9 replies to this topic

[Organic Astrochemist]

Unlike many more advanced amateur astronomical spectroscopists, I don’t have an observatory, but I do have small kids and a full-time job. Time to set up my spectroscopy rig under good skies does not come so often. So I decided that, for now, any equipment purchased would have to work on a portable rig that I could set up in minutes.
Polarimetry and spectropolarimetry are fascinating subjects in astronomy.

https://academic.oup...7/3/3.31/209077
https://academic.oup...9/4/4.30/321308
very interesting
https://www.hfstevance.com/specpol

 

So I bought a QHY550P camera
https://www.qhyccd.c...=94&id=51&cut=1

 

more information about these types of cameras here:
https://scholarworks...du/theses/9453/

 

For about a year I couldn’t get it all to work. I made lots of mistakes and learned a lot (which was the whole idea).
The basic idea of the camera is that rather than a color bayer array RGBG, this camera has a polarization filter array, 0°, 45°, 135°, and 90°.

 

Astronomical polarimetry is photon starved and poisson statistics are important. If I understand correctly, the fullwell of this camera, at about half the maximum gain, is 2000. So if I stack 100 spectra, pixels that are half full should have, on average, about 10^5 photons which should allow detection of polarization at about 10^-2.5 or +/-0.3%

 

QHY didn’t provide any way to separate the channels or calculate the Stokes parameters (maybe in the SDK?) The only way I was able to get this to work was the following: debayer, stack and separate the channels with Nebulosity TWICE, once with the 0° channel as the RED channel and AGAIN with the 45° channel as the RED channel. This is a pain, but nothing else worked (Fitswork etc.) I think that interpolating the values for all polarization angles is better than only using the data recorded from each pixel (this gives subtraction artifacts).

Also, as much as possible, I want the light that lands on two adjacent pixels to be different only with respect to polarization and not because of the image (or spectrum). I tried various ways to facilitate this including defocusing the image, dithering a focused image, and allowing the image to drift across the field of view, but I think the best solution was to increase the magnification to somewhat ridiculous levels to spread the light over more pixels.

Here is the Grab and Go portable spectropolarimetry rig:

The mount is an iOptron Sky-Tracker Pro camera mount on a camera tripod with a 3-way geared head.

The telescope is a Borg 55FL (250 mm FL increased to 1250 with a 5X focal extender). I can get nice 3 s acquisitions with this setup (using Sharpcap with darks subtracted on the fly). There is a visual and electronic finder.

 

The dispersing element is a Star Analyzer 100 set so close to the  camera to afford a dispersion of 1.9 nm per pixel!

 

The spectra for all four polarization channels were debayerd, stacked and extracted with Nebulosity (as above) and processed with RSpec!

 

 

The data file was then exported to excel to calculate Q and U (normalized) and the degree of linear polarization (DOLP or just P).
Here are some results for unpolarized stars

 

Obviously there is some instrumental polarization, but it is more pronounced for the Q channels (0° and 90°) than for the U channels. I think this must have something to do with the light being spread out parallel to the 90° channel and perpendicular to the 0° channel. Does the grating cause polarization? If anyone has any ideas to explain this or help correct for this instrumental polarization, I would appreciate it.

 

As a first approximation, I just used the polarization from these stars as a measure of instrumental polarization and to correct for this I simply subtracted the values from the other star. The results were as follows:

 

 

That is already looking a little better. The paper by Vorobiev suggest that such cameras will have a hard time measuring polarization less than 0.5%. Luckily there are many stars more polarized than this.

I also did the same thing with phi cas, which is a more polarized star (literature value around 0.032 – 0.034). Actually, degree of linear polarization, although widely used, is a biased indicator because it involves squaring values, it cannot be negative. This is why using the normalized Q and U values gives a better indication of the errors.
The result for phi cas was:

 

 

I am overestimating the amount of polarization. I think this is to be expected when the sources of error are not well corrected . 

I still have many more observations to make and calibrations to consider, but I do think there is some possibility of success for this project. Any comments are welcome. I am especially curious about the effects of the grating on polarization.

[Octans]

You can fairly easily test for instrumental polarization by just rotating your telescope. Any real polarization will stay fixed with respect to the sky, while any instrumental polarization will be fixed with respect to your camera. To test if your issues are coming from insufficiently oversampling, you can try going for a few unpolarized stars of similar spectral type to see if you get similar polarization signatures. If this turns out to be the problem, you can potentially overcome it by combining a bunch of dithered frames via a drizzle method, so that you end up sampling all 4 polarizations relatively evenly at every point.

