The multi-frequency lock-in thermography is coupled with efficient image processing to analyse infrared open crack footprint. It has been shown that the evolution of the Laplacian of modulated surface temperature amplitude image as a function of the diffusion length allows to estimate the depth of surface open defects but requires calibration abacus obtained by finite element method simulations. In this work, a method is proposed to avoid the tedious use of abacus by introducing an indicator of the crack depth using a simple expression depending on the Laplacian of both amplitude and phase images. This multi-frequency method is presented through numerical simulations. Besides, the analysis of experimental results obtained on artificial and real open vertical cracks in metallic samples show that the depth of the defects can be directly estimated.