÅÊ ÐÏÌÏÖÅÎÉÑ + ÍÁËÓÉÍÕÍÏ×), ÏÓÏÂÅÎÎÏ ÅÓÌÉ Ú×ÅÚÄ × ËÁÄÒÅ ÔÙÓÑÞÉ ÉÌÉ ÄÁÖÅ ÄÅÓÑÔËÉ ÔÙÓÑÞ. +\end{block} +\img[0.85]{fitting} +} +\end{frame} + +\begin{frame}{} +\only<1>{ +\begin{columns}\column{0.6\textwidth} +\img{airy} +\column{0.4\textwidth} +\begin{block}{} +äÉÓË üÊÒÉ~--- ÉÄÅÁÌØÎÁÑ æòô ×ÎÅ ÁÔÍÏÓÆÅÒÙ. +üÊÒÉ (ÓÐÌÏÛÎÁÑ) É ÇÁÕÓÓÉÁÎÁ (ÐÕÎËÔÉÒ). +\end{block} +\begin{light}\img{Airy_vs_gaus}\end{light} +\end{columns} +}\only<2>{ +\begin{columns}\column{0.5\textwidth} +\img{moffat} +\column{0.45\textwidth} +\begin{block}{} +óÐÅËÌÙ. òÁÓÐÒÅÄÅÌÅÎÉÑ çÁÕÓÓÁ (ÍÁÌÙÅ ÔÅÌÅÓËÏÐÙ) É íÏÆÆÁÔÁ (ÂÏÌØÛÉÅ)~--- ÂÌÉÚËÉÅ Ë ÉÄÅÁÌØÎÏÊ æòô ÎÁ +ÎÁÚÅÍÎÙÈ ÔÅÌÅÓËÏÐÁÈ. + +$$G(x,y) = \C\e^{-g},\quad g=\frac{(x-x_0)^2}{2\sigma^2_x}+\frac{(y-y_0)^2}{2\sigma^2_y}.$$ +$$M(x,y) = \C\left(1+\frac{(x-x_0)^2+(y-y_0)^2}{\alpha^2}\right)^\beta,$$ +$\alpha>0$~-- ÍÁÓÛÔÁÂ, $\beta>1$~-- ÆÏÒÍÁ. + +ðÒÏÂÌÅÍÁ: ÁÂÅÒÒÁÃÉÉ, ×ÁÒÉÁÃÉÑ æòô ÐÏ ËÁÄÒÕ. +\end{block} +\end{columns} +} +\end{frame} + +\subsection{äÉÆÆÅÒÅÎÃÉÁÌØÎÁÑ ÆÏÔÏÍÅÔÒÉÑ} +\begin{frame}{} +äÉÆÆÅÒÅÎÃÉÁÌØÎÁÑ ÆÏÔÏÍÅÔÒÉÑ +\img[0.75]{difff} +\end{frame} + +\subsection{áÂÓÏÌÀÔÎÁÑ ÆÏÔÏÍÅÔÒÉÑ} +\begin{frame}{} +\only<1>{ +\begin{block}{áÂÓÏÌÀÔÎÁÑ ÆÏÔÏÍÅÔÒÉÑ} +åÓÌÉ × ËÁÄÒÅ ÎÅÔ ÓÔÁÎÄÁÒÔÏ×: +\begin{itemize} +\item ÐÒÏ×ÅÓÔÉ ËÁË ÍÏÖÎÏ ÂÏÌØÛÅ ÉÚÍÅÒÅÎÉÊ ÒÁÚÌÉÞÎÙÈ ÓÔÁÎÄÁÒÔÏ× × ÎÕÖÎÙÈ ÆÉÌØÔÒÁÈ; +\item ÄÉÁÐÁÚÏÎ ×ÏÚÄÕÛÎÙÈ ÍÁÓÓ ÓÔÁÎÄÁÒÔÏ× ÄÏÌÖÅÎ ÐÅÒÅËÒÙ×ÁÔØ ÄÉÁÐÁÚÏÎ ×ÏÚÄÕÛÎÙÈ ÍÁÓÓ ÏÂßÅËÔÏ×; +\item