8 : Lateral calibration

As usual, to follow this part, download the corresponding observation data on this link: starex198.zip

You will find in this archive a sequence of raw images of the spectrum of the star Altair and the star 12 Vul. The telescope used is a C9.25 (Celestron), operated directly at direct focus f/10. The spectrograph is a Star'Ex configured in high resolution mode (2400 t/mm grating, 80x125 objective combination, 35 microns slit, ASI533MM camera).  The spectra are centered on the H-alpha line.

The data are acquired using a particular calibration technique, the "lateral" mode. From our point of view it is an advance that brings ease, comfort and precision. This technique also favors the use of spectrographs designed to be light and inexpensive, because they are the result of 3D printing - which is in itself a revolution. Often the instruments made from this technology have a weakness in terms of rigidity, which leaves something to be desired. They deform more or less under their own weight depending on the location of the sky targeted. We also know of heavy metal spectrographs that suffer from the same defect, it is indeed impossible to achieve absolute rigidity. In addition to this are the deformations called "term-elastic", related to temperature changes. This results in spectral calibration errors that affect the quality of the acquired spectra. The main idea of the "lateral mode" is to carry out a quasi continuous monitoring during the observation of the deformations which affect this calibration and to take them into account to obtain a better result.

At the same time, we acquire the spectrum of the celestial targets and the spectrum of emission lines of the calibration lamp. In the end, the image of the spectrum of the standard lamp overlaps the image of the spectrum of the star, one being printed on the other. The purpose is obvious: if during the exposure on a target, which can be long (10 minutes... 30 minutes) the spectrograph distorts, since the light of the calibration signal follows approximately the same optical path, and especially in the same time, the consequent movement of the spectrum affects both the spectrum of the star and the spectrum of the standard lamp, so the errors of spectral calibration are very reduced.

Incidentally, we eliminate a step, that of making a separate calibration spectrum at the end of the session on a star (or at the beginning, or both).

But isn't the acquisition of two spectra simultaneously on the same image a cause of information interference, as one can override the other? The question is legitimate. What saves us here is that the nature of the spectra is very different: a more or less continuous line of light in the situation of the spectrum of a star, a spectrum of discrete lines, very localized, for the reference standard lamp. Of course, there is an overlap, but it is only very local and not very annoying in practice before the interest that we draw from the method. 

Here is what it gives on the image 12vul-1.fits, that you will find in the session "starex198":

The horizontal line is the trace of the spectrum of the star 12 Vulpecula after an exposure of 900 seconds. Simultaneously, we see the emission lines of the neon lamp, in the same image. We have two spectra in one. Rest assured, the processing that follows will allow us to isolate the only spectrum of the star in the end. The information that we use to calibrate this spectrum is the one on either side of the track, in these lateral parts, hence the name "lateral calibration" given to this technique, or "lateral mode".

The general approach is not new: it is not unlike that used by almost all professionals who perform astronomical spectrography (that's a lot of people and a lot of equipment!). To avoid temporal biases (mechanical shifts ...), they also manage to capture simultaneously the spectrum of the studied star and the useful information for the calibration. This way of doing things has unfortunately been forgotten by the amateur community which practices spectrography, even though it is one of the foundations of instrumental spectrography and metrology. Professionals refine the technique a little more by arranging for the calibration spectrum to accompany that of the star, but without overlap thanks to more or less sophisticated optical systems, but the principle is the same. 

The most serious complaint is not that of the superposition of spectra, but the fact that when guiding on the star, the calibration signal, which also arrives permanently on the entrance slit of the spectrograph, produces a parasitic flux. We are somehow dazzled. Fortunately, it turns out that our calibration illumination must be of very low intensity so that the emission lines do not saturate the detector after 15 minutes of exposure (for example). As a result, this spurious signal mentioned is automatically tenuous, especially since in high spectral resolution (the lateral mode is especially suitable for high resolution) the targets are quite bright stars. The flux coming from the standard lamp is therefore not generally disturbing.

Even so, one can also imagine a semi-permanent illumination, switched on for more or less long periods (using a timer, commands sent by the acquisition computer, ...). But the ultimate solution, because very effective, consists in placing just in front of the guiding camera a spectral filter (31.75 mm diameter) whose bandwidth blocks the light of the standard lamp. In our case, all the intense emission lines of neon being located in the red part of the spectrum, the use of a green broadband filter constitutes an impassable barrier to the calibration photons (a relatively economic model of filter, such as those used in deep sky imaging to obtain color images from black and white sensors, is perfectly suitable). The background in the image of the guiding camera then becomes almost black. At the same time, by filtering at the guiding camera, we reduce some optical aberrations and the guidance is more accurate, with images of stars well clear.

After this aside on the lateral mode, necessary, because not necessarily known, let's come to the processing of spectra.

