Rayleigh criterion calculations, accurate for extra-long wavelengths?

[pipnina]

I have been trying to work out what size dish would be needed if I were to build a telescope for the 21cm hydrogen line. I built an equation set in desmos graphing calculator which works for optical telescopes but when trying to use it for long wavelengths it seems to break down.

The equation I was using before was "r = sin(1.22*λ/(a/1000))" (r being the angular resolution in radians, λ being the wavelength being observed in millimeters and "a" being the aperture of the telescope in millimeters). It worked for visual telescopes but when applying to radio things went awry.

Placing 210 as λ leads to the sine function bringing the value to negative numbers. Using the more traditional "r = 1.22*λ/d" I find that a 1 meter dish observing the hydrogen line gives me an angular resolution of 256 radians! Surely impossible!

Someone who knows the maths, please help me

Cheers!

[Stub Mandrel]

I recall reading that if you use a Sky TV type satellite dish about two feet wide to pick up microwaves resolution is about 4-5 degrees. That's about 10GHz so a wavelength of 3cm.

So for 21cm you must be looking at 30-35 degrees.

I have found this HERE:

θ = 2.5 x 10⁵ x λ/D, where θ is in arcseconds and λ and D are in meters

θ = 1.22 x λ/D, where θ is in radians and λ and D are in meters

I also found something that said any less than a 10 metre dish is considered amateur because the resolution is so poor!

That's why teh Very Large Array has three lines of 25m dishes 13 miles long....

[pipnina]

33 minutes ago, Stub Mandrel said:

I recall reading that if you use a Sky TV type satellite dish about two feet wide to pick up microwaves resolution is about 4-5 degrees. That's about 10GHz so a wavelength of 3cm.

So for 21cm you must be looking at 30-35 degrees.

I have found this HERE:

θ = 2.5 x 10⁵ x λ/D, where θ is in arcseconds and λ and D are in meters

θ = 1.22 x λ/D, where θ is in radians and λ and D are in meters

I also found something that said any less than a 10 metre dish is considered amateur because the resolution is so poor!

That's why teh Very Large Array has three lines of 25m dishes 13 miles long....

Ah! I realized that my λ was being measured in meters instead of millimeters! Hence the massive confusion between 256rad and 0.256 rad (14.6deg)

Oh dear

[7170]

What are you hoping to achieve? Detection of specific 21cm signals, mapping large areas or images of detailed structure of individual galaxies?

Amateur radio telescopes in general look for the existence of a signal in an area, or map larger areas because the size required to produce detailed structure images is huge, so is impractical.

The problem is shown nicely by the Arecibo Observatory dish, which is 305m in diameter and a only 3.5 arcminute angular resolution, so is generally used to map large areas of the sky. As a comparison an ESPRIT 80 ED Super APO is claimed to be 1.74 arc seconds resolution.

Obviously it varies but I would suggest most people who are serious about L-Band radio astronomy in some form are using dishes which are 3m or larger, or an array of home made yagis based on what I have seen/read. Also the LNA(s) you use have a massive impact on your results. A common starting point for people with 3m dishes would be galactic Hydrogen mapping to try and see the shape, structure and motion of the Milky Way.

Despite the inability for an amateur to made a high resolution image of an object, it in no way diminishes the interest in the subject. Which as I have said on here previously is more of an exercise in electrical/rf engineering and maths than anything else.

[pipnina]

25 minutes ago, 7170 said:

What are you hoping to achieve? Detection of specific 21cm signals, mapping large areas or images of detailed structure of individual galaxies?

Amateur radio telescopes in general look for the existence of a signal in an area, or map larger areas because the size required to produce detailed structure images is huge, so is impractical.

The problem is shown nicely by the Arecibo Observatory dish, which is 305m in diameter and a only 3.5 arcminute angular resolution, so is generally used to map large areas of the sky. As a comparison an ESPRIT 80 ED Super APO is claimed to be 1.74 arc seconds resolution.

Obviously it varies but I would suggest most people who are serious about L-Band radio astronomy in some form are using dishes which are 3m or larger, or an array of home made yagis based on what I have seen/read. Also the LNA(s) you use have a massive impact on your results. A common starting point for people with 3m dishes would be galactic Hydrogen mapping to try and see the shape, structure and motion of the Milky Way.

Despite the inability for an amateur to made a high resolution image of an object, it in no way diminishes the interest in the subject. Which as I have said on here previously is more of an exercise in electrical/rf engineering and maths than anything else.

Sadly I think I'm unlikely to build a dish in the near future. It'll probably be a project for when I have more time. I would probably be using it as a "scanning" setup for mapping the northern hemisphere if I made it. Dunno if it exactly works that way.