The diffraction grating will in theory add polarization, but in practice, a very low density transmission grating like this will probably have negligible polarization. However, you can again verify with an unpolarized standard star, and seeing if the polarization direction is always perfectly aligned with the grating. If it's pointing a random direction not parallel or perpendicular to the dispersion, it's not the grating.

[mwr]

Also, as much as possible, I want the light that lands on two adjacent pixels to be different only with respect to polarization and not because of the image (or spectrum). I tried various ways to facilitate this including defocusing the image, dithering a focused image, and allowing the image to drift across the field of view, but I think the best solution was to increase the magnification to somewhat ridiculous levels to spread the light over more pixels.

Hi Jim,

 

may be I did get you wrong but wouldn't it be better to use higher resolved spectra to detect the depolarization of the continuum by the hydrogen alpha emission lines in spectra of Be stars? According to Vink this depolarization is "easier" to detect and is independent from instrumental polarisation:

 

"In principle, linear continuum polarimetry would already be able to inform us about
the presence of an asymmetric (e.g. a disk or flattened wind) structure on the sky, but
in practice, this issue is complicated by the roles of intervening circumstellar and/or
interstellar dust, as well as instrumental polarization. This is one of the reasons linear
spectropolarimetry, measuring the change in the degree of linear polarization across

emission lines is such a powerful tool, as “clean” or “intrinsic” information can be directly
obtained from the QU plane."

 

I think you have demonstrated before that you can well resolve the emission line in Be stars with your grab and go setup.

 

The following figure was taken from Vink's publication and illustrates the concept:

 

[Organic Astrochemist]

Perhaps I should move the grating away from the camera to get greater dispersion (which will be reduced by the large star image size). Even as it is, I can see H-alpha emission in Be stars. There will be a price to pay in more acquisitions. It took me  a while to realize how photon starved the system is. It's easy to see the spectrum of a bright star against the sky, but what I'm trying to do is more like trying to look for the spectrum of a very faint star against a very bright sky.

 

I think the lines in Wolf Rayet stars will be easier to see (because they are so wide) and they show similar depolarization.

EZCMa

 

I thought continuum polarization would easier to start with, but perhaps because it is spread out over more wavelengths, artifacts appear due to the response of the microfilters vs wavelength and the grating vs poarization and wavelength.

 

Apparently the efficiency of gratings depends not only on wavelength but also on polarization.

(see figure 4)

Polarization induced artifacts

 

Even prisms respond to polarization

thorlabs

 

Octans gave good advice about rotating the telescope (easy to do in my  case). I see that the pros do something similar but I still don't exactly know what I would do with the results.

 

One experiment I started was using a green LED and polarizing filter. I rotated the filter 360° in steps of 45°, but I only have reduced the data for the first position.

 

Neither the polarizing filter nor the micro-polarizing filters on the chip are ideal, so I'm going to have to deal with that (transmitting or blocking polarization is never 100%). The LED + filter has higher polarization than any astronomical source, I think that is what is causing the sawtooth pattern to be so visible. Black and pink are orthogonal polarizations

 

Since the intensity is being affected by the polarization, this does seem to affect the normalized Q and U values and the polarization measurement. The plot of polarization looks like two plots because of the alternating intensity. I have never seen anything like this with stars but I did see some similar results in lab tests that others have done with similar cameras.

 

But miraculously, the QU plane shows great linearity and the angle should be twice the polarization angle. So I definitely think there is potential here.

Edited by Organic Astrochemist, 05 January 2021 - 03:11 PM.

[Octans]

Keep in mind the polarization of diffraction gratings tends to be greater for higher groove lines/mm, and are also higher for reflection than transmission gratings. You can get a rough idea by looking at the Thorlabs, Edmund, or Newport reflective gratings catalogs which give the relative response to parallel and perpendicular polarization (they don't provide it for transmission gratings though because the difference is so low).

 

With that in mind, the sawtooth pattern doesn't look like it's an artifact of the grating. How are measuring the intensity here? If you're using just the raw counts from the sensor, then you actually have alternating columns of 0+135 deg and 45+90 deg polarization, which are not the same thing as Stokes I intensity. I would expect sawtooth peaks 2 pixels apart that vary with changing polarization direction as you describe in this case, similar to the effect from treating a non-debayered color image as a monochrome image. If this is the problem, the simplest way to get intensity is to bin the whole image 2x2, and interpolate to scale it back up for polarization as necessary.

