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My 3D-printed DIY spectrograph

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#1 syam

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Posted 19 January 2021 - 03:08 PM

50831735836_2461c71fb5_b.jpgMy DIY spectroscope by First Last, on Flickr

 

This is too heavy (~1 kg) to be used with a telescope, albeit with a choice of smaller collimator/camera lenses this might work. I designed and built this primarily to test astro filters, and to try to get a spectrum of my light pollution. At the core, there is a 1000 l/mm diffraction grating slide (5$ on ebay). I use an old SLR 50mm f/2.0 lens by Ricoh as the collimator lens, a C-mount zoom f1.2 Computar lens as the camera lens, and a cheap B&W C-mount astrocamera ToupTek.

 

The 3D printer design is fully parametric (using free Autodesk Fusion 360), so can be adjusted for many other lenses, cameras, slits, and gratings. The design can be found here:

 

https://www.thingive...m/thing:4729351

 

The software used:

  • SharpCap - to record the spectra, and dark frames. I use ROI feature to limit myself to a small vertical  fraction of the spectrum. The only SharpCap regime which allows me to average spectra frames on the fly is the "Dark frame creation" option. I use it for both spectra, and dark frame imaging. The "Live stacking" feature messes up with brightness for some reason (using fits, png etc), so my dark frame actually becomes brighter than the spectrum, so I couldn't use it.

  • ImageMagick: to subtract dark frame, and produce a table of the spectrum data from PNG files.

  • My own Octave (MatLab) scripts, which autodetect all spectral lines, do non-linear Gaussian fitting to each line (for more accurate center position determination), and calibrate spectrometer using a slightly non-linear (parabolic) scaling between pixel coordinates and the wavelength.

 

After careful calibration (using a CFL bulb as the target; see https://commons.wiki...ks_labelled.gif ), I achieved the std error of 1.5nm (pixels) for the 18 spectral lines (blue line is my spectrum, red lines are the actual wavelengths of the 18 lines):

 

calib3.png


Edited by syam, 20 January 2021 - 10:52 AM.

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#2 aleigh

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Posted 19 January 2021 - 03:28 PM

That's pretty sweet. 



#3 Borodog

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Posted 19 January 2021 - 04:34 PM

That's excellent work, syam. I will be interested to see what the spectrum of your light pollution is.



#4 Borodog

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Posted 19 January 2021 - 04:40 PM

Do you think your remaining error is largely down to field curvature? If so you could perhaps reverse engineer a correction function for the spectrum.



#5 syam

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Posted 19 January 2021 - 04:54 PM

Do you think your remaining error is largely down to field curvature? If so you could perhaps reverse engineer a correction function for the spectrum.

My spectral resolution (with the slit ~0.1mm) is around the same number (1.5 - 2 nm), so this kind of error is expected. With a thinner slit I might be able to find a better model, but I'll loose even more light.



#6 syam

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Posted 20 January 2021 - 10:51 AM

Actually things are much better - my reported std was actually in pixels, not nm (my bad!). In terms of nanometers, my spectrometer's accuracy is 0.35 nm.

 

...  And if I discard 3 lines out of 18, with the largest residuals, my std goes down to 0.16 nm. But this is a slippery slope :)

 

The final calibration expression is

 

lambda (nm) = -0.000012353*x^2   -  0.236130442*x +   714.443352909

 

Here x is the pixel coordinate of the center of the detected line (full range: 0...1279).

 

So each pixel is 0.236 nm. The nonlinear correction (the one with x^2) is up to 20 nm, which is rather significant. Linear approximation definitely doesn't work here.


Edited by syam, 20 January 2021 - 11:16 AM.


#7 JoeVanGeaux

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Posted 20 January 2021 - 10:47 PM

I have been diving into spectroscopy for several months now (no equipment other than a few small scopes) and still stumble a bit when it comes to comparing spectrograph setups in terms of resolution.  You give a few numbers, here, that almost tempts me to make that calculation (as an "R-factor).  So, would you indulge me and tell me what is the resolution of your rig?

Also, I wondered how I missed this on Thingiverse since I scoured it just days ago but I see its a really new file. Great to see that!

