Spatial frequency: more thinking about wave number

I did a bit of research after posting yesterday. My thinking had given me the right questions. It turns out that a more stripped back version of wave number is called spatial frequency and is just 1/wavelength. It is given the Greek letter xi, which is the one I find hardest to draw. Frequency is 1/T (T is time period) so I teach it as the number of complete waves in one second. 1/wavelength is the number of complete waves in 1 metre; hence spatial frequency. I've been reminding myself about Fourier Transforms: that a Fourier Transform tells you which mix of frequencies make up a signal in real time. Remember the progressive wave y=Asin(kx-wt). w is paired with t. That is frequency with time, the Fourier Transform pair. So k is paired with x. It's beginning to dawn on me that a Fourier Transform of a repetitive pattern in space will tell me the mix of spatial frequencies involved. I'm almost convinced that the reciprocal lattice is the Fourier Transform of the real lattice for this reason. This hints at it https://agilescientific.com/blog/2012/5/1/k-is-for-wavenumber.html I sued this a lot https://en.wikipedia.org/wiki/Spatial_frequency