Edited by Octans, 07 January 2021 - 07:44 PM.

[Organic Astrochemist]

Dear Octans,
I am very much in the weeds here and I have the instrument to play with, so I'm quite appreciative of anyone willing to help me think this through.

Keep in mind the polarization of diffraction gratings tends to be greater for higher groove lines/mm, and are also higher for reflection than transmission gratings. You can get a rough idea by looking at the Thorlabs, Edmund, or Newport reflective gratings catalogs which give the relative response to parallel and perpendicular polarization (they don't provide it for transmission gratings though because the difference is so low).

The absence of evidence is not evidence of an absence.
Look at figure 6 here It's true that the surface relief transmission grating (SRTG) presented here has many more lines/mm and a different blaze angle than my SA 100, but that is a pretty nasty function of polarization and wavelength once you get very far away from the peak efficiency wavelength.

To some extent this is moot because the combination of my grating and my polarization filters clearly show a dependence on polarization (0 and 90 are more affected than 45 and135).

So I have attempted to correct for this.

Let me start with my general understanding of correcting for instrument response. The following are all functions of wavelength:

"observed signal" = "true signal" x "atmospheric effect" x "instrument effect, including polarization".

So we start with an A-type star for which we know the "true signal"

"atmospheric effect" x "instrument effect" = "observed signal" / "true signal" = "instrument response correction (IRC)"

then "observed signal" / IRC = "true signal"

So I observed Sirius, for which the relative flux spectra is a known reference spectrum

0° IRC = “observed 0° spectrum”/”reference spectrum”

But then things get interesting because Sirius is an “unpolarized standard star”

So “true 0° spectrum” – “true 90° spectrum” = 0

Therefore, “observed 0° spectrum”/0° IRC – “observed 90° spectrum”/ 90° IRC = 0

“observed 0° spectrum”/0° IRC = “observed 90° spectrum”/ 90° IRC

90° IRC = (“observed 90° spectrum” / “observed 0° spectrum”) x 0° IRC

So I calculated the 90° IRC and the 135° IRC so that the total polarization for Sirius would be zero. Then I applied the corresponding IRC to each channel I observed. The spectra were taken on different nights at different points in the sky. Even lots of high clouds for Zeta Tau. The results were as follows:





These are getting close to reported values (see here)

Edited by Organic Astrochemist, 10 January 2021 - 11:06 AM.

[Octans]

It's a general trend that polarization becomes really strong at high groove densities (where the groove size approaches the wavelength of light) and also tends to be greater for reflection than transmission gratings of the same density (as tilted mirrors, even big ones, already inherently polarize the light, while simple transparent windows don't necessarily do so). Instrumental polarization on the order of 1% is about right for your setup, and your correction process looks reasonable for most low instrument polarization setups. The procedure alone won't correct the sawtooth pattern in your previous post, however, if it's in fact a result of making an intensity approximation that breaks down for strongly polarized sources.

Edited by Octans, 10 January 2021 - 07:13 PM.

[Organic Astrochemist]

How are measuring the intensity here? If you're using just the raw counts from the sensor, then you actually have alternating columns of 0+135 deg and 45+90 deg polarization, which are not the same thing as Stokes I intensity. I would expect sawtooth peaks 2 pixels apart that vary with changing polarization direction as you describe in this case, similar to the effect from treating a non-debayered color image as a monochrome image. If this is the problem, the simplest way to get intensity is to bin the whole image 2x2, and interpolate to scale it back up for polarization as necessary.

I debayer the image (twice actually) which interpolates values for all four polarization angles. Interestingly for I, to normalize Q, it doesn't seem to matter much if I use 0+90 or (0+90+45+135)*0.5. I have seen both used in the literature. I am a little surprised that they give the same result, but I'm sure that reveals my ignorance. I guess it shows that I have corrected for the average response for each of these angles.

 

Although the data is still a little noisy, I am pleased that the polarization for phi Cas seems to look something like following Serkowski's law, peaking at around 500 nm, whereas Zeta Tau looks more typical for a Be star where the polarization decreases with increasing wavelength due opacity of hydrogen in the ring. Unfortunately I can't accurately measure polarization around the Balmer or Paschen jumps where big increases in polarization occur. 

