<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>Nonlinearity</TITLE> <META NAME="description" CONTENT="Nonlinearity"> <META NAME="keywords" CONTENT="vol2"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol2.css"> <LINK REL="next" HREF="node296.html"> <LINK REL="previous" HREF="node294.html"> <LINK REL="up" HREF="node293.html"> <LINK REL="next" HREF="node296.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html5113" HREF="node296.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html5110" HREF="node293.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html5104" HREF="node294.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html5112" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html5114" HREF="node296.html">Special systems</A> <B> Up:</B> <A NAME="tex2html5111" HREF="node293.html">Special problems</A> <B> Previous:</B> <A NAME="tex2html5105" HREF="node294.html">Missing bands</A> <BR> <BR> <!--End of Navigation Panel--> <H3><A NAME="SECTION001859200000000000000"> Nonlinearity</A> </H3> <P> Although it is possible to solve for nonlinearity (e.g., dead-time) corrections in both pulse-counting and DC photometry, <I>extreme</I> care should be used in doing so. The problem is that the nonlinearity is strongly coupled to other parameters in the solution. A common error is to include standard-star values in the solution; this aliases conformity errors for the 2 or 3 brightest stars into the nonlinearity parameter. Nonsensical values of both the nonlinearity and the transformation parameters are the usual result, accompanied by a misleadingly ``good'' fit (small residuals, and small standard errors on the coupled parameters). <P> To determine nonlinearity accurately, a neutral attenuator should be used to observe a considerable number (say, 15 or 20) of the brightest stars. The fainter stars serve to calibrate the attenuator; the brightest stars then determine the nonlinearity, through comparisons between their attenuated and unattenuated observations. A less precise determination of nonlinearity is possible by using the atmospheric extinction as the attenuator; unfortunately, this is not neutral, so the coupling between nonlinearity, extinction, and bandwidth parameters can produce systematic reduction errors. In either case, the transformation solution should be done separately from the extinction-and-nonlinearity fit. <P> It is particularly dangerous to have a single star much brighter than the rest, as its high leverage on the nonlinearity parameter will guarantee systematic errors. Such a star will stand out as isolated points on the right-hand side of the linearity plots. If the brightest star is extremely red or blue in any color index, the errors will affect the transformations more strongly. Try to find 2 or 3 bright stars of intermediate color within half a magnitude of one another, to determine the nonlinearity. <P> While the best linearity is obtained with a good DC system, used at small anode currents, an overloaded DC system can be just as nonlinear as an overloaded pulse counter. The best policy is to know and understand your equipment thoroughly, and (if possible) to avoid observing in the range where nonlinearity is known to be a problem. <P> <HR> <!--Navigation Panel--> <A NAME="tex2html5113" HREF="node296.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html5110" HREF="node293.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html5104" HREF="node294.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html5112" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html5114" HREF="node296.html">Special systems</A> <B> Up:</B> <A NAME="tex2html5111" HREF="node293.html">Special problems</A> <B> Previous:</B> <A NAME="tex2html5105" HREF="node294.html">Missing bands</A> <!--End of Navigation Panel--> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-15</I> </ADDRESS> </BODY> </HTML>
