4. (a) For a pinhole-style camera with focal length f, provide the coordinates on the detector (x, y) as a function of the angular coordinates of observation (√x, Sy). The angular coordinates are defined with respect to the optical axis going through the center of the detector, where (x, y) = (0,0). (b) The coordinates on the detector in (a) are the undistorted coordinates (xu, yu). Express the distorted coordinates (xa, ya) in terms of the undistorted coordinates for a camera that suffers from radial distortion, quantified by distortion parameter k. (c) For a camera that suffers from pincushion distortion, i.e. the opposite of barrel distortion, is k smaller or larger than zero? Illustrate your explanation with a sketch.

4. (a) For a pinhole-style camera with focal length f, provide the coordinates on the detector (x, y) as a function of the angular coordinates of observation (√x, Sy). The angular coordinates are defined with respect to the optical axis going through the center of the detector, where (x, y) = (0,0). (b) The coordinates on the detector in (a) are the undistorted coordinates (xu, yu). Express the distorted coordinates (xa, ya) in terms of the undistorted coordinates for a camera that suffers from radial distortion, quantified by distortion parameter k. (c) For a camera that suffers from pincushion distortion, i.e. the opposite of barrel distortion, is k smaller or larger than zero? Illustrate your explanation with a sketch.