How feasible is home radio astronomy?

[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.