[time-nuts] 1 pps Accuracy in two locations

[jimlux]

On 1/15/20 2:34 PM, Attila Kinali wrote:
> On Wed, 4 Dec 2019 09:40:34 -0000
> <martyn at ptsyst.com> wrote:
> 
>> I'm always being asked to provide equipment that can produce two 1 pps
>> outputs aligned to each other to within a few ps.
>>
>> These two 1 pps pulses are not in the same location and could be 100 metres
>> to a few km away.
> 
> As others have written, getting down to a few ps is not feasible, at least
> not with the amount of money your customers are likely willing to pay.
> To get down to these levels you will need to pull fibres from one location
> to another and using special circuitry to activly compensate variation
> in length due to temperature changes and vibration, even for burried fibres.
> Just to put into perspective what your customers are asking for: in 1ps
> light travels 300µm in vacuum/air or ~150µm in fibre/coax. This means,
> to get better than 10ps, you have to control the length of everything down
> to better than 1mm. Thermal expansion coefficient is somewhere between
> 1e-6 to 1e-4 for solids. Assuming you have 1e-6 and want to bridge 1km
> you would need to keep the temperature of the whole fibre stable to 1°C
> in order to keep the timing variation due to length change below 10ps.
> And that's not yet accounting for changes in refraction index (i.e. speed
> of light) due to temperature changes or a myriad other effects that you
> will have to deal with.
> 
> Even white rabbit, which is probably the most advanced system you will
> likely get your hands on (does two-way timing to compensate for length
> of fibre and length variation), gives you about 200ps of uncertainty
> from one node to the next (but <10ps rms jitter). Each WR switch/node
> costs ~3k€ so isn't exactly cheap either, but you get GBit ethernet
> ontop of the time transfer as well.
> 
>> So they are asking for two of my GNSS frequency standards with 1 pps
>> outputs.
> 
> State of the art time transfer using GPS, I am aware of, is what BIPM has
> demonstrated two years ago using iPPP and, IIRC a base line of a few 100km
> of 200ps uncertainty. But that's using calibrated GPS receivers in a
> temperature controlled environment with lots of post-processing.
> I.e. it's not real-time. For shorter baselines, I expect the uncertainty
> to come down a bit. But I would not assume for it to go below 100ps without
> verifying first, even at very short baseliens of a few 10s of meters.
> 
> If you have money to spare and line of sight between the locations,
> you could employ something like the NIST free space laser system
> https://www.nist.gov/programs-projects/optical-two-way-time-frequency-transfer
> But beware: it uses multiple frequency combs which cost as much as a very
> nice car. Each of them. But they get to sub-100fs stability, which means
> you could get to low-ps uncertainty, if done correctly.
> 
> Rule of thumb: if you need time transfer better than 1ns you need to think
> about what you are doing, even within the same room. If you leave the
> building, going below 1ns is going to be hard. Doing better than 1ns within
> a neighborhood, while possible, will need some serious equipment and proper
> planing. Any factor of 10 better will drive up your cost by a factor 100 to
> 1000.

Even free space optical would have to deal with propagation speed 
variations due to temperature and humidity. 1ns is 300 mm. 1ps is 0.3 
mm.  Out of 1km is is 0.3 ppm.
40C variation in temperature changes the refractive index by about 50 
ppm.  There's also a humidity effect, and a CO2 effect. At VHF 
frequencies, it's enough to allow "tropospheric ducting" to allow 
communications well beyond line of sight.

And, of course, measuring those chances at L-band GPS signals is a way 
to characterize the atmosphere using occultation - COSMIC and COSMIC 2 
do this.


   Gravitational effects on the beam path are probably not an issue.

But ultimately, this is the kind of problem that LIGO and other long 
path interferometers face (and why they use pipes with a vacuum).


> 
> Rule of thumb #2: if you need to control lengths to better than 10µm, your
> mechanics guy will throw a fit as he will most likely be unable to manufacture
> to that precision, unless you are building something tiny.
> 
> 			Attila Kinali
>