Skip to main content
SpringerLink
Log in

New theoretical and experimental results in fresnel optics with applications to matter-wave and X-ray interferometry

  • Atom Optics
  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

We present new methods and formulae for calculating the image amplitude and image spatial power spectral density produced by monochromatic point-source illumination of a finite (and/or infinite) periodic complex transmission grating. At specific finite-width resonances the image amplitude is seen to display periodic complex amplitude self-imaging of the grating, with interlaced alias images. The finite width grating resonances (as a function of spatial frequency) are broadened (from zero width) and displaced in frequency relative to those produced by an infinite grating, although the finite resonance width relative to illumination wavelength variation persists with infinite gratings. In the Fresnel domain the self images are generalizations of the Talbot and von Lau effects, while in the Fraunhofer to Fresnel transition domain, our formulae demonstrate the formation of these structures from Fraunhofer diffraction order side-lobes. Using these results, design criteria are provided for constructing lens-free three-grating interferometers with spatially diffuse illumination and detection. Such interferometers have a wide variety of applications for both X-rays and matter-waves, including a phase sensitive imaging device and/or narrow-band interference filter. For wavelengths in the Ångstrom to sub-Ångstrom range they feature high throughput and ease of fabrication. Experimental results using light with such an interferometer are presented. Our results conclusively demonstrate interference and image aliasing in such a device with spatially diffuse illumination and detection. The experiment is readily reproducible in any undergraduate physics laboratory.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. See, for example, J.W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York 1968) Chaps. 3, 4

    Google Scholar 

  2. M. Born, E. Wolf: Principles of Optics (Pergamon, Oxford 1987) Chap. 8

    Google Scholar 

  3. See, for example, G.L. Rogers: Br. J. Appl. Phys. 14, 657 (1963)

    Google Scholar 

  4. A. Zeilinger et al.: Revs. Mod. Phys. 60, 1067 (1988)

    Google Scholar 

  5. Q.A. Turchette, D.E. Pritchard, D.W. Keith: Numerical Modeling of a Multiple Grating Interferometer. MIT preprint (1991)

  6. J. Jahns, A.W. Lohmann: Opt. Commun. 28, 263 (1979)

    Google Scholar 

  7. See also J.T. Winthrop, C.R. Worthington: J. Opt. Soc. Am. 55, 373 (1965); 56, 588 (1966)

    Google Scholar 

  8. E.A. Hiedemann, Breazeale: J. Opt. Soc. Am. 49, 372 (1959)

    Google Scholar 

  9. B.J. Chang, R. Alferness, E.N. Leith: Appl. Opt. 14, 1592 (1975)

    Google Scholar 

  10. J.M. Cowley, A.F. Moodie: Proc. Phys. Soc. B 70, 486, 497, 505 (1970)

    Google Scholar 

  11. Cowley and Moodie comment: “In fact it is observed that with gratings of this type a large number of sharp and frequently complicated out-of-focus patterns are generated.” They called these intermediate images Fresnel images. In the present work we identify these images as those for which m is an integer not equal to one. They reserved the name Fourier images as those for which m=1 holds. Although the existence of m ≠ 1 images is indeed manifest in their formulae, the regularity of the patterns was not recognized by them, nor obvious from their formulae. Thus, they comment (p. 499) that “No obvious relationship exists between the positions of the delta functions and the maxima and minima of the real and imaginary parts of the Fourier transform of the Fresnel wave function.”...

  12. F. Gori: Opt. Commun. 31, 4 (1979)

    Google Scholar 

  13. R. Sudol, B.J. Thompson: Opt. Comm. 31, 105 (1979)

    Google Scholar 

  14. A.W. Lohman, D.E. Silva: Opt. Commun. 2, 413 (1971)

    Google Scholar 

  15. J.F. Clauser: Rotation, Acceleration, and Gravity Sensors Using Quantum Mechanical Matter-Wave Interferometry with Neutral Atoms and Molecules. United States Patents #4, 874, 942 (1987, 1989) and #4, 992, 656 (1989, 1991); Physica B 151, 262 (1988); Ultra-Sensitive Inertial Sensors via Neutral-Atom Interferometry, in Relativistic Gravitational Experiments in Space. NASA Conf. Publ. 3046, ed. by R.W. Hellings (1989)

  16. See B.G. Levi: Physics Today 44, #7, 17 (1991) for a discussion of the current experimental status

    Google Scholar 

  17. H. Talbot: Philos. Mag. 9, 401 (1836)

    Google Scholar 

  18. Lord Rayleigh: Philos. Mag. 11, 196 (1881)

    Google Scholar 

  19. E. Lau: Ann. Phys. 6, 417 (1948)

    Google Scholar 

  20. M.W. Reinsch, J.F. Clauser: Bul. Amer. Phys. Soc. 36, 1312 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, University of California, 94720, Berkeley, CA, USA

    J. F. Clauser & M. W. Reinsch

Authors
  1. J. F. Clauser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. W. Reinsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work supported by ONR Grant N00014-90-J-1475, by the firm J. F. Clauser & Assoc., and (MWR) by a U.S. Dept. of Education Fellowship

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clauser, J.F., Reinsch, M.W. New theoretical and experimental results in fresnel optics with applications to matter-wave and X-ray interferometry. Appl. Phys. B 54, 380–395 (1992). https://doi.org/10.1007/BF00325384

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00325384

PACS

Search

Navigation