Testing a Lunt LS50FHa etalon with a H spectrum tube.

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Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by p_zetner » Mon Feb 22, 2021 11:33 pm

Hello Everyone.

Inspired by the Zoom meeting yesterday, I thought I would make an attempt at etalon testing using a discharge tube lamp. Here are my preliminary results investigating a Lunt LS50FHa etalon. The setup is the same as that described by Christian in this thread:
viewtopic.php?f=8&t=30693
I used a hydrogen spectrum tube, glass diffuser, 2" Astronomik 12nm H alpha filter and a Computar 17mm focal length lens attached to my Point Grey camera (GS3-U3-60QS6M-C, Sony ICX694). The Computar lens was a relatively cheap eBay purchase and has fixed (infinity) focus. My experience with this lens shows it to be quite sharp so a good match for the testing procedure.
File_003_crop.jpg
File_003_crop.jpg (959.54 KiB) Viewed 400 times

Here are my initial images taken with three different adjustments of the Lunt tilt knob. These have a somewhat constricted field of view because the initial 1" Edmund Optics 656nm filter I was using limited the fov too severely. The centre pattern corresponds to the "on band" condition and is what you would aim for in an H alpha imaging session.
Montage_131626-742-821.jpg
Montage_131626-742-821.jpg (55.14 KiB) Viewed 400 times
To image a more extensive fringe pattern I switched to the 2" Astronomik filter. Here is the result and this is the fringe pattern I analyzed. You can see several circular fringes concentrically arranged around the central fringe ("spot") for this Lunt angle adjustment.
AVG_fc2_save_2021-02-22-145129-trace.jpg
AVG_fc2_save_2021-02-22-145129-trace.jpg (109.5 KiB) Viewed 400 times
The line indicates the direction in which I chose to measure intensities on the interferogram and the plot of these intensities is shown.
145129 plot.jpg
145129 plot.jpg (391.21 KiB) Viewed 400 times
I chose the four numbered fringes to carry out my analysis. I was interested in calculating the etalon finesse so began the procedure by finding the centre of the fringe pattern (by fitting the central feature). Then, knowing the centre of the pattern, the fringe radii were determined and their squares plotted against the fringe order (counted from the central fringe).
fringe rad2 vs ordr.jpg
fringe rad2 vs ordr.jpg (932.06 KiB) Viewed 400 times
The plot gives a linear relationship and the slope of the line contains valuable information used to measure the finesse. It allows one to convert pixel values into the phase angle associated with one back and forth traversal of the etalon by a light ray, this being the fundamental quantity that determines the etalon transmission. Maybe the most notable feature of this method is that it doesn't require a measurement of camera lens focal length, distances on the camera sensor, etc. I've discussed some of this and relevant formulas appear in this thread:
viewtopic.php?f=8&t=30741
Once the relationship between pixel value and phase is established, a plot of the fringe intensities in terms of phase rather than pixel values can be made. In this type of plot, the fringes should all have equal full width half maximum (fwhm) and this fwhm determines the finesse simply by: Finesse = 2*pi/fwhm. Here is the plot of the fringe intensities in terms of phase.
peaks vs phase.jpg
peaks vs phase.jpg (885.68 KiB) Viewed 400 times
The fwhm values were nearly identical for the four features I used in the analysis and their average value of 0.64 rad gives a finesse of 9.82. This seems a bit low considering Lunt specifies a finesse of 19.6 for their LS50THa unit, but maybe this is reasonable for an etalon like the LS50FHa which is used as the 2nd element in double stacking. Since the finesse determination involves the fringe fwhm, the focusing sharpness of the camera lens also comes into play. If I were to investigate this more thoroughly, I would have to try a variety of camera lenses and look for variation. Also, it worries me that I'm off by a factor of two and may have dropped a factor of two somewhere in my equation development. Can't say this hasn't happened to me before! I'll go through the theory again to check. It also occurs to me that I took these measurements with the Computar focal ratio at its extreme limit: f/16. There was definitely a trend to widening fringe widths as the lens was opened up. Maybe a higher focal ratio is called for in these measurements?

I plan to look at the Daystar QPE0.6A in the next couple of days. I'm mostly interested in using this testing scheme to calibrate the wavelength readout of the filter. This is pretty easy to do with the spectrum tube setup.

Thanks Zoom participants for the inspiration!

