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<H2>Vega Spectrum Angstroms Calibration Without Zero Order by RSpec<BR>Image August 2, 2011 at 11:00 am PDT</H2>
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<A HREF="VegaA06-012s06_20110802_1104.html"><IMG SRC="jpg/VegaA06-012s06crop.jpg" ALT="Vega Spectrum" WIDTH=624 HEIGHT=86 BORDER=0 ALIGN=MIDDLE></A>
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<P>
The above image is the 
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Star">star</A> 
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Vega">Vega  (Wikipedia)</A>. 

The round spectral order zero is on the left side of the image and its first order blazed 
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Diffraction_grating">grating</A> 
 spectrum is on the right side.  
</P>
<P>
This web page shows how 
<A TARGET="_top" HREF="http://www.rspec-astro.com">Field Tested Software</A> RSpec V1.3.0 (Build: 39)
non-linear Calibration Wizard was used to calibrate the horziontal axis in <A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Angstrom">angstroms (Å)</A> and shows the results of not including the zero order using the four different curves (1st, 2nd, 3rd and 4th). 
</P>
<P>
Below each spectrum is the Calibration Wizard window with the five residuals that are in angstroms and the 
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Root_mean_square">RMS</A> 
for that order. Residuals equal to zero are ideal and RMS equals to zero is ideal. 
</P>
<P>
Below is a summary table of the residuals and RMS value calculated in Excel <A HREF="data/VegaA06-012s06cropRMS.xlsx">VegaA06-012s06cropRMS.xlsx</A> for both with and without the zero order.  This web page shows the details of the calibration without the 0 order. This is the table on the right. Click on the table on the left to see the details of the calibration with the 0 order.
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<A HREF="VegaA06-012s06_20110802_1100NonLinearCal.html"><IMG SRC="jpg/capture_009_18092011_091950RMSwith0.jpg" ALT="Residuals and RMS value with 0 order" WIDTH=324 HEIGHT=209 BORDER=0 ALIGN=MIDDLE></A>
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<IMG SRC="jpg/capture_009_18092011_091950RMSwithout0.jpg" ALT="Residuals and RMS value without 0 order" WIDTH=325 HEIGHT=189 BORDER=0 ALIGN=MIDDLE>
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<P>
To put the values of the residuals in perspective the difference between CCD camera pixels at Hα is approximately 17.9 Å when using fourth order calibration without the zero order. 

<UL> 
<LI>The first order calibration which is linear has the Hα, Hβ and Hγ looking good on the spectrum chart.  Hδ, Hε and Hζ absorption lines are at the wrong wavelength. Using RMS the first order calibration falls between the second to third order calibration using the zero order.
<UL> 
<LI>The grating spectrum is non-linear and the focal plane is curved.
<LI><A TARGET="_top" HREF="http://users.erols.com/njastro/faas/articles/west01.htm">Resolution Calculation for a Slitless Spectrograph</A> By Dr. Doug West 
</UL>

<LI>The second order calibration improves the  Hδ, Hε, Hζ,  Hα  and A(O<sub>2</sub>) absorption lines. Hβ and Hγ absorption lines are worse than first order.
<LI>The third order calibration improves Hβ, Hα and A(O<sub>2</sub>) absorption lines.  But, Hγ and Hδ are worse than second order calibration.  
<LI>The forth order calibration has slight improvements over the third order calibration.  There is very little difference between third order and forth order calibration looking at the spectrum chart. The forth order has the lowest RMS values with 0.00 (RSpec) and 2.84 (Excel).
</UL>
</P>

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<UL> 
<LI>The spectrum chart vertical axis is the intensity values of the spectrum image.
<LI>The red + are measured data points.
<LI>The spectrum chart horizontal axis is wavelength in <A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Angstrom">angstroms (Å)</A>.
<LI>Reference yellow line markers show hydrogen Balmer absorption lines (Hα, Hβ, Hγ, Hδ, Hε and Hζ),
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Fraunhofer_lines">Fraunhofer</A>
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Telluric_contamination">telluric</A>
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Oxygen">O<sub>2</sub></A> 
<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Absorption_line">absorption bands</A> and
telluric H<sub>2</sub>O absorption band.
<UL> 
<LI>Fraunhofer telluric a (<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Oxygen">O<sub>2</sub></A>) band is 6276 Å to 6310 Å
(SPECTRAL CALIBRATION <A TARGET="_top" HREF="http://www.astrosurf.org/buil/us/spectro11/specalib.htm">Identification of tellurics lines</A>, by Christian Buil)

<LI>Fraunhofer telluric B (<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Oxygen">O<sub>2</sub></A>) band is 6867 Å to 6944 Å
(Table 95, page 100, 
<A TARGET="_top" HREF="http://www.ursusmajor.ch/astrospektroskopie/richard-walkers-page/index.html">Spectroscopic Atlas for Amateur Astronomers</A>, Verson 2.0 by Richard Walker)

