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# Ultra cheap full aperture grating?

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Never ending cloud cover is to blame ...

So here I was again thinking about different ways to utilize Star Analyzer and possibility of adding beam collimation and slit to the mix, when it struck me - why not full aperture grating?

SA can be used in front of the lens - this way it operates in collimated beam, but aperture is really small - 1.25" or there about. Could one easily build diffraction grating for let's say 200mm aperture and what resolution would one hope to achieve.

Fiddling around with SA resolution calculation spreadsheet I came up with roughly 17A resolution - mostly due to coma. Setup would be SA200 + 50mm spacing with large ASI1600 sensor on F/8 8" RC. This translates into ~R300 around H alpha line.

So with SA200 values around R100-R300 are possible. What can we achieve with full aperture DIY cheap solution then?

Idea is to create really low number of lines per mm full aperture grating, and here is what I came up with:

Overhead projector transparent sheets with laser printed grating on it. Can't do cheaper than that.

Let's do some math. Laser printers are capable of 600dpi, so we need to figure out what number of lines per mm can be printed with that. That translates into single point being 0.042333.... mm per printed point. We can't assume that line of single point with will be printed fine, but we can do lines let say 4 points wide? That would get us 6 lines per mm - does not sound like much.

But, 200mm with 6 lines per mm will give us 1200 lines - about the same resolution as SA200 with 6mm converging beam, and that is higher resolution than will be achieved with SA200 due to coma and seeing. So resolution wise it could work. But what about diffraction angles and spectrum size on sensor?

Simple formula gives angle of ~0.0054 radians for 900nm (max that I would record), and that translates into ~1114 arcsecs. With resolution of 0.5 arcsec/pixel - spectrum will be spread to over half of the sensor (sensor has 4600px in width) - but will fit nicely on sensor.

So if I'm not missing anything crucial, this indeed might work for my setup?

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As you say the printer would give 6 lines/mm....this is the figure you need for dispersion calculations - much less than the 100 /lmm gratings.

The aperture size gives you light grasp and some resolution....

I ended up with a 50mm sq 300 l/mm grating (thorlabs?) to use as an objective grating with a camera lens.

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Vlaiv,

Thinking more....

When you use the grating as an objective grating , coma should not be an issue. The attached spreadsheet TransSpec will help you.

Many observers are getting good resolution (<10A) and good results with the 100 l/mm objective grating notwithstanding the small aperture.

TransSpecV3.1.zip

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1 hour ago, Merlin66 said:

Vlaiv,

Thinking more....

When you use the grating as an objective grating , coma should not be an issue. The attached spreadsheet TransSpec will help you.

Many observers are getting good resolution (<10A) and good results with the 100 l/mm objective grating notwithstanding the small aperture.

Oh, new version of that spread sheet, thanks for that.

I was using V2.1 to do calculations for different configurations with SA200. This one has objective grating section as well.

According to spreadsheet, with 6 lines/mm and 200mm aperture I'll be seeing limited in resolution. Total of 1200 lines would give me theoretical resolution of R1200, but star size for 2" FWHM would limit me to R384 if I use native F/8. Dispersion would be 3.9 A/pixel - which is quite enough to record 15.6A resolution (even binned to boost SNR).

I'm going to see what difference makes using reducer, not sure if it will make any since it is objective grating - star size will be smaller, but so would be sampling resolution as well.

Yes, not much difference, so no point in using focal reducer (except for boosting SNR of spectrum), but at a small cost of spectrum resolution - R343 with reducer.

I have found a paper that describes using just the approach I came up with - printing with laser printer on overhead projector clear film. Author also concluded that 6 lines per mm is achievable with 600dpi laser printers.

Here is reference:

and also from abstract:

"A standard laser printer can print black lines (separated by a white line) at 60 black lines/cm (about 150 lines/in), which is a small enough spacing to produce a crude diffraction grating [see Fig. 1(a)] that is sufficient for the physics inquiry activities described in this paper"

(not sure what that paper is about, I just read abstract and found confirmation that printed grating will work).

So it looks like this could indeed be viable solution for ultra cheap way into spectroscopy.

I just ran numbers for smaller scope - something like 80mm F/6, and results are still good - still seeing limited - R227 for 2" seeing, again using same 6 lines per mm grating.

Probably only drawback of this method is efficiency - grating will not be blazed, so light will be equally spread on both sides of source.

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Since above clearly shows that spectrum will be seeing limited, have you ever tried some sort of frequency restoration method to "sharpen" seeing limited spectrum?

Deconvolution or maybe simple wavelet processing? I don't see a reason why it would not work if we assume gaussian PSF for long exposure subs, and one stack multiple frames to get good SNR of final result.

