Journal of Russian Laser Research | 2021
Analytical Approach to the Theory of X-Ray Observation of Pores in Bulk Materials
Abstract
We analytically study the problem of pore detection and certification in bulk objects by means of radiography. For an absorbent sample, the optimum thickness for pore imaging and detection is expressed in terms of the linear attenuation coefficient of the material. This can be used to maximize the signal-to-noise ratio by tuning the photon energy of the incident monochromatic beam. The problem is more complicated for transparent objects. An evident approach is radiography in coherent beams; in this case, we use a simple model allowing to find the field structure of the transmitted beam on the backside of the sample and beyond in the outer half space in terms of few dimensionless parameters, including the Fresnel number F = a 2 / λz , where a is the pore radius, λ is the wavelength, z is the distance from the back side of the sample to the detector, and the phase number Φ = akδ , with k = 2 π / λ and δ being the bulk material decrement. The detailed analysis of this field structure is performed that can be used to find the optimum position of a detector revealing the pores parameters from the intensity distribution measured. We present the numerical results for a Gaussian type of the pore shape function and provide the software to calculate the space field structure for other pore shape functions. The stationary phase method in higher orders, used here to simplify the Fresnel integral, can be applied to extend the obtained results to 3D geometry. The suggested qualitative picture of the formation of images of pores as phase objects complements modern methods of monitoring porous-sensitive materials.