<LI>Fraunhofer telluric A (<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Oxygen">O<sub>2</sub></A>) band is 7594 Å to 7684 Å
(Table 95, page 100, 
<A TARGET="_top" HREF="http://www.ursusmajor.ch/astrospektroskopie/richard-walkers-page/index.html">Spectroscopic Atlas for Amateur Astronomers</A>, Verson 2.0 by Richard Walker)

<LI><A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Fraunhofer_lines">Fraunhofer</A> telluric Z (<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Oxygen">O<sub>2</sub></A>) line is 8227 Å

<LI><A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Fraunhofer_lines">Fraunhofer</A> telluric y (<A TARGET="_top" HREF="http://en.wikipedia.org/wiki/Oxygen">O<sub>2</sub></A>) line is 8988 Å
</UL>
<LI>Telluric H<sub>2</sub>O band is 7168 Å to 7394 Å 
(Table 95, page 100, 
<A TARGET="_top" HREF="http://www.ursusmajor.ch/astrospektroskopie/richard-walkers-page/index.html">Spectroscopic Atlas for Amateur Astronomers</A>, Verson 2.0 by Richard Walker)
<LI>Below the spectrum chart is a synthesize color spectrum generated from the spectrum chart data.
</UL> 


<CENTER><P></P><IMG SRC="../gif/starsbar.gif" WIDTH=500 HEIGHT=8><BR><P></P></CENTER>
<UL>
<LI>Data files in <A HREF="data/VegaA06-012s06crop4orderNo0.zip">VegaA06-012s06crop4orderNo0.zip</A>
<UL> 
<LI>Spectrum image VegaA06-012s06crop.fit
<LI>RSpec V1.3.0 (Build: 39) VegaA06-012s06crop4orderData.dat and VegaA06-012s06crop4orderData.ini
<LI>RSpec V1.3.0 (Build: 39) VegaA06-012s06cropCal5pointsE.ini 
</UL> 
</UL> 

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<P><B>RSpec Non-Linear 1st Order Calibration</P></B>
<UL> 
<LI>The first order calibration which is linear has the Hα, Hβ and Hγ looking good on the spectrum chart.  Hδ, Hε and Hζ absorption lines are at the wrong wavelength.
</UL> 

<IMG SRC="jpg/VegaA06-012s06crop1orderNo0.jpg" ALT="RSpec Non-Linear 1st Order Calibration" WIDTH=1073 HEIGHT=587 BORDER=0>
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<IMG SRC="jpg/capture_004_18092011_082848.jpg" ALT="RSpec Non-Linear Calibration Wizard" WIDTH=483 HEIGHT=376 BORDER=0 ALIGN=MIDDLE>
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<P><B>RSpec Non-Linear 2nd Order Calibration</P></B>
<UL>
<LI>The second order calibration improves the  Hδ, Hε, Hζ,  Hα  and A(O<sub>2</sub>) absorption lines. Hβ and Hγ absorption lines are worse than first order.
</UL>
<IMG SRC="jpg/VegaA06-012s06crop2orderNo0.jpg" ALT="RSpec Non-Linear 2nd Order Calibration" WIDTH=1073 HEIGHT=587 BORDER=0>
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<IMG SRC="jpg/capture_005_18092011_082939.jpg" ALT="RSpec Non-Linear Calibration Wizard" WIDTH=483 HEIGHT=376 BORDER=0 ALIGN=MIDDLE>
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<CENTER><P></P><IMG SRC="../gif/starsbar.gif" WIDTH=500 HEIGHT=8><BR><P></P></CENTER>
<P><B>RSpec Non-Linear 3rd Order Calibration</P></B>
<UL>
<LI>The third order calibration improves Hβ, Hα and A(O<sub>2</sub>) absorption lines.  But, Hγ and Hδ are worse than second order calibration.   
</UL>
<IMG SRC="jpg/VegaA06-012s06crop3orderNo0.jpg" ALT="RSpec Non-Linear 3rd Order Calibration" WIDTH=1073 HEIGHT=587 BORDER=0>
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<IMG SRC="jpg/capture_006_18092011_083036.jpg" ALT="RSpec Non-Linear Calibration Wizard" WIDTH=483 HEIGHT=376 BORDER=0 ALIGN=MIDDLE>
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<A name="A"><P><B>RSpec Non-Linear 4th Order Calibration</P></B></A>
<UL>
<LI>The forth order calibration has slight improvements over the third order calibration.  There is very little difference between third order and forth order calibration looking at the spectrum chart. The forth order has the lowest RMS values with 0.00 (RSpec) and 2.84 (Excel).
</UL>
<IMG SRC="jpg/VegaA06-012s06crop4orderNo0.jpg" ALT="RSpec Non-Linear 4th Order Calibration" WIDTH=1073 HEIGHT=587 BORDER=0>
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<IMG SRC="jpg/capture_007_18092011_083148.jpg" ALT="RSpec Non-Linear Calibration Wizard" WIDTH=483 HEIGHT=376 BORDER=0 ALIGN=MIDDLE>
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Adjust monitor brightness and contrast to see all 16 gray scale levels. 
The most important adjustment when viewing astro images is to see the differences in all of the black bands. 
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