Method and device for determining the position of an edge of a marker structure with subpixel accuracy in an image, having a plurality of pixels, of the marker structure

• US 8,457,411 B2
• Filed: 03/30/2010
• Issued: 06/04/2013
• Est. Priority Date: 03/30/2009
• Status: Active Grant

• Current Assignee: CARL Zeiss SMT GmbH (Carl-Zeiss-Stiftung)
• Original Assignee: CARL Zeiss SMT GmbH (Carl-Zeiss-Stiftung)
• Inventors: Arnz, Michael
• Primary Examiner(s): TUCKER, WESLEY J
• Application Number:
  US12/749,938
• Publication Number:
  US 20100254611A1
• Time in Patent Office: 1,162 Days
• Field of Search: 382144-147, 382/190, 382/199
• US Class Current: 382/199
• CPC Class Codes: G03F 9/7088 Alignment mark detection, e.g. TTR, TTL, off-axis detection, array detector, video detection
• CPC Class Codes: G03F 9/7092 Signal processing

Abstract

The position of an edge of a marker structure in an image of the marker structure is determined with subpixel accuracy. A discrete intensity profile of the edge, having profile pixels, is derived from the image pixels, and a continuous profile function of the edge is determined based on the profile pixels. Profile pixels whose intensity values are near an intensity threshold value are selected as evaluation pixels. Based on the evaluation pixels, a curve of continuous intensity is calculated. A position coordinate at which the intensity value of the continuous intensity curve matches the threshold value is selected as a first position coordinate, and the distance is determined between the first position coordinate and the position coordinate of the evaluation pixel that, from among the evaluation pixels previously selected, has the closest intensity value to the threshold value. The determined distance is compared to a predetermined threshold, and if the distance is greater than the threshold, a shift is effected, and the process iteratively performs the steps of selects the adjacent profile pixels, calculates the curve of continuous intensity, and so forth. If the distance is not greater than the threshold, the position of the edge in the captured image is determined with subpixel accuracy from all the distances determined in step g).

Claims

1. A method for determining, with subpixel accuracy, the position of an edge of a marker structure in a captured image of the marker structure comprising a plurality of image pixels, the method comprising:

a) deriving a discrete intensity profile of the edge, having a plurality of profile pixels, from the image pixels along a position coordinate,

b) calculating a continuous profile function of the edge as a function of the position coordinate on the basis of the profile pixels,

c) specifying an intensity threshold value defining the edge position,

d) from the multiplicity of profile pixels, selecting a plurality of adjacent profile pixels whose intensity values lie in a region that encompasses the intensity threshold value as evaluation pixels,

e) based on the evaluation pixels, calculating a curve of continuous intensity as a function of the position coordinate for the region,

f) selecting the position coordinate at which the intensity value of the continuous intensity curve from step e) matches the threshold value as a first position coordinate,

g) determining the distance between the first position coordinate and the position coordinate of the evaluation pixel that, from among the evaluation pixels selected in step d), has the closest intensity value to the threshold value,

h) comparing the determined distance to a predetermined threshold, and if the distance is greater than the threshold, the process proceeds to step i), and if the distance is not greater than the threshold, the process proceeds to step k),

i) effecting a shift in such a way that the profile function from step b) is present as a shifted profile function that is shifted relative to the pixel coordinates in dependence on the distance determined in step g) or the distances determined in steps g), and the respective intensity values of the shifted profile function that are present at each pixel coordinate are now set as the intensity values of the profile pixels, and the process then proceeds to steps d)-h), and

k) determining the position of the edge in the captured image with subpixel accuracy from all the distances determined in step g).

2. The method of claim 1, wherein calculating a continuous profile function of the edge in step b) comprises performing an interpolation or a best-fit calculation in order to calculate the continuous profile function.

3. The method of claim 1, wherein selecting the evaluation pixels in step d) comprises determining the evaluation pixels by selecting as a first evaluation pixel the profile pixel whose intensity value is closest to the intensity threshold value, and selecting a given number of adjacent profile pixels as additional evaluation pixels associated with this first evaluation pixel.

4. The method of claim 1, wherein calculating a curve of continuous intensity in step e) comprises determining the continuous intensity curve by using a best fit calculation.

