Don’t fret over the phase problem
Aug 13, 2009 2 comments
The unfulfilled desire of crystallographers to measure the phase of diffracted beams produced by X–ray diffraction tools is actually rather pointless, according to Emil Wolf, a theoretical physicist at the University of Rochester in the US. Instead, Wolf believes that physicists should shift their attention to measuring other properties of a diffracted X-ray beam — which hold the same elusive structural information lurking in the inaccessible phase.
Wolf, who is famous for his co-authorship of the classic treatise Principles of Optics, says that many researchers erroneously believe that knowing the phase of the diffracted beams would lead to unambiguous determination of the atomic structure of solids.
"Such beams do not occur in nature, nor can they be produced in the laboratory" Emil Wolf, University of Rochester
But this mistaken view employs an unjustifiable assumption that beams of X–rays are monochromatic. “Such beams do not occur in nature, nor can they be produced in the laboratory,” says Wolf. His technique — which has not been confirmed experimentally — uses spatially coherent X–rays that can be produced in the lab.
When a beam of X-rays is fired at a crystalline material, the resulting diffraction pattern provides some insight into the locations of atoms within the material. The pattern is determined by measuring the amplitude of the diffracted X–rays as a function of position. The very act of measurement destroys important crystallographic information carried by the phase of the X–rays — the phase problem. Instead, the phase of every diffraction beam has to be estimated via approximations, leading to incomplete, unreliable information.
Wolf’s calculations suggest that it would be more fruitful to measure the amplitude and phase of another physical property of the X–rays — the degree of spectral coherence. This defines how X–rays of different wavelengths interfere with each other. Armed with this information, it is possible to determine the electron density throughout the crystal, and ultimately the physical properties of the solid, he claims.
His approach is similar to that taken about six years ago in the optical domain. “I did not appreciate until very recently the relevance of the work to the X–ray reconstruction problem”, he told physicsworld.com
In his calculations, Wolf considers spatially coherent X–ray sources, in which two different points on a wave front are correlated, leading to interference. These are routinely generated at optical wavelengths and they have been produced in the X–ray domain of the electromagnetic spectrum in recent years. Such X–ray sources are not monochromatic.
“The essential point is that the fluctuations at the two points should be in unison,” says Wolf. He cites the example of light from a star. “Such light originates in billions of independent radiating atoms; yet by the time light reaches the earth it becomes highly coherent over large areas.” This high degree of coherence produces telescopic images with sharp diffraction minima and maxima.
Obtaining the phase of the spectral degree of coherence in X–ray diffraction measurements is possible with interferometer-based techniques, explains Wolf. “I am now writing a longer paper explaining how my theoretical results can be implemented in practice.”
“I am [also] in touch with several experimental groups about the possibility of applying the theory to some reconstruction problems.”
Pawel Korecki of the Jagiellonian University in Poland believes that it is "very likely" that Wolf's proposal will be verified in the lab, describing the measurement as "possible but not trivial". However, the X–ray diffraction expert is more cautious about the possibility of practical applications.
Wolf’s calculations are reported in the 14 August edition of Physical Review Letters.
About the author
Richard Stevenson is a freelance science and technology writer based in Chepstow, Wales.