Multi-angle structured illumination lensless (MASIL) microscopy enables high-resolution image recovery over a large field of view. Successful image recovery of MASIL microscopy, however, relies on an accurate knowledge of the multi-angle illumination. System misalignments and slight deviations from the true illumination angle may result in image artifacts in reconstruction. Here we report a MASIL microscopy system that is robust against illumination misalignment. To calibrate the illumination angles, we design and use a double-sided mask, which is a glass wafer fabricated with a ring-array pattern on the upper surface and a disk-array pattern on the lower surface. As such, the illumination angles can be decoded from the captured images by estimating the relative displacement of the two patterns. We experimentally demonstrate that this system can achieve successful image recovery without any prior knowledge of the illumination angles. The reported approach provides a simple yet robust resolution for wide-field lensless microscopy. It can solve the LED array misalignment problem and calibrate angle-varied illumination for a variety of applications.