5. The method of claim 1, wherein effecting a shift in step i) comprises shifting the profile function.

6. The method of claim 1, wherein effecting a shift in step i) comprises effecting the shift in such a way that the shifted profile function is shifted by the negative of the sum of all the distances determined in steps g).

7. A device for subpixel-accurate determination of the position of an edge of a marker structure in a captured image of the marker structure comprising a plurality of image pixels, the device comprising an evaluation module that performs operations comprising:

a) deriving a discrete intensity profile of the edge, having a plurality of profile pixels, from the image pixels along a position coordinate,

b) calculating, on the basis of the profile pixels, a continuous profile function of the edge as a function of the position coordinate,

c) selecting as evaluation pixels, from the plurality of profile pixels, a plurality of adjacent profile pixels whose intensity values are in a region that encompasses an intensity threshold value,

d) calculating, on the basis of the evaluation pixels, a curve of continuous intensity as a function of the position coordinate for the region,

e) taking as position coordinate the position coordinate at which the intensity value of the continuous intensity curve from step d) matches a threshold value defining the edge position,

f) determining the distance between the first position coordinate and the position coordinate of the evaluation pixel that, from among the evaluation pixels selected in step c), has the closest intensity value to the threshold value,

g) comparing the determined distance to a predetermined threshold, whereupon, if the distance is greater than the threshold, the evaluation module proceeds to step h), and if the distance is not greater than the threshold, the evaluation module proceeds to step i),

h) effecting a shift such that the profile function from step b) is present as a shifted profile function that is shifted relative to the pixel coordinates in dependence on the distance determined in step f) or the distances determined in steps f), and setting as a new intensity value of each profile pixel the intensity value of the shifted profile function that is present at the corresponding pixel coordinate, whereupon the evaluation module then proceeds to steps c)-g), and

i) determining the position of the edge in the captured image with subpixel accuracy from all the distances determined in step f).

8. A method for determining, with subpixel accuracy, the position of an edge of a marker structure in a captured image of the marker structure comprising a multiplicity of image pixels, the method comprising:

a) deriving a discrete intensity profile of the edge, having a plurality of profile pixels, from the image pixels along a position coordinate,

b) calculating a continuous profile function of the edge as a function of the position coordinate is calculated on the basis of the profile pixels,

c) setting an intensity threshold value defining the edge position,

d) selecting the position coordinate at which the intensity value of the continuous profile function from step b) matches the threshold value as a first position coordinate of a first evaluation pixel,

e) defining additional evaluation pixels by setting additional evaluation pixel coordinates for the additional evaluation pixels at predetermined distances starting from the first position coordinate and by assigning the additional evaluation pixels the corresponding intensity values of the profile function at the evaluation pixel coordinates,

f) determining a line of best fit to the evaluation pixels,

g) determining a second position coordinate at which the intensity value of the line of best fit matches the threshold value, and

h) determining, based on the second position coordinate, the position of the edge in the captured image with subpixel accuracy.

9. The method of claim 8, wherein calculating a continuous profile function of the edge in step b) comprises performing a best-fit calculation or an interpolation.

10. The method of claim 8, wherein defining additional evaluation pixels in step e) comprises setting additional evaluation pixel coordinates for the additional evaluation pixels at predetermined distances, the predetermined distances being of equal magnitude.

11. The method of claim 8, wherein defining additional evaluation pixels in step e) comprises setting additional evaluation pixel coordinates for the additional evaluation pixels at predetermined distances, the predetermined distances being equal to the distance between the profile pixels of the discrete intensity profile from step a).

12. A device for determining, with subpixel accuracy, the position of an edge of a marker structure in a captured image of the marker structure comprising a multiplicity of image pixels, the device comprising an evaluation module that performs operations comprising:

a) deriving a discrete intensity profile of the edge, having a plurality of profile pixels, from the image pixels along a position coordinate,

b) calculating a continuous profile function of the edge as a function of the position coordinate on the basis of the profile pixels,

c) selecting as a first position coordinate of a first evaluation pixel the position coordinate at which the intensity value of the continuous profile function from step b) matches a threshold value defining the edge position,

d) defining additional evaluation pixels by setting additional evaluation pixel coordinates for them at predetermined distances starting from the first position coordinate and assigning the additional evaluation pixels the corresponding intensity values of the profile function at the evaluation pixel coordinates,

e) calculating a line of best fit to the evaluation pixels,

f) determining a second position coordinate at which the intensity value of the line of best fit matches a threshold value defining the edge position, and

g) determining the position of the edge in the captured image with subpixel accuracy on the basis of the second position coordinate.

