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
$$\mu _{M,D}$$
generated by an expanding matrix
$$M\in M_2(\mathbb {Z})$$
and a collinear digit set
$$D=\{0,d_1,d_2,d_3\}\varvec{v}$$
, where
$$\varvec{v}\in \mathbb {Z}^2\backslash \{\varvec{0}\}$$
and
$$d_1,d_2,d_3$$
are different non-zero integers. For the case that...
