Skip to main content
Log in

Statistical Theory of X-ray Diffraction Phase Contrast Formation

  • DIFFRACTION AND SCATTERING OF IONIZING RADIATIONS
  • Published:
Crystallography Reports Aims and scope Submit manuscript

Abstract

A successive consideration of the formation of X-ray diffraction phase contrast of weakly absorbing noncrystalline objects with statistically distributed small-scale density inhomogeneities has been performed. It was assumed that the incident X-ray beam has an arbitrary degree of spatial coherence, and the changes in the statistical characteristics of this radiation during Bragg diffraction reflection from the monochromator and analyzer were taken into account. The phenomena of the increase and/or decrease in the phase contrast from regions with randomly distributed microcalcifications, in dependence of their rms sizes, relative refractive index decrement, and the lengths of spatial coherence of radiation and phase correlation as a result of diffraction-enhanced diffuse scattering are explained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.

REFERENCES

  1. E. Forster, K. Goetz, and P. Zaumseil, Krist. Tech. 15, 937 (1980). https://doi.org/10.1002/crat.19800150812

    Article  Google Scholar 

  2. K. M. Podurets, V. A. Somenkov, and S. Sh. Shil’shtein, Sov. Tech. Phys. 34 (6), 654 (1989).

    Google Scholar 

  3. K. M. Podurets, V. A. Somenkov, and S. Sh. Shilstein, Physica B 156–157, 691 (1989). https://doi.org/10.1016/0921-4526(89)90765-5

    Article  ADS  Google Scholar 

  4. V. A. Somenkov, A. K. Tkalich, and S. Sh. Shil’shtein, Sov. Tech. Phys. 36, 1309 (1991).

    Google Scholar 

  5. V. N. Ingal and E. A. Belyaevskaya, Sov. Tech. Phys. 63, 137 (1993).

    Google Scholar 

  6. V. N. Ingal and E. A. Beliaevskaya, J. Phys. D 28, 2314 (1995). https://doi.org/10.1088/0022-3727/28/11/012

    Article  ADS  Google Scholar 

  7. D. Gao, T. J. Davis, and S. W. Wilkins, Aust. J. Phys. 48, 103 (1995). https://doi.org/10.1071/PH950103

    Article  ADS  Google Scholar 

  8. T. J. Davis, D. Gao, T. E. Gureyev, et al., Nature 373, 595 (1995). https://doi.org/10.1038/373595a0

    Article  ADS  Google Scholar 

  9. T. J. Davis, T. E. Gureyev, D. Gao, et al., Phys. Rev. Lett. 74, 3173 (1995). https://doi.org/10.1103/PhysRevLett.74.3173

    Article  ADS  Google Scholar 

  10. V. A. Bushuev, V. N. Ingal, and E. A. Belyaevskaya, Crystallogr. Rep. 41, 766 (1996).

    ADS  Google Scholar 

  11. D. Chapman, W. Thomlinson, F. Arfelli, et al., Rev. Sci. Instrum. 67, 3360 (1996). https://doi.org/10.1063/1.1147502

    Article  ADS  Google Scholar 

  12. S. Sh. Shil’shtein, K. M. Podurets, V. A. Somenkov, and A. A. Manushkin, Surf. Invest.: X-Ray, Synchrotron Neutron Tech. 12, 451 (1997).

    Google Scholar 

  13. V. N. Ingal and E. A. Beliaevskaya, Phys. Medica 12, 75 (1996).

    Google Scholar 

  14. V. N. Ingal and E. A. Belyaevskaya, Surf. Invest.: X-Ray, Synchrotron Neutron Tech. 12, 441 (1997).

    Google Scholar 

  15. V. N. Ingal and E. A. Belyaevskaya, Tech. Phys. 42, 59 (1997).

    Article  Google Scholar 

  16. V. A. Bushuev, E. A. Beliaevskaya, and V. N. Ingal, Nuovo Cimento Soc. Ital. Fis. 19 D, 513 (1997). https://doi.org/10.1007/BF03041011

    Article  ADS  Google Scholar 

  17. V. N. Ingal and E. A. Beliaevskaya, Nuovo Cimento Soc. Ital. Fis. 19 D, 553 (1997). https://doi.org/10.1007/BF03041016

    Article  ADS  Google Scholar 

  18. T. E. Gureyev and S. W. Wilkins, Nuovo Cimento Soc. Ital. Fis. 19 D, 545 (1997). https://doi.org/10.1007/BF03041015

    Article  ADS  Google Scholar 

  19. D. Chapman, W. Thomlinson, R. E. Johnston, et al., Phys. Med. Biol. 42, 2015 (1997). https://doi.org/10.1088/0031-9155/42/11/001

    Article  Google Scholar 

  20. E. A. Beliaevskaya, M. Gambaccini, V. N. Ingal, et al., Phys. Medica 14, 19 (1998).

    Google Scholar 

  21. V. N. Ingal, E. A. Beliaevskaya, A. P. Brianskaya, and R. D. Merkurieva, Phys. Med. Biol. 43, 2555 (1998). https://doi.org/10.1088/0031-9155/43/9/009

