# How is the wavelength of emitted EM radiation measured?

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## Summary:

I was thinking about the measurement instruments used to find the wavelength and frequency of EM waves. I was looking at the problem in historical perspective.

## Main Question or Discussion Point

Hi,

Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K). This length of a second was selected to correspond exactly to the length of the ephemeris second previously defined. Atomic clocks use such a frequency to measure seconds by counting cycles per second at that frequency. Radiation of this kind is one of the most stable and reproducible phenomena of nature. The current generation of atomic clocks is accurate to within one second in a few hundred million years.
Source: https://en.wikipedia.org/wiki/Second#"Atomic"_second

How were such huge number of periods per second measured originally? Was an instrument such as Michelson interferometer used? I think it was Albert Michelson who invented the interferometer to make calculations of wavelength and frequency of EM waves.

Another related question is that why the temperature of 0 K was chosen since 0 Kelvin couldn't be achieved practically. I understand that the atoms must be at complete rest while emitting the radiation but the problem is that absolute rest state is not possible so how do they go around this problem practically?

I'd really appreciate if you could help me with the queries above. Thank you.

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sophiecentaur
Gold Member
That's a very wide open question as the different frequencies suit different measurement methods. Wavelength is easiest to measure at optical frequencies, using easy to measure mechanical quantities and interference as a 'lever' to magnify a tiny distance (wavelength) into a large fringe separation.(Michelson and all the others)
Wavelength can be measured by looking at standing wave patterns on transmission lines (several MHz up to several Ghz). Very limited accuracy but better than nothing and all you could do when valves were struggling with frequencies above a few hundreds of MHz. In fact it's all historical.

BUT the possible accuracy of Frequency / Time measurement can take you into much much higher accuracy for Frequency measurement, once the electronics can handle it. Frequency and time are quantities that can be measured with much greater accuracy than any others. (1 in 1012 is easy in the Lab)

Klystron, vanhees71, PainterGuy and 1 other person
phyzguy
These are GHz frequencies, not optical frequencies, so I think the frequencies are simply measured with digital counters that count the number of cycles.

davenn
sophiecentaur
Gold Member
These are GHz frequencies, not optical frequencies, so I think the frequencies are simply measured with digital counters that count the number of cycles.
You can take an optical frequency source and mix it with another optical frequency (laser local oscillator) to produce a microwave signal, which can be measured with a 'counter'. The accuracy will depend on the accuracy and noise of the local oscillator - as always in any heterodyne system.
'Counting the number of cycles' is not necessarily as simple as just that.

vanhees71
That's a very wide open question as the different frequencies suit different measurement methods. Wavelength is easiest to measure at optical frequencies, using easy to measure mechanical quantities and interference as a 'lever' to magnify a tiny distance (wavelength) into a large fringe separation.(Michelson and all the others)
Thank you. I agree with you. I had optical frequencies in mind when I asked this question but didn't realize that "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" correspond to radio waves portion of EM spectrum. The 9,192,631,770 periods of the radiation per second is equivalent to frequency of 9.19263177 GHz. I checked online and there are radio interferometers like the shown below.

I'd appreciate if you could comment on the following. Thanks a lot!

Another related question is that why the temperature of 0 K was chosen since 0 Kelvin couldn't be achieved practically. I understand that the atoms must be at complete rest while emitting the radiation but the problem is that absolute rest state is not possible so how do they go around this problem practically?

vanhees71
Baluncore
2019 Award
If the measurement is made near Earth you will also need to correct for gravitational time dilation at that location.

vanhees71 and PainterGuy
Ibix
Summary:: I was thinking about the measurement instruments used to find the wavelength and frequency of EM waves. I was looking at the problem in historical perspective.

Another related question is that why the temperature of 0 K was chosen since 0 Kelvin couldn't be achieved practically.
Temperature actually makes no difference to the radiation an atom emits, but at temperatures above 0K the atom is moving, which means that the radiation you receive is Doppler shifted. That means that the frequency you receive isn't quite at the frequency standard. So the specification of 0K is meant to close off ambiguity from the Doppler effect.

In practice, you are correct that it is impossible to get to 0K, but we can cool to fractions of a Kelvin. And I think you can correct for the Doppler effect a bit - you know the distribution of velocities of atoms in a gas at a known temperature, so you know what the Dopplered distribution of frequencies should look like, so you can work out which part of the radiation is non-Dopplered and use that as your time standard.

vanhees71 and PainterGuy
If the measurement is made near Earth you will also need to correct for gravitational time dilation at that location.
I had thought about it. I don't think that the official definition mentions anything related to the time dilation or any specific point or location where the measurement should be taken. I understand that the second would be elongated if the measurement is taken, say, at moon, but strangely I didn't come across anything related to the time dilation.

The definition is:
the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at a temperature of 0 K.

Ibix
I don't think that the official definition mentions anything related to the time dilation or any specific point or location where the measurement should be taken.
As long as the emission and reception happen at the same height you don't have to worry about it. It's also a very small effect - just about detectable with great care - in a lab setting, whereas Doppler broadening is a large issue unless you insist on cryogenic temperatures.

PainterGuy and sophiecentaur
sophiecentaur
Gold Member
And I think you can correct for the Doppler effect a bit - you know the distribution of velocities of atoms in a gas at a known temperature,
Any precise frequency measurement uses a feedback loop of some kind to lock an oscillator to the source frequency and to reduce random perturbations. Feedback loop all have a low pass filter to 'slow down' the response of the feedback loop. In order to get a reliable measure of frequency in the order of say, 1 part in 1012 (and even a hundred times better) the time constant must be well in excess of 1012 cycles of the comparison frequency. Needless to say, the equipment needs to be switched on for hours - probably even days - to eliminate thermal variations.

PainterGuy and Ibix
vanhees71
Gold Member
2019 Award
The Cs-133 definition for the second is very precise. Of course you have to do it at absolute 0 temperature to avoid the Doppler broadening of the resonance to reduce it to the "natural line width", which is very small. On the other hand this hyperfine transition is not the most accurate thinkable definition, and metrologists work on even better standards using optical frequencies either from other atomic transitions. Due to the higher frequency they can get more accurate. Another path is to use nuclear transitions. Here the problem is that usually the frequencies are too high (in the X-ray or ##\gamma##-ray realm) which are hard to get stabilized in a "laser-type" system. Most accurate are frequency combs using a mode-locked laser. There's however a promising candidate, the Thorium-229 isomer transition, which is in the UV range (~150 nm), which can be stabilized using a frequency comb. The advantage of using a nuclear transition as compared to a atomic transistion is that it's much more insensitive to external perturbations.

https://en.wikipedia.org/wiki/Nuclear_clock
https://en.wikipedia.org/wiki/Mode-locking

Ibix and anorlunda
Staff Emeritus
2019 Award
There's however a promising candidate, the Thorium-229 isomer transition
If we could find it. There are several technical difficulties with nuclear clocks, but one fundamental one is that the uncertainty on the transition energy is ~1015 times larger than the width. That's a lot of places to look!

Staff Emeritus