(I wish the files could also be in OpenScad, though, since I have a few old lenses laying around that I may be able to attempt something similar.  If I study the STL well enough, I may be able to make a mod or two to the STL files.)

 

Thanks for sharing!

Joe

 

Edited:  I almost forgot, what filament are you using?  I have some black PLA and black PETG and those two look so dark on my printer bed, its hard for my eyes to focus on any detail, but when held up to the light, I'd consider them both to be fairly translucent.  Such light leakage is something I know other 3D printed spectrographs suffer from.


Edited by JoeVanGeaux, 20 January 2021 - 10:56 PM.


#8 syam

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Posted 21 January 2021 - 08:42 AM

I have been diving into spectroscopy for several months now (no equipment other than a few small scopes) and still stumble a bit when it comes to comparing spectrograph setups in terms of resolution.  You give a few numbers, here, that almost tempts me to make that calculation (as an "R-factor).  So, would you indulge me and tell me what is the resolution of your rig?

Also, I wondered how I missed this on Thingiverse since I scoured it just days ago but I see its a really new file. Great to see that!

(I wish the files could also be in OpenScad, though, since I have a few old lenses laying around that I may be able to attempt something similar.  If I study the STL well enough, I may be able to make a mod or two to the STL files.)

 

Thanks for sharing!

Joe

 

Edited:  I almost forgot, what filament are you using?  I have some black PLA and black PETG and those two look so dark on my printer bed, its hard for my eyes to focus on any detail, but when held up to the light, I'd consider them both to be fairly translucent.  Such light leakage is something I know other 3D printed spectrographs suffer from.

Why don't you use the Autodesk Fusion 360 file I provided? The software is free (for non-commercial use), and in my experience much nicer than OpenScad. My model is fully parametric - you simply change some parameters in the parameters list, and the whole 3D model adjusts. For example, if you choose smaller lenses, the whole enclosure will become smaller.

 

My spectral resolution is fully determined by the width of the slit. My magnification is 12.5mm/50mm (ratio of the focal lengths) = 0.25. If the slit width is 0.1mm, it's image will have the width of 0.025mm.  My sensor width is 4.8 mm, so the R-number is 4.8/0.025 = 192. The full spectral range (from my calibration parabolic equation) is 392 ... 714 nm, so the interval is 322 nm. The spectral resolution is then 322nm/192 = 1.7 nm. I still have a room for improvement - my pixel size is only 0.24 nm, which would by my ultimate resolution limit - but for that I'd have to use a much more narrow slit - 15 um. I'm already struggling with not enough light with my current slit width, so I don't think I do want to go for a better resolution. In fact, if I am to attempt to measure spectrum of sky glow, I suspect I'll have to make the slit wider - may be 0.5mm or so.

 

I used ABS (the only black filament I had) which was a mistake - there was a dramatic vertical shrinkage, so my camera lens wouldn't fit, and I had to spend ~2 hours filing/sanding it. Black PLA would be much better. My design is light leak-free - very thick walls (4mm or more), large interlocking parts on the two enclosure halves. You can always sand the interior and paint it with black acrylic paint - I used this in the past for other projects, it's comes out nice.


Edited by syam, 21 January 2021 - 08:45 AM.

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#9 syam

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Posted 21 January 2021 - 10:07 AM

The first practical application of my spectrometer. I just measured the spectral transmission curve of my non-branded OIII filter I got cheaply (~$35 shipped) on aliexpress. It was advertised as a 10 nm filter. And here are my measurements.

 

The highest transmission (90%) is at 506.5nm, which is a bit off the two OIII lines (two vertical black lines). At the main OIII line (500.7nm), the transmission is 83%, at the secondary one (495.9nm) it is 64%.

 

But the biggest disappointment is with the width of the spectral window (at the 50% height of the peak) - instead of the advertised 10 nm, I measured it to be 23.4 nm. So it's likely from the "25nm" cheapest variety of such filters.

 

The strongest background suppression is around 600 nm, with the contrast (relative to the central peak) ~640x.  But then I see contrast dropping significantly both on the far blue and red ends, when the contrast becomes only ~10x (blue end) and ~15x (red end).

