Difference between revisions of "Realspace"
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[[Image:BCP etch.jpg|thumb|300px|Example realspace image (SEM) of a [[block-copolymer]] pattern etched into silicon.]] | [[Image:BCP etch.jpg|thumb|300px|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 distribution|electron-density spatial distribution]] (as imaged in SEM, TEM, AFM, STM, etc.). | '''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 distribution|electron-density spatial distribution]] (as imaged in SEM, TEM, AFM, STM, etc.). | ||
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| + | ==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 [[Fourier_transform#Phase_problem|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 (known as a Pair Distribution Function, or [[PDF]]). | ||
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| + | Two-dimensional scattering data | ||
Revision as of 15:11, 19 December 2014
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.).
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 (known as a Pair Distribution Function, or PDF).
Two-dimensional scattering data
