For a substrate having fine convexoconcave patterns on its surface, the dimensions of the convexoconcave patterns in a vertical direction of a quartz glass substrate are controlled to be uniform with extreme accuracy and over the entire substrate surface. The quartz glass substrate is made to have a fictive temperature distribution of at most 40° C. and a halogen concentration of less than 400 ppm, and the etching rate of the surface of the quartz glass substrate is made uniform, whereby the dimensions of the convexoconcave patterns in a vertical direction of the quartz glass substrate are controlled to be uniform with good accuracy and over the entire substrate surface.