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Vlaiv,

Spectra are treasured resource and always treated with utmost respect. When it comes to science data there should be no adulteration or unnecessary processing. We are always looking at the integrity of the RAW data and maximum SNR. Processing is usually kept to a minimum - stacking, darks, flats, removal of cosmic ray hits and sky background removal.

It's not like astrophotos where filters and blending etc etc can be applied to "improve the look" - KISS is always the rule.

(Having said all that, if you're not going to use the data for anything "serious" then obviously you can play as you like - wavelet sharpening etc :-)     )

Edited by Merlin66

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Already been done by Bev at COAA. See https://www.coaa.co.uk/software_astronomy.htm

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I'd be interested in seeing the results.....

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29 minutes ago, BinocularSky said:

Already been done by Bev at COAA. See https://www.coaa.co.uk/software_astronomy.htm

I just love to re invent wheel , kind of my specialty

6 hours ago, Merlin66 said:

Vlaiv,

Spectra are treasured resource and always treated with utmost respect. When it comes to science data there should be no adulteration or unnecessary processing. We are always looking at the integrity of the RAW data and maximum SNR. Processing is usually kept to a minimum - stacking, darks, flats, removal of cosmic ray hits and sky background removal.

It's not like astrophotos where filters and blending etc etc can be applied to "improve the look" - KISS is always the rule.

(Having said all that, if you're not going to use the data for anything "serious" then obviously you can play as you like - wavelet sharpening etc :-)     )

I was not really after "improving the look" of the curve, but rather interested in having a go at actually improving the resolution of spectrum.

I think it would be interesting to see if one can do that. Math supports it, and techniques like RL deconvolution have such property that they preserve flux for example, so we are not talking about pure cosmetic alterations here.

Personally, I think wavelets when used to do multi-frequency analysis might be a better choice than RL deconvolution, but have no idea of Math properties of such transform (other than it can boost attenuated high frequency components).

I have simple idea how to test it. Good thing about full aperture grating is that dominant aberration will be seeing PSF (well actually Airy PSF convolved with seeing + tracking error Gaussian) which for long expsure can be well approximated with Gaussian shape - and Gaussian shape and its Fourier transform are well understood, so we have the idea which frequencies need to be boosted. So test would go like this: Record spectrum and calibrate it using standard calibration method without any alterations and compare it to reference high resolution spectrum of that star using some metric - like RMS error, or similar. Then process that spectrum in certain way and again compare to high resolution reference spectrum using same metric to see if we lowered the error and/or introduced some kind of unwanted artifacts.

I also have couple more ideas to test out. Like stacking spectrum images vs stacking extracted spectral data (in 1D) - I suspect that later will help with artifacts introduced if spectrum is not sampled aligned to sensor pixel matrix (but at certain angle) - some dithering would help here between exposures. Then there is matter of center line vs offset spectrum extraction - in Gaussian PSF blurred data - center line is most blurred, while offset will have lower SNR due to less signal getting there.

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Interesting project. If you google "diffraction grating sheet" you may be able to get what you propose making very cheaply.

What processing is advisable depends on what you what to measure. While processing may make the line clearer and while the apparent resolution may improve information on line shape maybe be lost. As a rule of thumb  I find measuring the wavelength of a single line should be accurate to 1/10 of a resolution element (~lamda/R) and with cross-correlation about 1/100 This depends not only on the resolution but on the accuracy of the wavelength calibration which can be difficult in an objective grating system. However, my experience is with slit and fibre fed spectrographs.

With a slit spectrograph you can (in theory) measure the instrument PSF and then use deconvolution to improve you spectra but I don't see how you can do this with an objective system.

If you were doing a search for emission star, for example, sharpening might make them "jump out" as in this case it is the discovery that matters not the details.

I will be interested to see you results

Regards Andrew

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48 minutes ago, vlaiv said:

: Record spectrum and calibrate it using standard calibration method without any alterations and compare it to reference high resolution spectrum of that star using some metric - like RMS error, or similar. Then process that spectrum in certain way and again compare to high resolution reference spectrum using same metric to see if we lowered the error and/or introduced some kind of unwanted artifacts.

I compare my spectra with reference spectra but you need to filter them to the resolution of your spectra otherwise the fact that lines are resolved in one but blended in the other can cause issues. I tend to use rectified spectra to avoid issues with the continuum.

Regards Andrew

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1 minute ago, andrew s said:

I compare my spectra with reference spectra but you need to filter them to the resolution of your spectra otherwise the fact that lines are resolved in one but blended in the other can cause issues. I tend to use rectified spectra to avoid issues with the continuum.

Regards Andrew

Good point, depending on how high resolution the reference spectra is - can do low pass filter on it to make it "softer", and I can choose filter cutoff frequency in such way that it still contains more information than both raw and processed captured spectra.

