In this paper we present a light field camera system where a flat-surface hexagonal array of nanostructured gradient index lenses was used as a lens matrix. In our approach we use an array of 469 gradient index microlenses with a diameter of 20 µm and 100% fill factor. To develop the single lens and the lenslet array we used a modified stack-and-draw technology. In this technique, variation of refractive index is achieved by using quantized gradient index profiles and rods from different types of glasses. We show experimental results of using this type of lenses for imaging in a system of two kinds of light field cameras. In the first one, the microlens array is located in the focal plane of the main lens. The image is reconstructed, in this case using a Fourier slice photography algorithm. This allowed a partial reconstruction of a 3D scene with spatial and depth resolution of 20 µm and field of view of 500×500×500 µm. In the second configuration, the microlens array is located between a sample and a microscopic objective, thus allowing for superresolution 3D reconstruction of a microscopic image. The scale-invariant feature transform method was used for image reconstruction and obtained a partial 3D reconstruction with a field of view of 150×115×80 µm and a spatial resolution of 2 µm and depth resolution of 10 µm.