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Example realspace image (SEM) of a block-copolymer pattern etched into silicon.

Realspace or direct-space is simply the regular 3D space that we inhabit. In scattering, it is introduced as a term to differentiate from reciprocal-space (a.k.a. inverse-space). Whereas reciprocal-space refers to the Fourier transform of the sample's structure, realspace refers to the actual structure: the electron-density spatial distribution (as imaged in SEM, TEM, AFM, STM, etc.).

Samples of scientific interest often exhibit well-defined packing in realspace, and are thus described by their lattice and/or unit cell. This gives rise to well-defined features in reciprocal-space (peaks, rings, etc.).

Realspace functions

Scattering data can be converted into a corresponding realspace representation. Normally, scattering data cannot be simply inverted (via Fourier transform) to recover the exact realspace structure. This is known as the phase problem: experiments typically record the intensity (but not phase) of scattered radiation, making unambiguous inversion impossible (note that coherent techniques, such as CDI or ptychography attempt to work around this). However, the inverse-space data of a scattering experiment can at least be converted into a statistical (or average) realspace representation. Total one-dimensional scattering can be converted into a realspace function that describes the amount of correlation across various distances

Indirect Fourier Transform (IFT)

Pair Distribution Function (PDF)

Autocorrelation Function



Two-dimensional scattering data can in principle also be converted into a two-dimensional realspace function. This realspace representation contains the same information, but emphasizes spatial distance correlations.

See Also

  • Q value: Conversion from reciprocal-space values to realspace distances can be accomplished using