We investigate spectral properties of planar Moran measures \(\mu _{\{M_n\},\{D_n\}}\) generated by sequences of expanding matrices \(\{M_n\}\subset M_2(\mathbb {Z})\) and digit sets \(\{D_n\}\subset \mathbb {Z}^2\) , where each digit set has the form \( D_n = \left\{ \begin{pmatrix} 0 \\ 0 \end{pmatrix}, \begin{pmatrix} \alpha _{n_1}\\ \alpha _{n_2} \end{pmatrix}, \begin{pmatrix} \beta _{n_1} \\ \beta _{n_2} \end{pmatrix}, \begin{pmatrix} -\alpha _{n_1}-\beta _{n_1}\\ -\alpha _{n_2}-\beta _{n_2} \end{pmatrix} \right\} \) satisfying \(\alpha _{n_1}\beta _{n_2}-\alpha _{n_2}\beta _{n_1} \ne 0 \pmod {2}\) . Under the hypotheses \(|\det (M_n)| > 4\) for all \(n\ge 1\) , \(\sup _{n\ge 1}\Vert M_n^{-1}\Vert < 1\) , and \(\{D_n\}\) is finite, we establish the following characterization: \( \mu _{\{M_n\},\{D_n\}} {\text { is a spectral measure}} \Longleftrightarrow {M_n\in M_2(2\mathbb {Z})} {\text { for all }} n\ge 2. \) Furthermore, for the critical case \(|\det (M_n)| = 4\) , we derive a complete spectral criterion for a significant class of Moran measures through combinatorial analysis of digit sets. These results extend current understanding of spectral self-affine measures to Moran-type constructions.