10 minutes ago, andrew s said:

While processing may make the line clearer and while the apparent resolution may improve information on line shape maybe be lost.

Not really getting this. Maybe because I'm talking about low resolution - R<1000 where no individual lines are resolved to actual shape. I'm interested in seeing if I could overcome seeing induced limit on spectrum resolution. So grating would be theoretically capable of ~R1200, but seeing would limit that to ~R350. Can I recover information and have spectrum resolution of let's say ~R600 using processing?

And by recovering resolution I mean - close spectral lines that appear as one "dent" on R350 would appear as two separate "dents" on R600 with "identifiable" central wavelengths, and relative strengths.

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5 minutes ago, vlaiv said:

And by recovering resolution I mean - close spectral lines that appear as one "dent" on R350 would appear as two separate "dents" on R600 with "identifiable" central wavelengths, and relative strengths.

You could (given your perma-cloud) simulate this by taking two lines then convoluting them with a seeing functions of various types and see if you can recover them.

You might be surprised at how broad some lines can be say in hot A stars where there is considerable pressure broadening - in which case they are very non-Gaussian

Regards Andrew

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11 minutes ago, andrew s said:

You could (given your perma-cloud) simulate this by taking two lines then convoluting them with a seeing functions of various types and see if you can recover them.

You might be surprised at how broad some lines can be say in hot A stars where there is considerable pressure broadening - in which case they are very non-Gaussian

Regards Andrew

Oh, I get it - shape of the line tells us something about star dynamic - did not think of that (but it is very logical - Ha scopes need tuning to account for doppler shift when observing features in motion).

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Hi Vlaiv

A few years ago for a bit of fun I used the COAA software and an inkjet printer at 300dpi to make a rough and ready diffraction grating for the front end of my refractor.  Other than proving it works I have done little with the data but I was interested to read your thoughts about this approach.

Regards George

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Hi

As a matter of interest, does anyone know the difference between these and the Star Analysers? I have an SA100 but not found it easy to use (it's probably just me...). An objective grating seems like a good idea but not sure you could achieve a decent lines/mm with an inkjet? My old Deskjet says it can do up to 2400 dpi which equates to ~ 94 pix/mm which I guess would be 47 lines/mm.

Louise

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18 minutes ago, Thalestris24 said:

Hi

As a matter of interest, does anyone know the difference between these and the Star Analysers? I have an SA100 but not found it easy to use (it's probably just me...). An objective grating seems like a good idea but not sure you could achieve a decent lines/mm with an inkjet? My old Deskjet says it can do up to 2400 dpi which equates to ~ 94 pix/mm which I guess would be 47 lines/mm.

Louise

Just a couple of points:

I think that it is better to aim for lines that are more than single point thick - I'm not sure if line that is made from single printed point is going to be strait enough or possibly have holes in it or something. Go for 4-5 dots per line instead. That will give you 10 lines per mm in case of 2400dpi (~90 dots per mm - 9 dots per line + space for 10 lines per mm, 4.5 dots line width).

Grating resolution is determined by total count of lines, so 10 lines per mm can sound very low, but put it on 80mm objective and you will have R800 resolution from it. So depending on aperture, few lines per mm is not such a bad thing in terms of resolution.

Another thing to consider is dispersion. More lines per mm you have, higher dispersion, or angle of diffracted light. This is important because it helps you determine how spread the spectrum will be on sensor. Here again you don't want very large dispersion in objective grating because you will need wide field instrument in order to record it.

For example SA100 has first order spectrum of 550nm light at angle of ~3.15 degrees (if I'm correct with this calculation). So you need very short focal length instrument capable of wide field in order to record it. My TS80 with ASI1600 has 2"/pixel and it would take 5670 pixels just to record 0 order to 550nm (ASI1600 does not have that many pixels ). But let's look at dispersion for 900nm and 10 lines per mm grating. Again if my calculation abilities are up to task, that would give us something like half a degree. That means that I would need about 900 pixels on my ASI1600 + TS80 to record full spectrum - from 0 to 900nm. This again is not really the best option, as sampling would lower achievable resolution - in this case to something like 2nm. So for 10 lines per mm I would probably use RC8" as it gives me 0.5"/pixel with ASI1600. 0-900nm would cover in this case 3600px (camera has 4600px in width). Sampling resolution would be 5A (pretty good), and the whole system would be seeing limited.

So one can fiddle with these numbers to get best match for their instrument (focal length, sensor size and resolution, etc). TransSpec v3.1 that Merlin66 attached above, gives you spreadsheet to play with some numbers, it has objective grating tab, but it is initially geared towards SA100 used as objective grating on short FL DSLR lens. By changing numbers you can see different calculations for this type of printed grating as well.

Btw I just realized that Bahtinov mask is very low resolution objective grating

And it really works well, here we can see at least 5 orders, and mask it self has grating that has many mm spacing.

