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Low resolution spectroscopy: improving visual resolution by 2nd derivative

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#1 mwr

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Posted 20 October 2019 - 10:08 AM

Overlapping peaks in spectroscopy can be visually resolved by applying numerical differentiation. The second derivative of a spectrum produces negative peaks and eventually achives enough resolution for two or more peaks to be identified as separate minima. 

 

I have applied this processing strategy to the low resolution spectrum of the cat eye nebula (NGC 6543) which I had previously posted by using RSpec (https://www.cloudyni...cat-eye-nebula/).

 

Re-processing was done in Excel using a Savitzky-Golay 11-point filter:

 

Cat_eye_derivative.jpg

 

The [O III] and H beta peaks can now be resolved. Also the resolution of H alpha and [N II] is improved. However, smaller peaks like H gamma and He I become to weak.

 

The manual processing in Excel is quite cumbersome: Are there software packages available that allow the computation of derivative spectra in amateur spectroscopy?


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#2 Organic Astrochemist

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Posted 20 October 2019 - 05:06 PM

I think that’s a really neat idea. I’m not entirely sure what new information is revealed, only made more obvious perhaps. I can see where H-beta and the [OIII] 4959 and 5007 peaks (humps) are in the original spectrum.

I think with the H-alpha and the [NII] peaks at 656.3 and 658.4 nm respectively, this procedure with slitless spectroscopy could be dangerous. The two dimensional structure of the nebula could produce two spectral peaks because the x-axis in the image corresponds to wavelengths in the spectrum — its not a pointlike star. So maybe the two peaks that you see around H-alpha show the width of the planetary nebula in your image.
I know you’re not suggesting that amplitudes of the derivative spectrum are the same as the original but look at the relative amplitudes (or EW) of H-alpha and [NII] in this slit-based spectrum:
http://www.astrosurf...877_cbuil_2.png

I’d still be interested in any application of the technique. Along a similar vein, I have seen some pros do difference spectroscopy (subtracting one spectrum from another, especially when there’s a temporal change). I’ve found it prone to subtraction artefacts but I’d like to see if anyone has tried that too.

Edited by Organic Astrochemist, 20 October 2019 - 05:19 PM.

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#3 mwr

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Posted 21 October 2019 - 12:51 AM

I think that’s a really neat idea. I’m not entirely sure what new information is revealed, only made more obvious perhaps. I can see where H-beta and the [OIII] 4959 and 5007 peaks (humps) are in the original spectrum

Absolutely right! No new information is revealed. It is only a visual enhancement and the physical resolution remains unchanged.

 

 

 

The two dimensional structure of the nebula could produce two spectral peaks because the x-axis in the image corresponds to wavelengths in the spectrum — its not a pointlike star. So maybe the two peaks that you see around H-alpha show the width of the planetary nebula in your image.

Very good point! I have assumed that the inhomogenous structure of the nebula along the x-axis is cancelled out by low instrumental resolution, spectral coma and seeing. This may be only true for very small planetary nebula. I will re-process the spectra by including the zero-order image of the nebula. This should be a good test for the validity of my assumption.


Edited by mwr, 21 October 2019 - 03:09 AM.


#4 mwr

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Posted 21 October 2019 - 02:30 PM

I will re-process the spectra by including the zero-order image of the nebula. This should be a good test for the validity of my assumption.

I have re-processed the spectrum of NGC 7027 which contained the zero order image of this small planetary nebula.

 

NGC 7027 / SA 100 spectrum

 

The zero order peak showed no splitting, so I assume that the visual resolution of [N II] and H alpha is not an artifact. 

 

The relative intensities of the peaks are severely altered when compared to CCD spectra of the same object due to conversion of the DSLR RGB image file to a luminace image file using the RGB to HSV conversion function of GIMP. 

 

A good introduction to the use of derivative techniques in astronomical spectroscopy can be found here:

 

http://adsabs.harvar...Ap&SS..89..377B


Edited by mwr, 22 October 2019 - 03:45 AM.


#5 robin_astro

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Posted 22 October 2019 - 08:20 AM

An interesting technique but I would urge caution.

 

A potential difficulty with Star Analyser spectra is the transfer function (the intrinsic shape of an infinitely narrow line) is not very well defined and varies along the spectrum due to aberrations.  See Christian Buil's analysis here for example

http://www.astrosurf...e1/spectro2.htm

 

Add to that the effect of telescope optics (eg the shadow of the secondary when slightly out of focus) and in this case where the line is effectively an image of the PN, the morphology of the target, and the shape can be quite complex and could potentially generate spurious features using the second derivative method. You could perhaps check this though measuring a well resolved narrow single line.

 

There are techniques around for resolving blended lines, usually using deconvolution where you assume the shape of the line and express the blended line as a sum of these (sort of like a fourier transform if you are familiar with this)  I think programs like SPLAT and IRAF have tools for this.  Note the measured shape of an unblended line is a combination of the resolution of the instrument (transfer function) and the actual line shape. Which dominates depends on the resolution of the spectrograph relative to the line width.  

