I How feasible is home radio astronomy?

[Vanadium 50]

TL;DR Summary

Is a homemade radio telescope realistic?

Is a homemade radio telescope realistic?

There seems to be a confluence of multiple technologies that makes the situation better than when I was a wee lad: software-defined radio (SDR), the easy availability of satellite dishes, surveillance drives, and fast CPUs.

Let's take a step back - it is trivial to see the sun in radio. An old analog TV, a set of "rabbit ears" antenna, and you're good to go. Point the antenna at the sun (i.e. the ears are perpendicular to it) and there is noticeably more snow and static than when pointing it away from the sun (i.e. lines up with it). But I am looking to see what else can be done.

I imagine getting a couple of DishTV dishes, and mounting them in the corners of my house or yard,. This gives the directionality of a house or yard sized dish, but of course not the sensitivity. Ballpark a few degree resolution for the array (more like 30 for one dish) It is likely easier to point with phase than with motors. Use SDR as receivers, record every night to disk and "stack" days or weeks of exposure together. Because its SDR you can look, e.g. on and off the 21 cm peak and map out hydrogen.

I'm wondering - is there anything to see with something like this? The sun obviously, but I did that already. When I was maybe 10. Probably it is limited to night use, as the sun is so bright and an array of small dishes is not so directional. What;s the next brightest source? Jupiter probably. After that, Cassiopeia A perhaps? Is seeing the Crab pulsar possible? It's dim, but it also pulses at a known frequency - a Fourier transform should show a peak. I wouldn't need to discover it de novo - I already know its properties. (Unfortunately, it's in Taurus, which doesn't get terribly high in the sky)

 

[Baluncore]

Is a homemade radio telescope realistic?

It is possible, but not realistic. There are better ways to invest your time and money.

The knowledge field is simply too big for one person, it requires a team. It takes electronics experience, numerical computing, and volunteer management, things that do not usually go together. The people interested in RA will be the amateur optical astronomers when there is cloud. For some reason, astronomers work best by themselves, alone at night. They self select. Good luck herding those cats.

Our Sun, during most of the solar cycle, is not as good a source as you might hope. Venus will radiate better signals more often. The best pulsars are in the southern sky, most people are in the Northern Hemisphere. To hear the brightest pulsar noise envelope in real time, you will need a 25-metre dish and a cooled receiver with a bandwidth of several MHz.
Position, position, position. If you live on a cliff above the sea, which is unlikely, you might make a "sea interferometer" with a single dish or a dipole array, then watch a radio source rise or set.

A steerable 15-metre dish, surfaced with wire mesh, is needed to get enough signal to be interesting. Cryogenic cooling a receiver is not simple, and eliminating the noise produced by switching power supplies, TV and microwave ovens will be difficult. An SDR is all mixer, so inherently noisy when you widen the bandwidth to a few MHz, to catch some astronomically small amount of energy.

HAM radio guys bounce signals from Earth to the Moon and back. If you cannot do EME, don't even think of trying RA.

Get creative. Find an unusual RA project, evaluate the cost of the engineering and building approvals needed for the antennas. Then think again. Rinse and repeat.

 

[Vanadium 50]

Let me push back a little.

I am not trying to compete with ALMA. I am thinking along the lines of the radio equivalent of Meade or Celestron. Real-time was never in the cards: but even amateur optical (Hi Russ!) stacks and processes the pictures - real time is not what it once was.

As far as expertise, the sketch looks a lot like the DAQ for a HEP experiment. Chosen because it is something I know something about. I know something about radio, and have done EME, although not with my own equipment. So while I am not an expert, I do have some expertise in relevant things.

This is going to be a learning experience, even if I did radio astronomy for a living, because it's got to be built out of what's readily available, which is certainly not goinng to be optimal. And that indicates a need for a progression of gradually more difficult targets - a gap of several orders of magnitude is difficult to recover from. Can one start at the sun, move to Venus, then Jupiter, then Cas A, then the pulsar in Vulpecula* and so on down to the Crab? Remember, real time is not an issue, but needing a month long exposure to see the sun would be. Nature has to be kind - you seem to be an expert - is she?

 

[Vanadium 50]

*Vulpecula? That's a real constellation? No named stars? It sounds to me like the IAU should declare it a Dwarf Constellation.

 

[Baluncore]

Can one start at the sun, move to Venus, then Jupiter, then Cas A, then the pulsar in Vulpecula* and so on down to the Crab? Remember, real time is not an issue, but needing a month long exposure to see the sun would be.

My first attempt to detect the Sun in about 1970 was a failure, even though it was active at the time. I have done my time keeping an RA observatory running, that was doing VLBI research. I have also tried to help an amateur RA group technically get it together. Maybe I am too honest, but there are limits to what can be done with such small signals. The Sun is simply too quiet most of the time.