13. A method for determining, with subpixel accuracy, the position of an edge of a marker structure in a captured image of the marker structure comprising a multiplicity of image pixels, the method comprising:

a) deriving a discrete intensity profile of the edge, having a multiplicity of profile pixels, from the image pixels along a position coordinate,

b) calculating a new intensity value for each profile pixel in dependence on the original intensity values of adjacent profile pixels in order to smooth the discrete intensity profile,

c) calculating a continuous profile function of the edge as a function of the position coordinate on the basis of the profile pixels from step b),

d) setting an intensity threshold value defining the edge position,

e) selecting the position coordinate at which the intensity value of the continuous profile function matches the threshold value as a first position coordinate, and

f) determining, based on the first position coordinate, the position of the edge in the captured image with subpixel accuracy.

14. The method of claim 13, wherein calculating a new intensity value for each profile pixel in step b) comprises performing a convolution in order to smooth the discrete intensity profile.

15. The method of claim 13, wherein calculating a new intensity value for each profile pixel in step b) comprises computing a sliding average for each profile pixel in order to smooth the discrete intensity profile.

16. The method of claim 13, wherein calculating a continuous profile function of the edge in step c) comprises performing a best-fit calculation or an interpolation.

17. A device for determining, with subpixel accuracy, the position of an edge of a marker structure in a captured image of the marker structure comprising a multiplicity of image pixels, the device comprising an evaluation module that performs operations comprising:

a) deriving a discrete intensity profile of the edge, having a multiplicity of profile pixels, from the image pixels along a position coordinate,

b) calculating a new intensity value for each profile pixel in dependence on the original intensity values of adjacent profile pixels in order to smooth the discrete intensity profile,

c) calculating a continuous profile function of the edge as a function of the position coordinate on the basis of the profile pixels from step b),

d) selecting as a first position coordinate the position coordinate at which the intensity value of the continuous profile function matches a threshold value defining the edge position,

e) determining the position of the edge in the captured image with subpixel accuracy on the basis of the first position coordinate.

18. A method of determining the position of an edge of a marker structure in an image, the method comprising:

determining a discrete intensity profile of an edge of a marker structure from an image of the marker structure, the discrete intensity profile having profile pixels that correspond to pixel coordinates;

determining a continuous profile of the edge based on at least some of the profile pixels;

determining a curve of continuous intensity based on at least some of the profile pixels whose intensity values lie in a neighborhood of an intensity threshold value;

iteratively shifting the continuous profile of the edge relative to the pixel coordinates,

setting respective intensity values of the shifted profile function that are present at each pixel coordinate as the intensity values of the profile pixels, the amount of shifting being based on a predetermined relationship between the curve of continuous intensity and the profile pixels, and

updating the curve of continuous intensity based on at least some of the profile pixels whose intensity values lie in the neighborhood of the intensity threshold value,

the iteration terminating when a predetermined condition is met; and

determining a position of the edge of the marker structure in the image with subpixel accuracy based on the amount of shifting occurred during the iterative shifting process.

19. The method of claim 18 in which the predetermined relationship comprises a distance between a first coordinate and a second coordinate, the continuous intensity curve matching the intensity threshold value at the first coordinate, and the second coordinate corresponding to the profile pixel that has an intensity value closest to the threshold value.

20. The method of claim 19, comprising terminating the iteration when the distance between the first and second coordinates is smaller than a predetermined threshold.

21. The method of claim 18 in which determining a curve of continuous intensity comprises determining a curve of continuous intensity based on a best fit calculation of at least some of the profile pixels.

22. The method of claim 18 in which determining a continuous profile of the edge comprises performing an interpolation or a best-fit calculation on the profile pixels to determine a continuous profile of the edge.