Original research articleA surface shape test method for a thin flat mirror

An optical test method of the surface shape for very thin flat mirrors is presented and discussed. The effect of gravity on the mirror shape is greatly reduced by floating the mirror on water while the surface is measured using a Zygo interferometer. The floating mirror is supported by the buoyant force and surface tension. Mechanical analysis and error analysis show that the tested flat mirror can be considered as a rim supported mirror with a reduced gravity. The surface error caused by the rim constraint can be rather small because of the reduced effective gravity. The surface error of a flat mirror which is Ф102 mm, 0.6 mm thick was tested using this method. The results were compared to the method successfully used for the Hinode project. The Hinode method supports the mirror at three points and measures the surface for both the mirror facing up and facing down. The average of the face up and face down measurements yields the zero gravity shape. The test results including the surface error and the fringe of the surface shape by these two methods were in good agreement. Compared to the Hinode method, the method can be carried on before the mirror's coating and can to be employed during the polishing process.