Cheers.
Peter
Last edited by p_zetner on Tue Feb 23, 2021 12:38 am, edited 1 time in total.



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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by thesmiths » Tue Feb 23, 2021 12:35 am

Peter: excellent work, as usual. In the very good paper by Cyril Bazin and Serge Koutchmy, "Photometric properties of new solar Ha commercial
Fabry-Perot etalons", they state:

We consider the use of the commercially available Fabry-Perot etalons (FP) of
Sidorin and Lunt type for the imaging of the solar chromosphere in the Ha line of
HI. Three etalons of 40, 60 and 90 mm diameter were evaluated and accurately
analysed. At normal incidence the maximum transmission wavelength was 656,285
nm for the 60 and 40 mm FP etalons. The finesse has been evaluated at 13,3 for the
FP 60mm, 8,7 for the FP 40 and 13,9 for the FP 90 mm.


Your value of 9.8 for a 50mm falls right in the trend which they measured. Perhaps it is Lunt that lost a factor of 2 somewhere. A finesse of 20 seems very high. At that value, the throughput of the etalon would be quite low, which would be a drawback for a visual observing device. In theory you would also need a surface roughness of lamba/40, which would be quite difficult to achieve at a reasonable cost.



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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by p_zetner » Tue Feb 23, 2021 12:39 am

Thanks very much, Douglas!



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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by marktownley » Tue Feb 23, 2021 6:36 am

Fascinating!


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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by Montana » Tue Feb 23, 2021 7:57 am

Wow! well done Peter :hamster: what is more amazing is that you had all this equipment already floating around your house to try it straight away :bow

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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by LTHB » Tue Feb 23, 2021 8:10 am

Very interesting, thanks, Peter!

I probably want to try testing with a hydrogen tube when I find some time in the next months. A question, if I may: Which software are you using for evaluating the images? (The plots look like it might be ImageJ?)

Regards,

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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by Bob Yoesle » Tue Feb 23, 2021 7:22 pm

Much thanks for this analysis Peter!

Your and Christian's quantitative analysis procedures could help consumers to better understand the performance and judge the quality of the commercial etalons we are paying for.

In addition to a FSR and FWHM = finesse determination, I think a really valuable piece of information to be determined is what the actual CWL of the etalon is. For a tilt-tuned etalon this has a direct bearing on the amount of tilt which would be required to come on-band. Qualitatively this is represented by the diameter of the inner ring without any tilt applied to the etalon. In my experience with tilt-tuned etalons, a large inner ring might indicate the etalon cannot be brought on-band, and even if it can, it might therefore be plagued by "banding" due needing excessive tilt from having a too high of a CWL. It might be just as important to define the outside limit for a CWL should be to insure good performance. For example less than or equal to +/- 0.5 Angstrom would ideal, +/- 1.0 Å would be marginal, and +/- 1.5 Å unacceptable. For a pressure tuned etalon, the CWL offset is less critical, but does indicate the amount of pressure that will be needed to bring the etalon on-band.

Likewise, there is usually some variation in the inner fringe dot/ring diameter across the etalon - indicating variation in the etalon gap uniformity, and this variation appears to affect the overall FWHM performance and is applicable to any type of etalon and tuning method. It therefore would be ideal to quantitatively determine how much variation across the etalon in at least 4 directions (e.g. center, up, down, left, right) at say 50 to75% of the etalon diameter. For example, an inner ring variation of </= 10% might be the ideal, 25% marginal, and > 40% unacceptable.

We could therefore then have some valid and reliable criteria by which to evaluate and judge an etalon's overall quality and resulting real-world performance.

Just my thoughts on where one could take such analysis, if possible, within the limits of the hardware and software you are using.


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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by christian viladrich » Wed Feb 24, 2021 9:58 am

Excellent Peter !

Some comments :
- if you take into account the lens focal length, then you can calculate the FWHM (and FSR) in Angstrom,
- François Rouvière is working on a short paper presenting the associated calculation,
- indeed, I found out that the quality of the lens is very important since some of the fringes are rather thin,
- an important point is that the aperture of the lens defines the surface of the etalon evaluated. If we want to evaluate the average quality over the full aperture of the etalon, we need a lens whose aperture is similar to the diameter of the etalon. Another option is to make several measurument over the aperture of the etalon and integrate the results.