Ã×ÅÔÁ ÓÔÁÎÄÁÒÔÏ× ÎÅ ÄÏÌÖÎÙ ÓÉÌØÎÏ ÏÔÌÉÞÁÔØÓÑ ÏÔ Ã×ÅÔÏ× ÏÂßÅËÔÏ×; +\item ÐÏ ÐÒÏ×ÅÄÅÎÎÙÍ ÎÁÂÌÀÄÅÎÉÑÍ ÓÔÁÎÄÁÒÔÏ× ÎÅÏÂÈÏÄÉÍÏ ÐÏÌÕÞÉÔØ ËÏÜÆÆÉÃÉÅÎÔÙ ÕÒÁ×ÎÅÎÉÊ +ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ ÏÔ ÉÎÓÔÒÕÍÅÎÔÁÌØÎÙÈ ×ÅÌÉÞÉÎ Ë ÓÔÁÎÄÁÒÔÎÙÍ; +\item ÉÓÐÏÌØÚÕÑ ÕÒÁ×ÎÅÎÉÑ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÊ, ÐÒÅÏÂÒÁÚÏ×ÁÔØ ÉÎÓÔÒÕÍÅÎÔÁÌØÎÙÅ ×ÅÌÉÞÉÎÙ ÏÂßÅËÔÏ× Ë +ÓÔÁÎÄÁÒÔÎÙÍ. + +\vskip8pt + +éÚÍÅÒÅÎÉÑ ÓÔÁÎÄÁÒÔÏ× ÎÅÏÂÈÏÄÉÍÏ ÐÒÏÉÚ×ÏÄÉÔØ Ó ÎÁÉÂÏÌØÛÉÍ \SNR. ðÕÓÔØ ÆÏÎ ÎÅÂÁ~--- 100~ÆÏÔÏÎÏ× ÎÁ +ÐÉËÓÅÌØ × ÓÅËÕÎÄÕ. $\sigma_{sky}=\sqrt{100}=10$. åÓÌÉ ÍÙ ÉÚÍÅÒÑÅÍ ÏÂßÅËÔ $N_\star=10$~Æ/Ð/Ó, ÔÏ +$\SNR=1$, Ô.Å. ÎÁÛÉ ÉÚÍÅÒÅÎÉÑ ÉÍÅÀÔ ÕÒÏ×ÅÎØ ×~$1\sigma$. ðÒÉ $N_\star=100$~Æ/Ð/Ó $\SNR=10$, ÕÒÏ×ÅÎØ +ÉÚÍÅÒÅÎÉÊ~--- $10\sigma$, ÞÔÏ ÄÏÓÔÁÔÏÞÎÏ ÈÏÒÏÛÏ ÄÌÑ ÎÁÕÞÎÙÈ ÉÚÍÅÒÅÎÉÊ, ÎÏ ÅÝÅ ÎÅÄÏÓÔÁÔÏÞÎÏ ÄÌÑ +ÉÚÍÅÒÅÎÉÊ ÓÔÁÎÄÁÒÔÏ× (ÄÌÑ ÎÉÈ \SNR ÏËÏÌÏ ÔÙÓÑÞÉ É ×ÙÛÅ). +\end{itemize} +\end{block} +}\only<2>{ +\begin{block}{õÒÁ×ÎÅÎÉÑ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÊ} +ðÕÓÔØ $B,V,R,I$~--- Ú×ÅÚÄÎÙÅ ×ÅÌÉÞÉÎÙ ÓÔÁÎÄÁÒÔÏ×, $b,v,r,i$~--- ÉÎÓÔÒÕÍÅÎÔÁÌØÎÙÅ, $X$~--- ×ÏÚÄÕÛÎÁÑ +ÍÁÓÓÁ. ôÏÇÄÁ ÐÏÌÕÞÉÍ ÎÁÂÏÒÙ ËÏÜÆÆÉÃÉÅÎÔÏ× ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ Ã×ÅÔÏ×, $T$; ËÏÜÆÆÉÃÉÅÎÔÏ× ÁÔÍÏÓÆÅÒÎÏÊ +ÜËÓÔÉÎËÃÉÉ, $K$; ÎÕÌØ-ÐÕÎËÔÏ×, $Z$. îÁÐÒÉÍÅÒ, ÄÌÑ Ã×ÅÔÏ×: +$$B-V = (b-v)T_{bv} + K_{bv}X + Z_{bv},$$ +$$V-R = (v-r)T_{vr} + K_{vr}X + Z_{vr},$$ +$$R-I = (r-i)T_{ri} + K_{ri}X + Z_{ri}\ldots$$ +äÌÑ ÐÏÌÏÓ: +$$B = bT_b + K_bX + Z_b,$$ +$$V = vT_v + K_vX + Z_v \ldots$$ +\end{block} +} +\end{frame} + +\section{áÓÔÒÏÍÅÔÒÉÑ} +\subsection{SExtractor} +\begin{frame}[fragile]{SExtractor} +SExtractor (Source-Extractor)\footnote{\url{https://sextractor.readthedocs.io/}}~--- ÕÔÉÌÉÔÁ ÐÏÉÓËÁ +ÏÂßÅËÔÏ× ÎÁ ÁÓÔÒÏÎÏÍÉÞÅÓËÏÍ ÉÚÏÂÒÁÖÅÎÉÉ (Emmanuel Bertin). ðÏÚ×ÏÌÑÅÔ +×ÙÑ×ÌÑÔØ Ú×ÅÚÄÏÐÏÄÏÂÎÙÅ É ÐÒÏÔÑÖÅÎÎÙÅ ÏÂßÅËÔÙ, ÐÒÏ×ÏÄÉÔØ ÐÒÏÓÔÕÀ ÆÏÔÏÍÅÔÒÉÀ. òÁÂÏÔÁÅÔ Ó ÕÍÅÒÅÎÎÏ +ÐÅÒÅÐÏÌÎÅÎÎÙÍÉ ÐÏÌÑÍÉ. óÉÎÔÁËÓÉÓ: +\begin{verbatim} +sex Image1 [Image2] -c configuration-file [-Parameter1 Value1 -Parameter2 Value2 ...] +\end{verbatim} +ëÏÎÆÉÇÕÒÁÃÉÑ ÐÏ ÕÍÏÌÞÁÎÉÀ: \verb'sex -d > default.sex' (ÉÌÉ \t{dd} ÄÌÑ ÂÏÌÅÅ ÉÎÔÅÎÓÉ×ÎÏÇÏ ÄÁÍÐÁ). +ðÒÏÓÔÁÑ ËÏÍÁÎÄÁ \t{sex} ×Ù×ÅÄÅÔ ËÒÁÔËÕÀ (ÏÞÅÎØ) ÓÐÒÁ×ËÕ. + +éÚÍÅÒÅÎÉÑ: ÂÁÒÉÃÅÎÔÒÙ ÐÏ ÉÚÏÆÏÔÁÍ, ÁÐÅÒÔÕÒÎÁÑ ÆÏÔÏÍÅÔÒÉÑ, ÁÐÐÒÏËÓÉÍÁÃÉÑ ÍÏÄÅÌØÎÏÊ ÆÕÎËÃÉÉ ÄÌÑ +ÐÏÉÓËÁ ÉÓÔÏÞÎÉËÏ×. + +ïÂÑÚÁÔÅÌØÎÏ Ë ÐÒÏÞÔÅÎÉÀ: <> by Dr.~Benne W.~Holverda. +\end{frame} + +\begin{frame} +\begin{columns} +\column{0.45\textwidth} +\vspace*{-1em} +\img{sexalgo} +\column{0.5\textwidth} +\begin{block}{áÌÇÏÒÉÔÍ} +\begin{itemize} +\item éÚÍÅÒÅÎÉÅ ÆÏÎÁ É ÅÇÏ RMS. +\item éÚ×ÌÅÞÅÎÉÅ ÆÏÎÁ. +\item ðÒÉÍÅÎÅÎÉÅ ÚÁÄÁÎÎÙÈ ÆÉÌØÔÒÏ×. +\item ðÏÉÓË ÏÂßÅËÔÏ× (ÐÏ ÐÏÒÏÇÕ). +\item òÁÚÄÅÌÅÎÉÅ <<ÓÌÉ×ÛÉÈÓÑ>> ÏÂßÅËÔÏ×. +\item éÚÍÅÒÅÎÉÅ ÉÈ ÆÏÒÍ É ÐÏÌÏÖÅÎÉÊ. +\item ÷ÙÄÅÌÅÎÉÅ ÉÎÄÉ×ÉÄÕÁÌØÎÙÈ ÏÂßÅËÔÏ×. +\item æÏÔÏÍÅÔÒÉÑ. +\item ëÌÁÓÓÉÆÉËÁÃÉÑ (Ú×ÅÚÄÁ ÉÌÉ ÎÅÔ?). +\item æÏÒÍÉÒÏ×ÁÎÉÅ ×ÙÈÏÄÎÙÈ ÆÁÊÌÏ×. +\end{itemize} +\end{block} +\end{columns} +\end{frame} + +\subsection{áÓÔÒÏÍÅÔÒÉÑ} +\begin{frame}{áÓÔÒÏÍÅÔÒÉÑ} +\begin{columns} +\column{0.57\textwidth} +\img{diffastrometry} +\column{0.4\textwidth} +\begin{block}{} +áÓÔÒÏÍÅÔÒÉÑ ÐÏÚ×ÏÌÑÅÔ ÉÚÍÅÒÉÔØ ÔÏÞÎÙÅ ËÏÏÒÄÉÎÁÔÙ Ú×ÅÚÄ ÎÁ ÎÅÂÅ, Á ÔÁËÖÅ ÏÐÒÅÄÅÌÉÔØ ÉÈ ÐÁÒÁÌÌÁËÓÙ É +ÓÏÂÓÔ×ÅÎÎÙÅ Ä×ÉÖÅÎÉÑ. ðÅÒ×ÙÊ ËÁÔÁÌÏÇ~--- éÐÐÁÒÈ, ÔÏÞÎÏÓÔØ ÎÅ ×ÙÛÅ~$1\degr$. +XVI~×ÅË~--- ôÉÈÏ âÒÁÇÅ, $1'$. XVII~×ÅË~-- ÔÏÞÎÏÓÔØ × ÅÄÉÎÉÃÙ ÓÅËÕÎÄ × ÏÞÅÎØ ÍÁÌÏÍ ÐÏÌÅ. +ðÁÒÁÌÌÁËÓÙ ÄÏ âÅÓÓÅÌÑ~--- 0! +íÉËÒÏÓÅËÕÎÄÎÏÊ ÔÏÞÎÏÓÔÉ ÄÏÓÔÉÇ ÚÁÐÕÝÅÎÎÙÊ × 1989\,Ç. ËÏÓÍÉÞÅÓËÉÊ ÔÅÌÅÓËÏÐ HIPPARCOS. + +ôÏÞÎÏÓÔØ GAIA~--- $0.00002''$ ($20\mu as$)~--- ÔÏÌÝÉÎÁ ÞÅÌÏ×ÅÞÅÓËÏÇÏ ×ÏÌÏÓÁ Ó ÒÁÓÓÔÏÑÎÉÑ × 1000\,ËÍ! +\end{block} +\end{columns} +\end{frame} + +\begin{frame}{} +\begin{block}{ëÁÔÁÌÏÇÉ} +\begin{enumerate} +\item \textbf{HIPPARCOS}~--- Ú×ÅÚÄÙ ÄÏ $m_V=7.3^m$, ÔÏÞÎÏÓÔØ ÁÓÔÒÏÍÅÔÒÉÉ ÄÏ $1\div3\,$mas +(J1991.25). ðÏÌÏÓÙ B É~V ÄÌÑ 188~ÔÙÓ Ú×ÅÚÄ. óÏÂÓÔ×ÅÎÎÙÅ Ä×ÉÖÅÎÉÑ (PM) $\sim1\div2\,$mas/y. +\item \textbf{TYCHO-2}~--- ÄÏ $m_V=11^m$, ÔÏÞÎÏÓÔØ $10\div100\,$mas. 2.5~ÍÌÎ. Ú×ÅÚÄ, PM +$\sim1\div3\,$mas/y. +\item \textbf{USNO B 1.0}~--- ÄÏ $m_V=21^m$, ÆÏÔÏÍÅÔÒÉÞÅÓËÉÊ ËÁÔÁÌÏÇ Ó ÔÏÞÎÏÓÔØÀ ÄÏ $0^m.3$. ó×ÙÛÅ +ÍÉÌÌÉÁÒÄÁ ÏÂßÅËÔÏ×. +\item \textbf{2MASS}~--- 470~ÍÉÌÌÉÏÎÏ× ÏÂßÅËÔÏ×, ÔÏÞÎÏÓÔØ ÄÏ $70\,$mas. ðÏÌÏÓÙ J, H É K. âÅÚ PM. +\item \textbf{SDSS}~--- ÆÏÔÏÍÅÔÒÉÞÅÓËÉÊ ËÁÔÁÌÏÇ ÞÅÔ×ÅÒÔÉ ÎÅÂÁ × ÐÑÔÉ ÆÉÌØÔÒÁÈ, 287~ÍÉÌÌÉÏÎÏ× +ÏÂßÅËÔÏ×. ÷ËÌÀÞÁÅÔ ÓÐÅËÔÒÙ ÇÁÌÁËÔÉË É Ë×ÁÚÁÒÏ×. + +âÉÂÌÉÏÔÅËÉ SOFA É ERFA (ÏÄÎÏ É ÔÏ ÖÅ Ó ÒÁÚÎÙÍÉ ÌÉÃÅÎÚÉÑÍÉ) ÐÏÚ×ÏÌÑÀÔ ÐÒÅÏÂÒÁÚÏ×Ù×ÁÔØ ËÏÏÒÄÉÎÁÔÙ +ÍÅÖÄÕ ÜÐÏÈÁÍÉ É ×ÙÞÉÓÌÑÔØ ×ÉÄÉÍÏÅ ÍÅÓÔÏ. +\end{enumerate} +\end{block} +\end{frame} + +\begin{frame}{} +\only<1>{ +\vspace*{-1em} +\begin{columns} +\column{0.5\textwidth} +\img{WCSfits} +\column{0.48\textwidth} +\begin{block}{WCS} +WCS~--- World Coordinate System. ICRS~--- International Celestial Reference System (ÐÒÉ×ÑÚËÁ Ë +ÂÁÒÉÃÅÎÔÒÕ óÏÌÎÅÞÎÏÊ ÓÉÓÔÅÍÙ). +ëÌÀÞÅ×ÙÅ ÓÌÏ×Á WCS × FITS--ÛÁÐËÅ ÐÏÚ×ÏÌÑÀÔ ÏÓÕÝÅÓÔ×ÉÔØ ÏÄÎÏÚÎÁÞÎÕÀ ÐÒÉ×ÑÚËÕ ÐÉËÓÅÌØÎÙÈ ËÏÏÒÄÉÎÁÔ Ë +ÍÉÒÏ×ÙÍ (É ÏÂÒÁÔÎÏ). äÌÑ ÌÉÎÅÊÎÙÈ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÊ: \textbf{CTYPEi}~-- ÔÉÐ ÏÓÉ, \textbf{CRPIXi}~-- +ÏÐÏÒÎÙÊ ÐÉËÓÅÌØ (× ÐÉËÓÅÌØÎÙÈ ËÏÏÒÄÉÎÁÔÁÈ), \textbf{CRVALi}~-- ÚÎÁÞÅÎÉÅ ÍÉÒÏ×ÙÈ ËÏÏÒÄÉÎÁÔ × ÜÔÏÍ +ÐÉËÓÅÌÅ (1~-- $\alpha$, 2~-- $\delta$), \textbf{CDELTi}~-- ÍÁÓÛÔÁ ÐÏ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÊ ÏÓÉ, +\textbf{CROTA2}~-- ÕÇÏÌ ÐÏ×ÏÒÏÔÁ, \textbf{CDi\_j}~-- ÍÁÔÒÉÃÁ ËÏÜÆÆÉÃÉÅÎÔÏ×, ÏÐÉÓÙ×ÁÀÝÉÈ ÐÏ×ÏÒÏÔ +ÏÓÅÊ É ÍÁÓÛÔÁÂ, \textbf{CUNITi}~-- ÅÄÉÎÉÃÙ ÉÚÍÅÒÅÎÉÑ ÐÏ ÄÁÎÎÏÊ ÏÓÉ. +\end{block} +\end{columns} +}\only<2>{ +\begin{columns} +\column{0.47\textwidth} +\begin{block}{ðÒÏÓÔÅÊÛÉÊ ÓÌÕÞÁÊ} +ïÂÏÚÎÁÞÉÍ \textbf{CRPIX}~-- $p$, \textbf{CRVAL}~-- $v$, \textbf{CDELT}~-- $d$, \textbf{CROTA2}~-- +$r$, \textbf{CD}~-- $c$, ÔÏÇÄÁ +$$\begin{cases} +\alpha = d_1(x-p_1)\cos r - d_2(y-p_2)\sin r,\\ +\delta = d_1(x-p_1)\sin r + d_2(y-p_2)\cos r;\end{cases}$$ + +$$\begin{cases}\alpha = c_{11}(x-p_1) - c_{12}(y-p_2),\\ +\delta = c_{21}(x-p_1) + c_{22}(y-p_2).\end{cases}$$ + +$$\begin{pmatrix}c_{11} & c_{12}\\ c_{21} & c_{22} \end{pmatrix} = +\begin{pmatrix} d_1\cos r &-d_2\sin r\\ d_1\sin r & d_2\cos r\end{pmatrix} +$$ +\end{block} +\column{0.47\textwidth} +\begin{block}{} +ðÁËÅÔ \t{wcstools}. õÔÉÌÉÔÙ \t{xy2sky} É \t{sky2xy}. ðÏÌÎÙÊ ÓÐÉÓÏË: \t{man wcstools} ÉÌÉ +ÕÔÉÌÉÔÁ \t{wcstools}. \t{imcat} ÏÔÏÂÒÁÖÁÅÔ ÏÂßÅËÔÙ ÉÚ ËÁÔÁÌÏÇÏ× (ËÁÔÁÌÏÇÉ ÎÅÏÂÈÏÄÉÍÏ ÓÏÈÒÁÎÉÔØ × +ÐÏÄÄÉÒÅËÔÏÒÉÉ \t{/data/astrocat/}). \t{imhead}~-- ÏÔÏÂÒÁÚÉÔØ ÛÁÐËÕ. é ÍÎÏÖÅÓÔ×Ï ÄÒÕÇÉÈ ÕÔÉÌÉÔ ÄÌÑ +ÒÁÂÏÔÙ Ó WCS É ÛÁÐËÏÊ ÆÁÊÌÏ×. + +õÔÉÌÉÔÁ \t{ds9} ÉÍÅÅÔ ×ÏÚÍÏÖÎÏÓÔØ ÏÔÏÂÒÁÖÁÔØ ÏÂßÅËÔÙ ÉÚ ÒÁÚÌÉÞÎÙÈ ËÁÔÁÌÏÇÏ×. +\end{block} +\end{columns} +} +\end{frame} + +\subsection{astrometry.net} +\begin{frame}{astrometry.net} +\only<1>{ +\begin{block}{} +ðÏÓÔÒÏÅÎÉÅ ÂÁÚÙ ÄÁÎÎÙÈ. +\begin{enumerate} +\item éÓÐÏÌØÚÕÑ ÁÓÔÒÏÍÅÔÒÉÞÅÓËÉÅ ËÁÔÁÌÏÇÉ ÐÏÓÔÒÏÉÔØ ÂÁÚÕ ÄÁÎÎÙÈ ÏÓÏÂÏÇÏ ×ÉÄÁ ÐÒÉÚÎÁËÏ× (ÈÅÛÅÊ). +\item èÅÛÉ ÄÏÌÖÎÙ ÂÙÔØ ÍÁÓÛÔÁÂÉÒÕÅÍÙÍÉ ÄÌÑ ÕÓËÏÒÅÎÉÑ ÐÏÉÓËÁ ÐÏ ÒÁÚÎÙÍ ÉÚÏÂÒÁÖÅÎÉÑÍ. +\item æÕÎËÃÉÑ ÓÒÁ×ÎÅÎÉÑ ÈÅÛÅÊ ÄÏÌÖÎÁ ÕÞÉÔÙ×ÁÔØ ÐÏÇÒÅÛÎÏÓÔÉ ËÁÔÁÌÏÇÏ×, ÛÕÍ É ÁÂÅÒÒÁÃÉÉ ÉÚÏÂÒÁÖÅÎÉÊ. +\item îÁ ÉÚÏÂÒÁÖÅÎÉÑÈ ×ÐÏÌÎÅ ÍÏÇÕÔ ÎÁÈÏÄÉÔØÓÑ Ú×ÅÚÄÙ, ËÏÔÏÒÙÈ ÎÅÔ × ËÁÔÁÌÏÇÁÈ É ÏÂÒÁÔÎÏ: ÞÁÓÔØ +Ú×ÅÚÄ ÍÏÖÅÔ ÏÔÓÕÔÓÔ×Ï×ÁÔØ. +\item æÕÎËÃÉÑ ÓÒÁ×ÎÅÎÉÑ ÈÅÛÅÊ ÄÏÌÖÎÁ ÂÙÔØ ÕÓÔÏÊÞÉ×ÏÊ É ÏÄÎÏÚÎÁÞÎÏÊ. +\item ÷ÎÁÞÁÌÅ ÎÁ ÓÎÉÍËÅ ÉÝÕÔÓÑ ÜÔÉ ÓÁÍÙÅ ÐÒÉÚÎÁËÉ, ÐÏ ÎÉÍ ÏÐÒÅÄÅÌÑÀÔÓÑ ÍÁÓÛÔÁÂ, ÏÒÉÅÎÔÁÃÉÑ É +ËÏÏÒÄÉÎÁÔÙ ÉÚÏÂÒÁÖÅÎÉÑ. äÁÌÅÅ ÐÒÏÉÓÈÏÄÉÔ ÓÏÂÓÔ×ÅÎÎÏ ÁÓÔÒÏÍÅÔÒÉÑ. +\savei +\end{enumerate} +\end{block} +}\only<2>{ +\begin{enumerate} +\conti +\item èÅÛÁÍÉ ÓÌÕÖÉÔ ÎÁÂÏÒ ÞÉÓÅÌ, ÏÐÒÅÄÅÌÑÀÝÉÈ ÏÔÎÏÓÉÔÅÌØÎÙÅ ËÏÏÒÄÉÎÁÔÙ ×ÎÕÔÒÅÎÎÉÈ Ä×ÕÈ Ú×ÅÚÄ ×ÎÕÔÒÉ +Ë×ÁÄÒÁÔÁ, ÓÆÏÒÍÉÒÏ×ÁÎÎÏÇÏ ×ÎÅÛÎÉÍÉ Ä×ÕÍÑ. ÷ ÒÅÚÕÌØÔÁÔÅ ÏÂÒÁÚÕÅÔÓÑ ÞÅÔÙÒÅÈÍÅÒÎÙÊ ËÏÄ, +ÈÁÒÁËÔÅÒÉÚÕÀÝÉÊ ÄÁÎÎÙÊ ÐÒÉÚÎÁË. úÅÒËÁÌÉÒÏ×ÁÎÉÅ ÉÚÏÂÒÁÖÅÎÉÑ ÐÒÉ×ÏÄÉÔ Ë ÚÅÒËÁÌÉÒÏ×ÁÎÉÀ ËÏÄÁ, ÐÒÉ×ÏÄÑ +Ë ×ÙÒÏÖÄÅÎÉÀ ÐÒÉÚÎÁËÁ ÏÔÎÏÓÉÔÅÌØÎÏ ÚÅÒËÁÌÉÒÏ×ÁÎÉÑ, ÏÄÎÁËÏ, ÈÅÛ ÉÎ×ÁÒÉÁÎÔÅÎ Ë ÍÁÓÛÔÁÂÉÒÏ×ÁÎÉÀ, +ÐÅÒÅÎÏÓÕ É ÐÏ×ÏÒÏÔÕ. +\item äÌÑ ÒÁ×ÎÏÍÅÒÎÏ ÒÁÓÐÒÅÄÅÌÅÎÎÙÈ × ÐÒÏÓÔÒÁÎÓÔ×Å Ú×ÅÚÄ ÈÅÛÉ ÒÁ×ÎÏÍÅÒÎÏ ÒÁÓÐÒÅÄÅÌÅÎÙ × 4D. +\item èÅÛ ÓÔÒÏÉÔÓÑ ÌÉÛØ ÐÏ ÔÁËÉÍ ÞÅÔ×ÅÒËÁÍ ÐÒÉÍÅÒÎÏ ÏÄÉÎÁËÏ×ÏÊ ÑÒËÏÓÔÉ, ÇÄÅ~C É~D ×ÎÕÔÒÉ ËÒÕÇÁ AB. +\item ëÁÔÁÌÏÇÉ: USNO-B (ÍÉÌÌÉÁÒÄ ÏÂßÅËÔÏ×) É TYCHO-2 (2.5~ÍÌÎ ÑÒÞÁÊÛÉÈ Ú×ÅÚÄ). +\item îÅÂÅÓÎÁÑ ÓÆÅÒÁ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏ ÍÁÓÛÔÁÂÉÒÕÅÔÓÑ, ÄÌÑ ËÁÖÄÏÇÏ ÍÁÓÛÔÁÂÁ ÏÔÂÉÒÁÅÔÓÑ ÎÅÓËÏÌØËÏ +ÑÒÞÁÊÛÉÈ ÐÒÉÚÎÁËÏ× ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÈ ÍÁÓÛÔÁÂÕ ÒÁÚÍÅÒÏ×. +\item ïÂßÅËÔÙ ËÁÖÄÏÊ ÑÞÅÊËÉ ËÏÄÉÒÕÀÔÓÑ É ÏÂÒÁÚÕÀÔ ÞÅÔÙÒÅÈÍÅÒÎÏÅ ÄÅÒÅ×Ï. +\end{enumerate} +}\only<3>{\img[0.6]{astrometrynet} +}\only<4>{ +ðÒÏÃÅÄÕÒÁ ÁÓÔÒÏÍÅÔÒÉÉ. +\begin{enumerate} +\item éÄÅÎÔÉÆÉËÁÃÉÑ ÏÂßÅËÔÏ× ÎÁ ÉÚÏÂÒÁÖÅÎÉÉ É ÏÐÒÅÄÅÌÅÎÉÅ ËÏÏÒÄÉÎÁÔ Ú×ÅÚÄ (ÎÁÐÒÉÍÅÒ, ÉÓÐÏÌØÚÕÑ +SExtractor). +\item ïÂÎÁÒÕÖÅÎÉÅ ×ÓÅÈ ÐÏÄÈÏÄÑÝÉÈ Ë×ÁÄÒÁÔÏ× É ×ÙÞÉÓÌÅÎÉÅ ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÉÈ ÉÍ ÈÅÛÅÊ. +\item ðÏÉÓË ÓÏ×ÐÁÄÅÎÉÊ (Ó ÚÁÄÁÎÎÏÊ ÔÏÞÎÏÓÔØÀ) × ÂÁÚÅ ÄÁÎÎÙÈ. +\item åÓÌÉ ÐÁÒÁ Ë×ÁÄÒÁÔÏ× ÏÔÏÖÄÅÓÔ×ÌÅÎÁ, ÐÏ ÏÓÔÁÌØÎÙÍ ÐÒÏ×ÏÄÉÔÓÑ ÕÔÏÞÎÅÎÉÅ ÏÒÉÅÎÔÁÃÉÉ ÐÏÌÏÖÅÎÉÑ É +ÍÁÓÛÔÁÂÁ ËÁÄÒÁ. +\item åÓÌÉ ÏÔÏÖÄÅÓÔ×ÌÅÎ ÌÉÛØ ÏÄÉÎ Ë×ÁÄÒÁÔ, ÐÏÉÓË ÓÞÉÔÁÅÔÓÑ ÎÅÕÄÁÞÎÙÍ. +\item äÌÑ ÕÓËÏÒÅÎÉÑ ÐÏÉÓËÁ ÖÅÌÁÔÅÌØÎÏ ÕËÁÚÁÔØ ÄÉÁÐÁÚÏÎ ÍÁÓÛÔÁÂÏ× ÉÚÏÂÒÁÖÅÎÉÑ, ÐÒÉÍÅÒÎÙÅ ËÏÏÒÄÉÎÁÔÙ +ÃÅÎÔÒÁ É ÄÏÐÕÓË ÎÁ ÒÁÄÉÕÓ ÐÏÉÓËÁ. +\end{enumerate} +} +\end{frame} + +\begin{frame}{óÐÁÓÉÂÏ ÚÁ ×ÎÉÍÁÎÉÅ!} +\centering +\begin{minipage}{5cm} +\begin{block}{mailto} +eddy@sao.ru\\ +edward.emelianoff@gmail.com +\end{block}\end{minipage} +\end{frame} +\end{document} diff --git a/Komp_obr_SFedU/additional/pic/Airy_vs_gaus.pdf b/Komp_obr_SFedU/additional/pic/Airy_vs_gaus.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f196ffe3cdf3a0dc53dfc3a62519470283522cb6 GIT binary patch literal 7532 zcmai3bzD?iyC#*A?i^x}o*9Pj96%Zbq`Rbtp#=k^B?M_f9BHIMN>aK(NokPoPVeA3 z=ey^-|J?nXwcfp+wcgzC-ha#k)KY-)LihynfYm!CS9k&dFu={~DV~G`0HkK?YL9RL z2%;bzJOBUyf;l=PY~d*BY>BW{u(fuxvBi^;!t+GHZ7p5!d@}+~`eFndG&0vX$MLlu zm%NieCnXKWY)3+60L>E65({~rV7N7L#p 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