摘要 |
The present invention provides a synthetic quartz glass having a diameter of 100 mm or more for using in an optical apparatus comprising a light source emitting a light having a wavelength of 250 nm or less, the synthetic quartz glass having, in a region located inward from the periphery thereof by 10 mm or more in a plane perpendicular to the optical axis of the synthetic quartz glass: a birefringence of 0.5 nm or less per thickness of 1 cm with respect to a light having a wavelength of 193 nm; an OH group concentration of 60 ppm or less; an averaged differential OH group concentration from the center of the synthetic quartz glass toward a peripheral direction thereof, normalized with respect to the radius of the synthetic quartz glass, of not less than -60 ppm and less than -8 ppm; and an unbiased standard deviation sigma of a differential OH group concentration from the center of the synthetic quartz glass toward a peripheral direction thereof, normalized with respect to the radius of the synthetic quartz glass, of 10 ppm or less, the unbiased standard deviation sigma being determined with the following formula (1): <maths id="MATH-US-00001" num="00001"> <MATH OVERFLOW="SCROLL"> <MTABLE> <MTR> <MTD> <MROW> <MROW> <MROW> <MROW> <MI>sigma</MI> <MO>=</MO> <MSQRT> <MFRAC> <MROW> <MUNDEROVER> <MO>∑</MO> <MROW> <MI>i</MI> <MO>=</MO> <MN>1</MN> </MROW> <MI>n</MI> </MUNDEROVER> <MO></MO> <MSUP> <MROW> <MO>(</MO> <MROW> <MSUB> <MI>X</MI> <MI>i</MI> </MSUB> <MO>-</MO> <MOVER> <MI>X</MI> <MI>_</MI> </MOVER> </MROW> <MO>)</MO> </MROW> <MN>2</MN> </MSUP> </MROW> <MROW> <MI>n</MI> <MO>-</MO> <MN>1</MN> </MROW> </MFRAC> </MSQRT> </MROW> <MO></MO> <MSTYLE> <MTEXT> </MTEXT> </MSTYLE> <MO></MO> <MI>providing</MI> </MROW> <MO>;</MO> </MROW> <MO></MO> <MSTYLE> <MTEXT> </MTEXT> </MSTYLE> <MO></MO> <MROW> <MSUB> <MI>X</MI> <MI>i</MI> </MSUB> <MO>=</MO> <MROW> <MFRAC> <MROW> <MI>Delta</MI> <MO></MO> <MSTYLE> <mspace width="0.3em" height="0.3ex"/> </MSTYLE> <MO></MO> <MSUB> <MOVER> <MI>n</MI> <MI>_</MI> </MOVER> <MI>OHi</MI> </MSUB> </MROW> <MROW> <MI>Delta</MI> <MO></MO> <MSTYLE> <mspace width="0.3em" height="0.3ex"/> </MSTYLE> <MO></MO> <MSUBSUP> <MI>r</MI> <MI>i</MI> <MO>*</MO> </MSUBSUP> </MROW> </MFRAC> <MO>=</MO> <MROW> <MFRAC> <MROW> <MSUB> <MOVER> <MI>n</MI> <MI>_</MI> </MOVER> <MI>OHi</MI> </MSUB> <MO>-</MO> <MSUB> <MOVER> <MI>n</MI> <MI>_</MI> </MOVER> <MROW> <MI>OHi</MI> <MO>+</MO> <MN>1</MN> </MROW> </MSUB> </MROW> <MROW> <MSUBSUP> <MI>r</MI> <MI>i</MI> <MO>*</MO> </MSUBSUP> <MO>-</MO> <MSUBSUP> <MI>r</MI> <MROW> <MI>i</MI> <MO>+</MO> <MN>1</MN> </MROW> <MO>*</MO> </MSUBSUP> </MROW> </MFRAC> <MO>:</MO> </MROW> </MROW> </MROW> </MROW> </MTD> <MTD> <MROW> <MO>(</MO> <MN>1</MN> <MO>)</MO> </MROW> </MTD> </MTR> </MTABLE> </MATH> </MATHS> differential OH group concentration at measurement point i normalized with respect to the radius R of the synthetic quartz glass; <maths id="MATH-US-00002" num="00002"> <MATH OVERFLOW="SCROLL"> <MROW> <MSUB> <MOVER> <MI>n</MI> <MI>_</MI> </MOVER> <MI>OHi</MI> </MSUB> <MO>=</MO> <MROW> <MFRAC> <MROW> <MSUB> <MI>n</MI> <MROW> <MI>OHi</MI> <MO>-</MO> <MN>1</MN> </MROW> </MSUB> <MO>+</MO> <MSUB> <MI>n</MI> <MI>OHi</MI> </MSUB> <MO>+</MO> <MSUB> <MI>n</MI> <MROW> <MI>OHi</MI> <MO>+</MO> <MN>1</MN> </MROW> </MSUB> </MROW> <MN>3</MN> </MFRAC> <MO>:</MO> </MROW> </MROW> </MATH> </MATHS> OH group concentration at measurement point i in terms of moving average for three points including the two points before and after the measurement point i; <maths id="MATH-US-00003" num="00003"> <MATH OVERFLOW="SCROLL"> <MROW> <MSUBSUP> <MI>r</MI> <MI>i</MI> <MO>*</MO> </MSUBSUP> <MO>=</MO> <MROW> <MFRAC> <MSUB> <MI>r</MI> <MI>i</MI> </MSUB> <MI>R</MI> </MFRAC> <MO>:</MO> </MROW> </MROW> </MATH> </MATHS> radius at measurement point i normarized with respect to the radius R of the synthetic quartz glass; <O OSTYLE="SINGLE">X: average of OH group concentrations Xi in the whole evaluation region; and n: number of measurement points in the evaluation region (integer of 2 or more).
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