A method of preparing a synthetic quartz glass substrate for a photomask or for nanoimprint lithography, comprising the steps of: furnishing a synthetic quartz glass block, optionally, slicing the block to form a synthetic quartz glass plate; coating an arbitrary surface and an opposite surface of the block, or of the plate, with a liquid having a transmittance of at least 99.0%/mm at the wavelength of a birefringence measurement, wherein the difference between the refractive index of the liquid and the refractive index of the synthetic quartz glass substrate is within ±0.1, measuring the birefringence of the block or plate by letting light enter one coated surface and exit the other coated surface, and sorting the block or plate to an acceptable group or unacceptable group, based on the measured birefringence value in relation to a birefringence specification for the synthetic quartz glass substrate, wherein the birefringence specification for the synthetic quartz glass substrate is of birefringence not above α nm/cm, and in the sorting step, the block or plate is sorted to the acceptable group when it has a maximum birefringence value not above 1.5α nm/cm in a region corresponding to an effective region of a synthetic quartz glass substrate to be sliced from the block or made from the plate, wherein when the measuring and sorting is applied to the block, and after the block is sorted to the acceptable group in the sorting step, said method further comprises the steps of slicing the block into a synthetic quartz glass plate, grinding or lapping, rough polishing, and final precise polishing the glass plate to form the substrate, or when the measuring and sorting is applied to the plate, and after the plate is sorted to the acceptable group in the sorting step, said method further comprises the steps of grinding or lapping, rough polishing, and final precise polishing the plate to form the substrate. furnishing a synthetic quartz glass block, optionally, slicing the block to form a synthetic quartz glass plate; coating an arbitrary surface and an opposite surface of the block, or of the plate, with a liquid having a transmittance of at least 99.0%/mm at the wavelength of a birefringence measurement, wherein the difference between the refractive index of the liquid and the refractive index of the synthetic quartz glass substrate is within ±0.1, measuring the birefringence of the block or plate by letting light enter one coated surface and exit the other coated surface, and sorting the block or plate to an acceptable group or unacceptable group, based on the measured birefringence value in relation to a birefringence specification for the synthetic quartz glass substrate, wherein the birefringence specification for the synthetic quartz glass substrate is of birefringence not above α nm/cm, and in the sorting step, the block or plate is sorted to the acceptable group when it has a maximum birefringence value not above 1.5α nm/cm in a region corresponding to an effective region of a synthetic quartz glass substrate to be sliced from the block or made from the plate, wherein when the measuring and sorting is applied to the block, and after the block is sorted to the acceptable group in the sorting step, said method further comprises the steps of slicing the block into a synthetic quartz glass plate, grinding or lapping, rough polishing, and final precise polishing the glass plate to form the substrate, or when the measuring and sorting is applied to the plate, and after the plate is sorted to the acceptable group in the sorting step, said method further comprises the steps of grinding or lapping, rough polishing, and final precise polishing the plate to form the substrate.