 

On the side of the observation file, since we have two series of spectra to process (Altair and 12 Vul), we write from the tab "Observations" :

Things are simple: we provide the name of the two objects, then "Auto". specINTI does not find a set of raw images for offset, dark, and flat-field, so it indicates a zero number of images. These are calibration master images provided in a pre-processed form that are used here, present in the "starex198" archive (_offset, _dark, and _flat). That's all from the observation file. 

Here is the recommended configuration file, but there may be variations depending on your equipment (see also the file "conf_starex2400_mode3.yaml", present in the specINTI distribution):

# ********************************************************************************

# Star'Ex high resolution configuration

# C9.25 = 2400 t/mm grating - 80x125 - 35 micron slot 

# Calibration in mode 3

# ********************************************************************************

# ---------------------------------------------------

# Working directory

# ---------------------------------------------------

working_path: D:/starex198

# ---------------------------------------------------

# Processing batch file

# ---------------------------------------------------

batch_name: obs_12vul

# ---------------------------------------------------

# Spectral calibration mode

# ---------------------------------------------------

calib_mode: 3

# ---------------------------------------------------

# Automatic search for calibration lines

# ---------------------------------------------------

auto_calib: [6500, 6700]

# ---------------------------------------------------

# Binning width (mandatory)

# ---------------------------------------------------

bin_size: 30

# ---------------------------------------------------

# Sky background calculation areas

# ---------------------------------------------------

sky: [150, 25, 25, 150]

# --------------------------------------------------

# Sky evaluation mode

# --------------------------------------------------

sky_mode: 1

# ------------------------------------------------

# Radius of curvature of the smile

# -----------------------------------------------

smile_radius: -16000

# ------------------------------------------------------------------------

# Remove artifact at the calibration lines wavelength

# -----------------------------------------------------------------------

clean_wave: [6506.52, 6532.88, 6598.95, 6678.28]

clean_wide: [0.9, 0.9, 0.9, 1.0]

# ---------------------------------------------------

# x-terminals for geometric measurements

# ---------------------------------------------------

xlimit: [450, 2000]

# ----------------------------------------------------------------

# Width in pixels of the line search area

# spectral calibration

# ----------------------------------------------------------------

search_wide: 100

# ----------------------------------------------------------------

# Order of the calibration polynomial to evaluate

# Mandatory if calib_mode = 0 or 3 

# ----------------------------------------------------------------

poly_order: 2

# ----------------------------------------------------------------

# Name of the instrumental response file (optional)

# ----------------------------------------------------------------

instrumental_response: reponse_C9

# ---------------------------------------------------------------------

# Tungsten lamp color temperature

# ---------------------------------------------------------------------

planck: 2900

# ----------------------------------------------------------------

# Median filter pattern

# ----------------------------------------------------------------

kernel_size: -3

# ----------------------------------------------------------------

# Gaussian filtering

# ----------------------------------------------------------------

sigma_gauss: 0.8

# ----------------------------------------------------------------

# Optimal extraction

# ----------------------------------------------------------------

extract_mode: 1

gain: 0.083

noise: 1.3

# ----------------------------------------------------------------

# Unit normalization area

# ----------------------------------------------------------------

norm_wave: [6640, 6660]

# ----------------------------------------------------------------

# Profile cropping area

# ----------------------------------------------------------------

crop_wave: [6501, 6700]

# ----------------------------------------------------------------

# Longitude of the observation place (optional)

# ----------------------------------------------------------------

Longitude: 7.0940

# ----------------------------------------------------------------

# Latitude of the observation point (optional)

# ----------------------------------------------------------------

Latitude: 43.5801

# ----------------------------------------------------------------

# Altitude of the observation point in meters (optional)

# ----------------------------------------------------------------

Altitude: 40

# ----------------------------------------------------------------

# Observation site (optional)

# ----------------------------------------------------------------

Site: Antibes Saint-Jean

# ----------------------------------------------------------------

# Instrument description (optional)

# ----------------------------------------------------------------

Inst: C9 + StarEx2400 + ASI544MM

# ----------------------------------------------------------------

# Observer (optional)

# ----------------------------------------------------------------

Observer: cbuil

# ----------------------------------------------------------------

# Goodies

# ----------------------------------------------------------------

check_mode: 1

spectral_shift_wave: 0.01

sky_remove: 1

An important modification with respect to the high spectral resolution processing performed in the previous section - the use of the lateral mode, which is signified in specINTI by writing :

calib_mode: 3

This calibration mode #3 exploits the lateral illumination. After the detection of the neon lines on both sides of the star spectrum, specINTI computes the optimal calibration polynomial, which it then applies to the star spectrum. Moreover, the neon spectrum is erased as well as possible in the final spectrum of the target.