You can build an interferometer from a fixed pair of antennas, then generate the sum and difference signals. Tune to a quiet RA reserved band, to detect Sagittarius, Cygnus, Cassiopeia, Canis Major, or Puppis, as they move through the combined beams of your interferometer. That may reward you with evidence of Earth rotation, and to show it was not terrestrial or solar, the length of the sidereal day.

 

[Vanadium 50]

Now we're getting somewhere!

My point was that if you need to span N orders of magnitude in sensitivity and you have 2N sources, it helps if they are roughly equally spaced (5 dB in my example) and there isn't a giant gap. Knowing the hierarchy of sources to target is therefore valuable.

In thinking of constraints...

I'm not going to clone Ariccebo. Even the NSF isn't going to clone Ariccebo. The question is whether it is possible to build something that is the radio equivalent of something between Meade/Celestron and the Cap'n Crunch Spy Scope.

So what's available - DishTV dishes are easy to come by, and the older C-band ones aren't much worse. (Although moving and shipping them is not cheap). However, if you want them on 1D mounts they get exepensive and 2D is even worse. Conclusion: "the earth is my mount" and use a combination of the earth's rotation and digital delay lto sweep the sky.

Operating band? The higher I go in frequency, the better my angular resolution gets, but the more expensive the radios become. I was thinking a relatively low 21 cm, because I know the sky has structure there. There is of course a lot of 2.4 GHz equipment on the market, but there's also a lot of interference, and even if there weren't, I suspect I'd just ghet a really good look at the atmosphere. SDR is one way to be able to experiment with different choices, within reason.

DAQ becomes an issue. If you think of a 21 cm receiver as a giant ADC, you will saturate the writing speed of an array of drives. And it will all be noise. The thinking was to trigger on differential signals (not exactly interferometry) above a threshold. This is a bandwidth limitation, but I can only afford so much. Bandwidth vs. capacity is the tradeoff with this design - the scale is 100 MHz is 1 disk/night. You need to either reduce the bandwidth, process the data immediately and free up the disk in time, or buy a lot of disks.

I am a bit surprised that you find the sun so hard to see when I found it so easy as a kid, but that was near the peak of Cycle 21. The sun has certainly quieted since then.

 

[Drakkith]

Here are a few links that may or may not help:

https://hackaday.com/2019/10/22/a-miniature-radio-telescope-in-every-backyard/
https://www.radio-astronomy.org/getting-started
https://radiojove.gsfc.nasa.gov/kits/

 

[Baluncore]

Operating band? The higher I go in frequency, the better my angular resolution gets, but the more expensive the radios become.

As frequency rises, the beam-width falls, and the dish needs to have a more accurate figure, with smaller holes, better steering and wind stability. It is difficult to make a sharp pointed thermometer at radio frequencies, without interference from Earth and satellite based sources. You need multiple channels with switching to separate the sources.

SDR is one way to be able to experiment with different choices, within reason.

You must start with FET LNAs and band-pass filters before any mixer, or everything will intermodulate. SDR is not the solution, it is a problem.

DAQ becomes an issue. If you think of a 21 cm receiver as a giant ADC, you will saturate the writing speed of an array of drives. And it will all be noise.

There is no need to ADC at twice the bandwidth, unless you are doing VLBI when you only need two bits. Use a log-detector-limiter chip to detect the envelope power of each channel, low-pass and digitise the RSSI output. Something like a $10 cheap AD8307 on a PCB will do that job.

With pulse type interference, you may need to detect the minimum power, that then follows the cosmic noise floor, so rejects the interfering pulses. It works a bit like the old analogue TV noise blanker, where over-bright pulses are made black.

 

[Vanadium 50]

SDR is not the solution, it is a problem.

I don't understand that. Can you elaborate?

FWIW, @Drakkith first link uses SDR.

 

[bob012345]

The first backyard radio telescope built specifically for radio astronomy was built by an ametuer named Grote Reber in Wheaton Illinois in 1937. The cost was $1300 which was a lot of money in 1937. Reber made the first radio maps of the Milky Way galaxy.

https://public.nrao.edu/gallery/grote-rebers-first-radio-telescope/

 

[Vanadium 50]

Um...OK. But it's not 1937, and we already have radio maps of the galaxy.

 

[Baluncore]

The first backyard radio telescope built specifically for radio astronomy was built by an ametuer named Grote Reber in Wheaton Illinois in 1937.

Reber was a qualified electrical engineer, who worked with J D Kraus, "Degauss with Kraus", de-gaussing ships in WWII. They discussed RA on breaks. Reber moved to Tasmania and lived at Bothwell, where he had an array of dipoles operating below 5 MHz, looking at cosmic signals, through "holes" that sometimes appear in the ionosphere.

I don't understand that. Can you elaborate?

FWIW, @Drakkith first link uses SDR.

SDR is the cheapest, which is why it is used, but that demo system does not do RA. When tested, it could not see the Sun.

"Unsurprisingly, the MRT also uses an RTL-SDR receiver for processing signals from the Low-Noise Block (LNB) in the dish. Professor Aguirre says that since they are still using the stock DirecTV LNB, the telescope is fairly limited in what it can actually “see”. But it’s good enough to image the sun or pick up satellites in orbit, which is sufficient for the purposes of demonstrating the basic operating principles of a radio telescope."

First; decide on the RA source you will view. Second; Given your antenna aperture, work out if it will be possible to extract a valid signal from the noise. Third; design your receiver chain. You need a wide-band receiver to capture sufficient energy for RA. If you are serious about RA, you will need something better than an SDR.

It is my observation that amateur RAs, who insist on using an item of equipment that they have now, lack the flexibility of mind and equipment essential to success in the difficult field. For a group, that effect is multiplied factorially.

 

[bob012345]

Reber was a qualified electrical engineer, who worked with J D Kraus, "Degauss with Kraus", de-gaussing ships in WWII. They discussed RA on breaks. Reber moved to Tasmania and lived at Bothwell, where he had an array of dipoles operating below 5 MHz, looking at cosmic signals, through "holes" that sometimes appear in the ionosphere.

Yes. He was brilliant. I have a book The Evolution of Radio Astronomy by J.S. Hey which states;

Radio astronomy would have lapsed into oblivion for a decade but for the inspired initiative of one man, Grote Reber, a young graduate radio engineer of Wheaton, Illinois, USA, who decided to pursue the research as a hobby at his own expense in his spare time.

 

[AndreasC]

Check this out: https://radio-astronomy.org/node/248

 

[Vanadium 50]

I'm still not getting the "can't see the sun" part.

How bright is the sun? Well, there is something over 1 kW/m2 integrated over wavelength, peaking in the visible. Call it 500 THz, and say we are looking at 5 GHz. So we're down 100,000 in frequency. Cubing it to get power, and we're at a picowatt-scale into the antenna.

How sensitve are radios? Microvolts are typical, and since impedances are ohm-scale, microvolts mean mictoamps. So again, picowatts.

So even a quiet, blackbody sun should be visible within terms of order one. As the sun's activity increases, it should be even more visible - the sun is far more interesting than a blackbody.

 

[Baluncore]

I'm still not getting the "can't see the sun" part.

Get yourself a copy of Radio Astronomy, John D. Kraus.
Chapter 8. look at the difference between quiet and disturbed Sun.

 

[Vanadium 50]

I will pick up a text before putting up an antenna, for sure. However, I am still unclear as to how people can miss the sun.

Is the active sun "louder" than the quiet sun? Absolutely. The plot shows it, and effects on the ionosphere are substantial. But the numbers I ran make it look like the sun can be seen even as a black body. It can't get quieter than that.

I'm willing to believe that the terms of order 1 that I didn't consider conspire to be large - there's a famous case where they work out to 192π³ (and I once ran into a case where it was 49152π⁶ - talk about bad luck!) but if that's the problem, I want to know that that's the problem.

If nothing else, it will push me to higher frequencies - you win on temperature (21 cm is quite cold), and you win on angular resolution. However, that also pushes the receiver cost up.

 

[Paul Colby]

I've seen people post observations of the 1420 MHz hydrogen line a few years back using an SDR and an antenna made from a yard waste totter and aluminum foil. There is a decent Doppler spread across the plane of the galaxy. I'll rummage around and see if I can cough up a link or 2.



So, it's definitely possible to do. My recommendation is to steer clear of the cheesy 8 bit RTL-SDRs in favor of the slightly less cheesy 16 bit Sdrplay offerings. Much better RF frontends on them. It's a 20dB noise reduction straight off the bat. They are just 300 bucks or so a clean factor of 10 over the RTL-SDRs.

 

[berkeman]

an antenna made from a yard waste totter and aluminum foil.

Very creative and cool.

 

[neilparker62]

Here are a few links that may or may not help:

https://hackaday.com/2019/10/22/a-miniature-radio-telescope-in-every-backyard/
https://www.radio-astronomy.org/getting-started
https://radiojove.gsfc.nasa.gov/kits/

Interesting that the "hacakaday" site comes up. Seems to deal with quite a variety of technical topics. It's off the subject here (apologies) but there was an excellent article on net booting raspberry pies which is something I've been working on recently. Reference below if of interest.

https://hackaday.com/2019/11/11/network-booting-the-pi-4/

 

[chemisttree]

I’ve heard of using a 20m dipole to listen to meteor showers?

 

[Baluncore]

I’ve heard of using a 20m dipole to listen to meteor showers?

https://en.wikipedia.org/wiki/Meteor_burst_communications
Does radio astronomy include bouncing radio signals off ionised trails in the atmosphere or ionosphere?
https://en.wikipedia.org/wiki/Super_Dual_Auroral_Radar_Network

 

[chemisttree]

I guess if you are communicating about radio astronomy?

