Diamond surface polishing method and apparatus for implementing same

A diamond surface polishing apparatus, comprising:

• means for holding a polished object;
• a polishing member having an elongated shape such as a linear or belt-like shape and containing at least a metal or a metal oxide;
• means for pressing the polishing member toward a machining surface of the polished object;
• and means for causing the polishing member and the polished object to relatively move and rub against each other, the diamond surface polishing apparatus further comprising:
• means for inputting and storing a shape or coordinate information of the polished object;
• and means for inputting or computing a pressing force in accordance with the shape of the polished object, wherein the pressing means is controlled in accordance with a prescribed pressing force that has been input or computed.