Reconstruction of a sample photoacoutic (PA) image is the research focus in PA imaging system that is based on acoustic lens. Among all existing reconstruction methods, the reconstructing PA image is usually obtained by the projection of the absorption distribution which is regarded as PA signal of a sample. However, this equivalent relationship is just approximate and not accurate in theory. In this paper, the accurate relationship between the absorption coefficients of the sample placed on the object plane and its PA pressure signals focused on the image plane is successfully demonstrated. Both the integral and the extraction envelope methods are firstly proposed to reconstruct the axial PA image of an absorbent sample. The resolution of the reconstructed PA image obtained by Hilbert transform is theoretically higher than that by integral method, and the reason is explained. Different samples are chosen to experiment on the acoustic lens PA imaging system. A three-dimensional fast PA imaging of the absorbent sample is realized by combining its axial imaging capability with its lateral imaging capability of acoustic lens. The reconstruction result shows that both the lateral and the axial resolutions of the reconstruction image are both about 1 mm. The quality of a sample PA image obtained by Hilbert transform is better than that by integral method.