  We compare the Lorentz violation terms of the pure photon sector between two
field theory models, namely the minimal standard model extension (SME) and the
standard model supplement (SMS). From the requirement of the identity of the
intersection for the two models, we find that the free photon sector of the SMS
can be a subset of the photon sector of the minimal SME. We not only obtain
some relations between the SME parameters, but also get some constraints on the
SMS parameters from the SME parameters. The CPT-odd coefficients
$(k_{AF})^{\alpha}$ of the SME are predicted to be zero. There are 15 degrees
of freedom in the Lorentz violation matrix $\Delta^{\alpha\beta}$ of free
photons of the SMS related with the same number of degrees of freedom in the
tensor coefficients $(k_F)^{\alpha\beta\mu\nu}$, which are independent from
each other in the minimal SME, but are inter-related in the intersection of the
SMS and the minimal SME. With the related degrees of freedom, we obtain the
conservative constraints ($2\sigma$) on the elements of the photon Lorentz
violation matrix. The detailed structure of the photon Lorentz violation matrix
suggests some applications to the Lorentz violation experiments for photons.