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Yeah, having an objective grating did make me think of a Bahtinov Mask . I think one of my main problems has been in getting sharp focus which I find difficult - even with a Bahtinov mask! I think it's the turbulent atmosphere here which is a big problem. I've been able to acquire spectra with the sa100 but resolution seems poor  - presumably because of the difficulties with focus. I'm using the SA100 with a TS F6 80mm APO and a qhy minicam5s mono.

I did wonder about printing high resolution lines accurately but I suppose it's a matter of trying it out.

Louise

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8 minutes ago, Thalestris24 said:

Yeah, having an objective grating did make me think of a Bahtinov Mask . I think one of my main problems has been in getting sharp focus which I find difficult - even with a Bahtinov mask! I think it's the turbulent atmosphere here which is a big problem. I've been able to acquire spectra with the sa100 but resolution seems poor  - presumably because of the difficulties with focus. I'm using the SA100 with a TS F6 80mm APO and a qhy minicam5s mono.

I did wonder about printing high resolution lines accurately but I suppose it's a matter of trying it out.

Louise

Try stopping down aperture. F/6 will introduce quite a bit chromatic coma into spectrum. Again above mentioned spreadsheet can be of help in determining correct parameters. If you want to minimize seeing impact, go with short focal length, or move grating away from sensor. Another important thing is not to focus on star! Focus instead on spectrum, or part of spectrum that you are most interested in. Due to angle of spectrum (that gives spread over sensor surface), that is made after objective, focal point is shifted between wavelengths - think isosceles triangle, but one side being perpendicular to sensor - other side will not touch sensor surface but rather end some distance to it. So if 0 order image is focused, first order image will fall short of sensor, and if you focus on first order, 0 order will fall behind sensor - therefore it will be defocused at sensor.

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1 minute ago, vlaiv said:

Try stopping down aperture. F/6 will introduce quite a bit chromatic coma into spectrum. Again above mentioned spreadsheet can be of help in determining correct parameters. If you want to minimize seeing impact, go with short focal length, or move grating away from sensor. Another important thing is not to focus on star! Focus instead on spectrum, or part of spectrum that you are most interested in. Due to angle of spectrum (that gives spread over sensor surface), that is made after objective, focal point is shifted between wavelengths - think isosceles triangle, but one side being perpendicular to sensor - other side will not touch sensor surface but rather end some distance to it. So if 0 order image is focused, first order image will fall short of sensor, and if you focus on first order, 0 order will fall behind sensor - therefore it will be defocused at sensor.

Thanks for the advice! I could try stopping down the lens. The SA100 is fitted to a nosepiece attached to the camera so about 6-7cm from the sensor. To be honest, I've not even used the scope/sa100 in over a year! (Busy with other things). I'll have a look at the transpec spreadsheet  though no chance of any clear sky in the near future...

Louise

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Hi

I've been trying to print out a grating on a transparency using the COAA  plot software but not having much luck. I've been able to print out ok at 600 dpi but if I change my printer settings to max dpi = 1200 dpi, it only prints the top 1/5th segment of the circle. I'm wondering if the software maybe wasn't written to cope with 1200 dpi - anyone else tried it?

Louise

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i printed some transparency gratings on the laser printer. Looking at them with a magnifier, I found that the 600/1200 dpi (according to specs) printer at work could really only achieve about 4 lines/mm.Lower than this, the lines are made up of circular dots so are too rough.

I also got a few printed on a big machine at the local print shop. A little better resolution.

However the main problem is that the transparencies are not very optically good (at least after being exposed to the heat of a laser printer), and seem a little...cloudy is the best way to describe it. Putting them on the front of my 200mmf6 newtonian, I can see spectra, but the zero order image and spectrum clarity is poor, presumably due to the transparency not being very good.

I did find an old paper by Arthur Vaughan made full aperture gratings (called amplitude gratings) for the Palomar 48 inch schmidt camera to make spectra of the very wide field survey pictures which this instrument could make (back in the days of glass plates bent onto a curved film holder (wince!). They used the thinnest commercially available grades of mylar film, and ruled the grating with a finely lapped fountain pen. Tedious I guess, but it worked apparently.  I guess the problem I had with overhead transparencies might have been related to them being much thicker, and then varying in thickness even more after exposure to the heat of a laser printer.

The paper has curves for the theoretical grating efficiency at different diffraction orders, which are a function of the amount of black / clear space per ruling.

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Hi Hamish

As mentioned previously, I had a go at printing on an inkjet last year but had similar problems. I wrote some custom software in C# but needed to overprint lines to make them more opaque but couldn't see how to do that. So put it to one side as I was busy with other things. If anyone knows of a routine that enables overprinting a line several times I might have another go.

Louise

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