lambda = A0 + A1. X + A2. X. X + A3. X. X. X

with lambda, the wavelength of a desired sample point X (X = position in pixels). The parameters A0, A1, A2, A3 are the terms (or coefficients) of the polynomial to be determined.

Figure 1. Calibration function for the spectrograph LHIRES III 1200 lines/mm with an Atik 314L CCD camera at 2x2 binning.

These coefficients are found by adjusting a polynomial function that best describe the relationship between pairs of points (X, lambda) in a reference image or image calibration. With the LHIRES III spectrograph, the calibration image is obtained by taking an internal neon lamp spectrum. This spectrum shows emission lines. The number is depending on the spectral region analyzed, the dispersion value (grating model) or the detector size. The operation calibration operation consist first to accurately measure the X position of lines which we know also the perfect wavelength. Then compute the best curve from these points. A 2th polynomial of order 2 is sufficient with a LHIRES III 2400 lines/mm (the term A3 is considered to be zero). In this situation, a minimum of 3 emisssionl lines is necessary for perform the calculation (the minimum number is equal to the value of the order increased by one unit). An adjustment to the 3th order 3 is appropriate for a Lhires III equipped with a 1200 groove/mm gratiing,, and and also for 600, 300 or 150 line mm grating. In contrast, calibration with a polynomial of 1st order (linear fit) gives an unsatisfactory result in all cases. The LISA spectrograph is always calibrated with a polynomial of 3th order 3.

Once the calibration function is known (terms A0, A1, A2), to calibrate a spectrum simply provide to ISIS the X coordinate in pixels of one line so we know the wavelength. ISIS updates the polynomial dispersion by calculating the term A0. The term A0 is the constant term which describes only the global spectrum translation along the spectral axis. One object to another A0 term may change of value, such that the spectrograph is mechanically deformed due to gravity or temperature changes. These structural changes in mechanical moving image spectrum on the detector.

This is the reason that it is imperative for every observed object to acquire at least a calibration spectrum for refresh A0 value. In this process, the terms A1, A2, A3 can be considered constant (characteristic of the instrument), However, for high accuracy, it is recommended to recalculate as often as possible in a night of observation the coeffiicient A1, A2, A3.

In the part #1, we describe three method for calibrate spectra. In the part #2, we decrible the standard mode and the lateral mode.

ISIS uses a set of lines in the neon spectrum selected internally for calibrate the spectra taken in common configurations of LHIRES spectrographs and LISA. This method does works only around the Halpha for LHIRES (whole spectral range in the case of LISA spectrograph).

No panic if your LHIRES is equipped with a 150 lines/mm, 300 grooves/mm or 600 lines mm grating, or if you use any other spectrograph model in fact! We will see another method lowest, at least as automatic, and more universal, which will surely solve your problem.

In the example in Figure 2 (screen copy of "General" tab) we prepare to calibrate a spectrum acquired with a 1200 lines/mm.

Also in Figure 2, note that we also provide the position in pixels in the calibration image of a given emission line. ISIS impose the line, here at located at the wavelength 6506.528 A - you must learn to identify the line in the spectrum. For the example, the position found is X = 594 (the possible error margin is of 4 or 5 pixels).

The screenshot of Figure 3 shows how specify calibration image name (neon type image). Note that the calibration  image is combined with those of the observed object (acquisitions were made at shortly intervals).

You just have to click on "Go" for process spectra. ISIS first calculates the coefficients A0, A1, A2 and A3 for the image calibration provided, then calibrates the sequence spectrum of the observed object.

At the end of processing, if you're curious, click the "Dispersion" button of the toolbar tab "Profile display" (Figure 4). The left column give the wavelength of the 6 calibration lines used by ISIS. In face, pixel coordinates values found. For example, the line wavelength at 6506.528 A was automatically measured at the X coordinate = 593.163 (pixels and fractions of pixels).

Although not mandatory, click the button "Compute polynom" att the top of the dialog (select aloso the 3th order first). ISIS calculates A0, A2, A3, A4 terms from the points raised in the spectrum of the neon lamp. At the bottom of the dialog box, ISIS returns the difference between the obsereved wavelength (calculated with the polynomial) and the catalog wavevelength.

The RMS deviation is 0.003 A, which is very small (but not necessarily the final precision calibration in spectrum of your object - other factors involved).

If now you are very curious, open the text file "_vega_20110529_875.log" that was created in the ISIS working directory at the time of processing (figure 5). In LOG file, you will find the value calibration coefficients values actually used by ISIS for actual Vega processing. Note that if we exclude rounding effect the coefficient are are the same than those calculated from the tool "Dispersion".

You can well calculate a polynomial of 2th order with the same data as shown in Figure 6. The precision obtained is very close to that achieved with a 3th order polynnom. However, try a polynomial of 1st order (linear interpolation), the result is much less satisfactory.

For a complete example of processing with the present method, for example, click on this link:

http://astrosurf.com/buil/isis/quicklhires/tuto_fr.htm

or here:

http://astrosurf.com/buil/isis/isis_tuto/tuto1.htm

Figure 3. Assign the calibration file image spectrum (neon) associated with the observed object. Provide also the dark map name associated with the calibration image (here for a 30 seconds exposure).
 


Figure 4. The "Dispersion" tool, available from "Profile display" tab.
 


Figure 5. Contain of LOG file.



Figure 6. 2th order polynom fitting.
 

You can perfectly calculate the calibration coefficients in software other than the ISIS and report the values in the "Dispersion" dialog box (figure. 8). In this case, by definition, the step of calculating the coefficients by ISIS is eliminated.

These coefficients may also have been calculated by you previously and used for present processing.

Then go to the "General" tab to select the calibration mode "Predefined polynom" (figure 8).

