It is remarkable that in several imaging and detection methods usually the presence of speckle is considered as a source of error and a disturbing factor. The residual roughness, in turn, cause an overlaid random field, called speckle pattern, on the Fresnel diffraction. Likewise to the case of sharpness, practically fabrication of a 100% optically flat and smooth phase step is impossible. Here, we address another important issue, which is the smoothness of the phase step surfaces. The bluntness parameter may be defined as the ratio of the conjunction length of the phase step to its height. We specifically proved that up to 10% bluntness can be tolerated in phase-step based OD without considerable effect on the measurements. Recently, we investigated the impact of bluntness of the phase steps on the OD measurements 1. Whilst it is certainly impossible to fabricate such sharp step and a level of bluntness is unavoidable. In the predated OD applications as well as in theoretical studies, the phase step always was considered to be a sharp step. Amongst, precise measurement of displacements at the scales down to nanometer 10, thin-film thickness 11, refractive indices of solids and liquids 12, 13, diffusion coefficient 3, temperature gradient 14, etching rate 15, coherence parameters and spectral line-shape 16, direct measurement of the x-ray refractive index 6, color dispersion 17, wavemetry 18, and quantitative 3D phase imaging 9 have been the most effective ones to name. These parameters vary as the optical path difference (OPD) changes, which in turn is resulted from variations in the incidence angle of light, height of the phase step, refractive index of the object, or refractive index of the surrounding medium (in transmission mode) 2.Ĭonsidering the robustness again vibrations, feasibility, and other advantages over optical interferometry, OD from phase steps has found several absorbing metrological and technological applications. The visibility of the diffraction fringes and the positions of its extrema usually serve as criteria in the aforementioned measurements 2, 9. In another interpretation, the phase step diffraction fringes may be considered as a hologram of the interfering light waves leaving the two sides of the phase step 8. Tavassoly showed that Fresnel diffraction is a basic quantum mechanical effect 7. Using wave optics analysis OD is formulated and studied rather comprehensively in both reflection and transmission modes 2, 3. Mostly OD is used with visible light, but it can be also performed by other wave sources such as X-ray 6. OD can be applied either in reflection from a reflective physical step, or in transmission by passing light through a boundary region of transparent media with different refractive indices. The technique of “Optical Diffractometry (OD)” extracts such information, which can be on the object’s light absorption behavior, optical phase changes, or polarization characteristics. Similar content being viewed by othersĪn abrupt change or confinement in the phase, amplitude, phase gradient, or polarization state of a light wavefront causes appreciable Fresnel diffraction, and the diffraction pattern includes information of the diffracting object 1, 2, 3, 4, 5. We derive the theoretical description and confirm the results with simulations and experiments. We define number of detectable fringes and autocorrelation functions of the diffraction patterns as the measures for evaluating the similarity of the rough phase step diffractions to the ideal case. We show that preserving the OD-diffraction-pattern characteristics of a phase step depends on the level of roughness in the surfaces of the phase step. However, practically, some amount of roughness and unflatness is unavoidable even in precise and careful fabrication process. So far, in all of the OD applications the surfaces of the incorporated phase steps are considered to be optically smooth and flat. Here, we address the issue of smoothness of the phase step surfaces. Recently, we showed that such measurements do not require infinitively sharp phase steps, although fabrication of such sharp elements is also impossible. OD utilizes a phase step to detect the influence of objects under measurement by the changes in the Fresnel diffraction pattern. Therefore, OD has found numerous interesting metrological and technological applications. Optical diffractometry (OD) using a phase step is an alternative for interferometry, further, has least sensitivity to environmental vibrations.
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