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Phase improvement by iterative density modification
Zhang, K. Y. J., Cowtan, K. D. and Main, P.  International Tables for Crystallography (2012). Vol. F, ch. 15.1, pp. 385-400 [ doi:10.1107/97809553602060000847 ]
... entire unit cell, including both the protein and the solvent. Zhang & Main (1988) systematically examined the electron-density histogram of several ... be taken from any known structure at the same resolution (Zhang & Main, 1988, 1990a). The ideal electron-density histogram can ... histograms of known structures. 15.1.2.2.3. The process of histogram matching | | Zhang & Main (1990a) demonstrated that, at better than 4 resolution, ...

Averaging
Cowtan, K. D., Zhang, K. Y. J. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.3.5.6, pp. 411-412 [ doi:10.1107/97809553602060000849 ]
... gradient information for the refinement of averaging operators. References Cowtan, K. D. & Main, P. (1998). Miscellaneous algorithms for density modification. ... Rossmann, M. G., McKenna, R., Tong, L., Xia, D., Dai, J.-B., Wu, H., Choi, H.-K. & Lynch, R. E. (1992). Molecular replacement real-space ...
     [more results from section 15.3.5 in volume F]

Phase-extension schemes
Cowtan, K. D., Zhang, K. Y. J. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.3.4.3, pp. 409-410 [ doi:10.1107/97809553602060000849 ]
Phase-extension schemes 15.3.4.3. Phase-extension schemes When performing phase extension, the order in which the structure factors are included will affect the final accuracy of the extended phases. The phases obtained from previous cycles of phase extension will be included in the calculation of new phases for the unphased structure ...
     [more results from section 15.3.4 in volume F]

Preparation of input data
Cowtan, K. D., Zhang, K. Y. J. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.3.3, pp. 407-408 [ doi:10.1107/97809553602060000849 ]
... ray crystallography and NMR. Yale University Press, New Haven. Cowtan, K. D. & Main, P. (1998). Miscellaneous algorithms for density modification. ... information. Acta Cryst. B26, 136-143. Jones, T. A., Zou, J.-Y., Cowan, S. W. & Kjeldgaard, M. (1991). Improved methods ...

Program operation
Cowtan, K. D., Zhang, K. Y. J. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.3.2, p. 407 [ doi:10.1107/97809553602060000849 ]
Program operation 15.3.2. Program operation DM and DMMULTI are largely automatic; in order to perform a phase-improvement calculation only two tasks are required of the user: (1) Provide the input data. These must include the reflection data and solvent content, and may also include averaging operators, solvent mask and averaging ...

Introduction
Cowtan, K. D., Zhang, K. Y. J. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.3.1, p. 407 [ doi:10.1107/97809553602060000849 ]
Introduction 15.3.1. Introduction DM is an automated procedure for phase improvement by iterated density modification. It is used to obtain a set of improved phases and figures of merit, using as a starting point the observed diffraction amplitudes and some initial poor estimates for the phases and figures of merit. DM ...

DM/DMMULTI software for phase improvement by density modification
Cowtan, K. D., Zhang, K. Y. J. and Main, P.  International Tables for Crystallography (2012). Vol. F, ch. 15.3, pp. 407-412 [ doi:10.1107/97809553602060000849 ]
... s equation calculation adds another level of complexity, described in Zhang & Main (1990b). Skeletonization imposes the protein histogram and solvent ... from 6 to 1.5, according to the method described by Zhang & Main (1990a). The histogram variances should be consistent with ... Institutes of Health for grant support (GM55663). References Abrahams, J. P. (1997). Bias reduction in phase refinement by ...

Example
Zhang, K. Y. J., Cowtan, K. D. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.1.7, pp. 398-399 [ doi:10.1107/97809553602060000847 ]
... merit and structure-factor amplitude, as a function of resolution (Zhang et al., 1997), This phase correlation over all reflections is ... analysis of 5-carboxymethyl-2-hydroxymuconate isomerase from Escherichia coli. J. Mol. Biol. 210, 881-882. Zhang, K. Y. J., Cowtan, K. D. & Main, P. (1997) ...

Statistical density-modification methods
Zhang, K. Y. J., Cowtan, K. D. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.1.6, p. 398 [ doi:10.1107/97809553602060000847 ]
Statistical density-modification methods 15.1.6. Statistical density-modification methods Statistical density-modification methods arise from a reinterpretation of the problem of phase improvement in statistical terms, and as a result reduce the problems of bias associated with the classical density-modification methods described above. This is achieved by expressing all information ...

The diagonal approximation
Zhang, K. Y. J., Cowtan, K. D. and Main, P.  International Tables for Crystallography (2012). Vol. F, Section 15.1.5.2.3, pp. 397-398 [ doi:10.1107/97809553602060000847 ]
The diagonal approximation 15.1.5.2.3. The diagonal approximation The full-matrix solution to equation (15.1.5.4) requires a significant amount of computing, although it can be achieved using FFTs. The diagonal approximation to the normal matrix has been used as an alternative method of solution to the electron-density shift in equation (15.1.5.4 ...
     [more results from section 15.1.5 in volume F]

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