As usual, enter the position in pixels of a reference line. Unlike the previous method #1, it is also your responsibility to provide the precise wavelength of this line.

When processing (when pressing the "Go" button from the "General" tab), ISIS will search polynomial coefficient values in dialog tool "Dispersion" (the dialog box can be opened or closed).

ISIS has interactive features that help to calculate the polynomial dispersion coefficients. For example, you will find here an example corresponding to complete calibration of a LHIRES III spectrum in the short wavelengths:

http://astrosurf.com/buil/isis/He_calibration/method.htm

Same operation near Halpha :

http://astrosurf.com/buil/isis/isis_tuto/tuto6.htm

You have here another example using telluric lines for calibrate:

http://astrosurf.com/buil/isis/quicklhires/advanced_fr.htm

 
Figure 7. Enter a predefined polynom.





Figure 8. ISIS use now a predefined polynom.

 

With the help of a text editor program (NotePad for example), write the text shown in Figure 9. Save in a file with the name of your choice in the working directory. You must however add the extension ". LST. In the example, the file will allow us to calibrate spectra LHIRES III 1200 lines mm, so we naturally call the file G1200.LST (G for Grating). We must respect the format of this file content.

The first line indicates the order of polynom that we wishes to adjust (here 3).

The second line shows the average dispersion in angstroms per pixel. You should evaluate this quantity (it is a constant from your instrument). The operation is simple. For example, in the image of neon spectrum we have noted that the position of the emission line at wavelength 6402.25 A is X = 343 pixels (use mouse pointer on the tab "View Image" for the measure). Similarly, the neon line at 6717.04 A is found at X coordinate = 1105.

The difference in wavelength between the two lines is lambda = 6717.04 - 6402.24 = 314.79 A.

The diffrence in pixels between two lines is dX = 1105 - 343 = 762 pixels.

The average dispersion is equal to the ratio dlambda / dX, or 314.79 / 762 = 0.413 A / pixel. It is the value adopted in our file G1200.LST. If possible select largely separated lines for maximum accuracy.

The following lines of file contain wavelength of selected spectral lines. We recognize in the example list of available neon lines around the Halpha, but you can also use light from a completely different type of spectral lamp spectrum (argon, thorium, ...). The requirement is that these lines are well on spectral range of your data.

Figure 10 shows how to complete the "General" tab to exploit this method of calibration. Of course, you must specify the file name of lines (without extension). Just as with method 2, you must also indicate the position of a reference line in pixels and the  wavelength of the lines (in this mode, an accurate value for the wavelength is not required).

By starting the process, ISIS reads the file G1200.LST, then locates itself pixel position of provided lines in the list, calculates the polynomial dispersion (3th order in the example), and finally graduated in wavelength unit your spectra.

Methods 1, 2 and 3 for your gives very similar resulatl (Figure 11).

In all, the method 3 is probably the most universal and simpler. For example, suppose you operate a LHIRES III with a 600 lines/mm grating. (1) You make first a neon image spectrum with this configuration. (2) You look for the strongest and better isolated lines. (3) You write a file G600.LST (for example) with these data, and now you can effortlessly and precisely calibrate your spectra. The G600.LST file was created once (you must simply remember to carry the current working directory if needed).

With Method 3 you can calibrate in wavelength unit virtually all types of spectra with ISIS taken with a large set of spectrograph.
 

Figure 9. Contain of G1200.LST.




Figure 10. Select the lines spectral file mode.


 

Figure 11. Contain of LOG file.

STANDARD MODE

ISIS organizing for the standard mode as explained in Figure 12.

We give the generic name of sequence images to process (here a sequence the star delta Scorpius delta, denoted DSCO-1, DSCO-2, ...,  DSCO-6). We provide also the name of calibration image (here an argon spectrum, not a neon spectrum, but the principle is the same).

The calibration spectrum can be acquired just before the object spectra, just after, or better yet, an average of a "neon" spectrum taken before and after the object sequence.

From the "Setup" tab, adjust the size of thebinning zone size so it is more greater than the overall width of the object spectra trace (no exaggeration, but it is always better to choose a binning width too large than too little wide). Here, the vertical biining width binning is 28 pixels.

ISIS evaluates itself the height of the binning area in the calibration spectrum in order to extract the profile. Specifically,  ISIS add to the objets binning height 30 additional pixels (in in the example the height of binning height is 28 + 30 = 58 pixels for extract argon emission spectral line).

After binning operations, ISIS has two spectral profiles. It can then calibrate object spectral profile by using the lamp calibration profile. Of course, these operations are performed automatically by clicking the "Go" button from "General" tab

 
Figure 12. Spectral calibration in the standard mode. Click on the image for enlarge.

 

LATERAL MODE

For further explanation about this powerfull and efficient observation method, click here.

The lateral calibration mode is accurate because the simultaneous shooting between the spectrum to calibrate and the calibration source (consequence of mechanical flexure and thermo-elactic effets are elliminated for example).

The operating procedure is shown in figure 13.

First, select the lateral mode option from "Setup" tab.

On both sides of the spectrum trace (and superimposed on it too), in "lateral" areas, the presence of the calibration spectrum canbe  noted (fine emission lines).

There is no reason to provide the "Neon" image name, since this reference is included in the spectrum of the object to be processed. It's the whole point of the technique.

ISIS average the two calibration spectrum computed after making binning at both sides of the target trace spectrum. The software uses the vertical coordinates for sky calculation (Yinf1, Yinf2, Ysup1, Ysup2) for define vertical size of these binning zones.

When the average profile of the reference lamp is calculated, ISIS calibrates the spectrum of the object so by using traditional method.

At the end, the emission spectral lines of calibration  lamp are eliminated during sky substraction operation.
 

Figure 13. Spectral calibration in the lateral mode. Click on the image for enlarge.