This paper investigates the spectral properties of a class of Moran measures \(\mu _{R,\{ D_n \}}\) on \(\mathbb {R}^2\) , generated by an expanding real diagonal matrix \(R={\operatorname {diag}}(\rho _1,\rho _2)\) and a sequence of non-collinear integer digit sets \(\begin{aligned} D_n=\{ (0,0)^{\textrm{t}}, (a_n,b_n)^{\textrm{t}}, (c_n,d_n)^{\textrm{t}}\} \end{aligned}\) satisfying \(\sup _{n\in \mathbb {Z}^{+}}\{a_n,b_n,c_n,d_n\}<\infty \) . We establish equivalent conditions for the existence of infinite orthogonal sets in \(L^2(\mu _{R,\{ D_n \}})\) . Furthermore, we derive necessary conditions for \(\mu _{R,\{ D_n \}}\) to be a spectral measure under the assumption that \(\tau _n:=\max \{u:3^u |(a_nd_n-b_nc_n)\}=\tau \) for all \(n \ge 1\) . Finally, for measures generated by a specific subclass of digit sets \(\{D_n\}_{n=1}^{\infty }\) , we obtain a necessary and sufficient condition for \(\mu _{R,\{ D_n \}}\) to be spectral.
