In a defect inspecting apparatus, a differential interference optical system forms a differential interference image which is produced from an optical interference of images in a predetermined direction, the images corresponding to inspecting parts of a pattern formed on a mask. The ice making device may include one or more fluid inlets that supply liquid water to the cavity, and one or more fluid outlets that drain water from the cavity after formation of ice having a desired shape. Also, in further embodiments, the particle collections have particle size distribution such that effectively no particles have a diameter greater than about four times the average diameter of the collection of particles. Once shifted, the frequency components about DC are removed by DC canceler circuit and the resulting spectrum is mixed with a subsequent synthesized frequency signal which shifts the spectrum back to its original representation and baseband. The hash identification quasi-uniquely identifies the mobile station.