Meaning of "reciprocal" in frequency space

[u0362565]

Hi all,

I'm curious about why reciprocal space is called precisely that. I always understood the reciprocal to be a word used in mathematics to describe the inverse or one divided by a number so how does that relate to frequency space unless in this case it means something completely different? Or is it perhaps linked to the mathematics of the Fourier transform?

Thanks

 

[MisterX]

I guess it's called that because frequency is the reciprocal of a time period,

$f = 1/T\;,$

and the corresponding things for wavelength, etc.

 

[u0362565]

Ah yes that must be it. Thanks!

 

[ZapperZ]

Please note that the term "reciprocal space" is more generic than that. In solid state/condensed matter, the reciprocal space is, literally, an inverse of real space. This is because things are described in units of wave number/vector, k, which is 1/length, and thus has a more appropriate designation of a "reciprocal space".

Zz.

 

[sophiecentaur]

Reciprocal space is used to describe repeating patterns and has the axis in units of 'number per unit distance', as opposed to 'spacing'. I first came across it in Crystalography lectures where it can be used very conveniently to describe lattice structures and to work out the directions of diffracted beams of X rays. (The sums all fall out nicely when you do it that way.)