 

[chemisttree]

Here is a description of listening to meteor showers.

 

[Vanadium 50]

That does bring up an interesting question. How high up does on object have to be to be considered "astronomy". I'd say 100 km, but I am no authority.

That makes the aurora "astronomy", which may be undesirable.

 

[Paul Colby]

https://www.spaceacademy.net.au/spacelab/projects/jovrad/jovrad.htm

Jupiter radio emissions certainly qualify as radio astronomy. The HF band is definitely in the SDR amateur scope.

 

[Tom.G]

Dish Antenna possibilities:
Satellite TV dish
a Snowboarding saucer. (roughly 2.5 feet dia., plastic, glue some Aluminum foil to it)

Spectrum magazine (IEEE publication) has an article about receivers/computers for same; (either October or November 2023 edition; I already tossed mine)

And an article on building your own system (with some links) at:
https://spectrum.ieee.org/track-the-movement-of-the-milky-way-with-this-diy-radio-telescope

And in case you have not already seen it:
https://www.physicsforums.com/posts/6940884

Cheers,
Tom

 

[TheOrionNebula]

Home made radio astronomy systems can be built easily (and cheaply) using off the shelf components from Amazon or EBay, a computer, and if you happen to have one, a Wok ! The 21 cm hydrogen line is not difficult to detect with a system like this since the HI is distributed over much of the sky, and you don't need to worry particularly about where you are pointing - just point it upwards, and wait for the Galactic Plane to come roughly overhead. Oh, and don't forget to eat whatever you were cooking in the wok and clean it off first ... ! https://www.astronomy.com/observing/wok-way-to-the-stars-radio-astronomy-with-kitchen-gear/

 

[nathanielbutts]

Home radio astronomy is more than feasible: it's possible, cheaper than you think, and you can do more than you think. If you start with failure in mind, you'll get there every time.

A link to a presentation I gave at the Society Amateur Radio Astronomers (SARA) Western Conference this past April.

https://docs.google.com/presentatio...ouid=103956535943816132717&rtpof=true&sd=true

A link to the video of the presentation.

 

[Vanadium 50]

Excellent talk.

@Baluncore , who is an EE, was very very negative about SDR. You seem more positive. Care to comment?

You also keep coming back to H-1. What do you fnd interesting about cold gas?

 

[marcusl]

Va50, let’s turn this discussion around. What would you like to observe? Once we know, we can talk about how to go about it (or if it is feasible).

 

[Vanadium 50]

First. we have a difference of opinion between experts on SDR. I'd like this explored so I can learn something.

As far as H1, I am curious why someone would find it interesting.

I am also working under the assumption - perhaps wrong - that the angular resolution isn't that great, so point sources are spread out and diffuse sources are even more diffuse.

I would like to see the Crab. This seems impossible.

• It's not that bright in radio
• The surrounding nebula is a radio source, and does not blink like the pulsar does.
• You get the 30 Hz signal, but getting the phase right, well, you're on your own.
• It's not that high in the sky.

 

[Baluncore]

I would like to see the Crab. This seems impossible.

You will need a radio quiet location, and a 15m diameter dish, covered in 1/2" chicken wire, that can track the source, while it is above the horizon.

Build for the hydrogen line, there is plenty of H1 about, and you can do other things with it later, like Doppler.
1420 MHz, λ = 21 cm, For 15 m dish; Beam Width = 57.3° * 0.21 m / 15 m = 0.8°
Make sure your tracking is better than that.

Build a two-channel, H&V polarised, low-noise receiver for the focus of the dish. Down-convert the two channels to IF, and send those signals for detection and recording in your shelter.

Find the exact rate of the crab pulsar now, then cyclically power spectrum accumulate into a circular buffer at that rate. The pulsar should climb out of the noise.

The difficulty is finding half a dozen voluntary assistants, with the skills and time needed to design and advance the hardware to the point where it will come together. A chain is only as strong as its weakest link, you are now the first and only link.

 

[nathanielbutts]

Radio astronomy is a difficult topic to tackle, regardless of your position, funds, and desires. RA hasn't been around long enough to be supported as well commercially for the amateur astronomer as much as it has been for the visual astronomy world. The barrier to entry requires knowledge of mechanical engineering, electrical engineering, programming, physics, EMF physics, etc.

The above is a great reason to start with HI and with SDR. SDR are finally cheap enough commercially, and "good enough" for their application. The construction of an antenna for HI is fairly straight forward (depending on your options) to the point anyone of enough gumption can build one with minimal assistance. HI is also easy to detect, giving you the quickest (nearly so) entry to RA to keep one interested in the craft.

With the wavelengths as large as they are, the physics get in your way of what's feasible to detect. It is capable of taking quite significant data though, you just have to tailor your equipment to your desires. I have associates who focus on masers using small dishes, between 6-12MHz. I have other associates with sub 1° resolution capabilities, but they have easily spent $50k on their equipment, and had to build it all themselves. We also have people detecting FRB with in-between equipment, and extensive knowledge.