The "auto_calib" parameter is present to facilitate your work, the automatic search for calibration lines being perfectly compatible with mode 3.

The binning height is set to 30 pixels ("bin_size" parameter) to be sure to collect almost all the signal from our targets. The areas defined by the "sky" parameter (150, 25, 25, 150), are as always chosen to exclude any signal coming from the target star, with margin, but also wide enough on both sides of the trace of the spectrum to correctly evolve the sky level without too much noise. But here, the "sky" parameter has a double function. First, to evaluate the signal of the sky background, but also to extract the profile of the neon lines of the lateral mode to then perform the spectral calibration. This spectrum of neon, taken in the spectrum of the star pointed, is calculated in the example by agglomerating column after column, the signal between the coordinates y = 150 to y = -25 relative to the track and below it, and the signal between the coordinates y = 25 to y = +150 relative to the track and above it.

The parameters "clean_wave" and "clean_wide" are optional and new. They are used jointly to reduce, if necessary, the residual artifacts during the removal of the calibration spectrum after the sky subtraction. As this removal is not always perfect, the calibration lines may leave traces, which can be removed with this additional procedure. The "clean_wave" parameter is a list of the lengths in angstroms of the lines concerned. The "clean_wide" parameter is a list of spectral widths in angstroms centered on the lines indicated in the "clean_wise" parameter. specINTI performs a linear interpellation in these intervals which removes the defects found there.

The instrumental response "reponse_C9" is provided in the distribution (typical of a high spectral resolution spectrum, see part 4 of this documentation).

The images undergo a classical noise reduction treatment in the context ("kernel_size", "sigma_gauss," "extract_mode"), to obtain a spectral power close to R = 12000, with a good signal to noise ratio.

At the end of the configuration file there are some optional parameters (the "goodies").

Start the processing with confidence. The result after a few moments:

Tip: If the optional parameter "check_mode" is set to 1, the software delivers a lot of information to the console, which makes it possible to monitor the results. specINTI also writes spectral profiles and check images to the working folder as the program runs. Of particular interest is a check image, the "_step101.fits" image, which should be learned to consult when starting a configuration file in case of doubts:

It is the sum of all the images of the 12 Vul sequence after pre-processing and sky removal. specINTI has added horizontal marks to facilitate your choices and diagnoses. 

We see first in the center an extract of the 2D spectrum trace of the star.

You can see that this trace is horizontal (the software does the processing to make it so, even if your raw data is not perfect on this point). The software has also recognized the vertical position of the spectrum (Y coordinate in the "log"), this in the individual images, in order to perform a vertical re-centering of all traces.

The two strong lines on either side of the trace define the binning height (parameter "bin_size"). You can judge if this height is sufficient by increasing the contrast to see the low lights and therefore the extension of the spectrum along the spatial axis.

The other horizontal lines specify the selected sky background evaluation areas. We recall that it is also from these areas that the profile of the lateral calibration spectrum is extracted.

It is useful to examine the details of low intensity, as here by playing on the thresholds of visualization:

It appears first that the processing is concentrated in the extremities defined by the "sky" parameter in relation to the spectrum trace. This is also the case for the removal of the sky background. It then appears that the removal of the neon lines is not perfect. A structural noise remains at their levels. This is what will cause artifacts in the profile of the spectrum of the star, very localized.

The origin of the defect is inherent in the way of illuminating the pupil with the calibration source, at points (fiber output) and with a relatively monochromatic light. The calibration beam thus has a certain level of optical coherence (like a laser) which is responsible for interference, resulting in "speckles" (granules in the image or specks). This result is not obtained if the source is wide at the entrance of the telescope because of the destruction of spatial coherence in this case. This phenomenon "speckle" is the Achilles heel of the technique of illumination in the pupil, given its implementation in this case. But the disadvantages are less than the advantages, clearly. We recall that the residue of the lines is very local (the shape of the H-alpha line is not affected, for example, but more annoyingly, the helium line at 6676 A is). The parameters "clean_wave" and "clean_size" can help here.

Note: A very small systematic spectral shift ("spectral_shift_wave"), of 0.01 A, hardly perceptible, is applied to take into account a spectral calibration bias, the entrance pupil being illuminated differently depending on whether the light comes from the sky or from the calibration source. If there is only one calibration source point, make sure to place it along the long axis of the slit. Finally, relative to the radial position, place the source, or sources, at about 0.7 radius from the center, an optically optimal corona as most representative of overall uniform illumination.

Tip: If you add the optional parameter "sky_remove" with the value 0 in the configuration file, the sky background is not removed, and thus the lateral calibration lines remain present in the profile as peaks above the continuum (this option is especially useful for, for example, the treatment of gaseous nebulae or comets that have an extended angular surface) :

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