VV Cep spectroscopy reference star ?

VV Cep 2017-2019 Campaign
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Re: VV Cep spectroscopy reference star ?

Postby Phil Bennett » Mon Aug 31, 2015 2:43 pm

After our object spectrum has been extracted (ie: after image preprocessing, geometry corrected, sky background removed, and signal extracted column by column) and calibrated in wavelength, we have to apply an instrumental correction to adjust the overall profile to correct from:
-atmospheric extinction (depending on your local air parameters & airmass of course)
-telescope optical response to wavelength
-spectrograph optical response to wavelength
-CCD sensor efficiency to wavelength


What you're describing is spectrophotometry, where the objective is to derive an absolute flux-calibrated spectrum. But this approach will only work for slitless spectroscopy or spectroscopy through a wide slit. It assumes that all of the star light falling on the detector is captured for both the target star (i.e., VV Cep) and the reference star.

But if you are using a narrow slit (as typical for higher spectral resolution observations), then not all of the light passes through the slit. The fraction of light through the slit will depend on the seeing image, and the details of the guiding. In general, this will be different for the target star and the reference star no matter how carefully the observations are carried out. For most locations, seeing images of 2-3" are typical. Only part of that seeing image will pass through a narrow slit, and that fraction is not easily determined.

This is why professional astronomers doing medium and high-resolution spectroscopy usually just rectify the spectrum to a continuum, although the "continuum" is not that well-defined or obvious for M stars. It is possible (as mentioned previously in this thread) to recover a flux-calibrated spectrum from a rectified spectrum in conjunction with simultaneous photometry.

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Re: VV Cep spectroscopy reference star ?

Postby Robin Leadbeater » Mon Aug 31, 2015 7:10 pm

Hi Phil,

I agree that where the continuum is not of interest (as appears to be the case with this project) there is no need to use a reference star (though I must admit I generally do in any case as it gives me confidence that all is well with my equipment) All that would be needed is some agreement on how the spectrum is to be rectified eg wavelength ranges considered to lie on the continuum and the order of (spline) fit to be used. Also, as you say, a calibration in absolute flux units can only be made using an (additional) a wide slit measurement so that all the flux is recorded. I am not sure I follow how an absolute flux calibrated spectrum can be recovered from a rectified spectrum and simultaneous photometry without making some assumptions about the shape of the continuum though.

More generally my experience has been that in practise it is possible to obtain a useful approximation to the continuum shape of the target star in relative flux units (though it depends on the level of accuracy you are looking for of course.) using a narrow slit and a reference star recorded during the same observing run, provided the conditions are stable between the two measurements. Here are some sample measurements I made to satisfy myself that it could be done.
http://www.threehillsobservatory.co.uk/ ... opy_21.htm
Lower document. (The upper document is a similar exercise using simple slitless spectrograph)

Spectra measured in relative flux terms this way could then be converted to absolute flux using a single photometric eg V band measurement

What do you think?
Robin
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Re: VV Cep spectroscopy reference star ?

Postby Thilo Bauer » Mon Aug 31, 2015 7:45 pm

Olivier,

I totally agree with using the reference star. The contributions 1-4 are all found in one single observation.

Usually, I would try to avoid to use a star with a low signal, as this kind of calibration might be crucial to estimate a signal and errors from the spectra.

From experience with imaging, this is comparable to taking a flatfield with low signal. I accidentally recorded once a series of flatfields underexposed with only 1/10 of the maximum possible signal from my Canon. Doesn't sound much, of course. However, it will mean an impact to noise computations. Basic noise properties evaluated for the image series was found totally different from the regular expectation value (i.e. twice the error expected).

The reason for such deviations is just the impact of a low signal, which introduces more noise by itself (I don't even mean the additional detector noise). In this case of low light level computations will become more difficult, as low Poisson values no longer follow a square-root like relationship between signal and noise. Such a low signal will be more complex and computations become more related to the Anscombe transformation, which is a normalization of the signal, typically used to correct low signal/noise computations. The Anscombe transformation is a complex function to be used to compute corrected signal-to-noise computations in the photon-limited case.

But we should not forget, we DO observe in typical use photon-limited case using our cameras for spectroscopy (even if we don't call these cameras photon-counting detectors).

Thilo
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Re: VV Cep spectroscopy reference star ?

Postby Robin Leadbeater » Mon Aug 31, 2015 8:04 pm

Here is another example of using a reference star to follow changes in the continuum which is perhaps useful example for this campaign. In 2012/13 I followed AZ Cas through eclipse in the violet region at medium resolution. The spectra were calibrated in relative flux using a reference star.
http://www.threehillsobservatory.co.uk/ ... tra_43.htm

In addition to the obvious changes in line strengths and profiles, the calibrated spectra were consistent enough to clearly see the change in shape of the continuum in this region during eclipse. This was despite the measurements being at short wavelengths where the potential errors in the shape of the continuum from using a narrow slit are greatest. These continuum changes would not have been seen had the spectra been rectified.