 

Cheers

Robin


Edited by robin_astro, 22 October 2019 - 08:23 AM.

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#6 mwr

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Posted 22 October 2019 - 12:10 PM

An interesting technique but I would urge caution.

 

A potential difficulty with Star Analyser spectra is the transfer function (the intrinsic shape of an infinitely narrow line) is not very well defined and varies along the spectrum due to aberrations. 

Thanks Robin! I wasn't aware of the wavelenght-dependency of the spectral coma. Can you recommend the use of a prism in front of the grating to reduce the chromatic coma? 



#7 robin_astro

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Posted 22 October 2019 - 05:08 PM

Thanks Robin! I wasn't aware of the wavelenght-dependency of the spectral coma. Can you recommend the use of a prism in front of the grating to reduce the chromatic coma? 

There is also the effect on focus due to field curvature which the wedge prism can help with too (Paton Hawksley market one mounted in a 1.25 inch cell which can be added to the Star Analyser) but to be honest I think the improvement with the SA100 is pretty marginal. (It probably has more effect with the SA200 where the dispersion angles are larger)  There are  disadvantages too such as the non linear calibration, the dispersion in the zero order making it difficult to use as a zero point and the astigmatism it introduces. There is a bit of a discussion on it here.

https://www.cloudyni...copy/?p=9671911


Edited by robin_astro, 22 October 2019 - 05:09 PM.

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#8 Organic Astrochemist

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Posted 22 October 2019 - 08:10 PM

I have re-processed the spectrum of NGC 7027 which contained the zero order image of this small planetary nebula.



The zero order peak showed no splitting, so I assume that the visual resolution of [N II] and H alpha is not an artifact.

The relative intensities of the peaks are severely altered when compared to CCD spectra of the same object due to conversion of the DSLR RGB image file to a luminace image file using the RGB to HSV conversion function of GIMP.

A good introduction to the use of derivative techniques in astronomical spectroscopy can be found here:

http://adsabs.harvar...Ap&SS..89..377B

Interesting article. Based on the results there I’m surprised that you can’t resolve [OIII] 495.9 nm and 500.7 nm although separated by more than [NII] and H-alpha. Also the intensities of the latter two are not equal, so the 2nd derivative spectrum doesn’t look like what is seen in the article.

Here’s my recent spectrum of NGC 7027. I can see [OIII] at 495.9 no but not much for [NII]

https://www.cloudyni...-1569193290.png

I didn’t identify Some of those other lines. Are they from the Wolf-Rayet central star? I think I had some field stars in my spectrum.

Edited by Organic Astrochemist, 22 October 2019 - 08:15 PM.


#9 mwr

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Posted 23 October 2019 - 12:46 AM

Based on the results there I’m surprised that you can’t resolve [OIII] 495.9 nm and 500.7 nm although separated by more than [NII] and H-alpha. Also the intensities of the latter two are not equal, so the 2nd derivative spectrum doesn’t look like what is seen in the article.

I also realized these inconsistencies. As Robin already has mentioned the lineshapes of the peaks may be severely altered by the transfer function which causes a non-Gaussian lineshape (taken from Wischnewski: "Astronomy in Theory and Practice"; only available in german):

 

coma.jpg

 

This is a real "killer objection" against the use of derivative spectroscopy for processing SA 100 spectra. However, I really enjoyed having clarified this during the dicussion with you and Robin. Beautiful science!

 

 


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#10 Organic Astrochemist

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Posted 24 October 2019 - 08:08 AM

Agreed. Thank you for sharing the topic.

#11 mwr

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Posted 25 October 2019 - 11:36 AM

Here’s my recent spectrum of NGC 7027. I can see [OIII] at 495.9 no but not much for [NII]

https://www.cloudyni...-1569193290.png

I didn’t identify Some of those other lines. Are they from the Wolf-Rayet central star? I think I had some field stars in my spectrum.

I have processed my spectrum of NGC 7027 in RSpec and compared it to yours:

 

cat_eye_compare.jpg

 

Indeed, two small peaks around 160 and 485 nm can be probably attributed to field stars. 

 

Apart from that, I'm really surprised that the spectra are quite comparable as far as line-shapes and -intensities are concerned (despite our very different imaging systems)!


Edited by mwr, 25 October 2019 - 11:40 AM.


#12 Organic Astrochemist

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Posted 25 October 2019 - 09:52 PM

Our systems are rather different. Robin understands optics much better than I do so hopefully he'll chime in if I say something stupid.

I think it might be helpful if we zoom in on these spectra. Here's my contribution. (In RSpec one can make the data points visible)

NGC 7027 O III.png

I think I've made some resolution of the emissions of [O III] at 495.9 nm and 500.7 nm. This affords a resolving power of ~ 100 at this wavelength given by the formula 495.9/(500.7-495.9).

 

I'm not sure your system affords such resolution but I'd be happy to see the zoom. My H-beta peak gets down pretty close to the baseline at 491 nm.