 

Now the big question is what is my sky glow spectrum (something I'll try to measure with my spectroscope) - this will determine what is the overall contrast improvement this filter provides.

 

OIII.png



#10 syam

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Posted 21 January 2021 - 10:48 AM

My second non-branded filter I tested. It has no markings, and I suspect I got it as an "UHC" filter very cheaply on ebay a few years back. So let's see what it actually does:

 

UHC1.png

 

I can see a peak around H-beta (thin red line) and OIII (two black lines), with the transmission ~80%, and width 32 nm. (The interval is 483 - 515 nm).

 

So far so good. But the H-alpha line (thick red line) is severely absorbed (transmission 6.5%), so not useful there. Instead, the filter has a far-red transmission peak (60% transmission) around 685nm. This is presumably for the SII doublet line (~672nm; two green lines), where the transmission is okay (47%).

 

On the far blue end, the contrast becomes low, ~6x.  There is also a small transmission peak (7.5%) at  458 nm - likely not by design, just a side effect.

 

Compared to proper UHC filters (like Astronomik):

 

  • The central peak for OIII and H-beta is reasonable (interval 483-515nm, vs Astronomik's 480-505nm): ~30% wider, 15% lower transmission.
  • H-alpha line is gutted, unlike Astronomik which handles it perfectly.
  • The SII doublet is covered, though transmission (47%) is much worse than Astronomik (95%).

 

So overall not great, but should still be semi-usable.


Edited by syam, 21 January 2021 - 10:50 AM.


#11 JoeVanGeaux

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Posted 21 January 2021 - 12:47 PM

Why don't you use the Autodesk Fusion 360 file I provided? The software is free (for non-commercial use), and in my experience much nicer than OpenScad. My model is fully parametric - you simply change some parameters in the parameters list, and the whole 3D model adjusts. For example, if you choose smaller lenses, the whole enclosure will become smaller.

I don't like cloud-based anything and I believe that where everyone's files go that use the free Fusion 360 (please, correct me if I'm wrong).  I don't want to digress too far, but many people are putting their lifetime collection of photos and files there and I can't help but think its vulnerable to loss - to say the least.

Anyway, I may just have to give up and give in to Fusion 360.  And, I do much prefer parametric modeling but others, like Blender, allow for "cute" little toy characters with amorphous shapes with 3 or 4 fingers.  But that's not for me (thank you very much), though it would be nice to make some "softer" edges without needing "Mankowski" that hungrily chews up CPU time!)

I frequently use Krylon Fusion spray paint ( I assume its available up north) after sanding pieces to remove stringing remnants and too sharp edges, etc and this also gives the printed surfaces a lot of "tooth" for the paint to bind. 

Thanks for sharing your work!

 

Joe



#12 syam

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Posted 21 January 2021 - 12:59 PM

I don't like cloud-based anything and I believe that where everyone's files go that use the free Fusion 360 (please, correct me if I'm wrong).  I don't want to digress too far, but many people are putting their lifetime collection of photos and files there and I can't help but think its vulnerable to loss - to say the least.

Anyway, I may just have to give up and give in to Fusion 360.  And, I do much prefer parametric modeling but others, like Blender, allow for "cute" little toy characters with amorphous shapes with 3 or 4 fingers.  But that's not for me (thank you very much), though it would be nice to make some "softer" edges without needing "Mankowski" that hungrily chews up CPU time!)

I frequently use Krylon Fusion spray paint ( I assume its available up north) after sanding pieces to remove stringing remnants and too sharp edges, etc and this also gives the printed surfaces a lot of "tooth" for the paint to bind. 

Thanks for sharing your work!

 

Joe

Cloud nature of Fusion 360 doesn't bother me - you can always export the file for local storage (that's how I produced the model file for my thingiverse page). So you can treat the cloud version as your "backup" copy.


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#13 syam

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Posted 21 January 2021 - 01:11 PM

To give you an idea how good the calibration is. Blue dots are the 17 spectral lines from the calibration target (CFL bulb) spectrum. The red curve is a (slightly) parabolic fit to the data. The spread of the points around the curve (std) is only 0.3nm.

