1. A method for inspecting foreign matter on a mirror-finished substrate-under-inspection, comprising: emitting illumination light to the substrate-under-inspection; obtaining image data based on an image which includes irregular reflection light that has been irregularly reflected from the substrate-under-inspection; performing arithmetic operation, using a microprocessor, based on either one of operational expressions given in (equation 1), (equation 2) or (equation 3) provided that a light-intensity value of a desired one pixel of the image data as P(i, j) (where “i”, “j”: an integer for specifying a desired position wherein “i” indicates an arrangement order in a direction of X-axis while “j” indicates an arrangement order in a direction of Y-axis), a mean value over a desired pixel and its peripheral pixels of the image data as M(i, j) and a deviation value over a desired pixel and its peripheral pixels of the image data as S(i, j), P ( i , j ) = max ⁡ [  P ( i + 1 , j - 1 ) - P ( i - 1 , j - 1 ) + P ( i + 1 , j ) - P ( i - 1 , j ) + P ( i + 1 , j + 1 ) - P ( i - 1 , j + 1 )  ,  P ( i - 1 , j + 1 ) - P ( i - 1 , j - 1 ) + P ( i , j + 1 ) - P ( i , j - 1 ) + P ( i + 1 , j + 1 ) - P ( i + 1 , j - 1 )  ] Equation ⁢ ⁢ 1 (where right-side operation represents to employ the greater one of two term's values (absolute value) segmented by an in-bracket commas, i.e. of the upper and lower terms) P ( i , j ) = max ⁡ [  P ( i + 1 , j - 1 ) - P ( i - 1 , j - 1 ) + 2 ⁢ P ( i + 1 , j ) - 2 ⁢ P ( i - 1 , j ) + P ( i + 1 , j + 1 ) - P ( i - 1 , j + 1 )  ,  P ( i - 1 , j + 1 ) - P ( i - 1 , j - 1 ) + 2 ⁢ P ( i , j + 1 ) - 2 ⁢ P ( i , j - 1 ) + P ( i + 1 , j + 1 ) - P ( i + 1 , j - 1 )  ] Equation ⁢ ⁢ 2 (where right-side operation represents to employ the greater one of two term's values (absolute value) segmented by an in-bracket commas, i.e. of the upper and lower terms), 
 If | P (i,j) −M (i,j) |>S (i,j) ,  Equation 3 
 then P (i,j) =P (i,j). 
 If | P (i,j) −M (i,j) |<S (i,j) , 
 then P (i,j) =M (i,j). Here, 
 M (i,j) = 1/9( P (i−1,j−1) +P (i,j−1) +P i+1,j−1) +P (i−1,j) +P (i,j) +P i+1,j) +P (i−1,j+1) +P (i,j+1) +P (i+1,j+1) ) 
 S 2 (i,j) = 1/9( P 2 (i−1,j−1) +P 2 (i,j−1) +P 2 (i+1,j−1) +P 2 (i−1,j) +P 2 (i,j) +P 2 (i+1,j) +P 2 (i−1,j+1) +P 2 (i,j+1) +P 2 (i+1,j+1) )− M 2 (i,j) detecting coordinates of a plurality of contour sampling points indicative of a contour of an inspection area from the image data; estimating the inspection area from the coordinates of the plurality of contour sampling points; preparing mask image data where masking is applied to an area other than the inspection area by use of the image data the image-processing has been done; and performing foreign-matter detection on the image data by using the mask image data.