The best use of RA at home is to enjoy it, learn something new. Add that data you get from RA to your visual images for a more complete understanding of your observations. What you learn from RA can be used to formulate ideas which can then turn into requests submitted to larger University or Professional observatories.

First. we have a difference of opinion between experts on SDR. I'd like this explored so I can learn something.

As far as H1, I am curious why someone would find it interesting.

I am also working under the assumption - perhaps wrong - that the angular resolution isn't that great, so point sources are spread out and diffuse sources are even more diffuse.

I would like to see the Crab. This seems impossible.

• It's not that bright in radio
• The surrounding nebula is a radio source, and does not blink like the pulsar does.
• You get the 30 Hz signal, but getting the phase right, well, you're on your own.
• It's not that high in the sky

 

[Vanadium 50]

You will need a 15m diameter dish

I don't buy that. Or any single parameter number. In principle, I can trade dish size for exposure time.

Bigger is better, sure. But in principle, I can see very weak sources if I integrate long enough. And one of the advantage of the SDR/record everything ecosystem is while I am looking at other things I an still collecting Crab data, Maybe it takes a year. So what?

The real problem with the Crab is that there is one number to pull it out of the background - 30 Hz. In North America, power is 60 Hz so you have 30 Hz broadband noise.

 

[Paul Colby]

The 21cm hydrogen line may seem dull to some but the data collected with this antenna looks nice.

https://16767887561855875192.google...4KkP3VIrWM-hyjb60s4fTizyPxL-6alSQSNOSTjUb1Nns

 

[berkeman]

The 21cm hydrogen line may seem dull to some but the data collected with this antenna looks nice.

https://16767887561855875192.google...4KkP3VIrWM-hyjb60s4fTizyPxL-6alSQSNOSTjUb1Nns

Wow!

 

[Baluncore]

I would like to see the Crab. This seems impossible.

It does seem impossible, but it can be possible. You will need to balance your resource investment in several dimensions if you are to stand a chance. My recommendations are for a minimum cost, minimum time entry into Crab pulsar RA.

I don't buy that. Or any single parameter number. In principle, I can trade dish size for exposure time.

I have already pushed that trade in my estimate of how to cross the impossible to possible boundary. I have put together a list of waypoints that can get you that 30 Hz accumulated result. You can reduce the dish, but it will make the signal processing significantly longer and more difficult. It is easiest to start with a dish that is low-cost and possible, something that an amateur could make, that would not be redundant tomorrow.

Dish area is important because that is really the lowest cost investment that will get you ahead in s/n ratio. Why a 15 metre dish? Because anything beyond that is too difficult to construct. 15 m can be built a little sloppy and still work. 15 m can be aimed without too much trouble. Building a smaller dish will take a similar amount of management and number of components, but the square law says, go on adding another 1 metre annulus, until it is too floppy, or will be damaged by strong winds, even with the lower windage of a chicken wire mesh surface. More on a dish at the end.

You will want to avoid the expense of developing and running cryogenic receivers at the focus, so will benefit from a stack of Peltier effect coolers for chilling the LNA front-end, through to the first down-converting mixer and IF line driver. Peltier is now the lowest cost cooling for the maximum advantage.

The advantage of an SDR is that it provides a channel that is highly flexible and dynamic in frequency. That never happens with RA, where you are restricted, by interference, to operate in quiet bands specifically reserved, allocated to RA. You should use the full bandwidth available in the band, to gather the maximum energy. You do not need a DC to daylight SDR to do RA, it is too hot and too noisy.

By using crossed dipoles at the focus, you get more energy from the same dish aperture. H & V polarisation requires a two channel (synchronous) receiver, with a single 1st LO, which can then also produce LH & RH signals. That cannot be done with an off-the-shelf SDR, which will generate too much heat for the cooling system at the focus.

OK, so pulsars produce more energy down in the 608 to 614 MHz RA band than at 1420 MHz, but you must aim for a 1420 MHz dish initially, because you can't go backwards to build another dish later for 1420 MHz. What you start to invest in, will be a long-term constraint on your RA.

How to build a low-cost and safe 15 m dish?
I would build an offset fed dish, that was hinged on an edge, close to the ground on a wide circular turntable. It would approximate a triangle, with three circular corners and three straight edges, for which the magic number is; 10=3²+1. In polar coordinates, the aperture would be;
Radius = 7.5 + Sin(3*theta) * 7.5 / 10.
That beam pattern is indistinguishable from a circular aperture.
It could be built safely, flat on a concrete slab, as an open octet truss, NOT as a heavy hub on a post with petals. All measurements would be vertical, from the flat concrete slab into the structure, using a stepladder where needed, with the critical key points painted onto the slab first.
The focus would descend to about 1 m above the ground when the dish was declined below the horizon, so you could work on the supports and receivers safely, without a cherry picker.
It would be excellent for tracking slow and steady targets creeping along near the horizon, but not good for targets that pass directly overhead, which would require high speed motors on the turntable.
Such a dish also has amateur radio applications.

