4. Suppose the surface of each detector in an array is of size d x d units. You may assume the array itself measures D x D units. If y(x,y) is the incident light intensity on the array, the output of each detector is the weighted volume of the intensity function falling on that detector, i.e. pixel value recrded by detector = Sl J(x,y) on detector X plx, y)drdy (1) detector aren where plx,y) is the weight function of each detector. We will assume each detector in the array has the same weight function. Show that the image recorded by the detector array amounts to taking samples at discrete spatial locations (ie., on a sampling grid) of the convolution, or correlation between Jx,y) and p(x,y). 4. Suppose the surface of each detector in an array is of size d x d units. You may assume the array itself measures D x D units. If y(x,y) is the incident light intensity on the array, the output of each detector is the weighted volume of the intensity function falling on that detector, i.e. pixel value recrded by detector = Sl J(x,y) on detector X plx, y)drdy (1) detector aren where plx,y) is the weight function of each detector. We will assume each detector in the array has the same weight function. Show that the image recorded by the detector array amounts to taking samples at discrete spatial locations (ie., on a sampling grid) of the convolution, or correlation between Jx,y) and p(x,y)