Flux calibrating the spectra using a reference star can only add information and does not harm the SNR of course as the measurement is only used to determine the shape of the continuum so is heavily filtered.(This is quite different from the effect of dark ad flat correction which are done on a pixel by pixel basis and care is needed if SNR is not to suffer) If maximum continuous coverage at high cadence is desired though and the continuum is not important then it is sensible to sacrifice the reference star measurements.

Robin

Edited:- AZ Cas not CH Cyg
Last edited by Robin Leadbeater on Tue Sep 01, 2015 12:21 pm, edited 1 time in total.
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Re: VV Cep spectroscopy reference star ?

Postby Thilo Bauer » Tue Sep 01, 2015 5:09 am

Robin,

This is a really impressive work. What reference star did you use?

Robin Leadbeater wrote:Flux calibrating the spectra using a reference star can only add information and does not harm the SNR of course as the measurement is only used to determine the shape of the continuum so is heavily filtered.


I wouldn't agree with this statement in general, without having described the method to compute S/N and without describing the method used for filtering. It is often believed that filtering (like binning) improves signal. In fact, this is not generally true, as S/N will remain in the data while only spatial information is blurred across pixels. Therefore, result and computed S/N depends on the question, if the spatial resolution will be changed by the filter (e.g. using binning) or not.

For the simple case of pixel binning it can be shown, that pixel binning for example is NOT a method to improve S/N: http://www.astroinformatics.de/index.php?option=com_content&view=article&id=87&Itemid=69

Summary: The theory is consistent here with the simple observation, that no fainter stars will appear in an astronomical image when applying binning to the original image. ;)

The case of spectroscopy and using any arbitrary method of one-dimensional filtering will be different from this, however. I never thought about that in more depth, so far.

Another question is, how the S/N is computed. Is it just a pixel based noise measure (based on computation of photo-electrons), or does the term S/N refer to something different.

The exact definition of the computation to obtain an arbitrary "S/N" in spectroscopy might be crucial for further discussion.

Thilo
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Re: VV Cep spectroscopy reference star ?

Postby Robin Leadbeater » Tue Sep 01, 2015 1:07 pm

Thanks Thilo,

I used various reference stars for the AZ Cas measurements (not CH Cyg, now corrected in the original post) Vega, Altair, Castor. They were not well matched in air mass of course and perhaps I should have tried to find a better matched reference but as the wavelength range covered was very limited any relative differences in extinction would be small over the wavelength range.

Sorry I did not explain properly concerning filtering and SNR. I agree that filtering or binning also potentially reduces information/resolution depending on the sampling interval. When quoting the SNR of a spectrum the sample size should really also be quoted as well eg per bin/pixel or better, per resolution element. (ie for a critically sampled spectrum with 2 bins per resolution element.) I was talking here though specifically about the use of a reference star to generate a correction curve for instrument response/extinction. Here we are only interested in the the broad continuum shape of the measured reference compared to the published version, not the fine detail so the loss of detail due to filtering does not matter and we can smooth out any small scale bin to bin noise for this particular application before applying the smooth correction curve to the target spectrum without adding noise.

Estimation of uncertainty in spectroscopy is an interesting and important area that amateurs have not really got into much yet. I have seen various techniques used to estimate the SNR in spectra. Apart from simple electron count statistics, perhaps the one most commonly used by amateurs at least is to measure the variation in a line free part of the continuum though this is not always possible to find of course . (There are some algorithms which claim to measure the noise even in the presence of spectrum features by looking at variability between adjacent bins but I think these require the spectrum to be oversampled) Alternatively if several exposures are taken to make up one observation, the variability from exposure to exposure can be used to estimate the uncertainty.

Robin

Edited for typos
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Re: VV Cep spectroscopy reference star ?

Postby Phil Bennett » Tue Sep 01, 2015 4:58 pm

Thilo wrote:
I wouldn't agree with this statement in general, without having described the method to compute S/N and without describing the method used for filtering. It is often believed that filtering (like binning) improves signal. In fact, this is not generally true, as S/N will remain in the data while only spatial information is blurred across pixels. Therefore, result and computed S/N depends on the question, if the spatial resolution will be changed by the filter (e.g. using binning) or not.

For the simple case of pixel binning it can be shown, that pixel binning for example is NOT a method to improve S/N: http://www.astroinformatics.de/index.ph ... &Itemid=69

Summary: The theory is consistent here with the simple observation, that no fainter stars will appear in an astronomical image when applying binning to the original image. ;)

The case of spectroscopy and using any arbitrary method of one-dimensional filtering will be different from this, however. I never thought about that in more depth, so far.

This isn't completely the case. If the source is extended, e.g., nebulosity on the sky, or in the case of spectroscopy, a continuous stellar spectrum, binning *will* improve the S/N when the noise is dominated by photon (Poisson) statistics.

In this case, the mean signal on a detector element (or "bin") is proportional to the number of photons N collected by the telescope/detector or telescope/spectrograph/detector optical system. The error, or statistical uncertainty of the mean is proportional to the square root of N. Therefore, the signal-to-noise ratio or S/N is just the ratio of these values, and so is also proportional to N/Sqrt(N), i.e. to Sqrt(N).

