Abstract
Mechanical vibrations of components of the optical system is one of the sources of blurring of interference pattern in coherent imaging systems. The problem is especially important in holography where the resolution of the reconstructed objects depends on the effective size of the hologram, which is on the extent of the interference pattern, and on the contrast of the interference fringes. We discuss the mathematical relation between the vibrations, the hologram contrast and the reconstructed object. We show how vibrations can be post-filtered out from the hologram or from the reconstructed object assuming a Gaussian distribution of the vibrations. We also provide a numerical example of compensation for directional motion blur. We demonstrate our approach for light optical and electron holograms, acquired with both, plane- as well as spherical-waves. As a result of such hologram deblurring, the resolution of the reconstructed objects is enhanced by almost a factor of 2. We believe that our approach opens up a new venue of post-experimental resolution enhancement in in-line holography by adapting the rich database/catalogue of motion deblurring algorithms developed for photography and image restoration applications.
Highlights
The diffraction-limited resolution of an in-line hologram is defined by the wavelength of the employed radiation λ and by the numerical aperture of the setup NA as RNA =λ 2NA [1,2,3], where the numerical aperture is defined by the angular extent of the interference pattern.Many factors can reduce the contrast and the extent of the interference pattern and diminish the resolution: noise, partial coherence, limited extent of the reference wave, mechanical vibrations etc
The problem is especially important in holography where the resolution of the reconstructed objects depends on the effective size of the hologram, which is on the extent of the interference pattern, and on the contrast of the interference fringes
We demonstrated resolution enhancement in holography in the case when holograms are blurred due to vibrations during data acquisition
Summary
Λ 2NA [1,2,3], where the numerical aperture is defined by the angular extent of the interference pattern. As the distance between source and sample gets shorter, the shifts of the hologram due to source or object vibrations are getting larger due to the higher magnification. This in turn blurs out the fine interference fringes and reduces the potentially achievable high resolution. To compensate for vibrations, a short time acquisition sequence of hologram can be recorded [8] and subsequently the holograms can be aligned by crosscorrelation [9] and averaged Such approach can be successfully applied for a systematic drift of the sample and/or when the acquisition time is much shorter that the period of vibrations. We show that deblurring can to some extent suppress the effect of vibrations and enhance the extent and the contrast of the interference pattern fringes which in turn enhances the resolution of the reconstructed objects
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