 

[marcusl]

The word-based arguments in this thread could go on all day, so I offer some numbers to tell us the true story. To wit, let's put together a rough link budget.
1. General Link Budget
The power spectral flux density L of an astronomical radio source is measured in Jansky's, where 1 Jy = 10^(-26) watts/Hz/square meter. The signal power at the antenna feed is $P_s=\eta LAB$, where $A=\frac{\pi D^2}{4}$ is the aperture area, B is the bandwidth and η is the antenna efficiency (around 0.8 for an antenna design with optimal balance between beam taper loss and feed spillover loss). Noise power $P_n = kT_{sys}B$, where Tsys is the receiver system noise temperature. The SNR is $$SNR=\frac {LAB\eta}{kT_{sys}B}=\frac {\pi \eta LD^2}{4kT_{sys}}$$Note that bandwidth drops out of the equation. Now we fill in values.

2. Source: The Crab Nebula power spectral flux density at 21 cm (1.420 GHz) is 930 Jy [Matveenko] and the pulsar (NP0532) amplitude is 3 orders of magnitude lower, if I'm reading Fig. 58 of [Apparo] correctly. We'll work the link for the bright nebula and then subtract 30 dB to get the SNR for the pulsar.

3. Receiver Noise Temperature: It's not too hard to design a single-transistor LNA at L band with a 0.5 dB noise figure (NF) at room temperature with no cooling, and, say, 12 dB of gain. (You can probably buy them off the shelf, too, since this is within the 950 - 2150 MHz band used by commercial satellite TV receivers.) The LNA is mounted on the dish feed horn to keep the feed loss low. Let's allocate 0.25 dB to that. (You'd have to add another .3 or .5 dB for a connectorized commercial preamp, but we'll assume a home brew LNA with a short microstrip feed line.) Put another amplifier right after to drive the coax from the antenna into your house. A commercial sat TV line driver might have a 4 dB NF with 20 dB gain; 50 feet of plain-Jane RG-8 style cable (Belden 9913) has about 2 dB of loss. and your SDR might have a noise figure of 2 dB. Using the noise figure cascade formula $$F=F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3- 1}{G_1G_2} + ... $$ where noise factor is F=10^(NF/10), gives a total noise figure of NF=1.09 dB, or a system noise temperature of Tsys=290(F-1)=83K. That's not great and we could do better with a more sophisticated design, shorter cable, etc., but it's representative of an easy-to-build system. We assume that the galactic background noise is small and may be ignored.

4. SNR: With Tsys in hand, we can compute SNR. For dish diameters of D=[5 10 15] meters, the SNR=[-15.0 -8.9 -5.4] dB. The nebula signal is well below the noise floor and the pulsar signal is about 30 dB lower, so there's no chance of seeing the pulsar's 30 Hz variation in real time on an oscilloscope. Let's see what kind of signal processing might reveal the signal if we use Baluncore's 15 m dish which gives an SNR of -35 dB.

4. Signal Processing:
The best chance of measuring the pulsar's rotation period is to record a long data string and perform an autocorrelation, that is, the string is convolved against itself with a variety of time offsets (lags). The lag corresponding to the first peak is the estimate of the period. This period can be used to accurately chop the record into discrete periods that can be averaged to reveal the time-domain shape of the pulse. The SNR for this time-domain process is proportional to the number of periods averaged, N1; to achieve SNR_out=15 dB, say, we need to average N1 = 50 dB or 100,000 periods, requiring a (reasonable) data record of ~1 hour duration. How many periods N are needed for the autocorrelation? We need an SNR out of the convolution of at least 10 dB and preferably more. The output SNR of an autocorrelation is $$SNR_{out}= N \frac {SNR^2} {1+2SNR}$$Note that the output is proportional to the input SNR when SNR>>1 but to SNR^2 when SNR<<1. The Crab signal in our notional system lies in the latter regime, unfortunately.

To get SNR_out=10 dB, we need N=10 dB - 2*(-35 dB) = 80 dB or N=10^8 periods, corresponding to 3.3e6 seconds or nearly 1 year of integration. This illustrates a maxim that I try to impress upon young scientists and engineers: an ounce of effort to increase signal strength in an experiment is worth a pound (or a ton) of effort to recover it in post-processing. We need more signal.

In fact, this integration time is actually an under-estimate because the noise is continuous but the signal pulse is short, so the time-averaged or effective SNR into the autocorrelation is even lower. This is looking really bad! We find some confirmation of its correctness in [Richards], where Fig. 8 plots SNR vs. antenna size at a range of frequencies. The SNR of the hydrogen line is off the bottom of the chart, even for a 300 m antenna! It seems that we might be correct, so what can we do?

