An image pickup apparatus is provided with a number-of-pixels reducing circuit arranged to form a reduced image by reducing to a predetermined number the effective pixels among all pixels owned by an image sensor in such a manner that the method for reducing the effective pixels changes when the image pickup mode of the apparatus is set to a first mode. More particularly, the present disclosure relates to methods for isolating and purifying silicon from saw kerf or the exhausted slurry, such that the resulting silicon may be used as a raw material, such as a solar grade silicon raw material. Focusing optics separate and focus the diffraction orders. A position of the object is estimated by maximizing a correlation between the first view and the second view by adjusting an estimated dielectric constant associated with medium between the object and the surface of the ground.