3. Extraction and Weights¶
3.1. Weighted Extraction Background¶
In any spectrograph extraction routine, pixels in the direction orthogonal to the wavelength axis have to be averaged or summed in order to maximise the signal to noise. In the case of multi-fiber spectroscopy where there is some overlap between neighboring fibers, the optimal algorithm is described in Sharp and Birchall (2010, PASA, 27, 91).
For GHOST, the situation is a little more complex, because the “object profile” is not fixed, as it is for the case of single fiber spectroscopy. Each object has a profile that comes from the slit viewing camera, which has to be scaled in the spectrograph x direction and also in flux.
3.2. Weighted Extraction Principle in 1D¶
Following the Sharp and Birchall notation (section 5.2), we will consider the profiles for object and sky along a single order. These profiles, normalised to 1 along the x direction, are given by
System Message: WARNING/2 (\phi_{ki})
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latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.with
System Message: WARNING/2 (w_i=0)
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.These weights are used to construct the following two matrices. First, the “cross-talk” matrix between profiles, which should be diagonal except for the (very large!) cross-talk between sky and object:
System Message: WARNING/2 (C = c_{kj} = \Sigma_i \phi_{ki} \phi_{ji} w_i )
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.and the naieve extraction matrix (which would be the extraction matrix in the case of no cross-talk):
System Message: WARNING/2 (B = b_{kj} = \phi_{kj} w_j )
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.This is slightly different to the Sharp and Birchall notation, and for a data vector
System Message: WARNING/2 (d=D_i)
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (C \cdot \eta = B \cdot d, )
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.which is solved by:
System Message: WARNING/2 (\eta_k = \Sigma_i z_{ki} D_i )
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.for an extraction weights matrix
System Message: WARNING/2 (Z=z_{ki})
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (Z = C^{-1} \cdot B )
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.This matrix also subtracts the sky as measured. The extraction weights
System Message: WARNING/2 (z_{kj})
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (\times)
latex exited with error [stdout] This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./math.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty (/usr/share/texmf/tex/latex/ucs/utf8x.def)) (/usr/share/texmf/tex/latex/ucs/ucs.sty (/usr/share/texmf/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?’ option. (/usr/share/texmf/tex/latex/amsmath/amstext.sty (/usr/share/texmf/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf/tex/latex/amscls/amsthm.sty) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.9 \usepackage {bm}^^M No pages of output. Transcript written on math.log.3.3. Slit Tilt and PSF Variation Issues¶
One problem with the algorithm above is that it assumes that the two-dimensional point-spread-function is the product of spectral and spatial point spread functions. This was the case for single fiber profiles imaged with spectrographs with typical aberrations as used by Sharp and Birchall, producing a near-Gaussian profile. However, for GHOST, even individual fiber profiles are not quite Gaussian. We avoid the most significant problems with this while preserving the need to weight differently at high versus low signal-to-noise by convolving the variance array both spatially and spectrally. In the current implementation, the spectral weights are convolved by a Hanning window of ~7 pixel FWHM, and the spatial variance is convolved by a function of ~2 pixels FWHM.
3.4. Weighted Extraction Principle in 2D¶
For object profiles in 2-dimensions, we choose to extract as in 1-dimension, but where we interpolate linearly between the nearest two pixels in the wavelength direction only, so that the mean wavelength extracted for each pixel in the x direction corresponds to the wavelength solution wavelength for the slit central pixel. This has the effect of adding an additional dimension to the extraction weights variables:
System Message: WARNING/2 (\eta_k = \Sigma_l \Sigma_i z_{kil} a_{il} D_i )
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System Message: WARNING/2 (a_{il})
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