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A lens-array-based integral imaging camera is studied in this work, which consists of a lens array, a main lens and a CCD camera. The lens array is placed on the object side of the main lens, thus can provide wider stereo baseline than other lens-array-based integral imaging cameras where the lens array is usually placed on the sensor side. However, the image captured by this system presents severe non-linear and discontinuous geometrical distortions, which are difficult to model by conventional pin-hole camera models or their direct variants. In this work, we propose a generic calibration method to calibrate the geometry of this integral imaging camera. Using a LCD panel as an active calibration object, correspondences between 2D image locations and 3D light rays captured by the camera are automatically established in high density. The obtained calibration results are applied in 2D reconstruction of integral images and 3D scene reconstruction. Experiments with real images show that 2D integral images can be reconstructed with accurate geometrical property from highly distorted raw images. In a 3D test environment, with only one raw image captured by the integral imaging camera, 3D structure of objects at different depth can be correctly reconstructed.