Relation between BF size and the PST Sweet Spot

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Relation between BF size and the PST Sweet Spot

Post by Starry Jack » Thu Jun 06, 2019 2:30 pm

What is the relationship between the size of the BF and the PST Sweet Spot?

With my f6.5 native 152mm refractor with the 1:7 glasspath and a 5mm BF I am around f11 and f16 with and without a Barlow.

Without a Barlow I see about 1/4 disk with a pronounced sweet spot. With the Barlow I see about 1/8th disk or so and the sweet spot is nearly gone.

Once I get a 15mm BF I believe I will see about a full disk without the Barlow but whT should I expect with the sweet spot?

Thanks,
Jack


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Re: Relation between BF size and the PST Sweet Spot

Post by bart1805 » Thu Jun 06, 2019 2:53 pm

Nothing will change in my opinion. Sweet spot is caused by the etalon, not by the BF.



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Re: Relation between BF size and the PST Sweet Spot

Post by Starry Jack » Thu Jun 06, 2019 3:37 pm

Thank you. So if that is true I should see a full disk sweet spot, but at least that gives me a much bigger Sweet FOV than current.

True?


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Re: Relation between BF size and the PST Sweet Spot

Post by bart1805 » Thu Jun 06, 2019 3:47 pm

Don't know what you mean exactly. The sweet spot is about the size of the sun in a 400mm telescope. So if your focal length is longer, the sweet spot is smaller than the whole sun.



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Re: Relation between BF size and the PST Sweet Spot

Post by marktownley » Thu Jun 06, 2019 5:28 pm

There is no relationship between the size of the sweetspot and the blocking filter. The size of the sweetspot is related to the size of the etalon in relation to the objective. By using a barlow you are just 'zooming' into the area of the sweetspot, It's size remains the same but the apparent field of view becomes smaller with the barlow so more of the (smaller) fov is filled with sweetspot.


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Re: Relation between BF size and the PST Sweet Spot

Post by Starry Jack » Thu Jun 06, 2019 6:01 pm

Oooooohhhhh....
I’ve almost got it. Nice description. So then, since I’m still conceptual here, if I get the BF15 I get a larger FOV which I can zoom into and out of using the Barlow, but how big is the sweet spot in relation to the FOV has in the upgraded rig. If the sweet spot is full disk in a native PST 400mm config, what is the sweet spot in my rig?


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Re: Relation between BF size and the PST Sweet Spot

Post by Starry Jack » Thu Jun 06, 2019 6:29 pm

I’m betting that the new system, operating at f11 will have a sweet spot as long as the non-barlowed FOV. True? I reason that since the 400mm PST at f10 has that characteristic.


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Re: Relation between BF size and the PST Sweet Spot

Post by Bob Yoesle » Fri Jun 07, 2019 4:36 pm

No, not true.

The "sweet spot," technically known as the Jacquinot spot, is generated by the field angles (and for the mica filters - instrument angles) produced by the optical configuration within which the etalon is placed. For collimator based etalon systems, it has little to do with the f ratios of the optics, and everything to so with the focal lengths and resulting field angle magnifications.

All H alpha narrow-band filters have an "acceptance angle," which defines how much of an angle can pass through an etalon before the design wavelength (or center wave-length - CWL) shifts un-acceptably "off-band." This is naturally one-half the diameter of the Jacquinot Spot diameter, other wise known as the "sweet spot." The Jacquinot spot is defined as the field about the optical axis within which the the peak wavelength variation [ Δλ ] with field angle does not exceed √2 of the etalon bandpass. This angular field can thereafter be used to perform close to monochromatic imaging or viewing.


Equation 1: Δλ = √2 x FWHM

The tilt (field) angle verses wavelength change can be found with formula for the CWL shift:

Equation 2: Δλ = ½ (CWL / n^2) θ^2

We can now solve for θ:

√2 x FWHM = ½ (CWL / n^2) θ^2

θ^2 = √2 x FWHM ÷ ½ (CWL / n^2)


For an air spaced etalon (n = 1.00) with a FWHM of 0.7 Å at the H alpha line (6563 Å), with θ in radians (1 radian = 57.2957795 degrees):


θ^2 = 1.4142 x 0.7 ÷ ½ (6563 / 1.00)

θ^2 = 0.98994 ÷ 3281.5

θ^2 = 0.000301673

θ = √0.000301673

θ = 0.017368736 (radians) x 57.2957795 degrees

θ = 0.9951553 degree


Therefore the Jacquinot spot is ~ 1.0 degree, and the “acceptance angle” (field angle) for this size a spot would be ~ 0.5 degree, as is the frequently cited acceptance value for a 0.7 Å FWHM etalon. Outside this "sweet spot" radius H alpha detail will begin to fade until it is completely off-band and one sees only continuum. We can also see that as the bandpass of the filter system narrows, the acceptance angle becomes smaller, and this explains why very narrow band filters require even better optimized ancillary lens systems to perform to their potential.

For an etalon placed ahead of the objective, the entire disc of the Sun (0.5 degree) lies within the "sweet spot." For an air-spaced etalon placed in a collimator system, such as a PST mod with a -200 mm collimator focal length, the Jacquinot spot is reduced in size due to field angle magnification, which just as with eyepieces - is simply the focal length of the objective divided by the focal length of the collimator lens. For your objective operating at f11, the focal length becomes 152 x 11 = 1,672 mm. So the field angle magnification becomes 1672 mm divided by 200 mm (the focal length of the PST collimator lens) = 8.36 x, and the Jacquinot spot is reduced in size by this amount 0.995 ÷ 8.36 = 0.11 degrees - or about 1/5th of the Sun's diameter. At f16 the Jacquinot spot is reduced even more is size - 152 mm x 16 = 2432 mm ÷ 200 mm = 12.2 x, so the Jacquinot spot is only 0.995 ÷ 12.2 = 0.08 degree.

As long as your eyepiece field of view does not exceed these values, you will be completely within the "sweet spot" and so no off-band issues will occur. As soon as your field of view exceeds the size of the "sweet spot," it will begin to become evident.


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Re: Relation between BF size and the PST Sweet Spot

Post by Starry Jack » Fri Jun 07, 2019 8:15 pm

Bob,
Your "Cool Geek Factor" just rose to a "10". :) That is an intricate and detailed explanation and I thank you for the time it took to write it and perform the calcs which I would not have been able to do...that was a gift.

I've read it several times and will digest more and more. I've gone to a FOV calculator at (https://astronomy.tools/calculators/field_of_view/) and used the various Barlow and non-Barlowed configs with my camera:

CAMERA: (2048x1536 px; 2.5 micron; 1/3" sCMOS)
FOV NO BARLOW: 0.17 degrees by 0.13 degrees
FOV 1.5 BARLOW: 0.12 x 0.09 degrees
FOV 2X BARLOW: 0.09 x 0.07 degrees

Image
Solar Image Calcs 3 - 1-5 Barlow.PNG
Solar Image Calcs 3 - 1-5 Barlow.PNG (536.38 KiB) Viewed 2569 times
Attachments
Solar Image Calcs No Barlow.PNG
Solar Image Calcs No Barlow.PNG (538.78 KiB) Viewed 2569 times
Solar Image Calcs 2x Barlow.PNG
Solar Image Calcs 2x Barlow.PNG (542.28 KiB) Viewed 2569 times


Explore Scientific 152mm f6.5 achromat
Aeries D-ERF
Quark Chromosphere f27 native, (f14 when focal reduced)
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12nm Filter
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