 

The same calculation suggests that a resolving power of ~ 300 would be required to resolve H-alpha and [N II], which I clearly don't have.

 

I think that in a slitless system, in addition to grating line spacing and distance between grating and camera, both the telescope aperture and also the focal ratio affect resolution because of their effect on spot size. Seeing also plays a great role. I have great seeing here in Florida, but this spectrum was taken in Canada. I think that both smaller aperture and faster focal ratio will afford smaller spot sizes and therefore the potential for greater resolution. Camera pixel size is also important; mine are 2.9 um, yours are 5.19 um.

 

Another difference between our systems, that I think is relevant here, is light gathering power of the telescope. In this I think your telescope is superior, but that means you will also have more field stars superimposed on the spectrum. Comparing our two spectra, I don't have much confidence in any peak that I can't see in BOTH spectra. I think this is a limitation of slitless spectroscopy. Unfortunately, most other spectra (like this) will be from slit systems, which will sample only a portion of the nebula that usually doesn't include the central star. I haven't found the spectrum of this central star. 


Edited by Organic Astrochemist, 25 October 2019 - 10:19 PM.


#13 mwr

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Posted 26 October 2019 - 04:13 AM

 

I'm not sure your system affords such resolution but I'd be happy to see the zoom. My H-beta peak gets down pretty close to the baseline at 491 nm.

 

Here is the zoom in:

 

NGC_7027.jpg

 

H beta is even not fully resolved from [O III]. As far as resolution is concerned I have obviously  a "ulta-low resolution" system. The sensor to grating-distance during the aquisition was only 7 cm and is thus far from its optimum which would be around 20 cm. So I have room for improvement....

Anyway, your "grab and go" system seems to be pretty well tuned. 

 

The central star of NGC 7027 is very difficult to detect and probably not visible in the SA 100 spectrum:

 

http://adsabs.harvar...ApJ...333..193J

 

http://adsabs.harvar...ApJ...353..200H

 

 



#14 robin_astro

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Posted 26 October 2019 - 07:56 AM

If you want to try getting the highest possible resolution out of  slitless grating systems then the work of Uwe Zurmuhl is worth looking at. By using very high dispersions and various combinations of wedge prisms he has reached resolving powers of over 1000. You can read about his remarkable achievements here in the German VdS spectroscopy journal

http://spektroskopie.../Spektrum51.pdf

pages 10-18

 

Cheers

Robin


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#15 Organic Astrochemist

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Posted 26 October 2019 - 02:37 PM

Here is the zoom in:

NGC_7027.jpg

H beta is even not fully resolved from [O III]. As far as resolution is concerned I have obviously a "ulta-low resolution" system. The sensor to grating-distance during the aquisition was only 7 cm and is thus far from its optimum which would be around 20 cm. So I have room for improvement....
Anyway, your "grab and go" system seems to be pretty well tuned.

The central star of NGC 7027 is very difficult to detect and probably not visible in the SA 100 spectrum:

http://adsabs.harvar...ApJ...333..193J

http://adsabs.harvar...ApJ...353..200H

I don’t think your resolution is that bad — greater than 30 maybe even 50.

As The article that Robin provided shows, my system is nowhere near optimized for resolution. I also wanted sensitivity and more than one spectrum to fit on the small (inexpensive) sensor at once.

Also in evidence in that article is the great expense required to increase resolution (those ATIK cameras aren’t cheap). Also the time required and the limited targets. Not what I was looking for.

If anyone was looking for a cheap system with reasonable resolution this might be my suggestion:

https://www.rspec-as.../star-analyser/

https://www.skywatch...0-apo-refractor

https://astronomy-im...290mm-mini-mono

https://www.ioptron....uct-p/3200-.htm

I haven’t tried the 50ED so I don’t know how good the focuser is but it’s less than half the price of my Borg.

Some kind of finderscope or camera is also necessary.

Edited by Organic Astrochemist, 26 October 2019 - 02:42 PM.


#16 robin_astro

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Posted 26 October 2019 - 03:14 PM

Yes Uwe's setups are just an example of what can be done if you are interested and are not particularly easy to use. For me the Star Analyser is about simplicity and ease of use. (In Europe the Star Analyser is significantly cheaper direct from the manufacturer) For a minimum cost spectroscopy setup I would probably go for a small  say 5- 6 inch Newtonian to be sure of freedom from chromatic aberrations. I have seen some ED  refractors to be far from free of chromatism when used for spectroscopy. 

 

Cheers

Robin


Edited by robin_astro, 26 October 2019 - 03:14 PM.


#17 Organic Astrochemist

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Posted 26 October 2019 - 04:16 PM

You are absolutely right. I started out with a cheap reflector. I’m sure that saved me lots of trouble. My first refractor wasn’t an apo and the results were amusing.

chromatism

I’m happy with the Borg. It seems to have color under control, it’s very light and far from the most expensive APO.


Edited by Organic Astrochemist, 26 October 2019 - 04:55 PM.



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