The SAS maximal principle: a new approach to the phase problem

Area of Science:

• Crystallography
• Structural Biology
• Materials Science

Background:

• The phase problem is a fundamental challenge in X-ray crystallography.
• Single-wavelength anomalous scattering (SAS) data provides probabilistic phase information.
• Existing methods struggle with the complexity of phase determination.

Purpose of the Study:

• To formulate the crystallographic phase problem as a global optimization task.
• To develop a direct method for determining crystal structure phases from SAS data.
• To leverage the properties of the objective function for accurate phase retrieval.

Main Methods:

• Formulating the phase problem as a global optimization problem.
• Analyzing the objective function for local and global maxima.
• Utilizing the isolation of global maxima for phase identification.
• Connecting objective function maxima to solutions of SAS tangent equations.

Main Results:

• The phase problem is successfully treated as a global optimization problem.
• The objective function exhibits easily identifiable, isolated global maxima (at most two).
• Direct determination of individual phases from probabilistic estimates is achieved.
• A novel system of SAS tangent equations is formulated and solved.

Conclusions:

• This global optimization approach offers a direct and successful solution to the phase problem.
• The method efficiently identifies unique phase solutions from SAS data.
• This advancement simplifies direct phase retrieval in crystallography.