[Octans]

I debayer the image (twice actually) which interpolates values for all four polarization angles. Interestingly for I, to normalize Q, it doesn't seem to matter much if I use 0+90 or (0+90+45+135)*0.5. I have seen both used in the literature. I am a little surprised that they give the same result, but I'm sure that reveals my ignorance. I guess it shows that I have corrected for the average response for each of these angles.

 

Although the data is still a little noisy, I am pleased that the polarization for phi Cas seems to look something like following Serkowski's law, peaking at around 500 nm, whereas Zeta Tau looks more typical for a Be star where the polarization decreases with increasing wavelength due opacity of hydrogen in the ring. Unfortunately I can't accurately measure polarization around the Balmer or Paschen jumps where big increases in polarization occur. 

Yes, 0+90 and 45+135 should both be the same thing, and equal to the intensity (think splitting the light into a perpendicular and parallel component; you can split it along 0/90 or 45/135 or any other orthogonal pair, but you should get the original light back if you put the split beams back together). Since you do have all 4 available, it's better (for lower noise) to "average" all of them together (and multiply by 2 as needed for the equations).

 

Your description sounds more or less like you're following the correct procedure, although it is a little perplexing that your strongly polarized sources show that sawtooth pattern in intensity, which might be affecting your ability to measure sharp polarization variations. Do you see the same problem in the individual debayered/interpolated 0, 45, 90, 135 channels as well? And is the sawtooth spacing (peak to peak) 2 pixels or 4+? If it's 2 and shows up in the debayered channels, I'd guess it's an issue with the interpolation since none of debayered channels should have features that small. If it doesn't show up in the debayered channels and only in the average, there might be a problem in your averaging step. If the sawtooth still appears in the individual debayered channels and are 4 or more pixels peak to peak, I would guess it's a detector artifact of some kind (nothing immediately comes to find that fits), though it looks well-behaved enough that it could probably calibrate out with a flat of sorts if it came down to it.

Edited by Octans, 12 January 2021 - 01:46 AM.

[Organic Astrochemist]

Making lots of progress (finally): acquisition, data reduction and interpretation.

 

Octans was right to be concerned about that sawtooth pattern. It was the result of the debayering algorithm. I managed a workaround for that. No more sawtooth.

 

I always knew that subtraction artifacts might be a problem. I have worked on reducing those.

 

I took a useful little detour into slit spectroscopy and I made a spectrograph! Thanks Robin for the SEPSA design and advice.

 

 Configuring the SEPSA was a bit of a pain, I bought an eyepiece projection tube but that didn't work so I rigged something up using a whole bunch of spacers, the body of my Alpy 600 and the cheap 32 mm eyepiece that Celestron gave me with a C90.

 

I also recycled the slit from my Alpy 600

 

Now I can use the camera with the star analyzer 100 in slit or slitless mode. This allowed me to get a spectrum of a 2900K halogen light bulb to use to calibrate an instrument response.

 

It also allows me to easily look at bright extended objects like the sky, sun, and moon.

 

I can force Sharpcap to debayer on-the-fly so the differences in polarization 90° and 0° appear as different colors. Pointing the telescope to a polarized region of the sky affords an image like this:

pointing the scope to an unpolarized area of the sky looks like this: (this is how stars, with their low polarization, always look):

 

Here is the spectrum of the blue sky (corrected using the 2900K lamp)

 

The radiometric correction is probably not great (for spectropolarimetry I don't need it) but it clearly shows that the sky is blue. This is due to Rayleigh scattering by small molecules, which is strongly wavelength dependent and theoretically is 100% linearly polarized at a scattering angle of 90 degrees. (I understand a little better why)

 

Here is the spectrum of the tip of a nearby white cloud.

This is also corrected for instrument response and looks much more like a G2V standard star (in pink). This is not produced by Rayleigh scattering by small molecules, but rather by Mie scattering by larger particles in the cloud.

 

I calculated Q and U and the degree of polarization for both and this was the result:

The blue sky is much more polarized than the white cloud and the polarization varies quite a bit by wavelength, with a maximum in the blue. The white cloud has much lower polarization and, except for the very bluest part, seems relatively insensitive to wavelength. I think those shortest wavelengths may have come predominantly not from the cloud by highly Rayleigh scattered sunlight.

 

Any comments are welcome. Thanks for reading. 

 

 

Edited by Organic Astrochemist, 18 February 2021 - 09:01 PM.