Ever since Jorgensen and Pedersen (J Anal Math 75:185-228, 1998) discovered the first singular spectral measure, the spectral and non-spectral problems of fractal measures have received a lot of attention in recent years. In this work, we study the planar self-affine measure μM,D\documentclass[12pt]{minimal}
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\begin{document}$$\mu _{M,D}$$\end{document} generated by an expanding matrix M∈M2(Z)\documentclass[12pt]{minimal}
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\begin{document}$$M\in M_2(\mathbb {Z})$$\end{document} and a collinear digit set D={0,d1,d2,d3}v\documentclass[12pt]{minimal}
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\begin{document}$$D=\{0,d_1,d_2,d_3\}\varvec{v}$$\end{document}, where v∈Z2\{0}\documentclass[12pt]{minimal}
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\begin{document}$$\varvec{v}\in \mathbb {Z}^2\backslash \{\varvec{0}\}$$\end{document} and d1,d2,d3\documentclass[12pt]{minimal}
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\begin{document}$$d_1,d_2,d_3$$\end{document} are different non-zero integers. For the case that {v,Mv}\documentclass[12pt]{minimal}
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\begin{document}$$\{\varvec{v},M\varvec{v}\}$$\end{document} is linearly dependent, the sufficient and necessary condition for μM,D\documentclass[12pt]{minimal}
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\begin{document}$$\mu _{M,D}$$\end{document} to be a spectral measure is given. Moreover, we estimate the number of orthogonal exponential functions in L2(μM,D)\documentclass[12pt]{minimal}
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\begin{document}$$L^2(\mu _{M,D})$$\end{document} and give the exact maximal cardinality when μM,D\documentclass[12pt]{minimal}
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\begin{document}$$\mu _{M,D}$$\end{document} is a non-spectral measure. At the same time, partial results are also obtained for the case that {v,Mv}\documentclass[12pt]{minimal}
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\begin{document}$$\{\varvec{v},M\varvec{v}\}$$\end{document} is linearly independent.