 

calibration_curve.png


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#14 JoeVanGeaux

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Posted 22 January 2021 - 02:23 PM

syam,  it probably means nothing, but the barely visible "parabolic" curve seems to show up where you have a higher density of plotted points.  If you were to include an evenly distributed set of data points would this small amount of deviation be observed throughout?  Or, do you think its a function of how the sensor reacts to that wavelength range in the spectrum?  (Or, maybe, I just want to know how you recognized this to be a "parabolic" curve??)

I was only curious because you made a point of noting the deviation - otherwise, from the point of view of someone who knows next to nothing calibration curves for this type of  instrument, it looks really exceptional!  If you didn't mention the curve at all, my reaction would have stopped at "awesome!"  - which I think it really is, anyway!!

Joe



#15 syam

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Posted 22 January 2021 - 04:42 PM

syam,  it probably means nothing, but the barely visible "parabolic" curve seems to show up where you have a higher density of plotted points.  If you were to include an evenly distributed set of data points would this small amount of deviation be observed throughout?  Or, do you think its a function of how the sensor reacts to that wavelength range in the spectrum?  (Or, maybe, I just want to know how you recognized this to be a "parabolic" curve??)

I was only curious because you made a point of noting the deviation - otherwise, from the point of view of someone who knows next to nothing calibration curves for this type of  instrument, it looks really exceptional!  If you didn't mention the curve at all, my reaction would have stopped at "awesome!"  - which I think it really is, anyway!!

Joe

I tried linear fit, it was significantly worse (a few nm). Parabola fits the data perfectly (basically, down to the pixels size). Dots placement cannot change this. I  suspect most of the non-linearity is due to the fact that the diffraction grating is not flat - it has a fairly obvious bump in the middle. I am actually surprised that I can still get a perfect scaling with a curved grating.


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#16 Octans

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Posted 22 January 2021 - 09:20 PM

I tried linear fit, it was significantly worse (a few nm). Parabola fits the data perfectly (basically, down to the pixels size). Dots placement cannot change this. I  suspect most of the non-linearity is due to the fact that the diffraction grating is not flat - it has a fairly obvious bump in the middle. I am actually surprised that I can still get a perfect scaling with a curved grating.

It's probably just from the distortion of your camera lens. Distortions of ~1% is not unusual for a lens, and would not be easily noticeable in most normal settings. The grating not being flat could in theory degrade the sharpness of the spectrum somewhat (like a telescope looking through an old window), but probably doesn't matter in practice as it's quite thin (like how solar filter film is often slightly wrinkled without impacting image quality).


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#17 robin_astro

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Posted 23 January 2021 - 10:06 AM

The non linearity is nothing to do with the grating not being flat The dispersion of a spectrograph is non linear due to geometry and trigonometry.

 

the grating equation tells us that sin(diffraction angle) = wavelength / grating line spacing

and the distance along the spectrum = tan(diffraction angle) x the focal length of the camera lens

This is approximately linear for coarse gratings and small angles like the 100l/mm Star Analyser for example but not for the large angles with your 1200l/mm grating

 

A quadratic is a good fit but if you look close enough you will find it is not perfect. With my spectrographs a 3rd order fit is good enough within the accuracy of the measurement.

 

Cheers

Robin


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#18 syam

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Posted 23 January 2021 - 10:15 AM

The non linearity is nothing to do with the grating not being flat The dispersion of a spectrograph is non linear due to geometry and trigonometry.

 

the grating equation tells us that sin(diffraction angle) = wavelength / grating line spacing

and the distance along the spectrum = tan(diffraction angle) x the focal length of the camera lens

This is approximately linear for coarse gratings and small angles like the 100l/mm Star Analyser for example but not for the large angles with your 1200l/mm grating

 

A quadratic is a good fit but if you look close enough you will find it is not perfect. With my spectrographs a 3rd order fit is good enough within the accuracy of the measurement.

 

Cheers

Robin

 
Thanks, good point! Looking at the equations of course this is obvious. I don't think I'll need more than second order, I'm happy I got down to pixel size (which is 0.25nm).



