Method for producing substrate

A method for producing a substrate, comprising the steps of:

• furnishing a working tool comprising a polishing plate which is disk-shaped and is rotatably mounted by a rotating shaft coupled to a rotating mechanism to rotate the polishing plate, an expandable elastomer sheet attached to a lower surface of the polishing plate, an abrasive cloth attached to a lower surface of the elastomer sheet, and means for pressing the elastomer sheet at a plurality of positions under respective predetermined different pressures such that a lower surface of the abrasive cloth is deformed to the desired inverted convex shape in accordance with differences of pressing force applied to the elastomer sheet at the plurality of positions,
• resting a substrate on a substrate holder and securing it thereto,
• bringing the inverted convexly deformed surface of the abrasive cloth in contact with the substrate, and
• rotating and moving the working tool for polishing the substrate over a selected area,
• wherein the substrate is a synthetic quartz glass substrate having a diagonal length of at least 1,000 mm.