A sheet processing apparatus capable of high-speed and accurate detection of a lateral displacement and a skew of a sheet. The binarization step binarizes the intensity of the PSF using a predetermined threshold value level. as a function of an echo delay time. End caps and molded across opposing sides of the screw housing cover maintain the position of the screw housing in the screw housing cover during assembly and prevent the sliding of the worm drive clamp. For LED with a bottom electrode and a top electrode, the LED can be mounted on the planar tops of the inner lead and the top electrode wire bonded to the outer lead, or the LED can be mounted on the side surface of the inner lead and the top electrode wire bonded to the outer lead.