The laser thermoelastic generation of ultrasound is a promising technique with many potential applications, but it is also a complicated process with many physical phenomena involved. Contrary to a conventional piezoelectric transducer generation, which is a surface phenomenon, a laser generation can activate acoustic sources within the material by optical penetration of the excitation wavelength, resulting in asynchronous wave arrivals at a given point. More generally, in the ideal case of a nondispersive isotropic material, the laser-ultrasonics displacement signals result from temporal convolutions between optical penetration, laser pulse duration, and laser spot extension effects. In this paper, a deconvolution technique is presented that extracts the laser pulse duration contribution from the experimental displacement signals. This deconvolution scheme applied to one-dimensional experiments, in which the laser excitation is spread over a sufficiently large area on the front side of the sample, allows the measurement of the optical absorption coefficient of the material at the excitation wavelength and also a precise evaluation of its longitudinal acoustic velocity.