Meaning
Electromagnetic wave propagation phenomena in the near-field region dictate the distribution of intensity when a wavefront encounters an aperture or an obstacle at a distance comparable to the size of the boundary. This physical behavior, described as fresnel diffraction, occurs when the curvature of the propagating wavefront cannot be neglected, resulting in a complex pattern of alternating light and dark bands. Analyzing these intensity patterns allows metrologists to extract surface and phase information from samples without requiring direct contact.
The mathematical approximation remains valid as long as the propagation distance is sufficient to avoid evanescent wave interference but short enough that the curvature of the wavefront is still pronounced.
Mathematical Framework
Numerical integration of the wave field utilizes the paraxial wave equation to compute the complex amplitude distribution at a given plane downstream from the object. This calculation solves for the phase shift introduced by the sample, which is particularly useful for light-element materials that do not attenuate X-rays or visible light significantly but do retard their phase. The resulting diffraction pattern contains high-frequency details that represent the boundaries and internal interfaces of the inspected specimen.
Industrial Implementation
Inline phase-contrast imaging setups exploit these diffraction effects to visualize microstructural boundaries in low-density composites and polymers. The technician adjusts the sample-to-detector distance to optimize the contrast of the diffraction fringes, allowing the boundary of the internal features to be resolved with high precision. This adjustment must be finely tuned because incorrect positioning will wash out the fringe details, leading to inaccurate boundary measurements.
Calibration Verification
Continuous calibration of the source-to-detector distance maintains the accuracy of the reconstructed phase maps.