Richards notes that the maximum signal emission occurs at much lower frequencies, around 100 - 200 MHz.

"The conclusion I want to draw is this: at Arecibo we have been able to see the pulsar at a frequency of 430 MHz with about a 20-minute integration time with reasonable signal-to-noise. At lower frequencies, down to about 100 MHz, the signal-to-noise ratio is much better, and it should be possible to observe the pulsar with antennas much smaller than ours, in fact, even with a 25-meter dish. This is the case because, over a wide range of frequency and collecting area, the Crab nebula continuum flux completely dominates the other factors and therefore determines signal-to-noise. As the most interesting of all pulsars, NP 0532 deserves the attention of many observatories."

Extrapolating within their plot suggests that a 15 m dish with 20 minutes of integration at 150 MHz is sufficient to recover the signal with reasonable SNR. Electronics becomes easier and cable loss lower at VHF, so this is a win all around.

5. Conclusion
Measuring the Crab pulsar NP 0532 with home-built equipment seems infeasible at the 21 cm hydrogen line, but feasible (though challenging) at 150 MHz with a large antenna.

I invite corrections, comments and rotten tomatoes

 

[Baluncore]

Extrapolating within their plot suggests that a 15 m dish with 20 minutes of integration at 150 MHz is sufficient to recover the signal with reasonable SNR.

This illustrates a maxim that I try to impress upon young scientists and engineers: an ounce of effort to increase signal strength in an experiment is worth a pound (or a ton) of effort to recover it in post-processing. We need more signal.

I cannot see how skilled amateur radio-astronomers, could regularly build bigger steerable dishes, than about 15 m diameter. Beyond 15 m, everything becomes more difficult. Think teamwork, building approval and engineering requirements, low-visibility, finance, safety, hours of labour, accuracy, durability, and the probability of project completion.

There was a 14 m diameter dish, with a chicken wire surface and warm LNAs, that recorded the brightest pulsar (Vela; 0833,-45°) for many years, looking for glitches. Last I heard, it was badly damaged by a windstorm.
https://en.wikipedia.org/wiki/Mount_Pleasant_Radio_Observatory#Equipment

 

[Baluncore]

Note that S400 (the flux at 400 MHz in mJ) of the Crab pulsar is 11% of Vela. The 14-metre dish can see single pulses from Vela, so power accumulation should extract the Crab pulsar without too much trouble.
PSR B0329+54 might be a better target in the Northern Hemisphere, although you cannot hear such a low audio frequency.
Here is a list of the 7 brightest pulsars.

PSR cat     RA            Dec         T sec     F Hz      S400  S1420 mJ
B0833-45    08:35:20.61  -45:10:34.8  0.089328  11.19464  5000   1050  Vela
B0329+54    03:32:59.40  +54:34:43.3  0.714519  1.399541  1500   203
B1749-28    17:52:58.68  -28:06:37.3  0.562557  1.777595  1100   48
J0437-4715  04:37:16.04  -47:15:10.0  0.005757  173.6879  550    150.2
B0531+21    05:34:31.93  +22:00:52.1  0.033392  29.94692  550    14    Crab
B0950+08    09:53:09.30  +07:55:35.7  0.253065  3.951551  400    100
B1641-45    16:44:49.27  -45:59:09.7  0.455078  2.197424  375    300

 

[marcusl]

I cannot see how skilled amateur radio-astronomers, could regularly build bigger steerable dishes, than about 15 m diameter. Beyond 15 m, everything becomes more difficult. Think teamwork, building approval and engineering requirements, low-visibility, finance, safety, hours of labour, accuracy, durability, and the probability of project completion.

Agreed. My point just was that signal processing isn't always a cure-all. In this case, larger signals are available at a lower frequency or, as you point out in your next post, from other sources. BTW, in reading some more of the papers out there, I learned that the Crab nebula throws out occasional pulses that are 3 orders of magnitude stronger than usual at both 430 MHz [Apparo] and at 1.4 GHz [Baht, 2008]. These occur relatively infrequently, however.

 

[Vanadium 50]

Vela is in the south, so for most of the population (including me) there is a planet in the way. The Crab has the same problem if you live in Argentina.

I should also mention that you don't get 12 months of observation of the Crab per year. Maybe 8 if you are lucky. It's in Taurus, and the sun passes through Taurus yearly. If it were in, say, Ursa Minor, things would be different.

You win as roughly the cube of dish size. You get two powers of R in light collection, and 1 in signal significance from better pointing. Note that the last power can be achieved by phasing multiple dishes, but that won't help with the first two.

I admit I am shocked that moving down in frequency helps.

1. The pulsar is the hottest thing in the nebula and in fact, is heating everything else. That suggests to go up in frequency.
2. Angular resolution and this S/B improves with frequency/

A year of data collection does not scare me. I do this all the time at work. The problem isn't that its a year - it's ensuring that you understand what is going on well enough to combine it.

