1. A detector for detecting a position of a mark, comprising: an image sensor; a first illuminator which emits illumination light for illuminating a mark; a second illuminator which emits illumination light for illuminating a pattern; a scope which illuminates the mark with the illumination light emitted from the first illuminator, projects the pattern illuminated by the second illuminator onto the mark, and projects, onto an image sensing surface of the image sensor, the illuminated mark and the pattern projected onto the mark; and a processor which calculates a position of the mark with respect to one of a position of the pattern and a position already known from the position of the pattern, based on a moiré pattern formed on the image sensing surface by the mark and the pattern, wherein the illumination light from the first illuminator does not illuminate the pattern.