Baseline Setting Method

A baseline setting method for a measured curve plotted on a reference axis X and a measured value axis Y extending in a direction orthogonal to the reference axis X, the measured curve having a single measured value yi identified with respect to each point xi on the reference axis X, the baseline setting method comprising the steps of:

• specifying a semicircle or semi-ellipse Cxi centered on the reference axis X and an X radius, expressed by
• x2+a2y2=r2
• y≦0
• fXi(x)={(r2−x2)1/2}/a
• if peaks of the measured curve are seen in the negative Y direction;
• comparing individual points (xi−r, fXi(xi−r)) to (xi+r, fXi(xi+r)) of the semicircle or semi-ellipse CXi centered at (xi, 0) with the corresponding points (xi−r, yXi+t) to (xi+r, yXi+r) on the measured curve to calculate
• 1
• Xi
• -
• r
• =
• f
• Xi
• 
• (
• x
• i
• -
• r
• )
• -
• y
• Xi
• -
• r
• ⋮
• 1
• Xi
• +
• r
• =
• f
• Xi
• 
• (
• x
• i
• +
• r
• )
• -
• y
• Xi
• +
• r
• and to specify the minimum value of 1Xi−r to 1Xi+r as 1(Xi)min;
• specifying the minimum value of
• f
• Xi
• -
• r
• 
• (
• x
• i
• )
• -
• 1
• 
• (
• x
• i
• -
• r
• )
• min
• ⋮
• f
• Xi
• +
• r
• 
• (
• x
• i
• )
• -
• 1
• 
• (
• x
• i
• +
• r
• )
• min
• obtained with respect to each of semicircles or semi-ellipses CXi−r to CXi+r centered at (xi−r, 0) to (xi+r, 0), as L(xi);
• setting a baseline point (xi, L(xi) corresponding to a specific point (xi, yi) on the measured curve;
• and
• connecting the baseline points corresponding to the individual points on the measured curve, to form a baseline.

A baseline setting method for a measured curve plotted on a reference axis X and a measured value axis Y extending in a direction orthogonal to the reference axis X, the measured curve having a single measured value yi identified with respect to each point x, on the reference axis X, the baseline setting method comprising the steps of:

• specifying a quadratic curve DXi centered on the reference axis X, expressed by
• y=a(x−b)2+c
• under the conditions:
• b−M≦x≦b+M
• M≧W
• a<0
• f(x)=a(x−b)2+c
• where W is the full width at half maximum of a peak having the greatest peak width among a plurality of peaks seen in the measured curve, if the peaks of the measured curve are seen in the positive Y direction;
• comparing individual points (xi−M, fXi(xi−M)) to (xi+M, fXi(xi+M)) of the quadratic curve DXi having its vertex at (xi, c) (xi=b at the beginning of the measurement) with the corresponding points (xi−M, yXi−M) to (xi+M, yXi+M) on the measured curve to calculate
• 1
• Xi
• -
• M
• =
• y
• Xi
• -
• M
• -
• f
• Xi
• 
• (
• x
• i
• -
• M
• )
• ⋮
• 1
• Xi
• +
• M
• =
• y
• Xi
• +
• M
• -
• f
• Xi
• 
• (
• x
• i
• +
• M
• )
• and to specify the minimum value of 1Xi−M to 1Xi+M as 1(Xi)min;
• specifying the maximum value of
• 1
• 
• (
• x
• i
• -
• M
• )
• min
• +
• f
• Xi
• -
• M
• 
• (
• x
• i
• )
• ⋮
• 1
• 
• (
• x
• i
• +
• M
• )
• min
• +
• f
• Xi
• +
• M
• 
• (
• x
• i
• )
• obtained with respect to each of quadratic curves DXi−M to DXi+M having their vertices at (xi−M, c) to (xi+M, c), as L(xi);
• setting a baseline point (xi, L(xi)) corresponding to a specific point (xi, yi) on the measured curve;
• setting baseline points corresponding to the individual points on the measured curve by moving the vertex in the X direction;
• and
• connecting the baseline points to form a baseline.

A baseline setting method for a measured curve plotted on a reference axis X and a measured value axis Y extending in a direction orthogonal to the reference axis X, the measured curve having a single measured value yi identified with respect to each point xi on the reference axis X, the baseline setting method comprising the steps of:

• specifying a quadratic curve DXi centered on the reference axis X, expressed by
• y=a(x−b)2+c
• under the conditions
• b−M≦x≦b+M
• M≧W
• a>0
• f(x)=a(x−b)2+c
• where W is the full width at half maximum of a peak having the greatest peak width among a plurality of peaks seen in the measured curve, if the peaks of the measured curve are seen in the negative Y direction;
• comparing individual points (xi−M, fXi(xi−M)) to (xi+M, fXi(xi+M)) of the quadratic curve DXi having its vertex at (xi, c) (xi=b at the beginning of the measurement) with the corresponding points (xi−M, yXi−M) to (xi+M, yXi+M) on the measured curve to calculate
• 1
• Xi
• -
• M
• =
• f
• Xi
• 
• (
• x
• i
• -
• M
• )
• -
• y
• Xi
• -
• M
• ⋮
• 1
• Xi
• +
• M
• =
• f
• Xi
• 
• (
• x
• i
• +
• M
• )
• -
• y
• Xi
• +
• M
• and to specify the minimum value of 1Xi−M to 1Xi+M as 1(Xi)min;
• specifying the minimum value of
• f
• Xi
• -
• M
• 
• (
• x
• i
• )
• -
• 1
• 
• (
• x
• i
• -
• M
• )
• min
• ⋮
• f
• Xi
• +
• M
• 
• (
• x
• i
• )
• -
• 1
• 
• (
• x
• i
• +
• M
• )
• min
• obtained with respect to each of quadratic curves DXi−M to DXi+M with their vertices at (xi−M, c) to (xi+M, c), as L(xi);
• setting a baseline point (xi, L(xi)) corresponding to a specific point (xi, yi) on the measured curve;
• setting baseline points corresponding to the individual points on the measured curve by moving the vertex in the X direction;
• and
• connecting the baseline points to form a baseline.