 

[Baluncore]

There is a hidden energy advantage in detecting pulsars in noise. Where is it specified, if the flux in mJy of a pulsar, is quoted as the integral of the flux over full cycles, or the flux at the peak of the average pulse?

My point just was that signal processing isn't always a cure-all.

And I agree.
Bigger antenna reflectors, or arrays of elements, are critical to capturing more energy, to getting a narrower beam, with higher s/n. My interest, two decades ago, was in lowering the cost of antennas, that can produce worthy results for radio astronomy amateurs.

Looking back at the history of RA, the "Sea Interferometer" involved an antenna high on a sea cliff, facing a rising radio source. As the source rises through the interference pattern, (generated by the antenna and its reflection from the sea surface), the interference pattern appears in the recorded data.
https://en.wikipedia.org/wiki/Sea_interferometry
That is a minimum antenna requirement for RA. It is a learning exercise, but it is also an unfortunate end to investment in that line of research.

 

[Baluncore]

Vela is in the south, so for most of the population (including me) there is a planet in the way. The Crab has the same problem if you live in Argentina.

Why look at it as a double problem, when it is really a double solution?
In the south, we can watch Vela, PSR B0833-45.
In the north, you can watch PSR B0329+54. (Maybe continuously).

If you are up for it, watch the Crab, PSR B0531+21. For most of the 11-year solar cycle, the Sun is surprisingly quiet at UHF frequencies.

You can tell from your latitude, what declination objects will always be above the horizon, for 24 hours per day, 365 days of the year.

A year of data collection does not scare me.

Why collect and combine a year, when it can all be done in 12 hours?

There are now, 3748 pulsars in the ATNF catalogue.
https://www.atnf.csiro.au/research/pulsar/psrcat/
If you only want a list of the 99 pulsars, brighter than 10% of Vela, I attach an extract of the above catalogue, sorted by flux at 400 MHz, S400.

Depending on your latitude, and using a 15-metre amateur built dish, you should be able to see them with less than 12 hours of accumulation. You will not see them if you never look.

 

[collinsmark]

[...]

You win as roughly the cube of dish size. You get two powers of R in light collection, and 1 in signal significance from better pointing. Note that the last power can be achieved by phasing multiple dishes, but that won't help with the first two.

I admit I am shocked that moving down in frequency helps.
[[...]

I think you're mostly on the right track.

My understanding, without breaking out my old textbooks, is the reason that free-space path loss is a function of frequency is that antenna size is (to some extent) baked into the path-loss equation.

A separate parameter in the link budget is the antenna efficiency. This parameter modifies a theoretical, unity gain antenna. But the thing is, a unity gain antenna tuned to 400 MHz, is just naturally bigger than a different unity gain antenna tuned to 1.4 GHz. However, the antenna efficiency doesn't account for the different antenna sizes.

So, this last difference in antenna size (separate from the antenna's area) gets folded into the free space path loss function.

So in summary,

• Free space does not attenuate RF signal strength as a function of frequency; it follows the inverse square law regardless of frequency.
• Other parameters in the link budget assume a unity gain antenna, and the unity gain antenna is a function of frequency. And that difference gets folded into the free space path-loss function, and that's why the free space path-loss function is a function of frequency.
• So this frequency dependency on free space path-loss is sort of like a unit conversion of sorts; it doesn't have any physical significance besides keeping track of assumptions put in separate parameters within the link budget.

On top of that, there may be some atmospheric attenuation involved that's frequency dependent, but I didn't discuss any of that here.

 

[marcusl]

You win as roughly the cube of dish size. You get two powers of R in light collection, and 1 in signal significance from better pointing. Note that the last power can be achieved by phasing multiple dishes, but that won't help with the first two.

Would you explain "signal significance," please?

 

[Vanadium 50]

Signal over square root of background,

 

[Paul Colby]

where noise factor is F=10^(NF/10), gives a total noise figure of NF=1.09 dB, or a system noise temperature of Tsys=290(F-1)=83K. That's not great and we could do better with a more sophisticated design, shorter cable, etc., but it's representative of an easy-to-build system. We assume that the galactic background noise is small and may be ignored.

One aspect of cheap SDRs and LNAs is one can afford to buy more than one. Using more than one signal path, one could potentially use correlation techniques to improve SNR by reducing system temperature. The thought is, while the random system noise in each signal path is large, they are uncorrelated while the random noise from the nebula, is correlated between paths.

Buy using two smaller HOA friendly telescopes can one gain on system temperature faster than one loses on light collection? I’ve done some experiments with SDRs and random noise sources. There a lots of gotchas but I’ve gotten limited success with two SDRplay slaved to a common clock.

 

[Vanadium 50]

Why collect and combine a year, when it can all be done in 12 hours?

Because a 15m disk is awkward, expensive and will make my neighbors sad.