The constant phase shift $- {{\text{π}}}/{2}$ generated by a turning point is an ideal approximation under high frequency conditions. In fact, when sound waves pass through a turning point, it will travel horizontally for a certain distance in the form of inhomogeneous plane wave and then be refracted back. At this time, a functional phase shift should also be included at the turning point. In addition, a refracted ray will bring about reflection phase shift when the turning point is close to the waveguide edge. These two kinds of phase shifts which are associated with the diffraction phenomenon are called diffraction phase shifts in this paper and are more notable when the frequency goes down. In order to accurately obtain the caustic structure at low frequency, the diffraction phase shift is used to correct the classical ray theory in calculating ray skip distance, traveling time, and group velocity in this work. On this basis, a simple and explicit analytical model is proposed which is suitable for calculating the low frequency deep water caustics. The numerical study of the first upper convergence zone in the complete deep water sound channel shows that there are three caustic lines in the refracted-refracted (RR) convergence zone and four caustic lines in the refracted surface-reflected (RSR) convergence zone under the condition of high frequency hypothesis. When the diffraction phase shifts at low frequency are included, and compares with high frequency results, it is found that the horizontal beam displacement caused by the reflection phase shift will make the RR caustics horizontally move towards the source and also lead the RSR rays to generate several new caustics, while the beam displacement caused by sound propagating in the form of inhomogeneous plan wave will make the RR caustics horizontally move away from the sound source. Accompanied with the increased frequency, the diffraction effect will decrease, and the caustic structure gradually tends to the classical ray theory results. The reliability of the correction results is verified by the normal mode theory. The model proposed in this work makes up for the deficiency of classical ray theory.