#19 robin_astro

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Posted 23 January 2021 - 10:51 AM

 
Thanks, good point! Looking at the equations of course this is obvious. I don't think I'll need more than second order, I'm happy I got down to pixel size (which is 0.25nm).

Provided the lines are well defined, by measuring the centroid of the lines it is possible to measure the positions to sub pixel accuracy. For example the RMS error of a 3rd order fit to 15 lines for my ALPY 600 is typically 0.2 Angstrom which is equivalent to ~0.5um at the ALPY dispersion. The calibration light source is a fluorescent lamp starter, discovered by Swiss amateur Richard Walker and now used in many commercial spectrographs

https://www.ursusmaj...n-lines-5.0.pdf

 

If you have not seen it already you might also find Christian Buil's similar LORIS design interesting (back in 2003). 

http://www.astrosurf...loris/loris.htm

These can be mounted on a telescope but the big problem is how to find, focus and guide the star on the slit. Practical astronomical slit spectrographs all have built in guiders these days where you see the slit and the star field in the guide camera.

 

3D printing really is opening up spectrograph design for the amateur astronomer now though with designs like the Lowspec, UVEX and the latest from Christian Buil, the Sol'Ex for solar spectroheliography 

http://www.astrosurf.com/solex/

 

 

Cheers

Robin


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#20 syam

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Posted 23 January 2021 - 12:42 PM

Provided the lines are well defined, by measuring the centroid of the lines it is possible to measure the positions to sub pixel accuracy. For example the RMS error of a 3rd order fit to 15 lines for my ALPY 600 is typically 0.2 Angstrom which is equivalent to ~0.5um at the ALPY dispersion. The calibration light source is a fluorescent lamp starter, discovered by Swiss amateur Richard Walker and now used in many commercial spectrographs

https://www.ursusmaj...n-lines-5.0.pdf

 

If you have not seen it already you might also find Christian Buil's similar LORIS design interesting (back in 2003). 

http://www.astrosurf...loris/loris.htm

These can be mounted on a telescope but the big problem is how to find, focus and guide the star on the slit. Practical astronomical slit spectrographs all have built in guiders these days where you see the slit and the star field in the guide camera.

 

3D printing really is opening up spectrograph design for the amateur astronomer now though with designs like the Lowspec, UVEX and the latest from Christian Buil, the Sol'Ex for solar spectroheliography 

http://www.astrosurf.com/solex/

 

 

Cheers

Robin

Thanks, great references!

 

Just for the heck of it, I tried cubic polynomial fitting. It's only 17 lines, so one has to be careful no to overfit. I do use accurate line centroid computations method (I fit Gaussians into the top 10% of the line), so subpixels resolutions are quite possible.

 

Here's what I got:

 

parameter  parabola     cubic

std              0.267nm  0.184nm

 

I'd need to compute chi-square statistic to learn if the std decrease is statistically significant. But it does get into sub-pixel regime (std=0.77 pixels for cubic). The fractional accuracy of the highest order fitting parameter is 0.055 for parabola (not so shabby), but for the cubic term it's only 0.26 (the error in the parameter determination is 1/4 of the parameter value), so cubic fitting is somewhat questionable with my setup.

 

The calibration data I am using might also have non-negligible error.

 

BTW, by rejecting two lines (out of 17) with the largest residuals (larger than 0.4nm), my cubic std is down to 0.084 nm (0.35 pixels).


Edited by syam, 23 January 2021 - 12:43 PM.


#21 syam

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Posted 23 January 2021 - 05:28 PM

A clouded sky spectrum at dusk:

 

spectrum_sky.png

 

 

After subtracting the trend (modeled with n=7 polynome):

 

spectrum_sky2.png

Main Fraunhofer lines shown with colored vertical lines:

 

red: O2

green: H

yellow: Na

black: Fe

magenta: Mg

cyan: Ca


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#22 syam

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Posted 24 January 2021 - 07:55 PM

We haven't had clear skies at night for a while, plus I'm not sure my spectrometer will be sensitive enough to measure the sky glow spectrum directly, so as a proxy last night I measured the spectra from a few powerful (large shopping mall, next to our house) street lights in the area. I had to use maximum gain, open the camera lens all the way to f1.2, and set exposures to 5 minutes. I did 10 such exposures for the light, then the same for dark frames. This is the spectrum I got after processing:

 

spectrum_street_lights.png

Unfortunately the calibration was a bit off (I accidently touched the zoom ring on my lens), but it's pretty clear that the brightest spectral line (cyan) comes from mercury, and that most of the street light comes from a non-narrow-lines sources (likely LED).

