Light sheet microscopy (LSM) - also known as selective plane illumination microscopy (SPIM) - enables high-speed, volumetric imaging by illuminating a two-dimensional cross-section of a specimen. Typically, this light sheet is created by table-top optics, which limits the ability to miniaturize the overall SPIM system. Replacing this table-top illumination system with miniature, integrated devices would reduce the cost and footprint of SPIM systems. One important element for a miniature SPIM system is a flat, easily manufactured lens that can form a light sheet. Here we investigate planar metallic lenses as the beam shaping element of an integrated SPIM illuminator. Based on finite difference time domain (FDTD) simulations, we find that diffraction from a single slit can create planar illumination with a higher light throughput than zone plate or plasmonic lenses. Metallic slit microlenses also show broadband operation across the entire visible range and are nearly polarization insensitive. Furthermore, compared to meta-lenses based on sub-wavelength-scale diffractive elements, metallic slit lenses have micron-scale features compatible with low-cost photolithographic manufacturing. These features allow us to create inexpensive integrated devices that generate light-sheet illumination comparable to tabletop microscopy systems. Further miniaturization of this type of integrated SPIM illuminators will open new avenues for flat, implantable photonic devices for in vivo biological imaging.