Errors in Hadamard spectroscopy or imaging caused by imperfect masks

An analysis is given of the errors in Hadamard spectroscopy that are caused by transparent slits in the mask being systematically wider or narrower than they should be. It is shown that if the input spectrum consists of a single line, the distorted spectrum that is actually calculated consists of this line, plus four small blips. When the transparent slits are too wide, these blips are of equal height and the same sign, one pair surrounding the line, and another pair displaced a certain distance from it. When the slits are too narrow, the displaced blips have the same amplitude, but are negative. The response to an arbitrary input spectrum is then determined from this. The same method of analysis may also be used to handle other types of errors.