In this paper we apply digital in-line holography to image opaque objects through a thick plano-concave pipe. Opaque fibers and opaque particles are considered}. Analytical expression of the intensity distribution in the CCD sensor plane is derived using generalized Fresnel transform. \textbf{The proposed model has the ability to deal with various pipe shape and thickness and compensates for the lack of versatility of classical DIH models. Holograms obtained with a 12 mm thick plano-concave pipe are then reconstructed using fractional Fourier transform (FRFT).} This method allows us to get rid of astigmatism. Numerical and experimental results are presented.