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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by christian viladrich » Wed Feb 24, 2021 10:08 am

thesmiths wrote:
Tue Feb 23, 2021 12:35 am
Peter: excellent work, as usual. In the very good paper by Cyril Bazin and Serge Koutchmy, "Photometric properties of new solar Ha commercial
Fabry-Perot etalons", they state:

We consider the use of the commercially available Fabry-Perot etalons (FP) of
Sidorin and Lunt type for the imaging of the solar chromosphere in the Ha line of
HI. Three etalons of 40, 60 and 90 mm diameter were evaluated and accurately
analysed. At normal incidence the maximum transmission wavelength was 656,285
nm for the 60 and 40 mm FP etalons. The finesse has been evaluated at 13,3 for the
FP 60mm, 8,7 for the FP 40 and 13,9 for the FP 90 mm.


Your value of 9.8 for a 50mm falls right in the trend which they measured. Perhaps it is Lunt that lost a factor of 2 somewhere. A finesse of 20 seems very high. At that value, the throughput of the etalon would be quite low, which would be a drawback for a visual observing device. In theory you would also need a surface roughness of lamba/40, which would be quite difficult to achieve at a reasonable cost.

This was for Coronado etalons (pre-Meade), not for Lunt etalons.

On my side, I found :
- SM 40 : FWHM= 0.74 A, FSR = 12.1 A => finesse = 16.3
- SM III 60 : FWHM < 0.55 A, FSR = 8.5 A => finesse = 15.5
- SM III 60 RichView : FWHM < 0.58 A, FSR = 8.9 A, finesse 15.3
This is relatively consitent with Serge K and Cyril B results.

When the COVID episode will be over (I hope one day ...) we are planning to compare results of these two approaches with Serge K and Cyril B, and also measure DayStar / SolarSpectrum etalons.


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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by christian viladrich » Wed Feb 24, 2021 10:12 am

Bob Yoesle wrote:
Tue Feb 23, 2021 7:22 pm
In my experience with tilt-tuned etalons, a large inner ring might indicate the etalon cannot be brought on-band, and even if it can, it might therefore be plagued by "banding" due needing excessive tilt from having a too high of a CWL. It might be just as important to define the outside limit for a CWL should be to insure good performance. For example less than or equal to +/- 0.5 Angstrom would ideal, +/- 1.0 Å would be marginal, and +/- 1.5 Å unacceptable. For a pressure tuned etalon, the CWL offset is less critical, but does indicate the amount of pressure that will be needed to bring the etalon on-band.
Hi Bob,
There is for sure something about banding due to etalons not being on Ha at normal incident. I hope to have something to share about it at the end of the WE.

All of this is very exciting indeed !


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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by p_zetner » Wed Feb 24, 2021 7:38 pm

Thanks everyone for the thoughtful feedback.

Christian: Your points are well taken.
Concerning your comment
if you take into account the lens focal length, then you can calculate the FWHM (and FSR) in Angstrom
I'd like to demonstrate a method that doesn't require knowledge of the camera lens focal length and sensor pixel pitch. It makes use of an auxiliary measurement of the well known sodium doublet splitting instead.

Here is a generic diagram of the testing setup (camera end):

Feb24_fig1.jpg
Feb24_fig1.jpg (84.99 KiB) Viewed 152 times


The angle theta is one of the critical parameters which determine the etalon transmission. The distance, x, in pixels, on the camera sensor is simply related to theta by the formula included in the figure. The scaling factor eta is determined by the focal length, f , and the pixel pitch, p , of the camera sensor (assuming a one to one mapping of the sensor pixels to the image pixels in the final interferogram that is analyzed). The simple relation is eta = p / f.

In order to avoid any direct measurement of f or a reliance on its nominal (stated) value, I have used an auxiliary interference measurement in sodium. Here is a sodium interferogram taken with the Lunt etalon (same lens and setup as H alpha configuration).

Feb24_fig2.jpg
Feb24_fig2.jpg (33.07 KiB) Viewed 152 times

A plot of fringe intensities was made along the direction of the white line in the interferogram. Here is the plot.

Feb24_fig3.jpg
Feb24_fig3.jpg (620.12 KiB) Viewed 152 times


The 2:1 intensity alternation of the D1 and D2 components visible in the interferogram is quite clear in the plot. A background "pedestal" was removed and Lorentzian lineshapes were fit to 6 fringes (3 doublet pairs).


