Difference between revisions of "Realspace"
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==Realspace functions== | ==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 | + | 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 |
| + | |||
| + | ===Pair Distribution Function, or [[PDF]]=== | ||
| + | * Porod, G. ''Acta Phys. Austriaca'' '''1948''', 2, 255–292. | ||
* Billinge, S. J. L. & Thorpe, M. F. (1998). [http://link.springer.com/book/10.1007%2Fb119172 Local Structure from Diffraction], edited by S. J. L. Billinge. New York: Plenum Press. | * Billinge, S. J. L. & Thorpe, M. F. (1998). [http://link.springer.com/book/10.1007%2Fb119172 Local Structure from Diffraction], edited by S. J. L. Billinge. New York: Plenum Press. | ||
* P. F. Peterson, M. Gutmann, Th. Proffen and S. J. L. Billinge [http://scripts.iucr.org/cgi-bin/paper?ks0034 PDFgetN: a user-friendly program to extract the total scattering structure factor and the pair distribution function from neutron powder diffraction data] ''J. Appl. Cryst.'' '''2000''', 33, 1192 [http://dx.doi.org/10.1107/S0021889800007123 doi: 10.1107/S0021889800007123] | * P. F. Peterson, M. Gutmann, Th. Proffen and S. J. L. Billinge [http://scripts.iucr.org/cgi-bin/paper?ks0034 PDFgetN: a user-friendly program to extract the total scattering structure factor and the pair distribution function from neutron powder diffraction data] ''J. Appl. Cryst.'' '''2000''', 33, 1192 [http://dx.doi.org/10.1107/S0021889800007123 doi: 10.1107/S0021889800007123] | ||
| − | + | ===Two-dimensional=== | |
| − | Two-dimensional scattering data | + | 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. |
* G. Fritz-Popovski [http://scripts.iucr.org/cgi-bin/paper?ks5437 Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures] ''J. Appl. Cryst.'' '''2015''', 48 [http://dx.doi.org/10.1107/S1600576714024972 doi: 10.1107/S1600576714024972] | * G. Fritz-Popovski [http://scripts.iucr.org/cgi-bin/paper?ks5437 Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures] ''J. Appl. Cryst.'' '''2015''', 48 [http://dx.doi.org/10.1107/S1600576714024972 doi: 10.1107/S1600576714024972] | ||
Revision as of 15:22, 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
Pair Distribution Function, or PDF
- Porod, G. Acta Phys. Austriaca 1948, 2, 255–292.
- Billinge, S. J. L. & Thorpe, M. F. (1998). Local Structure from Diffraction, edited by S. J. L. Billinge. New York: Plenum Press.
- P. F. Peterson, M. Gutmann, Th. Proffen and S. J. L. Billinge PDFgetN: a user-friendly program to extract the total scattering structure factor and the pair distribution function from neutron powder diffraction data J. Appl. Cryst. 2000, 33, 1192 doi: 10.1107/S0021889800007123
Two-dimensional
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.
- G. Fritz-Popovski Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures J. Appl. Cryst. 2015, 48 doi: 10.1107/S1600576714024972