Binning is simply a post-observation way of making the detector pixels larger, at the expense of (spatial or spectral) resolution, and so results in more photons being collected by the larger pixels (bins). It will result in an increase of S/N for the binned spectrum (but at the price of lower resolution).

Coadding individual images or spectra will also result in a lower S/N for exactly the same reason: more photons are collected per pixel or detector element.

The reason why binning a region around a faint star doesn't increase the S/N and result in more, fainter stars appearing in the field, is that the faint star is a point source that is unresolved by the detector. The surrounding pixels contain very few photons (or else obvious stellar images would be present). Therefore, binning the region around the faint star doesn't result in a significant increase in photons in the rebinned image pixel, because essentially all of the photons in the rebinned image of the star come from the original pixel containing that star. Binning only helps if the pixels being combined have photons to contribute, i.e., if the source on the sky is spatially extended, or if the spectrum is continuous.

For an example of how coadding independent channels of FUSE (Far Ultraviolet Spectroscopic Explorer) observations of 31 Cygni improves the coadded spectrum see Fig 2 of Bauer & Bennett (2014; ApJS 211, 27). The paper can be found here:
http://iopscience.iop.org/0067-0049/211/2/27/pdf/apjs_211_2_27.pdf


I hope this makes the situation a bit clearer.

Phil
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Re: VV Cep spectroscopy reference star ?

Postby Phil Bennett » Tue Sep 01, 2015 5:02 pm

Correction: that line in my previous post should read:
Coadding individual images or spectra will also result in a *higher* (not lower) S/N for exactly the same reason: more photons are collected per pixel or detector element.

Phil
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Re: VV Cep spectroscopy reference star ?

Postby Thilo Bauer » Tue Sep 01, 2015 6:19 pm

Hi Phil,

Phil Bennett wrote:This isn't completely the case. If the source is extended, e.g., nebulosity on the sky, or in the case of spectroscopy, a continuous stellar spectrum, binning *will* improve the S/N when the noise is dominated by photon (Poisson) statistics.


Generally, this is the case of incoherent light distributed across spatially independent regions of a nebula, but "merged" in the focal plane of the telescope. Therefore, sources of the signal are independent, may include different radial velocities, signatures of emission, chemical abundances... I would not really expect an increase of "signal" or S/N - but loss of information.

Phil Bennett wrote:Binning is simply a post-observation way of making the detector pixels larger, at the expense of (spatial or spectral) resolution, and so results in more photons being collected by the larger pixels (bins). It will result in an increase of S/N for the binned spectrum (but at the price of lower resolution).


Absolute d'accord: Binning is a post-processing step! Therefore, one cannot expect an increase of S/N. This is simply because the physical law of energy conservation would be violated, if an increase of signal is expected to be found. It is physically impossible to gain more photons by just processing an image. But gain of S/N will exactly mean this: gain of photo-counts to overcome the limitation that intensity and noise follow a square-root like relationship. Therefore, the question is: Where do these photo-counts come from? What information will be destroyed by just adding them (loss of spatial information, loss of spectral resolution, etc.).

Phil Bennett wrote:Coadding individual images or spectra will also result in a lower S/N for exactly the same reason: more photons are collected per pixel or detector element.


This statement is true, because energy conservation is not violated for this case. integration of photo events over time collects more light and thus energy.

Phil Bennett wrote:The reason why binning a region around a faint star doesn't increase the S/N and result in more, fainter stars appearing in the field, is that the faint star is a point source that is unresolved by the detector.


Try to think of the content of a spectral signature like a "point-source" having at least one dimensions: wavelength. Thus one-dimensional binning of a spectrum along the spectral dispersion should perform like binning of a two-dimensional image: No gain of signal, but destruction of spectral (=spatial) information.

Binning of a point-like light source (like a stellar source) vertical to the dispersion direction (e.g. to correct bad seeing or image motion) should behave like coadding images. This is because the light is, of course, still incoherent, but the point source could be thought of having no spatial information. In this case we are allowed to just add pixels vertical to spectral dispersion without loss of (spatial) information. I will ignore the case of super-resolution for making the discussion more easy.

- Yes, if thinking carefully about it, it should be like what I wrote.

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Re: VV Cep spectroscopy reference star ?

Postby Thilo Bauer » Thu Aug 10, 2017 5:54 pm

Just came back to this discussion, which seems a bit old, bit still up-to-date, when it comes to current observations of the ongoing occultation.

Yes, Olivier, I prefer a calibration star, which is very well known and flux calibrated, esp. when it comes to the question how to calibrate, what's going on in the far blue during the occultation of the binary system.

Ironically, the flux and magnitude of Vega has been corrected by Bohlin & Gilliland (2004). So Vega is no longer zero-point of stellar magnitudes. The paper also mentioned, however, results were based on over-exposed images and certain non-linearities. So there still are doubts about our best known magnitude reference zero-point. :D

Nevertheless, alpha Lyr ist still my favorite. Probably the flux standards provided by ESO should be taken into consideration.
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