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Shot Noise -another variable?


Merlin66

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So it sounds like it is measuring the mean and standard deviation (probably) of a set of pixels it assumes to be of equal flux (i.e. flat continuum). The SNR it is probably reporting is then mean/std-dev; and probably that is a SNR per pixel.

That's a fair way to start off -- but it is going to be a bit off if you are interested in measuring emission/absorption lines.

What is the resolution of your spectrograph (how many pixels does a monochromatic image of the slit project onto?). If, for example, you have three pixels per resolution element, your SNR_per_res is sqrt(3)*SNR_per_pixel -- because you can effectively average 3 pixels without losing any information in the spectrum.

What is your science goal with this project BTW Ken?

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I'm using one of my Spectra-L200 Littrow spectroscopes.

With a 7 micron pixel size I can get the Nyquist sampling above 2 with an average star image on the slit.

I can get normally a 3-4 pixel slit size on the image, and a resolution of 1.2A FWHM.

If and when I get organised (!??) I want to work on WR stars.

Ken

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That's a pretty decent resolution (R~7000?); you can do some pretty interesting stuff on stars at that sort of resolution. The converse of course is that you're going to be struggling for light a little bit. I'd suggest you maybe want to bin 2x1 so that you can get the slit down to 2 pixels, and that will help reduce your read-noise contribution.

For WR**, you're mostly going to be interested in the emission lines I guess? To get SNR estimate for this, you want to compare how much flux is in the emission line relative to the stddev of the underlying continuum. So you need to subtract of the continuum, sum up the flux in the line, and compare it to the stddev either side of the line.

The number you get from vspec is a good indicator, but is probably going to be an underestimate for bright emission lines.

** for other readers: WR = Wolf-Rayet -- very massive stars which are blowing off their outer atmospheres

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Thanks for the input.

I'm matching the slit width to the star size, taking into account the Nyquist requirement. The current slit height is 3mm, so I may look at reducing that to 1mm or so..

Trying to keep the star guided on the centre of the slit ( so it doesn't spread up the slit during exposure) is "interesting"

I've started to process the SNR data I've collected using a Fluoro reference spectrum (for convenience)...hope to show the results soon.

Ken

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Trying to keep the star guided on the centre of the slit ( so it doesn't spread up the slit during exposure) is "interesting"

Isn't it :)

Depending on your slit size compared to the seeing, you also need to keep it well aligned across the slit -- or you'll change the effective wavelength scale of your spectrum. Though that is only a worry if you want to start trying to measure wavelengths/velocities smaller than your resolution.

Looking forward to seeing your spectra!

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Some early data:

Same camera Atik16ic, same temp, same spectrum, same central wavelength.

Using the fit image in Vspec to prepare a profile.

Based on a comparison of a single 20 sec exposure (L1)

Measuring an emission line at the same position in each frame, x=436, and a sum of pixels Y=20-44 (44 pixel height)

SNR measured on the continuum X=463-563 (100 pixel width)

Subsequent exposure were 2 x 10s (L2), 4 x 5s (L3), 5 x 4s (L4), 10 x 2s(L5) all summed.

Maximum line intensity:

L1 234586

L2 326833

L3 342280

L4 334551

L5 429814

SNR

L1 75.15

L2 103.59

L3 101.47

L4 103.6

L5 78.45

So, based on the raw data 2 x 10s gives a better SNR than the 1 x 20s and better that all the other subs; 10 x 2s SNR is almost the same as 1 x 20s

I'm still processing the darks to see what impact they will have.

Ken

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Why the need to scale?

I'm looking for the maximum signal I can get for the spectrum..if the sum of the subs gives a higher max then that may be better for me.

The continuum (background in the spectrum) rises at the same ratio - almost, as the max signal.

It's interesting how the SNR changes....

The SNR in the first image is 78 and the second 103.6 - a 30% improvement.

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Sorry, I meant if you are going to compare them visually, THEN you need to scale them to the same min/max.

The 20sec one, is it saturated? If so, that would reduce the SNR (as you can't get a signal higher than the max so you only managed to increase the noise).

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Maximum line intensity:

L1 234586

L2 326833

L3 342280

L4 334551

L5 429814

This is very odd. It suggests that the brightness of your lamp is changing with time (as most gas discharge lamps do). How long did you let the lamp warm up for? You might want to interleave exposures of the same length to check the evolution of the lamp -- say a 10s exposure between every set to make sure the lamp is staying at constant brightness.

There may also be an effect of extra dark current coming in from the extra readout time of multiple exposures. As I understand it you haven't subtracted darks from these images?

It would be very interesting to see a 'lamps-off' frame also -- not a dark, but an exposure with the lamp turned off. That will help you calibrate any background light you might have.

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I've double checked and can confirm the results...yes the 20s exposure definately has a lower SNR.

The spectrum was taken using a fluoro lamp and 25micron slit so, there's no variation with the lamp intensity.... everything was pretty stable. The camera had cooled for at least 20mins before the series of images were taken.

The maximum line intensity position (X axis) over all the exposures never varied so the grating location would appear to be stable also.

Food for thought...

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I've double checked and can confirm the results...yes the 20s exposure definately has a lower SNR.

I don't understand how that can happen physically.

Have you looked at the linearity of the detector? Maybe the 20s exposure is going into the non-linear response region; but that's pretty unusual with modern detectors.

What is the individual peak line flux in the 20,10,5,4 and 2s exposures? does it form a nice line? it should...

I'm a bit confused when you say you measure the continuum from X=463-563 -- is that the dispersion direction I assume?? It doesn't look in the image like you have very much continuum -- as you'd expect with flouro-lamp. Maybe I'm misunderstanding what you mean?

Very interesting stuff Ken. Would you be happy to make your fits files available??

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T-D,

The dispersion is along the X axis...yes there is some continuum from the fluoro in this region of the spectrum.

I'll get some more data on the individual sub exposures (Max Line intensity ADU, SNR)

If you drop me a PM with your email I can send any/all original Fits files.

I was convinced from the earlier discussions that the 1 x 20s (L1) would have been the best???

The story continues.......

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I've re-tabulated the data ( and found a couple of errors)

The attached spreadsheet shows that all the exposures other than the short 2sec give a linear growth in ADU.

The single 2sec has a higher ADU than any of the rest which I can only assume is due to camera noise (See the Craig Stark summary for details on the ATiK16ic)

I have the raw fits files available if anyone else wants to check the results.

The data appears to show that the spectral SNR is improved with stacking - longer subs better (see graph).

Ken

SNR_trials_sept2010.zip

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