A Camera That Captures One Trillion Images Per Second

It doesn't actually. It uses equivalent-time sampling, like a stroboscope.

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John Larkin Highland Technology, Inc

jlarkin at highlandtechnology dot com

Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom laser drivers and controllers Photonics and fiberoptic TTL data links VME thermocouple, LVDT, synchro acquisition and simulation

A sampling scope?

The world is a mess of jiggly things ;)

Cheers

That also.

It's interesting to note that the fundamental characteristics of vision that we take for granted only work because (anthropic principle?) the wave equation is the way it is, and we live in a universe that has an odd number of spatial dimensions.

Mathematically speaking, if the wave equation were modified in almost any way, or the universe had an even number of spatial dimensions, the Green's function for the inhomogeneous wave equation wouldn't involve a Dirac delta function. Having delta function in the Green's function for the wave equation means that if there's an impulse at some point at the center of a sphere in a (2n + 1) dimensional space, what you observe as the wave front passes you at some later time t at some distance from the center of the sphere will also be an impulse - see Huygen's principle.

We take for granted that, when a lighthouse flashes, that at a distance we also see a single flash, but it doesn't hold true in general; consider the 2D case of a pebble dropped into a pond: the initial disturbance from the impulse radiates outwards, but the amplitude continues going up and down, exponentially decaying, within the radius of the expanding initial disturbance. Think about what vision would be like in a universe where that happened, where every impulse gets "smeared out" over time.

So you're saying, even dimensions are dispersive? Gravity waves (used in your analogy) are highly dispersive (low frequency travels faster than high frequency, which is also attenuated) and nonlinear in higher amplitudes (e.g., shock waves, breaking waves), though the example of a pebble suggests a small-signal linear approximation.

Tim

--
Deep Friar: a very philosophical monk. 
Website: http://webpages.charter.net/dawill/tmoranwms

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Yeah, I don't get that part either. Water waves are not all that dispersive... (until you get close to shore and the depth of the water starts to have an effect.) How else can a tsunami in Japan make it all the way across the ocean and pull someone off a beach in California?

George H.

Gravity waves (used in

Right, the pebble example was made assuming there was no contribution to the wave equation from the properties of the medium, and the depth of the water was very shallow. Maybe a vibrating drumhead would be a better example. But dispersion isn't the issue that I'm talking about. Dispersion is a frequency-domain effect that is caused by the properties of the medium, where the velocity of the wave in the medium is dependent on the wave's frequency.

You can have dispersive and non-dispersive wave equations in any number of dimensions you wish; for example the 1 dimensional wave equation PDE for a transmission line, assuming lossy conductors, leads to the telegraphers equation and the

of the line, the imaginary part of which is the dispersion relation for the line. If there's no loss then there's no dispersion, and wave velocity is independent of frequency. I assume something similar happens with waves in water, using whatever the fluid dynamics equivalent of series resistance and shunt conductance is.

The effect I'm talking about is more of a time domain effect: say you're in a 2 or 4 dimensional world that's filled with a non-dispersive medium, and shout "Hello!" into it. An observer at some distance will hear all the frequencies arrive at the same time, but the impulse will be "streched out" - you'll get "Heeeeeeeeelllllllooooooooooooo" just like the audio has been timestretched in some audio-editing program.

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Hi bitrex, Perhaps you're going to have to send us a link, or show us some math.

I think there is either a slight problem in your understanding (or in mine.)

(Neither is a big deal in my mind... I'm always having my physics understanding tweaked by my mistakes.)

I was doing some ultrasonic stuff earlier this year, and you can write down the wave equation in one dimension (elastic string), two dimensions (membrane) or three (solid) and they look pretty much the same. See for instance "Advanced Engineering Mathematics" by C.R. Wylie

George H.

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A 2-D geometry in 3-D has a tail in its impulse response due to all the spherical waves emanating from far-away axial points arriving later than ones travelling more nearly perpendicular to the axis. That doesn't mean that lightning bolts are hard to see, however.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

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It's interesting that supernova blasts and pulsars let us time em wave velocity to a resolution of microseconds out of billions of years of travel. As far as I know, there's no indication that c in vacuum varies with wavelength or anything else.

And we can image distant objects to tiny fractions of an arc-second.

--

John Larkin         Highland Technology, Inc 

jlarkin at highlandtechnology dot com 
http://www.highlandtechnology.com 

Precision electronic instrumentation 
Picosecond-resolution Digital Delay and Pulse generators 
Custom laser drivers and controllers 
Photonics and fiberoptic TTL data links 
VME thermocouple, LVDT, synchro   acquisition and simulation

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Oh, is that what bitrex was refering to? The lightning example is a good one. I seem to recall reading somewhere that a long "ccraaacckk" of thunder is due to a long bolt. (But then sound bouncing around the terrain and arriving at your ear via multiple paths might sound similar.)

George H.

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There's plasma dispersion in the interstellar medium that makes the higher radio frequencies arrive first. IIRC the first pulsar, discovered by Jocelyn Bell and Anthony Hewish, was the one in Vela, with a period of a couple of seconds--it sounds like a bird's chirp played backwards.

But then that isn't absolute vacuum.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

trillion: 10^12 SI prefix: T, tera

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?? 100% natural

I'm not sure that a trillion is a number. In any event, that's the attempted capture rate, not the capability/capacity of storage. Such a large sequence would be more hindrance to comprehension, than help.

RL

When talking about exposure times in the femptosecond area, there are not going to be too many photons in one exposure, unless you take pictures of the sun :-).

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Hi George,

I found a good page explaining the issues involved. See here: