Displacement calculation method, drawing data correction method, substrate manufacturing method, and drawing apparatus
Correction values (ΔX 1 to ΔX 4 ) at the X position (X=xe) of a target point (E (xe, ye)) are calculated by calculating the amounts of shift (ΔX) in the positions of alignment marks (M 11 to M 14 , M 21 to M 24 , M 31 to M 34 , M 41 to M 44 ) in the X direction and plotting first spline curves (SL 1 ) using the amounts of shift. Then, a first sub-spline curve (SL 1 S) is plotted using the correction values (ΔX 1 to ΔX 4 ) in order to calculate a correction value (ΔXe) at the Y position (Y=ye) of the target point (E (xe, ye)), and the calculated correction value is taken as the correction amount in the X direction. The correction amount in the Y direction is also calculated in the same manner.
1. A displacement calculation method for calculating a displacement of a target point based on displacements of a plurality of reference points arranged in a grid on a surface of a substrate, along a first coordinate axis direction and a second coordinate axis direction that intersect each other, the method comprising:
a step of obtaining position information of a plurality of reference points defined on a substrate surface;
a step of detecting, by a computing device, displacements of reference points in the vicinity of a target point in first and second coordinate axis directions based on said position information;
a step of performing a computation for a displacement of said target point, wherein
said step of performing the computation comprises, for displacements in one coordinate axis direction of said first and second coordinate axis directions, of said reference points in the vicinity of said target point,
A: a first spline calculation step of calculating a first spline curve that indicates a relationship between displacement values and first coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said first coordinate axis direction and having a same second coordinate axis value,
B: a first spline-indicated-value calculation step of calculating, as a first spline-indicated value, a value indicated by said first spline curve of said each group at a first coordinate axis value of said target point,
C: a first sub-spline calculation step of calculating a first sub-spline curve that indicates a relationship between first spline-indicated values of respective groups and second coordinate axis values of said respective groups, and
D: a first sub-spline-indicated-value calculation step of calculating a value indicated by said first sub-spline curve at a second coordinate axis value of said target point; and
outputting the displacement of the target point.
2. The displacement calculation method according to claim 1 , wherein
said step of performing a computation further executes, for said displacements in said one coordinate axis direction,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point, and
an average value of the value calculated in said first sub-spline-indicated-value calculation step and the value calculated in said second sub-spline-indicated-value calculation step is calculated.
3. The displacement calculation method according to claim 1 , wherein
said step of performing a computation further executes said steps A through D for displacements in the other coordinate axis direction out of said first and second coordinate axis directions, of said reference points in the vicinity of said target point.
4. The displacement calculation method according to claim 1 , wherein
said step of performing a computation further executes, for displacements in the other coordinate axis direction out of said first and second coordinate axis directions, of said reference points in the vicinity of said target point,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point.
5. The displacement calculation method according to claim 3 , wherein
said step of performing a computation further executes, for said displacements in said other coordinate axis direction,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in the second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point, and
an average value of the value calculated in said first sub-spline-indicated-value calculation step and the value calculated in said second sub-spline-indicated-value calculation step is calculated.
6. A drawing data correction method comprising:
a step of preparing drawing data;
a step of calculating a displacement of a target point based on displacements of a plurality of reference points that are arranged in a grid on a surface of a substrate along a first coordinate axis direction and a second coordinate axis direction that intersect each other; and
a drawing data correction step of creating drawing data in which a position of a pixel to be drawn at said target point in the prepared drawing data is displaced based on a calculated displacement of said target point,
wherein said step of calculating a displacement of a target point is performed by a computing device and comprises:
a step of obtaining position information of said plurality of reference points defined on the substrate surface;
a step of detecting displacements of reference points in the vicinity of said target point in said first and second coordinate axis directions based on said position information; and
a step of performing a computation for said displacement of said target point, and
said step of performing a computation comprises, for displacements in one coordinate axis direction of said first and second coordinate axis directions, of said reference points in the vicinity of said target point,
A: a first spline calculation step of calculating a first spline curve that indicates a relationship between displacement values and first coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said first coordinate axis direction and having a same second coordinate axis value,
B: a first spline-indicated-value calculation step of calculating, as a first spline-indicated value, a value indicated by said first spline curve of said each group at a first coordinate axis value of said target point,
C: a first sub-spline calculation step of calculating a first sub-spline curve that indicates a relationship between first spline-indicated values of respective groups and second coordinate axis values of said respective groups, and
D: a first sub-spline-indicated-value calculation step of calculating a value indicated by said first sub-spline curve at a second coordinate axis value of said target point; and
outputting the displacement of the target point.
7. The drawing data correction method according to claim 6 , wherein
said step of performing a computation further executes, for said displacements in said one coordinate axis direction,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point, and
an average value of the value calculated in said first sub-spline-indicated-value calculation step and the value calculated in said second sub-spline-indicated-value calculation step is calculated.
8. The drawing data correction method according to claim 6 , wherein
said step of performing a computation further executes said steps A through D for displacements in the other coordinate axis direction out of said first and second coordinate axis directions, of said reference points in the vicinity of said target point.
9. The drawing data correction method according to claim 6 , wherein
said step of performing a computation further executes, for displacements in the other coordinate axis direction out of said first and second coordinate axis directions, of said reference points in the vicinity of said target point,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point.
10. The drawing data correction method according to claim 8 , wherein
said step of performing a computation further executes, for said displacements in said other coordinate axis direction,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in the second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point, and
an average value of the value calculated in said first sub-spline-indicated-value calculation step and the value calculated in said second sub-spline-indicated-value calculation step is calculated.
11. A substrate manufacturing method comprising:
a step of preparing drawing data;
a step of calculating a displacement of a target point based on displacements of a plurality of reference points that are arranged in a grid on a surface of a substrate along a first coordinate axis direction and a second coordinate axis direction that intersect each other;
a drawing data correction step of creating drawing data in which a position of a pixel to be drawn at said target point in the prepared drawing data is displaced based on a calculated displacement of said target point; and
a drawing step of performing drawing on a substrate based on drawing data corrected in said drawing data correction step, wherein
said step of calculating a displacement of a target point is performed by a computing device and comprises:
a step of obtaining position information of said plurality of reference points defined on the substrate surface;
a step of detecting displacements of reference points in the vicinity of said target point in said first and second coordinate axis directions based on said position information; and
a step of performing a computation for said displacement of said target point, and
said step of performing a computation comprises, for displacements in one coordinate axis direction of said first and second coordinate axis directions, of said reference points in the vicinity of said target point,
A: a first spline calculation step of calculating a first spline curve that indicates a relationship between displacement values and first coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said first coordinate axis direction and having a same second coordinate axis value,
B: a first spline-indicated-value calculation step of calculating, as a first spline-indicated value, a value indicated by said first spline curve of said each group at a first coordinate axis value of said target point,
C: a first sub-spline calculation step of calculating a first sub-spline curve that indicates a relationship between first spline-indicated values of respective groups and second coordinate axis values of said respective groups, and
D: a first sub-spline-indicated-value calculation step of calculating a value indicated by said first sub-spline curve at a second coordinate axis value of said target point; and
outputting the displacement of the target point.
12. The substrate manufacturing method according to claim 11 , wherein
said step of performing a computation further executes, for said displacements in said one coordinate axis direction,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point, and
an average value of the value calculated in said first sub-spline-indicated-value calculation step and the value calculated in said second sub-spline-indicated-value calculation step is calculated.
13. The substrate manufacturing method according to claim 11 , wherein
said step of performing a computation further executes said steps A through D for displacements in the other coordinate axis direction out of said first and second coordinate axis directions, of said reference points in the vicinity of said target point.
14. The substrate manufacturing method according to claim 11 , wherein
said step of performing a computation further executes, for displacements in the other coordinate axis direction out of said first and second coordinate axis directions, of said reference points in the vicinity of said target point,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in said second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point.
15. The substrate manufacturing method according to claim 13 , wherein
said step of performing a computation further executes, for said displacements in said other coordinate axis direction,
E: a second spline calculation step of calculating a second spline curve that indicates a relationship between displacement values and second coordinate axis values of reference points included in each group, said reference points included in said each group being aligned in the second coordinate axis direction and having a same first coordinate axis value,
F: a second spline-indicated-value calculation step of calculating, as a second spline-indicated value, a value indicated by said second spline curve of said each group at said second coordinate axis value of said target point,
G: a second sub-spline calculation step of calculating a second sub-spline curve that indicates a relationship between second spline-indicated values of respective groups and first coordinate axis values of said respective groups, and
H: a second sub-spline-indicated-value calculation step of calculating a value indicated by said second sub-spline curve at said first coordinate axis value of said target point, and
an average value of the value calculated in said first sub-spline-indicated-value calculation step and the value calculated in said second sub-spline-indicated-value calculation step is calculated.
16. A drawing apparatus for drawing on a substrate having a surface on which a plurality of reference points are arranged in a grid along directions of a first coordinate axis and a second coordinate axis that intersect each other, the apparatus comprising:
a reception part configured to receive input of drawing data;
an image pickup part configured to capture an image of a surface of a substrate;
a position calculation part configured to calculate position information of a plurality of reference points in a captured image of a substrate surface;
a displacement detection part configured to detect displacements of reference points located in the vicinity of a target point in said drawing data in directions of first and second coordinate axes based on said position information;
a target-point displacement calculation part comprising a computing device and configured to calculate a displacement in the position of said target point based on displacement values detected by said displacement detection part;
a drawing data correction part configured to correct drawing data by displacing pixels to be drawn based on said displacement of said target point calculated by said displacement calculation part and the input drawing data; and
a drawing part configured to perform drawing in accordance with the drawing data corrected by said drawing data correction part, wherein
said target-point displacement calculation part comprises:
a first spline calculation part configured to calculate a first spline curve that indicates a relationship between displacement values of reference points included in each group and values of said reference points in one coordinate axis, said reference points included in said each group being aligned along the direction of said one coordinate axis and having a same value in the other coordinate axis;
a first spline-indicated-value calculation part configured to calculate, as a first spline-indicated value, a value indicated by said first spline curve of said each group at a value of said target point in said one coordinate axis;
a first sub-spline calculation part configured to calculate a first sub-spline curve that indicates a relationship between first spline-indicated values of respective groups and values of said respective groups in said other coordinate axis; and
a first sub-spline-indicated-value calculation part configured to calculate a value indicated by said first sub-spline curve at a value of said target point in said other coordinate axis.
17. The drawing apparatus according to claim 16 , further comprising:
a separation part configured to separate a displacement detected by said displacement detection part into a first coordinate axial component and a second coordinate axial component, wherein
said target-point displacement calculation part calculates first and second coordinate axial components of displacement of said target point based on said first and second coordinate axial components separated by said separation part, respectively.