Feb24_fig4.jpg
Feb24_fig4.jpg (860.24 KiB) Viewed 152 times


A Gaussian shape was fit to the central peak to determine its centre location thus establishing the zero location of the interferogram. Then, fringe radii could be measured for the six fringes. It can be shown that the fringe radii obey a simple relation (counting fringe order with respect to the central fringe order):

Feb24_fig5.jpg
Feb24_fig5.jpg (7.36 KiB) Viewed 152 times

This suggests that a plot of squared fringe radius versus fringe order is linear. Such a plot was made with a linear fit to find the slope.

Feb24_fig6.jpg
Feb24_fig6.jpg (141.28 KiB) Viewed 150 times

The splittings between components were also measured for the 3 pairs of fringes. It can be shown that this splitting is given by:

Feb24_fig7.jpg
Feb24_fig7.jpg (20.62 KiB) Viewed 152 times

Thus, the known sodium splitting can be used to find the scaling constant, eta, without any measurement of camera focal length etc. This value of eta is transferrable to the H alpha measurement under the assumption that the camera optics are achromatic, probably a reasonable assumption for a good quality lens. In conjunction with the slope of the line in the plot of fringe squared radii versus order number, this gives the ratio of wavelength to etalon spacing, lambda/D, from which many of the relevant parameters of the etalon can be calculated.

With this method, I calculated an etalon spacing of 120 microns and a free spectral range of 19 angstroms for the LS50FHa etalon (near 6563 angstroms). With the previously calculated value of the etalon finesse, this gives a wavelength fwhm bandpass of 1.6 angstroms (near 6563 angstroms). I take this fwhm result with a grain of salt because there is a question of whether the camera optics were sharp enough to image the fringes properly as mentioned above.

If I use the simple geometrical relation for eta, namely eta = p / f, I get a value of eta which is 17% lower than that extracted from the sodium measurement. I think I have more confidence in the sodium result.

Finally, here is a photo of the setup with the sodium lamp in place.


Feb24_fig8.jpg
Feb24_fig8.jpg (180.62 KiB) Viewed 152 times


Cheers.
Peter
Last edited by p_zetner on Thu Feb 25, 2021 9:59 pm, edited 1 time in total.



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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by Carbon60 » Wed Feb 24, 2021 10:23 pm

Excellent, Peter.

Fascinating.

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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by christian viladrich » Thu Feb 25, 2021 7:54 pm

Hi Peter,
I am puzzled by the factor 2x between the "expected" and measured values. As you said, it could be because of the f/16 ratio used. I tested different values from f/1.8 to f/11. It was a good way to learn about the true optical quality of my lenses.


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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by p_zetner » Thu Feb 25, 2021 10:08 pm

Hi Christian.

A factor of two in the fwhm bothers me a little but not too much because this is dependent on a measurement of the fringe width which depends on image sharpness and hence camera lens quality and f ratio. At least I can understand how a discrepancy between my measured fwhm of 1.6 angstroms versus Lunt’s specification of < 0.7 angstroms could arise.

On the other hand, the calculation of free spectral range should be independent of lens characteristics. This calculation utilizes the slope of the line in the plot of fringe squared radii versus order number which simply requires fringe radii to be well measured. In the absence of any strong geometric distortion from the lens this should be a pretty robust measurement. When the value of this slope is combined with a measurement of the “scale” factor eta this gives the ratio of wavelength to etalon spacing, lambda/D. The scale factor calculated by the sodium splitting measurement and by a simple determination (pixel pitch)/(camera focal length) differ by 17% so the results for eta seem good.

I am left with lambda/D = 0.005 for this etalon (at 589 nm). Checking this with my H alpha measurement gives consistency, with lambda/D = 0.0057. That implies a cavity spacing of ~ 120 microns and fsr of 19 angstroms.

Is this reasonable?



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Re: Testing a Lunt LS50FHa etalon with a H spectrum tube.

Post by christian viladrich » Fri Feb 26, 2021 10:22 am

Hi Peter,
The only measure I know of a Lunt etalon is this one :
https://luntsolarsystems.com/were-proud-of-our-etalons/
They say :
Specifications: Lunt Solar 50mm Etalon
Center Wavelength: 656.28nm
Peak Transmission: 79.89%
Bandwidth: 0.7 Angstroms (FWHM)
R: 12.5 Angstroms

Image
https://luntsolarsystems.com/author/andy-lunt/


I have no idea of the dispersion of the FSR from one etalon to the other.


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