    Article  Google Scholar 

  22. V. A. Bushuev, V. N. Ingal, and E. A. Belyaevskaya, Crystallogr. Rep. 43, 538 (1998).

    ADS  Google Scholar 

  23. V. A. Bushuev and A. A. Sergeev, Tech. Phys. Lett. 24, 851 (1998).

    Article  ADS  Google Scholar 

  24. V. A. Bushuev and A. Kone, Surf. Invest.: X-Ray, Synchrotron Neutron Tech. 14, 1245 (1999).

    Google Scholar 

  25. V. A. Bushuev and A. A. Sergeev, Tech. Phys. Lett. 25, 83 (1999). https://doi.org/10.1134/1.1262407

    Article  ADS  Google Scholar 

  26. V. A. Bushuev and A. A. Sergeev, Surf. Invest.: X-Ray, Synchrotron Neutron Tech. 16, 1429 (2001).

    Google Scholar 

  27. V. A. Bushuev and A. P. Petrakov, Crystallogr. Rep. 46, 171 (2001). https://doi.org/10.1134/1.1358388

    Article  ADS  Google Scholar 

  28. V. A. Bushuev and A. A. Sergeev, Surf. Invest.: X-Ray, Synchrotron Neutron Tech., No. 1, 52 (2003).

  29. V. A. Bushuev and M. A. Gus’kova, Bull. Russ. Acad. Sci. Phys.69, 253 (2005).

    Google Scholar 

  30. K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, J. Phys. D: Appl. Phys. 34, A168 (2001). https://doi.org/10.1088/0022-3727/34/10A/335

    Article  Google Scholar 

  31. K. M. Pavlov, T. E. Gureyev, D. Paganin, et al., J. Phys. D: Appl. Phys. 37, 2746 (2004). https://doi.org/10.1088/0022-3727/37/19/021

    Article  ADS  Google Scholar 

  32. A. Snigirev, I. Snigireva, V. Kohn, et al., Rev. Sci. Instrum. 66, 5486 (1995). https://doi.org/10.1063/1.1146073

    Article  ADS  Google Scholar 

  33. A. Snigirev, I. Snigireva, V. G. Kohn, and S. M. Kuznetsov, Nucl. Instrum. Methods Phys. Res. A 370, 634 (1996). https://doi.org/10.1016/0168-9002(95)00849-7

    Article  ADS  Google Scholar 

  34. S. W. Wilkins, T. E. Gureyev, D. Gao, et al., Nature 384, 335 (1996). https://doi.org/10.1038/384335a0

    Article  ADS  Google Scholar 

  35. P. Cloetens, R. Barrett, J. Baruchel, et al., J. Phys. D 29, 133 (1996). https://doi.org/10.1088/0022-3727/29/1/023

    Article  ADS  Google Scholar 

  36. T. E. Gureyev and S. W. Wilkins, J. Opt. Soc. Am. A 15, 579 (1998).

    Article  ADS  Google Scholar 

  37. T. E. Gureyev and S. W. Wilkins, Opt. Commun. 147, 229 (1998). https://doi.org/10.1016/S0030-4018(97)00637-8

    Article  ADS  Google Scholar 

  38. T. E. Gureyev, C. Raven, A. Snigirev, et al., J. Phys. D 32, 563 (1999). https://doi.org/10.1088/0022-3727/32/5/010

    Article  ADS  Google Scholar 

  39. Ya. I. Nesterets, Opt. Commun. 281, 533 (2008). https://doi.org/10.1016/j.optcom.2007.10.025

    Article  ADS  Google Scholar 

  40. V. Ya. Shovkun, Med. Fiz., No. 2, 25 (2007).

  41. A. S. Akhmanov, Yu. E. D’yakov, and A. S. Chirkin, Introduction into Statistical Radiophysics and Optics (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  42. V. A. Bushuev, Bull. Russ. Acad. Sci. Phys. 73, 52 (2009). https://doi.org/10.3103/S1062873809010158

  43. V. A. Bushuev, Bull. Russ. Acad. Sci. Phys. 74, 41 (2010). https://doi.org/10.3103/S1062873810010119

    Article  Google Scholar 

  44. M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Theory of Waves (Nauka, Moscow, 1990) [in Russian].

    MATH  Google Scholar 

  45. R. James, Optical Principles of X-ray Diffraction (Bell, London, 1950).

    Google Scholar 

  46. Z. G. Pinsker, Dynamical Scattering of X Rays in Crystals (Springer, Berlin, 1978).

    Book  Google Scholar 

  47. Z. G. Pinsker, X-ray Crystal Oprics (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  48. V. I. Iveronova and G. P. Revkevich, Theory of X-ray Scattering (Mosk. Gos. Univ., Moscow, 1978) [in Russian].

    Google Scholar 

  49. A. Authier, Dynamical Theory of X-ray Diffraction (Oxford Univ. Press, New York, 2001), p. 455.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Bushuev.

Ethics declarations

The author declares that he has no conflicts of interest.

Additional information

Translated by Yu. Sin’kov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bushuev, V.A. Statistical Theory of X-ray Diffraction Phase Contrast Formation. Crystallogr. Rep. 68, 388–395 (2023). https://doi.org/10.1134/S1063774523700074

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063774523700074

Navigation