 

So now I can scientifically measure the contrast which my narrow band filter would provide when imaging narrow-band sources (nebulae in OIII etc.). For that, I just need to compute integral (add up values at each wavelength) for the above "skyglow" spectrum, and divide that by the integral of the product of the filter transmission function (the graphs I posted here earlier, for my OIII and UHC filters) and the "skyglow" spectrum. Basically we divide the total sky glow light by the total filtered sky glow light.

 

For my cheap (advertised as 10nm, but actually 23nm) OIII filter, the computed ratio is 9. As a minor correction, I should also account for the fact that the filter is not 100% transparent at the OIII line. As it's 83% transparent at the main line, the contrast increase becomes slightly worse - 7.5.  So if I could use exposures up to 30 seconds in my f5 scope (limited by sky glow), now I should be able to get to 30s*9=4.5 minutes or so, and the contrast between the nebula and sky glow should increase by 7.5x.

 

For my cheap UHC filter, the integrals ratio is only 6.1 - meaning I can increase exposures by that factor. Accounting for <100% filter transparency at specific nebula lines, for OIII and H-beta the contrast increase will be ~5x, for SII: ~3x, and for H-alpha it will be a dismal 0.4x (meaning that with the filter the contrast will actually go down by 2.5x).

 

So my filters are useful, but not super useful. A 10nm or less filter would provide much better contrast.

 

In fact, I just computed a contrast increase an ideal OIII filter with a given width would produce, for my street light spectrum. It's just a Gaussian centered at OIII, with a given width at half-brightness.

 

This is what I got: contrast increase for ideal filters of different width:

 

23.4nm:  8.8x  (close to the actual number for my OIII filter)

10nm: 20x 

5nm: 39x

 

So nicer (and much more expensive) filters would definitely make things much better!



#23 syam

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Posted 25 January 2021 - 11:28 AM

I found data on my camera's spectral response curve, and within the range covered by my spectrometer it can be fitted nicely with a 6-degree polynomial:

 

Camera_curve2.png

 

And these are my first fully calibrated (in both wavelength and amplitude) spectra - for "5000K" (blue) and "3000K" (red) household LED lights. It's not surprising that I never liked the light from "5000K" variety - it is much more spiky than the warm bulbs, with a giant blue peak around 450nm.

 

LED_spectra.png

 

The zigzaggy parts on the red side don't seem to be measurement noise (I am averaging 1000 frames at lowest gain; the blue side of the spectra are super smooth), but rather are real spectral features of these LED bulbs.


Edited by syam, 25 January 2021 - 11:31 AM.


#24 robin_astro

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Posted 25 January 2021 - 03:37 PM

I found data on my camera's spectral response curve, 

Remember though that the camera  is only part of the system response. The response of the grating in particular is as important as the camera, for example

 

https://www.thorlabs...mission_780.gif

 

Then if you are using lenses, a telescope etc  these also have an effect, as well as the effect of absorption in the atmosphere if you are making astronomical observations. Flux calibration, even just relative can be quite a challenging process. The document  on my website here gives a practical overview

http://www.threehill...troscopy_21.htm

Essentially you need a reference source with a known spectrum. For astronomical objects, this is done by measuring standard stars but perhaps here  you could use a halogen lamp which would have a black body spectrum with an assumed temperature as a reference .  

 

Cheers

Robin


Edited by robin_astro, 25 January 2021 - 03:38 PM.


#25 robin_astro

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Posted 25 January 2021 - 03:43 PM

Note also that real sensors are not smooth like your polynomial fit but have humps and bumps and ripples, some of which you are probably seeing eg like the selection here

 

http://blog.astrofot...avelpech/?p=864

 

Cheers

Robin


Edited by robin_astro, 25 January 2021 - 03:43 PM.



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